id
int64 1
44.4k
| title
stringlengths 3
986
| slug
stringlengths 9
159
| question
stringlengths 34
62.2k
| tags
stringlengths 23
126
| options
stringlengths 4
149k
| correct_option
stringlengths 4
50.2k
| answer
stringlengths 29
69.3k
| source_db
stringclasses 14
values |
|---|---|---|---|---|---|---|---|---|
2,352 | there-are-n-elastic-balls-placed-on-a-smooth-horizontal-plane-the-masses-of-the-balls-are-m-fracm2-fracm22-ldots-fracm2n1-respectively-if-the-first-ba | there-are-n-elastic-balls-placed-on-a-smooth-horizontal-plane-the-masses-of-the-balls-are-m-fracm2-fracm22-ldots-fracm2n1-respectively-if-the-first-ba-96173 | <div class="question">There are \(n\) elastic balls placed on a smooth horizontal plane. The masses of the balls are \(m, \frac{m}{2}, \frac{m}{2^2}, \ldots . \frac{m}{2^{n-1}}\) respectively. If the first ball hits the second ball with velocity \(\mathrm{v}_0\), then the velocity of the \(\mathrm{n}^{\text {th }}\) ball will be,</div> | ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2023'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\frac{4}{3} v_0\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\left(\frac{4}{3}\right)^n v_0\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\left(\frac{4}{3}\right)^{n-1} v_0\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(v_0\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(\left(\frac{4}{3}\right)^{n-1} v_0\)</span> </div> | <div class="solution">Hint : 1st Collision<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/iIk52JQ0L4PGQPuwPX_lr98sRIUuQbSS2IJ_XZOy45s.original.fullsize.png"/><br/><br/>\(\mathrm{V}_1=\frac{2 \times \mathrm{m}}{\frac{\mathrm{m}}{2}+\mathrm{m}} \mathrm{V}_0=\frac{4}{3} \mathrm{~V}_0\)<br/>2nd Collision<br/>\(V_2=\frac{2 \times \frac{m}{2}}{\frac{m}{2}+\frac{m}{2^2}} \times V_0=\left(\frac{4}{3}\right)^2 V_0\)<br/>3rd Collision<br/>\(\left(\frac{4}{3}\right)^3 \mathrm{~V}_0\)<br/>\(\ldots(n-1)\) collision, \(\therefore V_{n-1}=\left(\frac{4}{3}\right)^{n-1} V_0\)</div> | db\MarksBatch2_P3.db |
2,353 | there-are-n-white-and-n-black-balls-marked-1-2-3-n-the-number-of-ways-in-which-we-can-arrange-these-balls-in-a-row-so-that-neighbouring-balls-are-of-d | there-are-n-white-and-n-black-balls-marked-1-2-3-n-the-number-of-ways-in-which-we-can-arrange-these-balls-in-a-row-so-that-neighbouring-balls-are-of-d-64809 | <div class="question">There are $n$ white and $n$ black balls marked $1,2,3, \ldots . n$. The number of ways in which we can arrange these balls in a row so that neighbouring balls are of different colours is</div> | ['Mathematics', 'Permutation Combination', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(n !)^2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">(2n)!</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$2(n !)^2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{(2 n) !}{(n !)^2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$2(n !)^2$</span> </div> | <div class="solution">BW BW ..... $=n ! \times n !$<br/>or<br/>WB WB ..... $=2(n !)^2$</div> | db\MarksBatch2_P3.db |
2,354 | there-are-two-coins-one-unbiased-with-probaility-2-1-or-getting-heads-and-the-other-one-is-biased-with-probability-4-3-of-getting-heads-a-coin-is-sele | there-are-two-coins-one-unbiased-with-probaility-2-1-or-getting-heads-and-the-other-one-is-biased-with-probability-4-3-of-getting-heads-a-coin-is-sele-74742 | <div class="question">There are two coins, one unbiased with probaility $\frac{1}{2}$ or getting heads and the other one is biased with probability $\frac{3}{4}$ of getting heads. A coin is selected at random and tossed. It shows heads up. Then, the probability that the unbiased coin wa selected is</div> | ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2013'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2}{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{5}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{2}{5}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2}{5}$</span> </div> | <div class="solution">Let $E \rightarrow$ Event of head showing up
<br/>$E_{1} \rightarrow$ Event of biased coin chosen
<br/>$E_{2} \rightarrow$ Event of unbiased coin chosen Now, $P\left(E_{2}\right)=\frac{1}{2}$ and $P\left(E_{1}\right)=\frac{1}{2}$
<br/>Also, $P\left(\frac{E}{E_{2}}\right)=\frac{1}{2}$ and $P\left(\frac{E}{E_{1}}\right)=\frac{3}{4}$
<br/>(by conditional probability) By Baye's theorem
<br/>$$
<br/>\begin{aligned}
<br/>P\left(\frac{E_{2}}{E}\right)=& \frac{P\left(E_{2}\right) \cdot P\left(\frac{E}{E_{2}}\right)}{P\left(E_{2}\right) \cdot P\left(\frac{E}{E_{2}}\right)+P\left(E_{1}\right) \cdot P\left(\frac{E}{E_{1}}\right)} \\
<br/>&=\frac{\frac{1}{2} \times \frac{1}{2}}{\frac{1}{2} \times \frac{1}{2}+\frac{1}{2} \times \frac{3}{4}}=\frac{2}{5}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,355 | there-is-a-group-of-265-persons-who-like-either-singing-or-dancing-or-painting-in-this-group-200-like-singing-110-like-dancing-and-55-like-painting-if | there-is-a-group-of-265-persons-who-like-either-singing-or-dancing-or-painting-in-this-group-200-like-singing-110-like-dancing-and-55-like-painting-if-36185 | <div class="question">There is a group of 265 persons who like either singing or dancing or painting. In this group 200 like singing, 110 like dancing and 55 like painting. If 60 persons like both singing and dancing, 30 like both singing and painting and 10 hike all three activities, then the number of persons who like only dancing and painting is</div> | ['Mathematics', 'Sets and Relations', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">10</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">20</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">30</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">40</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">10</span> </div> | <div class="solution">Let $D$ denotes dancing. $P$ denotes painting and $S$ denotes singing.
<br/>$\begin{array}{l}
<br/>\therefore \quad n(D \cup P \cup S)=265 \\
<br/>n(S)=200, n(D)=110, n(P)=55 \\
<br/>n(S \cap D)=60, n(S \cap P)=30 \\
<br/>\text { and } n(D \cap P \cap S)=10 \\
<br/>\because n(D \cup P \cup S)=n(D)+n(P)+n(S)-n(D \cap P) \\
<br/>-n(P \cap S)-n(S \cap D)+n(D \cap P \cap S) \\
<br/>\therefore \quad 265=110+55+200-n(D \cap P) \\
<br/>\Rightarrow \quad 265=285-n(D \cap P) \\
<br/>\Rightarrow \quad n(D \cap P)=20
<br/>\end{array}$
<br/>$\therefore$ Only person who like dancing and painting
<br/>$\begin{array}{l}
<br/>=n(D \cap P)-n(D \cap P \cap S) \\
<br/>=20-10=10
<br/>\end{array}$</div> | db\MarksBatch2_P3.db |
2,356 | there-is-a-small-air-bubble-at-the-centre-of-a-solid-glass-sphere-of-radius-r-and-refractive-index-what-will-be-the-apparent-distance-of-the-bubble-fr | there-is-a-small-air-bubble-at-the-centre-of-a-solid-glass-sphere-of-radius-r-and-refractive-index-what-will-be-the-apparent-distance-of-the-bubble-fr-45434 | <div class="question">There is a small air bubble at the centre of a solid glass sphere of radius $r$ and refractive index $\mu .$ What will be the apparent distance of the bubble from the centre of the sphere, when viewed from outside?</div> | ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2018'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">r</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{r}{\mu}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$r\left(1-\frac{1}{\mu}\right)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">Zero</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a5.png"/>'
<br/>As the object is at centre of the sphere.
<br/>$\therefore$ All rays will fall normally on surface, hence they do not deflect. Thus, a virtual image is formed at the
<br/>centre $O$.
<br/>$\therefore$ Apparent depth $=$ Real depth</div> | db\MarksBatch2_P3.db |
2,357 | this-alcohol-is | this-alcohol-is-47814 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/OuIzkWd7tdEVUIxdwpFolXF9fHqmsqk2fwop2GSO72M.original.fullsize.png"/><br/> <br/>This alcohol is</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2020'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/yqkfUJ6pWsTKHX48TzYb0-cxOeiw9BDFrs_il8BY4xI.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/bQApZWXE6yqOVLp1Twp6HUhJTo8ocxteHdZISCoNjec.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/6xOo3wjL690I6RMawi0hEbdBsQwtyR5FbWue52hgBUA.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/681yXnGw3BCaKVKJOnb7e6RPKJBhGEv7FihaAgF3CVw.original.fullsize.png"/></span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/6xOo3wjL690I6RMawi0hEbdBsQwtyR5FbWue52hgBUA.original.fullsize.png"/></span> </div> | <div class="solution">Hint:
<br/>Hydride shift, here $\mathrm{D}^{-}$, shift decides the product
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/sd59hYrkcvnp_HpqFGA-_UmDEQvn_PKv-8YH_njMJTk.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,358 | this-product-in-the-above-reaction-is | this-product-in-the-above-reaction-is-98324 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/z7nZD2oy9ro3VoAMCV7YMJsbT-PVIQ-MOJLQqLrnFME.original.fullsize.png"/><br/> <br/>This product in the above reaction is</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2020'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/dp-8QNyItmxJqcCn0GDrV1qNGaJF5tePfyzJFtu0Y2A.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/5H4ff_Q6hdzXdim19ES7lnbnTDLpt5jkehleIKKVrCM.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/51pvrgNj7cbH-O9yauQyQwQFpPxYg7rukEnu9ZTK_Aw.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/gPRUexZ7LQGtpERYoz2g3CTjlkoZdLqs_TQN8qhBUNQ.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/gPRUexZ7LQGtpERYoz2g3CTjlkoZdLqs_TQN8qhBUNQ.original.fullsize.png"/></span> </div> | <div class="solution">Hint:
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/G-Yb1WegHReCz1Hw0lT0zCAIJPyzEWUBV_tATZzE9Gs.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,359 | three-blocks-are-pushed-with-a-force-f-across-a-frictionless-table-as-shown-in-figure-let-n-1-be-the-contact-force-between-the-left-two-blocks-and-n-2-1 | three-blocks-are-pushed-with-a-force-f-across-a-frictionless-table-as-shown-in-figure-let-n-1-be-the-contact-force-between-the-left-two-blocks-and-n-2-1-24354 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/hivLux1gxm-68i8rx47G0ckDQm2RqVJiMEvcl5puoVo.original.fullsize.png"/><br/> <br/>Three blocks are pushed with a force $\mathrm{F}$ across a frictionless table as shown in figure. Let $\mathrm{N}_{1}$ be the contact force between the left two blocks and $\mathrm{N}_{2}$ be the contact force between the right two blocks. Then</div> | ['Physics', 'Laws of Motion', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$F>N_{1}>N_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$F>N_{2}>N_{1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad F>N_{1}=N_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F=N_{1}=N_{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$F>N_{1}>N_{2}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/5rt-M6QIPQ290KVjI_hLaD-cd7Kogi_ADrT08xYP84w.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/uokVwzVezMmEMbM4SfiojlwOy1gAftYBdeQUdkRD2Ow.original.fullsize.png"/><br/> <br/>$\mathrm{F}=6 \mathrm{a}, \mathrm{N}_{1}=5 \mathrm{a}, \mathrm{N}_{2}=3 \mathrm{a}$
<br/>$\mathrm{F}>\mathrm{N}_{1}>\mathrm{N}_{2}$</div> | db\MarksBatch2_P3.db |
2,360 | three-blocks-are-pushed-with-a-force-f-across-a-frictionless-table-as-shown-in-figure-let-n-1-be-the-contact-force-between-the-left-two-blocks-and-n-2 | three-blocks-are-pushed-with-a-force-f-across-a-frictionless-table-as-shown-in-figure-let-n-1-be-the-contact-force-between-the-left-two-blocks-and-n-2-88321 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/hivLux1gxm-68i8rx47G0ckDQm2RqVJiMEvcl5puoVo.original.fullsize.png"/><br/> <br/>Three blocks are pushed with a force $\mathrm{F}$ across a frictionless table as shown in figure. Let $\mathrm{N}_{1}$ be the contact force between the left two blocks and $\mathrm{N}_{2}$ be the contact force between the right two blocks. Then</div> | ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$F>N_{1}>N_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$F>N_{2}>N_{1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\quad F>N_{1}=N_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F=N_{1}=N_{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$F>N_{1}>N_{2}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/5rt-M6QIPQ290KVjI_hLaD-cd7Kogi_ADrT08xYP84w.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/uokVwzVezMmEMbM4SfiojlwOy1gAftYBdeQUdkRD2Ow.original.fullsize.png"/><br/> <br/>$\mathrm{F}=6 \mathrm{a}, \mathrm{N}_{1}=5 \mathrm{a}, \mathrm{N}_{2}=3 \mathrm{a}$
<br/>$\mathrm{F}>\mathrm{N}_{1}>\mathrm{N}_{2}$</div> | db\MarksBatch2_P3.db |
2,361 | three-blocks-of-masses-4-kg-2-kg-1-kg-respectively-are-in-contact-on-a-frictionless-table-as-shown-in-the-figure-if-a-force-of-14-n-is-applied-on-the- | three-blocks-of-masses-4-kg-2-kg-1-kg-respectively-are-in-contact-on-a-frictionless-table-as-shown-in-the-figure-if-a-force-of-14-n-is-applied-on-the-82563 | <div class="question">Three blocks of masses 4 kg. 2 kg. 1 kg respectively are in contact on a frictionless table as shown in the figure. If a force of $14 \mathrm{N}$ is applied on the 4 kg block, the contact force between the $4 \mathrm{kg}$ and the $2 \mathrm{kg}$ block will be <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_phy_q35.png"/></div> | ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{N}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6 \mathrm{N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$8 \mathrm{N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$14 \mathrm{N}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$6 \mathrm{N}$</span> </div> | <div class="solution">We know that, $F=m a$
<br/>$$
<br/>a=\frac{F}{m}=\frac{14}{7}=2 \mathrm{ms}^{-2}
<br/>$$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2012_phy_a35.png"/> <br/> <br/>Hence, from the figure
<br/>$$
<br/>14-N=4 a
<br/>$$
<br/>$$
<br/>\begin{array}{r}
<br/>14-N=8 \\
<br/>N=6 \mathrm{N}
<br/>\end{array}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,362 | three-bodies-of-the-same-material-and-having-masses-m-m-and-3-m-are-at-temperatures-4-0-c-5-0-c-and-6-0-c-respectively-if-the-bodies-are-brought-in-th | three-bodies-of-the-same-material-and-having-masses-m-m-and-3-m-are-at-temperatures-4-0-c-5-0-c-and-6-0-c-respectively-if-the-bodies-are-brought-in-th-93123 | <div class="question">Three bodies of the same material and having masses $m, m$ and $3 m$ are at temperatures $40^{\circ} \mathrm{C}, \quad 50^{\circ} \mathrm{C} \quad$ and $\quad 60^{\circ} \mathrm{C}$ respectively. If the bodies are brought in thermal contact, the final temperature will be</div> | ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$45^{\circ} \mathrm{C}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$54^{\circ} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$52^{\circ} \mathrm{C}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$48^{\circ} \mathrm{C}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$54^{\circ} \mathrm{C}$</span> </div> | <div class="solution">Let the final temperature after the masses in thermal contact is $\theta$, then from the principle of calonimetry.
