# questions

tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-phydroxybenzoic-acid-has-a-lower-boiling-point-than-ohydroxybenzoic-acid-statement-ii-ohydroxybenzoic-acid-has-intramolecular-hydrogen-bon

slug:
statement-i-phydroxybenzoic-acid-has-a-lower-boiling-point-than-ohydroxybenzoic-acid-statement-ii-ohydroxybenzoic-acid-has-intramolecular-hydrogen-bon-33667

question:
<div class="question">Statement I p-hydroxybenzoic acid has a lower boiling point than o-hydroxybenzoic acid.<br/>Statement II o-hydroxybenzoic acid has intramolecular hydrogen bonding.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true, Statement II is not a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</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>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/MOtOUfxobjJjqb-CQckuxAPH5FCfWdzfvPVBLkeL73U.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Parabola', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-the-curve-y-2-x-2-x-1-is-symmetric-with-respect-to-the-line-x-1-statement-ii-a-parabola-is-symmetric-about-its-axis

slug:
statement-i-the-curve-y-2-x-2-x-1-is-symmetric-with-respect-to-the-line-x-1-statement-ii-a-parabola-is-symmetric-about-its-axis-99329

question:
<div class="question">Statement I The curve $y=-\frac{x^2}{2}+x+1$ is symmetric with respect to the line $x=1$<br/>Statement II A parabola is symmetric about its axis.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></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"><br/>Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{array}{rlrl}<br/>y &amp; =-\frac{x^2}{2}+x+1 \\<br/>\Rightarrow &amp; y-\frac{3}{2} &amp; =-\frac{1}{2}(x-1)^2<br/>\end{array}<br/>$$<br/>It is symmetric about $x=1$.</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-the-formula-connecting-u-v-and-f-for-a-spherical-mirror-is-valid-only-for-mirrors-whose-sizes-are-very-small-compared-to-their-radii-of-cu

slug:
statement-i-the-formula-connecting-u-v-and-f-for-a-spherical-mirror-is-valid-only-for-mirrors-whose-sizes-are-very-small-compared-to-their-radii-of-cu-53681

question:
<div class="question">Statement I The formula connecting $u, v$ and $f$ for a spherical mirror is valid only for mirrors whose sizes are very small compared to their radii of curvature. <br/>Statement II Laws of reflection are strictly valid for plane surfaces, but not for large spherical surfaces.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></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"><br/>Statement I is false, Statement II is true</span> </li> </ul>

answer:
<div class="solution">Laws of reflection can be applied to any type of surface.<br/>$\therefore$ Correct option is (c).</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
statement-i-the-total-translational-kinetic-energy-of-all-the-molecules-of-a-given-mass-of-an-ideal-gas-is-15-times-the-product-of-its-pressure-and-it

slug:
statement-i-the-total-translational-kinetic-energy-of-all-the-molecules-of-a-given-mass-of-an-ideal-gas-is-15-times-the-product-of-its-pressure-and-it-91352

question:
<div class="question">Statement I The total translational kinetic energy of all the molecules of a given mass of an ideal gas is $1.5$ times the product of its pressure and its volume.<br/>Statement II The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is NOT a correct explanation for Statement I<br/></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"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

answer:
<div class="solution">Total translational kinetic energy $=\frac{3}{2} n R T=\frac{3}{2} P V=1.5 P \mathrm{~V}$<br/>$\therefore$ Correct option is (b).</div>


tags: ['Physics', 'Thermal Properties of Matter', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P2.db
title:
steel-wire-of-length-l-at-4-0-c-is-suspended-from-the-ceiling-and-then-a-mass-m-is-hung-from-its-free-end-the-wire-is-cooled-down-from-4-0-c-to-3-0-c-

slug:
steel-wire-of-length-l-at-4-0-c-is-suspended-from-the-ceiling-and-then-a-mass-m-is-hung-from-its-free-end-the-wire-is-cooled-down-from-4-0-c-to-3-0-c-51468

question:
<div class="question">Steel wire of length $L$ at $40^{\circ} \mathrm{C}$ is suspended from the ceiling and then a mass $m$ is hung from its free end. The wire is cooled down from $40^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ to regain its original length $L$. The coefficient of linear thermal expansion of the steel is $10^{-5} /{ }^{\circ} \mathrm{C}$, Young's modulus of steel is $10^{11} \mathrm{~N} / \mathrm{m}^2$ and radius of the wire is $1 \mathrm{~mm}$. Assume that $L&gt;$ diameter of the wire. Then, the value of $m$ in $\mathrm{kg}$ is nearly</div>

answer:
<div class="solution">$\Delta l_1=\frac{F L}{A Y}=\frac{m g L}{\pi r^2 Y}=$ Increase in length $\Delta l_2=L \alpha \Delta \theta=$ Decrease in length To regain its original length,<br/>$$<br/>\begin{aligned}<br/>&amp; \Delta l_1 &amp; =\Delta l_2 \\<br/>\therefore &amp; \frac{m g L}{\pi r^2 Y} &amp; =L \alpha \Delta \theta \\<br/>\therefore &amp; m &amp; =\left(\frac{r^2 Y \alpha \Delta \theta}{g}\right)<br/>\end{aligned}<br/>$$<br/>Substituting the values, we get<br/>$$<br/>m \simeq 3 \mathrm{~kg}<br/>$$<br/>$\therefore$ Answer is 3 .<br/>Analysis of Question<br/>Question is very simple. In my opinion any student who have gone through the syllabus once can solve this problem easily.</div>


tags: ['Physics', 'Experimental Physics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
students-i-ii-and-iii-perform-an-experiment-for-measuring-the-acceleration-due-to-gravity-g-using-a-simple-pendulum-they-use-different-lengths-of-the-

slug:
students-i-ii-and-iii-perform-an-experiment-for-measuring-the-acceleration-due-to-gravity-g-using-a-simple-pendulum-they-use-different-lengths-of-the-99274

question:
<div class="question">Students I, II and III perform an experiment for measuring the acceleration due to gravity $(g)$ using a simple pendulum. They use different lengths of the pendulum and/or record time for different number of oscillations. The observations are shown in the table.<br/>Least count for length $=0.1 \mathrm{~cm}$<br/>Least count for time $=0.1 \mathrm{~s}$<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vlvGSLty-Nbgt7ypLoTmhc8v_JV4M1IqFcYxvSHpk0I.original.fullsize.png"/><br/><br/><br/><br/>If $E_{\mathrm{I}}, E_{\mathrm{II}}$ and $E_{\mathrm{III}}$ are the percentage errors in $g$, i.e., $\left(\frac{\Delta g}{g} \times 100\right)$ for students I, II and III, respectively.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E_{\mathrm{I}}=0$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$E_{\mathrm{I}}$ is minimum<br/></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"><br/>$E_{\mathrm{I}}=E_{\mathrm{II}}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$E_{\mathrm{II}}$ is maximum</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_{\mathrm{I}}$ is minimum<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; T &amp; =2 \pi \sqrt{\frac{l}{g}} \quad \text { or } \quad \frac{t}{n}=2 \pi \sqrt{\frac{l}{g}} \\<br/>\therefore \quad &amp; g &amp; =\frac{\left(4 \pi^2\right)\left(n^2\right) l}{t^2}<br/>\end{aligned}<br/>$$<br/><br/>$\%$ error in $g=\frac{\Delta g}{g} \times 100=\left(\frac{\Delta l}{l}+\frac{2 \cdot \Delta t}{t}\right) \times 100$<br/>$$<br/>\begin{aligned}<br/>&amp; E_{\mathrm{I}}=\left(\frac{0.1}{64}+\frac{2 \times 0.1}{128}\right) \times 100=0.3125 \% \\<br/>&amp; E_{\mathrm{II}}=\left(\frac{0.1}{64}+\frac{2 \times 0.1}{64}\right) \times 100=0.46875 \% \quad E_{\mathrm{III}}=\left(\frac{0.1}{20}+\frac{2 \times 0.1}{36}\right) \times 100=1.055 \%<br/>\end{aligned}<br/>$$<br/>Hence, $E_{\mathrm{I}}$ is minimum.<br/>$\therefore$ correct option is (b).</div>


tags: ['Mathematics', 'Sequences and Series', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
suppose-four-distinct-positive-numbers-a-1-a-2-a-3-and-a-4-are-in-gp-let-b-1-a-1-b-2-b-1-a-2-b-3-b-2-a-3-and-b-4-b-3-a-4-statement-1-the-numbers-b-1-b

slug:
suppose-four-distinct-positive-numbers-a-1-a-2-a-3-and-a-4-are-in-gp-let-b-1-a-1-b-2-b-1-a-2-b-3-b-2-a-3-and-b-4-b-3-a-4-statement-1-the-numbers-b-1-b-84071

question:
<div class="question">Suppose four distinct positive numbers $a_1, a_2, a_3$ and $a_4$ are in GP. Let $b_1=a_1$, $b_2=b_1+a_2, b_3=b_2+a_3$ and $b_4=b_3+a_4$.<br/>Statement 1 The numbers $b_1, b_2, b_3$ and $b_4$ are neither in AP nor in GP.<br/>Statement 2 The numbers $b_1, b_2, b_3$ and $b_4$ are in HP.</div>

answer:
<div class="solution">Let $a_1=1, a_2=2, a_3=4, a_4=8$<br/>$$<br/>\therefore b_1=1, b_2=3, b_3=7, b_4=15<br/>$$<br/>Clearly, $b_1, b_2, b_3$ and $b_4$ are not in HP.<br/>Statement 2 is false.</div>


tags: ['Physics', 'Laws of Motion', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
system-shown-in-figure-is-in-equilibrium-and-at-rest-the-spring-and-string-are-massless-now-the-string-is-cut-the-acceleration-of-mass-2-m-and-m-just-

slug:
system-shown-in-figure-is-in-equilibrium-and-at-rest-the-spring-and-string-are-massless-now-the-string-is-cut-the-acceleration-of-mass-2-m-and-m-just-73421

question:
<div class="question">System shown in figure is in equilibrium and at rest. The spring and string are massless, now the string is cut. The acceleration of mass $2 m$ and $m$ just after the string is cut will be<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/F_gWz2vcxbWlp6GGjRBL5jHFqffW0hYXVd6i_8l9-YM.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$g / 2$ upwards, $g$ downwards<br/></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"><br/>$g$ upwards, $g / 2$ downwards<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$g$ upwards, $2 g$ downwards<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2 g$ upwards, $g$ downwards</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$g / 2$ upwards, $g$ downwards<br/></span> </div>

answer:
<div class="solution">Initially under equilibrium of mass ' $m$ '<br/>$$<br/>T=m g<br/>$$<br/>Now, the string is cut. Therefore, $T=m g$ force is decreased on mass $m$ upwards and downwards on mass $2 m$.<br/>$$<br/>a_m=\frac{m g}{m}=g \text { (downwards) and }<br/>$$<br/>$$<br/>a_{2 m}=\frac{m g}{2 m}=\frac{g}{2} \text { (upwards) }<br/>$$</div>


tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
tangent-is-drawn-at-any-point-p-of-a-curve-which-passes-through-1-1-cutting-x-axis-and-y-axis-at-a-and-b-respectively-if-a-p-bp-3-1-then

slug:
tangent-is-drawn-at-any-point-p-of-a-curve-which-passes-through-1-1-cutting-x-axis-and-y-axis-at-a-and-b-respectively-if-a-p-bp-3-1-then-23768

question:
<div class="question">Tangent is drawn at any point $P$ of a curve which passes through $(1,1)$ cutting $X$-axis and $Y$-axis at $A$ and $B$, respectively. If $A P: B P=3: 1$, then</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>differential equation of the curve is $3 x \frac{d y}{d x}+y=0$<br/></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"><br/>differential equation of the curve is $3 x \frac{d y}{d x}-y=0$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>curve is passing through $\left(\frac{1}{8}, 2\right)$<br/></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"><br/>normal at $(1,1)$ is $x+3 y=4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>differential equation of the curve is $3 x \frac{d y}{d x}+y=0$<br/>, <br/>curve is passing through $\left(\frac{1}{8}, 2\right)$<br/></span> </div>

answer:
<div class="solution">Since, $\quad A P: B P=3: 1$<br/>where, equation of tangent is $y-y_1=f^{\prime}(x)\left(x-x_1\right)$<br/>$$<br/>\begin{aligned}<br/>\therefore &amp; A\left(x_1-\frac{y_1}{f^{\prime}\left(x_1\right)}, 0\right) \text { and } B\left(0, y_1-x_1 f^{\prime}(x)\right) \\<br/>&amp; A P: B P=3: 1 \Rightarrow \frac{d y}{d x}=\frac{y}{-3 x} \\<br/>\therefore \quad &amp; 3 x \frac{d y}{d x}+y=0 \quad \text { or } \quad \frac{d y}{y}=-\frac{1}{3 x} d x,<br/>\end{aligned}<br/>$$<br/>On integrating both sides, we get<br/>$$<br/>\begin{array}{lrlr}<br/>\Rightarrow &amp; x y^3 &amp; =1 \\<br/>&amp; \therefore \text { At } &amp; x &amp; =\frac{1}{8} \quad \text { and } \quad y=2<br/>\end{array}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/dhtulUI2EIb1uiFaZHVNmaiQS7PbvVRaxjWm9Q8Gdlo.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
tangents-are-drawn-from-the-point-17-7-to-the-circle-x-2-y-2-169-statement-i-the-tangents-are-mutually-perpendicular-statement-ii-the-locus-of-the-poi

slug:
tangents-are-drawn-from-the-point-17-7-to-the-circle-x-2-y-2-169-statement-i-the-tangents-are-mutually-perpendicular-statement-ii-the-locus-of-the-poi-24284

question:
<div class="question">Tangents are drawn from the point $(17,7)$ to the circle $x^2+y^2=169$.<br/>Statement I The tangents are mutually perpendicular.<br/>Statement II The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2+y^2=338$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></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"><br/>Statement I is true, Statement II is true; Statement II is not a correct explanation for Statement I<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement I is true, Statement II is false<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Statement I is false, Statement II is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I<br/></span> </div>

answer:
<div class="solution">Since, the tangents are perpendicular.<br/>So, locus of perpendicular tangents to circle $x^2+y^2=169$ is a director circle having equation<br/>$$<br/>x^2+y^2=338 .<br/>$$</div>


tags: ['Mathematics', 'Hyperbola', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
tangents-are-drawn-to-the-hyperbola-9-x-2-4-y-2-1-parallel-to-the-straight-line-2-x-y-1-the-points-of-contact-of-the-tangents-on-the-hyperbola-are

slug:
tangents-are-drawn-to-the-hyperbola-9-x-2-4-y-2-1-parallel-to-the-straight-line-2-x-y-1-the-points-of-contact-of-the-tangents-on-the-hyperbola-are-53349

question:
<div class="question">Tangents are drawn to the hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$, parallel to the straight line $2 x-y=1$. The points of contact of the tangents on the hyperbola are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$</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="correct"> <span class="option-label">B</span> <span class="option-data">$\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$</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">C</span> <span class="option-data">$(3 \sqrt{3},-2 \sqrt{2})$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(-3 \sqrt{3}, 2 \sqrt{2})$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">$\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$, $\left(-\frac{9}{2 \sqrt{2}},-\frac{1}{\sqrt{2}}\right)$</span> </div>

answer:
<div class="solution">If slope of tangents to hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ is $m$,
<br/> <br/>then equations of tangent to the hyperbola is
<br/> <br/>$y=m x \pm \sqrt{a^{2} m^{2}-b^{2}} \quad$ with the points of contact
<br/> <br/>$\quad\left(\quad \pm a^{2} m\right.$
<br/> <br/>$\left.\frac{\pm \sqrt{a^{2} m^{2}-b^{2}}}{\sqrt{a^{2} m^{2}-b^{2}}}\right)$
<br/> <br/>$\therefore$ Tangent to hyperbola $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$ is parallel to $2 x-y=1$,
<br/> <br/>$\therefore$ Slope of tangent $=2$
<br/> <br/>$\therefore$ Points of contact are $\left(\frac{\pm 9 \times 2}{\sqrt{9 \times 4-4}}, \frac{\pm 4}{\sqrt{9 \times 4-4}}\right)$
<br/> <br/>i.e. $\left(\frac{9}{2 \sqrt{2}}, \frac{1}{\sqrt{2}}\right)$ and $\left(\frac{-9}{2 \sqrt{2}}, \frac{-1}{\sqrt{2}}\right)$</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
tangents-drawn-from-the-point-p-1-8-to-the-circle-x-2-y-2-6-x-4-y-11-0-touch-the-circle-at-the-points-a-and-b-the-equation-of-the-circumcircle-of-p-a-

slug:
tangents-drawn-from-the-point-p-1-8-to-the-circle-x-2-y-2-6-x-4-y-11-0-touch-the-circle-at-the-points-a-and-b-the-equation-of-the-circumcircle-of-p-a-35614

question:
<div class="question">Tangents drawn from the point $P(1,8)$ to the circle $x^2+y^2-6 x-4 y-11=0$ touch the circle at the points $A$ and $B$. The equation of the circumcircle of $\triangle P A B$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$x^2+y^2+4 x-6 y+19=0$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$x^2+y^2-4 x-10 y+19=0$<br/></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"><br/>$x^2+y^2-2 x+6 y-29=0$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$x^2+y^2-6 x-4 y+19=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$x^2+y^2-4 x-10 y+19=0$<br/></span> </div>

answer:
<div class="solution">For required circle, $P(1,8)$ and $O(3,2)$ will be the end point of its diameter.<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore(x-1)(x-3)+(y-8)(y-2)=0 \\<br/>&amp; \Rightarrow \quad x^2+y^2-4 x-10 y+19=0<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P2.db
title:
the-activity-of-a-freshly-prepared-radioactive-sample-is-1-0-10-disintegrations-per-second-whose-mean-life-is-1-0-9-s-the-mass-of-an-atom-of-this-radi

slug:
the-activity-of-a-freshly-prepared-radioactive-sample-is-1-0-10-disintegrations-per-second-whose-mean-life-is-1-0-9-s-the-mass-of-an-atom-of-this-radi-25226

question:
<div class="question">The activity of a freshly prepared radioactive sample is $10^{10}$ disintegrations per second, whose mean life is $10^{-9} \mathrm{~s}$. The mass of an atom of this radioisotope is $10^{-25} \mathrm{~kg}$. The mass (in $\mathrm{mg}$ ) of the radioactive sample is</div>

answer:
<div class="solution">Activity $\left(-\frac{d N}{d t}\right)=\lambda N=\left(\frac{1}{t_{\text {mean }}}\right) \times N$<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \quad N=\left(-\frac{d N}{d t}\right) \times t_{\text {mean }} \\<br/>&amp; \quad=\text { Total number of atoms } \\<br/>&amp; \text { Mass of one atom is } 10^{-25} \mathrm{~kg}=m \text { (say) } \\<br/>&amp; \therefore \quad \text { Total mass of radioactive substance } \\<br/>&amp; =(\text { number of atoms) } \\<br/>&amp; \quad \times(\text { mass of one atom) } \\<br/>&amp; =\left(-\frac{d N}{d t}\right)\left(t_{\text {mean }}\right)(m)<br/>\end{aligned}<br/>$$<br/>Substituting the values, we get<br/>Total mass of radioactive substance<br/>$$<br/>=1 \mathrm{mg}<br/>$$<br/>$\therefore$ Answer is 1 .<br/>Analysis of Question<br/>Question is very simple. Again in my opinion one can solve it.</div>


tags: ['Mathematics', 'Area Under Curves', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-area-of-the-region-between-the-curves-y-c-o-s-x-1-s-i-n-x-and-y-c-o-s-x-1-s-i-n-x-bounded-by-the-lines-x-0-and-x-4-is

slug:
the-area-of-the-region-between-the-curves-y-c-o-s-x-1-s-i-n-x-and-y-c-o-s-x-1-s-i-n-x-bounded-by-the-lines-x-0-and-x-4-is-29782

question:
<div class="question">The area of the region between the curves $y=\sqrt{\frac{1+\sin x}{\cos x}}$ and $y=\sqrt{\frac{1-\sin x}{\cos x}}$ bounded by the lines $x=0$ and $x=\frac{\pi}{4}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\int_0^{\sqrt{2}-1} \frac{t}{\left(1+t^2\right) \sqrt{1-t^2}} d t$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\int_0^{\sqrt{2}-1} \frac{4 t}{\left(1+t^2\right) \sqrt{1-t^2}} d t$<br/></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"><br/>$\int_0^{\sqrt{2}+1} \frac{4 t}{\left(1+t^2\right) \sqrt{1-t^2}} d t$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\int_0^{\sqrt{2}+1} \frac{t}{\left(1+t^2\right) \sqrt{1-t^2}} d t$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\int_0^{\sqrt{2}-1} \frac{4 t}{\left(1+t^2\right) \sqrt{1-t^2}} d t$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \text { Required area }=\int_0^{\pi / 4}\left(\sqrt{\frac{1+\sin x}{\cos x}}-\sqrt{\frac{1-\sin x}{\cos x}}\right) d x \quad\left[\because \frac{1+\sin x}{\cos x}&gt;\frac{1-\sin x}{\cos x}&gt;0\right] \\<br/>&amp; \left.=\int_0^{\pi / 4} \sqrt{\frac{1+\frac{2 \tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}}{\frac{1-\tan ^2 \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}}} \sqrt{\frac{1-\frac{2 \tan \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}}{\frac{1-\tan ^2 \frac{x}{2}}{1+\tan ^2 \frac{x}{2}}}}\right) d x \\<br/>&amp; \left.=\int_0^{\pi / 4} \sqrt{\frac{1+\tan \frac{x}{2}}{1-\tan \frac{x}{2}}}-\sqrt{\frac{1-\tan \frac{x}{2}}{1+\tan \frac{x}{2}}}\right) d x \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>=\int_0^{\pi / 4} \frac{1+\tan \frac{x}{2}-1+\tan \frac{x}{2}}{\sqrt{1-\tan ^2 \frac{x}{2}}} d x=\int_0^{\pi / 4} \frac{2 \tan \frac{x}{2}}{\sqrt{1-\tan ^2 \frac{x}{2}}} d x<br/>$$<br/>Put $\tan \frac{x}{2}=t$<br/>$$<br/>\begin{aligned}<br/>\Rightarrow \quad \frac{1}{2} \sec ^2 \frac{x}{2} d x &amp; =d t \\<br/>\therefore \text { Required area } &amp; =\int_0^{\tan \frac{\pi}{8}} \frac{4 t d t}{\left(1+t^2\right) \sqrt{1-t^2}} \\<br/>&amp; =\int_0^{\sqrt{2}-1} \frac{4 t}{\left(1+t^2\right) \sqrt{1-t^2}} d t \quad\left[\text { astan } \frac{\pi}{8}=\sqrt{2}-1\right]<br/>\end{aligned}<br/>$$</div>


title: the-bond-energy-in-kcal-mol-1-of-c-c-single-bond-is-approximately
slug: the-bond-energy-in-kcal-mol-1-of-c-c-single-bond-is-approximately-86764
source_db: MarksBatch2_P2.db
question:
<div class="question">The bond energy (in $\mathrm{kcal} \mathrm{mol}^{-1}$ ) of $\mathrm{C}-\mathrm{C}$ single bond is approximately</div>

tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>10<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>100<br/></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"><br/>1000</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>100<br/></span> </div>

answer:
<div class="solution">The bond energy of a $\mathrm{C}-\mathrm{C}$ single bond is approximately $100 \mathrm{kcal} \mathrm{mol}^{-1}$.<br/>Energetics<br/>Factual (usually it is not expected to be learnt)<br/>III</div>


