# questions

tags: ['Mathematics', 'Circle', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-tangent-pt-is-drawn-to-the-circle-x-2-y-2-4-at-the-point-p-3-1-a-straight-line-l-perpendicular-to-pt-is-a-tangent-to-the-circle-x-3-2-y-2-1-question

slug:
a-tangent-pt-is-drawn-to-the-circle-x-2-y-2-4-at-the-point-p-3-1-a-straight-line-l-perpendicular-to-pt-is-a-tangent-to-the-circle-x-3-2-y-2-1-question-17994

question:
<div class="question">A tangent $P T$ is drawn to the circle $x^{2}+y^{2}=4$ at the point $P(\sqrt{3}, 1)$. A straight line $L$, perpendicular to $P T$ is a tangent to the circle $(x-3)^{2}+y^{2}-1$.
<br/> <br/><strong> Question:</strong> A common tangent of the two circles is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$x=4$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$y=2$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x+\sqrt{3} y=4$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$x+2 \sqrt{2} y=6$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x+2 \sqrt{2} y=6$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/QQHQDexIe4QpBIu0mS-rhYwFoOQq3AnLfPid0Gx6fiQ.original.fullsize.png"/><br/> <br/> <br/>From the figure it is clear that the intersection point of two direct common tangents lies on $x$-axis.
<br/> <br/>Also $\Delta P T_{1} C_{1} \sim \Delta P T_{2} C_{2}$
<br/> <br/>$\therefore \quad P C_{1}: P C_{2}=2: 1$
<br/> <br/>or $P$ divides $C_{1} C_{2}$ in the ratio $2: 1$ externally
<br/> <br/>$\therefore \quad$ Coordinates of $P$ are $(6,0)$.
<br/> <br/>Let the equation of tangent through $P$ be
<br/> <br/>$y=m(x-6)$
<br/> <br/>Asit touches $x^{2}+y^{2}=4$
<br/> <br/>$\therefore\left|\frac{6 m}{\sqrt{m^{2}+1}}\right|=2 \Rightarrow 36 m^{2}=4\left(m^{2}+1\right)$
<br/> <br/>$\therefore \quad m=\pm \frac{1}{2 \sqrt{2}}$
<br/> <br/>$\therefore \quad$ Equations of common tangents are
<br/> <br/>$y=\pm \frac{1}{2 \sqrt{2}}(x-6)$
<br/> <br/>Also $x=2$ is the common tangent to the two circles.</div>


tags: ['Physics', 'Work Power Energy', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-tennis-ball-is-dropped-on-a-horizontal-smooth-surface-it-bounces-back-to-its-original-position-after-hitting-the-surface-the-force-on-the-ball-durin-1

slug:
a-tennis-ball-is-dropped-on-a-horizontal-smooth-surface-it-bounces-back-to-its-original-position-after-hitting-the-surface-the-force-on-the-ball-durin-1-71601

question:
<div class="question">A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi mathvariant="normal">t</mi><mo> </mo></math>time most appropriately? The figures are only illustrative and not to the scale.</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/image4-1e99a962-648e-46be-b66d-d13f2ccfb89b.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image5-acd58d2d-97d6-4054-bef7-b77eee2b43fd.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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image6-e5690aec-d459-4476-86c2-350328db9694.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/image7-9faa711c-f9aa-4c10-bf54-355e02b010f9.png"/></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/image5-acd58d2d-97d6-4054-bef7-b77eee2b43fd.png"/></span> </div>

answer:
<div class="solution"><p>When ball of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">m</mi><mo>'</mo></math> dropped from height and strikes to ground.It's kinetic energy is converting into elastic potential energy due to compression.</p><p>So after time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">t</mi><mo>'</mo></math> its final velocity,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mi mathvariant="normal">u</mi><mo>+</mo><mi>at</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">u</mi></math> is initial velocity of ball, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi></math> is acceleration of ball and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">t</mi></math> is time.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">v</mi><mo>=</mo><mn>0</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mi mathvariant="normal">g</mi></mrow></mfenced><mi mathvariant="normal">t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mo>-</mo><mi>gt</mi></math></p><p>Negative sign shows downward direction.</p><p>Now kinetic energy of ball,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>mv</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">m</mi><msup><mfenced><mrow><mo>-</mo><mi>gt</mi></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>mg</mi><mn>2</mn></msup><msup><mi mathvariant="normal">t</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>∝</mo><msup><mi mathvariant="normal">t</mi><mn>2</mn></msup></math></p><p>So, it is upward parabola. But after complete compression, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo></math> becomes zero, then ball will reshape again. Kinetic energy will not be constant.</p><p> </p></div>


tags: ['Physics', 'Work Power Energy', 'JEE Advanced', 'JEE Advanced 2014 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-tennis-ball-is-dropped-on-a-horizontal-smooth-surface-it-bounces-back-to-its-original-position-after-hitting-the-surface-the-force-on-the-ball-durin

slug:
a-tennis-ball-is-dropped-on-a-horizontal-smooth-surface-it-bounces-back-to-its-original-position-after-hitting-the-surface-the-force-on-the-ball-durin-77420

question:
<div class="question">A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi></math> with <math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi mathvariant="normal">t</mi><mo> </mo></math>time most appropriately? The figures are only illustrative and not to the scale.</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/image4-1e99a962-648e-46be-b66d-d13f2ccfb89b.png"/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image5-acd58d2d-97d6-4054-bef7-b77eee2b43fd.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"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/image6-e5690aec-d459-4476-86c2-350328db9694.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/image7-9faa711c-f9aa-4c10-bf54-355e02b010f9.png"/></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/image5-acd58d2d-97d6-4054-bef7-b77eee2b43fd.png"/></span> </div>

answer:
<div class="solution"><p>When ball of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">m</mi><mo>'</mo></math> dropped from height and strikes to ground.It's kinetic energy is converting into elastic potential energy due to compression.</p><p>So after time <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi mathvariant="normal">t</mi><mo>'</mo></math> its final velocity,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mi mathvariant="normal">u</mi><mo>+</mo><mi>at</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">u</mi></math> is initial velocity of ball, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">a</mi></math> is acceleration of ball and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">t</mi></math> is time.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">v</mi><mo>=</mo><mn>0</mn><mo>+</mo><mfenced><mrow><mo>-</mo><mi mathvariant="normal">g</mi></mrow></mfenced><mi mathvariant="normal">t</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">v</mi><mo>=</mo><mo>-</mo><mi>gt</mi></math></p><p>Negative sign shows downward direction.</p><p>Now kinetic energy of ball,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>mv</mi><mn>2</mn></msup><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mi mathvariant="normal">m</mi><msup><mfenced><mrow><mo>-</mo><mi>gt</mi></mrow></mfenced><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><msup><mi>mg</mi><mn>2</mn></msup><msup><mi mathvariant="normal">t</mi><mn>2</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo><mo>∝</mo><msup><mi mathvariant="normal">t</mi><mn>2</mn></msup></math></p><p>So, it is upward parabola. But after complete compression, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">K</mi><mo>.</mo><mi mathvariant="normal">E</mi><mo>.</mo></math> becomes zero, then ball will reshape again. Kinetic energy will not be constant.</p><p> </p></div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-thin-flexible-wire-of-length-l-is-connected-to-two-adjacent-fixed-points-and-carries-a-current-i-in-the-clockwise-direction-as-shown-in-the-figure-w-1

slug:
a-thin-flexible-wire-of-length-l-is-connected-to-two-adjacent-fixed-points-and-carries-a-current-i-in-the-clockwise-direction-as-shown-in-the-figure-w-1-82157

question:
<div class="question">A thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bF_Vs5zbWXF13GK9k5D-6QuFUCOToY-1ar4BeybdPbw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$I B L$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{I B L}{\pi}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{I B L}{2 \pi}$<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/>$\frac{I B L}{4 \pi}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{I B L}{2 \pi}$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4veaaxxLY6EsrGuXWp0Zi06fUxuiwtTpsIf1XwC9re8.original.fullsize.png"/><br/><br/>$L=2 \pi R$<br/>$R=\frac{L}{2 \pi}$<br/>$2 T \sin (d \theta)=F_m$<br/>for small angles, $\sin (d \theta) \approx d \theta$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad 2 T(d \theta) &amp; =I(d L) B \sin 90^{\circ} \\<br/>&amp; =I(2 R \cdot d \theta) \cdot B \\<br/>\therefore \quad T &amp; =I R B=\frac{I L B}{2 \pi}<br/>\end{aligned}<br/>$$<br/>$\therefore$ correct option is (c)</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-thin-flexible-wire-of-length-l-is-connected-to-two-adjacent-fixed-points-and-carries-a-current-i-in-the-clockwise-direction-as-shown-in-the-figure-w-2

slug:
a-thin-flexible-wire-of-length-l-is-connected-to-two-adjacent-fixed-points-and-carries-a-current-i-in-the-clockwise-direction-as-shown-in-the-figure-w-2-50033

question:
<div class="question">A thin flexible wire of length $L$ is connected to two adjacent fixed points and carries a current $I$ in the clockwise direction, as shown in the figure. When the system is put in a uniform magnetic field of strength $B$ going into the plane of the paper, the wire takes the shape of a circle. The tension in the wire is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bF_Vs5zbWXF13GK9k5D-6QuFUCOToY-1ar4BeybdPbw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$I B L$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{I B L}{\pi}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{I B L}{2 \pi}$<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/>$\frac{I B L}{4 \pi}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{I B L}{2 \pi}$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4veaaxxLY6EsrGuXWp0Zi06fUxuiwtTpsIf1XwC9re8.original.fullsize.png"/><br/><br/>$L=2 \pi R$<br/>$R=\frac{L}{2 \pi}$<br/>$2 T \sin (d \theta)=F_m$<br/>for small angles, $\sin (d \theta) \approx d \theta$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad 2 T(d \theta) &amp; =I(d L) B \sin 90^{\circ} \\<br/>&amp; =I(2 R \cdot d \theta) \cdot B \\<br/>\therefore \quad T &amp; =I R B=\frac{I L B}{2 \pi}<br/>\end{aligned}<br/>$$<br/>$\therefore$ correct option is (c)</div>


tags: ['Physics', 'Center of Mass Momentum and Collision', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-thin-ring-of-mass-2-kg-and-radius-05-m-is-rolling-without-slipping-on-a-horizontal-plane-with-velocity-1-m-s-a-small-ball-of-mass-01-kg-moving-with-

slug:
a-thin-ring-of-mass-2-kg-and-radius-05-m-is-rolling-without-slipping-on-a-horizontal-plane-with-velocity-1-m-s-a-small-ball-of-mass-01-kg-moving-with-83569

question:
<div class="question">A thin ring of mass $2 \mathrm{~kg}$ and radius $0.5 \mathrm{~m}$ is rolling without slipping on a horizontal plane with velocity 1 $\mathrm{m} / \mathrm{s}$. A small ball of mass $0.1 \mathrm{~kg}$, moving with velocity $20 \mathrm{~m} / \mathrm{s}$ in the opposite directions, hits the ring at a height of $0.75 \mathrm{~m}$ and goes vertically up with velocity 10 $\mathrm{m} / \mathrm{s}$. Immediately after the collision<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/b_iTmXS449TQOBtntRYyDOl_btn80W1GvOxad36oYOY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>the ring has pure rotation about its stationary $\mathrm{CM}$<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 ring comes to a complete stop<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>friction between the ring and the ground is to the left<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/>there is no friction between the ring and the ground</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>the ring has pure rotation about its stationary $\mathrm{CM}$<br/>, <br/>friction between the ring and the ground is to the left<br/></span> </div>

answer:
<div class="solution">The data is incomplete. Let us assume that friction from ground on ring is not impulsive during impact.<br/>From linear momentum conservation in horizontal direction, we have<br/>$$<br/>\begin{aligned}<br/>&amp; (-2 \times 1)+(0.1 \times 20) \\<br/>&amp; =(0.1 \times 0)+(2 \times v) \stackrel{\text {-ve }}{\leftarrow} \stackrel{+v e}{\rightarrow}<br/>\end{aligned}<br/>$$<br/>Here, $v$ is the velocity of $\mathrm{CM}$ of ring after impact.<br/>Solving the above equation, we have<br/>$$<br/>v=0<br/>$$<br/>Thus, CM becomes stationary.<br/>$\therefore$ Correct answer is (a).<br/>Linear impulse during impact<br/>(i) In horizontal direction $J_1=\Delta P=0.1 \times 20=2 \mathrm{Ns}$<br/>(ii) In vertical direction<br/>$$<br/>J_2=\Delta P=0.1 \times 10=1 \mathrm{Ns}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ow5BiaaU6F8Bf2ZfKVZjQC4-SC5QnholKJUAnm1RHr8.original.fullsize.png"/><br/><br/>Writing the equation (about $\mathrm{CM}$ )<br/>Angular impulse<br/>$=$ Change in angular momentum<br/>$$<br/>\begin{aligned}<br/>&amp; 1 \times\left(\frac{\sqrt{3}}{2} \times \frac{1}{2}\right)-2 \times 0.5 \times \frac{1}{2} \\<br/>&amp; =2 \times(0.5)^2\left[\omega-\frac{1}{0.5}\right]<br/>\end{aligned}<br/>$$<br/>Solving this equation $\omega$ comes out to be positive or $\omega$ anti-clockwise. So just after collision rightwards slipping is taking place.<br/>Hence, friction is leftwards.<br/>Therefore, option (c) is also correct.<br/>$\therefore$ Correct options are (a) and (c).<br/>Note In JEE 2011 official answer key, correct option were given $\mathrm{a}, \mathrm{ac}$.<br/>Analysis of Question<br/>(i) Question is moderately difficult.<br/>(ii) In such type of problems impulse due to friction during collision is ignored.</div>


tags: ['Physics', 'Gravitation', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-thin-uniform-annular-disc-see-figure-of-mass-m-has-outer-radius-4-r-and-inner-radius-3-r-the-work-required-to-take-a-unit-mass-from-point-p-on-its-a-1