<br/>Heat lost $=$ Heat gained
<br/>$\begin{aligned} \Rightarrow 3 m s(60-\theta) &=m s(\theta-50)+m s(\theta-40) \\ \Rightarrow \quad 3(60-\theta) &=\theta-50+\theta-40 \\ \Rightarrow \quad 180-3 \theta &=2 \theta-90 \\ \theta &=\frac{270}{5}=54^{\circ} \mathrm{C} \end{aligned}$</div> | db\MarksBatch2_P3.db |
2,363 | three-capacitors-3-f-6-f-and-6-f-are-connected-in-aeries-to-a-source-of-120-v-the-potential-difference-in-volt-across-the-3-f-capacitor-will-be | three-capacitors-3-f-6-f-and-6-f-are-connected-in-aeries-to-a-source-of-120-v-the-potential-difference-in-volt-across-the-3-f-capacitor-will-be-61589 | <div class="question">Three capacitors $3 \mu \mathrm{F}, 6 \mu \mathrm{F}$ and $6 \mu \mathrm{F}$ are connected in aeries to a source of $120 \mathrm{V}$. The potential difference, in volt, across the $3 \mu \mathrm{F}$ capacitor will be</div> | ['Physics', 'Capacitance', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">24</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">30</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">40</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">60</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">60</span> </div> | <div class="solution">The combination of three charges in series
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}} \\
<br/>\frac{1}{C}=\frac{1}{3}+\frac{1}{6}+\frac{1}{6} \Rightarrow C=\frac{6}{4}=1.5 \mu \mathrm{F}
<br/>\end{array}
<br/>$$
<br/>The charge of this circuit
<br/>$$
<br/>\begin{array}{l}
<br/>q=C V=1.5 \times 120 \\
<br/>q=180 \mu \mathrm{C}
<br/>\end{array}
<br/>$$
<br/>The potential difference across the $3 \mu \mathrm{F}$
<br/>$$
<br/>q=C V
<br/>$$
<br/>$$
<br/>V=\frac{q}{C}=\frac{180}{3}=60 \mathrm{V}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,364 | three-capacitors-of-capacitance-1020-and-50-f-are-connected-in-series-to-a-10-v-source-the-potential-difference-across-the-20-f-capacitor-is | three-capacitors-of-capacitance-1020-and-50-f-are-connected-in-series-to-a-10-v-source-the-potential-difference-across-the-20-f-capacitor-is-19761 | <div class="question">Three capacitors of capacitance 1.0,2.0 and $5.0 \mu \mathrm{F}$ are connected in series to a $10 \mathrm{V}$ source. The potential difference across the $2.0 \mu \mathrm{F}$ capacitor is</div> | ['Physics', 'Capacitance', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{100}{17} \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{20}{17} \mathrm{v}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{50}{17} \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$10 \mathrm{V}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{50}{17} \mathrm{V}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a9.png"/> <br/> <br/>When the capacitors are connected in series, the resultant capacitance of combination
<br/>$$
<br/>\frac{1}{C}=\frac{1}{C_{1}}+\frac{1}{C_{2}}+\frac{1}{C_{3}}
<br/>$$
<br/>$$
<br/>\begin{array}{l}
<br/>=\frac{1}{1}+\frac{1}{2}+\frac{1}{5}=\frac{17}{10} \\
<br/>C=\frac{10}{17} \mu \mathrm{F}
<br/>\end{array}
<br/>$$
<br/>The charge will be same on all the capacitors in series
<br/>$$
<br/>Q=C V=\frac{10}{17} \times 10=\frac{100}{17}
<br/>$$
<br/>The potential difference across $2.0 \mu \mathrm{F}$ capacitor
<br/>$$
<br/>V^{*}=\frac{Q}{C}=\frac{100 / 17}{2}=\frac{50}{17} \text { volt}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,365 | three-concentric-metallic-shells-a-b-and-c-of-radii-a-b-and-c-a-b-c-have-surface-charge-densities-and-respectively-the-potential-of-shell-b-is | three-concentric-metallic-shells-a-b-and-c-of-radii-a-b-and-c-a-b-c-have-surface-charge-densities-and-respectively-the-potential-of-shell-b-is-40451 | <div class="question">Three concentric metallic shells A, B and C of radii $a, b$ and $c(a < b < c)$ have surface charge densities $+\sigma,-\sigma$ and $+\sigma$ respectively. The potential of shell B is<img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/OYuD0-ig4j2tGp871QhyUNd5PLDJuwWDM1qJANtet7o.original.fullsize.png"/></div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad(a+b+c) \frac{\sigma}{\varepsilon_0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sigma \mathrm{c}}{\varepsilon_0}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\frac{a^2}{c}-\frac{b^2}{c}+c\right) \frac{\sigma}{e_0}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{e_0}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{a^2}{b}-b+c\right) \frac{\sigma}{e_0}$</span> </div> | <div class="solution">$V_b=V_{A, b}+V_{B, b}+V_{C, b}$<br/>$=\frac{K \sigma 4 \pi a^2}{b}-\frac{K \sigma 4 \pi b^2}{b}+\frac{K \sigma 4 \pi c^2}{c}$<br/>$=\frac{\sigma}{\varepsilon_0}\left(\frac{a^2}{b}-b+c\right)$</div> | db\MarksBatch2_P3.db |
2,366 | three-identical-convex-lenses-each-of-focal-length-f-are-placed-in-a-straight-line-separated-by-a-distance-f-from-each-other-an-object-is-located-at-m | three-identical-convex-lenses-each-of-focal-length-f-are-placed-in-a-straight-line-separated-by-a-distance-f-from-each-other-an-object-is-located-at-m-84549 | <div class="question">Three identical convex lenses each of focal length \(f\) are placed in a straight line separated by a distance \(f\) from each other. An object is located at \(\mathrm{f} / 2\) in front of the leftmost lens. Then,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ZFT3Clo6gRk89WOI3nH1D-BkebjvTreZR2zUpTFqDlU.original.fullsize.png"/><br/></div> | ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2023'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Final image will be at \(f / 2\) behind the rightmost lens and its magnification will be -1 .</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Final image will be at \(f / 2\) behind the rightmost lens and its magnification will be +1 .</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Final image will be at \(f\) behind the rightmost lens and its magnification will be -1 .</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Final image will be at \(f\) behind the rightmost lens and its magnification will be +1 .</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">Final image will be at \(f / 2\) behind the rightmost lens and its magnification will be -1 .</span> </div> | <div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/U76JsHF5grWW2aZUHd4-kxLH1LGGfp7jCm0esAibRUA.original.fullsize.png"/><br/><br/>For first lens<br/>\(\begin{aligned}<br/>& u=-\frac{f}{2} \\<br/>& \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \Rightarrow \frac{1}{f}=\frac{1}{v}-\frac{1}{\frac{-f}{2}} \Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{2}{f} \Rightarrow \frac{1}{v}=\frac{-1}{f} \\<br/>& v=-f \\<br/>& m_1=\frac{v}{u}=\frac{-f}{\frac{-f}{2}}=2<br/>\end{aligned}\)<br/>For second lens<br/>\(u=-(f+f)=-2 f\)<br/>\(\begin{aligned}<br/>& \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{v}-\frac{1}{-2 f}=\frac{1}{f} \Rightarrow \frac{1}{v}=\frac{1}{f}-\frac{1}{2 f} \Rightarrow \frac{1}{v}=\frac{1}{2 f} \\<br/>& v=2 f \\<br/>& m_1=\frac{v}{u}=\frac{2 f}{-2 f}=-1<br/>\end{aligned}\)<br/>For third lens<br/>\(\begin{aligned}<br/>& u=f \\<br/>& f=f \\<br/>& \frac{1}{v}-\frac{1}{u}=\frac{1}{f} \Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u} \Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{f} \Rightarrow \frac{1}{v}=\frac{2}{f} \Rightarrow v=\frac{f}{2}<br/>\end{aligned}\)<br/>\(m_3=\frac{v}{u}=\frac{\frac{f}{2}}{f}=\frac{1}{2}\)<br/>Total magnification \(=m_1 m_2 m_3=2 \times(-1) \times \frac{1}{2}=-1\)</div> | db\MarksBatch2_P3.db |
2,367 | three-identical-square-plates-rotate-about-the-axes-shown-in-the-figure-in-such-a-way-that-their-kinetic-energies-are-equal-each-of-the-rotation-axes--1 | three-identical-square-plates-rotate-about-the-axes-shown-in-the-figure-in-such-a-way-that-their-kinetic-energies-are-equal-each-of-the-rotation-axes-1-48027 | <div class="question">Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds $\omega_{1}: \omega_{2}: \omega_{3}$ is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_q51.png"/></div> | ['Physics', 'Rotational Motion', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">01:01:01</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{2}: \sqrt{2}: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1: \sqrt{2}: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1: 2: \sqrt{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{2}: \sqrt{2}: 1$</span> </div> | <div class="solution">We know that
<br/>$$
<br/>K=\frac{1}{2} \mathrm{l} \omega^{2}
<br/>$$
<br/>where $K=$ kinetic energy
<br/>$$
<br/>\begin{array}{l}
<br/>I=\text { moment of inertia } \\
<br/>\omega=\text { angular speed }
<br/>\end{array}
<br/>$$
<br/>So, $\quad \omega \propto \frac{1}{\sqrt{I}}$
<br/>$$
<br/>\begin{aligned}
<br/>\omega_{1}: \omega_{2}: \omega_{3} &=\frac{1}{\sqrt{I_{1}}}: \frac{1}{\sqrt{I_{2}}}: \frac{1}{\sqrt{I_{3}}} \\
<br/>&=\frac{1}{\sqrt{1}}: \frac{1}{\sqrt{1}}: \frac{1}{\sqrt{2}}=\sqrt{2}: \sqrt{2}: 1
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,368 | three-identical-square-plates-rotate-about-the-axes-shown-in-the-figure-in-such-a-way-that-their-kinetic-energies-are-equal-each-of-the-rotation-axes- | three-identical-square-plates-rotate-about-the-axes-shown-in-the-figure-in-such-a-way-that-their-kinetic-energies-are-equal-each-of-the-rotation-axes-97094 | <div class="question">Three identical square plates rotate about the axes shown in the figure in such a way that their kinetic energies are equal. Each of the rotation axes passes through the centre of the square. Then the ratio of angular speeds $\omega_{1}: \omega_{2}: \omega_{3}$ is <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_q51.png"/></div> | ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">01:01:01</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sqrt{2}: \sqrt{2}: 1$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1: \sqrt{2}: 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1: 2: \sqrt{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{2}: \sqrt{2}: 1$</span> </div> | <div class="solution">We know that
<br/>$$
<br/>K=\frac{1}{2} \mathrm{l} \omega^{2}
<br/>$$
<br/>where $K=$ kinetic energy
<br/>$$
<br/>\begin{array}{l}
<br/>I=\text { moment of inertia } \\
<br/>\omega=\text { angular speed }
<br/>\end{array}
<br/>$$
<br/>So, $\quad \omega \propto \frac{1}{\sqrt{I}}$
<br/>$$
<br/>\begin{aligned}
<br/>\omega_{1}: \omega_{2}: \omega_{3} &=\frac{1}{\sqrt{I_{1}}}: \frac{1}{\sqrt{I_{2}}}: \frac{1}{\sqrt{I_{3}}} \\
<br/>&=\frac{1}{\sqrt{1}}: \frac{1}{\sqrt{1}}: \frac{1}{\sqrt{2}}=\sqrt{2}: \sqrt{2}: 1
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,369 | three-infinite-plane-sheets-carrying-uniform-charge-densities-2-4-are-placed-parallel-to-xz-plane-at-y-a-3-a-4a-respectively-the-electric-field-at-the | three-infinite-plane-sheets-carrying-uniform-charge-densities-2-4-are-placed-parallel-to-xz-plane-at-y-a-3-a-4a-respectively-the-electric-field-at-the-28504 | <div class="question">Three infinite plane sheets carrying uniform charge densities $-\sigma, 2 \sigma, 4 \sigma$ are placed parallel to $X Z$ plane at $Y=a, 3 a$, 4a respectively. The electric field at the point $(0,2 a, 0)$ is</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5 \sigma}{2 \varepsilon_{0}} \hat{j}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-\frac{7 \sigma}{2 \varepsilon_{0}} \hat{j}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\sigma}{2 \varepsilon_{0}} \hat{j}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{5 \sigma}{-2 \varepsilon_{0}} \hat{\mathrm{j}}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{7 \sigma}{2 \varepsilon_{0}} \hat{j}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/I-3gxMkSPk3XfRMJPTzROU218KdXkLg1ZTpxuCoVhrA.original.fullsize.png"/><br/> <br/>$\begin{aligned} \mathrm{E}_{\text {net }} &=7 \mathrm{E} \\ &=7 \frac{\sigma}{2 \varepsilon_{0}} \text { alone }-\text { ve } \mathrm{Y} \text {-axis } \\ & \therefore \overrightarrow{\mathrm{E}}=-\frac{7 \sigma}{2 \varepsilon_{0}} \hat{\mathrm{j}} \end{aligned}$</div> | db\MarksBatch2_P3.db |
2,370 | three-lines-are-drawn-from-the-origin-o-with-direction-cosines-proportional-to-111-230-and-1-0-3-the-three-lines-are | three-lines-are-drawn-from-the-origin-o-with-direction-cosines-proportional-to-111-230-and-1-0-3-the-three-lines-are-26897 | <div class="question">Three lines are drawn from the origin $O$ with direction cosines proportional to (1,-1,1) (2,-3,0) and $(1,0,3) .$ The three lines are</div> | ['Mathematics', 'Three Dimensional Geometry', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">not coplanar</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">coplanar</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">perpendicular to each other</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">coincident</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">coplanar</span> </div> | <div class="solution">$\quad$ $\Delta=\left|\begin{array}{ccc}1 & -1 & 1 \\ 2 & -3 & 0 \\ 1 & 0 & 3\end{array}\right|$
<br/>$=1(-9-0)-(-1) \cdot(6-0)+1(0-(-3))$
<br/>$=-9+6+3=0$
<br/>since, $\Delta=0$
<br/>$\therefore$ Lines are coplanar.</div> | db\MarksBatch2_P3.db |
2,371 | three-numbers-are-chosen-at-random-from-1-to-20-the-probability-that-they-are-consecutive-is | three-numbers-are-chosen-at-random-from-1-to-20-the-probability-that-they-are-consecutive-is-72051 | <div class="question">Three numbers are chosen at random from 1 to 20 . The probability that they are consecutive is</div> | ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{190}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{120}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{3}{190}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{5}{190}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{3}{190}$</span> </div> | <div class="solution">Hints: Total number of cases ; ${ }^{20} \mathrm{C}_3=\frac{20 \times 19 \times 18}{2 \times 3}=20 \times 19 \times 3=1140$<br/>Total number of favourable cases $=18$<br/>$\therefore$ Required probability $=\frac{18}{1140}=\frac{3}{190}$</div> | db\MarksBatch2_P3.db |
2,372 | three-particles-each-of-mass-m-grams-situated-at-the-vertices-of-an-equilateral-a-bc-of-side-a-cm-as-shown-in-the-figure-the-moment-of-inertia-of-the--1 | three-particles-each-of-mass-m-grams-situated-at-the-vertices-of-an-equilateral-a-bc-of-side-a-cm-as-shown-in-the-figure-the-moment-of-inertia-of-the-1-73558 | <div class="question">Three particles, each of mass ' $m$ ' grams situated at the vertices of an equilateral $\triangle A B C$ of side ' $a$ ' $\mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line $\mathrm{AX}$ perpendicular to $\mathrm{AB}$ and in the plane of $\mathrm{ABC}$ in $\mathrm{g}-\mathrm{cm}^2$ units will be<br/> <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/S9zLAXTSN2hHR9l1fM2m1M1YMAwZ4W-vXsH7YOpxsmo.original.fullsize.png"/></div> | ['Physics', 'Rotational Motion', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{ma}^2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{2} \mathrm{ma}^2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{4} \mathrm{ma}^2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{5}{4} \mathrm{ma}^2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{4} \mathrm{ma}^2$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/GwLG36TkLPUkUWkYSuhZnrmH2VnSgOGUFPGGvgCpPZk.original.fullsize.png"/><br/><br/>$\mathrm{I}=\mathrm{~ma}^2+\mathrm{m}\left(\mathrm{a} \cos 60^{\circ}\right)^2=m \mathrm{a}^2+\frac{\mathrm{ma}^2}{4}=\frac{5 \mathrm{ma}^2}{4}$</div> | db\MarksBatch2_P3.db |
2,373 | three-particles-each-of-mass-m-grams-situated-at-the-vertices-of-an-equilateral-a-bc-of-side-a-cm-as-shown-in-the-figure-the-moment-of-inertia-of-the- | three-particles-each-of-mass-m-grams-situated-at-the-vertices-of-an-equilateral-a-bc-of-side-a-cm-as-shown-in-the-figure-the-moment-of-inertia-of-the-73298 | <div class="question">Three particles, each of mass ' $m$ ' grams situated at the vertices of an equilateral $\triangle A B C$ of side ' $a$ ' $\mathrm{cm}$ (as shown in the figure). The moment of inertia of the system about a line $\mathrm{AX}$ perpendicular to $\mathrm{AB}$ and in the plane of $\mathrm{ABC}$ in $\mathrm{g}-\mathrm{cm}^2$ units will be<br/> <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/S9zLAXTSN2hHR9l1fM2m1M1YMAwZ4W-vXsH7YOpxsmo.original.fullsize.png"/></div> | ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{ma}^2$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{2} \mathrm{ma}^2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3}{4} \mathrm{ma}^2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{5}{4} \mathrm{ma}^2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{4} \mathrm{ma}^2$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/GwLG36TkLPUkUWkYSuhZnrmH2VnSgOGUFPGGvgCpPZk.original.fullsize.png"/><br/><br/>$\mathrm{I}=\mathrm{~ma}^2+\mathrm{m}\left(\mathrm{a} \cos 60^{\circ}\right)^2=m \mathrm{a}^2+\frac{\mathrm{ma}^2}{4}=\frac{5 \mathrm{ma}^2}{4}$</div> | db\MarksBatch2_P3.db |