title: the-carboxyl-functional-group-cooh-is-present-in-1
slug: the-carboxyl-functional-group-cooh-is-present-in-1-44416
question: <div class="question">The carboxyl functional group $(-\mathrm{COOH})$ is present in</div>
tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">picricacid</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">barbituric acid</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">ascorbic acid</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">aspirin</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">aspirin</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/k7WmyASwckIsJjDhjh_uSBzZYXTpaYekwJJYDtvj4NA.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Lx1913Cy53_MT4XdgRq0yhP74rb0KP77fzdxGMTr0eU.original.fullsize.png"/></div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P2.db
title:
the-centres-of-two-circles-c-1-and-c-2-each-of-unit-radius-are-at-a-distance-of-6-units-from-each-other-let-p-be-the-midpoint-of-the-line-segment-join-1

slug:
the-centres-of-two-circles-c-1-and-c-2-each-of-unit-radius-are-at-a-distance-of-6-units-from-each-other-let-p-be-the-midpoint-of-the-line-segment-join-1-83250

question:
<div class="question">The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other. Let $P$ be the mid-point of the line segment joining the centres of $C_1$ and $C_2$ and $C$ be a circle touching circles $C_1$ and $C_2$ externally. If a common tangents to $C_1$ and $C$ passing through $P$ is also a common tangent to $C_2$ and $C$, then the radius of the circle $C$ is</div>

answer:
<div class="solution">$(r+1)^2=\alpha^2+9$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P12uKGaiUhyU7Pkj_8wW1RmlxbN2wB15mKll54U7qWE.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{array}{lc}<br/>\Rightarrow &amp; r^2+8=\alpha^2 \\<br/>\Rightarrow &amp; r^2+2 r+1=r^2+8+9 \\<br/>\Rightarrow &amp; 2 r=16 \Rightarrow r=8<br/>\end{array}<br/>$$</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P2.db
title:
the-centres-of-two-circles-c-1-and-c-2-each-of-unit-radius-are-at-a-distance-of-6-units-from-each-other-let-p-be-the-midpoint-of-the-line-segment-join-2

slug:
the-centres-of-two-circles-c-1-and-c-2-each-of-unit-radius-are-at-a-distance-of-6-units-from-each-other-let-p-be-the-midpoint-of-the-line-segment-join-2-85432

question:
<div class="question">The centres of two circles $C_1$ and $C_2$ each of unit radius are at a distance of 6 units from each other. Let $P$ be the mid-point of the line segment joining the centres of $C_1$ and $C_2$ and $C$ be a circle touching circles $C_1$ and $C_2$ externally. If a common tangents to $C_1$ and $C$ passing through $P$ is also a common tangent to $C_2$ and $C$, then the radius of the circle $C$ is</div>

answer:
<div class="solution">$(r+1)^2=\alpha^2+9$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/P12uKGaiUhyU7Pkj_8wW1RmlxbN2wB15mKll54U7qWE.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{array}{lc}<br/>\Rightarrow &amp; r^2+8=\alpha^2 \\<br/>\Rightarrow &amp; r^2+2 r+1=r^2+8+9 \\<br/>\Rightarrow &amp; 2 r=16 \Rightarrow r=8<br/>\end{array}<br/>$$</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-circle-passing-through-the-point-1-0-and-touching-the-y-axis-at-0-2-also-passes-through-the-point

slug:
the-circle-passing-through-the-point-1-0-and-touching-the-y-axis-at-0-2-also-passes-through-the-point-57429

question:
<div class="question">The circle passing through the point $(-1,0)$ and touching the $Y$-axis at $(0,2)$, also passes through the point</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(-\frac{3}{2}, 0\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(-\frac{5}{2}, 2\right)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\left(-\frac{3}{2}, \frac{5}{2}\right)$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$(-1,-4)$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$(-1,-4)$</span> </div>

answer:
<div class="solution">Equation of circle passing through a point $\left(x_1, y_1\right)$ and touching the straight line $L$, is given by<br/>$$<br/>\left(x-x_1\right)^2+\left(y-y_1\right)^2=\lambda L=0<br/>$$<br/>$\therefore$ Equation of circle passing through $(0,2)$ and touching $x=0$.<br/>Now, $(x-0)^2+(y-2)^2+\lambda x=0 \ldots$ (i)<br/>Also, it passes through $(-1,0)$.<br/>So, $1+4-\lambda=0 \Rightarrow \lambda=5$<br/>Eq. (i) becomes,<br/>$$<br/>\begin{aligned}<br/>&amp; x^2+y^2-4 y+4+5 x=0 \\<br/>\Rightarrow \quad x^2+y^2+5 x-4 y+4 &amp; =0<br/>\end{aligned}<br/>$$<br/>For $x$-intercept, put $y=0$,<br/>$$<br/>\begin{array}{rlrl} <br/>&amp; x^2+5 x+4 &amp; =0 \\<br/>\Rightarrow &amp; &amp; (x+1)(x+4) &amp; =0 \\<br/>\therefore &amp; &amp; x &amp; =-1,-4<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Experimental Physics', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
the-circular-scale-of-a-screw-gauge-has-50-divisions-and-pitch-of-05-mm-find-the-diameter-of-sphere-main-scale-reading-is-2

slug:
the-circular-scale-of-a-screw-gauge-has-50-divisions-and-pitch-of-05-mm-find-the-diameter-of-sphere-main-scale-reading-is-2-51827

question:
<div class="question">The circular scale of a screw gauge has 50 divisions and pitch of $0.5 \mathrm{~mm}$. Find the diameter of sphere. Main scale reading is 2 .<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/VASXFazDcy_MWn37WFedHJCS7GriIFZHYPqEImRmNPU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$1.2$<br/></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"><br/>$1.25$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$2.20$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$2.25$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1.2$<br/></span> </div>

answer:
<div class="solution">Least count $\mathrm{LC}=\frac{\text { Pitch }}{\text { Number of divisions on circular scale }}=\frac{0.1}{50}$ $=0.01 \mathrm{~mm}$<br/>Now, diameter of ball $=(2 \times 0.5 \mathrm{~mm})+(25-5)(0.01)=1.2 \mathrm{~mm}$</div>


title: the-colour-of-light-absorbed-by-an-aqueous-solution-of-cuso-4-is
slug: the-colour-of-light-absorbed-by-an-aqueous-solution-of-cuso-4-is-22097
tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The colour of light absorbed by an aqueous solution of $\mathrm{CuSO}_{4}$ is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">orange-red</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">blue-green</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">yellow</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">violet</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">orange-red</span> </div>

answer:
<div class="solution">$\mathrm{CuSO}_{4}$ will be absorbing orange-red colour and hence will be of blue colour.</div>


title: the-complex-showing-a-spinonly-magnetic-moment-of-282-bm-is
slug: the-complex-showing-a-spinonly-magnetic-moment-of-282-bm-is-98641
question: <div class="question">The complex showing a spin-only magnetic moment of $2.82$ B.M. is</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Ni}(\mathrm{CO})_4$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{NiCl}_4\right]^{2-}$<br/></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"><br/>$\mathrm{Ni}\left(\mathrm{PPh}_3\right)_4$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left[\mathrm{NiCl}_4\right]^{2-}$<br/></span> </div>

answer:
<div class="solution">$\mathrm{Ni}: 3 d^8 4 s^2 \quad \mathrm{Ni}^{2+}: 3 d^8$<br/>Since, $\mathrm{Cl}$ is a weak field ligand, it doesn't cause pairing of electron.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NqBDIyIyxDmnzpl5LYWkzWtsQzfrj9ZlmzRlmwZq6lw.original.fullsize.png"/><br/><br/>Number of unpaired electrons, $n=2$<br/>$$<br/>\mu=\sqrt{n(n+2)}=\sqrt{2(2+2)} \mathrm{BM}=\sqrt{8} \mathrm{BM}=2.82 \mathrm{BM}<br/>$$<br/>Coordination compound<br/>Conceptual<br/>III</div>


title: the-compound-s-that-exhibit-s-geometrical-isomerism-is-are
slug: the-compound-s-that-exhibit-s-geometrical-isomerism-is-are-21134
question: <div class="question">The compound (s) that exhibit (s) geometrical isomerism is (are)</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left[\mathrm{Pt}(\mathrm{en}) \mathrm{Cl}_2\right]$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{Pt}(\mathrm{en})_2 \mathrm{Cl}_2\right]$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left[\mathrm{Pt}(\text { en })_2 \mathrm{Cl}_2\right] \mathrm{Cl}_2$<br/></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"><br/>$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\left[\mathrm{Pt}(\text { en })_2 \mathrm{Cl}_2\right] \mathrm{Cl}_2$<br/>, <br/>$\left[\mathrm{Pt}\left(\mathrm{NH}_3\right)_2 \mathrm{Cl}_2\right]$</span> </div>

answer:
<div class="solution">Only $C$ and $D$ can show geometrical isomerism as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oNNEy5FP3eIxU4w1aVEnafpTW2KrAjq7a1C5pufgCiw.original.fullsize.png"/><br/></div>


title: the-compound-that-undergoes-decarboxylation-most-readily-under-mild-condition-is-3
slug: the-compound-that-undergoes-decarboxylation-most-readily-under-mild-condition-is-3-32021
tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The compound that undergoes decarboxylation most readily under mild condition is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U2XxpDah8RlZahhfYNUqIu-gjAcZnKCXlvbBXQEpvgc.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/G2x3j3M6lfNfK05A9ZA9JsDVocPDwd-9R2JVbkklaAc.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">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ux7_FRzB9HRZws8RKmycNUVoeM2NsY5kdYo5mLv9OYM.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PbAnLAq5Y0zlI-nWPLYC8WiBGsoMPLOVB7eg_OYy4R4.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/G2x3j3M6lfNfK05A9ZA9JsDVocPDwd-9R2JVbkklaAc.original.fullsize.png"/></span> </div>

answer:
<div class="solution">$\beta-$ Ketoacids undergo decarboxylation easily. It is due to the stability of transition state formed after decarboxylation of $\beta$-keto acids. This is not possible in case of other acids.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/G9onUPiY5nAanJf2o70Ze_djJIj72IOTdMvWWFJiWO8.original.fullsize.png"/></div>


title: the-compounds-formed-upon-combustion-of-sodium-metal-in-excess-air-is-are
slug: the-compounds-formed-upon-combustion-of-sodium-metal-in-excess-air-is-are-24157
tags: ['Chemistry', 's Block Elements', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
answer: <div class="solution">Sodium on heating in air forms both normal oxide and peroxides.</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The compound(s) formed upon combustion of sodium metal in excess air is (are)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{O}_2$<br/></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">B</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{O}$<br/></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"><br/>$\mathrm{NaO}_2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{NaOH}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\mathrm{Na}_2 \mathrm{O}_2$<br/>, <br/>$\mathrm{Na}_2 \mathrm{O}$<br/></span> </div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-compounds-p-q-and-s-where-separately-subjected-to-nitration-using-hno-3-h-2-so-4-mixture-the-major-product-formed-in-each-case-respectively-is-1

slug:
the-compounds-p-q-and-s-where-separately-subjected-to-nitration-using-hno-3-h-2-so-4-mixture-the-major-product-formed-in-each-case-respectively-is-1-44184

question:
<div class="question">The compounds $P, Q$ and $S$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Eb5yU0rtzH_JRhe7UZrjS_RXcRpvUohkLgo8eGZw-O4.original.fullsize.png"/><br/><br/>where separately subjected to nitration using $\mathrm{HNO}_3 / \mathrm{H}_2 \mathrm{SO}_4$ mixture. The major product formed in each case respectively, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/5fn2cX0PRSS-Q3Rc6Griwtk7zhDCtf4zljGI3iWFTS8.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/w6MJrzpelJRNR9mOL_v7xGTVkMRMfFnKz4VUHq3Ilmw.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TaUa4E3kZWru_WgXOzMYELnRXb3AkpcVWb0d58IqKX8.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Cwf3WR6IeXgRg3yc8PBWAKR3855gN-gCJvJAS0-7ESQ.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TaUa4E3kZWru_WgXOzMYELnRXb3AkpcVWb0d58IqKX8.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U2g6dE2wR0rqegKIxuloCV_SUN2EISpVWkDnfalVGjU.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FyxG8UWvd1x4cHOcjM9gvTv4wkxKO7tDJ59OPfKyYIg.original.fullsize.png"/><br/><br/>General organic chemistry (GOC)<br/>Conceptual<br/>II</div>


tags: ['Chemistry', 'Hydrocarbons', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-compounds-p-q-and-s-where-separately-subjected-to-nitration-using-hno-3-h-2-so-4-mixture-the-major-product-formed-in-each-case-respectively-is

slug:
the-compounds-p-q-and-s-where-separately-subjected-to-nitration-using-hno-3-h-2-so-4-mixture-the-major-product-formed-in-each-case-respectively-is-55858

question:
<div class="question">The compounds $P, Q$ and $S$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Eb5yU0rtzH_JRhe7UZrjS_RXcRpvUohkLgo8eGZw-O4.original.fullsize.png"/><br/><br/>where separately subjected to nitration using $\mathrm{HNO}_3 / \mathrm{H}_2 \mathrm{SO}_4$ mixture. The major product formed in each case respectively, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/5fn2cX0PRSS-Q3Rc6Griwtk7zhDCtf4zljGI3iWFTS8.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/w6MJrzpelJRNR9mOL_v7xGTVkMRMfFnKz4VUHq3Ilmw.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TaUa4E3kZWru_WgXOzMYELnRXb3AkpcVWb0d58IqKX8.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Cwf3WR6IeXgRg3yc8PBWAKR3855gN-gCJvJAS0-7ESQ.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TaUa4E3kZWru_WgXOzMYELnRXb3AkpcVWb0d58IqKX8.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U2g6dE2wR0rqegKIxuloCV_SUN2EISpVWkDnfalVGjU.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FyxG8UWvd1x4cHOcjM9gvTv4wkxKO7tDJ59OPfKyYIg.original.fullsize.png"/><br/><br/>General organic chemistry (GOC)<br/>Conceptual<br/>II</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P2.db
title:
the-concentration-of-r-in-the-reaction-r-p-was-measured-as-a-function-of-time-and-the-following-data-is-obtained-r-molar-t-min-10-00-075-005-040-012-0

slug:
the-concentration-of-r-in-the-reaction-r-p-was-measured-as-a-function-of-time-and-the-following-data-is-obtained-r-molar-t-min-10-00-075-005-040-012-0-59559

question:
<div class="question">The concentration of $R$ in the reaction $R \longrightarrow P$ was measured as a function of time and the following data is obtained :<br/>$\begin{array}{lllll}{[R] \text { (molar) }} &amp; 1.0 &amp; 0.75 &amp; 0.40 &amp; 0.10 \\ t \text { (min) } &amp; 0.0 &amp; 0.05 &amp; 0.12 &amp; 0.18\end{array}$<br/>The order of the reaction is</div>

answer:
<div class="solution">$k_{\mathrm{I}}=\frac{\Delta[R]}{\Delta t}=\frac{0.25}{0.05}=5$<br/>$$<br/>k_{\text {II }}=\frac{\Delta[R]}{\Delta t}=\frac{0.60}{0.12}=5<br/>$$<br/>So, reaction must be of zero order.<br/>Chemical kinetics<br/>Straight conceptual<br/>II</div>


title: the-coordination-number-of-al-in-the-crystalline-state-of-alcl-3-is
slug: the-coordination-number-of-al-in-the-crystalline-state-of-alcl-3-is-47607
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
answer: <div class="solution">Coordination number of $\mathrm{Al}=6$.</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The coordination number of $\mathrm{Al}$ in the crystalline state of $\mathrm{AlCl}_3$ is</div>


title: the-correct-acidity-order-of-the-following-is
slug: the-correct-acidity-order-of-the-following-is-77026
tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct acidity order of the following is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7b6qdMHsSZY6-VDA-Ft2vqn1SuYfdt-U_Nh6myMTsgA.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>III $&gt;$ IV $&gt;$ II $&gt;$ I<br/></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"><br/>IV $&gt;$ III $&gt;$ I $&gt;$ II<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>III $&gt;$ II $&gt;$ I $&gt;$ IV<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>II $&gt;$ III $&gt;$ IV $&gt;$ I</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>III $&gt;$ IV $&gt;$ II $&gt;$ I<br/></span> </div>

answer:
<div class="solution">A carboxylic acid is stronger acid than phenol, hence both III and IV are stronger acids than both I and II. Also IV has a methyl group that gives electron donating inductive effect and decreases the acid strength. Therefore, III is stronger acid that IV. Between I and II, the dominant electron withdrawing inductive effect of chlorine increases acid strength of phenol slightly, hence II is stronger acid than I. Thus, the overall order is :<br/>(a) III $&gt;$ IV $&gt;$ II $&gt;$ I</div>


tags: ['Chemistry', 'Polymers', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-correct-functional-group-x-and-the-reagentreaction-conditions-y-in-the-following-schemes-are-x-ch-2-4-x

slug:
the-correct-functional-group-x-and-the-reagentreaction-conditions-y-in-the-following-schemes-are-x-ch-2-4-x-44941

question:
<div class="question">The correct functional group $X$ and the reagent/reaction conditions $Y$ in the following schemes are $\mathrm{X}-\left(\mathrm{CH}_2\right)_4-X$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/B4PneOQG7lvxe2R4OUEi1a5OrGBqkYzPVj-l4HcsdTo.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$X=\mathrm{COOCH}_3, Y=\mathrm{H}_2 / \mathrm{Ni} /$ heat<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$X=\mathrm{CONH}_2, Y=\mathrm{H}_2 / \mathrm{Ni} /$ heat<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$X=\mathrm{CONH}_2, \quad Y=\mathrm{Br}_2 / \mathrm{NaOH}$<br/></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"><br/>$X=\mathrm{CN}, Y=\mathrm{H}_2 / \mathrm{Ni} /$ heat</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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$X=\mathrm{CONH}_2, \quad Y=\mathrm{Br}_2 / \mathrm{NaOH}$<br/>, <br/>$X=\mathrm{CN}, Y=\mathrm{H}_2 / \mathrm{Ni} /$ heat</span> </div>

answer:
<div class="solution">(a) <img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8yG7DY1gJXc4iUCEOER-m_1UdvdV_gvkjBLqdA44bzg.original.fullsize.png"/><br/><br/>(b)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rxpqZzH3d5lVE-WlPs6Ut1ZgpUDmVb5crAU54xotfFY.original.fullsize.png"/><br/><br/>(c)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zfi7JK9uaNGjLxX4gh4PcKfwAYM_ZAmsnxT4axnqnfM.original.fullsize.png"/><br/><br/>(d)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/C7pT7CVPeovTexhOTafI8TbQNslCMk0IIPvS_s7dq_I.original.fullsize.png"/><br/><br/>$$<br/>\text { In author's opinion (a) and (b) should also be the answer. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/E4Bs3vfZ3lfBPb9mHMQ0te9i4wAnWAY_P_eo5gvqx2A.original.fullsize.png"/><br/><br/>Polyester, a condensation polymer<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tneLqzL0MI0skr6ZHl-Xj1c_DETeEDMLAn8BbF1KN7Q.original.fullsize.png"/><br/></div>


title: the-correct-stability-order-for-the-following-species-is-1
slug: the-correct-stability-order-for-the-following-species-is-1-11606
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct stability order for the following species is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3mHc2rFhfY275-Kb4arV3fiS2BJntZC-QFCwz2StHOg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(II) $&gt;$ (IV) $&gt;$ (I) $&gt;$ (III)<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(I) $&gt;$ (II) $&gt;$ (III) $&gt;$ (IV)<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(II) $&gt;$ (I) $&gt;$ (IV) $&gt;$ (III)<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>(I) $&gt;$ (III) $&gt;$ (II) $&gt;$ (IV)</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(I) $&gt;$ (III) $&gt;$ (II) $&gt;$ (IV)</span> </div>

answer:
<div class="solution">I $&gt;$ III $&gt;$ II $&gt;$ IV<br/>$+M$-effect, hyperconjugation $(6 \mathrm{Hs})$ and $+$ I-effect (2 Me groups)<br/>$+M$-effect, hyperconjugation ( $3 \mathrm{Hs}$ ) and $+I$-effect (1 Me group)<br/>$\overbrace{2^{\circ} \text { carbocation) }}^{+}$Hyperconjugation (5Hs) and +I-effect<br/>Hyperconjugation (2Hs) and $+I$ effect</div>


title: the-correct-stability-order-of-the-following-resonance-structure-is
slug: the-correct-stability-order-of-the-following-resonance-structure-is-18789
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct stability order of the following resonance structure is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ke2zkfkwW4j_l81tZraCKw8pk8IMJhvv-_R0VaW3EeI.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>I $&gt;$ II $&gt;$ IV $&gt;$ III<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>I $&gt;$ III $&gt;$ II $&gt;$ IV<br/></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"><br/>II $&gt;$ I $&gt;$ III $&gt;$ IV<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>III $&gt;$ I $&gt;$ IV $&gt;$ II</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>I $&gt;$ III $&gt;$ II $&gt;$ IV<br/></span> </div>

answer:
<div class="solution">(I) has maximum covalent bonds and negative charge on electronegative nitrogen, most stable. III has more covalent bond than both II and IV, III is second most stable. Between II and IV, II is more stable since it has negative charge on nitrogen while IV has negative charge on carbon.</div>


title: the-correct-statement-about-the-following-disaccharide-is
slug: the-correct-statement-about-the-following-disaccharide-is-89763
tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct statement about the following disaccharide is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QqT6oLSrnkeSquiGQCGACjGNdqT2hMxckER2bHRinJk.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Ring (a) is pyranose with $\alpha$-glycosidic link<br/></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"><br/>Ring (a) is furanose with $\alpha$-glycosidic link<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Ring (b) is furanose with $\alpha$-glycosidic link<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Ring (b) is pyranose with $\beta$-glycosidic link</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Ring (a) is pyranose with $\alpha$-glycosidic link<br/></span> </div>

answer:
<div class="solution">Ring $A$ is pyranose ( 6 membered ring containing one O-atom) with $\alpha$-glycosidic linkage and ring $B$ is furanose with $\beta$-glycosidic linkage.<br/>Biomolecules Conceptual structural interpretation III</div>


title: the-correct-statements-about-the-compound-given-below-is-are
slug: the-correct-statements-about-the-compound-given-below-is-are-62681
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct statement(s) about the compound given below is are<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/aL1RkKvmuEL72EuOZnVWmcRwQQ-3oX4k4CRZRzgSwPQ.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>the compound is optically active<br/></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">B</span> <span class="option-data"><br/>the compound possesses centre of symmetry<br/></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"><br/>the compound possesses plane of symmetry<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>the compound possesses axis of symmetry</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>the compound is optically active<br/>, <br/>the compound possesses centre of symmetry<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/pujQAF5GvuV7s7FOrRYHUmXAyrXYAeuWPtnFBBMcDAc.original.fullsize.png"/><br/><br/>The compound does not possess centre of symmetry and plane of symmetry but possesses the proper axis of symmetry $\left(C_n\right)$. A $C_n$ axis of symmetry is an axis about which the molecule can be rotated by $360^{\circ} / n$ and thereby produce a molecule indistinguishable from the original molecule.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/GfTUnX7IhPZKkqGw2PoQrHURZ07D5y9JfLg1ngLyhKI.original.fullsize.png"/><br/><br/>From this face $\mathrm{H}$ (on right) and $\mathrm{Cl}$ (on left) are facing towards us and again on rotating at $180^{\circ} \mathrm{C}-2$ comes at $\mathrm{C}-1$ place and again $\mathrm{H}$ (on right) and $\mathrm{Cl}$ (on left) are facing. We get an indistinguishable form on $180^{\circ}$ rotation, so it has a proper axis of symmetry $\left(C_2\right)$.<br/>If a molecule is not superimposable on its mirror image, that molecule can exhibit optical activity, if these have proper axis but no improper axis or if a $C_n$ axis be the only symmetry element present in a molecule, that molecule is optically active.</div>