slug:
a-thin-uniform-annular-disc-see-figure-of-mass-m-has-outer-radius-4-r-and-inner-radius-3-r-the-work-required-to-take-a-unit-mass-from-point-p-on-its-a-1-41336

question:
<div class="question">A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$. The work required to take a unit mass from point $P$ on its axis to infinity is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u1HhU5_8GCE3eAfbnGgQixJxmCei9YbhtDWUexYer5w.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<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">B</span> <span class="option-data"><br/>$-\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{G M}{4 R}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{2 G M}{5 R}(\sqrt{2}-1)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<br/></span> </div>

answer:
<div class="solution">$$<br/>\text { } \begin{aligned}<br/>W=\Delta U &amp; =U_f-U_i=U_{\infty}-U_p \\<br/>&amp; =-U_P \\<br/>&amp; =-m V_P \\<br/>&amp; =-V_P \quad(\text { as } m=1)<br/>\end{aligned}<br/>$$<br/>Potential at point $P$ will be obtained by integration as given below<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jJmBXKLu523-AnbaAkWokVGroIl4PK3pdsvhCw-qfao.original.fullsize.png"/><br/><br/><br/>Let $d M$ be the mass of small ring as shown<br/>$$<br/>\begin{aligned}<br/>d M &amp; =\frac{M}{\pi(4 R)^2-\pi(3 R)^2}(2 \pi r) d r \\<br/>&amp; =\frac{2 M r d r}{7 R^2} \\<br/>d V_P &amp; =-\frac{G \cdot d M}{\sqrt{16 R^2+r^2}} \\<br/>&amp; =-\frac{2 G M}{7 R^2} \int_{3 R}^{4 R} \frac{r}{\sqrt{16 R^2+r^2}} \cdot d r \\<br/>&amp; =-\frac{2 G M}{7 R}(4 \sqrt{2}-5) \\<br/>\therefore \quad W &amp; =+\frac{2 G M}{7 R}(4 \sqrt{2}-5)<br/>\end{aligned}<br/>$$<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Gravitation', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-thin-uniform-annular-disc-see-figure-of-mass-m-has-outer-radius-4-r-and-inner-radius-3-r-the-work-required-to-take-a-unit-mass-from-point-p-on-its-a

slug:
a-thin-uniform-annular-disc-see-figure-of-mass-m-has-outer-radius-4-r-and-inner-radius-3-r-the-work-required-to-take-a-unit-mass-from-point-p-on-its-a-76925

question:
<div class="question">A thin uniform annular disc (see figure) of mass $M$ has outer radius $4 R$ and inner radius $3 R$. The work required to take a unit mass from point $P$ on its axis to infinity is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u1HhU5_8GCE3eAfbnGgQixJxmCei9YbhtDWUexYer5w.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<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">B</span> <span class="option-data"><br/>$-\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{G M}{4 R}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{2 G M}{5 R}(\sqrt{2}-1)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{2 G M}{7 R}(4 \sqrt{2}-5)$<br/></span> </div>

answer:
<div class="solution">$$<br/>\text { } \begin{aligned}<br/>W=\Delta U &amp; =U_f-U_i=U_{\infty}-U_p \\<br/>&amp; =-U_P \\<br/>&amp; =-m V_P \\<br/>&amp; =-V_P \quad(\text { as } m=1)<br/>\end{aligned}<br/>$$<br/>Potential at point $P$ will be obtained by integration as given below<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jJmBXKLu523-AnbaAkWokVGroIl4PK3pdsvhCw-qfao.original.fullsize.png"/><br/><br/><br/>Let $d M$ be the mass of small ring as shown<br/>$$<br/>\begin{aligned}<br/>d M &amp; =\frac{M}{\pi(4 R)^2-\pi(3 R)^2}(2 \pi r) d r \\<br/>&amp; =\frac{2 M r d r}{7 R^2} \\<br/>d V_P &amp; =-\frac{G \cdot d M}{\sqrt{16 R^2+r^2}} \\<br/>&amp; =-\frac{2 G M}{7 R^2} \int_{3 R}^{4 R} \frac{r}{\sqrt{16 R^2+r^2}} \cdot d r \\<br/>&amp; =-\frac{2 G M}{7 R}(4 \sqrt{2}-5) \\<br/>\therefore \quad W &amp; =+\frac{2 G M}{7 R}(4 \sqrt{2}-5)<br/>\end{aligned}<br/>$$<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Mechanical Properties of Fluids', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-thin-uniform-cylindrical-shell-closed-at-both-ends-is-partially-filled-with-water-it-is-floating-vertically-in-water-in-halfsubmerged-state-if-c-is-

slug:
a-thin-uniform-cylindrical-shell-closed-at-both-ends-is-partially-filled-with-water-it-is-floating-vertically-in-water-in-halfsubmerged-state-if-c-is-81166

question:
<div class="question">A thin uniform cylindrical shell, closed at both ends, is partially filled with water. It is floating vertically in water in half-submerged state. If $\rho_{c}$ is the relative density of the material of the shell with respect to water, then the correct statement is that the shell is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">more than half-filled if $\rho_{c}$ is less than $0.5$.</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">B</span> <span class="option-data">more than half-filled if $\rho_{c}$ is more than 1.0.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">half-filled if $\rho_{c}$ is more than $0.5$.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">less than half-filled if $\rho_{c}$ is less than $0.5$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">more than half-filled if $\rho_{c}$ is less than $0.5$.</span> </div>

answer:
<div class="solution">Let $V_{1}=$ total material volume of cylindrical shell $V_{2}=$ total inside volume of cylindrical shell and $y=$ fraction of $V_{2}$ volume filled with water.
<br/> <br/>Total weight $=$ Upthrust (Condition of floatation)
<br/> <br/>$\therefore \quad V_{1} \rho_{c} g+\left(y V_{2}\right)(1) g=\left(\frac{V_{1}+V_{2}}{2}\right)(1) g$
<br/> <br/>or $y=0.5+\left(0.5-\rho_{c}\right) \frac{V_{1}}{V_{2}}$
<br/> <br/>So, if $\rho_{c} &lt; 0.5$ then $y&gt;0.5$</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-thin-uniform-rod-pivoted-at-o-is-rotating-in-the-horizontal-plane-with-constant-angular-speed-as-shown-in-the-figure-at-time-t-0-a-small-insect-star

slug:
a-thin-uniform-rod-pivoted-at-o-is-rotating-in-the-horizontal-plane-with-constant-angular-speed-as-shown-in-the-figure-at-time-t-0-a-small-insect-star-19411

question:
<div class="question">A thin uniform rod, pivoted at $O$, is rotating in the horizontal plane with constant angular speed $\omega$, as shown in the figure. At time $t=0$, a small insect starts from $O$ and moves with constant speed $v$, with respect to the rod towards the other end. It reaches the end of the rod at $t=T$ and stops. The angular speed of the system remains $\omega$ throughout. The magnitude of the torque $(|\vec{\tau}|)$ about $O$, as a function of time is best represented by which plot?
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/D4qHR3kXxQw6NbMLkBtO9TW1QGRypd96ve3On6ChqNg.original.fullsize.png"/></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/YZA_tdu7hU-1UnpybndJ61X2EOcXE9hAPJc5fDKmVJY.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/vTc1iaLLg4kLiB2WHfB91R_RUWZ70BDYfiSEJY-bAHM.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/Fh6V0xW0LC0CNRRu5hMKPGt486zi4PUfQPjlBxZsCfU.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/kpnn2a64UUJbMQi2cKVz2kiPhxnaZAsUPdI-G7gtl9Y.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/vTc1iaLLg4kLiB2WHfB91R_RUWZ70BDYfiSEJY-bAHM.original.fullsize.png"/></span> </div>

answer:
<div class="solution">Angular momentum, $|\mathbf{L}|$ or $L=I \omega$ (about axis of rod) Moment of inertia of the rod-insect system. $I=I_{\text {rod }}+m x^{2}=I_{\text {rod }}+m v^{2} t^{2}$ Here, $m=$ mass of insect $\therefore \quad L=\left(I_{\mathrm{rod}}+m v^{2} t^{2}\right) \omega$
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/9RD2eTh1EaGOdXYV8qzSrSNBVSZ6WeliEFsILJ2Rqgg.original.fullsize.png"/><br/> <br/> <br/>Now $|\tau|=\frac{d L}{d t}=\left(2 m v^{2} t \omega\right)$ or $|\tau| \propto t$
<br/> <br/>i.e. the graph is straight line passing through origin.
<br/> <br/>After time $T, L=$ constant
<br/> <br/>$\therefore \quad|\tau| \text { or } \frac{d L}{d t}=0$
<br/> <br/>i.e., when the insect stops moving, $L$ does not change and therefore $T$ becomes constant.</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-tiny-spherical-oil-drop-carrying-a-net-charge-q-is-balanced-in-still-air-with-a-vertical-uniform-electric-field-of-strength-7-81-1-0-5-vm-1-when-the

slug:
a-tiny-spherical-oil-drop-carrying-a-net-charge-q-is-balanced-in-still-air-with-a-vertical-uniform-electric-field-of-strength-7-81-1-0-5-vm-1-when-the-71125

question:
<div class="question">A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \mathrm{Vm}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity $2 \times 10^{-3} \mathrm{~ms}^{-1}$. Given $g=9.8 \mathrm{~ms}^{-2}$, viscosity of the air $=1.8 \times 10^{-5} \mathrm{Ns} \mathrm{m}^{-2}$ and the density of oil $=900 \mathrm{~kg} \mathrm{~m}^{-3}$, the magnitude of $q$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1.6 \times 10^{-19} \mathrm{C}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$3.2 \times 10^{-19} \mathrm{C}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$4.8 \times 10^{-19} \mathrm{C}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$8.0 \times 10^{-19} \mathrm{C}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$8.0 \times 10^{-19} \mathrm{C}$</span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; q E=m g \\<br/>&amp; \quad 6 \pi \eta r v=m g \\<br/>&amp; \frac{4}{3} \pi r^3 \rho g=m g \\<br/>&amp; \therefore \quad r=\left(\frac{3 m g}{4 \pi \rho g}\right)^{1 / 3}<br/>\end{aligned}<br/>$$<br/>Substituting the value of $r$ in Eq. (ii) we get,<br/>$$<br/>6 \pi \eta v\left(\frac{3 m g}{4 \pi \rho g}\right)^{1 / 3}=m g<br/>$$<br/>or $\quad(6 \pi \eta v)^3\left(\frac{3 m g}{4 \pi \rho g}\right)=(m g)^3$<br/>Again substituting $m g=q E$ we get,<br/>$$<br/>(q E)^2=\left(\frac{3}{4 \pi \rho g}\right)(6 \pi \eta v)^3<br/>$$<br/>or $\quad q E=\left(\frac{3}{4 \pi \rho g}\right)^{1 / 2}(6 \pi \eta v)^{3 / 2}$<br/>$$<br/>\therefore \quad q=\frac{1}{E}\left(\frac{3}{4 \pi \rho g}\right)^{1 / 2}(6 \pi \eta v)^{3 / 2}<br/>$$<br/>Substituting the values we get ,<br/>$$<br/>\begin{aligned}<br/>q= &amp; \frac{7}{81 \pi \times 10^5} \sqrt{\frac{3}{4 \pi \times 900 \times 9.8} \times 216 \pi^3} \\<br/>&amp; \times \sqrt{\left(1.8 \times 10^{-5} \times 2 \times 10^{-3}\right)^3} \\<br/>&amp; =8.0 \times 10^{-19} \mathrm{C}<br/>\end{aligned}<br/>$$<br/>$\therefore$ correct option is $(\mathrm{d})$.</div>


tags: ['Physics', 'Motion In Two Dimensions', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch1_P1.db
title:
a-train-is-moving-along-a-straight-line-with-a-constant-acceleration-a-a-boy-standing-in-the-train-throws-a-ball-forward-with-a-speed-of-10-m-s-at-an-

slug:
a-train-is-moving-along-a-straight-line-with-a-constant-acceleration-a-a-boy-standing-in-the-train-throws-a-ball-forward-with-a-speed-of-10-m-s-at-an-50373

question:
<div class="question">A train is moving along a straight line with a constant acceleration a. A boy standing in the train throws a ball forward with a speed of $10 \mathrm{~m} / \mathrm{s}$, at an angle of $60^{\circ}$ to the horizontal. The boy has to move forward by $1.15 \mathrm{~m}$ inside the train to catch the ball back at the initial height. The acceleration of the train in $\mathrm{m} / \mathrm{s}^2$, is</div>

answer:
<div class="solution">$\begin{aligned} t &amp; =T=\frac{2 u \sin \theta}{g} \\ &amp; =\frac{2 \times 10 \times \sin 60^{\circ}}{10}=\sqrt{3} \mathrm{~s}\end{aligned}$<br/>Displacement of train in time $t=\frac{1}{2} a t^2$<br/>Displacement of boy with respect to train<br/>$$<br/>=1.15 \mathrm{~m}<br/>$$<br/>$\therefore$ Displacement of boy with respect to ground $=\left(1.15+\frac{1}{2} a t^2\right)$<br/>Displacement of ball with respect to ground $=\left(u \cos 60^{\circ}\right) t$<br/>To catch the ball back at initial height,<br/>$$<br/>\begin{aligned}<br/>1.15+\frac{1}{2} a t^2 &amp; =\left(u \cos 60^{\circ}\right) t \\<br/>\therefore 1.15+\frac{1}{2} a(\sqrt{3})^2 &amp; =10 \times \frac{1}{2} \times \sqrt{3}<br/>\end{aligned}<br/>$$<br/>Solving this equation, we get<br/>$$<br/>a=5 \mathrm{~ms}^{-2}<br/>$$<br/>$\therefore$ Answer is 5 .<br/>Analysis of Question<br/>(i) Question is moderately tough.<br/>(ii) Velocity of ball given in the question is with respect to ground.</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-transverse-sinusoidal-wave-moves-along-a-string-in-the-positive-x-direction-at-a-speed-of-10-cm-s-the-wavelength-of-the-wave-is-05-m-and-its-amplitu-1