2,374 | three-unequal-positive-numbers-a-b-c-are-such-that-a-b-c-are-in-gp-while-lo-g-2-a-5-c-lo-g-5-c-7-b-lo-g-7-b-2-a-are-in-ap-then-a-b-c-are-the-lengths-o | three-unequal-positive-numbers-a-b-c-are-such-that-a-b-c-are-in-gp-while-lo-g-2-a-5-c-lo-g-5-c-7-b-lo-g-7-b-2-a-are-in-ap-then-a-b-c-are-the-lengths-o-98289 | <div class="question">Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $\log \left(\frac{5 c}{2 a}\right), \log \left(\frac{7 b}{5 c}\right), \log \left(\frac{2 a}{7 b}\right)$ are in A.P. Then $\mathrm{a}, \mathrm{b}, \mathrm{c}$ are the lengths of the sides of</div> | ['Mathematics', 'Sequences and Series', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">an isosceles triangle</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">an equilateral triangle</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">a scalene triangle</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">a right-angled triangle</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">a scalene triangle</span> </div> | <div class="solution">$\log \frac{5 c}{2 a}+\log \frac{2 a}{7 b}=2 \log \frac{7 b}{5 c} \Rightarrow \log \frac{5 c}{7 b}=\log \frac{49 b^{2}}{25 c^{2}}$
<br/>$\begin{array}{l}
<br/>\Rightarrow 5^{3} \mathrm{c}^{3}=7 \mathrm{~b}^{3} \Rightarrow 5 \mathrm{c}=7 \mathrm{~b} \Rightarrow \mathrm{c}=\frac{7}{5} \mathrm{~b} \\
<br/>\because \mathrm{b}^{2}=\mathrm{ac}=\mathrm{a} \cdot \frac{7}{5} \mathrm{~b} \Rightarrow \mathrm{a}=\frac{5 \mathrm{~b}}{7}
<br/>\end{array}$
<br/>Sides are $\frac{5 b}{7}, b, \frac{7}{5} b$</div> | db\MarksBatch2_P3.db |
2,375 | three-vectors-a-a-i-j-k-b-i-b-j-k-and-c-i-j-c-k-are-mutually-perpendicular-i-j-and-k-are-unit-vectors-along-x-y-and-z-axes-respectively-the-respective | three-vectors-a-a-i-j-k-b-i-b-j-k-and-c-i-j-c-k-are-mutually-perpendicular-i-j-and-k-are-unit-vectors-along-x-y-and-z-axes-respectively-the-respective-37533 | <div class="question">Three vectors $\mathbf{A}=a \mathbf{i}+\mathbf{j}+\mathbf{k} ; \mathbf{B}=\mathbf{i}+b \mathbf{j}+\mathbf{k}$
<br/>and $\mathbf{C}=\mathbf{i}+\mathbf{j}+c \mathbf{k}$ are mutually perpendicular (i, $\mathbf{j}$ and $\mathbf{k}$ are unit vectors along $X, Y$ and $Z$ axes respectively). The respective values of $a$, $b$ and $c$ are</div> | ['Physics', 'Mathematics in Physics', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">0,0,0</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1,-1,1</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}, \frac{1}{2}, \frac{1}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{1}{2},-\frac{1}{2},-\frac{1}{2}$</span> </div> | <div class="solution">Three vectors are mutually perpendicular, so the scalar or dot product of two vectors will zero. So,<br/>$\mathbf{A} \cdot \mathbf{B}=0, \mathbf{B} \mathbf{C}=0,$<br/>So, $\mathbf{A} \cdot \mathbf{B}=(a \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}) \cdot(\hat{\mathbf{i}}+b \hat{\mathbf{j}}+\hat{\mathbf{k}})=0$<br/>$\Rightarrow a+b+1=0$<br/>$\mathbf{B} \cdot \mathbf{C}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}} \cdot \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}=$<br/>$\Rightarrow 1+b+c=0$<br/>$\mathbf{A} \cdot \mathbf{C}=(a \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}) \cdot(\hat{\mathbf{i}}+\hat{\mathbf{j}}+c \hat{\mathbf{k}})=0$<br/>$\mathbf{A} \cdot \mathbf{C}=0$<br/>$\Rightarrow \quad a+1+c=0$<br/>(iii Addition of Eqs. (i), (ii) and (iii),<br/>$\begin{array}{l}<br/>2(a+b+c)+3=0 \\<br/>a+b+c=-\frac{3}{2}<br/>\end{array}$<br/>$\Rightarrow \quad-1+c=-\frac{3}{2}$<br/>$\begin{aligned}<br/>c &=-\frac{3}{2}+1 \\<br/>&=-\frac{1}{2}=0.5 \\<br/>a &=-\frac{1}{2} \\<br/>b &=-\frac{1}{2} \\<br/>c &=-\frac{1}{2}<br/>\end{aligned}$</div> | db\MarksBatch2_P3.db |
2,376 | time-period-t-of-a-simple-pendulum-of-length-l-is-given-by-t-2-g-l-if-the-length-is-increased-by-2-then-an-approximate-change-in-the-time-period-is | time-period-t-of-a-simple-pendulum-of-length-l-is-given-by-t-2-g-l-if-the-length-is-increased-by-2-then-an-approximate-change-in-the-time-period-is-50530 | <div class="question">Time period $T$ of a simple pendulum of length $l$ is given by $T=2 \pi \sqrt{\frac{l}{g}}$. If the length is increased by $2 \%$, then an approximate change in the time period is</div> | ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2016'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \%$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2} \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \%$</span> </div> | <div class="solution">Given, $T=2 \pi \sqrt{\frac{1}{g}}$
<br/>On differentiating w.r.t. $l,$ we get
<br/>$\begin{aligned} \frac{d T}{d l} &=\frac{2 \pi}{\sqrt{g}} \cdot \frac{1}{2 \sqrt{I}} \\ \Delta T &=\frac{d T}{d l} \Delta l=\frac{\pi}{\sqrt{g} l} \cdot\left(\frac{2 I}{100}\right) \\ &=2 \pi \sqrt{\frac{1}{g}} \cdot \frac{1}{100}=\frac{T}{100} \\ \frac{\Delta T}{T} &=\frac{1}{100}=1 \% \end{aligned}$
<br/>Hence, approximate change in the time period is $1 \%$.</div> | db\MarksBatch2_P3.db |
2,377 | to-a-solution-of-a-colourless-efflorescent-sodium-salt-when-dilute-acid-is-added-a-colourless-gas-is-evolved-along-with-formation-of-a-white-precipita | to-a-solution-of-a-colourless-efflorescent-sodium-salt-when-dilute-acid-is-added-a-colourless-gas-is-evolved-along-with-formation-of-a-white-precipita-60085 | <div class="question">To a solution of a colourless efflorescent sodium salt, when dilute acid is added, a colourless gas is evolved along with formation of a white precipitate. Acidified dichromate solution turns green when the colourless gas is passed through it. The sodium salt is</div> | ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2020'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{SO}_{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$</span> </div> | <div class="solution">Hint:
<br/>$\underset{\text { (colouriess, efflorescent) }}{\mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}(\mathrm{~s})}+2 \mathrm{H}^{+}(\mathrm{dil} .) \rightarrow \mathrm{S}(\mathrm{s})+2 \mathrm{Na}^{+}(\mathrm{aq})+\mathrm{SO}_{2} \uparrow+\mathrm{H}_{2} \mathrm{O}(\ell)$
<br/>$\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}($ aq. $)+3 \mathrm{SO}_{2}(\mathrm{~g})+2 \mathrm{H}^{+}(\mathrm{aq} .) \longrightarrow 2 \mathrm{~K}^{+}($ aq. $)+\underset{(\text { green })}{2 \mathrm{Cr}^{+3}}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\ell)+3 \mathrm{SO}_{4}^{-2}(\mathrm{aq})$</div> | db\MarksBatch2_P3.db |
2,378 | to-a-solution-of-colourless-sodium-salt-a-solution-of-lead-nitrate-was-added-to-have-a-white-precipitate-which-dissolves-in-warm-water-and-reprecipita | to-a-solution-of-colourless-sodium-salt-a-solution-of-lead-nitrate-was-added-to-have-a-white-precipitate-which-dissolves-in-warm-water-and-reprecipita-37771 | <div class="question">To a solution of colourless sodium salt, a solution of lead nitrate was added to have a white precipitate which dissolves in warm water and reprecipitates on cooling. Which of the following acid radical is present in the salt?</div> | ['Chemistry', 'Practical Chemistry', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Cl}^{-}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{SO}_4{ }^{2-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{S}^{2-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{NO}_3^{-}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cl}^{-}$</span> </div> | <div class="solution">$2 \mathrm{NaCl}+\mathrm{Pb}\left(\mathrm{NO}_3\right)_2 \rightarrow \mathrm{PbCl}_2(\mathrm{ppt})+2 \mathrm{NaNO}_3$</div> | db\MarksBatch2_P3.db |
2,379 | to-determine-the-coefficient-of-friction-between-a-rough-surface-and-a-block-the-surface-is-kept-inclined-at-4-5-and-the-block-is-released-from-rest-t | to-determine-the-coefficient-of-friction-between-a-rough-surface-and-a-block-the-surface-is-kept-inclined-at-4-5-and-the-block-is-released-from-rest-t-42358 | <div class="question">To determine the coefficient of friction between a rough surface and a block, the surface is kept inclined at $45^{\circ}$ and the block is released from rest. The block takes a time $t$ in moving a distance $d$. The rough surface is then replaced by a smooth surface and the same experiment is repeated. The block now takes a time $t / 2$ in moving down the same distance d. The coefficient of friction is</div> | ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3 / 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5 / 4$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1 / \sqrt{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$3 / 4$</span> </div> | <div class="solution">If the same wedge is made rough then time taken by it to come down becomes $n$ times more. The coefficient of friction <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2014_phy_a17.png"/> <br/>$$
<br/>\begin{array}{l}
<br/>\mu=\left[1-\frac{1}{n^{2}}\right] \tan \theta \Rightarrow \mu=\left[1-\frac{1}{2^{2}}\right] \tan 45^{\circ} \\
<br/>\mu=\frac{4-1}{4} \Rightarrow \mu=\frac{3}{4}
<br/>\end{array}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,380 | to-determine-the-composition-of-a-bimetallic-alloy-a-sample-is-first-weighed-in-air-and-then-in-water-these-weights-are-found-to-be-w-1-and-w-2-respec | to-determine-the-composition-of-a-bimetallic-alloy-a-sample-is-first-weighed-in-air-and-then-in-water-these-weights-are-found-to-be-w-1-and-w-2-respec-98453 | <div class="question">To determine the composition of a bimetallic alloy, a sample is first weighed in air and then in water. These weights are found to be $w_{1}$ and $w_{2}$ respectively. If the densities of the two constituents metals are $\rho_{1}$ and $\rho_{2}$ respectively. then the weight of the first metal in the sample is (where $\rho_{w}$ is the density of water)</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)-w_{2} \rho_{2}\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}+\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)+w_{2} \rho_{2}\right]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}+\rho_{w}\right)-w_{2} \rho_{1}\right]$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{1}-\rho_{w}\right)-w_{z} \rho_{1}\right]$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)-w_{2} \rho_{2}\right]$</span> </div> | <div class="solution">By Archimedes' Principle
<br/>$$
<br/>F=v \rho_{w} g \Rightarrow\left(w_{1}-w_{2}\right) g=v \rho_{w} g
<br/>$$
<br/>Let, the total volume be $v$ and first metal weight be $x$
<br/>$$
<br/>\begin{array}{l}
<br/>w_{1}-w_{2}=\left(v_{1}+v_{2}\right) \rho_{w} \\
<br/>w_{1}-w_{2}=v_{1} \rho_{w}+v_{2} g_{w} \\
<br/>w_{1}-w_{2}=\left(\frac{x}{\rho_{1}} \rho_{w}+\frac{w_{1}-x}{\rho_{2}} \rho_{w}\right)
<br/>w_{1}-w_{2}=\frac{x \rho_{\mathcal{P}} \rho_{w}+\left(w_{1}-x\right) \rho_{w} \rho_{1}}{\rho_{\jmath} \rho_{2}}
<br/>\end{array} \quad\left(\because v=\frac{m}{\rho}\right)
<br/>$$
<br/>$$
<br/>\begin{aligned} w_{1} \rho_{1} \rho_{2}-w_{2} \rho_{1} \rho_{2} &=x \rho_{2} \rho_{w}+w_{1} \rho_{w} \rho_{1}-x \rho_{w} \rho_{1} \\ x\left(\rho_{2}-\rho_{1}\right) \rho_{w} &=\rho_{1}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)-w_{2} \rho_{2}\right] \end{aligned}\\
<br/>x=\frac{\rho_{1}}{\rho_{w}\left(\rho_{2}-\rho_{1}\right)}\left[w_{1}\left(\rho_{2}-\rho_{w}\right)-w_{z} \rho_{2}\right]
<br/>$$</div> | db\MarksBatch2_P3.db |
2,381 | to-observe-an-elevation-of-boiling-point-of-00-5-c-the-amount-of-a-solute-mol-wt-100-to-be-added-to-100-g-of-water-k-b-05-is | to-observe-an-elevation-of-boiling-point-of-00-5-c-the-amount-of-a-solute-mol-wt-100-to-be-added-to-100-g-of-water-k-b-05-is-62275 | <div class="question">To observe an elevation of boiling point of $0.05^{\circ} \mathrm{C},$ the amount of a solute (mol. wt. $=100$ ) to be added to $100 \mathrm{g}$ of water $\left(K_{b}=0.5\right)$ is</div> | ['Chemistry', 'Solutions', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \mathrm{g}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.5 \mathrm{g}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1 \mathrm{g}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.75 \mathrm{g}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \mathrm{g}$</span> </div> | <div class="solution">Elevation of boiling point,
<br/>$$
<br/>\Delta T_{b}=\frac{w \times K_{b} \times 1000}{M \times W}
<br/>$$
<br/>(Here, w and $W=$ weights of solute and solvent respectively.
<br/>$M=$ molecular weight of solute and $K_{b}=$ constant
<br/>On substituting values, we get
<br/>of
<br/>$$
<br/>\begin{aligned}
<br/>0.05 &=\frac{W \times 0.5 \times 1000}{100 \times 100} \\
<br/>w &=\frac{0.05 \times 100 \times 100}{0.5 \times 1000}=1 \mathrm{g}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,382 | to-which-of-the-following-quantities-the-radius-of-the-circular-path-of-a-charged-particle-moving-at-right-angles-to-a-uniform-magnetic-field-is-direc | to-which-of-the-following-quantities-the-radius-of-the-circular-path-of-a-charged-particle-moving-at-right-angles-to-a-uniform-magnetic-field-is-direc-37651 | <div class="question">To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?</div> | ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">energy of the particle</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">magnetic field</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">charge of the particle</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">momentum of the particle</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">momentum of the particle</span> </div> | <div class="solution">If velocity of particle, $\mathrm{v}$ is perpendicular to magnetic field, $\mathbf{B}$ i.e. $\theta=90^{\circ},$ then particle will experience maximum magnetic force, i.e. $F_{\max }=q v B .$ This force acts in a direction perpendicular to the motion of charged particle. Therefore the trajectory of the particle is a circle. In this case path of charged particle is circular and magnetic force provides the necessary centripetal force,
<br/>i.e.
<br/>$$
<br/>q v B=\frac{m v^{2}}{r}
<br/>$$
<br/>$\Rightarrow$ Radius of path, $r=\frac{m v}{q B}$
<br/>$$
<br/>r=\frac{p}{q B} \quad[\because p=m v]
<br/>$$
<br/>where, $p=$ momentum of the particle
<br/>$\therefore r$ momentum
<br/>Hence, option (d) is correct</div> | db\MarksBatch2_P3.db |
2,383 | to-which-of-the-following-the-angular-velocity-of-the-electron-in-the-n-th-bohr-orbit-is-proportional | to-which-of-the-following-the-angular-velocity-of-the-electron-in-the-n-th-bohr-orbit-is-proportional-98112 | <div class="question">To which of the following the angular velocity of the electron in the $n$ -th Bohr orbit is proportional?</div> | ['Physics', 'Atomic Physics', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$n^{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{n^{2}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{n^{3 / 2}}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{n^{3}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{n^{3}}$</span> </div> | <div class="solution">According to the Bohr's atomic model.<br/>$\text {Angular momentum, } L=m v=\frac{n h}{2 \pi}....(i)$<br/>since, angular velocity $\omega=\frac{v}{r}$<br/>$\Rightarrow v=r \omega$<br/>From Eq. (i), we get<br/>$\begin{aligned}<br/>m(r \omega) r &=\frac{n h}{2 \pi} \\<br/>m \omega r^{2} &=\frac{n h}{2 \pi} \\<br/>\omega &=\frac{n h}{2 \pi m r^{2}}....(ii)<br/>\end{aligned}$<br/>since, the radius of the electron in $n^{t h}$ orbit of<br/>Bohr's atomic model is given as, $r=\frac{n^{2} h^{2} \varepsilon_{0}}{\pi m z e^{2}} \ldots$ (iii)<br/>Squaring the Eq. (iii) and substituting its value in Eq. (ii), we get<br/>$\omega=\frac{n h(\pi n z e)^{2}}{2 \pi m\left(n^{4} h^{4} \varepsilon_{0}^{2}\right)} \Rightarrow \omega \propto \frac{1}{n^{3}}$</div> | db\MarksBatch2_P3.db |
2,384 | to-write-the-decimal-number-37-in-binary-how-many-binary-digits-are-required | to-write-the-decimal-number-37-in-binary-how-many-binary-digits-are-required-88414 | <div class="question">To write the decimal number 37 in binary, how many binary digits are required?</div> | ['Physics', 'Semiconductors', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$6$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$6$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/6webiQL9ra45EgmWbDIKJrNVnE0Ol6anpfjR9BSl9WI.original.fullsize.png"/><br/></div> | db\MarksBatch2_P3.db |
2,385 | transforming-to-parallel-axes-through-a-point-p-q-the-equation-2-x-2-3-x-y-4-y-2-x-18-y-25-0-becomes-2-x-2-3-x-y-4-y-2-1-then | transforming-to-parallel-axes-through-a-point-p-q-the-equation-2-x-2-3-x-y-4-y-2-x-18-y-25-0-becomes-2-x-2-3-x-y-4-y-2-1-then-11664 | <div class="question">Transforming to parallel axes through a point $(p, q), \quad$ the $\quad$ equation $2 x^{2}+3 x y+4 y^{2}+x+18 y+25=0$ becomes
<br/>$2 x^{2}+3 x y+4 y^{2}=1 .$ Then</div> | ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$p=-2, q=3$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$p=2, q=-3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$p=3, q=-4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$p=-4, q=3$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$p=2, q=-3$</span> </div> | <div class="solution">Given equations are
<br/>$$
<br/>\begin{array}{r}
<br/>2 x^{2}+3 x y+4 y^{2}+x+18 y+25=0 ...(i)\\
<br/>2 x^{2}+3 x y+4 y^{2}+1=0 ....(ii)
<br/>\end{array}
<br/>$$
<br/>Let the origin be transferred to $(p, q)$ axes being parallel to the previous axes; then the equation
<br/>(i) becomes.
<br/>$$
<br/>\begin{array}{l}
<br/>2\left(x^{\prime}+p\right)^{2}+3\left(x^{\prime}+p\right)\left(y^{\prime}+q\right) \\
<br/>+4\left(y^{\prime}+q\right)^{2}+\left(x^{\prime}+p\right)+18\left(y^{\prime}+q\right)+25=0 \\
<br/>\Rightarrow 2 x^{2}+2 p^{2}+4 x^{\prime} p+3 x^{\prime} y^{\prime}+3 x^{\prime} q+3 p y^{\prime} \\
<br/>+3 p q+4 y^{2}+4 q^{2}+8 y^{\prime} q+x^{\prime}+p \\
<br/>+18 y^{\prime}+18 q+25=0 \\
<br/>\Rightarrow 2 x^{2}+4 y^{a}+3 x^{\prime} y^{\prime}+(4 p+3 q+1) x^{\prime} \\
<br/>1+(3 p+8 q+18) y^{\prime}+2 p^{2}+3 p q \\
<br/>+4 q^{2}+p+25=0
<br/>\end{array}
<br/>$$
<br/>From Eq. (ii) coefficient of $x^{\prime}$ and $y^{\prime}$ must be
<br/>zero.