title: the-correct-statements-about-the-compound-h-3-c-ho-hc-ch-ch-ch-oh-ch-3-x-is-are
slug: the-correct-statements-about-the-compound-h-3-c-ho-hc-ch-ch-ch-oh-ch-3-x-is-are-67164
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct statement(s) about the compound, $\mathrm{H}_3 \mathrm{C}(\mathrm{HO}) \mathrm{HC}-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}$ (OH) $\mathrm{CH}_3(\mathrm{X})$ is (are)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>the total number of stereoisomers possible for $X$ is 6<br/></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"><br/>the total number of diastereomers possible for $X$ is 3<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>if the stereochemistry about the double bond in $X$ is trans, the number of enantiomers possible for $X$ is 4<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>if the stereochemistry about the double bond in $X$ is cis, the number of enantiomers possible for $X$ is 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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>the total number of stereoisomers possible for $X$ is 6<br/>, <br/>if the stereochemistry about the double bond in $X$ is cis, the number of enantiomers possible for $X$ is 2</span> </div>

answer:
<div class="solution">$$<br/>\text { The various isomers of } X \text { are, }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/SNkfWfyCGMqQlnVBINqHWOlQBtIbh726hqp51-wy0oU.original.fullsize.png"/><br/><br/>Xhas six stereoisomers (I-VI). The total number of diasteromers of $X$ are more than three e.g, I + II, I + III, I + IV, I + V, I + VI etc. When stereochemistry at double bond is trans it has only two enantiomers (V and VI). When stereochemistry at doubld bond is cis, it has two enantiomers II and III. Hence, only $A$ and $D$ are correct answers.</div>


title: the-correct-statements-about-the-following-sugars-x-and-y-is-are
slug: the-correct-statements-about-the-following-sugars-x-and-y-is-are-34695
tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct statement(s) about the following sugars $X$ and $Y$ is (are)<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZoedRdBPYAC6fLpcvG-PfllkpSpBdM5GZHTcYr8M3iU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$X$ is a reducing sugar and $Y$ is a non-reducing sugar<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$X$ is a non-reducing sugar and $Y$ is a reducing sugar<br/></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"><br/>the glucosidic linkages in $X$ and $Y$ are $\alpha$ and $\beta$, respectively<br/></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"><br/>the glucosidic linkages in $X$ and $Y$ are $\beta$ and $\alpha$, respectively</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$X$ is a non-reducing sugar and $Y$ is a reducing sugar<br/>, <br/>the glucosidic linkages in $X$ and $Y$ are $\alpha$ and $\beta$, respectively<br/></span> </div>

answer:
<div class="solution">$X$ has acetal linkage and $Y$ has hemiacetal linkage. Carbohydrate with hemiacetal linkage are reducing sugars and carbohydrate with acetal linkage are non reducing sugars.<br/>$X$ is $\alpha$ anomer and $Y$ is $\beta$-anomer of $D(+)$ glucose.</div>


title: the-correct-statements-concerning-the-structures-e-f-and-g-is-are
slug: the-correct-statements-concerning-the-structures-e-f-and-g-is-are-45768
source_db: MarksBatch2_P2.db
question:
<div class="question">$$<br/>\text { The correct statement(s) concerning the structures } E, F \text { and } G \text { is are }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/E1DRlpw-v7S_epyvhb6ESOm6smSseP2oHONHZp5boiU.original.fullsize.png"/><br/></div>

tags:
['Chemistry', 'Classification of Elements and Periodicity in Properties', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$E, F$ and $G$ are resonance structures<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$E, F$ and $E, G$ are tautomers<br/></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"><br/>$F$ and $G$ are geometrical isomers<br/></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"><br/>$F$ and $G$ are diastereomers</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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$E, F$ and $E, G$ are tautomers<br/>, <br/>$F$ and $G$ are geometrical isomers<br/>, <br/>$F$ and $G$ are diastereomers</span> </div>

answer:
<div class="solution">$E$ and $F$ possess different place of atoms, in addition to electron pair, can be isomers only and not the resonance structures. Geometrical isomers are stereoisomers but not enantiomers called diastereomers</div>


title: the-correct-statements-pertaining-to-the-adsorption-of-a-gas-on-a-solid-surface-isare
slug: the-correct-statements-pertaining-to-the-adsorption-of-a-gas-on-a-solid-surface-isare-88135
tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The correct statement(s) pertaining to the adsorption of a gas on a solid surface is(are)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Adsorption is always exothermic<br/></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">B</span> <span class="option-data"><br/>Physisorption may transform into chemisorption at high temperature<br/></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"><br/>Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation</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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>Adsorption is always exothermic<br/>, <br/>Physisorption may transform into chemisorption at high temperature<br/>, <br/>Chemisorption is more exothermic than physisorption, however it is very slow due to higher energy of activation</span> </div>

answer:
<div class="solution">(a) In the process of adsorption, a bond is formed between adsorbate and adsorbent, hence always exothermic.<br/>(b) Physisorption require very low activation energy while chemisorption require high activation energy. Therefore a physisorption may transform into chemisorption but only at high temperature.<br/>(c) It is wrong statement as at higher temperature, physically adsorbed substance starts desorbing.<br/>(d) In physical adsorption, van der Waals' force hold the adsorbate and adsorbent together which is a weak electrostatic attraction. In chemisorption, strong chemical bond binds the adsorbate to the adsorbent. Therefore, chemisorption is more exothermic than physical adsorption.</div>


title: the-correct-statements-regarding-defects-in-solids-is-are
slug: the-correct-statements-regarding-defects-in-solids-is-are-55076
question: <div class="question">The correct statement(s) regarding defects in solids is (are)</div>
tags: ['Chemistry', 'Solid State', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Frenkel defect is usually favoured by a very small difference in the sizes of cation and anion<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Frenkel defect is a dislocation defect<br/></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"><br/>Trapping of an electron in the lattice leads to the formation of F-centre<br/></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"><br/>Schottky defects have no effect on the physical properties of solids</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>Frenkel defect is a dislocation defect<br/>, <br/>Trapping of an electron in the lattice leads to the formation of F-centre<br/></span> </div>

answer:
<div class="solution">(a) Wrong Frenkel defect is favoured when the difference in ionic radii is very large. In the given case Schottky defect is favoured.<br/>(b) Correct Frenkel defect arises due to dislocation of smaller ion from its normal lattice point to the interstitial space.<br/>(c) Correct When alkali metal in the gaseous state is passed over salts like $\mathrm{NaCl}$, electrons from metal are trapped in the interstitial space giving rise to F-centre defect which is a type of Frenkel defect.<br/>(d) Wrong Schottky defect affects physical properties of solids.</div>


title: the-correct-structure-of-ethylenediaminetetraacetic-acid-edta-is-1
slug: the-correct-structure-of-ethylenediaminetetraacetic-acid-edta-is-1-21130
question: <div class="question">The correct structure of ethylenediaminetetraacetic acid (EDTA) is</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8GgLCrc7i-rnz2nL1exjSeFaKCii1C-qGdAO8PwBkqo.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FNEdIxB8FRfEsHGt6B3Zsjo291kjm2hjserWOFCLYy4.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d__M8JjK520943LpxCCCC7V3TMWvq7lJL5MgTZy54C4.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QzWXMfirWZtL4R2FN-tMynlad8vCZZ7hyrVZKfsmCJY.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d__M8JjK520943LpxCCCC7V3TMWvq7lJL5MgTZy54C4.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">EDTA structure is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fPfCX68rome_F7sEPc1QEBWJHv03jYorE-rORCmN6Ec.original.fullsize.png"/><br/><br/>Coordination chemistry<br/>Factual<br/>I</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-decay-process-discovered-around-1900-is-basically-the-decay-of-a-neutron-n-in-the-laboratory-a-proton-p-and-an-electron-e-are-observed-as-the-deca-1

slug:
the-decay-process-discovered-around-1900-is-basically-the-decay-of-a-neutron-n-in-the-laboratory-a-proton-p-and-an-electron-e-are-observed-as-the-deca-1-88089

question:
<div class="question">The $\beta$-decay process, discovered around 1900 , is basically the decay of a neutron $(n)$. In the laboratory, a proton $(p)$ and an electron $\left(e^{-}\right)$are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, i.e.
<br/> <br/>$n \rightarrow p+e^{-}+\bar{v}_{e}$, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino $\left(\bar{v}_{e}\right)$ to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is $0.8 \times 10^{6} \mathrm{eV}$. The kinetic energy carried by the proton is only the recoil energy.
<br/> <br/><strong> Question:</strong> If the anti-neutrino had a mass of $3 \mathrm{eV} / \mathrm{c}^{2}$ (where $\mathrm{c}$ is the speed of light) instead of zero mass, what should be the range of the kinetic energy, $K$, of the electron?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0 \leq K \leq 0.8 \times 10^{6} \mathrm{eV}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3.0 \mathrm{eV} \leq K \leq 0.8 \times 10^{6} \mathrm{eV}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3.0 \mathrm{eV} \leq K &lt; 0.8 \times 10^{6} \mathrm{eV}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0 \leq K &lt; 0.8 \times 10^{6} \mathrm{eV}$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0 \leq K &lt; 0.8 \times 10^{6} \mathrm{eV}$</span> </div>

answer:
<div class="solution">Kinetic energy $(K)$ of electron will be minimum or zero when total energy is shared by proton and anti-neutrino $\therefore 0 \leq \mathrm{K} &lt; 0.8 \times 10^{6} \mathrm{eV}$</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-decay-process-discovered-around-1900-is-basically-the-decay-of-a-neutron-n-in-the-laboratory-a-proton-p-and-an-electron-e-are-observed-as-the-deca

slug:
the-decay-process-discovered-around-1900-is-basically-the-decay-of-a-neutron-n-in-the-laboratory-a-proton-p-and-an-electron-e-are-observed-as-the-deca-56155

question:
<div class="question">The $\beta$-decay process, discovered around 1900 , is basically the decay of a neutron $(n)$. In the laboratory, a proton $(p)$ and an electron $\left(e^{-}\right)$are observed as the decay products of the neutron. Therefore, considering the decay of a neutron as a two-body decay process, it was predicted theoretically that the kinetic energy of the electron should be a constant. But experimentally, it was observed that the electron kinetic energy has continuous spectrum. Considering a three-body decay process, i.e.
<br/> <br/>$n \rightarrow p+e^{-}+\bar{v}_{e}$, around 1930, Pauli explained the observed electron energy spectrum. Assuming the anti-neutrino $\left(\bar{v}_{e}\right)$ to be massless and possessing negligible energy, and the neutron to be at rest, momentum and energy conservation principles are applied. From this calculation, the maximum kinetic energy of the electron is $0.8 \times 10^{6} \mathrm{eV}$. The kinetic energy carried by the proton is only the recoil energy.
<br/> <br/><strong> Question:</strong> What is the maximum energy of the anti-neutrino?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Much less than $0.8 \times 10^{6} \mathrm{eV}$.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Nearly $0.8 \times 10^{6} \mathrm{eV}$</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">Much larger than $0.8 \times 10^{6} \mathrm{eV}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Nearly $0.8 \times 10^{6} \mathrm{eV}$</span> </div>

answer:
<div class="solution">$\because K_{p}^{-}+K_{e}^{-}+K_{v}^{-}=0.8 \times 10^{6} \mathrm{eV}$
<br/> <br/>When $K_{e}^{-}=0$ then $K_{p}^{-}+K_{v}^{-}=0.8 \times 10^{6} \mathrm{eV}$
<br/> <br/>Mass of $\bar{v}&lt; &lt; P \therefore$ maximum energy of anti-neutrino is nearly $0.8 \times 10^{6} \mathrm{eV}$.</div>


tags: ['Physics', 'Mathematics in Physics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-density-of-a-solid-ball-is-to-be-determined-in-an-experiment-the-diameter-of-the-ball-is-measured-with-a-screw-gauge-whose-pitch-is-05-mm-and-ther

slug:
the-density-of-a-solid-ball-is-to-be-determined-in-an-experiment-the-diameter-of-the-ball-is-measured-with-a-screw-gauge-whose-pitch-is-05-mm-and-ther-50977

question:
<div class="question">The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is $0.5 \mathrm{~mm}$ and there are 50 divisions on the circular scale. The reading on the main scale is $2.5 \mathrm{~mm}$ and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of $2 \%$, the relative percentage error in the density is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$0.9 \%$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$2.4 \%$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$3.1 \%$<br/></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"><br/>$4.2 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$3.1 \%$<br/></span> </div>

answer:
<div class="solution">Least count of screw gauge $=\frac{0.5}{50}$<br/>$$<br/>=0.01 \mathrm{~mm}=\Delta r<br/>$$<br/>Diameter, $r=2.5 \mathrm{~mm}+20 \times \frac{0.5}{50}$<br/>$$<br/>=270 \mathrm{~mm}<br/>$$<br/>$$<br/>\frac{\Delta r}{r}=\frac{0.01}{2.70}<br/>$$<br/>or $\frac{\Delta r}{r} \times 100=\frac{1}{2.7}$<br/>Now, density $d=\frac{m}{V}=\frac{m}{\frac{4}{3} \pi\left(\frac{r}{2}\right)^3}$<br/>Here, $r$ is the diameter.<br/>$$<br/>\begin{aligned}<br/>\therefore \quad \frac{\Delta d}{d} &amp; \times 100=\left\{\frac{\Delta m}{m}+3\left(\frac{\Delta r}{r}\right)\right\} \times 100 \\<br/>= &amp; \frac{\Delta m}{m} \times 100+3 \times\left(\frac{\Delta r}{r}\right) \times 100<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; =2 \%+3 \times \frac{1}{27} \\<br/>&amp; =3.11 \%<br/>\end{aligned}<br/>$$<br/>Analysis of Question<br/>(i) Question is moderately difficult.<br/>(ii) In practical part, questions in JEE are asked from vernier callipers and screw gauge.</div>


title: the-difference-in-the-oxidation-numbers-of-the-two-types-of-sulphur-atoms-in-na-2-s-4-o-6-is-1
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P2.db
slug:
the-difference-in-the-oxidation-numbers-of-the-two-types-of-sulphur-atoms-in-na-2-s-4-o-6-is-1-58568

question:
<div class="question">The difference in the oxidation numbers of the two types of sulphur atoms in $\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6$ is</div>

answer:
<div class="solution">$$<br/>\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6 \text { is a salt of } \mathrm{H}_2 \mathrm{~S}_4 \mathrm{O}_6 \text { which has the following structure }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0-8axulfQ-DixHOvoN22BhSXEH57SKTvMteSI3efq2s.original.fullsize.png"/><br/><br/>$$<br/>\Rightarrow \text { Difference in oxidation number of two types of sulphur }=5<br/>$$</div>


title: the-differential-equation-d-x-d-y-y-1-y-2-determines-a-family-of-circles-with
slug: the-differential-equation-d-x-d-y-y-1-y-2-determines-a-family-of-circles-with-96799
tags: ['Mathematics', 'Differential Equations', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>variable radii and a fixed centre at $(0,1)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>variable radii and a fixed centre at $(0,-1)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>fixed radius 1 and variable centres along the $\mathrm{X}$-axis<br/></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"><br/>fixed radius 1 and variable centres along the $\mathrm{Y}$-axis</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>fixed radius 1 and variable centres along the $\mathrm{X}$-axis<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y} \\<br/>&amp; \Rightarrow \quad \int \frac{y}{\sqrt{1-y^2}} d y=\int d x \\<br/>&amp; \Rightarrow \quad-\sqrt{1-y^2}=x+C \\<br/>&amp; \Rightarrow \quad(x+c)^2+y^2=1 \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Centre $(-C, 0)$ and radius $=1$.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
the-direct-conversion-of-a-to-b-is-difficult-hence-it-is-carried-out-by-the-following-shown-path-given-s-a-c-50-eu-s-c-d-30-eu-s-b-d-20-eu-where-eu-is

slug:
the-direct-conversion-of-a-to-b-is-difficult-hence-it-is-carried-out-by-the-following-shown-path-given-s-a-c-50-eu-s-c-d-30-eu-s-b-d-20-eu-where-eu-is-34236

question:
<div class="question">The direct conversion of $A$ to $B$ is difficult, hence it is carried out by the following shown path.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iJ5njgEP0uFQ1pVFhbAFJsbaHKjkZKwmpTu4qcej07g.original.fullsize.png"/><br/><br/>Given $\Delta S_{(A \rightarrow C)}=50 \mathrm{eu}, \quad \Delta S_{(C \rightarrow D)}=30 \mathrm{eu}, \quad \Delta S_{(B \rightarrow D)}=20 \mathrm{eu}$ where eu is entropy unit, then $\Delta S_{(A \rightarrow B)}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$+100 \mathrm{eu}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$+60 \mathrm{eu}$<br/></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"><br/>$-100 \mathrm{eu}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$-60$ eu</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$+60 \mathrm{eu}$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T6t400ny5IwMNx15Gjzndta8lkrq8lZA6m3hH2r5tXo.original.fullsize.png"/><br/><br/>Given: $\quad \Delta S_{(A \rightarrow C)}=50 \mathrm{eu}, \Delta S_{(C \rightarrow D)}=30 \mathrm{eu}, \Delta S_{(B \rightarrow D)}=20 \mathrm{eu}$ where eu is entropy unit.<br/>$$<br/>\text { Therefore, } \begin{aligned}<br/>\Delta S_{(A \rightarrow B)} &amp; =\Delta S_{(A \rightarrow C)}+\Delta S_{(C \rightarrow D)}+\Delta S_{(D \rightarrow B)} \\<br/>&amp; =\Delta S_{(A \rightarrow C)}+\Delta S_{(C \rightarrow D)}-\Delta S_{(B \rightarrow D)} \\<br/>&amp; =50+30-20=60 \mathrm{eu}<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P2.db
title:
the-dissociation-constant-of-a-substituted-benzoic-acid-at-2-5-c-is-10-1-0-4-the-ph-of-001-m-solution-of-its-sodium-salt-is

slug:
the-dissociation-constant-of-a-substituted-benzoic-acid-at-2-5-c-is-10-1-0-4-the-ph-of-001-m-solution-of-its-sodium-salt-is-78742

question:
<div class="question">The dissociation constant of a substituted benzoic acid at $25^{\circ} \mathrm{C}$ is $1.0 \times 10^{-4}$. The $\mathrm{pH}$ of $0.01 \mathrm{M}$ solution of its sodium salt is</div>

answer:
<div class="solution">$$<br/>\text { The hydrolysis reaction of conjugate base of acid is }<br/>$$<br/><br/>$$<br/>\begin{gathered}<br/>A^{-}(a q)+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{HO}^{-}+\mathrm{HA} \\<br/>K_h=\frac{K_w}{K_a}=\frac{10^{-14}}{10^{-4}}=10^{-10}<br/>\end{gathered}<br/>$$<br/><br/>Since, degree of hydrolysis is negligible;<br/>$$<br/>\left[\mathrm{OH}^{-}\right]=\sqrt{K_h C}=10^{-6} \cdot p[\mathrm{OH}]=6 \text { and } \mathrm{pH}=14-6=8<br/>$$</div>


tags: ['Physics', 'Experimental Physics', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.82</span> </div>
source_db: MarksBatch2_P2.db
title:
the-distance-advanced-by-the-screw-of-a-screw-gauge-is-2-m-m-in-4-rotations-its-cap-is-divided-into-50-divisions-there-is-no-zero-error-if-the-screw-r

slug:
the-distance-advanced-by-the-screw-of-a-screw-gauge-is-2-m-m-in-4-rotations-its-cap-is-divided-into-50-divisions-there-is-no-zero-error-if-the-screw-r-19320

question:
<div class="question">The distance advanced by the screw of a screw gauge is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">m</mi></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> rotations. Its cap is divided into <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math> divisions. There is no zero error. If the screw reads <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn></math> divisions on the main scale and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>32</mn></math> divisions on the cap, then the diameter (in <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mm</mi></math>) of the wire is</div>

answer:
<div class="solution"><math><mi mathvariant="normal">p</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">h</mi><mi mathvariant="normal"> </mi><mo>=</mo><mrow><mrow><mn>2</mn></mrow><mo>/</mo><mrow><mn>4</mn></mrow></mrow></math><br/><br/><math><mi mathvariant="normal">L</mi><mi mathvariant="normal">C</mi><mi mathvariant="normal"> </mi><mo>=</mo><mfrac><mrow><mrow><mrow><mn>2</mn></mrow><mo>/</mo><mrow><mn>4</mn></mrow></mrow></mrow><mrow><mn>50</mn></mrow></mfrac><mo>=</mo><mi mathvariant="normal"> </mi><mo>.</mo><mn>01</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">m</mi></math><br/><br/><math><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal"> </mi><mo>=</mo><mi mathvariant="normal"> </mi><mn>3</mn><mi mathvariant="normal"> </mi><mo>Ã</mo><mi mathvariant="normal"> </mi><mn>0.5</mn><mi mathvariant="normal"> </mi><mo>+</mo><mi mathvariant="normal"> </mi><mn>32</mn><mi mathvariant="normal"> </mi><mo>Ã</mo><mi mathvariant="normal"> </mi><mo>.</mo><mn>01</mn></math><br/><br/><math><mo>=</mo><mn>1.5</mn><mi mathvariant="normal"> </mi><mo>+</mo><mi mathvariant="normal"> </mi><mo>.</mo><mn>32</mn></math><br/><br/><math><mo>=</mo><mi mathvariant="normal"> </mi><mn>1.82</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">m</mi></math></div>


tags: ['Chemistry', 'Solid State', 'JEE Advanced', 'JEE Advanced 2006']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">216.5</span> </div>
source_db: MarksBatch2_P2.db
title:
the-edge-length-of-unit-cell-of-a-metal-having-molecular-weight-75-g-mol-is-5-which-crystallizes-in-cubic-lattice-if-the-density-is-2-g-cc-then-find-t

slug:
the-edge-length-of-unit-cell-of-a-metal-having-molecular-weight-75-g-mol-is-5-which-crystallizes-in-cubic-lattice-if-the-density-is-2-g-cc-then-find-t-15529

question:
<div class="question">The edge length of unit cell of a metal having molecular weight $75 \mathrm{~g} / \mathrm{mol}$ is 5 Ã which crystallizes in cubic lattice. If the density is $2 \mathrm{~g} / \mathrm{cc}$ then find the radius of metal atom, $\left(N_A=6 \times 10^{23}\right)$. Give the answer in pm.</div>