slug:
a-transverse-sinusoidal-wave-moves-along-a-string-in-the-positive-x-direction-at-a-speed-of-10-cm-s-the-wavelength-of-the-wave-is-05-m-and-its-amplitu-1-77280

question:
<div class="question">A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \mathrm{~cm} / \mathrm{s}$. The wavelength of the wave is $0.5 \mathrm{~m}$ and its amplitude is $10 \mathrm{~cm}$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{~cm}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mhi0oq-_KYK-esNT29R9yjrzmdQ4wioIwrP6eQjavKg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$<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/>$-\frac{\sqrt{3} \pi}{50} \hat{j} \mathrm{~m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$<br/></span> </div>

answer:
<div class="solution">Particle velocity $v_p=-v$ (slope of $y-x$ graph)<br/>Here,$v=+v e$, as the wave is travelling in positive $x$-direction.<br/>Slope at $P$ is negative.<br/>$\therefore$ Velocity of particle is in positive $y(+\overrightarrow{\mathbf{j}})$ direction.<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-transverse-sinusoidal-wave-moves-along-a-string-in-the-positive-x-direction-at-a-speed-of-10-cm-s-the-wavelength-of-the-wave-is-05-m-and-its-amplitu

slug:
a-transverse-sinusoidal-wave-moves-along-a-string-in-the-positive-x-direction-at-a-speed-of-10-cm-s-the-wavelength-of-the-wave-is-05-m-and-its-amplitu-62202

question:
<div class="question">A transverse sinusoidal wave moves along a string in the positive $x$-direction at a speed of $10 \mathrm{~cm} / \mathrm{s}$. The wavelength of the wave is $0.5 \mathrm{~m}$ and its amplitude is $10 \mathrm{~cm}$. At a particular time $t$, the snap-shot of the wave is shown in figure. The velocity of point $P$ when its displacement is $5 \mathrm{~cm}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mhi0oq-_KYK-esNT29R9yjrzmdQ4wioIwrP6eQjavKg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$<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/>$-\frac{\sqrt{3} \pi}{50} \hat{j} \mathrm{~m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$-\frac{\sqrt{3} \pi}{50} \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{\sqrt{3} \pi}{50} \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}$<br/></span> </div>

answer:
<div class="solution">Particle velocity $v_p=-v$ (slope of $y-x$ graph)<br/>Here,$v=+v e$, as the wave is travelling in positive $x$-direction.<br/>Slope at $P$ is negative.<br/>$\therefore$ Velocity of particle is in positive $y(+\overrightarrow{\mathbf{j}})$ direction.<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Motion In Two Dimensions', 'JEE Advanced', 'JEE Advanced 2020 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
a-uniform-electric-field-e-400-3-j-n-c-1-is-applied-in-a-region-a-charged-particle-of-mass-m-carrying-positive-charge-q-is-projected-in-this-region-wi

slug:
a-uniform-electric-field-e-400-3-j-n-c-1-is-applied-in-a-region-a-charged-particle-of-mass-m-carrying-positive-charge-q-is-projected-in-this-region-wi-59327

question:
<div class="question"><p>A uniform electric field, <math xmlns="http://www.w3.org/1998/Math/MathML"><mover><mi>E</mi><mo>â</mo></mover><mo>=</mo><mo>-</mo><mn>400</mn><msqrt><mn>3</mn></msqrt><mo>Â </mo><mover><mi mathvariant="normal">j</mi><mo>^</mo></mover><mo>Â </mo><mi mathvariant="normal">N</mi><mo>Â </mo><msup><mi mathvariant="normal">C</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> is applied in a region. A charged particle of mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math> carrying positive charge <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi></math> is projected in this region with an initial speed of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msqrt><mn>10</mn></msqrt><mo>Ã</mo><msup><mn>10</mn><mn>6</mn></msup><mo>Â </mo><mi mathvariant="normal">m</mi><mo>Â </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. This particle is aimed to hit a target <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi></math>, which isÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>Â </mo><mi mathvariant="normal">m</mi></math> away from its entry point into the field as shown schematically in the figure. Take <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>q</mi><mi>m</mi></mfrac><mo>=</mo><msup><mn>10</mn><mn>10</mn></msup><mo>Â </mo><mi mathvariant="normal">C</mi><mo>Â </mo><msup><mi>kg</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. Then</p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/7a2b89eb-38aa-4693-b2b8-03e4c1edc461-image.png"/></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">the particle will hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> if projected at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn><mo>°</mo></math> from the horizontal</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">the particle will hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> if projected either at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo></math> or  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>°</mo></math> from the horizontal</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">time taken by the particle to hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> could be <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>6</mn></mfrac></msqrt><mi>μ</mi><mi mathvariant="normal">s</mi></math> as well as <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>2</mn></mfrac></msqrt><mi>μ</mi><mi mathvariant="normal">s</mi></math></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">time taken by the particle to hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> is <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>3</mn></mfrac></msqrt><mi>μ</mi><mi>s</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value">the particle will hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> if projected either at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo></math> or  <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>°</mo></math> from the horizontal, time taken by the particle to hit <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">T</mi></math> could be <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>6</mn></mfrac></msqrt><mi>μ</mi><mi mathvariant="normal">s</mi></math> as well as <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>2</mn></mfrac></msqrt><mi>μ</mi><mi mathvariant="normal">s</mi></math></span> </div>

answer:
<div class="solution"><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>a</mi><mi>y</mi></msub><mo>=</mo><mfrac><mi>E</mi><mi>M</mi></mfrac><mo>=</mo><mn>4</mn><msqrt><mn>3</mn></msqrt><mo>Ã</mo><msup><mn>10</mn><mn>12</mn></msup><mo>Â </mo><mi mathvariant="normal">m</mi><mo>Â </mo><msup><mi mathvariant="normal">s</mi><mn>2</mn></msup></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/d26e9e69-5cd5-443d-a87f-508327036d0b-image.png"/></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>=</mo><mfrac><mrow><msup><mi mathvariant="normal">u</mi><mn>2</mn></msup><mi>sin</mi><mn>2</mn><mi>Î¸</mi></mrow><msub><mi mathvariant="normal">a</mi><mi mathvariant="normal">y</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mn>2</mn><mi>Î¸</mi><mo>=</mo><mfrac><mrow><mi>R</mi><msub><mi>a</mi><mi>y</mi></msub></mrow><msup><mi>u</mi><mn>2</mn></msup></mfrac><mo>=</mo><mfrac><msqrt><mn>3</mn></msqrt><mn>2</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Î¸</mi><mo>=</mo><mn>30</mn><mo>Â°</mo></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn><mo>Â°</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>u</mi><mi>sin</mi><mo>Â </mo><mn>30</mn><mo>Â°</mo></mrow><msub><mi>a</mi><mi>y</mi></msub></mfrac></math>Â orÂ  <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>2</mn><mi>u</mi><mi>sin</mi><mo>Â </mo><mn>60</mn><mo>Â°</mo></mrow><msub><mi>a</mi><mi>y</mi></msub></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msqrt><mfrac><mn>5</mn><mn>6</mn></mfrac></msqrt><mi>Î¼</mi><mi mathvariant="normal">s</mi></math>Â orÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mfrac><mn>5</mn><mn>2</mn></mfrac></msqrt><mi>Î¼</mi><mi mathvariant="normal">s</mi></math></p></div>


tags: ['Physics', 'Oscillations', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
a-uniform-rod-of-length-l-and-mass-m-is-pivoted-at-the-centre-its-two-ends-are-attached-to-two-springs-of-equal-spring-constants-k-the-springs-are-fix-1

slug:
a-uniform-rod-of-length-l-and-mass-m-is-pivoted-at-the-centre-its-two-ends-are-attached-to-two-springs-of-equal-spring-constants-k-the-springs-are-fix-1-81577

question:
<div class="question">A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zEebOkNjPBbVUWGAOGgVtZ1z2igySczwe95j7PSisvY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{2 k}{M}}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{k}{M}}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}$<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/>$\frac{1}{2 \pi} \sqrt{\frac{24 k}{M}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DrdMlLTmdrM4vZuHYllhDZoQTWGug-jp8kdYa7DO4KM.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \text { Restoring torque }=-(2 k x) \cdot \frac{L}{2} \\<br/>&amp; \qquad \alpha=-\frac{k L(L / 2 \theta)}{I}=-\left[\frac{k L^2 / 2}{M L^2 / 12}\right] \cdot \theta<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; =-\left(\frac{6 k}{M}\right) \theta \\<br/>\therefore \quad f &amp; =\frac{1}{2 \pi} \sqrt{\left|\frac{\alpha}{\theta}\right|}=\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-uniform-rod-of-length-l-and-mass-m-is-pivoted-at-the-centre-its-two-ends-are-attached-to-two-springs-of-equal-spring-constants-k-the-springs-are-fix

slug:
a-uniform-rod-of-length-l-and-mass-m-is-pivoted-at-the-centre-its-two-ends-are-attached-to-two-springs-of-equal-spring-constants-k-the-springs-are-fix-32560

question:
<div class="question">A uniform rod of length $L$ and mass $M$ is pivoted at the centre. Its two ends are attached to two springs of equal spring constants $k$. The springs are fixed to rigid supports as shown in the figure, and rod is free to oscillate in the horizontal plane. The rod is gently pushed through a small angle $\theta$ in one direction and released. The frequency of oscillation is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/zEebOkNjPBbVUWGAOGgVtZ1z2igySczwe95j7PSisvY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{2 k}{M}}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{k}{M}}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}$<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/>$\frac{1}{2 \pi} \sqrt{\frac{24 k}{M}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}$<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/DrdMlLTmdrM4vZuHYllhDZoQTWGug-jp8kdYa7DO4KM.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \text { Restoring torque }=-(2 k x) \cdot \frac{L}{2} \\<br/>&amp; \qquad \alpha=-\frac{k L(L / 2 \theta)}{I}=-\left[\frac{k L^2 / 2}{M L^2 / 12}\right] \cdot \theta<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; =-\left(\frac{6 k}{M}\right) \theta \\<br/>\therefore \quad f &amp; =\frac{1}{2 \pi} \sqrt{\left|\frac{\alpha}{\theta}\right|}=\frac{1}{2 \pi} \sqrt{\frac{6 k}{M}}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-uniformly-charged-thin-spherical-shell-of-radius-r-carries-uniform-surface-charge-density-of-per-unit-area-it-is-made-of-two-hemispherical-shells-he

slug:
a-uniformly-charged-thin-spherical-shell-of-radius-r-carries-uniform-surface-charge-density-of-per-unit-area-it-is-made-of-two-hemispherical-shells-he-22938

question:
<div class="question">A uniformly charged thin spherical shell of radius $R$ carries uniform surface charge density of $\sigma$ per unit area. It is made of two hemispherical shells, held together by pressing them with force $F$ (see figure). $F$ is proportional to<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/A0LPxshUYthNRpDGevwWOIT_cWEGeR4PLHMxnCFounw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\frac{1}{\varepsilon_0} \sigma^2 R^2$<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/>$\frac{1}{\varepsilon_0} \sigma^2 R$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\frac{1}{\varepsilon_0} \frac{\sigma^2}{R}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\frac{1}{\varepsilon_0} \frac{\sigma^2}{R^2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{1}{\varepsilon_0} \sigma^2 R^2$<br/></span> </div>

answer:
<div class="solution">Electrical force per unit area $=\frac{1}{2} \varepsilon_0 E^2$<br/>$$<br/>=\frac{1}{2} \varepsilon_0\left(\frac{\sigma}{\varepsilon_0}\right)^2=\frac{\sigma^2}{2 \varepsilon_0}<br/>$$<br/>Projected area $=\pi R^2$<br/>$\therefore$ net electrical force $=\left(\frac{\sigma^2}{2 \varepsilon_0}\right)\left(\pi R^2\right)$<br/>In equilibrium, this force should be equal to the applied force.<br/>$\therefore \quad F=\frac{\pi \sigma^2 R^2}{2 \varepsilon_0}$<br/>or $\quad F \propto \frac{\sigma^2 R^2}{\varepsilon_0}$<br/>$\therefore$ The correct option is (a).</div>


tags: ['Physics', 'Experimental Physics', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-vernier-calipers-has-1-mm-marks-on-the-main-scale-it-has-20-equal-divisions-on-the-vernier-scale-which-match-with-16-main-scale-divisions-for-this-v

slug:
a-vernier-calipers-has-1-mm-marks-on-the-main-scale-it-has-20-equal-divisions-on-the-vernier-scale-which-match-with-16-main-scale-divisions-for-this-v-54210

question:
<div class="question">A vernier calipers has $1 \mathrm{~mm}$ marks on the main scale. It has 20 equal divisions on the vernier scale which match with 16 main scale divisions. For this vernier calipers, the least count is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$0.02 \mathrm{~mm}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$0.05 \mathrm{~mm}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$0.1 \mathrm{~mm}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$0.2 \mathrm{~mm}$</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/>$0.2 \mathrm{~mm}$</span> </div>

answer:
<div class="solution">Least count of vernier calipers<br/>$$<br/>\begin{aligned}<br/>&amp; \text { LC }=1 \mathrm{MSD}-1 \text { VSD } \\<br/>&amp; =\frac{\text { Smallest division on main scale }}{\text { Number of divisions on vernier scale }} \\<br/>&amp; 20 \text { divisions of vernier scale } \\<br/>&amp; =16 \text { divisions of main scale } \\<br/>&amp; \therefore \quad 1 \mathrm{VSD}=\frac{16}{20} \mathrm{~mm}=0.8 \mathrm{~mm} \\<br/>&amp; \therefore \quad \text { LC }=1 \mathrm{MSD}-1 \mathrm{VSD} \\<br/>&amp; =1 \mathrm{~mm}-0.8 \mathrm{~mm} \\<br/>&amp; \therefore \quad=0.2 \mathrm{~mm} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>$\therefore$ The correct option is (d).</div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-vibrating-string-of-certain-length-l-under-a-tension-t-resonates-with-a-mode-corresponding-to-the-first-overtone-third-harmonic-of-an-air-column-of-