<br/>$\therefore$
<br/>$$
<br/>4 p+3 q+1=0 ...(iii)
<br/>$$
<br/>$$
<br/>3 p+8 q+18=0 ...(iv)
<br/>$$
<br/>By solving Eqs. (iii) and (iv), we get
<br/>$$
<br/>p=2, q=-3
<br/>$$</div> | db\MarksBatch2_P3.db |
2,386 | treatment-of-with-nanh-2-liq-nh-3-gives-1 | treatment-of-with-nanh-2-liq-nh-3-gives-1-58300 | <div class="question">Treatment of <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54.png"/> $\text { with } \mathrm{NaNH}_{2} \text { /liq. } \mathrm{NH}_{3}$ gives</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optb.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optd.png"/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a54.png"/></div> | db\MarksBatch2_P3.db |
2,387 | treatment-of-with-nanh-2-liq-nh-3-gives | treatment-of-with-nanh-2-liq-nh-3-gives-71921 | <div class="question">Treatment of <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54.png"/> $\text { with } \mathrm{NaNH}_{2} \text { /liq. } \mathrm{NH}_{3}$ gives</div> | ['Chemistry', 'Alcohols Phenols and Ethers', 'WBJEE', 'WBJEE 2013'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_opta.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optb.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optc.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optd.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_q54_optd.png"/></span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_che_a54.png"/></div> | db\MarksBatch2_P3.db |
2,388 | twenty-metres-of-wire-is-available-to-fence-off-a-flower-bed-in-the-form-of-a-circular-sector-what-must-the-radius-of-the-circle-be-if-the-area-of-the | twenty-metres-of-wire-is-available-to-fence-off-a-flower-bed-in-the-form-of-a-circular-sector-what-must-the-radius-of-the-circle-be-if-the-area-of-the-79119 | <div class="question">Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed be greatest?</div> | ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$5 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6 m$</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$5 \mathrm{~m}$</span> </div> | <div class="solution">Let, radius $=r$, arc length $=\ell$<br/>$2 \mathrm{r}+\ell=20 \Rightarrow \ell=20-2 \mathrm{r}$<br/>$\Rightarrow \mathrm{A}=\frac{1}{2}\mathrm{r}^{2} \theta = \frac{1}{2} \ell \mathrm{r} \Rightarrow \frac{\mathrm{dA}}{\mathrm{dr}}=\frac{1}{2}(20-4 \mathrm{r})=0 \Rightarrow \mathrm{r}=5 \quad \therefore \mathrm{r}=5 \mathrm{~m}\right.$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/JRbJrKnFUlvZADQFyXNXNZKKvSVzhvIuDZAe_uq25ls.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,389 | two-aromatic-compounds-having-formula-mathrmc7-mathrmh8-mathrmo-which-are-easily-identifiable-by-mathrmfecl3-solution-test-violet-colouration-are | two-aromatic-compounds-having-formula-mathrmc7-mathrmh8-mathrmo-which-are-easily-identifiable-by-mathrmfecl3-solution-test-violet-colouration-are-19580 | <div class="question">Two aromatic compounds having formula \(\mathrm{C}_7 \mathrm{H}_8 \mathrm{O}\) which are easily identifiable by \(\mathrm{FeCl}_3\) solution test (violet colouration) are</div> | ['Chemistry', 'Hydrocarbons', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">o- cresol and benzyl alcohol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">m-cresol and p-cresol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">o-cresol and p-cresol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">methyl phenyl ether and benzyl alcohol</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">o- cresol and benzyl alcohol</span> </div> | <div class="solution">Hints: \(\mathrm{O}\) - cresol contains phenolic group, thus it gives violet coloration with \(\mathrm{FeCl}_3\) where as benzylalchol donot contains phenolic group, hence no coloration with \(\mathrm{FeCl}_3\). Hence Identifiable</div> | db\MarksBatch2_P3.db |
2,390 | two-base-balls-masses-m1100-mathrmg-and-m250-mathrmg-are-thrown-both-of-them-move-with-uniform-velocity-but-the-velocity-of-m2-is-15-times-that-of-m1- | two-base-balls-masses-m1100-mathrmg-and-m250-mathrmg-are-thrown-both-of-them-move-with-uniform-velocity-but-the-velocity-of-m2-is-15-times-that-of-m1-47144 | <div class="question">Two base balls (masses: \(m_1=100 \mathrm{~g}\), and \(m_2=50 \mathrm{~g}\) ) are thrown. Both of them move with uniform velocity, but the velocity of \(m_2\) is 1.5 times that of \(m_1\). The ratio of de Broglie wavelengths \(\lambda\left(m_1\right): \lambda\left(m_2\right)\) is given by</div> | ['Chemistry', 'Structure of Atom', 'WBJEE', 'WBJEE 2023'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(4: 3\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(3: 4\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(2: 1\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(1: 2\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(3: 4\)</span> </div> | <div class="solution">Hint : \(\frac{\lambda_1}{\lambda_2}=\frac{m_2 \mathrm{~V}_2}{m_1 \mathrm{~V}_1}=\frac{50 \times 1.5 \mathrm{~V}_1}{100 \times \mathrm{V}_1}=\frac{1.5}{2}=\frac{3}{4}\)</div> | db\MarksBatch2_P3.db |
2,391 | two-black-bodies-a-and-b-have-equal-surface-areas-and-are-maintained-at-temperatures-2-7-c-and-17-7-c-respectively-what-will-be-the-ratio-of-the-therm | two-black-bodies-a-and-b-have-equal-surface-areas-and-are-maintained-at-temperatures-2-7-c-and-17-7-c-respectively-what-will-be-the-ratio-of-the-therm-27897 | <div class="question">Two black bodies $A$ and $B$ have equal surface areas and are maintained at temperatures $27^{\circ} \mathrm{C}$ and $177^{\circ} \mathrm{C}$ respectively. What will be the ratio of the thermal energy radiated per second by $A$ to that by $B ?$</div> | ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4: 9$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2: 3$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$16: 81$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$27:177$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$16: 81$</span> </div> | <div class="solution">According to the question, Area of both bodies $A$ and $B=A$
<br/>Temperature of body $A=27^{\circ} \mathrm{C}=27+273 \mathrm{K}$
<br/>Temperature of body $B=177^{\circ} \mathrm{C}=177+273 \mathrm{K}$
<br/>Now, by Stefan-Boltzmann law, thermal energy radiated per second by a body
<br/>$$
<br/>Q=\sigma A T^{4}
<br/>$$
<br/>where, $A=$ Area
<br/>$T=$ temperature and $\quad \sigma=$ Stefan-Boltzmam's constant
<br/>So, the ratio of thermal energy radiated per second by $A$ to that by $B$ is
<br/>$$
<br/>\frac{Q_{1}}{Q_{2}}=\frac{\sigma A}{\sigma A}\left(\frac{T_{1}}{T_{2}}\right)^{4}
<br/>$$
<br/>Now, $\frac{Q_{1}}{Q_{2}}=\left(\frac{T_{1}}{T_{2}}\right)^{4}$
<br/>$$
<br/>\begin{array}{l}
<br/>\frac{Q_{1}}{Q_{2}}=\left(\frac{273+27}{273+177}\right)^{4} \\
<br/>\frac{Q_{1}}{Q_{2}}=\left(\frac{300}{450}\right)^{4}
<br/>\end{array}
<br/>$$
<br/>$$
<br/>\frac{Q_{1}}{Q_{2}}=\left(\frac{2}{3}\right)^{4}=\left(\frac{16}{81}\right)
<br/>$$
<br/>Ratio of thermal energy radiated per second
<br/>$$
<br/>Q_{1}: Q_{2}=16: 81
<br/>$$</div> | db\MarksBatch2_P3.db |
2,392 | two-black-bodies-at-temperatures-32-7-c-and-42-7-c-are-kept-in-an-evacuated-chamber-at-2-7-c-the-ratio-of-their-rates-of-loss-of-heat-are | two-black-bodies-at-temperatures-32-7-c-and-42-7-c-are-kept-in-an-evacuated-chamber-at-2-7-c-the-ratio-of-their-rates-of-loss-of-heat-are-17989 | <div class="question">Two black bodies at temperatures $327^{\circ} \mathrm{C}$ and $427^{\circ} \mathrm{C}$ are kept in an evacuated chamber at $27^{\circ} \mathrm{C}$. The ratio of their rates of loss of heat are :</div> | ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2010'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{6}{7}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\frac{6}{7}\right)^2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\frac{6}{7}\right)^3$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{243}{464}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{243}{464}$</span> </div> | <div class="solution">Hints: Rate ofloss of heat $\propto\left(\mathrm{T}^4-\mathrm{T}_0^4\right)$<br/>$$<br/>\frac{\mathrm{E}_1}{\mathrm{E}_2}=\frac{\mathrm{T}_1^4-\mathrm{T}_0^4}{\mathrm{~T}_2^4-\mathrm{T}_0^4}=\frac{(600)^4-(300)^4}{(700)^4-(300)^4}=\frac{6^4-3^4}{7^4-3^4}<br/>$$<br/><br/>$$<br/>\frac{E_1}{E_2}=\frac{243}{464}<br/>$$</div> | db\MarksBatch2_P3.db |
2,393 | two-blocks-of-2-kg-and-1-kg-are-in-contact-on-a-frictionless-table-if-a-force-of-3-n-is-applied-on-2-kg-block-then-the-force-of-contact-between-the-tw-1 | two-blocks-of-2-kg-and-1-kg-are-in-contact-on-a-frictionless-table-if-a-force-of-3-n-is-applied-on-2-kg-block-then-the-force-of-contact-between-the-tw-1-40309 | <div class="question">Two blocks of $2 \mathrm{~kg}$ and $1 \mathrm{~kg}$ are in contact on a frictionless table. If a force of $3 \mathrm{~N}$ is applied on $2 \mathrm{~kg}$ block, then the force of contact between the two blocks will be :<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Ua9vbh_hS921PTPp-RPqXh_u3jBcYsg9YCzqfVyij14.original.fullsize.png"/><br/></div> | ['Physics', 'Laws of Motion', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \mathrm{~N}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \mathrm{~N}$</span> </div> | <div class="solution">Hints: Common acceleration $=\frac{3}{3}=1 \mathrm{~m} / \mathrm{sec}^2$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/VNczpMjsBPK9g6tl-vRGyHIFEEZWSF6wWjizp_uYUls.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{N}_1=1 \mathrm{~N}<br/>$$</div> | db\MarksBatch2_P3.db |
2,394 | two-blocks-of-2-kg-and-1-kg-are-in-contact-on-a-frictionless-table-if-a-force-of-3-n-is-applied-on-2-kg-block-then-the-force-of-contact-between-the-tw | two-blocks-of-2-kg-and-1-kg-are-in-contact-on-a-frictionless-table-if-a-force-of-3-n-is-applied-on-2-kg-block-then-the-force-of-contact-between-the-tw-88516 | <div class="question">Two blocks of $2 \mathrm{~kg}$ and $1 \mathrm{~kg}$ are in contact on a frictionless table. If a force of $3 \mathrm{~N}$ is applied on $2 \mathrm{~kg}$ block, then the force of contact between the two blocks will be :<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/Ua9vbh_hS921PTPp-RPqXh_u3jBcYsg9YCzqfVyij14.original.fullsize.png"/><br/></div> | ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2010'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0 \mathrm{~N}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1 \mathrm{~N}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \mathrm{~N}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \mathrm{~N}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \mathrm{~N}$</span> </div> | <div class="solution">Hints: Common acceleration $=\frac{3}{3}=1 \mathrm{~m} / \mathrm{sec}^2$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/VNczpMjsBPK9g6tl-vRGyHIFEEZWSF6wWjizp_uYUls.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{N}_1=1 \mathrm{~N}<br/>$$</div> | db\MarksBatch2_P3.db |
2,395 | two-bodies-of-masses-m-1-and-m-2-are-separated-by-a-distance-r-the-distance-of-the-centre-of-mass-of-the-bodies-from-the-mass-m-1-is-1 | two-bodies-of-masses-m-1-and-m-2-are-separated-by-a-distance-r-the-distance-of-the-centre-of-mass-of-the-bodies-from-the-mass-m-1-is-1-92861 | <div class="question">Two bodies of masses $m_{1}$ and $m_{2}$ are separated by a distance $R$. The distance of the centre of mass of the bodies from the mass $m_{1}$ is</div> | ['Physics', 'Center of Mass Momentum and Collision', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{m_{2} R}{m_{1}+m_{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{m_{1} R}{m_{1}+m_{2}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{m_{1} m_{2}}{m_{1}+m_{2}} R$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{m_{1}+m_{2}}{m_{1}} R$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{m_{2} R}{m_{1}+m_{2}}$</span> </div> | <div class="solution">The bodies are separated by a distance $R$. so the coordinates of $m_{1}$ and $m_{2}$ will be (0,0) and $(R, 0)$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a13.png"/> <br/> <br/>From the formula of centre of mass,
<br/>$$
<br/>\begin{aligned}
<br/>X_{\mathrm{cm}} &=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}} \\
<br/>&=\frac{m_{1} \times 0+m_{2} \times R}{m_{1}+m_{2}} \\
<br/>X_{\mathrm{cm}} &=\frac{m_{2} \cdot R}{m_{1}+m_{2}}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,396 | two-bodies-of-masses-m-1-and-m-2-are-separated-by-a-distance-r-the-distance-of-the-centre-of-mass-of-the-bodies-from-the-mass-m-1-is | two-bodies-of-masses-m-1-and-m-2-are-separated-by-a-distance-r-the-distance-of-the-centre-of-mass-of-the-bodies-from-the-mass-m-1-is-30320 | <div class="question">Two bodies of masses $m_{1}$ and $m_{2}$ are separated by a distance $R$. The distance of the centre of mass of the bodies from the mass $m_{1}$ is</div> | ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2016'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{m_{2} R}{m_{1}+m_{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{m_{1} R}{m_{1}+m_{2}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{m_{1} m_{2}}{m_{1}+m_{2}} R$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{m_{1}+m_{2}}{m_{1}} R$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{m_{2} R}{m_{1}+m_{2}}$</span> </div> | <div class="solution">The bodies are separated by a distance $R$. so the coordinates of $m_{1}$ and $m_{2}$ will be (0,0) and $(R, 0)$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2016_phy_a13.png"/> <br/> <br/>From the formula of centre of mass,
<br/>$$
<br/>\begin{aligned}
<br/>X_{\mathrm{cm}} &=\frac{m_{1} x_{1}+m_{2} x_{2}}{m_{1}+m_{2}} \\
<br/>&=\frac{m_{1} \times 0+m_{2} \times R}{m_{1}+m_{2}} \\
<br/>X_{\mathrm{cm}} &=\frac{m_{2} \cdot R}{m_{1}+m_{2}}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,397 | two-cells-a-and-b-of-emf-2-v-and-15-v-respectively-are-connected-as-shown-in-figure-through-an-external-resistance-10-the-internal-resistance-of-each- | two-cells-a-and-b-of-emf-2-v-and-15-v-respectively-are-connected-as-shown-in-figure-through-an-external-resistance-10-the-internal-resistance-of-each-49561 | <div class="question">Two cells $A$ and $B$ of emf $2 \mathrm{V}$ and $1.5 \mathrm{V}$ respectively, are connected as shown in figure through an external resistance $10 \Omega$ The internal resistance of each cell is $5 \Omega$. The potential difference $E_{A}$ and $E_{B}$ across the terminals of the cells $A$ and $B$ respectively are
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q35.png"/></div> | ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$E_{A}=20 \mathrm{V}, E_{B}=1.5 \mathrm{V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$E_{A}=2.125 \mathrm{V}, E_{B}=1.375 \mathrm{V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$E_{A}=1.875 \mathrm{V}, E_{B}=1.625 \mathrm{V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$E_{A}=1.875 \mathrm{V}, E_{B}=1.375 \mathrm{V}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$E_{A}=1.875 \mathrm{V}, E_{B}=1.625 \mathrm{V}$</span> </div> | <div class="solution">The figure can be redrawn as,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a35.png"/> <br/> <br/>The current through the circuit
<br/>$$
<br/>\begin{aligned}
<br/>i &=\frac{\text { net emf }}{\text { effective resistance }} \\
<br/>&=\frac{2-1.5}{5+5+10}=\frac{0.5}{20} \\
<br/>&=\frac{1}{40}=0.025 \mathrm{A}
<br/>\end{aligned}
<br/>$$
<br/>The terminal potential difference of the batteries
<br/>and
<br/>$$
<br/>\begin{aligned}
<br/>V_{A} &=\varepsilon_{A}-i I_{A}=2-0.025 \times 5 \\
<br/>&=2-0.0125=1.875 \mathrm{V} \\
<br/>V_{B} &=\varepsilon_{B}+i I_{B}
<br/>\end{aligned}
<br/>$$
<br/>$$
<br/>=1.5+0.025 \times 5
<br/>$$
<br/>$$
<br/>=1,5+0.0125=1.625 \mathrm{V}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,398 | two-cells-with-the-same-emf-e-and-different-internal-resistances-r1-and-r2-are-connected-in-series-to-an-external-resistance-r-the-value-of-r-so-that- | two-cells-with-the-same-emf-e-and-different-internal-resistances-r1-and-r2-are-connected-in-series-to-an-external-resistance-r-the-value-of-r-so-that-43442 | <div class="question">Two cells with the same e.m.f. \(E\) and different internal resistances \(r_1\) and \(r_2\) are connected in series to an external resistance \(R\). The value of \(R\) so that the potential difference across the first cell be zero is</div> | ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\sqrt{r_1 r_2}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(r_1+r_2\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(\mathrm{r}_1-\mathrm{r}_2\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{r_1+r_2}{2}\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(\mathrm{r}_1-\mathrm{r}_2\)</span> </div> | <div class="solution">Hints: <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/TodE7DDcwNUogLWejDavnergZeS6AhGJo9h8BFrGFz0.original.fullsize.png"/><br/><br/>\(I=\frac{2 E}{R+r_1+r_2}\)<br/>Potential difference across first cell \(\mathrm{V}=\mathrm{E}-\mathrm{Ir}_1=0\)<br/>\(\begin{aligned}<br/>& E-\frac{2 E r_1}{R+r_1+r_2}=0 \\<br/>& {\left[\frac{R+r_1+r_2-2 r_1}{R+r_1+r_2}\right]=0} \\<br/>& \Rightarrow R+r_2-r_1=0 \\<br/>& R=r_1-r_2<br/>\end{aligned}\)</div> | db\MarksBatch2_P3.db |
2,399 | two-charges-each-equal-to-q-are-kept-at-a-0-and-a-0-a-charge-q-is-placed-at-the-origin-if-q-is-given-a-small-displacement-along-y-direction-the-force- | two-charges-each-equal-to-q-are-kept-at-a-0-and-a-0-a-charge-q-is-placed-at-the-origin-if-q-is-given-a-small-displacement-along-y-direction-the-force-18716 | <div class="question">Two charges, each equal to $-q$ are kept at $(-a, 0)$ and $(a, 0)$. A charge $q$ is placed at the origin. If $q$ is given a small displacement along y direction, the force acting on q is proportional to</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$y$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">-y</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{y}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-\frac{1}{y}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">-y</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/t7TQ3LqJc-JSEbuvMknpZS5icu7vTFH6H9NU7ErQnIo.original.fullsize.png"/><br/><br/>$\vec{F}=+q$ (Electric field due to the two negative charges $=\vec{E}$ )<br/>$$<br/>\vec{F}=+q\left[\frac{k(-2 q) \vec{y}}{a^3}\right] \Rightarrow \vec{F}=-\frac{2 k q^2 y}{a^3} \Rightarrow \vec{F} \propto-\vec{y}<br/>$$</div> | db\MarksBatch2_P3.db |
2,400 | two-charges-q-and-q-are-placed-at-a-distance-a-in-a-uniform-electric-fleld-the-dipole-moment-of-the-combination-is-2-q-a-cos-i-sin-where-is-the-angle- | two-charges-q-and-q-are-placed-at-a-distance-a-in-a-uniform-electric-fleld-the-dipole-moment-of-the-combination-is-2-q-a-cos-i-sin-where-is-the-angle-60235 | <div class="question">Two charges $+q$ and $-q$ are placed at a distance $a$ in a uniform electric fleld. The dipole moment of the combination is $2 q a(\cos \theta i+\sin \theta)$. where, $\theta$ is the angle between the direction of the field and the line joining the two charges. Which of the following statement(s) is/ase correct?</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The torque exerted by the field on the dipole vanishes</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The net force on the dipole vanishes</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">The torque is independent of the choice of coordinates</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The net force is independent of a</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">The net force on the dipole vanishes, The torque is independent of the choice of coordinates, The net force is independent of a</span> </div> | <div class="solution">The situation can be diagrammatically as,
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a36.png"/> <br/> <br/>The dipole moment,
<br/>$$
<br/>\mathbf{P}=2 q a(\cos \theta \hat{\mathbf{i}}+\sin \theta \hat{\mathbf{j}})
<br/>$$
<br/>The net force on the dipole is always zero while net torque on the dipole is not zero.</div> | db\MarksBatch2_P3.db |
2,401 | two-circle-s-1-p-x-2-p-y-2-2-g-x-2-f-y-d-0-and-s-2-x-2-y-2-2-gx-2-f-y-d-0-have-a-common-chord-pq-the-equation-of-pq-is | two-circle-s-1-p-x-2-p-y-2-2-g-x-2-f-y-d-0-and-s-2-x-2-y-2-2-gx-2-f-y-d-0-have-a-common-chord-pq-the-equation-of-pq-is-60905 | <div class="question">Two circle $S_1=p x^2+p y^2+2 g^{\prime} x+2 f^{\prime} y+d=0$ and $S_2=x^2+y^2+2 g x+2 f y+d^{\prime}=0$ have a common chord $P Q$. The equation of $\mathrm{PQ}$ is</div> | ['Mathematics', 'Circle', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$S_1-S_2=0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$S_1+S_2=0$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{S}_1-\mathrm{pS}_2=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{S}_1+\mathrm{pS}_2=0$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{S}_1-\mathrm{pS}_2=0$</span> </div> | <div class="solution">$\frac{\mathrm{S}_1}{\mathrm{p}}-\mathrm{S}_2=0 \Rightarrow \mathrm{S}_1-\mathrm{pS}_2=0$</div> | db\MarksBatch2_P3.db |
2,402 | two-coherent-monochromatic-beams-of-intensities-i-and-4-i-respectively-are-superposed-the-maximum-and-minimum-intensitien-in-the-reaulting-pattern-are | two-coherent-monochromatic-beams-of-intensities-i-and-4-i-respectively-are-superposed-the-maximum-and-minimum-intensitien-in-the-reaulting-pattern-are-29727 | <div class="question">Two coherent monochromatic beams of intensities $I$ and $4 I$ respectively are superposed. The maximum and minimum intensitien in the reaulting pattern are</div> | ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5I and 3I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">9I and 3I</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">4I and I</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">9I and I</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">9I and I</span> </div> | <div class="solution">We know that The maximum intensities
<br/>$$
<br/>I_{\max }=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}
<br/>$$
<br/>The minimum intensities
<br/>$$
<br/>I_{\min }=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}
<br/>$$
<br/>So, the ratio of the maximum and minimum of intensities is
<br/>$$
<br/>\begin{aligned}
<br/>\frac{I_{\max }}{I_{\min }} &=\frac{\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2}}{\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2}} \\
<br/>\frac{I_{\max }}{I_{\min }} &=\frac{(\sqrt{4 I}+\sqrt{I})^{2}}{(\sqrt{4 I}-\sqrt{I})^{2}} \\
<br/>&=\left(\frac{3 \sqrt{I}}{\sqrt{I}}\right)^{2} \\
<br/>=& \frac{9}{1}=9: 1
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,403 | two-coils-of-selfinductances-6-mh-and-8-mh-are-connected-in-series-and-are-adjusted-for-highest-coefficient-of-coupling-equivalent-selfinductance-l-fo | two-coils-of-selfinductances-6-mh-and-8-mh-are-connected-in-series-and-are-adjusted-for-highest-coefficient-of-coupling-equivalent-selfinductance-l-fo-84851 | <div class="question">Two coils of self-inductances $6 \mathrm{mH}$ and $8 \mathrm{mH}$ are connected in series and are adjusted for highest coefficient of coupling. Equivalent self-inductance $L$ for the assembly is approximately</div> | ['Physics', 'Electromagnetic Induction', 'WBJEE', 'WBJEE 2016'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{mH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$36 \mathrm{mH}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$28 \mathrm{mH}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$18 \mathrm{mH}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$28 \mathrm{mH}$</span> </div> | <div class="solution">Given, $L_{1}=6 \mathrm{mH}=6 \times 10^{-3} \mathrm{H}$
<br/>$$
<br/>L_{2}=8 \mathrm{mH}=8 \times 10^{-3} \mathrm{H}
<br/>$$
<br/>If two coills $L_{1}$ and $L_{2}$ are connected in series, the equivalent self-inductance $L$ for assembly
<br/>$$
<br/>L=L_{1}+L_{2}+2 \sqrt{L_{1} L_{2}}
<br/>$$
<br/>$$
<br/>\begin{array}{l}
<br/>=6 \times 10^{-3}+8 \times 10^{-3}+2 \sqrt{6 \times 8 \times 10^{-6}} \\
<br/>=14 \times 10^{-3}+2 \sqrt{48} \times 10^{-3} \\
<br/>=14 \times 10^{-3}+2 \times 7 \times 10^{-3} \\
<br/>=28 \times 10^{-3} \mathrm{H}=28 \mathrm{mH}
<br/>\end{array} \quad(\because \sqrt{48}=6.92=7)
<br/>$$</div> | db\MarksBatch2_P3.db |
2,404 | two-coins-are-available-one-fair-and-the-other-twoheaded-choose-a-coin-and-toss-it-once-assume-that-the-unbiased-coin-is-chosen-with-probability-4-3-g | two-coins-are-available-one-fair-and-the-other-twoheaded-choose-a-coin-and-toss-it-once-assume-that-the-unbiased-coin-is-chosen-with-probability-4-3-g-50266 | <div class="question">Two coins are available, one fair and the other two-headed. Choose a coin and toss it once; assume that the unbiased coin is chosen with probability $\frac{3}{4}$, Given that the outcome is head, the probability that the two-headed coin was chosen, is</div> | ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{5}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2}{5}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{5}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2}{7}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2}{5}$</span> </div> | <div class="solution">Let $F$ denotes fair coin $T$ denotes two headed $H$ denotes head occurs
<br/>$$
<br/>\begin{array}{lc}
<br/>\therefore \quad P(F)=\frac{3}{4}, P(T)=1-\frac{3}{4}=\frac{1}{4} \\
<br/>\therefore \quad P\left(\frac{T}{H}\right)=\frac{P\left(\frac{H}{T}\right) \cdot P(T)}{P\left(\frac{H}{T}\right) \cdot P(T)+P\left(\frac{H}{F}\right) \cdot P(F)}
<br/>\end{array}
<br/>$$
<br/>By Baye's theorem
<br/>$$
<br/>=\frac{1 \cdot \frac{1}{4}}{1 \cdot \frac{1}{4}+\frac{1}{2} \cdot \frac{3}{4}}=\frac{2}{5}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,405 | two-decks-of-playing-cards-are-well-shuffled-and-26-cards-are-randomly-distributed-to-a-player-then-the-probability-that-the-player-gets-all-distinct- | two-decks-of-playing-cards-are-well-shuffled-and-26-cards-are-randomly-distributed-to-a-player-then-the-probability-that-the-player-gets-all-distinct-65784 | <div class="question">Two decks of playing cards are well shuffled and 26 cards are randomly distributed to a player. Then, the probability that the player gets all distinct cards is</div> | ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">${ }^{52} C_{26} /{ }^{104} C_{26}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \times{ }^{52} \mathrm{C}_{26} /{ }^{104} \mathrm{C}_{26}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2^{3} \times{ }^{52} C_{26} /{ }^{104} C_{26}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$2^{26} \times{ }^{52} \mathrm{C}_{26} /{ }^{104} \mathrm{C}_{26}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$2^{26} \times{ }^{52} \mathrm{C}_{26} /{ }^{104} \mathrm{C}_{26}$</span> </div> | <div class="solution">Since, these are 52 distinct cards in decks and each distinct card is 2 in number. Therefore, 2 decks will also contain only 52 distinet cards two each.