answer:
<div class="solution">For cubic lattice, $\rho=\frac{Z \times A}{N_A \times V}$ or $Z=\frac{\rho \times N_A \times V}{A}$<br/>Given that,<br/>$$<br/>\begin{aligned}<br/>&amp; A=75 \mathrm{~g} / \mathrm{mol} \\<br/>&amp; V=(5 Ã)^3=\left(5 \times 10^{-8}\right)^3 \mathrm{~cm}^3 \\<br/>&amp; =125 \times 10^{-24} \mathrm{~cm}^3 \\<br/>&amp; N_{\mathrm{A}}=6.02 \times 10^{23} \\<br/>&amp; \rho=2 \mathrm{gm} / \mathrm{cc} \\<br/>&amp; \therefore \quad Z=\frac{2 \times 6.02 \times 10^{23} \times 125 \times 10^{-24}}{75} \approx 2 \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>The value of $Z$ represents that element must have body centred cubic (bcc) structure.<br/>For bcc structure atomic radius $(r)=\frac{\sqrt{3}}{4} a=\frac{\sqrt{3}}{4} \times 5=2.165 Ã$<br/>$$<br/>=216.5 \mathrm{pm}<br/>$$</div>


tags: ['Mathematics', 'Vector Algebra', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
the-edges-of-a-parallelopiped-are-of-unit-length-and-are-parallel-to-noncoplanar-unit-vectors-a-b-c-such-that-a-b-b-c-c-a-2-1-then-the-volume-of-the-p

slug:
the-edges-of-a-parallelopiped-are-of-unit-length-and-are-parallel-to-noncoplanar-unit-vectors-a-b-c-such-that-a-b-b-c-c-a-2-1-then-the-volume-of-the-p-35675

question:
<div class="question">The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors $\hat{\mathbf{a}}, \hat{\mathbf{b}}, \hat{\mathbf{c}}$ such that $\hat{\mathbf{a}} \cdot \hat{\mathbf{b}}=\hat{\mathbf{b}} \cdot \hat{\mathbf{c}}=\hat{\mathbf{c}} \cdot \hat{\mathbf{a}}=\frac{1}{2}$. Then, the volume of the parallelopiped is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{\sqrt{2}} \mathrm{cu}$ units<br/></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"><br/>$\frac{1}{2 \sqrt{2}}$ cu units<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{\sqrt{3}}{2}$ cu units<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{\sqrt{3}} \mathrm{cu}$ units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{\sqrt{2}} \mathrm{cu}$ units<br/></span> </div>

answer:
<div class="solution">The volume of the parallelopiped with coterminus edges as $\hat{\mathbf{a}}, \hat{\mathbf{b}}, \hat{\mathbf{c}}$ is given by $[\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]=\hat{\mathbf{a}} \cdot(\hat{\mathbf{b}} \times \hat{\mathbf{c}})$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/k6mlluFRBwuUL93v1nZlZbKz5YVAY5Vxu0VK15DpLN0.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \text { Now, }[\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]^2=\left|\begin{array}{ccc}<br/>\hat{\mathbf{a}} \cdot \hat{\mathbf{a}} &amp; \hat{\mathbf{a}} \cdot \hat{\mathbf{b}} &amp; \hat{\mathbf{a}} \cdot \hat{\mathbf{c}} \\<br/>\hat{\mathbf{b}} \cdot \hat{\mathbf{a}} &amp; \hat{\mathbf{b}} \cdot \hat{\mathbf{b}} &amp; \hat{\mathbf{b}} \cdot \hat{\mathbf{c}} \\<br/>\hat{\mathbf{c}} \cdot \hat{\mathbf{a}} &amp; \hat{\mathbf{c}} \cdot \hat{\mathbf{b}} &amp; \hat{\mathbf{c}} \cdot \hat{\mathbf{c}}<br/>\end{array}\right|=\left|\begin{array}{ccc}<br/>1 &amp; 1 / 2 &amp; 1 / 2 \\<br/>1 / 2 &amp; 1 &amp; 1 / 2 \\<br/>1 / 2 &amp; 1 / 2 &amp; 1<br/>\end{array}\right|=\frac{1}{2} \\<br/>&amp; \Rightarrow \quad[\hat{\mathbf{a}} \hat{\mathbf{b}} \hat{\mathbf{c}}]^2=\frac{1}{2} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Thus, the required volume of the parallelopiped $=\frac{1}{\sqrt{2}} \mathrm{cu}$ units</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-electrochemical-cell-shown-below-is-a-concentration-cell-m-m-2-saturated-solution-of-a-sparingly-soluble-salt-mx-2-m-2-0001-mol-dm-3-m-the-emf-of--1

slug:
the-electrochemical-cell-shown-below-is-a-concentration-cell-m-m-2-saturated-solution-of-a-sparingly-soluble-salt-mx-2-m-2-0001-mol-dm-3-m-the-emf-of-1-63791

question:
<div class="question">The electrochemical cell shown below is a concentration cell. $\mathrm{M} \mid \mathrm{M}^{2+}$ (saturated solution of a sparingly soluble salt, $\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}$.
<br/> <br/>The emf of the cell depends on the difference in concentrations of $\mathrm{M}^{2+}$ ions at the two electrodes. The emf of the cell at $298 \mathrm{~K}$ is $0.059 \mathrm{~V}$.
<br/> <br/><strong> Question:</strong> The value of $\Delta \mathrm{G}\left(\mathrm{kJ} \mathrm{mol}^{-1}\right)$ for the given cell is (take 1 $\mathrm{F}=96500 \mathrm{Cmol}^{-1}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-5.7$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$5.7$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$11.4$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-11.4$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-11.4$</span> </div>

answer:
<div class="solution">At anode : $M(\mathrm{~s})+2 X^{-}(\mathrm{aq}) \longrightarrow M X_{2}(\mathrm{aq})+2 \mathrm{e}^{-}$
<br/> <br/>At cathode $: M^{+2}(\mathrm{aq})+2 \mathrm{e}^{-} \longrightarrow M(\mathrm{~s})$
<br/> <br/>Thus, here $n=2$
<br/> <br/>$\Delta G=-n F E_{\text {cell }}$
<br/> <br/>$=-2 \times 96500 \times 0.059 \times 10^{-3} \mathrm{~kJ} / \mathrm{mole}=-11.4 \mathrm{~kJ} / \mathrm{mole}$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-electrochemical-cell-shown-below-is-a-concentration-cell-m-m-2-saturated-solution-of-a-sparingly-soluble-salt-mx-2-m-2-0001-mol-dm-3-m-the-emf-of-

slug:
the-electrochemical-cell-shown-below-is-a-concentration-cell-m-m-2-saturated-solution-of-a-sparingly-soluble-salt-mx-2-m-2-0001-mol-dm-3-m-the-emf-of-69014

question:
<div class="question">The electrochemical cell shown below is a concentration cell. $\mathrm{M} \mid \mathrm{M}^{2+}$ (saturated solution of a sparingly soluble salt, $\left.\mathrm{MX}_{2}\right) \| \mathrm{M}^{2 \perp}\left(0.001 \mathrm{~mol} \mathrm{dm}^{-3}\right) \mid \mathrm{M}$.
<br/> <br/>The emf of the cell depends on the difference in concentrations of $\mathrm{M}^{2+}$ ions at the two electrodes. The emf of the cell at $298 \mathrm{~K}$ is $0.059 \mathrm{~V}$.
<br/> <br/><strong> Question:</strong> The solubility product $\left(\mathrm{K}_{s p} ; \mathrm{mol}^{3} \mathrm{dm}^{-9}\right)$ of $\mathrm{MX}_{2}$ at $298 \mathrm{~K}$ based on the information available for the given concentration cell is (take $2.303 \times \mathrm{R} \times 298 / \mathrm{F}=0.059 \mathrm{~V}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1 \times 10^{-15}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$4 \times 10^{-15}$</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">$1 \times 10^{-12}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \times 10^{-12}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \times 10^{-15}$</span> </div>

answer:
<div class="solution">$M \mid M^{2+}$ (aq) $\| M^{2+}$ (aq) $\mid M$
<br/> <br/>$0.001 \mathrm{M}$
<br/> <br/>Anode : $\quad M \longrightarrow M^{2+}(\mathrm{aq})+2 e^{-}$
<br/> <br/>Cathode : $M^{2+}(\mathrm{aq})+2 e^{-} \longrightarrow M$
<br/> <br/>$M^{2+}(\mathrm{aq})_{c} \rightleftharpoons M^{2+}(\mathrm{aq})_{a}$
<br/> <br/>$\begin{array}{c}
<br/> <br/>E_{\text {cell }}=0-\frac{0.059}{2} \log \left\{\frac{M^{2+}(\mathrm{aq})_{a}}{10^{-3}}\right\} \\
<br/> <br/>\Rightarrow 0.059=-\frac{0.059}{2} \log \left\{\frac{M^{2+}(\mathrm{aq})_{a}}{10^{-3}}\right\} \\
<br/> <br/>-2=\log \left\{\frac{M^{2+}(\mathrm{aq})_{a}}{10^{-3}}\right\}
<br/> <br/>\end{array}$
<br/> <br/>$\Rightarrow \quad 10^{-2} \times 10^{-3}=\mathrm{M}^{2+}(\mathrm{aq})_{a}=$ solubility $=s$
<br/> <br/>$\quad M X_{2} \rightleftharpoons M^{2+}+2 X^{-}$
<br/> <br/>$K_{s p}=S .(2 S)^{2} \quad 2 S$
<br/> <br/>$\Rightarrow \quad K_{s p}=4 s^{3}=4 \times\left(10^{-5}\right)^{3}=4 \times 10^{-15}$</div>


tags: ['Mathematics', 'Ellipse', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-ellipse-e-1-9-x-2-4-y-2-1-is-inscribed-in-a-rectangle-r-whose-sides-are-parallel-to-the-coordinate-axes-another-ellipse-e-2-passing-through-the-po-1

slug:
the-ellipse-e-1-9-x-2-4-y-2-1-is-inscribed-in-a-rectangle-r-whose-sides-are-parallel-to-the-coordinate-axes-another-ellipse-e-2-passing-through-the-po-1-23676

question:
<div class="question">The ellipse $E_{1}: \frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0,4)$ circumscribes the rectangle $R$. The eccentricity of the ellipse $E_{2}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{2}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</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">D</span> <span class="option-data">$\frac{3}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2}$</span> </div>

answer:
<div class="solution">As rectangle $A B C D$ circumscribed the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1, \quad \therefore A=(3,2)$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/aet9wmBJVgdIkqK5Yu0olFJanD-DZd2Mf-55gTg95GY.original.fullsize.png"/><br/> <br/> <br/>Let the ellipse circumscribing the rectangle $A B C D$ is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1...(i)$
<br/> <br/>Given that ellipse (i) passes through $(a, 4)$ $\therefore b^{2}=16$
<br/> <br/>Also ellipse (i) passes through $A(3,2)$
<br/> <br/>$\therefore \quad \frac{9}{a^{2}}+\frac{4}{16}=1 \Rightarrow a^{2}=12$
<br/> <br/>$\therefore \quad e=\sqrt{1-\frac{12}{16}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$</div>


tags: ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
the-ellipse-e-1-9-x-2-4-y-2-1-is-inscribed-in-a-rectangle-r-whose-sides-are-parallel-to-the-coordinate-axes-another-ellipse-e-2-passing-through-the-po

slug:
the-ellipse-e-1-9-x-2-4-y-2-1-is-inscribed-in-a-rectangle-r-whose-sides-are-parallel-to-the-coordinate-axes-another-ellipse-e-2-passing-through-the-po-93904

question:
<div class="question">The ellipse $E_{1}: \frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is inscribed in a rectangle $R$ whose sides are parallel to the coordinate axes. Another ellipse $E_{2}$ passing through the point $(0,4)$ circumscribes the rectangle $R$. The eccentricity of the ellipse $E_{2}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{2}}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{3}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{2}$</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">D</span> <span class="option-data">$\frac{3}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{2}$</span> </div>

answer:
<div class="solution">As rectangle $A B C D$ circumscribed the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1, \quad \therefore A=(3,2)$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/aet9wmBJVgdIkqK5Yu0olFJanD-DZd2Mf-55gTg95GY.original.fullsize.png"/><br/> <br/> <br/>Let the ellipse circumscribing the rectangle $A B C D$ is $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1...(i)$
<br/> <br/>Given that ellipse (i) passes through $(a, 4)$ $\therefore b^{2}=16$
<br/> <br/>Also ellipse (i) passes through $A(3,2)$
<br/> <br/>$\therefore \quad \frac{9}{a^{2}}+\frac{4}{16}=1 \Rightarrow a^{2}=12$
<br/> <br/>$\therefore \quad e=\sqrt{1-\frac{12}{16}}=\sqrt{\frac{1}{4}}=\frac{1}{2}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-equation-of-a-plane-passing-through-the-line-of-intersection-of-the-planes-x-2-y-3-z-2-and-x-y-z-3-and-at-a-distance-3-2-from-the-point-3-1-1-is

slug:
the-equation-of-a-plane-passing-through-the-line-of-intersection-of-the-planes-x-2-y-3-z-2-and-x-y-z-3-and-at-a-distance-3-2-from-the-point-3-1-1-is-90577

question:
<div class="question">The equation of a plane passing through the line of intersection of the planes $x+2 y+3 z=2$ and $x-y+z=3$
<br/> <br/>and at a distance $\frac{2}{\sqrt{3}}$ from the point $(3,1,-1)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$5 x-11 y+z=17$</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">$\sqrt{2} x+y=3 \sqrt{2}-1$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x+y+z=\sqrt{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$x-\sqrt{2} y=1-\sqrt{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$5 x-11 y+z=17$</span> </div>

answer:
<div class="solution">Equation of the plane passing through the intersection line of given planes is
<br/> <br/>$\begin{array}{ll} 
<br/> <br/>&amp; (x+2 y+3 z-2)+\lambda(x-y+z-3)=0 \\
<br/> <br/>\text { or } &amp; (1+\lambda) x+(2-\lambda) y+(3+\lambda) z+(-2-3 \lambda)=0
<br/> <br/>\end{array}$
<br/> <br/>$\because \quad$ Its distance from the point $(3,1,-1)$ is $\frac{2}{\sqrt{3}}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\therefore\left|\frac{3(1+\lambda)+1(2-\lambda)-1(3+\lambda)+(-2-3 \lambda)}{\sqrt{(1+\lambda)^{2}+(2-\lambda)^{2}+(3+\lambda)^{2}}}\right|=\frac{2}{\sqrt{3}} \\
<br/> <br/>\Rightarrow\left|\frac{-2 \lambda}{\sqrt{3 \lambda^{2}+4 \lambda+14}}\right|=\frac{2}{\sqrt{3}} \\
<br/> <br/>\Rightarrow 3 \lambda^{2}+4 \lambda+14=3 \lambda^{2} \Rightarrow \lambda=-\frac{7}{2}
<br/> <br/>\end{array}$
<br/> <br/>$\therefore$ Required equation of plane is
<br/> <br/>$(x+2 y+3 z-2)-\frac{7}{2}(x-y+z-3)=0$
<br/> <br/>or $5 x-11 y+z=17$</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-equilibrium-2-cu-i-cu-0-cu-ii-in-aqueous-medium-at-2-5-c-shifts-towards-the-left-in-the-presence-of

slug:
the-equilibrium-2-cu-i-cu-0-cu-ii-in-aqueous-medium-at-2-5-c-shifts-towards-the-left-in-the-presence-of-39479

question:
<div class="question">The equilibrium $2 \mathrm{Cu}^{\mathrm{I}} \rightleftharpoons \mathrm{Cu}^0+\mathrm{Cu}^{\text {II }}$ in aqueous medium at $25^{\circ} \mathrm{C}$ shifts towards the left in the presence of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{NO}_3^{-}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{Cl}^{-}$<br/></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"><br/>$\mathrm{SCN}^{-}$<br/></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"><br/>$\mathrm{CN}^{-}$</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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\mathrm{Cl}^{-}$<br/>, <br/>$\mathrm{SCN}^{-}$<br/>, <br/>$\mathrm{CN}^{-}$</span> </div>

answer:
<div class="solution">$\mathrm{Cl}^{-}, \mathrm{CN}^{-}$and $\mathrm{SCN}^{-}$froms precipitate with $\mathrm{Cu}$ (I), remove $\mathrm{Cu}$ (I) ion from equilibrium and reaction shift in direction shift in backward direction according to Le-Chatelier's principle.</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-a-system-consisting-of-i-a-ring-of-outer-radius-3-r-rolling-clockwise-without-slipping-on-a-horizontal-surface-with-angular-speed-and

slug:
the-figure-shows-a-system-consisting-of-i-a-ring-of-outer-radius-3-r-rolling-clockwise-without-slipping-on-a-horizontal-surface-with-angular-speed-and-83736

question:
<div class="question">The figure shows a system consisting of (i) a ring of outer radius $3 R$ rolling clockwise without slipping on a horizontal surface with angular speed $\omega$ and (ii) an inner disc of radius $2 R$ rotating anti-clockwise with angular speed $\omega / 2$. The ring and disc are separated by frictionless ball bearings. The point $P$ on the inner disc is at a distance $R$ from the origin, where $O P$ makes an angle of $30^{\circ}$ with the horizontal. Then with respect to the horizontal surface,
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ge9QixmoxOpuMhx_qKFq8uhBUqr8BxjSA_VoLSc8lA0.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">the point $O$ has linear velocity $3 R \omega \hat{i}$</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><li class="correct"> <span class="option-label">B</span> <span class="option-data">the point $P$ has linear velocity $\frac{11}{4} R \omega \hat{i}+\frac{\sqrt{3}}{4} R \omega \hat{k}$.</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">the point $P$ has linear velocity $\frac{13}{4} R \omega \hat{i}-\frac{\sqrt{3}}{4} R \omega \hat{k}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">the point $P$ has linear velocity
<br/> <br/>$\left(3-\frac{\sqrt{3}}{4}\right) R \omega \hat{i}+\frac{1}{4} R \omega \hat{k}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">the point $O$ has linear velocity $3 R \omega \hat{i}$, the point $P$ has linear velocity $\frac{11}{4} R \omega \hat{i}+\frac{\sqrt{3}}{4} R \omega \hat{k}$.</span> </div>

answer:
<div class="solution">Velocity at centre 'O' $\quad \therefore \quad \vec{v}_{o}=3 R \omega \hat{i}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/BTLX1MyJcyw68QSy9fxOwAPZRL8YvKBprcNEUT_hdtg.original.fullsize.png"/><br/> <br/> <br/>$\vec{V}_{P}=3 R \omega \hat{i}-\frac{R \omega}{2} \sin 30^{\circ} \hat{i}+\frac{R \omega}{2} \cos 30^{\circ} \hat{k}$
<br/> <br/>$\therefore \quad \vec{V}_{P}=\left[3 R_{\omega} \hat{i}-\frac{R_{\omega}}{4} \hat{i}\right]+\frac{\sqrt{3} R_{\omega}}{4} \hat{k}$
<br/> <br/>or, $\quad \vec{V}_{P}=\frac{11}{4} R_{\omega} \hat{i}+\frac{\sqrt{3}}{4} R_{\omega} \hat{k}$</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-certain-wire-segments-joined-together-to-form-a-coplanar-loop-the-loop-is-placed-in-a-perpendicular-magnetic-field-in-the-direction-g-1

slug:
the-figure-shows-certain-wire-segments-joined-together-to-form-a-coplanar-loop-the-loop-is-placed-in-a-perpendicular-magnetic-field-in-the-direction-g-1-33250

question:
<div class="question">The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular<br/>magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments $a b$ and $c d$. Then,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FmoUDf4PAoABJAyyVwSzfFcrzpNV9UnhNo5asTpqQW8.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$I_1&gt;I_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$I_1 &lt; I_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$I_1$ is in the direction ba and $I_2$ is in the direction $c d$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$</span> </div>

answer:
<div class="solution">Cross $\otimes$ magnetic field passing from the closed loop is increasing. Therefore, from Lenz's law induced current will product $\operatorname{dot} \odot$ magnetic field. Hence, induced current is anticlockwise.</div>


tags: ['Physics', 'Electromagnetic Induction', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-certain-wire-segments-joined-together-to-form-a-coplanar-loop-the-loop-is-placed-in-a-perpendicular-magnetic-field-in-the-direction-g

slug:
the-figure-shows-certain-wire-segments-joined-together-to-form-a-coplanar-loop-the-loop-is-placed-in-a-perpendicular-magnetic-field-in-the-direction-g-35385

question:
<div class="question">The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular<br/>magnetic field in the direction going into the plane of the figure. The magnitude of the field increases with time. $I_1$ and $I_2$ are the currents in the segments $a b$ and $c d$. Then,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/FmoUDf4PAoABJAyyVwSzfFcrzpNV9UnhNo5asTpqQW8.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$I_1&gt;I_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$I_1 &lt; I_2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$I_1$ is in the direction ba and $I_2$ is in the direction $c d$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$I_1$ is in the direction $a b$ and $I_2$ is in the direction $d c$</span> </div>

answer:
<div class="solution">Cross $\otimes$ magnetic field passing from the closed loop is increasing. Therefore, from Lenz's law induced current will product $\operatorname{dot} \odot$ magnetic field. Hence, induced current is anticlockwise.</div>


tags: ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-figure-shows-the-p-v-plot-of-an-ideal-gas-taken-through-a-cycle-a-bc-d-a-the-part-a-bc-is-a-semicircle-and-c-d-a-is-half-of-an-ellipse-then

slug:
the-figure-shows-the-p-v-plot-of-an-ideal-gas-taken-through-a-cycle-a-bc-d-a-the-part-a-bc-is-a-semicircle-and-c-d-a-is-half-of-an-ellipse-then-40028

question:
<div class="question">The figure shows the $p-V$ plot of an ideal gas taken through a cycle $A B C D A$. The part $A B C$ is a semi-circle and $C D A$ is half of an ellipse. Then,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8ZOM6QJfZljyoG_Z3IXKXCQGTFnt5TyhRv-MeUNK0Pw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the process during the path $A \rightarrow B$ is isothermal<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>heat flows out of the gas during the path $B \rightarrow C \rightarrow D$<br/></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"><br/>work done during the path $A \rightarrow B \rightarrow C$ is zero<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>positive work is done by the gas in the cycle $A B C D A$.</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>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>heat flows out of the gas during the path $B \rightarrow C \rightarrow D$<br/>, <br/>positive work is done by the gas in the cycle $A B C D A$.</span> </div>

answer:
<div class="solution">(A) $p-V$ graph is not rectangular hyperbola. Therefore, process $A-B$ is not isothermal.<br/>(B) In process $B C D$, product of $p V$ (therefore temperature and intemal energy) is decreasing. Further, volume is decreasing. Hence, work done is also negative. Hence, $Q$ will be negative or heat will flow out of the gas.<br/>(C) $W_{A B C}=$ positive<br/>(D) For clockwise cycle on $p-V$ diagram with $P$ on $y$-axis, net work done is positive.</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P2.db
title:
the-focal-length-of-a-thin-biconvex-lens-is-20-cm-when-an-object-is-moved-from-a-distance-of-25-cm-in-front-of-it-to-50-cm-the-magnification-of-its-im

slug:
the-focal-length-of-a-thin-biconvex-lens-is-20-cm-when-an-object-is-moved-from-a-distance-of-25-cm-in-front-of-it-to-50-cm-the-magnification-of-its-im-50462

question:
<div class="question">The focal length of a thin biconvex lens is $20 \mathrm{~cm}$. When an object is moved from a distance of $25 \mathrm{~cm}$ in front of it to $50 \mathrm{~cm}$, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is</div>