slug:
a-vibrating-string-of-certain-length-l-under-a-tension-t-resonates-with-a-mode-corresponding-to-the-first-overtone-third-harmonic-of-an-air-column-of-71096

question:
<div class="question">A vibrating string of certain length $l$ under a tension $T$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \mathrm{~cm}$ inside a tube closed at one end. The string also generates 4 beat/s when excited along with a tuning fork of frequency $n$. Now when the tension of the string is slightly increased the number of beats reduces to 2 per second. Assuming the velocity of sound in air to be $340 \mathrm{~m} / \mathrm{s}$, the frequency $n$ of the tuning fork (in $\mathrm{Hz}$ ) is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>344<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/>336<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$117.3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$109.3$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>344<br/></span> </div>

answer:
<div class="solution">With increase in tension, frequency of vibrating string will increase. Since number of beats are decreasing. Therefore, frequency of vibrating string or third harmonic frequency of closed pipe should be less than the frequency of tuning fork by 4 .<br/>$\therefore$ Frequency of tuning fork $=$ Third harmonic frequency of closed pipe $+4$<br/>$$<br/>=3\left(\frac{v}{4 l}\right)+4=3\left(\frac{340}{4 \times 0.75}\right)+4=344 \mathrm{~Hz} .<br/>$$<br/>$\therefore$ correct option is (a).</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
a-wooden-block-performs-shm-on-a-frictionless-surface-with-frequency-v-0-the-block-carries-a-charge-q-on-its-surface-if-now-a-uniform-electric-field-e

slug:
a-wooden-block-performs-shm-on-a-frictionless-surface-with-frequency-v-0-the-block-carries-a-charge-q-on-its-surface-if-now-a-uniform-electric-field-e-28087

question:
<div class="question">A wooden block performs SHM on a frictionless surface with frequency $v_0$. The block carries a charge $+Q$ on its surface. If now a uniform electric field $\mathbf{E}$ is switched on as shown, then the SHM of the block will be<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/qXPG7CDJEoYLFvBG9vbluBL11de7ItNaHitrFT3js1A.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>of the dame frequency and with shifted mean position<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/>of the same frequency and with the same mean position<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>of changed frequency and with shifted mean position<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>of changed frequency and with the same mean position</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>of the dame frequency and with shifted mean position<br/></span> </div>

answer:
<div class="solution">Frequency or time period of SHM depends on variable forces. It does not depend on constant external force. Constant external force can only change the mean position. For example, in the given question mean position is at natural length of spring in the absence of electric field. Whereas in the presence of electric field mean position will be obtained after a compression of $x_0$. Where $x_0$ is given by<br/>or<br/>$$<br/>\begin{aligned}<br/>k x_0 &amp; =Q E \\<br/>x_0 &amp; =\frac{Q E}{k}<br/>\end{aligned}<br/>$$<br/>$\therefore$ Correct answer is (a).<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) I think almost all the serious aspirants of JEE can solve this problem easily.</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
according-to-bohrs-theory-e-n-total-energy-k-n-kinetic-energy-v-n-potential-energy-r-n-radius-of-n-th-orbit-1

slug:
according-to-bohrs-theory-e-n-total-energy-k-n-kinetic-energy-v-n-potential-energy-r-n-radius-of-n-th-orbit-1-66642

question:
<div class="question">According to Bohr's theory $E_n=$ Total energy, $K_n=$ Kinetic energy, $V_n=$ Potential energy, $r_n=$ Radius of $n$th orbit<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Cb6U5AB4zBiuysMvwpBDhXLurpODMACUGrh8ZacVi7c.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) R, (B) Q, (C) P, (D) Q<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) S, (B) R, (C) R, (D) S<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) R, (B) Q, (C) P, (D) S<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/>(A) S, (B) P, (C) R, (D) Q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) R, (B) Q, (C) P, (D) S<br/></span> </div>

answer:
<div class="solution">According to Bohr's theory,<br/>Total energy is $E_n=K_n+V_n$<br/>Kinetic energy $=K_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>Potential energy $=V_n=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>$\therefore \quad E_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>Radius of $n$th orbit $\left(r_n\right)=\frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}$ $$ E_n=-\frac{m e^4}{8 \varepsilon_0^2 h^2} \times \frac{1}{n^2} $$ (A) $\frac{V_n}{K_n}=\frac{-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}{\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}=-2$<br/>Hence, $(A)$ match with $(R)$.<br/>(B) $E_n \propto \frac{1}{n^2}$ or $E_n \propto \frac{1}{r_n}$<br/>Radius of $n$th orbit $r_n \propto E_n^x$ $\therefore \quad x=-1$<br/>Hence, (B) match with (Q).<br/>(C) Angular momentum $=\frac{h}{2 \pi} \sqrt{l(l+1) l}=0,1,2, \ldots$<br/>For the lower orbit $n=1$<br/>$\therefore \quad l=0$ and $m=0$<br/>Hence, angular momentum of lowest orbit $=\frac{h}{2 \pi} \sqrt{0(0 H)}=0$<br/>(C) match with (P)<br/>(D) $\frac{1}{r^n} \propto Z^y$ as $r_n \propto \frac{1}{Z} \therefore y=1$<br/>Hence, (D) match with (S).</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P1.db
title:
according-to-bohrs-theory-e-n-total-energy-k-n-kinetic-energy-v-n-potential-energy-r-n-radius-of-n-th-orbit

slug:
according-to-bohrs-theory-e-n-total-energy-k-n-kinetic-energy-v-n-potential-energy-r-n-radius-of-n-th-orbit-67322

question:
<div class="question">According to Bohr's theory $E_n=$ Total energy, $K_n=$ Kinetic energy, $V_n=$ Potential energy, $r_n=$ Radius of $n$th orbit<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Cb6U5AB4zBiuysMvwpBDhXLurpODMACUGrh8ZacVi7c.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) R, (B) Q, (C) P, (D) Q<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) S, (B) R, (C) R, (D) S<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) R, (B) Q, (C) P, (D) S<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/>(A) S, (B) P, (C) R, (D) Q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) R, (B) Q, (C) P, (D) S<br/></span> </div>

answer:
<div class="solution">According to Bohr's theory,<br/>Total energy is $E_n=K_n+V_n$<br/>Kinetic energy $=K_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>Potential energy $=V_n=\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>$\therefore \quad E_n=\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}$<br/>Radius of $n$th orbit $\left(r_n\right)=\frac{n^2 h^2 \varepsilon_0}{\pi m Z e^2}$ $$ E_n=-\frac{m e^4}{8 \varepsilon_0^2 h^2} \times \frac{1}{n^2} $$ (A) $\frac{V_n}{K_n}=\frac{-\frac{1}{4 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}{\frac{1}{8 \pi \varepsilon_0} \cdot \frac{Z e^2}{r}}=-2$<br/>Hence, $(A)$ match with $(R)$.<br/>(B) $E_n \propto \frac{1}{n^2}$ or $E_n \propto \frac{1}{r_n}$<br/>Radius of $n$th orbit $r_n \propto E_n^x$ $\therefore \quad x=-1$<br/>Hence, (B) match with (Q).<br/>(C) Angular momentum $=\frac{h}{2 \pi} \sqrt{l(l+1) l}=0,1,2, \ldots$<br/>For the lower orbit $n=1$<br/>$\therefore \quad l=0$ and $m=0$<br/>Hence, angular momentum of lowest orbit $=\frac{h}{2 \pi} \sqrt{0(0 H)}=0$<br/>(C) match with (P)<br/>(D) $\frac{1}{r^n} \propto Z^y$ as $r_n \propto \frac{1}{Z} \therefore y=1$<br/>Hence, (D) match with (S).</div>


title: according-to-kinetic-theory-of-gases
slug: according-to-kinetic-theory-of-gases-60800
question: <div class="question">According to kinetic theory of gases</div>
tags: ['Chemistry', 'States of Matter', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>collisions are always elastic<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/>heavier molecules transfer more momentum to the wall of the container<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/>only a small number of molecules have very high velocity<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>between collisions, the molecules move in straight lines with constant velocities</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/>collisions are always elastic<br/>, <br/>heavier molecules transfer more momentum to the wall of the container<br/>, <br/>between collisions, the molecules move in straight lines with constant velocities</span> </div>

answer:
<div class="solution">(a) According to a postulate of kinetic theory of gases, collision between the molecules as well as with the wall of container is perfectly elastic in nature.<br/>(b) If a gas molecule of man ' $m$ ' moving with speed ' $u$ ' collide to the wall of container, the change in momentum is $\Delta p=-2 \mathrm{mu}$. Therefore, heavier molecule will transfer more momentum to the wall as there will be greater change in momentum of the colliding gas malecule. However this was not postulated in kinetic theory of Gases.<br/>(c) According to Maxwell-Boltzmann distribution of molecular speed, very few molecules have either very high or very low speeds. Most of the molecules moves in a specific, intermediate speed range.<br/>(d) According to kinetic theory of gases, a gas molecule moves in straight line unless it collide with another molecular or to the wall of container and change in momentum is observed only after collision.</div>


title: advanced-oogamous-sexual-reproduction-is-found-in
slug: advanced-oogamous-sexual-reproduction-is-found-in-34029
question: <div class="question">Advanced oogamous sexual reproduction is found in:</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Bryophytes</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Pteridophytes</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Gymnosperms</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">More than one option is correct</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">More than one option is correct</span> </div>

answer:
<div class="solution">Oogamy is the form of sexual reproduction and it is a type of heterogamy. Also comes under the part of anisogamy. Oogamy is the fertilization process where the male gamete is received by the female and fusion occurs within the female gamete cell.<br/><br/>In it, the male and female gamete are not of same size and shape.<br/><br/>Such type of reproductive fertilization is observed in Gymnosperm, Bryophytes, and even Pteridophytes</div>


tags: ['Chemistry', 'Chemical Equilibrium', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P1.db
title:
ag-nh-3-ag-nh-3-k-1-35-1-0-3-ag-nh-3-nh-3-ag-nh-3-2-k-2-17-1-0-3-then-the-formation-constant-of-ag-nh-3-2-is

slug:
ag-nh-3-ag-nh-3-k-1-35-1-0-3-ag-nh-3-nh-3-ag-nh-3-2-k-2-17-1-0-3-then-the-formation-constant-of-ag-nh-3-2-is-97855

question:
<div class="question">$\mathrm{Ag}^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+} ; k_1=3.5 \times 10^{-3}$ $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+} ; k_2=1.7 \times 10^{-3}$ then the formation constant of $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$6.08 \times 10^{-6}$<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/>$6.08 \times 10^6$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$6.08 \times 10^{-9}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$6.08 \times 10^{-6}$<br/></span> </div>

answer:
<div class="solution">(i) $\mathrm{Ag}^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+} ; k_1=3.5 \times 10^{-3}$<br/>(ii) $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}+\mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}, k_2=1.7 \times 10^{-3}$<br/>on the basis of above reaction<br/>$$<br/>\begin{aligned}<br/>&amp; k_1=\frac{\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}}{\left[\mathrm{Ag}^{+}\right]\left[\mathrm{NH}_3\right]} \\<br/>&amp; k_2=\frac{\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}}{\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)\right]^{+}\left[\mathrm{NH}_3\right]}<br/>\end{aligned}<br/>$$<br/>For the formation of $\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}$<br/>$$<br/>\mathrm{Ag}^{+}+2 \mathrm{NH}_3 \rightleftharpoons\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}<br/>$$<br/>Formation constant $(K)=\frac{\left[\mathrm{Ag}\left(\mathrm{NH}_3\right)_2\right]^{+}}{\left[\mathrm{Ag}^{+}\right]\left[\mathrm{NH}_3\right]^2}$<br/>From eq. (i) and (ii)<br/>$$<br/>K=k_1 \times k_2=3.5 \times 10^{-3} \times 1.7 \times 10^{-3}=5.95 \times 10^{-6} \approx 6.08 \times 10^{-6}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
agno-3-a-q-was-added-to-an-aqueous-kcl-solution-gradually-and-the-conductivity-of-the-solution-was-measured-the-plot-of-conductance-versus-the-volume-

slug:
agno-3-a-q-was-added-to-an-aqueous-kcl-solution-gradually-and-the-conductivity-of-the-solution-was-measured-the-plot-of-conductance-versus-the-volume-68128

question:
<div class="question">$\mathrm{AgNO}_3(a q)$ was added to an aqueous $\mathrm{KCl}$ solution gradually and the conductivity of the solution was measured. The plot of conductance $(\Lambda)$ versus the volume of $\mathrm{AgNO}_3$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/x4Pn93AWrdiTkVBRs6YPrh21nwy2nt14bs0_b-LZpos.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$P$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$Q$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$R$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$S$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">As $\mathrm{AgNO}_3$ is added to solution, $\mathrm{KCl}$ will be displaced accrding to following reaction<br/>$$<br/>\mathrm{AgNO}_3(a q)+\mathrm{KCl}(a q) \longrightarrow \operatorname{AgCl}(s)+\mathrm{KNO}_3(a q)<br/>$$<br/>For every mole of $\mathrm{KCl}$ displaced from solution, one mole of $\mathrm{KNO}_3$ comes in solution resulting in almost constant conductivity. As the end point is reached, added $\mathrm{AgNO}_3$ remain in solution increasing ionic concentration, hence conductivity increases.</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Main']
source_db: MarksBatch1_P1.db
title:
all-the-compounds-listed-in-column-i-react-with-water-match-the-result-of-the-respective-reactions-with-the-appropriate-options-listed-in-column-ii-1

slug:
all-the-compounds-listed-in-column-i-react-with-water-match-the-result-of-the-respective-reactions-with-the-appropriate-options-listed-in-column-ii-1-18130