<br/>$\therefore$ Probability that the player gets all distinct cards
<br/>$$
<br/>=\frac{{ }^{52} C_{26} \times 2^{26}}{104_{C_{26}}}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,406 | two-dice-are-tossed-once-the-probability-of-getting-an-even-number-at-the-first-die-or-a-total-of-8-is | two-dice-are-tossed-once-the-probability-of-getting-an-even-number-at-the-first-die-or-a-total-of-8-is-90813 | <div class="question">Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is</div> | ['Mathematics', 'Probability', 'WBJEE', 'WBJEE 2010'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{36}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{36}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{11}{36}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of these</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">None of these</span> </div> | <div class="solution">Hints: $A=$ getting even no on 1st dice<br/>$$<br/>\mathrm{B}=\text { getting sum } 8<br/>$$<br/>So $|\mathrm{A}|=18 \quad|\mathrm{~B}|=5 \quad|\mathrm{~A} \cap \mathrm{B}|=3$<br/><br/>$$<br/>\text { So } P(A \cup B)=\frac{18+5-3}{36}=\frac{20}{36} \text {}<br/>$$</div> | db\MarksBatch2_P3.db |
2,407 | two-elements-a-and-b-with-atomic-numbers-z-a-and-z-b-are-used-to-produce-characteristic-xrays-with-frequencies-v-a-and-v-b-respectively-if-z-a-z-b-1-2 | two-elements-a-and-b-with-atomic-numbers-z-a-and-z-b-are-used-to-produce-characteristic-xrays-with-frequencies-v-a-and-v-b-respectively-if-z-a-z-b-1-2-87806 | <div class="question">Two elements $A$ and $B$ with atomic numbers $Z_{A}$ and $Z_{B}$ are used to produce characteristic X-rays with frequencies $v_{A}$ and $v_{B}$ respectively. If $Z_{A}: Z_{B}=1: 2,$ then $v_{A}: v_{B}$ will be</div> | ['Physics', 'Atomic Physics', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1: \sqrt{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1: 8$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4: 1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1: 4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1: 4$</span> </div> | <div class="solution">Given $Z_{A}: Z_{B}=1: 2$ We know<br/>$v \propto Z^{2}$<br/>Hence,<br/>$\begin{array}{l}<br/>\frac{v_{A}}{v_{B}}=\frac{(1)^{2}}{(2)^{2}} \\<br/>v_{A}: v_{B}=1: 4<br/>\end{array}$</div> | db\MarksBatch2_P3.db |
2,408 | two-equal-resistances-400-each-are-connected-in-series-with-a-8-v-battery-if-the-resistance-of-first-one-increases-by-05-the-change-required-in-the-re | two-equal-resistances-400-each-are-connected-in-series-with-a-8-v-battery-if-the-resistance-of-first-one-increases-by-05-the-change-required-in-the-re-94449 | <div class="question">Two equal resistances, $400 \Omega$ each, are connected in series with a $8 \mathrm{V}$ battery. If the resistance of first one increases by $0.5 \%$, the change required in the resistance of the second one in order to keep the potential difference across it unaltered is to</div> | ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2016'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">increase it by $1 \Omega$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">increase it by $2 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">increase it by $4 \Omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">decrease it by $4 \Omega$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">increase it by $2 \Omega$</span> </div> | <div class="solution">In series combination,
<br/>$$
<br/>R=R_{1}+R_{2}
<br/>$$
<br/>Same current will pass in $A_{1}$ and $R_{2}$. According to question, $R_{1}$ is increased by $0.5 \%$
<br/>$\therefore$ Increment in the resistance
<br/>$$
<br/>\begin{array}{l}
<br/>=\frac{0.5}{100} \times 400 \\
<br/>=2.0 \Omega
<br/>\end{array}
<br/>$$
<br/>So to keep the potential unchanged in second resistance the change required will be $2.0 ~ \Omega$ increment.</div> | db\MarksBatch2_P3.db |
2,409 | two-gases-x-molecular-weight-m-x-and-y-molecular-weight-m-y-m-y-m-x-are-at-the-same-temperature-t-in-two-different-containers-their-root-mean-square-v | two-gases-x-molecular-weight-m-x-and-y-molecular-weight-m-y-m-y-m-x-are-at-the-same-temperature-t-in-two-different-containers-their-root-mean-square-v-55467 | <div class="question">Two gases $X$ (molecular weight $M_{X}$ ) and Y (molecular weight $M_{Y} ; M_{Y}>M_{X}$ ) are at the same temperature $T$ in two different containers. Their root mean square velocities are $C_{X}$ and $C_{Y}$ respectively. If the average kinetic energies per molecule of two gases $X$ and $Y$ are $E_{x}$ and $E_{Y}$ respectively then which of the following relation(s) is(are) true?</div> | ['Chemistry', 'States of Matter', 'WBJEE', 'WBJEE 2014'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$E_{X}>E_{Y}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$C_{X}>C_{Y}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$E_{X}=E_{Y}=(3 / 2) R T$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$E_{X}=E_{Y}=(3 / 2) k_{B} T$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$C_{X}>C_{Y}$, $E_{X}=E_{Y}=(3 / 2) k_{B} T$</span> </div> | <div class="solution">Given, molecular weight of $X=M_{X}$
<br/>Mol. wt. of $Y=M_{Y}$ and $M_{Y}>M_{x}$
<br/>Root mean square velocitios $=C_{X}$ and $C_{Y}$ respectively
<br/>Average $\mathrm{KE}$/molecule $=E_{X}$ and $E_{Y}$ respectively We know that. Root mean square velocity.
<br/>$$
<br/>C=\sqrt{\frac{3 R T}{M}} \text { or } C \propto \sqrt{\frac{1}{M}}
<br/>$$
<br/>$\therefore \quad \frac{C_{X}}{C_{Y}}=\frac{M_{Y}}{M_{X}}$
<br/>since $\quad M_{Y}>M_{X}$
<br/>$\therefore$
<br/>$$
<br/>C_{X}>C_{Y}
<br/>$$
<br/>KE/molecules $=\frac{3}{2} n R T$
<br/>$\Rightarrow \quad E_{X} \not \subset E_{Y} \not = \frac{3}{2} R T$
<br/>Further. $\quad E_{X}=E_{Y}=\frac{3}{2} \boldsymbol{k}_{\boldsymbol{B}} \boldsymbol{T}$</div> | db\MarksBatch2_P3.db |
2,410 | two-identical-blocks-of-ice-move-in-opposite-directions-with-equal-speed-and-collide-with-cach-other-what-will-be-the-minimum-speed-required-to-make-b | two-identical-blocks-of-ice-move-in-opposite-directions-with-equal-speed-and-collide-with-cach-other-what-will-be-the-minimum-speed-required-to-make-b-90985 | <div class="question">Two identical blocks of ice move in opposite directions with equal speed and collide with cach other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $-8^{\circ} \mathrm{C}$ each? (Specific heat of ice is $2100 \mathrm{Jkg}^{-1} \mathrm{K}^{-1}$ and latent heat of fusion of ice is $3.36 \times 10^{5} \mathrm{Jkg}^{-1}$ )</div> | ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$840 \mathrm{ms}^{-1}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$420 \mathrm{ms}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$84 m s^{-1}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$84 \mathrm{ms}^{-1}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$840 \mathrm{ms}^{-1}$</span> </div> | <div class="solution">Maximum loss in $K . E=$ Total $K . E$ energy before collision of two ice blocks
<br/>$$
<br/>K . E_{\max } \text { loss }=\frac{1}{2} m v^{2}+\frac{1}{2} m v^{2}=m v^{2}
<br/>$$
<br/>This maximum loss in kinetic energy will be equal to loss in heat to melt two ice block.
<br/>$$
<br/>\Rightarrow \quad m v^{2}=(m s \Delta \theta+m L) 2
<br/>$$
<br/>According to question,
<br/>$$
<br/>\begin{aligned}
<br/>L &=336 \times 10^{5} \mathrm{J} \mathrm{kg}^{-1} \\
<br/>S=& 2100 \mathrm{J} \mathrm{kg}^{-1} \mathrm{K}^{-1} \\
<br/>\Delta \theta=8^{\circ} \mathrm{C}
<br/>\end{aligned}
<br/>$$
<br/>From Eq.
<br/>(i) $v=\sqrt{2(s-\Delta \theta+L)}$
<br/>$$
<br/>\begin{array}{l}
<br/>=\sqrt{2\left(2100 \times 8+336 \times 10^{5}\right)} \\
<br/>v=840 \mathrm{ms}^{-1}
<br/>\end{array}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,411 | two-identical-cells-each-of-emf-e-and-internal-resistance-r-are-connected-in-parallel-with-an-external-resistance-r-to-get-maximum-power-developed-acr | two-identical-cells-each-of-emf-e-and-internal-resistance-r-are-connected-in-parallel-with-an-external-resistance-r-to-get-maximum-power-developed-acr-27240 | <div class="question">Two identical cells each of emf $\mathrm{E}$ and internal resistance $\mathrm{r}$ are connected in parallel with an external resistance $\mathrm{R}$. To get maximum power developed across $R$, the value of $R$ is</div> | ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$R=r / 2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R}=\mathrm{r}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$R=r / 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{R}=2 \mathrm{r}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$R=r / 2$</span> </div> | <div class="solution">$R_{e q}=\frac{r}{2}$<br/>$I=\frac{2 E}{r+2 R}$<br/>For max. power consumption. I should be max. So denominator should be min. for that<br/>$r+2 R=(\sqrt{r}, \quad)$</div> | db\MarksBatch2_P3.db |
2,412 | two-identical-equiconvex-lenses-each-of-focal-length-f-are-placed-side-by-side-in-contact-with-each-other-with-a-layer-of-water-in-between-them-as-sho | two-identical-equiconvex-lenses-each-of-focal-length-f-are-placed-side-by-side-in-contact-with-each-other-with-a-layer-of-water-in-between-them-as-sho-43444 | <div class="question">Two identical equiconvex lenses, each of focal length $f$ are placed side by side in contact with each other with a layer of water in between them as shown in the figure. If refractive index of the material of the lenses is greater than that of water, how the combined focal length $F$ is related to $f ?$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_q4.png"/></div> | ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2018'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$F>f$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{f}{2} < F < f$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$F < \frac{f}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$F=f$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{f}{2} < F < f$</span> </div> | <div class="solution">The given combination of lenses
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a4.png"/> <br/> <br/>Here, $f_{1}=$ focal length of equiconvex lenses of glass. $f_{2}=$ focal length of lens formed by water (concave). The focal length of the combination.
<br/>$$
<br/>\therefore \quad \frac{1}{F}=\frac{1}{f_{1}}+\frac{1}{f_{2}}+\frac{1}{f_{3}}=\frac{1}{f_{1}}-\frac{1}{f_{2}}+\frac{1}{f_{1}}=\frac{2}{f_{1}}-\frac{1}{f_{2}}
<br/>$$
<br/>$$
<br/>\begin{aligned}
<br/>\frac{1}{F}=\frac{2 f_{2}-f_{1}}{f_{1} f_{2}} \Rightarrow F &=\frac{f_{1} f_{2}}{2 f_{2}-f_{1}} \\
<br/>F &=\frac{f_{1}}{2-\frac{f_{1}}{f_{2}}}
<br/>\end{aligned}
<br/>$$
<br/>$\left[\because f_{3}=f_{1}\right]$
<br/>Here, $\frac{1}{f_{1}}=\left(\mu_{g}-1\right) \frac{2}{R},$ for $L_{1}$ and $L_{3}$
<br/>and $\frac{1}{f_{2}}=\left(\mu_{w}-1\right)\left(-\frac{2}{R}\right),$ for $L_{2}$
<br/>$$
<br/>\text { Given, } \mu_{w} < \mu_{g}
<br/>$$
<br/>Thus, $\frac{f_{1}}{f_{2}} < 1$
<br/>So.
<br/>$$
<br/>F>\frac{f_{1}}{2}
<br/>$$
<br/>From Eqs.