answer:
<div class="solution">$\frac{1}{v}-\frac{1}{u}=\frac{1}{f}$ or<br/>$$<br/>\frac{u}{v}-1=\frac{u}{f}<br/>$$<br/>$\begin{array}{rlrl} &amp; \text { or } &amp; \frac{u}{v} &amp; =\left(\frac{u+f}{f}\right) \\ \therefore &amp; m=\frac{v}{u} &amp; =\left(\frac{f}{u+f}\right) \\ \frac{m_{25}}{m_{50}} &amp; =\frac{\left(\frac{20}{-25+20}\right)}{\left(\frac{20}{-50+20}\right)}=6\end{array}$<br/>$\therefore$ answer is 6 .</div>


title: the-following-carbohydrate-is-1
slug: the-following-carbohydrate-is-1-67564
tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The following carbohydrate is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LZMccHCZciAHoKNne5T0u7qX1eX5ii5OxbVFDwr8UXk.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>a ketohexose<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>an aldohexose<br/></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"><br/>an $\alpha$-furanose<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>an $\alpha$-pyranose</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>an aldohexose<br/></span> </div>

answer:
<div class="solution">Here, the- $\mathrm{OH}$ of hemiacetal group is equatorial therefore, it is a $\beta$-pyranose of an aldohexose.</div>


tags: ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-freezing-point-in-c-of-solution-containing-01-g-of-k-3-fe-cn-6-molecular-weight-329-in-100-g-of-water-k-f-186-k-kg-mol-1-is

slug:
the-freezing-point-in-c-of-solution-containing-01-g-of-k-3-fe-cn-6-molecular-weight-329-in-100-g-of-water-k-f-186-k-kg-mol-1-is-47570

question:
<div class="question">The freezing point (in ${ }^{\circ} \mathrm{C}$ ) of solution containing $0.1 \mathrm{~g}$ of $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]$ (molecular weight 329$)$ in $100 \mathrm{~g}$ of water $\left(K_f=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$-2.3 \times 10^{-2}$<br/></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"><br/>$-5.7 \times 10^{-2}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$-5.7 \times 10^{-3}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$-1.2 \times 10^{-2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$-2.3 \times 10^{-2}$<br/></span> </div>

answer:
<div class="solution">vant Hoff's factor $(i)=4\left\{3 \mathrm{~K}^{+}+\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}\right\} \quad$ Molality $=\frac{0.1}{329} \times \frac{1000}{100}=\frac{1}{329}$<br/>$$<br/>\Rightarrow \quad-\Delta T_f=i K_f \cdot m=4 \times 1.86 \times \frac{1}{329}=2.3 \times 10^{-2} \Rightarrow T_f=-2.3 \times 10^{-2}{ }^{\circ} \mathrm{C}<br/>$$<br/>(As freezing point of water is $0^{\circ} \mathrm{C}$ )</div>


title: the-function-f-0-3-1-29-defined-by-f-x-2-x-3-15-x-2-36-x-1-is
slug: the-function-f-0-3-1-29-defined-by-f-x-2-x-3-15-x-2-36-x-1-is-29860
tags: ['Mathematics', 'Functions', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The function $f:[0,3] \rightarrow[1,29]$, defined by $f(x)=2 x^{3}-15 x^{2}+36 x+1$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">one-one and onto</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">onto but not one-one</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">one-one but not onto</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">neither one-one nor onto</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">onto but not one-one</span> </div>

answer:
<div class="solution">Given : $f(x)=2 x^{3}-15 x^{2}+36 x+1$
<br/> <br/>$\Rightarrow f^{\prime}(x)=6 x^{2}-30 x+36$
<br/> <br/>$=6\left(x^{2}-5 x+6\right)=6(x-2)(x-3)$
<br/> <br/>$\because f^{\prime}(x)&gt;0 \forall x \in[0,2)$ and $f^{\prime}(x) &lt; 0 \forall x \in(2,3)$
<br/> <br/>$\therefore f(x)$ is increasing on $[0,2)$ and decreasing
<br/> <br/>on $(2,3)$
<br/> <br/>$\therefore \quad f(x)$ is many one on $[0,3]$
<br/> <br/>Also $f(0)=1, f(2)=29, f(3)=28$
<br/> <br/>$\therefore \quad$ Absolute min $=1$ and Absolute max $=29$
<br/> <br/>$\therefore \quad$ Range of $f=[1,29]=$ codomain
<br/> <br/>Hence $f$ is onto.</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-general-motion-of-a-rigid-body-can-be-considered-to-be-a-combination-of-i-a-motion-of-its-centre-of-mass-about-an-axis-and-ii-its-motion-about-an--1

slug:
the-general-motion-of-a-rigid-body-can-be-considered-to-be-a-combination-of-i-a-motion-of-its-centre-of-mass-about-an-axis-and-ii-its-motion-about-an-1-60780

question:
<div class="question">The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
<br/> <br/>These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless, stick, as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed $\omega$, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the $z$-axis and (ii) a rotation
<br/> <br/>of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points $P$ and $Q$ ). Both these motions have the same angular speed $\omega$ in this case
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/k9a0gkqrk76de5TNo7FCtM_RG3uk_Hkg5fwnlMuz3ck.original.fullsize.png"/><br/> <br/> <br/>Now consider two similar systems as shown in the figure: Case
<br/> <br/>(a) the disc with its face vertical and parallel to $x-z$ plane; Case
<br/> <br/>(b) the disc with its face making an angle of
<br/> <br/>$45^{\circ}$ with $x-y$ plane and its horizontal diameter parallel to $x$-axis. In both the cascs, the disc is welded at point $\mathrm{P}$, and the systems are rotated with constant angular speed $\omega$ about the $z$ axis.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T1wfRP1771rg9BSl6YWy11DgkMTVq3us_XJ7HlJYEoE.original.fullsize.png"/><br/><strong> Question:</strong> Which of the following statements about the instantaneous axis (passing through the centre of mass) is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">It is vertical for both the cases (a) and (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">It is vertical for case (a); and is at $45^{\circ}$ to the $x-z$ plane and lies in the plane of the disc for case (b).</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">It is horizontal for case (a); and is at $45^{\circ}$ to the $x$ - $z$ plane and is normal to the plane of the disc for case (b).</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">It is vertical for case (a); and is $45^{\circ}$ to the $x-z$ plane and is normal to the plane of the disc for case (b).</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It is vertical for both the cases (a) and (b)</span> </div>

answer:
<div class="solution">Axis of rotation is parallel to z-axis. Hence for both the cases, in stantaneous axis passing through is vertical.</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
answer: <div class="solution">For rigid body $\omega$ is same for any point of the body.</div>
source_db: MarksBatch2_P2.db
title:
the-general-motion-of-a-rigid-body-can-be-considered-to-be-a-combination-of-i-a-motion-of-its-centre-of-mass-about-an-axis-and-ii-its-motion-about-an-

slug:
the-general-motion-of-a-rigid-body-can-be-considered-to-be-a-combination-of-i-a-motion-of-its-centre-of-mass-about-an-axis-and-ii-its-motion-about-an-17287

question:
<div class="question">The general motion of a rigid body can be considered to be a combination of (i) a motion of its centre of mass about an axis, and (ii) its motion about an instantaneous axis passing through the centre of mass.
<br/> <br/>These axes need not be stationary. Consider, for example, a thin uniform disc welded (rigidly fixed) horizontally at its rim to a massless, stick, as shown in the figure. When the disc-stick system is rotated about the origin on a horizontal frictionless plane with angular speed $\omega$, the motion at any instant can be taken as a combination of (i) a rotation of the centre of mass of the disc about the $z$-axis and (ii) a rotation
<br/> <br/>of the disc through an instantaneous vertical axis passing through its centre of mass (as is seen from the changed orientation of points $P$ and $Q$ ). Both these motions have the same angular speed $\omega$ in this case
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/k9a0gkqrk76de5TNo7FCtM_RG3uk_Hkg5fwnlMuz3ck.original.fullsize.png"/><br/> <br/> <br/>Now consider two similar systems as shown in the figure: Case
<br/> <br/>(a) the disc with its face vertical and parallel to $x-z$ plane; Case
<br/> <br/>(b) the disc with its face making an angle of
<br/> <br/>$45^{\circ}$ with $x-y$ plane and its horizontal diameter parallel to $x$-axis. In both the cascs, the disc is welded at point $\mathrm{P}$, and the systems are rotated with constant angular speed $\omega$ about the $z$ axis.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T1wfRP1771rg9BSl6YWy11DgkMTVq3us_XJ7HlJYEoE.original.fullsize.png"/><br/><strong> Question:</strong> Which of the following statements regarding the angular speed about the instantaneous axis (passing through the centre of mass) is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">It is $\sqrt{2} \omega$ for both the cases</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">It is $\omega$ for case (a); and $\omega / \sqrt{2}$ for case (b)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">It is $\omega$ for case (a); and $\sqrt{2 \omega}$ for case (b)</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">It is $\omega$ for both the cases.</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It is $\omega$ for both the cases.</span> </div>


tags: ['Chemistry', 'States of Matter', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
the-given-graph-represent-the-variations-of-compressibility-factor-z-n-rt-p-v-versus-p-for-three-real-gases-a-b-and-c-identify-the-only-incorrect-stat

slug:
the-given-graph-represent-the-variations-of-compressibility-factor-z-n-rt-p-v-versus-p-for-three-real-gases-a-b-and-c-identify-the-only-incorrect-stat-57599

question:
<div class="question">The given graph represent the variations of compressibility factor $(Z)=\frac{P V}{n R T}$ versus $P$, for three real gases $A, B$ and $C$. Identify the only incorrect statement<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/52Wx1mVwB4vyZ4MyG80f3pQP85ulQXzBavIvYDsPoPI.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/doMmwjz6OWgda2Ocr7mXg2RRo0HlCLjLWfsXTkufUb8.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>For the gas $A, a=0$ and its dependence on $P$ is linear at all pressure.<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>For the gas $B, b=0$ and its dependence on $P$ is linear at all pressure.<br/></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"><br/>For the gas $C$, which is typical real gas for which neither $a$ nor $b=0$. By knowing the minima and point of the intersection, with $Z=1, a$ and $b$ can be calculated.<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>At high pressure, the slope is positive for all real gases.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>For the gas $B, b=0$ and its dependence on $P$ is linear at all pressure.<br/></span> </div>

answer:
<div class="solution">From the graph it is clear that the value of $Z$ decreases with increase of pressure. We can explain as follows on the basis of van der Waals' equation.<br/>At high pressure, when ' $P$ ' is large, $V$ will be small and one can not ignore ' $b$ ' in comparison to $V$.<br/>However, the term $\frac{a}{V^2}$ may be considered negligible in comparison to ' $p$ ' in van der Waals' equation<br/>or<br/>$$<br/>\begin{aligned}<br/>\left(p+\frac{a}{V^2}\right)(V-b) &amp; =n R T \\<br/>P(V-b) &amp; =n R T \\<br/>p V-p b &amp; =n R T \\<br/>\frac{p V}{n R T} &amp; =1+\frac{p b}{n R T} \\<br/>Z &amp; =1+\frac{p b}{n R T}<br/>\end{aligned}<br/>$$<br/>or<br/>Here, $Z$ is greater than one and it increases linearly with pressure. Hence, statement (b) is false.</div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-given-graphsdata-i-ii-iii-and-iv-represent-general-trends-observed-for-different-physisorption-and-chemisorption-processes-under-mild-conditions-o

slug:
the-given-graphsdata-i-ii-iii-and-iv-represent-general-trends-observed-for-different-physisorption-and-chemisorption-processes-under-mild-conditions-o-53499

question:
<div class="question">The given graphs/data I, II, III and IV represent general trends observed for different physisorption and chemisorption processes under mild conditions of temperature and presure. Which of the following choice(s) about I, II, III and IV is (are) correct?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iiL_O4N_ATV7e7GF7H2Gvm0IrJRq38lolz7oPh6F5oM.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/6SI6tnEJ1AqqkUONXv8LTSzBpJSoMt1zcMfr5HT9mSU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">I is physisorption and II is chemisorption</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">$\mathrm{I}$ is physisorption and $\mathrm{III}$ is chemisorption</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">IV is chemisorption and II is chemisorption</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">IV is chemisorption and III is chemisorption</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">I is physisorption and II is chemisorption, IV is chemisorption and II is chemisorption</span> </div>

answer:
<div class="solution">Graph (I) and (III) represent physisorption because, in physisorption, the amount of adsorption decreases with the increase of temperature and increases with the increase of pressure.
<br/> <br/>Graph (II) represent chemisorption, because in chemisorption amount of adsorption increases with the increase of temperature. Graph (IV) is showing the formation of a chemical bond, hence chemisorption.</div>


tags: ['Physics', 'Dual Nature of Matter', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
the-graph-between-1-and-stopping-potential-v-of-three-metals-having-work-function-1-2-and-3-in-an-experiment-of-photoelectric-effect-is-plotted-as-sho

slug:
the-graph-between-1-and-stopping-potential-v-of-three-metals-having-work-function-1-2-and-3-in-an-experiment-of-photoelectric-effect-is-plotted-as-sho-65861

question:
<div class="question">The graph between $1 / \lambda$ and stopping potential $(V)$ of three metals having work function $\phi_1, \phi_2$ and $\phi_3$ in an experiment of photoelectric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here $\lambda$ is the wavelength of the incident ray].<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fn5xOb21duNxkrB5xCJ-bdVJUfvk6qC36_-esP5Eqzw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Ratio of work functions $\phi_1: \phi_2: \phi_3=1: 2: 4$.<br/></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"><br/>Ratio of work functions $\phi_1: \phi_2: \phi_3=4: 2: 1$.<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\tan \theta$ is directly proportional to $h c / e$, where $h$ is Planck's constant and $c$ is the speed of light.<br/></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"><br/>The violet colour light can eject photoelectrons from metals 2 and 3.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>Ratio of work functions $\phi_1: \phi_2: \phi_3=1: 2: 4$.<br/>, <br/>$\tan \theta$ is directly proportional to $h c / e$, where $h$ is Planck's constant and $c$ is the speed of light.<br/></span> </div>

answer:
<div class="solution">From the relation, $e V=\frac{h c}{\lambda}-\phi$ or $V=\left(\frac{h c}{e}\right)\left(\frac{1}{\lambda}\right)-\frac{\phi}{e}$ This is equation of straight line.<br/>Slope is $\tan \theta=\frac{h c}{e}$<br/>$$<br/>\begin{aligned}<br/>\phi_1: \phi_2: \phi_3 &amp; =\frac{h c}{\lambda_{01}}: \frac{h c}{\lambda_{02}}: \frac{h c}{\lambda_{03}}=\frac{1}{\lambda_{01}}: \frac{1}{\lambda_{02}}: \frac{1}{\lambda_{03}}=1: 2: 4 \\<br/>\frac{1}{\lambda_{01}} &amp; =0.001 \mathrm{~nm}^{-1} \text { or } \lambda_{01}=10000 Ã \\<br/>\frac{1}{\lambda_{02}} &amp; =0.002 \mathrm{~nm}^{-1} \text { or } \lambda_{02}=5000 Ã \\<br/>\frac{1}{\lambda_{03}} &amp; =0.004 \mathrm{~nm}^{-1} \text { or } \lambda_{03}=25000 Ã<br/>\end{aligned}<br/>$$<br/>Violet colour has wavelength $4000 Ã$.<br/>So, violet colour can eject photoelectrons from metal-1 and metal-2.</div>


tags: ['Physics', 'Ray Optics', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-graph-between-object-distance-u-and-image-distance-v-for-a-lens-is-given-below-the-focal-length-of-the-lens-is-1

slug:
the-graph-between-object-distance-u-and-image-distance-v-for-a-lens-is-given-below-the-focal-length-of-the-lens-is-1-81363

question:
<div class="question">The graph between object distance $u$ and image distance $v$ for a lens is given below. The focal length of the lens is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tZGEdXFAc0DtJjAK-FuGT4bxrDz1-0-4HbvVzxWT4rE.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$5 \pm 0.1$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$5 \pm 0.05$<br/></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"><br/>$0.5 \pm 0.1$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$0.5 \pm 0.05$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$5 \pm 0.05$<br/></span> </div>

answer:
<div class="solution">From the lens formula:<br/>$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ we have, $\frac{1}{f}=\frac{1}{10}-\frac{1}{-10}$ or $f=+5$<br/>Further, $\Delta u=0.1$ and $\Delta v=0.1$<br/>(from the graph)<br/>Now, differentiating the lens formula we have,<br/>$$<br/>\frac{\Delta f}{f^2}=\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2} \text { or } \Delta f=\left(\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}\right) f^2<br/>$$<br/>Substituting the values we have,<br/>$$<br/>\Delta f=\left(\frac{0.1}{10^2}+\frac{0.1}{10^2}\right)(5)^2 \Rightarrow f \pm \Delta f=5 \pm 0.05<br/>$$</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
title:
the-graph-between-object-distance-u-and-image-distance-v-for-a-lens-is-given-below-the-focal-length-of-the-lens-is

slug:
the-graph-between-object-distance-u-and-image-distance-v-for-a-lens-is-given-below-the-focal-length-of-the-lens-is-86297

question:
<div class="question">The graph between object distance $u$ and image distance $v$ for a lens is given below. The focal length of the lens is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tZGEdXFAc0DtJjAK-FuGT4bxrDz1-0-4HbvVzxWT4rE.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$5 \pm 0.1$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$5 \pm 0.05$<br/></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"><br/>$0.5 \pm 0.1$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$0.5 \pm 0.05$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$5 \pm 0.05$<br/></span> </div>

answer:
<div class="solution">From the lens formula:<br/>$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$ we have, $\frac{1}{f}=\frac{1}{10}-\frac{1}{-10}$ or $f=+5$<br/>Further, $\Delta u=0.1$ and $\Delta v=0.1$<br/>(from the graph)<br/>Now, differentiating the lens formula we have,<br/>$$<br/>\frac{\Delta f}{f^2}=\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2} \text { or } \Delta f=\left(\frac{\Delta v}{v^2}+\frac{\Delta u}{u^2}\right) f^2<br/>$$<br/>Substituting the values we have,<br/>$$<br/>\Delta f=\left(\frac{0.1}{10^2}+\frac{0.1}{10^2}\right)(5)^2 \Rightarrow f \pm \Delta f=5 \pm 0.05<br/>$$</div>


tags: ['Chemistry', 'Solutions', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
the-henrys-law-constant-for-the-solubility-of-n-2-gas-in-water-at-298-k-is-10-105-atm-the-mole-fraction-of-n-2-in-air-is-08-the-number-of-moles-of-n-2

slug:
the-henrys-law-constant-for-the-solubility-of-n-2-gas-in-water-at-298-k-is-10-105-atm-the-mole-fraction-of-n-2-in-air-is-08-the-number-of-moles-of-n-2-22298

question:
<div class="question">The Henry's law constant for the solubility of $\mathrm{N}_2$ gas in water at $298 \mathrm{~K}$ is $1.0 \times 105 \mathrm{~atm}$. The mole fraction of $\mathrm{N}_2$ in air is $0.8$. The number of moles of $\mathrm{N}_2$ from air dissolved in 10 moles of water of $298 \mathrm{~K}$ and $5 \mathrm{~atm}$ pressure is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$4 \times 10^{-4}$<br/></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"><br/>$4.0 \times 10^{-5}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$5.0 \times 10^{-4}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$4.0 \times 10^{-6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$4 \times 10^{-4}$<br/></span> </div>

answer:
<div class="solution">$P_{\mathrm{N}_2}=K_{\mathrm{H}} \times$ mole-fraction $\left(\mathrm{N}_2\right)$ mole-fraction<br/>$$<br/>\mathrm{N}_2 \frac{1}{10^5} \times 0.8 \times 5=4 \times 10^{-5} \mathrm{~mol}^{-1}<br/>$$<br/>In 10 mole solubility in $4 \times 10^{-4}$.</div>


title: the-integral-s-e-c-x-t-a-n-x-2-9-s-e-c-2-x-d-x-equals-for-some-arbitrary-constant-k
slug: the-integral-s-e-c-x-t-a-n-x-2-9-s-e-c-2-x-d-x-equals-for-some-arbitrary-constant-k-68507
tags: ['Mathematics', 'Indefinite Integration', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The integral $\int \frac{\sec ^{2} x}{(\sec x+\tan x)^{\frac{9}{2}}} d x$ equals (for some arbitrary constant $\mathrm{K}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-\frac{1}{(\sec x+\tan x)^{\frac{11}{2}}}\left\{\frac{1}{11}-\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{(\sec x+\tan x)^{\frac{11}{2}}}\left\{\frac{1}{11}-\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$-\frac{1}{(\sec x+\tan x)^{\frac{11}{2}}}\left\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K$</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">$\frac{1}{(\sec x+\tan x)^{\frac{11}{2}}}\left\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{1}{(\sec x+\tan x)^{\frac{11}{2}}}\left\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K$</span> </div>

answer:
<div class="solution">$\begin{array}{l}
<br/> <br/>I=\int \frac{\sec ^{2} x}{(\sec x+\tan x)^{9 / 2}} d x \\
<br/> <br/>\text { Let } \sec x+\tan x=t \Rightarrow \sec x-\tan x=\frac{1}{t} \\
<br/> <br/>\Rightarrow \sec x=\frac{1}{2}\left(t+\frac{1}{t}\right) \text { and } \sec x(\sec x+\tan x) d x=d t \\
<br/> <br/>\Rightarrow \sec x d x=\frac{d t}{t} \\
<br/> <br/>\therefore \quad I=\frac{1}{2} \int \frac{\left(t+\frac{1}{t}\right) d t}{t^{9 / 2} \cdot t}=\frac{1}{2} \int\left(t^{-9 / 2}+t^{-13 / 2}\right) d t \\
<br/> <br/>=\frac{-1}{7} t^{-7 / 2}-\frac{1}{11} t^{-1 / 2}+K \\
<br/> <br/>=-\frac{1}{7 t^{7 / 2}}-\frac{1}{11 t^{11 / 2}}+K=-\frac{1}{t^{11 / 2}}\left(\frac{1}{11}+\frac{t^{2}}{7}\right)+K \\
<br/> <br/>=\frac{-1}{(\sec x+\tan x)^{11 / 2}}\left\{\frac{1}{11}+\frac{1}{7}(\sec x+\tan x)^{2}\right\}+K
<br/> <br/>\end{array}$</div>


title: the-ionization-isomer-of-cr-h-2-o-4-cl-no-2-cl-is
slug: the-ionization-isomer-of-cr-h-2-o-4-cl-no-2-cl-is-37455
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The ionization isomer of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4\left(\mathrm{O}_2 \mathrm{~N}\right)\right] \mathrm{Cl}_2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right]\left(\mathrm{NO}_2\right)$<br/></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"><br/>$\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}(\mathrm{ONO})\right] \mathrm{Cl}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\left(\mathrm{NO}_2\right)\right] \cdot \mathrm{H}_2 \mathrm{O}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right]\left(\mathrm{NO}_2\right)$<br/></span> </div>

answer:
<div class="solution">The ionization isomer of $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}\left(\mathrm{NO}_2\right)\right] \mathrm{Cl}$ is $\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_4 \mathrm{Cl}_2\right] \mathrm{NO}_2$ because of exchanging of ligand and counter ions<br/>Coordination chemistry<br/>Straight conceptual<br/>II</div>


title: the-iupac-name-of-c-6-h-5-cocl-is
slug: the-iupac-name-of-c-6-h-5-cocl-is-80276
question: <div class="question">The IUPAC name of $\mathrm{C}_6 \mathrm{H}_5 \mathrm{COCl}$ is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Benzoyl chloride<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Benzene chloro ketone<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Benzene carbonyl chloride<br/></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"><br/>Chloro phenyl ketone</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Benzene carbonyl chloride<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QgLMmXAODCHmydBEpDz4ul8rO4WCXPNCCiE8aACEAr4.original.fullsize.png"/><br/><br/>is known as benzene carbonyl chloride. Although its trivial name but it is also accepted in IUPAC System</div>