question:
<div class="question">All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0hk2ELITLGEeE6FsrD3YGnb7BhaBybjkCUYWJE087tg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) P,Q, (B) P,Q,R,T, (C) P,Q,T, (D) P<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) P,Q, (B) P,Q,T, (C) P,Q,R,T, (D) Q<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) P,S, (B) P,Q,R,T, (C) P,Q,T, (D) P<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/>(A) P,S, (B) P,Q,T, (C) P,Q,R,T, (D) Q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) P,S, (B) P,Q,R,T, (C) P,Q,T, (D) P<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oweF3s_sEGUv-gYhQtMusEWCNTt0D1g6YYpgxpH50pg.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \quad 3 \mathrm{XeF}_4+6 \mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{XeO}_3+2 \mathrm{Xe}+\frac{3}{2} \mathrm{O}_2+12 \mathrm{HF} \\<br/>&amp; \quad \mathrm{Cl}_2+\mathrm{H}_2 \mathrm{O} \longrightarrow 2 \mathrm{HCl}+\frac{1}{2} \mathrm{O}_2 \\<br/>&amp; \quad \mathrm{VCl}_5+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{VOCl}_3+2 \mathrm{HCl} \\<br/>&amp; \text { Representative elements } \\<br/>&amp; \text { Factual } \\<br/>&amp; \text { III }<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
all-the-compounds-listed-in-column-i-react-with-water-match-the-result-of-the-respective-reactions-with-the-appropriate-options-listed-in-column-ii

slug:
all-the-compounds-listed-in-column-i-react-with-water-match-the-result-of-the-respective-reactions-with-the-appropriate-options-listed-in-column-ii-14384

question:
<div class="question">All the compounds listed in Column I react with water. Match the result of the respective reactions with the appropriate options listed in Column II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/0hk2ELITLGEeE6FsrD3YGnb7BhaBybjkCUYWJE087tg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) P,Q, (B) P,Q,R,T, (C) P,Q,T, (D) P<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) P,Q, (B) P,Q,T, (C) P,Q,R,T, (D) Q<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) P,S, (B) P,Q,R,T, (C) P,Q,T, (D) P<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/>(A) P,S, (B) P,Q,T, (C) P,Q,R,T, (D) Q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) P,S, (B) P,Q,R,T, (C) P,Q,T, (D) P<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oweF3s_sEGUv-gYhQtMusEWCNTt0D1g6YYpgxpH50pg.original.fullsize.png"/><br/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; \quad 3 \mathrm{XeF}_4+6 \mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{XeO}_3+2 \mathrm{Xe}+\frac{3}{2} \mathrm{O}_2+12 \mathrm{HF} \\<br/>&amp; \quad \mathrm{Cl}_2+\mathrm{H}_2 \mathrm{O} \longrightarrow 2 \mathrm{HCl}+\frac{1}{2} \mathrm{O}_2 \\<br/>&amp; \quad \mathrm{VCl}_5+\mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{VOCl}_3+2 \mathrm{HCl} \\<br/>&amp; \text { Representative elements } \\<br/>&amp; \text { Factual } \\<br/>&amp; \text { III }<br/>\end{aligned}<br/>$$</div>


title: alzhimer-disease-in-humans-is-associated-with-the-deficiency-of-1
slug: alzhimer-disease-in-humans-is-associated-with-the-deficiency-of-1-27314
question: <div class="question">Alzhimer disease in humans is associated with the deficiency of</div>
tags: ['Biology', 'Neural Control and Coordination', 'NEET', 'NEET 2009 (Screening)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">dopamine</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">glutamic acid</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">acetylcholine</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">Gamma Amino Butyric Acid (GABA)</span> </li> </ul>

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

answer:
<div class="solution">Alzhimer disease in humans is associated with the deficiency of acetylcholine. Alzhimer's Disease (AD) is an irreversible, progressive disorder, in which brain cells (neurons) deteriorate, resulting in the loss of cognitive functions, primarily memory, judgement and reasoning, movement coordination and pattern recognition. In advanced stages of the disease, all memory and mental functioning may be lost.<br/>Dopamine and glutamic acid are excitatory neurotransmitters, while Gama Amino Butyric Acid (GABA) is inhibitory neurotransmitter.</div>


tags: ['Chemistry', 'Polymers', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
among-cellulose-polyvinyl-chloride-nylon-and-natural-rubber-the-polymer-in-which-the-intermolecular-force-of-attraction-is-weakest-in

slug:
among-cellulose-polyvinyl-chloride-nylon-and-natural-rubber-the-polymer-in-which-the-intermolecular-force-of-attraction-is-weakest-in-45199

question:
<div class="question">Among cellulose, polyvinyl chloride, nylon and natural rubber, the polymer in which the intermolecular force of attraction is weakest in</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>nylon<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>polyvinyl chloride<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>cellulose<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>natural rubber</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/>natural rubber</span> </div>

answer:
<div class="solution">$$<br/>\text { Nylon has amid linkage capable of forming intermolecular } \mathrm{H} \text {-bonding as }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/2Z4rUd48WCf_t7lkv_gHa5HajDJtInxtryet1Vuhhl8.original.fullsize.png"/><br/><br/>Due to $\mathrm{H}$-bonding, nylon has strong intermolecular attraction.<br/>Cellulose is a polyhydroxy compound, also capable of forming strong intermolecular $\mathrm{H}$-bonding. Polyvinyl chloride is a polar polymer due to carbon chlorine bond and it possess strong dipole-dipole attraction. Natural rubber is poly (isoprene), a hydrocarbon, possess weak van der Waal's attraction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/f5i0Bw1-Ql-QNczMQa41ENvUzZ4r3kWg82G8MZwPurQ.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
among-the-electrolytes-na-2-so-4-cacl-2-al-2-so-4-3-and-nh-4-cl-the-most-effective-coagulating-agent-for-sb-2-s-3-sol-is

slug:
among-the-electrolytes-na-2-so-4-cacl-2-al-2-so-4-3-and-nh-4-cl-the-most-effective-coagulating-agent-for-sb-2-s-3-sol-is-37265

question:
<div class="question">Among the electrolytes $\mathrm{Na}_2 \mathrm{SO}_4, \mathrm{CaCl}_2 \quad \mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$ and $\mathrm{NH}_4 \mathrm{Cl}$, the most effective coagulating agent for $\mathrm{Sb}_2 \mathrm{~S}_3$ sol is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{SO}_4$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{CaCl}_2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$<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=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{NH}_4 \mathrm{Cl}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$<br/></span> </div>

answer:
<div class="solution">$\mathrm{Sb}_2 \mathrm{~S}_3$ is an anionic $\mathrm{sol}_2$, therefore cation of highest valency ( $\mathrm{Al}^{3+}$ in the present case) would be most effective coagulating agent.</div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
among-the-following-complexes-k-p-k-3-fe-cn-6-k-co-nh-3-6-cl-3-l-na-3-co-ox-3-m-ni-h-2-o-6-cl-2-n-k-2-pt-cn-4-o-and-zn-h-2-o-6-no-3-2-p-the-diamagneti

slug:
among-the-following-complexes-k-p-k-3-fe-cn-6-k-co-nh-3-6-cl-3-l-na-3-co-ox-3-m-ni-h-2-o-6-cl-2-n-k-2-pt-cn-4-o-and-zn-h-2-o-6-no-3-2-p-the-diamagneti-73372

question:
<div class="question">Among the following complexes $(K-P), \mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right](K)$,<br/>$\left[\right.$ Co $\left.\left(\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3(L), \mathrm{Na}_3\left[\mathrm{Co}(\mathrm{ox})_3\right](M)$,<br/>$\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2(\mathrm{~N}) ; \mathrm{K}_2\left[\mathrm{Pt}(\mathrm{CN})_4\right](\mathrm{O})$ and $\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]\left(\mathrm{NO}_3\right)_2(P)$<br/>the diamagnetic complexes are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$K, L, M, N$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$K, M, O, P$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$L, M, O, P$<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/>$L, M, N, O$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$L, M, O, P$<br/></span> </div>

answer:
<div class="solution">For a diamagnetic complex, there should not be any unpaired electron in the valence shell of central metral. In $\mathrm{K}_3\left[\mathrm{Fe}(\mathrm{CN})_6\right]$, Fe (III) has $d^5$-configuration (odd electrons), hence it is paramagnetic. In [Co( $\left.\left.\mathrm{NH}_3\right)_6\right] \mathrm{Cl}_3$, Co (III) has $d^6$ configuration in a strong ligand field, hence all the electrons are paired and the complex is diamagnetic. In $\mathrm{Na}_3\left[\mathrm{Co}(\mathrm{ox})_3\right]$, $\mathrm{Co}$ (III) has $d^6$-configuration and oxalate being a chelating ligand, very strong ligand and all the six electrons remains paired in lower $t_{2 g}$ level, diamagnetic. In $\left[\mathrm{Ni}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2, \mathrm{Ni}$ (II) has $3 d^8$-configuration and $\mathrm{H}_2 \mathrm{O}$ is a weak ligand hence<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/T0l1eNBPbT2HADRNqn874uc1D_ERRV9xCGH61v78SvM.original.fullsize.png"/><br/><br/>In $\mathrm{K}_2\left[\mathrm{Pt}(\mathrm{CN})_4\right]$, Pt (II) has $d^8$-configuration and $\mathrm{CN}^{-}$is a strong ligand, hence all the eight electrons are spin-paired. Therefore, complex is diamagnetic.<br/>In $\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]\left(\mathrm{NO}_3\right)_2, \mathrm{Zn}$ (II) has ${ }_3 \mathrm{~d}^{10}$ configuration spin paired, hence diamagnetic.</div>


title: among-the-following-compounds-the-most-acidic-is-1
slug: among-the-following-compounds-the-most-acidic-is-1-95462
question: <div class="question">Among the following compounds, the most acidic is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>p-nitrophenol<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>p-hydroxybenzoic acid<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>o-hydroxybenzoic acid<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/>p-toluic acid</span> </li> </ul>

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

answer:
<div class="solution">A monosubstituted benzoic acid is stronger than a monosubstituted phenol as former being a carboxylic acid. Among the given substituted benzoic acid, ortho-hydroxy acid is strongest acid although - $\mathrm{OH}$ cause electron donation by resonance effect which tends to decrease acid strength. It is due to a very high stabilization of conjugate base by intramolecular $\mathrm{H}$-bond which outweight the electron donating resonance effect of $-\mathrm{OH}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/-_R3456jzv-jkE5o0JKkL7Pr1EIFv0fQR1bIMd_tOC8.original.fullsize.png"/><br/><br/>The overall order of acid-strength of given four acids is ortho-hydro $x y$ benzoic acid $\left(p K_a=298\right)&gt;$ Toluic acid $\left.p K_a=4.37\right)&gt;p$-hydroxybenzoic acid $\left(p K_a=4.58\right)&gt;$ $p$-nitrophenol $\left(p K_a=7.15\right)$.</div>


title: among-the-following-intensive-property-is-properties-are
slug: among-the-following-intensive-property-is-properties-are-79683
question: <div class="question">Among the following, intensive property is (properties are)</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>molar conductivity<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/>electromotive force<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/>resistance<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>heat capacity</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>molar conductivity<br/>, <br/>electromotive force<br/></span> </div>

answer:
<div class="solution">Intensive property is one whose magnitude does not depend on the mass of the substance. Opposite to that is extensive property.<br/>Energetics<br/>Conceptual, concept analysis<br/>III</div>


title: among-the-following-metal-carbonyls-the-c-o-bond-order-is-lowest-in
slug: among-the-following-metal-carbonyls-the-c-o-bond-order-is-lowest-in-81936
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch1_P1.db
question:
<div class="question">Among the following metal carbonyls, the $\mathrm{C}-\mathrm{O}$ bond order is lowest in</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\left[\mathrm{MO}(\mathrm{CO})_6\right]^{+}$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\left[\mathrm{Fe}(\mathrm{CO})_5\right]$	<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/>$\left[\mathrm{Cr}(\mathrm{CO})_6\right]$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\left[\mathrm{V}(\mathrm{CO})_6\right]^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\left[\mathrm{Fe}(\mathrm{CO})_5\right]$	<br/></span> </div>

answer:
<div class="solution">(a) $\mathrm{Mn}^{+}=3 d^5 4 s^1$ In presence of $\mathrm{CO}$ effective configuration $=3 d^6 4 s^0, 3$ lone pair for back bonding with vacant orbital of $\mathrm{C}$ in $\mathrm{CO}$.<br/>(b) $\mathrm{Fe}^{\circ}=3 d^6 4 s^2$ in presence of $\mathrm{CO}$ effective configuration $=3 d^8, 4$ lone pair for back bonding with $\mathrm{CO}$.<br/>(c) $\mathrm{Cr}^{\circ}=3 d^5 4 s^1$, effective configuration $=3 d^6$<br/>3 lone pair for back bonding with $\mathrm{CO}$.<br/>(d) $\mathrm{V}^{-}=3 d^4 s^2$, effective configuration $=3 d^6, 3$ lone pair for back bonding with $\mathrm{CO}$. Maximum back bonding in $\mathrm{Fe}(\mathrm{CO})_5$, therefore $\mathrm{CO}$ bond order is lowest here.</div>


title: among-the-following-the-coloured-compound-is-1
slug: among-the-following-the-coloured-compound-is-1-27219
question: <div class="question">Among the following, the coloured compound is</div>
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{CuCl}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{K}_3\left[\mathrm{Cu}(\mathrm{CN})_4\right]$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{CuF}_2$<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">D</span> <span class="option-data"><br/>$\left[\mathrm{Cu}\left(\mathrm{CH}_3 \mathrm{CN}_4\right)\right] \mathrm{BF}_4$</span> </li> </ul>