<br/>(i) and (ii), we get
<br/>$$
<br/>\frac{f_{1}}{2} < F < f_{1} \quad \text { or } \frac{f}{2} < F < f
<br/>$$</div> | db\MarksBatch2_P3.db |
2,413 | two-identical-light-waves-propagating-in-the-same-direction-have-a-phase-difference-after-they-superpose-the-intensity-of-the-resulting-wave-will-be-p | two-identical-light-waves-propagating-in-the-same-direction-have-a-phase-difference-after-they-superpose-the-intensity-of-the-resulting-wave-will-be-p-14298 | <div class="question">Two identical light waves, propagating in the same direction, have a phase difference $\delta$. After they superpose the intensity of the resulting wave will be proportional to</div> | ['Physics', 'Wave Optics', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\cos \delta$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\cos (\delta / 2)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\cos ^2(\delta / 2)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\cos ^2 \delta$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos ^2(\delta / 2)$</span> </div> | <div class="solution">$I=4 I_0 \cos ^2\left(\frac{\delta}{2}\right) \Rightarrow I \propto \cos ^2\left(\frac{\delta}{2}\right)$</div> | db\MarksBatch2_P3.db |
2,414 | two-identical-springs-are-connected-to-mass-mathrmm-as-shown-mathrmk-spring-constant-if-the-period-of-the-configuration-in-a-is-2-mathrms-the-period-o | two-identical-springs-are-connected-to-mass-mathrmm-as-shown-mathrmk-spring-constant-if-the-period-of-the-configuration-in-a-is-2-mathrms-the-period-o-58802 | <div class="question">Two identical springs are connected to mass \(\mathrm{m}\) as shown \((\mathrm{k}=\) spring constant). If the period of the configuration in (a) is \(2 \mathrm{~S}\), the period of the configuration (b) is</div> | ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(\sqrt{2} \mathrm{~S}\)</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">\(1 \mathrm{~S}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(\frac{1}{\sqrt{2}} \mathrm{~S}\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(2 \sqrt{2} \mathrm{~s}\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(1 \mathrm{~S}\)</span> </div> | <div class="solution">\(\begin{aligned} & \text {Hints: } \frac{\mathrm{T}_1}{\mathrm{~T}_2}=\sqrt{\frac{\mathrm{k}_2}{\mathrm{k}_1}} \Rightarrow \frac{2}{\mathrm{~T}}=\sqrt{\frac{2 \mathrm{k}}{\frac{\mathrm{k}}{2}}}=2 \\ & \therefore \mathrm{T}=1 \mathrm{~S}\end{aligned}\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/0l5EkFSmtartzOmFLKUuJIPB5LoZJyRurXlHA5pNWOA.original.fullsize.png"/><br/></div> | db\MarksBatch2_P3.db |
2,415 | two-infinite-linecharges-parallel-to-each-other-are-moving-with-a-constant-velocity-v-in-the-same-direction-as-shown-in-the-figure-the-separation-betw-1 | two-infinite-linecharges-parallel-to-each-other-are-moving-with-a-constant-velocity-v-in-the-same-direction-as-shown-in-the-figure-the-separation-betw-1-57616 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8qF_D8cxY0oJEvgIMravf0Jl66wI-SInUSu27DoJ6M4.original.fullsize.png"/><br/><br/>Two infinite line-charges parallel to each other are moving with a constant velocity $v$ in the same direction as shown in the figure. The separation between two line-charges is $d$. The magnetic attraction balances the electric repulsion when, [c = speed of light in free space]</div> | ['Physics', 'Magnetic Effects of Current', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad v=\sqrt{2} c$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$v=\frac{c}{\sqrt{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$v=c$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$v=\frac{c}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$v=c$</span> </div> | <div class="solution">$\mathrm{F}_{\mathrm{E}}=\mathrm{q}_2 \mathrm{E}_1=\lambda_2 \ell \frac{2 \mathrm{k} \lambda_1}{\mathrm{~d}}$<br/>$\mathrm{~F}_{\mathrm{B}}=\frac{\mu_0 \mathrm{i}_1 \mathrm{i}_2 \ell}{2 \pi \mathrm{d}}=\frac{\mu_0 \lambda_1 \mathrm{~V} \lambda_2 \mathrm{~V}}{2 \pi \mathrm{d}} \times \ell$<br/>$\mathrm{F}_{\mathrm{E}}=\mathrm{F}_{\mathrm{B}}$<br/>$\Rightarrow \frac{2 \mathrm{k} \lambda_1 \lambda_2 \ell}{\mathrm{d}}=\frac{\mu_0 \lambda_1 \lambda_2 \mathrm{~V}^2 \ell}{2 \pi \mathrm{d}}$<br/>$\Rightarrow \frac{2 \lambda_1 \lambda_2 \ell}{4 \pi \varepsilon_0}=\frac{\mu_0 \lambda_1 \lambda_2 \mathrm{~V}^2 \ell}{2 \pi}$<br/>$\mathrm{V}^2=\frac{1}{\mu_0 \varepsilon_0}=\mathrm{c}^2 \Rightarrow \mathrm{V}=\mathrm{c}$</div> | db\MarksBatch2_P3.db |
2,416 | two-infinite-linecharges-parallel-to-each-other-are-moving-with-a-constant-velocity-v-in-the-same-direction-as-shown-in-the-figure-the-separation-betw | two-infinite-linecharges-parallel-to-each-other-are-moving-with-a-constant-velocity-v-in-the-same-direction-as-shown-in-the-figure-the-separation-betw-61070 | <div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/8qF_D8cxY0oJEvgIMravf0Jl66wI-SInUSu27DoJ6M4.original.fullsize.png"/><br/><br/>Two infinite line-charges parallel to each other are moving with a constant velocity $v$ in the same direction as shown in the figure. The separation between two line-charges is $d$. The magnetic attraction balances the electric repulsion when, [c = speed of light in free space]</div> | ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2022'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad v=\sqrt{2} c$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$v=\frac{c}{\sqrt{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$v=c$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$v=\frac{c}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$v=c$</span> </div> | <div class="solution">$\mathrm{F}_{\mathrm{E}}=\mathrm{q}_2 \mathrm{E}_1=\lambda_2 \ell \frac{2 \mathrm{k} \lambda_1}{\mathrm{~d}}$<br/>$\mathrm{~F}_{\mathrm{B}}=\frac{\mu_0 \mathrm{i}_1 \mathrm{i}_2 \ell}{2 \pi \mathrm{d}}=\frac{\mu_0 \lambda_1 \mathrm{~V} \lambda_2 \mathrm{~V}}{2 \pi \mathrm{d}} \times \ell$<br/>$\mathrm{F}_{\mathrm{E}}=\mathrm{F}_{\mathrm{B}}$<br/>$\Rightarrow \frac{2 \mathrm{k} \lambda_1 \lambda_2 \ell}{\mathrm{d}}=\frac{\mu_0 \lambda_1 \lambda_2 \mathrm{~V}^2 \ell}{2 \pi \mathrm{d}}$<br/>$\Rightarrow \frac{2 \lambda_1 \lambda_2 \ell}{4 \pi \varepsilon_0}=\frac{\mu_0 \lambda_1 \lambda_2 \mathrm{~V}^2 \ell}{2 \pi}$<br/>$\mathrm{V}^2=\frac{1}{\mu_0 \varepsilon_0}=\mathrm{c}^2 \Rightarrow \mathrm{V}=\mathrm{c}$</div> | db\MarksBatch2_P3.db |
2,417 | two-infinite-parallel-metal-planes-contain-electric-charges-with-charge-densities-and-respectively-and-they-are-separated-by-a-small-distance-in-air-i | two-infinite-parallel-metal-planes-contain-electric-charges-with-charge-densities-and-respectively-and-they-are-separated-by-a-small-distance-in-air-i-14849 | <div class="question">Two infinite parallel metal planes, contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively and they are separated by a small distance in air. If the permittivity of air is $\varepsilon_{0}$, then the magnitude of the field between the two planes with its direction will be</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sigma / \varepsilon_{0}$ towards the positively charged plane</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\sigma / \varepsilon_{0}$ towards the negatively charged plane</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sigma /\left(2 \varepsilon_{0}\right)$ towards the positively charged plane</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0 and towards any direction</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\sigma / \varepsilon_{0}$ towards the negatively charged plane</span> </div> | <div class="solution">$E=\frac{\sigma}{2 \varepsilon_{0}}+\frac{\sigma}{2 \varepsilon_{0}}$
<br/>$E=\frac{\sigma}{\varepsilon_{0}}$ towards negative charged plate.</div> | db\MarksBatch2_P3.db |
2,418 | two-long-parallel-wires-separated-by-01-m-carry-currents-of-1-a-and-2-a-respectively-in-opposite-directions-a-third-currentcarrying-wire-parallel-to-b-1 | two-long-parallel-wires-separated-by-01-m-carry-currents-of-1-a-and-2-a-respectively-in-opposite-directions-a-third-currentcarrying-wire-parallel-to-b-1-28241 | <div class="question">Two long parallel wires separated by $0.1 \mathrm{m}$ carry currents of 1 A and 2 A, respectively in opposite directions. A third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of</div> | ['Physics', 'Magnetic Effects of Current', 'JEE Main'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.5 \mathrm{m}$ from the 1 st wire, towards the 2nd wire</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.2 \mathrm{m}$ from the 1 st wire, towards the 2nd wire</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.1 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.2 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$0.1 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a37.png"/> <br/> <br/>According to question, the third wire should not feel magnetic force due to wire (1) and
<br/>(2). It can be only possible in the condition
<br/>that fields due to wire (1) and (2) must act opposite to each other and must be equal. The magnetic field due to long straight wire,
<br/>$$
<br/>B=\frac{\mu_{0} \cdot I}{2 \pi x}
<br/>$$
<br/>$\therefore \quad B_{1}=B_{2}$
<br/>$$
<br/>\frac{\mu_{j_{1}}}{2 \pi x}=\frac{\mu_{d_{2}}}{2 \pi(0 \cdot 1+x)}
<br/>$$
<br/>Here
<br/>$$
<br/>\begin{aligned}
<br/>i_{1} &=1 \mathrm{A} \\
<br/>i_{2} &=2 \mathrm{A} \\
<br/>\frac{\mu_{0} \times 1}{2 \pi x} &=\frac{\mu_{0} \times 2}{2 \pi(0 \cdot 1+x)} \\
<br/>2 x &=(0 \cdot 1+x) \\
<br/>x &=0 \cdot 1 \mathrm{m}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,419 | two-long-parallel-wires-separated-by-01-m-carry-currents-of-1-a-and-2-a-respectively-in-opposite-directions-a-third-currentcarrying-wire-parallel-to-b | two-long-parallel-wires-separated-by-01-m-carry-currents-of-1-a-and-2-a-respectively-in-opposite-directions-a-third-currentcarrying-wire-parallel-to-b-43734 | <div class="question">Two long parallel wires separated by $0.1 \mathrm{m}$ carry currents of 1 A and 2 A, respectively in opposite directions. A third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of</div> | ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.5 \mathrm{m}$ from the 1 st wire, towards the 2nd wire</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.2 \mathrm{m}$ from the 1 st wire, towards the 2nd wire</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.1 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.2 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$0.1 \mathrm{m}$ from the 1 st wire, away from the 2nd wire</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2017_phy_a37.png"/> <br/> <br/>According to question, the third wire should not feel magnetic force due to wire (1) and
<br/>(2). It can be only possible in the condition
<br/>that fields due to wire (1) and (2) must act opposite to each other and must be equal. The magnetic field due to long straight wire,
<br/>$$
<br/>B=\frac{\mu_{0} \cdot I}{2 \pi x}
<br/>$$
<br/>$\therefore \quad B_{1}=B_{2}$
<br/>$$
<br/>\frac{\mu_{j_{1}}}{2 \pi x}=\frac{\mu_{d_{2}}}{2 \pi(0 \cdot 1+x)}
<br/>$$
<br/>Here
<br/>$$
<br/>\begin{aligned}
<br/>i_{1} &=1 \mathrm{A} \\
<br/>i_{2} &=2 \mathrm{A} \\
<br/>\frac{\mu_{0} \times 1}{2 \pi x} &=\frac{\mu_{0} \times 2}{2 \pi(0 \cdot 1+x)} \\
<br/>2 x &=(0 \cdot 1+x) \\
<br/>x &=0 \cdot 1 \mathrm{m}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,420 | two-massless-springs-of-force-constants-k-1-and-k-2-are-joined-end-to-end-the-resultant-force-constant-k-of-the-system-is | two-massless-springs-of-force-constants-k-1-and-k-2-are-joined-end-to-end-the-resultant-force-constant-k-of-the-system-is-86721 | <div class="question">Two massless springs of force constants $\mathrm{K}_1$ and $\mathrm{K}_2$ are joined end to end. The resultant force constant $\mathrm{K}$ of the system is</div> | ['Physics', 'Laws of Motion', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{K}=\frac{\mathrm{K}_1+\mathrm{K}_2}{\mathrm{~K}_1 \mathrm{~K}_2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{K}=\frac{\mathrm{K}_1-\mathrm{K}_2}{\mathrm{~K}_1 \mathrm{~K}_2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_1+\mathrm{K}_2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_1-\mathrm{K}_2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_1+\mathrm{K}_2}$</span> </div> | <div class="solution">In series $\mathrm{K}_{\text {eff }}=\frac{K_1 K_2}{K_1+K_2}$</div> | db\MarksBatch2_P3.db |
2,421 | two-metal-wires-of-identical-dimensions-are-connected-in-series-if-1-and-2-are-the-electrical-conductivities-of-the-metal-wires-respectively-the-effec | two-metal-wires-of-identical-dimensions-are-connected-in-series-if-1-and-2-are-the-electrical-conductivities-of-the-metal-wires-respectively-the-effec-81405 | <div class="question">Two metal wires of identical dimensions are connected in series. If $\sigma_{1}$ and $\sigma_{2}$ are the electrical conductivities of the metal wires respectively, the effective conductivity of the combination is</div> | ['Physics', 'Current Electricity', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sigma_{1}+\sigma_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\sigma_{1}+\sigma_{2}}{2 \sigma_{1} \sigma_{2}}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}$</span> </div> | <div class="solution">$R_{e q}=R_{1}+R_{2}$
<br/>$\frac{1}{\sigma_{e q}} \frac{2 l}{A}=\frac{1}{\sigma_{1}} \frac{1}{A}+\frac{1}{\sigma_{2}} \frac{1}{A}\left[\sigma_{e q}=\frac{2 \sigma_{1} \sigma_{2}}{\sigma_{1}+\sigma_{2}}\right]$</div> | db\MarksBatch2_P3.db |
2,422 | two-metallic-spheres-of-equal-outer-radii-are-found-to-have-same-moment-of-inertia-about-their-respective-diameters-then-which-of-the-following-statem | two-metallic-spheres-of-equal-outer-radii-are-found-to-have-same-moment-of-inertia-about-their-respective-diameters-then-which-of-the-following-statem-52344 | <div class="question">Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. Then which of the following statement(s) is/are true?</div> | ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2020'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The two spheres have equal masses</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The ratio of their masses is nearly $1.67: 1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The spheres are made of different materials</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Their rotational kinetic energies will be equal when rotated with equal uniform angular speed about their respective diameters</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">Their rotational kinetic energies will be equal when rotated with equal uniform angular speed about their respective diameters</span> </div> | <div class="solution">Hint:
<br/>Inner radius is not given
<br/>$\therefore$ only option (D) is correct</div> | db\MarksBatch2_P3.db |
2,423 | two-mirrors-at-an-angle-produce-5-images-of-a-point-the-number-of-images-produced-when-is-decreased-to-3-0-is | two-mirrors-at-an-angle-produce-5-images-of-a-point-the-number-of-images-produced-when-is-decreased-to-3-0-is-56608 | <div class="question">Two mirrors at an angle $\theta^{\circ}$ produce 5 images of a point. The number of images produced when $\theta$ is decreased to $\theta^{\circ}-30^{\circ}$ is</div> | ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2010'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">9</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">10</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">11</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">12</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">11</span> </div> | <div class="solution">Hints: No. of images $=5$<br/>$\therefore \theta=60^{\circ}$<br/>New angle $=\theta-30^{\circ}=30^{\circ}$. No of images $=\frac{360^{\circ}}{30^{\circ}}-1=11$</div> | db\MarksBatch2_P3.db |
2,424 | two-monochromatic-coherent-light-beams-a-and-b-have-intensities-l-and-4-l-respectively-if-these-beams-are-superposed-the-maximum-and-minimum-intensiti | two-monochromatic-coherent-light-beams-a-and-b-have-intensities-l-and-4-l-respectively-if-these-beams-are-superposed-the-maximum-and-minimum-intensiti-71673 | <div class="question">Two monochromatic coherent light beams $A$ and $B$ have intensities $L$ and $\frac{L}{4},$ respectively. If these beams are superposed, the maximum and minimum intensities will be</div> | ['Physics', 'Waves and Sound', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{9 L}{4}, \frac{L}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{5 L}{4}, 0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{5 L}{2}, 0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 L, \frac{L}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{9 L}{4}, \frac{L}{4}$</span> </div> | <div class="solution">For maximum intensity,