title: the-iupac-name-of-ni-nh-3-4-nicl-4-is
slug: the-iupac-name-of-ni-nh-3-4-nicl-4-is-39524
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
answer: <div class="solution">IUPAC name is tetraamminenickel (II) tetrachloronickelate (II).</div>
source_db: MarksBatch2_P2.db
question:
<div class="question">The IUPAC name of $\left[\mathrm{Ni}\left(\mathrm{NH}_3\right)_4\right]\left[\mathrm{NiCl}_4\right]$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>tetrachloronickel (II) - tetraamminenickel (II)<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>tetraamminenickel (II) - tetrachloronickel (II)<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>tetraamminenickel (II) - tetrachloronickelate (II)<br/></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"><br/>tetrachloronickel (II) - tetraamminenickelate (0)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>tetraamminenickel (II) - tetrachloronickelate (II)<br/></span> </div>


title: the-iupac-name-of-the-following-compound-is-8
slug: the-iupac-name-of-the-following-compound-is-8-94446
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The IUPAC name of the following compound, is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/w6azp8ZVwNJRA1UqThrHxICtM2Jrt8nnrnaVDxHR0ak.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>4-bromo-3-cyanophenol<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>2-bromo-5-hydroxybenzonitrile<br/></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"><br/>2-cyano-4-hydroxybromobenzene<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>6-bromo-3-hydroxybenzonitrile</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>2-bromo-5-hydroxybenzonitrile<br/></span> </div>

answer:
<div class="solution">Cyano group has the highest priority therefore, parent name must be benzonitrile. $\mathrm{Br}$ occurs at 2-position, and hydroxyl at 3-position, hence clockwise numbering will be the correct one.</div>


title: the-kinetic-energy-of-an-electron-in-the-second-bohr-orbit-of-a-hydrogen-atom-is-a-0-is-bohr-radius
tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P2.db
slug:
the-kinetic-energy-of-an-electron-in-the-second-bohr-orbit-of-a-hydrogen-atom-is-a-0-is-bohr-radius-50365

question:
<div class="question">The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is $\left[a_{0}\right.$ is Bohr radius $]$ :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{h^{2}}{4 \pi^{2} m a_{0}^{2}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{h^{2}}{16 \pi^{2} m a_{0}^{2}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{h^{2}}{32 \pi^{2} m a_{0}^{2}}$</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">$\frac{h^{2}}{64 \pi^{2} m a_{0}^{2}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{h^{2}}{32 \pi^{2} m a_{0}^{2}}$</span> </div>

answer:
<div class="solution">As per Bohr's postulate,
<br/> <br/>$\begin{array}{l}
<br/> <br/>m v r=\frac{n h}{2 \pi} \quad \text { So, } v=\frac{n h}{2 \pi m r} \\
<br/> <br/>\mathrm{KE}=\frac{1}{2} m v^{2} \quad \text { So, } \mathrm{KE}=\frac{1}{2} m\left(\frac{n h}{2 \pi m r}\right)^{2}
<br/> <br/>\end{array}$
<br/> <br/>$\text { Since, } r=\frac{a_{\mathrm{o}} \times n^{2}}{z}$
<br/> <br/>So, for $2^{\text {nd }}$ Bohr orbit
<br/> <br/>$\begin{array}{l}
<br/> <br/>r=\frac{a_{\mathrm{o}} \times 2^{2}}{1}=4 a_{\mathrm{o}} \\
<br/> <br/>\mathrm{KE}=\frac{1}{2} m\left(\frac{2^{2} h^{2}}{4 \pi^{2} m^{2} \times\left(4 a_{\mathrm{o}}\right)^{2}}\right)=\frac{h^{2}}{32 \pi^{2} m a_{\mathrm{o}}^{2}}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Atomic Physics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
the-largest-wavelength-in-the-ultraviolet-region-of-the-hydrogen-spectrum-is-122-nm-the-smallest-wavelength-in-the-infrared-region-of-the-hydrogen-spe-1

slug:
the-largest-wavelength-in-the-ultraviolet-region-of-the-hydrogen-spectrum-is-122-nm-the-smallest-wavelength-in-the-infrared-region-of-the-hydrogen-spe-1-89170

question:
<div class="question">The largest wavelength in the ultraviolet region of the hydrogen spectrum is $122 \mathrm{~nm}$. The smallest wavelength in the infrared region of the hydrogen spectrum (to the nearest integer) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$802 \mathrm{~nm}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$823 \mathrm{~nm}$<br/></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"><br/>$1882 \mathrm{~nm}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$1648 \mathrm{~nm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$823 \mathrm{~nm}$<br/></span> </div>

answer:
<div class="solution">The series in $U-V$ region is Lymen series. Longest wavelength corresponds to minimum energy which occurs in transition from $n=2$ to $n=1$.<br/>$$<br/>\therefore \quad 122=\frac{\frac{1}{R}}{\left(\frac{1}{1^2}-\frac{1}{2^2}\right)}<br/>$$<br/>The smallest wavelength in the infrared region corresponds to maximum energy of Paschen series.<br/>$$<br/>\lambda=\frac{\frac{1}{R}}{\left(\frac{1}{3^2}-\frac{1}{\infty}\right)}<br/>$$<br/>Solving Eqs. (i) and (ii), we get<br/>$\therefore$ Correct option is (b).<br/>$$<br/>\lambda=823.5 \mathrm{~nm}<br/>$$</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P2.db
title:
the-letters-of-the-word-cochin-are-permuted-and-all-the-permutations-are-arranged-in-an-alphabetical-order-as-in-an-english-dictionary-the-number-of-w

slug:
the-letters-of-the-word-cochin-are-permuted-and-all-the-permutations-are-arranged-in-an-alphabetical-order-as-in-an-english-dictionary-the-number-of-w-72909

question:
<div class="question">The letters of the word $\mathrm{COCHIN}$ are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word $\mathrm{COCHIN}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>360<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>192<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>97<br/></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"><br/>48</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>97<br/></span> </div>

answer:
<div class="solution">In a word $\mathrm{COCHIN}$, the second place can be filled in ${ }^4 C_1$ ways and the remaining four alphabets can be arranged in $4 !$ ways in four different places. The next $97^{\text {th }}$ word will be COCHIN.</div>


tags: ['Mathematics', 'Hyperbola', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P2.db
title:
the-line-2-x-y-1-is-tangent-to-the-hyperbola-a-2-x-2-b-2-y-2-1-if-this-line-passes-through-the-point-of-intersection-of-the-nearest-directrix-and-the--1

slug:
the-line-2-x-y-1-is-tangent-to-the-hyperbola-a-2-x-2-b-2-y-2-1-if-this-line-passes-through-the-point-of-intersection-of-the-nearest-directrix-and-the-1-63045

question:
<div class="question">The line $2 x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes through the point of intersection of the nearest directrix and the $x$-axis, then the eccentricity of the hyperbola is</div>

answer:
<div class="solution">On substituting $\left(\frac{a}{e}, 0\right)$ in $y=-2 x+1$, we get<br/>$$<br/>\begin{aligned}<br/>0 &amp; =-\frac{2 a}{e}+1 \\<br/>\Rightarrow \quad \frac{a}{e} &amp; =\frac{1}{2}<br/>\end{aligned}<br/>$$<br/>Also, $y=-2 x+1$ is tangent to hyperbola<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; 1=4 a^2-b^2 \\<br/>\Rightarrow &amp; \frac{1}{a^2}=4-\left(e^2-1\right)<br/>\end{array}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NgSyx4jXoTQYo478MXUkIxfQykfFt5KH9BzzdvmUBQE.original.fullsize.png"/><br/><br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; \frac{4}{e^2}=5-e^2 \\<br/>\Rightarrow &amp; e^4-5 e^2+4=0 \\<br/>\Rightarrow &amp; \left(e^2-4\right)\left(e^2-1\right)=0 \\<br/>\Rightarrow &amp; e=2, e=1<br/>\end{array}<br/>$$<br/>$e=1$ gives the conic as parabola. But conic is given as hyperbola, hence $e=2$</div>


tags: ['Mathematics', 'Hyperbola', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P2.db
title:
the-line-2-x-y-1-is-tangent-to-the-hyperbola-a-2-x-2-b-2-y-2-1-if-this-line-passes-through-the-point-of-intersection-of-the-nearest-directrix-and-the-

slug:
the-line-2-x-y-1-is-tangent-to-the-hyperbola-a-2-x-2-b-2-y-2-1-if-this-line-passes-through-the-point-of-intersection-of-the-nearest-directrix-and-the-50964

question:
<div class="question">The line $2 x+y=1$ is tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$. If this line passes through the point of intersection of the nearest directrix and the $x$-axis, then the eccentricity of the hyperbola is</div>

answer:
<div class="solution">On substituting $\left(\frac{a}{e}, 0\right)$ in $y=-2 x+1$, we get<br/>$$<br/>\begin{aligned}<br/>0 &amp; =-\frac{2 a}{e}+1 \\<br/>\Rightarrow \quad \frac{a}{e} &amp; =\frac{1}{2}<br/>\end{aligned}<br/>$$<br/>Also, $y=-2 x+1$ is tangent to hyperbola<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; 1=4 a^2-b^2 \\<br/>\Rightarrow &amp; \frac{1}{a^2}=4-\left(e^2-1\right)<br/>\end{array}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NgSyx4jXoTQYo478MXUkIxfQykfFt5KH9BzzdvmUBQE.original.fullsize.png"/><br/><br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; \frac{4}{e^2}=5-e^2 \\<br/>\Rightarrow &amp; e^4-5 e^2+4=0 \\<br/>\Rightarrow &amp; \left(e^2-4\right)\left(e^2-1\right)=0 \\<br/>\Rightarrow &amp; e=2, e=1<br/>\end{array}<br/>$$<br/>$e=1$ gives the conic as parabola. But conic is given as hyperbola, hence $e=2$</div>


tags: ['Mathematics', 'Ellipse', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-line-passing-through-the-extremity-a-of-the-major-axis-and-extremity-b-of-the-minor-axis-of-the-ellipse-x-2-9-y-2-9-meets-its-auxiliary-circle-at--3

slug:
the-line-passing-through-the-extremity-a-of-the-major-axis-and-extremity-b-of-the-minor-axis-of-the-ellipse-x-2-9-y-2-9-meets-its-auxiliary-circle-at-3-38645

question:
<div class="question">The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9 y^2=9$ meets its auxiliary circle at the point $M$. Then, the area of the triangle with vertices at $A, M$ and the origin $O$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{31}{10}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{29}{10}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{21}{10}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{27}{10}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{27}{10}$</span> </div>

answer:
<div class="solution">Equation of auxiliary circle is<br/>$$<br/>x^2+y^2=9<br/>$$<br/>Equation of $A M$ is $\frac{x}{3}+\frac{y}{1}=1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Hod-rW6Zn2B0oS-2r5NrPWUUUlN7neIAYNLN1KktmLY.original.fullsize.png"/><br/><br/>On solving Eqs. (i) and (ii), we get Coordinates of $M=\left(-\frac{12}{5}, \frac{9}{5}\right)$ Now, area of $\triangle A O M=\frac{1}{2} \times O A \times M N$ $=\frac{27}{10}$ sq units</div>


tags: ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-line-passing-through-the-extremity-a-of-the-major-axis-and-extremity-b-of-the-minor-axis-of-the-ellipse-x-2-9-y-2-9-meets-its-auxiliary-circle-at-

slug:
the-line-passing-through-the-extremity-a-of-the-major-axis-and-extremity-b-of-the-minor-axis-of-the-ellipse-x-2-9-y-2-9-meets-its-auxiliary-circle-at-82305

question:
<div class="question">The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9 y^2=9$ meets its auxiliary circle at the point $M$. Then, the area of the triangle with vertices at $A, M$ and the origin $O$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{31}{10}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{29}{10}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{21}{10}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{27}{10}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{27}{10}$</span> </div>

answer:
<div class="solution">Equation of auxiliary circle is<br/>$$<br/>x^2+y^2=9<br/>$$<br/>Equation of $A M$ is $\frac{x}{3}+\frac{y}{1}=1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Hod-rW6Zn2B0oS-2r5NrPWUUUlN7neIAYNLN1KktmLY.original.fullsize.png"/><br/><br/>On solving Eqs. (i) and (ii), we get Coordinates of $M=\left(-\frac{12}{5}, \frac{9}{5}\right)$ Now, area of $\triangle A O M=\frac{1}{2} \times O A \times M N$ $=\frac{27}{10}$ sq units</div>


tags: ['Mathematics', 'Circle', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-locus-of-the-midpoint-of-the-chord-of-contact-of-tangents-drawn-from-points-lying-on-the-straight-line-4-x-5-y-20-to-the-circle-x-2-y-2-9-is-1

slug:
the-locus-of-the-midpoint-of-the-chord-of-contact-of-tangents-drawn-from-points-lying-on-the-straight-line-4-x-5-y-20-to-the-circle-x-2-y-2-9-is-1-37025

question:
<div class="question">The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4 x-$ $5 y=20$ to the circle $x^{2}+y^{2}=9$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</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">B</span> <span class="option-data">$20\left(x^{2}+y^{2}\right)+36 x-45 y=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$36\left(x^{2}+y^{2}\right)-20 x+45 y=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$36\left(x^{2}+y^{2}\right)+20 x-45 y=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</span> </div>

answer:
<div class="solution">Any point $P$ on line $4 x-5 y=20$ can be considered as $\left(\alpha, \frac{4 \alpha-20}{5}\right)$.
<br/> <br/>Equation of chord of contact $A B$ to the circle $x^{2}+y^{2}=9$
<br/> <br/>drawn from point $\mathrm{P}\left(\alpha, \frac{4 \alpha-20}{5}\right)$ is
<br/> <br/>x. $\alpha+$ y. $\left(\frac{4 \alpha-20}{5}\right)=9...(i)$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zkFIWBdkdHID8Ep1HUGZDpd4kkJTYXASn79_Szm3a1E.original.fullsize.png"/><br/> <br/> <br/>Also the equation of chord $A B$ whose mid point is $(h, k)$ is $h x+k y=h^{2}+k^{2}....(ii)$
<br/> <br/>$\because \quad$ Equations (i) and (ii) represent the same line,
<br/> <br/>$\therefore \quad \frac{h}{\alpha}=\frac{k}{\frac{4 \alpha-20}{5}}=\frac{h^{2}+k^{2}}{9}$
<br/> <br/>$\Rightarrow 5 k \alpha=4 h \alpha-20 h$ and $9 h=\alpha\left(h^{2}+k^{2}\right)$
<br/> <br/>$\Rightarrow \alpha=\frac{20 h}{4 h-5 k} \quad$ and $\alpha=\frac{9 h}{h^{2}+k^{2}}$
<br/> <br/>$\Rightarrow \quad \frac{20 h}{4 h-5 k}=\frac{9 h}{h^{2}+k^{2}} \Rightarrow 20\left(h^{2}+k^{2}\right)=9(4 h-5 k)$
<br/> <br/>$\therefore \quad$ Locus of $(h, k)$ is $20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</div>


tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-locus-of-the-midpoint-of-the-chord-of-contact-of-tangents-drawn-from-points-lying-on-the-straight-line-4-x-5-y-20-to-the-circle-x-2-y-2-9-is

slug:
the-locus-of-the-midpoint-of-the-chord-of-contact-of-tangents-drawn-from-points-lying-on-the-straight-line-4-x-5-y-20-to-the-circle-x-2-y-2-9-is-52305

question:
<div class="question">The locus of the mid-point of the chord of contact of tangents drawn from points lying on the straight line $4 x-$ $5 y=20$ to the circle $x^{2}+y^{2}=9$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</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">B</span> <span class="option-data">$20\left(x^{2}+y^{2}\right)+36 x-45 y=0$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$36\left(x^{2}+y^{2}\right)-20 x+45 y=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$36\left(x^{2}+y^{2}\right)+20 x-45 y=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</span> </div>

answer:
<div class="solution">Any point $P$ on line $4 x-5 y=20$ can be considered as $\left(\alpha, \frac{4 \alpha-20}{5}\right)$.
<br/> <br/>Equation of chord of contact $A B$ to the circle $x^{2}+y^{2}=9$
<br/> <br/>drawn from point $\mathrm{P}\left(\alpha, \frac{4 \alpha-20}{5}\right)$ is
<br/> <br/>x. $\alpha+$ y. $\left(\frac{4 \alpha-20}{5}\right)=9...(i)$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zkFIWBdkdHID8Ep1HUGZDpd4kkJTYXASn79_Szm3a1E.original.fullsize.png"/><br/> <br/> <br/>Also the equation of chord $A B$ whose mid point is $(h, k)$ is $h x+k y=h^{2}+k^{2}....(ii)$
<br/> <br/>$\because \quad$ Equations (i) and (ii) represent the same line,
<br/> <br/>$\therefore \quad \frac{h}{\alpha}=\frac{k}{\frac{4 \alpha-20}{5}}=\frac{h^{2}+k^{2}}{9}$
<br/> <br/>$\Rightarrow 5 k \alpha=4 h \alpha-20 h$ and $9 h=\alpha\left(h^{2}+k^{2}\right)$
<br/> <br/>$\Rightarrow \alpha=\frac{20 h}{4 h-5 k} \quad$ and $\alpha=\frac{9 h}{h^{2}+k^{2}}$
<br/> <br/>$\Rightarrow \quad \frac{20 h}{4 h-5 k}=\frac{9 h}{h^{2}+k^{2}} \Rightarrow 20\left(h^{2}+k^{2}\right)=9(4 h-5 k)$
<br/> <br/>$\therefore \quad$ Locus of $(h, k)$ is $20\left(x^{2}+y^{2}\right)-36 x+45 y=0$</div>


tags: ['Mathematics', 'Straight Lines', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-locus-of-the-orthocentre-of-the-triangle-formed-by-the-lines-1-p-x-p-y-p-1-p-0-1-q-x-q-y-q-1-q-0-and-y-0-where-p-q-is-1

slug:
the-locus-of-the-orthocentre-of-the-triangle-formed-by-the-lines-1-p-x-p-y-p-1-p-0-1-q-x-q-y-q-1-q-0-and-y-0-where-p-q-is-1-69232

question:
<div class="question">The locus of the orthocentre of the triangle formed by the lines $(1+p) x-p y+p(1+p)=0$, $(1+q) x-q y+q(1+q)=0$ and $y=0$, where $p \neq q$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>a hyperbola<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>a parabola<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>an ellipse<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>a straight line</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>a straight line</span> </div>

answer:
<div class="solution">Given, lines are<br/>$$<br/>(1+p) x-p y+p(1+p)=0<br/>$$<br/>and $(1+q) x-q y+q(1+q)=0$<br/>On solving Eqs. (i) and (ii), we get<br/>$$<br/>C\{p q,(1+p)(1+q)\}<br/>$$<br/><br/>$\therefore$ Equation of altitude $C M$ passing through $C$ and perpendicular to $A B$ is<br/>$$<br/>x=p q<br/>$$<br/>$\because$ Slope of line (ii) is $\left(\frac{1+q}{q}\right)$.<br/>$\therefore$ Slope of altitude $B N$ (as shown in figure) is $\frac{-q}{1+q}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KuYdPR9jmFax0y6klYaQcg1EstIIJR540LdVt85WdZk.original.fullsize.png"/><br/><br/>$\therefore$ Equation of $B N$ is $y-0=\frac{-q}{1+q}(x+p)$<br/>$$<br/>\Rightarrow \quad y=\frac{-q}{(1+q)}(x+p)<br/>$$<br/>Let orthocentre of triangle be $H(h, k)$, which is the point of intersection of Eqs. (iii) and (iv)<br/>On solving Eqs. (iii) and (iv), we get $x=p q$ and $y=-p q \Rightarrow h=p q$ and $k=-p q \Rightarrow h+k=0$<br/>$\therefore$ Locus of $H(h, k)$ is $x+y=0$.</div>


tags: ['Mathematics', 'Straight Lines', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
the-locus-of-the-orthocentre-of-the-triangle-formed-by-the-lines-1-p-x-p-y-p-1-p-0-1-q-x-q-y-q-1-q-0-and-y-0-where-p-q-is

slug:
the-locus-of-the-orthocentre-of-the-triangle-formed-by-the-lines-1-p-x-p-y-p-1-p-0-1-q-x-q-y-q-1-q-0-and-y-0-where-p-q-is-10916

question:
<div class="question">The locus of the orthocentre of the triangle formed by the lines $(1+p) x-p y+p(1+p)=0$, $(1+q) x-q y+q(1+q)=0$ and $y=0$, where $p \neq q$, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>a hyperbola<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>a parabola<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>an ellipse<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>a straight line</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>a straight line</span> </div>

answer:
<div class="solution">Given, lines are<br/>$$<br/>(1+p) x-p y+p(1+p)=0<br/>$$<br/>and $(1+q) x-q y+q(1+q)=0$<br/>On solving Eqs. (i) and (ii), we get<br/>$$<br/>C\{p q,(1+p)(1+q)\}<br/>$$<br/><br/>$\therefore$ Equation of altitude $C M$ passing through $C$ and perpendicular to $A B$ is<br/>$$<br/>x=p q<br/>$$<br/>$\because$ Slope of line (ii) is $\left(\frac{1+q}{q}\right)$.<br/>$\therefore$ Slope of altitude $B N$ (as shown in figure) is $\frac{-q}{1+q}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/KuYdPR9jmFax0y6klYaQcg1EstIIJR540LdVt85WdZk.original.fullsize.png"/><br/><br/>$\therefore$ Equation of $B N$ is $y-0=\frac{-q}{1+q}(x+p)$<br/>$$<br/>\Rightarrow \quad y=\frac{-q}{(1+q)}(x+p)<br/>$$<br/>Let orthocentre of triangle be $H(h, k)$, which is the point of intersection of Eqs. (iii) and (iv)<br/>On solving Eqs. (iii) and (iv), we get $x=p q$ and $y=-p q \Rightarrow h=p q$ and $k=-p q \Rightarrow h+k=0$<br/>$\therefore$ Locus of $H(h, k)$ is $x+y=0$.</div>


title: the-major-product-h-of-the-given-reaction-sequence-is-1
slug: the-major-product-h-of-the-given-reaction-sequence-is-1-90266
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Main']
source_db: MarksBatch2_P3.db
question:
<div class="question">$\text { The major product } \mathbf{H} \text { of the given reaction sequence is }$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9hGH0plbQZZ667B_58RWt98VP52jn-WInJEET-LZnuc.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QpA8INzF4E1M4tIYuD1xmRVW7S48A7hUSjScbsMJlIw.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">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/_TSEKRfkSKCrQ3N9q4TmPIAyyTicyZdGQWD-dYzu2Uo.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/jee_advanced/Drjn_Tiw6rTmih42lwfbKCDui_GrO0h19j4SXufvoFY.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tp54PuL5MFst9JPLLhKAD7LndK5gS-59QLfiiy9s2oI.original.fullsize.png"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QpA8INzF4E1M4tIYuD1xmRVW7S48A7hUSjScbsMJlIw.original.fullsize.png"/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Ydx81jlla_heO3neqGbY5AJctDIwmVGM4DhnC1sOLNk.original.fullsize.png"/></div>