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

answer:
<div class="solution">In $\mathrm{CuF}_2, \mathrm{Cu}^{2+}$ ions exist, having $d^9$-configuration. Unpaired electron causes colour ( $d-d$ transition)<br/>In the crystalline form, $\mathrm{CuF}_2$ is blue coloured</div>


title: among-the-following-the-least-stable-resonance-structure-is
slug: among-the-following-the-least-stable-resonance-structure-is-39215
question: <div class="question">Among the following, the least stable resonance structure is</div>
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
source_db: MarksBatch1_P1.db
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/fh4TbbuuKEpBc6Ts7ZXX92g0Nu3Oagls8l3X0BbobGc.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/elxRC_ZohVOwtwsXsTNVfTRvxuaI6_oW4WX50r6lVBw.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/zO0CjtGAZALcUInCFs1aIgmue-GO7dTmyj9y40yETsM.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/Nl1Ztle3JkBXT41gmN_ITqiSD_ino4Gfo-ADjO5czd8.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/fh4TbbuuKEpBc6Ts7ZXX92g0Nu3Oagls8l3X0BbobGc.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Tow positive charges are present at the adjacent place, elevates the energy lowers the stability most.</div>


options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P1.db
title:
among-the-following-the-number-of-compounds-than-can-react-with-pcl-5-to-give-pocl-3-is-o-2-co-2-so-2-h-2-o-h-2-so-4-p-4-o-10

slug:
among-the-following-the-number-of-compounds-than-can-react-with-pcl-5-to-give-pocl-3-is-o-2-co-2-so-2-h-2-o-h-2-so-4-p-4-o-10-64169

question:
<div class="question">Among the following, the number of compounds than can react with $\mathrm{PCl}_5$ to give $\mathrm{POCl}_3$ is $\mathrm{O}_2, \mathrm{CO}_2, \mathrm{SO}_2, \mathrm{H}_2 \mathrm{O}, \mathrm{H}_2 \mathrm{SO}_4, \mathrm{P}_4 \mathrm{O}_{10}$.</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']

answer:
<div class="solution">$$<br/>\text { } \mathrm{PCl}_5 \text { produces } \mathrm{POCl}_3 \text { with the following reagents }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/cekVD76OhILpF3olLzcENWVbk3RxyUJJzJVPltU7UI4.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch1_P1.db
title:
among-the-following-the-number-of-elements-showing-only-one-nonzero-oxidation-state-is-o-cl-f-n-p-sn-tl-na-ti

slug:
among-the-following-the-number-of-elements-showing-only-one-nonzero-oxidation-state-is-o-cl-f-n-p-sn-tl-na-ti-20611

question:
<div class="question">Among the following, the number of elements showing only one non-zero oxidation state is O, Cl, F, N, P, Sn, Tl, $\mathrm{Na}, \mathrm{Ti}$</div>

answer:
<div class="solution">F is the most electronegative element which cannot loose electron to other so only $-1$ Na is alkali metal which can loose only one electron so $+1$ Basics of general chemistry Basic understanding I</div>


title: among-the-following-the-paramagnetic-compound-is-2
slug: among-the-following-the-paramagnetic-compound-is-2-36704
question: <div class="question">Among the following, the paramagnetic compound is</div>
source_db: MarksBatch1_P1.db
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/>$\mathrm{Na}_2 \mathrm{O}_2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{O}_3$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{N}_2 \mathrm{O}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{KO}_2$</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/>$\mathrm{KO}_2$</span> </div>

answer:
<div class="solution">For $\mathrm{KO}_2, \mathrm{O}_2^{-}$has unpaired $e^{-} \Rightarrow$ paramagnetic<br/>$$<br/>\begin{gathered}<br/>\mathrm{O}_2^{-} \text {: Total } e^{-} s=16+1=17 \\<br/>\sigma 1 s^2, \sigma^* 1 s^2 \sigma 2 s^2, \sigma^* 2 s^2, \sigma 2 p_z^2 \pi 2 p_x^{1+1} \\<br/>=\pi 2 p_y^{1+1}, \pi^* 2 p_x^{1+1}=\pi 2 p_y^1<br/>\end{gathered}<br/>$$</div>


title: among-the-following-the-state-functions-is-are
slug: among-the-following-the-state-functions-is-are-63034
question: <div class="question">Among the following, the state function(s) is (are)</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch1_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>internal energy<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/>irreversible expansion work<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>reversible expansion work<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/>molar enthalpy</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/>internal energy<br/>, <br/>reversible expansion work<br/>, <br/>molar enthalpy</span> </div>

answer:
<div class="solution">State function are internal energy and molar enthalpy. Work is a path dependent function, however in reversible process the path is fixed i.e. between a given initial and final state there is just on reversible path and one work. Hence, reversible work is also a state function.</div>


tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
among-the-following-the-surfactant-that-will-form-micelles-in-aqueous-solution-at-the-lowest-molar-concentration-at-ambient-conditions-is

slug:
among-the-following-the-surfactant-that-will-form-micelles-in-aqueous-solution-at-the-lowest-molar-concentration-at-ambient-conditions-is-27800

question:
<div class="question">Among the following, the surfactant that will form micelles in aqueous solution at the lowest molar concentration at ambient conditions is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{15} \mathrm{~N}^{+}\left(\mathrm{CH}_3\right)_3 \mathrm{Br}^{-}$<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/>$\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{11} \mathrm{OSO}_3^{-} \mathrm{Na}^{+}$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{CH}_3\left(\mathrm{CH}_2\right)_6 \mathrm{COO}^{-} \mathrm{Na}^{+}$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{11} \mathrm{~N}^{+}\left(\mathrm{CH}_3\right)_3 \mathrm{Br}^{-}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{CH}_3\left(\mathrm{CH}_2\right)_{15} \mathrm{~N}^{+}\left(\mathrm{CH}_3\right)_3 \mathrm{Br}^{-}$<br/></span> </div>

answer:
<div class="solution">Sodium Hexadecyl trimethylammonium bromide (CTAB) dodecylsulphate<br/>(SDS)<br/>CMC $(\mathrm{mm})&gt;-10$<br/>1</div>


tags: ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
amongst-the-compounds-given-the-one-that-would-form-a-brilliant-coloured-dye-on-treatment-with-nano-2-in-dil-hcl-followed-by-addition-to-an-alkaline-s

slug:
amongst-the-compounds-given-the-one-that-would-form-a-brilliant-coloured-dye-on-treatment-with-nano-2-in-dil-hcl-followed-by-addition-to-an-alkaline-s-43895

question:
<div class="question">Amongst the compounds given, the one that would form a brilliant coloured dye on treatment with $\mathrm{NaNO}_2$ in dil. $\mathrm{HCl}$ followed by addition to an alkaline solution of $\beta$-naphthol 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/mQ-BS1F3lcaW9px3IYKgxkGB_DU0EalH19k0RQlvJQg.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/hH39OZYv9JS3aVtao692gBsysk2jzAV5wCmVqF9IHhw.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/wdTrtd5glbmjWpCGRy2P-V_cVmw414733MSMbZfgziU.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/-6j4s02v4yqgr57bpjac9YYSCvou2_kNFVFtWIk8cXc.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/wdTrtd5glbmjWpCGRy2P-V_cVmw414733MSMbZfgziU.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">As we know, benzenediazonium salt forms brilliant coloured dye with $\beta$-naphthol, the compound under consideration must be $p$-toludine (c) as it is a primary aromatic amine. Primary aromatic amine, on treatment with $\mathrm{NaNO}_2$ in dil. $\mathrm{HCl}$ forms the corresponding diazonium chloride salt.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3Jskadp3YQ0Ek6wFzvnzKRKAsV2LXoPiQgOeJrI_FoQ.original.fullsize.png"/><br/></div>


title: amongst-the-following-the-total-number-of-compounds-soluble-in-aqueous-naoh-is-1
slug: amongst-the-following-the-total-number-of-compounds-soluble-in-aqueous-naoh-is-1-19886
tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P1.db
question:
<div class="question">Amongst the following, the total number of compounds soluble in aqueous $\mathrm{NaOH}$ is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tCOmZXRhtaAWdcteEiQe0pj46L45cc7M-cV_wIxgNfw.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/A8qfPc8i9DqJcVuDcNsgF-ooEeQkWYQTrnAd7UAuciI.original.fullsize.png"/><br/></div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/aT7yYOKEEAj6wXDCt7ay0_W2OlTN5PGqF3R47uO0zFw.original.fullsize.png"/><br/><br/>are soluble in aqueous $\mathrm{NaOH}$. Benzylic alcohol is less acidic than water so not soluble in aq. $\mathrm{NaOH}$, General organic chemistry Conceptual (structural interpretation) III</div>


tags: ['Chemistry', 'Ionic Equilibrium', '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: MarksBatch1_P1.db
title:
amongst-the-following-the-total-number-of-compounds-whose-aqueous-solution-turns-red-litmus-paper-blue-is-kcn-zn-no-3-2-licn-k-2-so-4-fecl-3-nh-4-2-c-

slug:
amongst-the-following-the-total-number-of-compounds-whose-aqueous-solution-turns-red-litmus-paper-blue-is-kcn-zn-no-3-2-licn-k-2-so-4-fecl-3-nh-4-2-c-11516

question:
<div class="question">Amongst the following, the total number of compounds whose aqueous solution turns red litmus paper blue is<br/>$$<br/>\begin{array}{llll}<br/>\mathrm{KCN} &amp; \mathrm{K}_2 \mathrm{SO}_4 &amp; \left(\mathrm{NH}_4\right)_2 \mathrm{C}_2 \mathrm{O}_4 &amp; \mathrm{NaCl} \\<br/>\mathrm{Zn}\left(\mathrm{NO}_3\right)_2 &amp; \mathrm{FeCl}_3 &amp; \mathrm{~K}_2 \mathrm{CO}_3 &amp; \mathrm{NH}_4 \mathrm{NO}_3 \\<br/>\mathrm{LiCN} &amp; &amp; &amp;<br/>\end{array}<br/>$$</div>

answer:
<div class="solution">The aqueous solution of $\mathrm{KCN}, \mathrm{K}_2 \mathrm{CO}_3$ and LiCN turn red litmus blue because of alkaline nature.<br/>The anionic hydrolysis turns the solution alkaline.<br/>Ionic equilibrium<br/>Conceptual<br/>III</div>


tags: ['Chemistry', 'General Organic Chemistry', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
amongst-the-given-options-the-compound-s-in-which-all-the-atoms-are-in-one-plane-in-all-the-possible-conformations-if-any-is-are

slug:
amongst-the-given-options-the-compound-s-in-which-all-the-atoms-are-in-one-plane-in-all-the-possible-conformations-if-any-is-are-53931

question:
<div class="question">Amongst the given options, the compound (s) in which all the atoms are in one plane in all the possible conformations (if any), is (are)</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/jG4RkpxSj1LVUKzumBuq3a1DSrf4PgBWZvVtBWiuWqw.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ruZFKo_HK-Z1YGDQ8DdN4SmNiEgIYWUxBYoaB3dvFIw.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="correct"> <span class="option-label">C</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/RFSIrSeRErxsfzhrjqQjrtAvHCsNEXwwDJC46s124pI.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/QtfDoX70mB4XtKhZscYmBjjRFPK9YS8xhh_MEiFrcNg.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/ruZFKo_HK-Z1YGDQ8DdN4SmNiEgIYWUxBYoaB3dvFIw.original.fullsize.png"/><br/>, <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/RFSIrSeRErxsfzhrjqQjrtAvHCsNEXwwDJC46s124pI.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$$<br/>\text { In both (b) and (c), all the atoms are present in one single plane }<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/U9RMovarqczfIWlyG0E67-jhWyQok5ZC2oMUBk3nh4M.original.fullsize.png"/><br/><br/>In (a) 1, 3-butadiene, conformational change is possible between $\mathrm{C}_2-\mathrm{C}_3$ bond in which atoms will be present in more than one single plane.<br/>In (d) allene, the terminals $\mathrm{H}-\mathrm{C}-\mathrm{H}$ planes are perpendicular to one another.<br/>$$<br/>\text { Paragraph (12 and 13) The final ozonolysis product indicates that the alkene before }<br/>$$<br/>Ozonolysis is<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/PLevuZkZG3_QAMbDUFsU94aLkCRRp7kYv9omXZfxoaA.original.fullsize.png"/><br/><br/>Also $\mathrm{P}\left(\mathrm{C}_6 \mathrm{H}_{10}\right)$ has two degree of unsaturation and oxymercuration demercuration hydration indicates that it is an alkyne. As alkyne, on hydration, gives a carbonyl compound which on reduction with $\mathrm{NaBH}_4$ gives a $2^{\circ}$ alcohol.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LOWh-Q3QFd-wT8dVOKSxuXWYH-Mo91UCITkLenTqJWs.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/vtYBeQq5ceBO-5LO96nBteHn3WVwrPXQa8753naBenc.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
an-ac-voltage-source-of-variable-angular-frequency-and-fixed-amplitude-v-0-is-connected-in-series-with-a-capacitance-c-and-an-electric-bulb-of-resista-1

slug:
an-ac-voltage-source-of-variable-angular-frequency-and-fixed-amplitude-v-0-is-connected-in-series-with-a-capacitance-c-and-an-electric-bulb-of-resista-1-97224

question:
<div class="question">An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>the bulb glows dimmer<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>the bulb glows brighter<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/>total impedance of the circuit is unchanged<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>total impedance of the circuit increases</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>the bulb glows brighter<br/></span> </div>

answer:
<div class="solution">$Z=\sqrt{R^2+X_C^2}: I_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{Z}: P=I_{\mathrm{rms}}^2 R$ where, $\quad X_C=\frac{1}{\omega C}$<br/>As $\omega$ is increased, $X_C$ will decrease or $Z$ will decrease. Hence $I_{\mathrm{mms}}$ or $P$ will increase. Therefore, bulb glows brighter.<br/>Hence the correct option is (b).</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
an-electron-and-a-proton-are-moving-on-straight-parallel-paths-with-same-velocity-they-enter-a-semiinfinite-region-of-uniform-magnetic-field-perpendic

slug:
an-electron-and-a-proton-are-moving-on-straight-parallel-paths-with-same-velocity-they-enter-a-semiinfinite-region-of-uniform-magnetic-field-perpendic-84509

question:
<div class="question">An electron and a proton are moving on straight parallel paths with same velocity. They enter a semi-infinite region of uniform magnetic field perpendicular to the velocity. Which of the following statement(s) is/are true?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>They will never come out of the magnetic field region<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>They will come out travelling along parallel paths<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/>They will come out at the same time<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>They will come out at different times</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/>They will come out travelling along parallel paths<br/>, <br/>They will come out at different times</span> </div>