<br/>$$
<br/>I_{\max }=I_{1}+I_{2}+2 \sqrt{I_{1} I_{2}} \cos \delta
<br/>$$
<br/>$$
<br/>\begin{aligned}
<br/>\delta &=0 \\
<br/>I_{\max } &=L+\frac{L}{4}+2 \sqrt{L \times \frac{L}{4}} \cdot \cos 0 \\
<br/>&=\frac{5 L}{4}+\frac{2 L}{2} \\
<br/>&=\frac{5 L+4 L}{4} \\
<br/>&=\frac{9 L}{4} \\
<br/>I_{\min } &=I_{1}+I_{2}-2 \sqrt{I_{1} I_{2}} \cos \theta \\
<br/>\theta &=0^{\circ} \\
<br/>&=L+\frac{L}{4}-2 \sqrt{L \times \frac{L}{4}} \times 1 \\
<br/>&=\frac{5 L}{4}-L=\frac{L}{4}
<br/>\end{aligned}
<br/>$$
<br/>Thus, maximum and minimum intensities will be $\left(\frac{9 L}{4}, \frac{L}{4}\right)$</div> | db\MarksBatch2_P3.db |
2,425 | two-particles-a-and-b-are-moving-as-shown-in-the-figure-their-total-angular-momentum-about-the-point-o-is-1 | two-particles-a-and-b-are-moving-as-shown-in-the-figure-their-total-angular-momentum-about-the-point-o-is-1-26811 | <div class="question">"Two particles $A$ and $B$ are moving as shown. in the figure.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_q17.png"/> <br/>Their total angular momentum about the point $O$ is</div> | ['Physics', 'Rotational Motion', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$9.8 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$52.7 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$37.9 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$9.8 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$</span> </div> | <div class="solution">Total angular momentum about $O$ is given as,
<br/>$$
<br/>\begin{aligned}
<br/>\mathbf{L} &=\mathbf{L}_{1}+\mathbf{L}_{2}=m_{1} V_{1} I_{1}+m_{2} V_{2} I_{2} \\
<br/>&=-6.5 \times 2.2 \times 1.5+3.1 \times 3.6 \times 2.8 \\
<br/>&=-21.45+31.248=9.8 \mathrm{kgm}^{2} / \mathrm{s}
<br/>\end{aligned}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,426 | two-particles-a-and-b-both-initially-at-rest-start-moving-towards-each-other-under-a-mutual-force-of-attraction-at-the-instant-when-the-speed-of-a-is- | two-particles-a-and-b-both-initially-at-rest-start-moving-towards-each-other-under-a-mutual-force-of-attraction-at-the-instant-when-the-speed-of-a-is-79463 | <div class="question">Two particles $A$ and $B$ (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of $A$ is $v$ and the speed of $B$ is $2 v$, the speed of the centre of mass is</div> | ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$v$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{3 v}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-\frac{3 v}{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">zero</span> </div> | <div class="solution">In the absence of external force the speed
<br/>$$
<br/>u_{\mathrm{co}}=0
<br/>$$
<br/>$F_{ext}=0$ then
<br/>$$
<br/>v_{\mathrm{cm} .}=0 \text { always }
<br/>$$</div> | db\MarksBatch2_P3.db |
2,427 | two-particles-a-and-b-having-different-masses-are-projected-from-a-tower-with-same-speed-a-is-projected-vertically-upward-and-b-vertically-downward-on | two-particles-a-and-b-having-different-masses-are-projected-from-a-tower-with-same-speed-a-is-projected-vertically-upward-and-b-vertically-downward-on-35571 | <div class="question">Two particles $A$ and $B$ having different masses are projected from a tower with same speed. $A$ is projected vertically upward and $B$ vertically downward. On reaching the ground</div> | ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">velocity of $A$ is greator than that of $B$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">velocity of $B$ is greater than that of $A$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">both $A$ and $B$ attain the same velocity</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the particle with the larger mass attains higher velocily</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">both $A$ and $B$ attain the same velocity</span> </div> | <div class="solution">The situation is diagrammatically as below
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2015_phy_a26.png"/> <br/> <br/>When $A$ is projected with a vertical speed after sometime it comes on the same level with same
<br/>speed as it was projected. Now, the downward speeds of $A$ and $B$ at the level- $X$ is same. So, on reaching the ground, velocity of $A$ and $B$ are same.</div> | db\MarksBatch2_P3.db |
2,428 | two-particles-a-and-b-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-into-a-region-of-uniform-magnetic-field | two-particles-a-and-b-having-equal-charges-after-being-accelerated-through-the-same-potential-difference-enter-into-a-region-of-uniform-magnetic-field-23382 | <div class="question">Two particles, $A$ and $B$, having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii $R_{1}$ and $R_{2}$ resporctively. The ratio of the masses of $A$ and $B$ is</div> | ['Physics', 'Magnetic Effects of Current', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sqrt{R_{1}} / R_{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$R_{1} / R_{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(R_{1} / R_{2}\right)^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(R_{2} / R_{1}\right)^{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(R_{1} / R_{2}\right)^{2}$</span> </div> | <div class="solution">Radius of circular path followed by charged particle is given by
<br/>$$
<br/>R=\frac{m v}{q B}=\frac{\sqrt{2 m K}}{q B} \quad[\because p=m v=\sqrt{2 m K}]
<br/>$$
<br/>where, $K$ is kinetic energy of particle. Charged particle $q$ is accelerated through some potential difference $V$, such that kinetic energy of particle is
<br/>$\therefore$
<br/>$$
<br/>\begin{aligned}
<br/>K &=q V \\
<br/>R &=\frac{\sqrt{2 m q V}}{q B}
<br/>\end{aligned}
<br/>$$
<br/>As the two charged particles of same magnitude and being accelerated through same potential, enters into a uniform magnetic field region, then $R \propto \sqrt{m}$
<br/>So,
<br/>$$
<br/>\frac{R_{1}}{R_{2}}=\sqrt{\frac{m_{A}}{m_{B}}} \Rightarrow \frac{m_{A}}{m_{B}}=\left(\frac{R_{1}}{R_{2}}\right)^{2}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,429 | two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-f-respectively-if-a-takes-m-sec-more-than-that-of-b-and-d | two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-f-respectively-if-a-takes-m-sec-more-than-that-of-b-and-d-64494 | <div class="question">Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $f$ ' respectively. If $A$ takes $\mathrm{m}$ sec. more than that of $\mathrm{B}$ and describes $\mathrm{n}$ units more than that of $\mathrm{B}$ in acquiring the same velocity, then</div> | ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left(f+f^{\prime}\right) m^{2}=$ ff'n</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(f-f f^{\prime}\right) m^{2}=f f^{\prime} n$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}\left(\mathrm{f}+\mathrm{f}^{\prime}\right) \mathrm{m}=\mathrm{ff}^{\prime} \mathrm{n}^{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(f^{\prime}-f\right) n=\frac{1}{2} f f^{\prime} m^{2}$</span> </div> | <div class="solution">$\begin{array}{llll}A:\quad u=0 & a_{1}=f & t_{1}=t+m & s_{1}=n+s \\ B: \quad u=0 & a_{2}=f^{\prime} & t_{2}=t & s_{2}=s\end{array}$
<br/>$\mathrm{s}+\mathrm{n}=\frac{1}{2} \mathrm{f} .(\mathrm{t}+\mathrm{m})^{2} \ldots \ldots(\mathrm{i}) \quad$ and $\mathrm{s}=\frac{1}{2} \mathrm{f}^{\prime}(\mathrm{t})^{2} \ldots(\mathrm{ii}) \quad \therefore \mathrm{f}^{\prime}(\mathrm{t})^{2}+\mathrm{n}=\frac{1}{2} \mathrm{f}(\mathrm{t}+\mathrm{m})^{2} \ldots (iii)$
<br/>$\begin{array}{l}
<br/>v_{1}=u_{1}+a_{1} t_{1}=0+f .(t+m) \\
<br/>v_{2}=u_{2}+a_{2} t_{2}=0+f^{\prime} . t \\
<br/>\therefore f(t+m)=f^{\prime} t \\
<br/>t=\frac{f m}{f^{\prime}-f}
<br/>\end{array}$
<br/>from (iii)
<br/>$\frac{1}{2} f^{\prime} \cdot\left(\frac{f m}{f^{\prime}-f}\right)^{2}+n=\frac{1}{2} f\left(\frac{f m}{f^{\prime}-f}+m\right)^{2}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/CDyhZd61FNn0CEu7Wm3zW5Q56fG_FwHiL0sTOSg56wA.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,430 | two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-h-respectively-if-a-takes-m-seconds-more-than-b-and-descr | two-particles-a-and-b-move-from-rest-along-a-straight-line-with-constant-accelerations-f-and-h-respectively-if-a-takes-m-seconds-more-than-b-and-descr-15007 | <div class="question">Two particles $A$ and $B$ move from rest along a straight line with constant accelerations $f$ and $h,$ respectively. If $A$ takes $m$ seconds more than $B$ and describes $n$ units more than that of $B$ acquiring the same speed, then</div> | ['Mathematics', 'Functions', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(f+h) m^{2}=h n$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(f-f h) m^{2}=f h n$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(h-f) n=\frac{1}{2}$ $fhm^{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{2}(f+h) n=$ $fhm^{2}$</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$(h-f) n=\frac{1}{2}$ $fhm^{2}$</span> </div> | <div class="solution">Let $B$ travels $x$ units, $v=u+a t$
<br/>According to problem, $h t=f(t+m)$ $\begin{aligned} h t=& f t+f m \\ h t-f t &=f m \\ t(h-f) &=f m \\ \frac{h-f}{f} &=\frac{m}{t} \end{aligned}$
<br/>$t=m\left(\frac{f}{h-f}\right)$
<br/>$\Rightarrow \quad t^{2}=m^{2}\left(\frac{f}{h-f}\right)^{2}$
<br/>Again, $n+x=\frac{1}{2} f(t+m)^{2}$
<br/>$\Rightarrow \quad h+\frac{1}{2} h t^{2}=\frac{1}{2} f(t+m)^{2}$
<br/>From Eqs. (i) and (ii) $\frac{m}{n}=\frac{2(h-f)}{m f h}$
<br/>$\Rightarrow \quad(h-f) n=\frac{m^{2} f h}{2}$</div> | db\MarksBatch2_P3.db |
2,431 | two-particles-are-simultaneously-projected-in-the-horizontal-direction-from-a-point-p-at-a-certain-height-the-initial-velocities-of-the-particles-are- | two-particles-are-simultaneously-projected-in-the-horizontal-direction-from-a-point-p-at-a-certain-height-the-initial-velocities-of-the-particles-are-32704 | <div class="question">Two particles are simultaneously projected in the horizontal direction from a point $P$ at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude $v$ each. The separation between the particles at a time when their position vectors (drawn from the point $P$ ) are mutually perpendicular, is</div> | ['Physics', 'Motion In One Dimension', 'WBJEE', 'WBJEE 2019'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{v^{2}}{2 g}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{v^{2}}{g}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{4 v^{2}}{g}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 v^{2}}{g}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{4 v^{2}}{g}$</span> </div> | <div class="solution">According to the question,
<br/>Representation of position vectors of two particles (drawn from the point $P$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2019_phy_a11.png"/> <br/>In two dimension, the position vectors $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$ represented as
<br/>$$
<br/>\begin{array}{l}
<br/>\mathbf{r}_{1}=v t \hat{\mathbf{i}}-\frac{1}{2} g t^{2} \mathbf{j} ...(i) \\
<br/>\mathbf{r}_{2}=v t(-\hat{\mathbf{i}})-\frac{1}{2} g t^{2}(\mathbf{j})...(ii)
<br/>\end{array}
<br/>$$
<br/>$\because$ We know that, when the two vectors are mutually perpendicular, i.e.
<br/>$$
<br/>\theta=90^{\circ}
<br/>$$
<br/>So,
<br/>$$
<br/>\begin{array}{l}
<br/>\mathbf{r}_{1} \cdot \mathbf{r}_{2}=r_{1} r_{2} \cos 90^{\circ} \\
<br/>\mathbf{r}_{1} \cdot \mathbf{r}_{2}=0
<br/>\end{array}
<br/>$$
<br/>Substituting the values $\mathbf{r}_{1}$ and $\mathbf{r}_{2}$ in the above relation, we get
<br/>$$
<br/>\left((v t) \hat{\mathbf{i}}-\frac{1}{2} g t^{2} \mathbf{j}\right) \cdot\left(v t(-\hat{\mathbf{i}})-\frac{1}{2} g t^{2}(\mathbf{j})\right)=0
<br/>$$
<br/>$-v^{2} t^{2}+\frac{1}{4} 4 g^{2} t^{4}=0($ where, $\hat{\mathbf{i}} \cdot \hat{\mathbf{i}}=\hat{\mathbf{j}} \cdot \hat{\mathbf{j}}=\mathbf{k} \cdot \mathbf{k}=1)$
<br/>$$
<br/>\begin{aligned}
<br/>v^{2} t^{2} &=\frac{1}{4} g^{2} t^{4} \\
<br/>\Rightarrow \quad v^{2} &=\frac{1}{4} g^{2} t^{2}
<br/>\end{aligned}
<br/>$$
<br/>$\therefore$ Magnitude of velocity of the particles, $v=\frac{1}{2} g t$
<br/>We know that, separation distance between particles at a time $t$
<br/>$$
<br/>\begin{array}{c}
<br/>\Delta x=2 v t \\
<br/>\Delta x=2 \times v \times \frac{2 v}{g} \Rightarrow \dot{\Delta} x=\frac{4 v^{2}}{g}
<br/>\end{array}
<br/>$$</div> | db\MarksBatch2_P3.db |
2,432 | two-particles-have-masses-m-4-m-and-their-kinetic-energies-are-in-the-ratio-2-1-what-is-the-ratio-of-their-linear-momenta | two-particles-have-masses-m-4-m-and-their-kinetic-energies-are-in-the-ratio-2-1-what-is-the-ratio-of-their-linear-momenta-90477 | <div class="question">Two particles have masses $\mathrm{m} \& 4 \mathrm{~m}$ and their kinetic energies are in the ratio $2: 1$. What is the ratio of their linear momenta?</div> | ['Physics', 'Center of Mass Momentum and Collision', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\sqrt{2}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{16}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{2}}$</span> </div> | <div class="solution">$\frac{K E_1}{K E_2}=\frac{\frac{p_1^2}{2 m}}{\frac{p_2^2}{2 \times 4 m}}=\frac{2}{1} \Rightarrow \frac{p_1}{p_2}=\frac{1}{\sqrt{2}}$</div> | db\MarksBatch2_P3.db |
2,433 | two-particles-move-in-the-same-straight-line-starting-at-the-same-moment-from-the-same-point-in-the-same-direction-the-first-moves-with-constant-veloc | two-particles-move-in-the-same-straight-line-starting-at-the-same-moment-from-the-same-point-in-the-same-direction-the-first-moves-with-constant-veloc-29722 | <div class="question">Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity $u$ and the second starts from rest with constant acceleration $f$. Then,</div> | ['Mathematics', 'Application of Derivatives', 'WBJEE', 'WBJEE 2017'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">they will be at the greatest distance at the end of time $\frac{u}{2 f}$ from the start</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">they will be at the greatest distance at the end of time $\frac{u}{f}$ from the start</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">their greatest distance is $\frac{u^{2}}{2 f}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">their greatest distance is $\frac{u^{2}}{f}$</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">they will be at the greatest distance at the end of time $\frac{u}{f}$ from the start, their greatest distance is $\frac{u^{2}}{2 f}$</span> </div> | <div class="solution">We know, $S=u t+\frac{1}{2} a t^{2}$
<br/>Condition for first, As, velocity is constant $u=u, v=u$ (constant)
<br/>$\therefore \quad a=0, s=u t \ldots(i)$
<br/>[from Eq. (i) Condition for second $u=0, a=f$ (constant)
<br/>$\therefore$
<br/>$$
<br/>s=\frac{1}{2}a t^{2}
<br/>$$
<br/>$s=\frac{1}{2} f t^{2}$
<br/>(ui) [from Eq. (i))
<br/>On differentiating Eqs. (ii) and (iui), we get $\frac{d S}{d t}=u$
<br/>and $\frac{d S}{d t}=\frac{1}{2} f(2t)$
<br/>$\frac{d S}{d t}=f t$
<br/>$u=f t$
<br/>[from Eq.
<br/>$t=\frac{u}{f}$
<br/>Thus, they will be at the greatest distance at the end of the $\frac{u}{f}$ from the start. For greatest distance
<br/>$$
<br/>S=\frac{1}{2} f t^{2}
<br/>$$
<br/>Put $\quad t=\frac{u}{f}$
<br/>$$
<br/>\begin{array}{l}
<br/>S=\frac{1}{2} f\left(\frac{u^{2}}{f^{2}}\right) \\
<br/>S=\frac{u^{2}}{2 f}
<br/>\end{array}
<br/>$$
<br/>Hence, option (b) and (c) are correct.</div> | db\MarksBatch2_P3.db |
2,434 | two-particles-of-mass-m-1-and-m-2-approach-each-other-due-to-their-mutual-gravitational-attraction-only-then | two-particles-of-mass-m-1-and-m-2-approach-each-other-due-to-their-mutual-gravitational-attraction-only-then-52080 | <div class="question">Two particles of mass $m_{1}$ and $m_{2}$; approach each other due to their mutual gravitational attraction only. Then,</div> | ['Physics', 'Gravitation', 'WBJEE', 'WBJEE 2015'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">accelerations of both the particles are equal</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is proportional to $\overline{m_{1}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is proportional to $m_{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">acceleration of the particle of mass $m_{1}$ is inversely proportional to $m_{1}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">acceleration of the particle of mass $m_{1}$ is proportional to $m_{2}$</span> </div> | <div class="solution">The gravitational force acting between the two masses $m_{1}$ and $m_{2}$ is given by
<br/>$$
<br/>F_{O}=\frac{G m_{1} m_{2}}{r^{2}}
<br/>$$
<br/>Force on mass $m_{1}$.