title: the-major-product-of-the-following-reaction-is-63
slug: the-major-product-of-the-following-reaction-is-63-97585
tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The major product of the following reaction is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/J7J35P-8NLJdFJ-RzFRBhfDQZUbpXGRhXFBSYHoanlw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4st1lqaE10UHFMQ7JmH7Lg6vOQToMH5oi1a_oQzkL8g.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/uNZqKlaG27-DQEvSAzj74McBjUUreeZnYIPSt8Q_bis.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/gM200u5M1w27QYcSryLLfsW9mFjyaIft53WYLGgpy2I.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iHfyg4ahMiQYBDcY_d9Mt9Qh78VanpbjHNdrxVTHV94.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4st1lqaE10UHFMQ7JmH7Lg6vOQToMH5oi1a_oQzkL8g.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$\mathrm{PhS}^{-}$is a strong nucleophile and dimethylformamide (DMF) is a highly polar aprotic solvent. Condition indicates that nucleophilic substitution $\left(\mathrm{S}_{\mathrm{N}} 2\right)$ takes place at $2^{\circ}$ benzylic place, stereochemically it involves inversion of configuration.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/lCIeCvJ3B6Mr_ZmG8u7nddUDMXVFitGj550V4s_YDQU.original.fullsize.png"/><br/><br/>Aryl group can exhibit neighbouring group or can show anchimeric assistance but not possible here due to deactivity imparted by $-\mathrm{NO}_2$ and $-\mathrm{F}$. It can be if $-\mathrm{OCH}_3$ would have been instead of $-\mathrm{NO}_2$.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jKeexw3aFTvCJAqz9sT8rE6xkc0YtE6Wmhx8gjSO0C4.original.fullsize.png"/><br/></div>


title: the-major-product-of-the-following-reaction-is-64
slug: the-major-product-of-the-following-reaction-is-64-34619
tags: ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The major product of the following reaction is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/lh0_INxc7OX6W4ob4oDr3E7UOOL2542bF-c8IJP35Fc.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fpYJTUKv8yDLVc5YLPbIZk7cBRJ5wwyHKsvALs5lQAQ.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-5QbZjQAM1ugZsv0WMrUyaCw7u9QgzqUs4b4tEDJzFM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/aTDXxOCHz7QylfUuGoy6uCg-Jwnxg0IHEr5w16_XWaU.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/GAds1b1SMKyU1lcKE12Y1Jpg6vwu1snRPFZPwe2Aieg.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fpYJTUKv8yDLVc5YLPbIZk7cBRJ5wwyHKsvALs5lQAQ.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">It is the first step of Gabriel's phthalimide synthesis. The hydrogen bonded to nitrogen is sufficiently acidic due to two $\alpha$-carbonyls.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/MpnEYdJ1f8onZDPwkextCp1o9AxM-68WlKCLasdgo8A.original.fullsize.png"/><br/><br/>The conjugate base formed above act as nucleophile in the subsequent step of reaction. As shown above, the nucleophile exist in three resonating form, one may think of oxygen being the donor atom in the nucleophilic attack. However, nitrogen act as donor as it is better donor than oxygen.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/hZVnJUCQWIQNQThoHTPjsAuy-_t2OXdFoSbBZMthPOA.original.fullsize.png"/><br/><br/>Bromine is not substituted in the above reaction as it is in resonance with benzene ring giving partial double bond character to $\mathrm{C}-\mathrm{Br}$ bond, hence difficult to break.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/TlGg23g9rmm8w6E90tvBxn16wIOKwVTC99xBlYY_EQA.original.fullsize.png"/><br/></div>


title: the-major-product-of-the-following-reaction-is-65
slug: the-major-product-of-the-following-reaction-is-65-47237
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The major product of the following reaction is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/RAVy9LmbIZ5H6K9Afv6-dXiW2Nsl65kK4Ku386PMIEE.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>a hemiacetal<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>an acetal<br/></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"><br/>an ether<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>an ester</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>an acetal<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZDjGkM4X0TwBQKUBRrdBkR7LWj9drrM5Jlzj-hHqJcc.original.fullsize.png"/><br/></div>


title: the-major-products-p-and-q-are
slug: the-major-products-p-and-q-are-99455
tags: ['Chemistry', 'Carboxylic Acid Derivatives', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch2_P3.db
question:
<div class="question"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/62dw58hJjDT5agcIqqoV_iZjFa0BgQl3GCNmB-4lPVk.original.fullsize.png"/><br/><br/>$$<br/>\text { The major products } P \text { and } Q \text { are }<br/>$$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/CxAlF9x3M8ofU8sdbG8RZUGYcQxw3frmFWoatGb0rNA.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/cRB80stYqMstJ7l0uceGKED2_Qyu5Akp2S3yIpWtxnU.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/AdVu5GqXKXCVEsekuDCafp64f_LTIbbzuaAGwtlAGQk.original.fullsize.png"/><br/></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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/16IQPa_HcUkC256-20gMuXpxGhMvg2DtvlKC1ronOlc.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/AdVu5GqXKXCVEsekuDCafp64f_LTIbbzuaAGwtlAGQk.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$$<br/>\text { It is cumene hydroperoxide rearrangement. }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kb2FysgWaVf9kjWs39YI3KcutzetM-BTXr-u-PAXU_8.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-mass-m-shown-in-the-figure-oscillates-in-simple-harmonic-motion-with-amplitude-a-the-amplitude-of-the-point-p-is-1

slug:
the-mass-m-shown-in-the-figure-oscillates-in-simple-harmonic-motion-with-amplitude-a-the-amplitude-of-the-point-p-is-1-14339

question:
<div class="question">The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/qNHPtmQUqjn_4Y0wNq4MzTRZTsXxFflTW9vRyMulmy4.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{k_a A}{k_2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{k_2 A}{k_1}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{k_1 A}{k_1+k_2}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{k_2 A}{k_1+k_2}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{k_2 A}{k_1+k_2}$</span> </div>

answer:
<div class="solution">$x_1+x_2=A$ and $k_1 x_1=k_2 x_2$ or $\frac{x_1}{x_2}=\frac{k_2}{k_1}$<br/>Solving these equations, we get<br/>$$<br/>x_1=\left(\frac{k_2}{k_1+k_2}\right) A<br/>$$</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
the-mass-m-shown-in-the-figure-oscillates-in-simple-harmonic-motion-with-amplitude-a-the-amplitude-of-the-point-p-is

slug:
the-mass-m-shown-in-the-figure-oscillates-in-simple-harmonic-motion-with-amplitude-a-the-amplitude-of-the-point-p-is-96603

question:
<div class="question">The mass $M$ shown in the figure oscillates in simple harmonic motion with amplitude $A$. The amplitude of the point $P$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/qNHPtmQUqjn_4Y0wNq4MzTRZTsXxFflTW9vRyMulmy4.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{k_a A}{k_2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{k_2 A}{k_1}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{k_1 A}{k_1+k_2}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{k_2 A}{k_1+k_2}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{k_2 A}{k_1+k_2}$</span> </div>

answer:
<div class="solution">$x_1+x_2=A$ and $k_1 x_1=k_2 x_2$ or $\frac{x_1}{x_2}=\frac{k_2}{k_1}$<br/>Solving these equations, we get<br/>$$<br/>x_1=\left(\frac{k_2}{k_1+k_2}\right) A<br/>$$</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch2_P3.db
title:
the-maximum-number-of-electrons-that-can-have-principal-quantum-number-n-3-and-spin-quantum-number-m-s-2-1-is

slug:
the-maximum-number-of-electrons-that-can-have-principal-quantum-number-n-3-and-spin-quantum-number-m-s-2-1-is-14588

question:
<div class="question">The maximum number of electrons that can have principal quantum number, $n=3$ and spin quantum number, $m_s=-\frac{1}{2}$, is</div>

answer:
<div class="solution">When $n=3, l=0,1,2$ i.e., there are $3 s, 3 p$ and $3 d$ orbitals. If all these orbitals are completely occupied as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/--JalBtpZ6vJYh3xV-8N3LQdEEDqdYJirgMbN3GBHeE.original.fullsize.png"/><br/><br/>$$<br/>\text { Total } 18 \text { electrons, } 9 \text { electrons with } s=+\frac{1}{2} \text { and } 9 \text { with } s=-\frac{1}{2} .<br/>$$<br/>Alternatively In any $n$th orbit, there can be a maximum of $2 n^2$ electrons. Hence, when $n=3$, number of maximum electrons $=18$. Out of these 18 electrons, 9 can have spin $-\frac{1}{2}$ and remaining nine with spin $=+\frac{1}{2}$.</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
title:
the-maximum-number-of-isomers-including-stereoisomers-that-are-possible-on-monochlorination-of-the-following-compounds-is

slug:
the-maximum-number-of-isomers-including-stereoisomers-that-are-possible-on-monochlorination-of-the-following-compounds-is-97846

question:
<div class="question">The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compounds, is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JeNF0d7k61aH5ughmPwYN1pnR6BelAftYr5mz-uA5aI.original.fullsize.png"/><br/></div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/IOaa7WUzCUYZoSZPBoLtPiymdayUAM8RrraVu0baORI.original.fullsize.png"/><br/><br/>I has one chiral carbon $=$ two isomers II has two chiral carbons and no symmetry $=$ four isomers.<br/>III and IV have no chiral carbon, no stereoisomers.</div>


title: the-maximum-value-of-the-expression-s-i-n-2-3-s-i-n-c-o-s-5-c-o-s-2-1-is
slug: the-maximum-value-of-the-expression-s-i-n-2-3-s-i-n-c-o-s-5-c-o-s-2-1-is-74063
tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The maximum value of the expression $\frac{1}{\sin ^2 \theta+3 \sin \theta \cos \theta+5 \cos ^2 \theta}$ is</div>

answer:
<div class="solution">Let<br/>$$<br/>\begin{aligned}<br/>&amp; f(\theta)=\frac{1}{\sin ^2 \theta+3 \sin \theta \cos \theta+5 \cos ^2 \theta} \\<br/>&amp; \text { Again let } \\<br/>&amp; g(\theta)=\sin ^2 \theta+3 \sin \theta \cos \theta+5 \cos ^2 \theta \\<br/>&amp; =\frac{1-\cos 2 \theta}{2}+5\left(\frac{1+\cos 2 \theta}{2}\right)+\frac{3}{2} \sin 2 \theta \\<br/>&amp; =3+2 \cos 2 \theta+\frac{3}{2} \sin 2 \theta \\<br/>&amp; \therefore \quad g(\theta)_{\min }=3-\sqrt{4+\frac{9}{4}}=3-\frac{5}{2}=\frac{1}{2} \\<br/>&amp; \therefore \quad f(\theta)=\frac{1}{g(\theta)_{\min }}=2<br/>\end{aligned}<br/>$$</div>


title: the-maximum-value-of-the-function-f-x-2-x-3-15-x-2-36-x-48-on-the-set-a-x-x-2-20-9-x-is
slug: the-maximum-value-of-the-function-f-x-2-x-3-15-x-2-36-x-48-on-the-set-a-x-x-2-20-9-x-is-76225
tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The maximum value of the function $f(x)=2 x^3-15 x^2+36 x-48$ on the set $A=\left\{x \mid x^2+20 \leq 9 x\right\}$ is</div>

answer:
<div class="solution">Given, $\quad A=\left\{x \mid x^2+20 \leq 9 x\right\}$ $=\{x \mid x \in[4,5]\}$<br/>Now, $f^{\prime}(x)=6\left(x^2-5 x+6\right)$<br/>Put $\quad f^{\prime}(x)=0 \Rightarrow x=2,3$<br/>$f(2)=-20, f(3)=-21$,<br/>$f(4)=-16, f(5)=7$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mEW_vIq8xq9QBru_tFUMUU1wi-RfOrrWT0nYPgn4aLo.original.fullsize.png"/><br/><br/>From graph, maximum of $f(x)$ on set $A$ is $f(5)=7$.</div>


title: the-minimum-value-of-the-sum-of-real-numbers-a-5-a-4-3-a-3-1-a-8-and-a-10-with-a-0-is
slug: the-minimum-value-of-the-sum-of-real-numbers-a-5-a-4-3-a-3-1-a-8-and-a-10-with-a-0-is-83855
tags: ['Mathematics', 'Sequences and Series', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The minimum value of the sum of real numbers $a^{-5}, a^{-4}, 3 a^{-3}, 1, a^8$ and $a^{10}$ with $a&gt;0$ is</div>

answer:
<div class="solution">Using $A M \geq G M$,<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{a^{-5}+a^{-4}+a^{-3}+a^{-3}+a^{-3}+1+a^8+a^{10}}{8} \\<br/>&amp; \geq\left(a^{-5} \cdot a^{-4} \cdot a^{-3} \cdot a^{-3} \cdot a^{-3} \cdot 1 \cdot a^8 \cdot a^{10}\right)^{\frac{1}{8}} \\<br/>&amp; \Rightarrow a^{-5}+a^{-4}+3 a^{-3}+1+a^8+a^{10} \geq 8 \cdot 1<br/>\end{aligned}<br/>$$<br/>Hence, minimum value is 8 .</div>


title: the-nitrogen-oxides-that-contains-nn-bonds-is-are
slug: the-nitrogen-oxides-that-contains-nn-bonds-is-are-99782
question: <div class="question">The nitrogen oxide(s) that contain(s) N.N bond(s) is (are)</div>
source_db: MarksBatch2_P3.db
tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{N}_2 \mathrm{O}$<br/></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">B</span> <span class="option-data"><br/>$\mathrm{N}_2 \mathrm{O}_3$<br/></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"><br/>$\mathrm{N}_2 \mathrm{O}_4$<br/></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"><br/>$\mathrm{N}_2 \mathrm{O}_5$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\mathrm{N}_2 \mathrm{O}$<br/>, <br/>$\mathrm{N}_2 \mathrm{O}_3$<br/>, <br/>$\mathrm{N}_2 \mathrm{O}_4$<br/></span> </div>

answer:
<div class="solution">(a) <img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/HVJ5m1pJ3hYCSttiQB34MosIV8_zEG62xhnxyAnV5PM.original.fullsize.png"/><br/><br/>(b)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/00sH_Dr9ZwSwzKvxfxgUgOxQPrfM9jvNLxkhXKwXzvo.original.fullsize.png"/><br/><br/>(c)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/JN_jTHSw9fXDiA-m7uDlw1qSSFjTqziJ1WxKhVRz87M.original.fullsize.png"/><br/><br/>(d)<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U2BhVoXzwXPQ4pLAr47LKrD5KZKTb1iXR_GByQ5GBWI.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Ellipse', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
the-normal-at-a-point-p-on-the-ellipse-x-2-4-y-2-16-meets-the-x-axis-at-q-if-m-is-the-midpoint-of-the-line-segment-pq-then-the-locus-of-m-intersects-t-1

slug:
the-normal-at-a-point-p-on-the-ellipse-x-2-4-y-2-16-meets-the-x-axis-at-q-if-m-is-the-midpoint-of-the-line-segment-pq-then-the-locus-of-m-intersects-t-1-78746

question:
<div class="question">The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid-point of the line segment $P Q$, then the locus of $M$ intersects the latusrectum of the given ellipse at the points</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(\pm \frac{3 \sqrt{5}}{2}, \pm \frac{2}{7}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\pm \frac{3 \sqrt{5}}{2}, \pm \frac{\sqrt{19}}{4}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$<br/></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"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{4 \sqrt{3}}{7}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$<br/></span> </div>

answer:
<div class="solution">Given, $\quad \frac{x^2}{16}+\frac{y^2}{4}=1$<br/>Here, $\quad a=4, b=2$<br/>Equation of normal is<br/>$$<br/>\begin{aligned}<br/>&amp; 4 x \sec \theta-2 y \operatorname{cosec} \theta=12 \\<br/>&amp; M\left(\frac{7 \cos \theta}{2}, \sin \theta\right)=(h, k) \text { (say) } \\<br/>&amp; \therefore \quad h=\frac{7 \cos \theta}{2} \Rightarrow \cos \theta=\frac{2 h}{7} \\<br/>&amp; {\left[\because \cos ^2 \theta+\sin ^2 \theta=1\right]} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Hence, locus is $\frac{4 x^2}{49}+y^2=1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h5Ha-7vIkDAyJhn9AIK2wVfBtoXgLlrlSF9VVmEZDp0.original.fullsize.png"/><br/><br/>For given ellipse, $e^2=1-\frac{4}{16}=\frac{3}{4}$<br/>$$<br/>\begin{array}{rc}<br/>\therefore \quad e=\frac{\sqrt{3}}{2} \\<br/>\therefore \quad x=\pm 4 \times \frac{\sqrt{3}}{2}=\pm 2 \sqrt{3} \\<br/>&amp; {[\because x=\pm a e] \ldots \text { (ii) }}<br/>\end{array}<br/>$$<br/>On solving Eqs. (i) and (ii), we get<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{4}{49} \times 12+y^2=1 \Rightarrow y^2=1-\frac{48}{49}=\frac{1}{49} \\<br/>&amp; \Rightarrow \quad y=\pm \frac{1}{7}<br/>\end{aligned}<br/>$$<br/>$\therefore$ Required points $\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$.</div>


tags: ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch2_P3.db
title:
the-normal-at-a-point-p-on-the-ellipse-x-2-4-y-2-16-meets-the-x-axis-at-q-if-m-is-the-midpoint-of-the-line-segment-pq-then-the-locus-of-m-intersects-t

slug:
the-normal-at-a-point-p-on-the-ellipse-x-2-4-y-2-16-meets-the-x-axis-at-q-if-m-is-the-midpoint-of-the-line-segment-pq-then-the-locus-of-m-intersects-t-80857

question:
<div class="question">The normal at a point $P$ on the ellipse $x^2+4 y^2=16$ meets the $x$-axis at $Q$. If $M$ is the mid-point of the line segment $P Q$, then the locus of $M$ intersects the latusrectum of the given ellipse at the points</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left(\pm \frac{3 \sqrt{5}}{2}, \pm \frac{2}{7}\right)$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\left(\pm \frac{3 \sqrt{5}}{2}, \pm \frac{\sqrt{19}}{4}\right)$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$<br/></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"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{4 \sqrt{3}}{7}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$<br/></span> </div>

answer:
<div class="solution">Given, $\quad \frac{x^2}{16}+\frac{y^2}{4}=1$<br/>Here, $\quad a=4, b=2$<br/>Equation of normal is<br/>$$<br/>\begin{aligned}<br/>&amp; 4 x \sec \theta-2 y \operatorname{cosec} \theta=12 \\<br/>&amp; M\left(\frac{7 \cos \theta}{2}, \sin \theta\right)=(h, k) \text { (say) } \\<br/>&amp; \therefore \quad h=\frac{7 \cos \theta}{2} \Rightarrow \cos \theta=\frac{2 h}{7} \\<br/>&amp; {\left[\because \cos ^2 \theta+\sin ^2 \theta=1\right]} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Hence, locus is $\frac{4 x^2}{49}+y^2=1$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h5Ha-7vIkDAyJhn9AIK2wVfBtoXgLlrlSF9VVmEZDp0.original.fullsize.png"/><br/><br/>For given ellipse, $e^2=1-\frac{4}{16}=\frac{3}{4}$<br/>$$<br/>\begin{array}{rc}<br/>\therefore \quad e=\frac{\sqrt{3}}{2} \\<br/>\therefore \quad x=\pm 4 \times \frac{\sqrt{3}}{2}=\pm 2 \sqrt{3} \\<br/>&amp; {[\because x=\pm a e] \ldots \text { (ii) }}<br/>\end{array}<br/>$$<br/>On solving Eqs. (i) and (ii), we get<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{4}{49} \times 12+y^2=1 \Rightarrow y^2=1-\frac{48}{49}=\frac{1}{49} \\<br/>&amp; \Rightarrow \quad y=\pm \frac{1}{7}<br/>\end{aligned}<br/>$$<br/>$\therefore$ Required points $\left(\pm 2 \sqrt{3}, \pm \frac{1}{7}\right)$.</div>


tags: ['Mathematics', 'Matrices', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-number-of-3-3-matrices-a-whose-entries-are-either-0-or-1-and-for-which-the-system-a-x-y-z-1-0-0-has-exactly-two-distinct-solutions-is

slug:
the-number-of-3-3-matrices-a-whose-entries-are-either-0-or-1-and-for-which-the-system-a-x-y-z-1-0-0-has-exactly-two-distinct-solutions-is-96312

question:
<div class="question">The number of $3 \times 3$ matrices $A$ whose entries are either 0 or 1 and for which the system $A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ has exactly two distinct solutions, is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></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"><br/>$2^9-1$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>168<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>0<br/></span> </div>

answer:
<div class="solution">Since, $A\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$ is linear equation in three variables and that could have only unique, no solution or infinitely many solution.<br/>$\therefore$ It is not possible to have two solutions.<br/>Hence, number of matrices $A$ is zero.</div>


title: the-number-of-aldol-reactions-that-occurs-in-the-given-transformation-is-1
slug: the-number-of-aldol-reactions-that-occurs-in-the-given-transformation-is-1-53342
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of aldol reaction(s) that occurs in the given transformation is :
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U0AbEP_iygJaMY3hn2NEhIhRGhN4vq4IyPd8VoFoWkg.original.fullsize.png"/></div>

options:
<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">2</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">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">4</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h5rkmFGETMkvFcE0OfNTHNhX_tcLHGeKPhNb7sORbHU.original.fullsize.png"/></div>


tags: ['Mathematics', 'Trigonometric Equations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-all-possible-values-of-where-0-for-which-the-system-of-equations-y-z-cos-3-x-yz-sin-3-x-sin-3-y-2-c-o-s-3-z-2-s-i-n-3-an-d-x-y-z-sin-3-t

slug:
the-number-of-all-possible-values-of-where-0-for-which-the-system-of-equations-y-z-cos-3-x-yz-sin-3-x-sin-3-y-2-c-o-s-3-z-2-s-i-n-3-an-d-x-y-z-sin-3-t-61131

question:
<div class="question">The number of all possible values of $\theta$, where $0 &lt; \theta &lt; \pi$, for which the system of equations<br/>$$<br/>\begin{array}{r}<br/>(y+z) \cos 3 \theta=(x y z) \sin 3 \theta \\<br/>x \sin 3 \theta=\frac{2 \cos 3 \theta}{y}+\frac{2 \sin 3 \theta}{z}<br/>\end{array}<br/>$$<br/>and $(x y z) \sin 3 \theta=(y+2 z) \cos 3 \theta$<br/>$+y \sin 3 \theta$<br/>have a solution $\left(x_0, y_0, z_0\right)$<br/>with $\quad y_0 z_0 \neq 0$, is</div>

answer:
<div class="solution">Given equations can be written as<br/>$$<br/>\begin{gathered}<br/>x \sin 3 \theta-\frac{\cos 3 \theta}{y}-\frac{\cos 3 \theta}{z}=0 \\<br/>x \sin 3 \theta-\frac{2 \cos 3 \theta}{y}-\frac{2 \sin 3 \theta}{z}=0 \\<br/>\text { and } x \sin 3 \theta-\frac{2}{y} \cos 3 \theta \\<br/>-\frac{1}{z}(\cos 3 \theta+\sin 3 \theta)=0<br/>\end{gathered}<br/>$$<br/>Eqs. (ii) and (iii), implies<br/>$$<br/>\begin{aligned}<br/>&amp; 2 \sin 3 \theta=\cos 3 \theta+\sin 3 \theta \\<br/>\Rightarrow &amp; \sin 3 \theta=\cos 3 \theta \\<br/>\therefore &amp; \tan 3 \theta=1 \\<br/>\Rightarrow &amp; 3 \theta=\frac{\pi}{4}, \frac{5 \pi}{4}, \frac{9 \pi}{4} \text { or } \theta=\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{9 \pi}{12} .<br/>\end{aligned}<br/>$$</div>