answer:
<div class="solution">$\quad r=\frac{m v}{B q}$<br/>or $\quad r \propto m$<br/>$\therefore r_e &lt; r_p$ as $m_e &lt; m_p$<br/>Further, $\quad T=\frac{2 \pi m}{B q}$<br/>or $\quad T \propto m$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/g_AtYJ68EHOj3DMGv-AIig9FQDGi2RQeeQhj7Awaryo.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>\therefore \quad T_e &amp; &lt; T_p \\<br/>t_e &amp; =\frac{T_e}{2}<br/>\end{aligned}<br/>$$<br/>and<br/>or $\quad t_e &lt; t_p$<br/>$\therefore$ Correct options are (b) and (d).<br/>Note In JEE 2011, official answer key, correct options were given bc, bd, bcd, here student should realise that both the electron and proton enter the magnetic field at the same time or at different times.<br/>Analysis of Question<br/>(i) Question is simple.<br/>(ii) In the situation given above particle will never complete the circle unless magnetic field is all around.</div>


tags: ['Mathematics', 'Ellipse', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
an-ellipse-intersects-the-hyperbola-2-x-2-2-y-2-1-orthogonally-the-eccentricity-of-the-ellipse-is-reciprocal-to-that-of-the-hyperbola-if-the-axes-of-t

slug:
an-ellipse-intersects-the-hyperbola-2-x-2-2-y-2-1-orthogonally-the-eccentricity-of-the-ellipse-is-reciprocal-to-that-of-the-hyperbola-if-the-axes-of-t-40381

question:
<div class="question">An ellipse intersects the hyperbola $2 x^2-2 y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>equation of ellipse is $x^2+2 y^2=2$<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/>the foci of ellipse are $(\pm 1,0)$<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/>equation of ellipse is $x^2+2 y^2=4$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>the foci of ellipse are $(\pm \sqrt{2}, 0)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>equation of ellipse is $x^2+2 y^2=2$<br/>, <br/>the foci of ellipse are $(\pm 1,0)$<br/></span> </div>

answer:
<div class="solution">Given, $2 x^2-2 y^2=1$<br/>$$<br/>\Rightarrow \quad \frac{x^2}{\left(\frac{1}{2}\right)}-\frac{y^2}{\left(\frac{1}{2}\right)}=1<br/>$$<br/>Eccentricity of hyperbola $=\sqrt{2}$<br/>So, eccentricity of ellipse $=1 / \sqrt{2}$<br/>Let equation of ellipse be<br/>$$<br/>\begin{aligned}<br/>&amp; \frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a&gt;b) \Rightarrow \frac{1}{\sqrt{2}}=\sqrt{1-\frac{b^2}{a^2}} \\<br/>&amp; \Rightarrow \quad \frac{b^2}{a^2}=\frac{1}{2} \Rightarrow a^2=2 b^2 \\<br/>&amp; \therefore \quad x^2+2 y^2=2 b^2 \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Let ellipse and hyperbola intersect at<br/>$$<br/>A\left(\frac{1}{\sqrt{2}} \sec \theta, \frac{1}{\sqrt{2}} \tan \theta\right)<br/>$$<br/>On differentiating Eq. (i),<br/>$$<br/>4 x-4 y \frac{d y}{d x}=0 \Rightarrow \frac{d y}{d x}=\frac{x}{y}<br/>$$<br/><br/>$$<br/>\therefore \quad\left(\frac{d y}{d x}\right)_{\text {at } A}=\frac{\sec \theta}{\tan \theta}=\operatorname{cosec} \theta<br/>$$<br/>On differentiating Eq. (ii),<br/>$$<br/>2 x+4 y \frac{d y}{d x}=0<br/>$$<br/><br/>$$<br/>\therefore \quad\left(\frac{d y}{d x}\right)_{\text {at } A}=-\frac{x}{2 y}=-\frac{1}{2} \operatorname{cosec} \theta<br/>$$<br/>Since, ellipse and hyperbola are orthogonal.<br/>$$<br/>\begin{aligned}<br/>&amp; \therefore \quad-\frac{1}{2} \operatorname{cosec}^2 \theta=-1 \\<br/>&amp; \Rightarrow \quad \operatorname{cosec}^2 \theta=2 \Rightarrow \theta=\pm \frac{\pi}{4} \\<br/>&amp; \therefore A\left(1, \frac{1}{\sqrt{2}}\right) \text { or }\left(1,-\frac{1}{\sqrt{2}}\right)<br/>\end{aligned}<br/>$$<br/>From Eq. (i), $1+2\left(\frac{1}{\sqrt{2}}\right)^2=2 b^2$ $\Rightarrow \quad b^2=1$<br/>Equation of ellipse is $x^2+2 y^2=2$<br/>Coordinate of foci $(\pm a e, 0)$<br/>$$<br/>=\left(\pm \sqrt{2} \cdot \frac{1}{\sqrt{2}}, 0\right)=(\pm 1,0)<br/>$$<br/>Hence, options (a) and (b) are correct. If major axis is along $Y$-axis, then<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \frac{1}{\sqrt{2}}=\sqrt{1-\frac{a^2}{b^2}} \Rightarrow b^2=2 a^2 \\<br/>&amp; \therefore 2 x^2+y^2=2 a^2 \Rightarrow y^{\prime}=-\frac{2 x}{y} \\<br/>&amp; \Rightarrow \quad y^{\prime}\left(\frac{1}{\sqrt{2}} \sec \theta \frac{1}{\sqrt{2}} \tan \theta\right)=\frac{-2}{\sin \theta} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>As ellipse and hyperbola are orthogonal.<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; -\frac{2}{\sin \theta} \cdot \operatorname{cosec} \theta=-1 \\<br/>\Rightarrow &amp; \operatorname{cosec}^2 \theta=1 \Rightarrow \theta=\pm \frac{\pi}{4} \\<br/>\therefore &amp; 2 x^2+y^2=2 a^2 \Rightarrow 2+\frac{1}{2}=2 a^2 \\<br/>\Rightarrow &amp; a^2=\frac{5}{4} \Rightarrow 2 x^2+y^2=\frac{5}{2}<br/>\end{array}<br/>$$<br/>Corresponding foci are $(0, \pm 1)$.</div>


tags: ['Mathematics', 'Probability', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
an-experiment-has-10-equally-likely-outcomes-let-a-and-b-be-two-nonempty-events-of-the-experiment-if-a-consists-of-4-outcomes-the-number-of-outcomes-t

slug:
an-experiment-has-10-equally-likely-outcomes-let-a-and-b-be-two-nonempty-events-of-the-experiment-if-a-consists-of-4-outcomes-the-number-of-outcomes-t-77915

question:
<div class="question">An experiment has 10 equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of 4 outcomes, the number of outcomes that $B$ must have so that $A$ and $B$ are independent, is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>2,4 or 8<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>3,6 or 9<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>4 or 8<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>5 or 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/>5 or 10</span> </div>

answer:
<div class="solution">$P(A)=\frac{2}{5}$<br/>For independent events,<br/>$$<br/>\begin{aligned}<br/>&amp; P(A \cap B)=P(A) P(B) \Rightarrow P(A \cap B) \leq \frac{2}{5} \\<br/>&amp; \Rightarrow P(A \cap B)=\frac{1}{10}, \frac{2}{10}, \frac{3}{10}, \frac{4}{10} \\<br/>&amp; \text { (i) } P(A \cap B)=\frac{1}{10} \\<br/>&amp; \Rightarrow P(A) \cdot P(B)=\frac{1}{10} \\<br/>&amp; \Rightarrow \quad P(B)=\frac{1}{10} \times \frac{5}{2}=\frac{1}{4}, \text { not possible. } \\<br/>&amp; \text { (ii) } P(A \cap B)=\frac{2}{10} \Rightarrow \frac{2}{5} \times P(B)=\frac{2}{10} \\<br/>&amp; \Rightarrow \quad P(B)=\frac{5}{10}, \text { outcomes of } B=5<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\text { (iii) } \begin{aligned}<br/>&amp; P(A \cap B)=\frac{3}{10} \Rightarrow P(A) \cdot P(B)=\frac{3}{10} \\<br/>&amp; \Rightarrow \quad \frac{2}{5} \times P(B)=\frac{3}{10} \\<br/>&amp; P(B)=\frac{3}{4}, \text { not possible }<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\text { (iv) } \begin{aligned}<br/>&amp; P(A \cap B)=\frac{4}{10} \\<br/>\Rightarrow &amp; P(A) \cdot P(B)=\frac{4}{10} \\<br/>\Rightarrow &amp; P(B)=1, \text { outcomes of } B=10 .<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
an-ideal-gas-is-expanding-such-that-p-t-2-constant-the-coefficient-of-volume-expansion-of-the-gas-is-4

slug:
an-ideal-gas-is-expanding-such-that-p-t-2-constant-the-coefficient-of-volume-expansion-of-the-gas-is-4-82473

question:
<div class="question">An ideal gas is expanding such that $p T^2=$ constant. The coefficient of volume expansion of the gas is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\frac{3}{T}$<br/></span> </div>

answer:
<div class="solution">$p T^2=$ constant<br/>$\begin{array}{ll}\therefore \quad &amp; \left(\frac{n R T}{V}\right) T^2=\text { constant } \\ \text { or } \quad T^3 V^{-1}=\text { constant }\end{array}$<br/>Differentiating the equation, we get<br/>$$<br/>\frac{3 T^2}{V} \cdot d T-\frac{T^3}{V^2} \cdot d V=0<br/>$$<br/>or<br/>$$<br/>3 \cdot d T=\frac{T}{V} \cdot d V<br/>$$<br/>From the equation, $d V=V \gamma \cdot d T$<br/>$\gamma$ = coefficient of volume expansion of gas $=\frac{d V}{V \cdot d T}$<br/>From Eq. (i) $\gamma=\frac{d V}{V \cdot d T}=\frac{3}{T}$<br/>$\therefore$ correct answer is (c).</div>


tags: ['Physics', 'Magnetic Effects of Current', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
an-infinitely-long-hollow-conducting-cylinder-with-inner-radius-r-2-and-outer-radius-r-carries-a-uniform-current-density-along-its-length-the-magnitud-2

slug:
an-infinitely-long-hollow-conducting-cylinder-with-inner-radius-r-2-and-outer-radius-r-carries-a-uniform-current-density-along-its-length-the-magnitud-2-74885

question:
<div class="question">An infinitely long hollow conducting cylinder with inner radius $R / 2$ and outer radius $R$ carries a uniform current density along its length. The magnitude of the magnetic field, $|\vec{B}|$ as a function of the radial distance $r$ from the axis is best represented by</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/nogly2qu41QUFjjYDYRBYd2O1nKbcEG9EkYhE-wGHv8.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/11ra4vfG_g5i1dSHFpvRQ_Oc_nY4vLdxCirEX2zmS48.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/ddT7E2nMz1YfYqHzkbWSmoyWbSjQvsUx5h0w9kTpVRI.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/u2khswZTB9LqZ62DIuYZfd7SksSKM-Gr0bba9WDifiM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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/u2khswZTB9LqZ62DIuYZfd7SksSKM-Gr0bba9WDifiM.original.fullsize.png"/></span> </div>

answer:
<div class="solution">For $r &lt; \frac{R}{2}, \quad B=0$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\text { For } \frac{R}{2} \leq r &lt; R, \\
<br/> <br/>B=\frac{\mu_{0}}{2}\left[r-\frac{R^{2}}{2 r}\right] J
<br/> <br/>\end{array}$
<br/> <br/>$\begin{array}{l}
<br/> <br/>\text { For } r&gt;R, \quad B=\frac{\mu_{0} i}{2 \pi r} \\
<br/> <br/>\text { i.e., } B \propto \frac{1}{r}
<br/> <br/>\end{array}$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/qgGu_YEvBp-rvLqpOSE1-9SlVH-Eol7TfBpkYVClRQA.original.fullsize.png"/><br/> <br/> <br/>Hence graph $(d)$ correctly depicts $|\vec{B}|$ versus $r$ graph.</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch1_P1.db
title:
an-infinitely-long-solid-cylinder-of-radius-r-has-a-uniform-volume-charge-density-it-has-a-spherical-cavity-of-radius-r-2-with-its-centre-on-the-axis-

slug:
an-infinitely-long-solid-cylinder-of-radius-r-has-a-uniform-volume-charge-density-it-has-a-spherical-cavity-of-radius-r-2-with-its-centre-on-the-axis-37077

question:
<div class="question">An infinitely long solid cylinder of radius $R$ has a uniform volume charge density $\rho$. It has a spherical cavity of radius $R / 2$ with its centre on the axis of the cylinder, as shown in the figure. The magnitude of the electric field at the point $P$, which is at a distance $2 R$ from the axis of the cylinder, is given by the expression $\frac{23 \rho R}{16 K \varepsilon_{0}}$. The value of $k$ is
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/15_y_691fMjVqxPj46o6aPJTbNG1a2Xo_PRx3KcLgj4.original.fullsize.png"/></div>

answer:
<div class="solution">The magnitude of the electric field at the point $P$ which is at a distance $2 R$ from the axis of the cylinder
<br/> <br/>$\begin{array}{l}
<br/> <br/>\mathrm{E}=\mathrm{E}_{\text {total }}-\mathrm{E}_{\text {cavity }} \\
<br/> <br/>=\frac{\gamma}{2 \pi \varepsilon_{0}(2 R)}-\frac{1}{4 \pi \varepsilon_{0}} \frac{Q}{(2 R)^{2}} \\
<br/> <br/>\mathrm{Q}_{\text {sphere }}=\frac{4}{3} \pi\left(\frac{R}{2}\right)^{3} \rho=\frac{\pi R^{3} \rho}{6} \\
<br/> <br/>\begin{array}{l}
<br/> <br/>\lambda_{\text {cylinder }}=\pi R^{2} \rho \\
<br/> <br/>\therefore E=\frac{\pi R^{2} \rho}{4 \pi \varepsilon_{0} R}-\frac{1}{4 \pi \varepsilon_{0}} \cdot \frac{\pi R^{3} \rho / 6}{4 R^{2}} \\
<br/> <br/>=\frac{23 \rho R}{96 \varepsilon_{0}}=\frac{23 \rho R}{16 \times 6 \times \varepsilon_{0}} \\
<br/> <br/>\therefore k=6
<br/> <br/>\end{array}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Ray Optics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
an-optical-component-and-an-object-s-placed-along-its-optic-axis-are-given-in-column-i-the-distance-between-the-object-and-the-component-can-be-varied