<br/>$$
<br/>F_{1}=\frac{G m_{1} m_{2}}{r^{2}}=m_{1} a_{1}
<br/>$$
<br/>where, $a_{1}=$ acceleration
<br/>$$
<br/>\Rightarrow \quad a_{1}=\frac{G m_{2}}{I^{2}} \Rightarrow a_{1} \propto m_{2}
<br/>$$
<br/>and similarly, $a_{2} \propto m_{1}$</div> | db\MarksBatch2_P3.db |
2,435 | two-pith-balls-each-carrying-charge-q-are-hung-from-a-hook-by-two-strings-it-is-found-that-when-each-charge-is-tripled-angle-between-the-strings-doubl | two-pith-balls-each-carrying-charge-q-are-hung-from-a-hook-by-two-strings-it-is-found-that-when-each-charge-is-tripled-angle-between-the-strings-doubl-25972 | <div class="question">Two pith balls, each carrying charge $+q$ are hung from a hook by two strings. It is found that when each charge is tripled, angle between the strings double. What was the initial angle between the strings?</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2020'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$90^{\circ}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$60^{\circ}$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/l560Wm-h7Kt0Prm-zYokeSVJA651QftOYIjBJYHaxnc.original.fullsize.png"/><br/> <br/>Hint:
<br/>$\mathrm{T} \sin \theta=\mathrm{Fe}, \mathrm{T} \cos \theta=\mathrm{mg}$
<br/>$\tan \theta=\frac{\mathrm{Fe}}{\mathrm{mg}}=\frac{\mathrm{k} \cdot \mathrm{q}^{2}}{(2 \mathrm{~L} \sin \theta)^{2} \mathrm{mg}}$
<br/>In 2 nd case
<br/>$\begin{array}{l}
<br/>\tan 2 \theta=\frac{\mathrm{kq} \mathrm{q}^{2}}{(2 \mathrm{~L} \sin 2 \theta)^{2} \cdot \mathrm{mg}} \\
<br/>\frac{\tan 2 \theta}{\tan \theta}=\frac{9 \sin ^{2} \theta}{\sin ^{2} 2 \theta} \\
<br/>\frac{2}{1-\tan ^{2} \theta}=\frac{9}{4 \cos ^{2} \theta}=\frac{9}{4} \sec ^{2} \theta \\
<br/>\frac{2}{1-\tan ^{2} \theta}=\frac{9}{4}\left(1-\tan ^{2} \theta\right)
<br/>\end{array}$
<br/>$\tan ^{2} \theta=x, \frac{2}{1-x}=\frac{9}{4}(1+x)$
<br/>$\Rightarrow 8=9-9 x^{2} \Rightarrow x=\frac{1}{3} \Rightarrow \tan ^{2} \theta=\frac{1}{3} \Rightarrow \theta=30^{\circ}$
<br/>Angle between the strings $=2 \theta=60^{\circ}$</div> | db\MarksBatch2_P3.db |
2,436 | two-point-charges-q-1-and-q-2-are-placed-a-finite-distance-d-apart-it-is-desired-to-put-a-third-charge-q-3-in-between-these-two-charges-so-that-q-3-is | two-point-charges-q-1-and-q-2-are-placed-a-finite-distance-d-apart-it-is-desired-to-put-a-third-charge-q-3-in-between-these-two-charges-so-that-q-3-is-83193 | <div class="question">Two point charges $+\mathrm{q}_{1}$ and $+\mathrm{q}_{2}$ are placed a finite distance ' $\mathrm{d}$ ' apart. It is desired to put a third charge $\mathrm{q}_{3}$ in between these two charges so that $\mathrm{q}_{3}$ is in equilibrium. This is</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">possible only if $q_{3}$ is negative.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">possible only if $\mathrm{q}_{3}$ is positive.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">possible irrespective of the sign of $q_{3}$.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">not possible at all.</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">possible irrespective of the sign of $q_{3}$.</span> </div> | <div class="solution">At null point $\vec{E}=0$
<br/>$\therefore$ any charge placed at that point will remain in equilibrium.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2oTpscfeg0AneUAMcb35wvwaAuuZSW0yTmh1G50wME8.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,437 | two-positive-charges-q-and-4-q-are-placed-at-points-a-and-b-respectively-where-b-is-at-a-distance-d-units-to-the-right-of-a-the-total-electric-potenti | two-positive-charges-q-and-4-q-are-placed-at-points-a-and-b-respectively-where-b-is-at-a-distance-d-units-to-the-right-of-a-the-total-electric-potenti-62878 | <div class="question">Two positive charges $Q$ and $4 Q$ are placed at points $A$ and $B$ respectively, where $B$ is at a distance $d$ units to the right of $A$. The total electric potential due to these charges is minimum at $P$ on the line through $A$ and $B$. What is (are) the distance (s) of $P$ from $A ?$</div> | ['Physics', 'Electrostatics', 'WBJEE', 'WBJEE 2018'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{d}{3}$ units to the right of $A$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{d}{3}$ units to the left of $A$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{d}{5}$ units to the right of $A$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$d$ units to the left of $A$</span> </li> </ul> | <div class="correct-answer">
The correct answers are:
<span class="option-value">$\frac{d}{3}$ units to the right of $A$</span> </div> | <div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2018_phy_a40.png"/> <br/> <br/>$\because V_{P}$ is minimum. $\therefore$
<br/>$E_{p}=0 \Rightarrow E_{A}=E_{B}$
<br/>$\Rightarrow \quad \frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{Q}{r^{2}}=\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{4 Q}{(d-r)^{2}}$
<br/>$\Rightarrow \quad \frac{1}{r}=\frac{2}{d-r} \Rightarrow d-r=2 r$
<br/>$\therefore$ Distance of $P$ from the $A r=\frac{d}{3}$ units to the right of $A .$</div> | db\MarksBatch2_P3.db |
2,438 | two-radionctive-substances-a-and-b-have-decay-constants-5-and-respectively-at-t-0-they-have-the-same-number-of-nuclei-the-ratio-of-number-of-nuclei-of | two-radionctive-substances-a-and-b-have-decay-constants-5-and-respectively-at-t-0-they-have-the-same-number-of-nuclei-the-ratio-of-number-of-nuclei-of-91230 | <div class="question">Two radionctive substances $A$ and $B$ have decay constants $5 \lambda$ and $\lambda$ respectively. At $t=0,$ they have the same number of nuclei. The ratio of number of nuclei of $A$ to that of $B$ will be $(1 / e)^{2}$
<br/>after a time interval of</div> | ['Physics', 'Nuclear Physics', 'WBJEE', 'WBJEE 2012'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{\lambda}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{1}{2 \lambda}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{3 \lambda}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{4 \lambda}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2 \lambda}$</span> </div> | <div class="solution">We know that<br/>$N=N_{0} e^{-\lambda t}$<br/>For $A$,<br/>$N_{A}=N_{0} e^{-5 \lambda_{L}}$<br/>For $B$,<br/>$N_{B}=N_{0} e^{-\lambda t}$<br/>Given,<br/>$\begin{aligned}<br/>\frac{N_{A}}{N_{B}} &=\frac{1}{e^{2}} \\<br/>\frac{N}{N_{B}} &=\frac{1}{e^{4 \lambda t}} \\<br/>t &=\frac{1}{2 \lambda}<br/>\end{aligned}$</div> | db\MarksBatch2_P3.db |
2,439 | two-rods-of-equal-length-and-diameter-have-thermal-conductivities-3-and-4-units-respectively-if-they-are-joined-in-series-the-thermal-conductivity-of- | two-rods-of-equal-length-and-diameter-have-thermal-conductivities-3-and-4-units-respectively-if-they-are-joined-in-series-the-thermal-conductivity-of-35041 | <div class="question">Two rods of equal length and diameter have thermal conductivities 3 and 4 units respectively. If they are joined in series, the thermal conductivity of the combination would be</div> | ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$3.43$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3.34$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$3.43$</span> </div> | <div class="solution">In series $R=R_1+R_2$<br/>$\begin{aligned} & \frac{2 \ell}{K_{e f f} A}=\frac{\ell}{K_1 A}+\frac{\ell}{K_2 A} \\ & K_{e f f}=\frac{24}{7}=3.43\end{aligned}$</div> | db\MarksBatch2_P3.db |
2,440 | two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the--1 | two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the-1-36209 | <div class="question">Two simple harmonic motions are given by $x_{1}=a \sin \omega t+a \cos \omega t$ and $x_{2}=a \sin \omega t+\frac{a}{\sqrt{3}} \cos \omega t$ The ratio of the amplitudes of first and second motion and the phase difference between them are respectively</div> | ['Physics', 'Oscillations', 'JEE Main'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{\sqrt{3}}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{6}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> </div> | <div class="solution">The given situation can be shown as <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a51.png"/> <br/> <br/>Fon second SHM
<br/>Ratio of amplitude $=\frac{a_{1}}{a_{2}}=\frac{\sqrt{3}}{\sqrt{2}}$
<br/>and phase difference, $\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}$</div> | db\MarksBatch2_P3.db |
2,441 | two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the- | two-simple-harmonic-motions-are-given-by-x-1-a-sin-t-a-cos-t-and-x-2-a-sin-t-3-a-cos-t-the-ratio-of-the-amplitudes-of-first-and-second-motion-and-the-32357 | <div class="question">Two simple harmonic motions are given by $x_{1}=a \sin \omega t+a \cos \omega t$ and $x_{2}=a \sin \omega t+\frac{a}{\sqrt{3}} \cos \omega t$ The ratio of the amplitudes of first and second motion and the phase difference between them are respectively</div> | ['Physics', 'Oscillations', 'WBJEE', 'WBJEE 2013'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2}{\sqrt{3}}$ and $\frac{\pi}{12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{6}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$\sqrt{\frac{3}{2}}$ and $\frac{\pi}{12}$</span> </div> | <div class="solution">The given situation can be shown as <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_a51.png"/> <br/> <br/>Fon second SHM
<br/>Ratio of amplitude $=\frac{a_{1}}{a_{2}}=\frac{\sqrt{3}}{\sqrt{2}}$
<br/>and phase difference, $\frac{\pi}{4}-\frac{\pi}{6}=\frac{\pi}{12}$</div> | db\MarksBatch2_P3.db |
2,442 | two-soap-bubbles-of-radii-mathrmx-and-mathrmy-coalesee-to-constitute-a-bubble-of-radius-mathrmz-then-mathrmz-is-requal-to | two-soap-bubbles-of-radii-mathrmx-and-mathrmy-coalesee-to-constitute-a-bubble-of-radius-mathrmz-then-mathrmz-is-requal-to-99143 | <div class="question">Two soap bubbles of radii \(\mathrm{x}\) and \(\mathrm{y}\) coalesee to constitute a bubble of radius \(\mathrm{z}\). Then \(\mathrm{z}\) is requal to</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(\sqrt{x^2+y^2}\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(\sqrt{x+y}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(x+y\)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\frac{x+y}{2}\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(\sqrt{x^2+y^2}\)</span> </div> | <div class="solution">Hints: \(\mathrm{n}=\mathrm{n}_1+\mathrm{n}_2\)<br/>\(\mathrm{pv}=\mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2\)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/XMbF46P1_4rauZD99MrGtCywrlzAbXwRbTsy7Nfaq8g.original.fullsize.png"/><br/><br/>\(\mathrm{p}_1=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\mathrm{p}_0+\frac{4 \mathrm{~T}}{\mathrm{z}}\)<br/>If the process takes place is vaccume then \(\mathrm{p}_0=0\)<br/>\(\mathrm{p}_1=\frac{4 \mathrm{~T}}{\mathrm{x}}, \mathrm{p}_2=\frac{4 \mathrm{~T}}{\mathrm{y}}, \mathrm{p}=\frac{4 \mathrm{~T}}{\mathrm{z}}\)<br/>If process is isothermal<br/>\(\begin{aligned}<br/>& \therefore \mathrm{p}_1 \mathrm{v}_1+\mathrm{p}_2 \mathrm{v}_2=\mathrm{pv} \\<br/>& \therefore \mathrm{z}=\sqrt{\mathrm{x}^2+\mathrm{y}^2}<br/>\end{aligned}\)</div> | db\MarksBatch2_P3.db |
2,443 | two-soap-bubbles-of-radii-r-and-2-r-are-arrangement-shown-in-the-diagram-the-valve-is-now-opened-then-which-one-of-the-following-will-result | two-soap-bubbles-of-radii-r-and-2-r-are-arrangement-shown-in-the-diagram-the-valve-is-now-opened-then-which-one-of-the-following-will-result-98920 | <div class="question">Two soap bubbles of radii $r$ and $2 r$ are arrangement shown in the diagram. The valve is now opened. Then which one of the following will result.
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/2013_phy_q5_.png"/></div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2013'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The radii of the bubbles will remain unchanged</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The bubbles will have equal radii</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The radius of the smaller bubble will decrease and that of the bigger bubble will decrease</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The radius of the smaller bubble will decrease and that of the bigger bubble will increase</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">The radius of the smaller bubble will decrease and that of the bigger bubble will increase</span> </div> | <div class="solution">Pressure difference $=\frac{4 T}{r}$
<br/>For smaller soap. $\mathrm{p_{atm}}-\mathrm{p}_{i1}=\frac{4 \mathrm{T}}{\mathrm{r}}$
<br/>For bigger soap, $\mathrm{p_{atm}}-\mathrm{p}_{i2}=\frac{4 \mathrm{T}}{2 \mathrm{r}}$
<br/>As the pressure inside smaller bubble is greater than pressure inside bigger bubble, so ar fown from smaller to bigger and thu's radius of the smaller bubble will decrease and that of the bigger bubble will increase.</div> | db\MarksBatch2_P3.db |
2,444 | two-solid-spheres-of-same-metal-but-of-mass-m-and-8-m-fall-simultaneously-on-a-viscous-liquid-and-their-terminal-velocities-are-v-and-n-v-then-value-o | two-solid-spheres-of-same-metal-but-of-mass-m-and-8-m-fall-simultaneously-on-a-viscous-liquid-and-their-terminal-velocities-are-v-and-n-v-then-value-o-78040 | <div class="question">Two solid spheres of same metal but of mass $\mathrm{M}$ and $8 \mathrm{M}$ fall simultaneously on a viscous liquid and their terminal velocities are $v$ and $n v$ then value of $n$ is</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2010'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">16</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">4</span> </div> | <div class="solution">$$<br/>\begin{aligned}<br/>& \text { Hints: } m=\frac{4}{3} \pi r^3 \times \rho \\<br/>& m \propto r^3 \\<br/>& \left(\frac{r_1}{r_2}\right)^3=\frac{1}{8} \\<br/>& \frac{r_1}{r_2}=\frac{1}{2} \\<br/>& 6 \pi n r \mathrm{~V}=\frac{4}{3} \pi r^3(d=\rho) \\<br/>& \mathrm{V} \propto r^2, \frac{\mathrm{V}_1}{\mathrm{~V}_2}=\frac{1}{4} \\<br/>& n=4<br/>\end{aligned}<br/>$$</div> | db\MarksBatch2_P3.db |
2,445 | two-solid-spheres-s-1-and-s-2-of-same-uniform-density-fall-from-rest-under-gravity-in-a-viscous-medium-and-after-some-time-reach-terminal-velocities-v | two-solid-spheres-s-1-and-s-2-of-same-uniform-density-fall-from-rest-under-gravity-in-a-viscous-medium-and-after-some-time-reach-terminal-velocities-v-96819 | <div class="question">Two solid spheres $S_{1}$ and $S_{2}$ of same uniform density fall from rest under gravity in a viscous medium and after some time, reach terminal velocities $v_{1}$ and $v_{2}$ respectively. If ratio of masses $\frac{m_{1}}{m_{2}}=8$, then $\frac{v_{1}}{v_{2}}$ will be equal to</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{1}{4}$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">4</span> </div> | <div class="solution">$\mathrm{v}=\frac{2 \mathrm{r}^{2}}{9 \mathrm{n}}(\mathrm{d}-\rho) \mathrm{y}$
<br/>$\mathrm{m}=\frac{4}{3} \pi \mathrm{r}^{3} \cdot \mathrm{d}$
<br/>$\mathrm{r} \propto \mathrm{m}^{1 / 3}$
<br/>$\Rightarrow \mathrm{v}_{\mathrm{T}} \propto \mathrm{r}^{2} \propto \mathrm{m}^{2 / 3}$
<br/>$\therefore \frac{\mathrm{v}_{1}}{\mathrm{v}_{2}}=\left[\frac{\mathrm{m}_{1}}{\mathrm{~m}_{2}}\right]^{2 / 3}=(8)^{2 / 3}=4$</div> | db\MarksBatch2_P3.db |
2,446 | two-spheres-of-equal-masses-but-radii-r-1-and-r-2-are-allowed-to-fall-in-a-liquid-of-infinite-column-the-ratio-of-their-terminal-velocities-is | two-spheres-of-equal-masses-but-radii-r-1-and-r-2-are-allowed-to-fall-in-a-liquid-of-infinite-column-the-ratio-of-their-terminal-velocities-is-85075 | <div class="question">Two spheres of equal masses but radii $r_1$ and $r_2$ are allowed to fall in a liquid of infinite column. The ratio of their terminal velocities is</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2009'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$r_1: r_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{r}_2: \mathrm{r}_1$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">None of the above</span> </div> | <div class="solution">We have $\mathrm{v}_{\mathrm{T}}=\frac{2 r^2(\sigma-\rho) g}{9 \eta}$<br/>$\frac{\mathrm{v}_1}{\mathrm{v}_2}=\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^2 \frac{\left(\sigma_1-\rho\right)}{\left(\sigma_2-\rho\right)} ;$ given $\mathrm{m}_1=\mathrm{m}_2 \Rightarrow\left(\frac{\mathrm{r}_1}{\mathrm{r}_2}\right)^3=\frac{\sigma_2}{\sigma_1}$</div> | db\MarksBatch2_P3.db |
2,447 | two-spheres-of-the-same-material-but-of-radii-r-and-3-r-are-allowed-to-fall-vertically-downwards-through-a-liquid-of-density-the-ratio-of-their-termin | two-spheres-of-the-same-material-but-of-radii-r-and-3-r-are-allowed-to-fall-vertically-downwards-through-a-liquid-of-density-the-ratio-of-their-termin-23075 | <div class="question">Two spheres of the same material, but of radii $R$ and $3 R$ are allowed to fall vertically downwards through a liquid of density $\rho$. The ratio of their terminal velocities is</div> | ['Physics', 'Mechanical Properties of Fluids', 'WBJEE', 'WBJEE 2013'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1: 3$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1: 6$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1: 9$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1: 1$</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$1: 9$</span> </div> | <div class="solution">The terminal velocity, $v=\frac{2 r^{2}(p-\sigma) g}{9 \eta}$
<br/>As, all other parameters are constant, therefore $v\propto r^{2}$
<br/>$\Rightarrow \quad \frac{v_{R}}{v_{3 R}}=\frac{(R)^{2}}{(3 R)^{2}}=\frac{1}{9}$</div> | db\MarksBatch2_P3.db |
2,448 | two-substance-a-and-b-of-same-mass-are-heated-at-constant-rate-the-variation-of-temperature-theta-of-the-substance-with-time-mathrmt-is-shown-in-the-f | two-substance-a-and-b-of-same-mass-are-heated-at-constant-rate-the-variation-of-temperature-theta-of-the-substance-with-time-mathrmt-is-shown-in-the-f-96662 | <div class="question">Two substance \(A\) and \(B\) of same mass are heated at constant rate. The variation of temperature \(\theta\) of the substance with time \(\mathrm{t}\) is shown in the figure. Choose the correct statement<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/ccSauqwXcVu54I_HPIJe0EFmTcK443auWof6hyxKVuY.original.fullsize.png"/><br/></div> | ['Physics', 'Thermodynamics', 'WBJEE', 'WBJEE 2023'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Specific heat of \(A\) is greater than that of \(B\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Specific heat of \(B\) is greater than that of \(A\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Both have same specific heat</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above is true</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">Specific heat of \(A\) is greater than that of \(B\)</span> </div> | <div class="solution">Hint : <img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/4Hast7wAh7ENs-5mGJRApF0kx-JDYx7YVfcfRFmtIuU.original.fullsize.png"/><br/><br/>\(\begin{aligned} & \Delta \mathrm{H}=\mathrm{mC} \Delta \theta \\ & \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{mC} \frac{\mathrm{d} \theta}{\mathrm{dt}} \quad \frac{\mathrm{dH}}{\mathrm{dt}}=\mathrm{a} \text { constant } \\ & \therefore \frac{d \theta}{d t} \propto \frac{1}{C} \\ & \text { i.e. slope } \propto \frac{1}{C} \quad \therefore C_B < C_A \\ & \end{aligned}\)</div> | db\MarksBatch2_P3.db |
2,449 | two-tangents-to-the-circle-x-2-y-2-4-at-the-points-a-and-b-meet-at-m-4-0-the-area-of-the-quadrilateral-maob-where-o-is-the-origin-is | two-tangents-to-the-circle-x-2-y-2-4-at-the-points-a-and-b-meet-at-m-4-0-the-area-of-the-quadrilateral-maob-where-o-is-the-origin-is-22806 | <div class="question">Two tangents to the circle $x^{2}+y^{2}=4$ at the points $A$ and $B$ meet at $M(-4,0)$. The area of the quadrilateral MAOB, where $O$ is the origin is</div> | ['Mathematics', 'Straight Lines', 'WBJEE', 'WBJEE 2021'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4 \sqrt{3}$ sq. units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{3}$ sq. units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{3}$ sq. units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 \sqrt{3}$ sq. units</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \sqrt{3}$ sq. units</span> </div> | <div class="solution">$\begin{aligned} & O M=4, O A=2 \\ \therefore & M A=\sqrt{16-4}=\sqrt{12}=2 \sqrt{3} \\ \therefore & \text { Area }(M A O B) \\=& 2 \times \text { area } \Delta M A O \\=& 2 \times \frac{1}{2} \times M A \times O A \\=& 2 \sqrt{3} \times 2=4 \sqrt{3} \text { sq. units } \end{aligned}$
<br/><img src="https://cdn-question-pool.getmarks.app/pyq/wbjee/mHbngJDPQA34-M3ZfLeYOZk_FSwYLa44yNd4f-ZX-do.original.fullsize.png"/></div> | db\MarksBatch2_P3.db |
2,450 | two-temperature-scales-mathrma-and-mathrmb-are-related-by-fracmathrma42110fracmathrmb72220-at-which-temperature-two-scales-have-the-same-reading | two-temperature-scales-mathrma-and-mathrmb-are-related-by-fracmathrma42110fracmathrmb72220-at-which-temperature-two-scales-have-the-same-reading-50035 | <div class="question">Two temperature scales \(\mathrm{A}\) and \(\mathrm{B}\) are related by \(\frac{\mathrm{A}-42}{110}=\frac{\mathrm{B}-72}{220}\). At which temperature two scales have the same reading ?</div> | ['Physics', 'Thermal Properties of Matter', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(-42^0\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(-72^0\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(+12^0\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(-40^{\circ}\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">\(+12^0\)</span> </div> | <div class="solution">Hints: \(\frac{\mathrm{A}-42}{110}=\frac{\mathrm{B}-72}{220}, \mathrm{~A}=\mathrm{B}\)<br/>\(\frac{A-42}{110}=\frac{A-72}{220}\)<br/>\(\begin{aligned}<br/>& 2 \mathrm{A}-84=\mathrm{A}-72 \\<br/>& \mathrm{~A}=12<br/>\end{aligned}\)</div> | db\MarksBatch2_P3.db |
2,451 | two-thin-lenses-of-focal-lengths-20-mathrmcm-and-25-mathrmcm-are-placed-in-cotact-the-effective-power-of-the-combination-is | two-thin-lenses-of-focal-lengths-20-mathrmcm-and-25-mathrmcm-are-placed-in-cotact-the-effective-power-of-the-combination-is-81337 | <div class="question">Two thin lenses of focal lengths \(20 \mathrm{~cm}\) and \(25 \mathrm{~cm}\) are placed in cotact. The effective power of the combination is</div> | ['Physics', 'Ray Optics', 'WBJEE', 'WBJEE 2011'] | <ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">9D</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(2 \mathrm{D}\)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3D</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(\mathrm{TD}\)</span> </li> </ul> | <div class="correct-answer">
The correct answer is:
<span class="option-value">9D</span> </div> | <div class="solution">Hints: \(P=P_1+P_2\)<br/>\(=\frac{1}{f_1}+\frac{1}{f_2}=\frac{100}{20}+\frac{100}{25}=5+4=9 D\)</div> | db\MarksBatch2_P3.db |