title: the-number-of-distinct-real-roots-of-x-4-4-x-3-12-x-2-x-1-0-is
slug: the-number-of-distinct-real-roots-of-x-4-4-x-3-12-x-2-x-1-0-is-30026
question: <div class="question">The number of distinct real roots of $x^4-4 x^3+12 x^2+x-1=0$ is</div>
tags: ['Mathematics', 'Application of Derivatives', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P3.db
answer:
<div class="solution">$f(x)=x^4-4 x^3+12 x^2+x-1$<br/>$$<br/>\begin{aligned}<br/>f^{\prime}(x) &amp; =4 x^3-12 x^2+24 x+1 \\<br/>f^{\prime \prime}(x) &amp; =12 x^2-24 x+24 \\<br/>&amp; =12\left(x^2-2 x+2\right) \\<br/>&amp; =12\left\{(x-1)^2+1\right\}&gt;0, \text { for all } x<br/>\end{aligned}<br/>$$<br/>$\Rightarrow f^{\prime}(x)$ is increasing.<br/>Since, $f^{\prime}(x)$ is cubic and increasing. $\Rightarrow f^{\prime}(x)$ has only one real root and two imaginary roots.<br/>$\therefore f(x)$ cannot have all distinct root.<br/>$\Rightarrow$ Atmost 2 real roots.<br/>Now, $f(-1)=15$,<br/>$f(0)=-1$ and $f(1)=9$<br/>$\therefore f(x)$ must have one root in $(-1,0)$ and other in $(0,1)$.<br/>$\Rightarrow 2$ real roots.</div>


tags: ['Mathematics', 'Vector Algebra', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-number-of-distinct-real-values-of-for-which-the-vectors-2-i-j-k-i-2-j-k-and-i-j-2-k-are-coplanar-is

slug:
the-number-of-distinct-real-values-of-for-which-the-vectors-2-i-j-k-i-2-j-k-and-i-j-2-k-are-coplanar-is-77377

question:
<div class="question">The number of distinct real values of $\lambda$, for which the vectors $-\lambda^2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$, $\hat{\mathbf{i}}-\lambda^2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}-\lambda^2 \hat{\mathbf{k}}$ are coplanar, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>zero<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>one<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>two<br/></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"><br/>three</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>two<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \left|\begin{array}{ccc}<br/>-\lambda^2 &amp; 1 &amp; 1 \\<br/>1 &amp; -\lambda^2 &amp; 1 \\<br/>1 &amp; 1 &amp; -\lambda^2<br/>\end{array}\right|=0 \Rightarrow \lambda^6-3 \lambda^2-2=0 \\<br/>&amp; \Rightarrow \quad\left(1+\lambda^2\right)^2\left(\lambda^2-2\right)=0 \Rightarrow \lambda=\pm \sqrt{2} \\<br/>&amp;<br/>\end{aligned}<br/>$$</div>


title: the-number-of-hexagonal-faces-that-are-present-in-a-truncated-octahedron-is
slug: the-number-of-hexagonal-faces-that-are-present-in-a-truncated-octahedron-is-53926
tags: ['Chemistry', 'Solid State', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of hexagonal faces that are present in a truncated octahedron is</div>

answer:
<div class="solution">The truncated octahedron is the 14 -faced Archimedean solid, with 14 total faces. 6 squares and 8 regular hexagons. The truncated octahedron is formed by removing the six right square pyramids one from each point of a regular octahedron as:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0Ays1Y-sIvRd3Z-6kSPicKswM180avyRcr1VQ0V2Nyg.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-JlvmLRDxeTV2uTP4_0yf8aXiTq-5DXDl3m_3A87Uvo.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-neutrons-emitted-when-92-235-u-undergoes-controlled-nuclear-fission-to-54-142-xe-and-38-90-sr-is

slug:
the-number-of-neutrons-emitted-when-92-235-u-undergoes-controlled-nuclear-fission-to-54-142-xe-and-38-90-sr-is-86969

question:
<div class="question">The number of neutrons emitted when ${ }_{92}^{235} \mathrm{U}$ undergoes controlled nuclear fission to ${ }_{54}^{142} \mathrm{Xe}$ and ${ }_{38}^{90} \mathrm{Sr}$ is</div>

answer:
<div class="solution">${ }_{92} \mathrm{U}^{235} \longrightarrow{ }_{54} \mathrm{Xe}^{142}+{ }_{38} \mathrm{Sr}^{90}+3{ }_0 n^1$<br/>Nuclear chemistry<br/>Basic application<br/>II</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-optically-active-products-obtained-from-the-complete-ozonolysis-of-the-given-compound-is-1

slug:
the-number-of-optically-active-products-obtained-from-the-complete-ozonolysis-of-the-given-compound-is-1-39680

question:
<div class="question">The number of optically active products obtained from the complete ozonolysis of the given compound is :
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ihtYwShcD6FtuVky34gGEuq92xHdAqgFfSymYH2-EF4.original.fullsize.png"/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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">B</span> <span class="option-data">1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/iXF3AwBuCp2h5BscLH5bIBP9aiiswsT2-vc55-CVdWY.original.fullsize.png"/></div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-number-of-seven-digit-integers-with-sum-of-the-digits-equal-to-10-and-formed-by-using-the-digits-12-and-3-only-is

slug:
the-number-of-seven-digit-integers-with-sum-of-the-digits-equal-to-10-and-formed-by-using-the-digits-12-and-3-only-is-27845

question:
<div class="question">The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>55<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>66<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>77<br/></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"><br/>88</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>77<br/></span> </div>

answer:
<div class="solution">There are two possible cases arise:<br/>Case I Five 1's, one 2's, one 3's<br/>$\therefore$ Number of numbers $=\frac{7 !}{5 !}=42$<br/>Case II Four 1's, three 2's<br/>$\therefore$ Number of numbers $=\frac{7 !}{4 ! 3 !}=35$<br/>$\therefore$ Total number of numbers $=42+35=77$</div>


tags: ['Mathematics', 'Trigonometric Equations', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-number-of-solutions-of-the-pair-of-equations-2-sin-2-cos-2-0-and-2-cos-2-3-sin-0-in-the-interval-0-2-is

slug:
the-number-of-solutions-of-the-pair-of-equations-2-sin-2-cos-2-0-and-2-cos-2-3-sin-0-in-the-interval-0-2-is-95291

question:
<div class="question">The number of solutions of the pair of equations $2 \sin ^2 \theta-\cos 2 \theta=0$ and $2 \cos ^2 \theta-3 \sin \theta=0$ in the interval $[0,2 \pi]$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>zero<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>one<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>two<br/></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"><br/>four</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>two<br/></span> </div>

answer:
<div class="solution">$2 \sin ^2 \theta-\cos 2 \theta=0 \Rightarrow \sin ^2 \theta=\frac{1}{4}$<br/>Also, $2 \cos ^2 \theta=3 \sin \theta \Rightarrow \sin \theta=\frac{1}{2}$<br/>$\Rightarrow$ Two solutions in $[0,2 \pi]$.</div>


title: the-number-of-stereoisomers-obtained-by-bromination-of-trans2butene-is-1
slug: the-number-of-stereoisomers-obtained-by-bromination-of-trans2butene-is-1-37739
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of stereoisomers obtained by bromination of trans-2-butene is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>1<br/></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"><br/>2<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>3<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>4</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Hz45PVk-tYUOsNb8AArpiuOeSRVqUH3Bwctfr6lTAXU.original.fullsize.png"/><br/></div>


title: the-number-of-structural-isomers-for-c-6-h-14-is-3
slug: the-number-of-structural-isomers-for-c-6-h-14-is-3-30989
question: <div class="question">The number of structural isomers for $\mathrm{C}_6 \mathrm{H}_{14}$ is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>3<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>4<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>5<br/></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"><br/>6</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>5<br/></span> </div>

answer:
<div class="solution">$$<br/>\text { Molecular Formula } \mathrm{C}_6 \mathrm{H}_{14}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Xi_cYSZ-3PXQqeUI1D2xF03RsxtSRfOAfHjG_eSY1xo.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Trigonometric Equations', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P3.db
title:
the-number-of-values-of-in-the-interval-2-2-such-that-5-n-for-n-0-1-2-and-tan-cot-5-as-well-as-sin-2-cos-4-is

slug:
the-number-of-values-of-in-the-interval-2-2-such-that-5-n-for-n-0-1-2-and-tan-cot-5-as-well-as-sin-2-cos-4-is-50685

question:
<div class="question">The number of values of $\theta$ in the interval $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ such that $\theta \neq \frac{n \pi}{5}$ for $n=0, \pm 1, \pm 2$ and $\tan \theta=\cot 5 \theta$ as well as $\sin 2 \theta=\cos 4 \theta$ is</div>

answer:
<div class="solution">Given, $\tan \theta=\cot 5 \theta$<br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow \quad \tan \theta=\tan \left(\frac{\pi}{2}-5 \theta\right) \\<br/>&amp; \Rightarrow \quad \frac{\pi}{2}-5 \theta=n \pi+\theta \\<br/>&amp; \Rightarrow \quad 6 \theta=\frac{\pi}{2}-n \pi \\<br/>&amp; \Rightarrow \quad \theta=\frac{\pi}{12}-\frac{n \pi}{6} \\<br/>&amp; \text { Also, } \cos 4 \theta=\sin 2 \theta=\cos \left(\frac{\pi}{2}-2 \theta\right) \\<br/>&amp; \Rightarrow \quad 4 \theta=2 n \pi \pm\left(\frac{\pi}{2}-2 \theta\right)<br/>\end{aligned}<br/>$$<br/>Taking positive<br/>$$<br/>6 \theta=2 n \pi+\frac{\pi}{2} \Rightarrow \theta=\frac{n \pi}{3}+\frac{\pi}{12}<br/>$$<br/>Taking negative<br/>$$<br/>2 \theta=2 n \pi-\frac{\pi}{2} \Rightarrow \theta=n \pi-\frac{\pi}{4}<br/>$$<br/>Above values of $\theta$ suggests that there are only 3 common solutions.</div>


title: the-number-of-water-molecules-directly-bonded-to-the-metal-centre-in-cuso-4-5-h-2-o-is
slug: the-number-of-water-molecules-directly-bonded-to-the-metal-centre-in-cuso-4-5-h-2-o-is-26611
tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The number of water molecule(s) directly bonded to the metal centre in $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ is</div>

answer:
<div class="solution">$\left[\mathrm{Cu}\left(\mathrm{H}_2 \mathrm{O}\right)_4\right] \mathrm{SO}_4 \cdot \mathrm{H}_2 \mathrm{O}$. Coordination number of $\mathrm{Cu}$ is 4 .</div>


title: the-oxidation-number-of-mn-in-the-product-of-alkaline-oxidative-fusion-of-mno-2-is
slug: the-oxidation-number-of-mn-in-the-product-of-alkaline-oxidative-fusion-of-mno-2-is-85104
tags: ['Chemistry', 'd and f Block Elements', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">The oxidation number of $\mathrm{Mn}$ in the product of alkaline oxidative fusion of $\mathrm{MnO}_2$ is</div>

answer:
<div class="solution">$2 \mathrm{MnO}_2+4 \mathrm{KOH}+\mathrm{O}_2 \stackrel{\text { Fusion }}{\longrightarrow} 2 \mathrm{~K}_2 \mathrm{MnO}_4+2 \mathrm{H}_2 \mathrm{O}$</div>


title: the-packing-efficiency-of-the-twodimensional-square-unit-cell-shown-below-is
slug: the-packing-efficiency-of-the-twodimensional-square-unit-cell-shown-below-is-57338
tags: ['Chemistry', 'Solid State', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The packing efficiency of the two-dimensional square unit cell shown below is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1GI_qPidPegKD2EP9BSvUDM_IF5A73pwDlxMTT4J-P4.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$39.27 \%$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$68.02 \%$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$74.05 \%$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$78.54 \%$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$78.54 \%$</span> </div>

answer:
<div class="solution">$a=(2 \sqrt{2} r)$<br/>Packing fraction $=\frac{2 \times \pi r^2}{2(\sqrt{2} r)^2}=\frac{2 \pi r^2}{8 r^2}=\frac{\pi}{4}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T5RShQcdyOg6O3iKjmyk2CpslG7xobqZhsV4L4FM-8k.original.fullsize.png"/><br/><br/>Solid state<br/>Basic analysis (understanding)<br/>II</div>


title: the-percentage-of-p-character-in-the-orbitals-forming-p-p-bonds-in-p-4-is
slug: the-percentage-of-p-character-in-the-orbitals-forming-p-p-bonds-in-p-4-is-28528
source_db: MarksBatch2_P3.db
question:
<div class="question">The percentage of $p$-character in the orbitals forming $\mathrm{P}-\mathrm{P}$ bonds in $\mathrm{P}_4$ is</div>

tags:
['Chemistry', 'Chemical Bonding and Molecular Structure', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>25<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>33<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>50<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>75</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>75</span> </div>

answer:
<div class="solution">Phosphorus atom is $s p^3$ hybridised in $\mathrm{P}_4$ usually.<br/>Thus, $p$ character $75 \%$</div>


options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P3.db
title:
the-periodic-table-consists-of-18-groups-an-isotope-of-copper-on-bombardment-with-protons-undergoes-a-nuclear-reaction-yielding-element-x-as-shown-bel

slug:
the-periodic-table-consists-of-18-groups-an-isotope-of-copper-on-bombardment-with-protons-undergoes-a-nuclear-reaction-yielding-element-x-as-shown-bel-99287

question:
<div class="question">The periodic table consists of 18 groups. An isotope of copper, on bombardment with protons, undergoes a nuclear reaction yielding element $X$ as shown below. To which group, element $X$ belongs in the periodic table?
<br/> <br/>${ }_{29}^{63} \mathrm{Cu}+{ }_{1}^{1} \mathrm{H} \rightarrow 6_{0}^{1} n+{ }_{2}^{4} \alpha+2{ }_{1}^{1} \mathrm{H}+\mathrm{X}$</div>

tags:
['Chemistry', 'Classification of Elements and Periodicity in Properties', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']

answer:
<div class="solution">${ }_{29}^{63} \mathrm{Cu}+{ }_{1}^{1} \mathrm{H} \rightarrow 6{ }_{0}^{1} n+{ }_{2}^{4} \mathrm{He}+2{ }_{1}^{1} \mathrm{H}+{ }_{Z}^{A} X$
<br/> <br/>Balancing the atomic mass and atomic number
<br/> <br/>$63+1=(6 \times 1)+4+2+A \Rightarrow A=52$
<br/> <br/>$29+1=(6 \times 0)+2+2+Z \Rightarrow Z=26$
<br/> <br/>Thus ${ }_{Z}^{A} X={ }_{26}^{52} X$ or ${ }_{26}^{52} \mathrm{Fe}$
<br/> <br/>Hence, $X$ belongs to group 8 in the periodic table.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch2_P3.db
title:
the-point-p-is-the-intersection-of-the-straight-line-joining-the-points-q-2-3-5-and-r-1-1-4-with-the-plane-5-x-4-y-z-1-if-s-is-the-foot-of-the-perpend

slug:
the-point-p-is-the-intersection-of-the-straight-line-joining-the-points-q-2-3-5-and-r-1-1-4-with-the-plane-5-x-4-y-z-1-if-s-is-the-foot-of-the-perpend-19028

question:
<div class="question">The point $P$ is the intersection of the straight line joining the points $Q(2,3,5)$ and $R(1,-1,4)$ with the plane $5 x-4 y-$ $z=1$. If $S$ is the foot of the perpendicular drawn from the point $T(2,1,4)$ to $Q R$, then the length of the line segment $P S$ is</div>

options:
<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">$\sqrt{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \sqrt{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{1}{\sqrt{2}}$</span> </div>

answer:
<div class="solution">Equation of st. line joining $Q(2,3,5)$ and $R(1,-1,4)$ is
<br/> <br/>$\frac{x-2}{-1}=\frac{y-3}{-4}=\frac{z-5}{1}=\lambda$
<br/> <br/>Let $P(-\lambda+2,-4 \lambda+3,-\lambda+5)$
<br/> <br/>Since $P$ also lies on $5 x-4 y-z=1$
<br/> <br/>$\therefore-5 \lambda+10+16 \lambda-12+\lambda-5=1$
<br/> <br/>$\Rightarrow 12 \lambda=8 \Rightarrow \lambda=\frac{2}{3} \quad \therefore P=\left(\frac{4}{3}, \frac{1}{3}, \frac{13}{3}\right)$
<br/> <br/>Now let another point $S$ on $Q R$ be
<br/> <br/>$(-\mu+2,-4 \mu+3,-\mu+5)$
<br/> <br/>Since $S$ is the foot of perpendicular drawn from
<br/> <br/>$T(2,1,4)$ to $Q R$, where dr's of $S T$ are $\mu, 4 \mu-2, \mu-1$ and dr's of $Q R$ are $-1,-4,-1$
<br/> <br/>$\begin{array}{ll}
<br/> <br/>\therefore &amp; -\mu-16 \mu+8-\mu+1=0 \Rightarrow 18 \mu=9 \Rightarrow \mu=\frac{1}{2} \\
<br/> <br/>\therefore &amp; S=\left(\frac{3}{2}, 1, \frac{9}{2}\right)
<br/> <br/>\end{array}$
<br/> <br/>$\therefore \quad$ Distance between $P$ and $S$
<br/> <br/>$\begin{array}{l}
<br/> <br/>=\sqrt{\left(\frac{4}{3}-\frac{3}{2}\right)^{2}+\left(\frac{1}{3}-1\right)^{2}+\left(\frac{13}{3}-\frac{9}{2}\right)^{2}} \\
<br/> <br/>=\sqrt{\frac{1}{36}+\frac{4}{9}+\frac{1}{36}}=\frac{1}{\sqrt{2}}
<br/> <br/>\end{array}$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1Mtc8ys_t6stqipxTkbwUmoLcXdKw_dHQOJ0oBV5RNY.original.fullsize.png"/></div>


title: the-positive-integer-value-of-n-3-satisfying-the-equation-s-i-n-n-1-s-i-n-n-2-1-s-i-n-n-3-1-is
tags: ['Mathematics', 'Trigonometric Equations', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
slug:
the-positive-integer-value-of-n-3-satisfying-the-equation-s-i-n-n-1-s-i-n-n-2-1-s-i-n-n-3-1-is-56582

question:
<div class="question">The positive integer value of $n&gt;3$ satisfying the equation<br/>$$<br/>\frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)} \text { is }<br/>$$</div>

answer:
<div class="solution">Given, $n&gt;3 \in$ Integer<br/>$$<br/>\begin{aligned}<br/>&amp; \text { and } \frac{1}{\sin \left(\frac{\pi}{n}\right)}=\frac{1}{\sin \left(\frac{2 \pi}{n}\right)}+\frac{1}{\sin \left(\frac{3 \pi}{n}\right)} \\<br/>&amp; \Rightarrow \frac{1}{\sin \frac{\pi}{n}}-\frac{1}{\sin \frac{3 \pi}{n}}=\frac{1}{\sin \frac{2 \pi}{n}} \\<br/>&amp; \Rightarrow \quad \frac{\sin \frac{3 \pi}{n}-\sin \frac{\pi}{n}}{\sin \frac{\pi}{n} \cdot \sin \frac{3 \pi}{n}}=\frac{1}{\sin \frac{2 \pi}{n}}<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow \quad 2 \cos \left(\frac{2 \pi}{n}\right) \cdot \sin \frac{\pi}{n}=\frac{\sin \frac{\pi}{n} \cdot \sin \frac{3 \pi}{n}}{\sin \frac{2 \pi}{n}} \\<br/>&amp; \Rightarrow \quad 2 \sin \frac{2 \pi}{n} \cdot \cos \frac{2 \pi}{n}=\sin \frac{3 \pi}{n} \\<br/>&amp; \Rightarrow \quad \quad \sin \frac{4 \pi}{n}=\sin \frac{3 \pi}{n} \\<br/>&amp; \Rightarrow \frac{4 \pi}{n}=\pi-\frac{3 \pi}{n} \Rightarrow \frac{7 \pi}{n}=\pi \Rightarrow n=7<br/>\end{aligned}<br/>$$</div>


title: the-reaction-of-p-2-with-x-leads-selectively-to-p-4-o-6-the-x-is
slug: the-reaction-of-p-2-with-x-leads-selectively-to-p-4-o-6-the-x-is-37197
source_db: MarksBatch2_P3.db
question:
<div class="question">The reaction of $P_2$ with $X$ leads selectively to $\mathrm{P}_4 \mathrm{O}_6$. The $\mathrm{X}$ is</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>dry $\mathrm{O}_2$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>a mixture of $\mathrm{O}_2$ and $\mathrm{N}_2$<br/></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"><br/>moist $\mathrm{O}_2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{O}_2$ in the presence of aq. $\mathrm{NaOH}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>a mixture of $\mathrm{O}_2$ and $\mathrm{N}_2$<br/></span> </div>

answer:
<div class="solution">White phosphorus on reaction with limited supply of oxygen gives lower oxide $P_4 \mathrm{O}_6$. Therefore, air $\left(\mathrm{O}_2+\mathrm{N}_2\right)$ is a good source for controlled supply of oxygen and the best choice for controlled oxidation of white phosphorus into lower oxide $\mathrm{P}_4 \mathrm{O}_6$.</div>


source_db: MarksBatch2_P3.db
title:
the-reaction-of-white-phosphorus-with-aqueous-naoh-gives-phosphine-along-with-another-phosphorus-containing-compound-the-reaction-type-the-oxidation-s-1

slug:
the-reaction-of-white-phosphorus-with-aqueous-naoh-gives-phosphine-along-with-another-phosphorus-containing-compound-the-reaction-type-the-oxidation-s-1-92783

question:
<div class="question">The reaction of white phosphorus with aqueous $\mathrm{NaOH}$ gives phosphine along with another phosphorus containing compound. The reaction type; the oxidation states of phosphorus in phosphine and the other product are respectively</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">redox reaction; $-3$ and $-5$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">redox reaction; $+3$ and $+5$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">disproportionation reaction; $-3$ and $+5$</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">D</span> <span class="option-data">disproportionation reaction; $-3$ and $+3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">disproportionation reaction; $-3$ and $+5$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3PwXxOSYBkdxDVyIN1cvKcuQJF7DHqAX43VH128PVDQ.original.fullsize.png"/></div>


title: the-reagents-for-the-following-conversion-isare-1
slug: the-reagents-for-the-following-conversion-isare-1-63233
tags: ['Chemistry', 'Hydrocarbons', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">The reagent(s) for the following conversion,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/A9a7Okowiwpx3PIHLDTJJVAdAOx9rgHb5pxdhCabhY0.original.fullsize.png"/><br/><br/>is/are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>alcoholic $\mathrm{KOH}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>alcoholic KOH followed by $\mathrm{NaNH}_2$<br/></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"><br/>aqueous $\mathrm{KOH}$ followed by $\mathrm{NaNH}_2$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{Zn} / \mathrm{CH}_3 \mathrm{OH}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>alcoholic KOH followed by $\mathrm{NaNH}_2$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9AQ1xDYToHFJ_rT3ki-PBfrhDGNAVnOQaAcZv5LN_Do.original.fullsize.png"/><br/></div>