slug:
an-optical-component-and-an-object-s-placed-along-its-optic-axis-are-given-in-column-i-the-distance-between-the-object-and-the-component-can-be-varied-56113

question:
<div class="question">An optical component and an object $S$ placed along its optic axis are given in Column I. The distance between the object and the component can be varied. The properties of images are given in Column II. Match all the properties of images from Column II with the appropriate components given in Column I. Indicate your answer by darkening the appropriate bubble of the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/a1-aaRPovRdjUoHsKChoGEYxMsUGD-_F4TDY-anpnbs.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) p,q,r,s, (B) q, (C) p,q,r,s, (D) p,q,s<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>(A) p,q,r,s, (B) q, (C) p,q,r,s, (D) p,q,r,s<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/>(A) p,s, (B) q, (C) p,q,r,s, (D) p,q,s<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,q,r,s, (B) p,q,r, (C) p,q,r,s, (D) p,q,s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,q,r,s, (B) q, (C) p,q,r,s, (D) p,q,r,s<br/></span> </div>

answer:
<div class="solution">(A) : (C) and (D) : In case of concave mirror or convex lens image can be real, virtual, diminished magnified or of same size. (B) : In case of convex mirror image is always virtual (for real object)</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
source_db: MarksBatch1_P1.db
title:
an-organic-compound-undergoes-firstorder-decomposition-the-time-taken-for-its-decomposition-to-1-8-and-110-of-its-initial-concentration-are-t-18-and-t

slug:
an-organic-compound-undergoes-firstorder-decomposition-the-time-taken-for-its-decomposition-to-1-8-and-110-of-its-initial-concentration-are-t-18-and-t-31249

question:
<div class="question">An organic compound undergoes first-order decomposition. The time taken for its decomposition to $1 /$ 8 and $1 / 10$ of its initial concentration are $t_{1 / 8}$ and $t_{1 / 10}$ respectively. What is the value of $\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right] \times 10$ ? $\left(\log _{10} 2=0.3\right)$</div>

answer:
<div class="solution">$\begin{array}{l}
<br/> <br/> t_{1 / 8}=\frac{2.303 \log 8}{k}=\frac{2.303 \times 3 \log 2}{k} \\
<br/> <br/>t_{1 / 10}=\frac{2.303}{k} \log 10=\frac{2.303}{k} \\
<br/> <br/>{\left[\frac{t_{1 / 8}}{t_{1 / 10}}\right] \times 10=\frac{\left(\frac{2.303 \times 3 \log 2}{k}\right)}{\left(\frac{2.303}{k}\right)} \times 10=9}
<br/> <br/>\end{array}$</div>


tags: ['Physics', 'Dual Nature of Matter', '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: MarksBatch1_P1.db
title:
an-particle-and-a-proton-are-accelerated-from-rest-by-a-potential-difference-of-100-v-after-this-their-de-broglie-wavelengths-are-and-p-respectively-t

slug:
an-particle-and-a-proton-are-accelerated-from-rest-by-a-potential-difference-of-100-v-after-this-their-de-broglie-wavelengths-are-and-p-respectively-t-94507

question:
<div class="question">An $\alpha$-particle and a proton are accelerated from rest by a potential difference of $100 \mathrm{~V}$. After this, their de Broglie wavelengths are $\lambda_\alpha$ and $\lambda_p$ respectively. The ratio $\frac{\lambda_p}{\lambda_\alpha}$, to the nearest integer, is</div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>\lambda &amp; =\frac{h}{P}=\frac{h}{\sqrt{2 q q V m}} \text { or } \lambda \propto \frac{1}{\sqrt{q m}} \\<br/>\frac{\lambda_p}{\lambda_\alpha} &amp; =\sqrt{\frac{q_\alpha}{q_p} \cdot \frac{m_{\propto}}{m_p}}=\sqrt{\frac{(2)(4)}{(1)(1)}}=2.828<br/>\end{aligned}<br/>$$<br/>The nearest integer is 3 .<br/>$\therefore$ answer is 3 .</div>


title: aqueous-solution-of-na-2-s-2-o-3-on-reaction-with-cl-2-gives
slug: aqueous-solution-of-na-2-s-2-o-3-on-reaction-with-cl-2-gives-76187
source_db: MarksBatch1_P1.db
question:
<div class="question">$$<br/>\text { Aqueous solution of } \mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3 \text { on reaction with } \mathrm{Cl}_2 \text { gives }<br/>$$</div>

tags:
['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{NaHSO}_4$<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">C</span> <span class="option-data"><br/>$\mathrm{NaCl}$<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 answer is:
<span class="option-value"><br/>$\mathrm{NaHSO}_4$<br/></span> </div>

answer:
<div class="solution">Sodium thiosulphate, $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ gets oxidised by chlorine water.<br/>$$<br/>\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3+4 \mathrm{Cl}_2+5 \mathrm{H}_2 \mathrm{O} \longrightarrow 2 \mathrm{NaHSO}_4+8 \mathrm{HCl}<br/>$$<br/>$\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ gets oxidised by $\mathrm{FeCl}_3$ into $\mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6$<br/>$$<br/>2 \mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3+2 \mathrm{FeCl}_3 \longrightarrow \mathrm{Na}_2 \mathrm{~S}_4 \mathrm{O}_6+2 \mathrm{FeCl}_2+2 \mathrm{NaCl}<br/>$$<br/>Further, $\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3$ decomposes on treatment with dilute acids<br/>$$<br/>\mathrm{Na}_2 \mathrm{~S}_2 \mathrm{O}_3+2 \mathrm{HCl} \longrightarrow 2 \mathrm{NaCl}+\mathrm{SO}_2+\mathrm{S}+\mathrm{H}_2 \mathrm{O}<br/>$$</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
aqueous-solutions-of-hno-3-koh-ch-3-cooh-and-ch-3-coona-of-identical-concentrations-are-provided-the-pairs-of-solutions-which-form-a-buffer-upon-mixin

slug:
aqueous-solutions-of-hno-3-koh-ch-3-cooh-and-ch-3-coona-of-identical-concentrations-are-provided-the-pairs-of-solutions-which-form-a-buffer-upon-mixin-64398

question:
<div class="question">Aqueous solutions of $\mathrm{HNO}_3, \mathrm{KOH}$, $\mathrm{CH}_3 \mathrm{COOH}$, and $\mathrm{CH}_3 \mathrm{COONa}$ of identical concentrations are provided. The pair(s) of solutions which form a buffer upon mixing is(are)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$\mathrm{HNO}_3$ and $\mathrm{CH}_3 \mathrm{COOH}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\mathrm{KOH}$ and $\mathrm{CH}_3 \mathrm{COONa}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$\mathrm{HNO}_3$ and $\mathrm{CH}_3 \mathrm{COONa}$<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/>$\mathrm{CH}_3 \mathrm{COOH}$ and $\mathrm{CH}_3 \mathrm{COONa}$</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/>$\mathrm{HNO}_3$ and $\mathrm{CH}_3 \mathrm{COONa}$<br/>, <br/>$\mathrm{CH}_3 \mathrm{COOH}$ and $\mathrm{CH}_3 \mathrm{COONa}$</span> </div>

answer:
<div class="solution">$\mathrm{HNO}_3$ and $\mathrm{CH}_3 \mathrm{COONa}$ can form buffer if the amount of $\mathrm{HNO}_3$ is limited. However concentrations are same but the amount can differ with manipulation of volume.<br/>Ionic equilibrium<br/>Conceptual<br/>II</div>


title: area-of-the-region-bounded-by-the-curve-y-e-x-and-lines-x-0-and-y-e-is
slug: area-of-the-region-bounded-by-the-curve-y-e-x-and-lines-x-0-and-y-e-is-95280
tags: ['Mathematics', 'Area Under Curves', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">Area of the region bounded by the curve $y=e^x$ and lines $x=0$ and $y=e$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$e-1$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$\int_1^e \ln (e+1-y) d y$<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/>$e-\int_0^1 e^x d x$<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/>$\int_1^e \ln y d y$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answers are:
<span class="option-value"><br/>$\int_1^e \ln (e+1-y) d y$<br/>, <br/>$e-\int_0^1 e^x d x$<br/>, <br/>$\int_1^e \ln y d y$</span> </div>

answer:
<div class="solution">Shaded area $=e-\left(\int_0^1 e^x d x\right)=1$<br/>Also, $\quad \int_1^e \ln (e+1-y) d y$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oZ4wxm1sBB6e6-hxsJA-BK35ZdmsmKWhMSod8yCCHEg.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; =\int_e^q \ln t(-d t) \\<br/>&amp; \text { [put } e+1-y=t \Rightarrow-d y=d t \text { ] } \\<br/>&amp; =\int_1^e \ln t d t=\int_1^e \ln y d y=1<br/>\end{aligned}<br/>$$</div>


title: as-per-iupac-nomenclature-the-name-of-the-complex-co-h-2-o-4-nh-3-2-cl-3-is
slug: as-per-iupac-nomenclature-the-name-of-the-complex-co-h-2-o-4-nh-3-2-cl-3-is-54865
tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch1_P1.db
question:
<div class="question">As per IUPAC nomenclature, the name of the complex $\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}_{3}$ is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Tetraaquadiaminecobalt (III) chloride</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Tetraaquadiamminecobalt (III) chloride</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Diaminetetraaquacoblat (II) chloride</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Diamminetetraaquacobalt (III) chloride</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">Diamminetetraaquacobalt (III) chloride</span> </div>

answer:
<div class="solution">(achiral)
<br/> <br/>$\left[\mathrm{Co}\left(\mathrm{H}_{2} \mathrm{O}\right)_{4}\left(\mathrm{NH}_{3}\right)_{2}\right] \mathrm{Cl}_{3}$
<br/> <br/>Diamminetetraaquacobalt (III) chloride.</div>


tags: ['Biology', 'The Living World', 'AIIMS', 'AIIMS 2016']
source_db: MarksBatch1_P1.db
title:
assertion-consciousness-is-considered-as-the-defining-property-of-living-organisms-reason-all-organisms-from-the-prokaryotes-to-the-most-complex-eukar

slug:
assertion-consciousness-is-considered-as-the-defining-property-of-living-organisms-reason-all-organisms-from-the-prokaryotes-to-the-most-complex-eukar-19195

question:
<div class="question">Assertion: Consciousness is considered as the defining property of living organisms.<br/>Reason : All organisms, from the prokaryotes to the most complex eukaryotes can sense and respond to environmental stimuli.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">If both assertion and reason are true and reason is the correct explanation of assertion.</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">If both assertion and reason are true but reason is not the correct explanation of assertion.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">If assertion is true but reason is false.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">If both assertion and reason are false.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">If both assertion and reason are true and reason is the correct explanation of assertion.</span> </div>

answer:
<div class="solution">Consciousness is awareness of the surroundings and responding to external stimuli. The external stimuli can be physical, chemical or biological. All organisms, from primitive prokaryotes to most advanced and complex eukaryotes, are able to sense and respond to environmental factors. Consciousness is thus said to be the defining property of living organisms.</div>


title: assertion-protostele-is-the-simplest-stele-reason-protostele-is-the-most-advanced-type-of-stele
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2013']
source_db: MarksBatch1_P1.db
slug:
assertion-protostele-is-the-simplest-stele-reason-protostele-is-the-most-advanced-type-of-stele-43656

question:
<div class="question">Assertion : Protostele is the simplest stele.<br/>Reason : Protostele is the most advanced type of stele.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">If both assertion and reason are true and reason is the correct explanation of assertion.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">If both assertion and reason are true but reason is not the correct explanation of assertion.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">If assertion is true but reason is false</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">If both assertion and reason are false</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">If assertion is true but reason is false</span> </div>

answer:
<div class="solution">Protostele is the simplest and considered to be the most primitive type of stele. It consists of a solid core of xylem surrounded by the cylinder of phloem, enclosing no pith. All other types of steles have evolved from it in the course of evolutionary specialization. Protosteles may be found in Selaginella, Lycopodium, Gleichenia and Lygodium among present day forms.</div>


tags: ['Physics', 'Nuclear Physics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch1_P1.db
title:
assume-that-the-nuclear-binding-energy-per-nucleon-b-a-versus-mass-number-a-is-as-shown-in-the-figure-use-this-plot-to-choose-the-correct-choice-s-giv

slug:
assume-that-the-nuclear-binding-energy-per-nucleon-b-a-versus-mass-number-a-is-as-shown-in-the-figure-use-this-plot-to-choose-the-correct-choice-s-giv-21148

question:
<div class="question">Assume that the nuclear binding energy per nucleon $(B / A)$ versus mass number $(A)$ is as shown in the figure. Use this plot to choose the correct choice (s) given below.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8daLYXnAHbRMuW4bm8P5NMtlpoBl5lLiBQYLvZ8dg2w.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Fusion of two nuclei with mass numbers lying in the range of $1 &lt; A &lt; 50$ will release energy</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>Fusion of two nuclei with mass numbers lying in the range of $51 &lt; A &lt; 100$ will release energy</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/>Fission of a nucleus lying in the mass range of $100 &lt; A &lt; 200$ will release energy when broken into two equal fragments</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Fission of a nucleus lying in the mass range $200 &lt; A &lt; 260$ will release energy when broken into two equal fragments</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/>Fusion of two nuclei with mass numbers lying in the range of $51 &lt; A &lt; 100$ will release energy, <br/>Fission of a nucleus lying in the mass range $200 &lt; A &lt; 260$ will release energy when broken into two equal fragments</span> </div>

answer:
<div class="solution">In fusion two or more lighter nuclei combine to make a comparatively heavier nucleus. In fission, a heavy nucleus breaks into two or more comparatively lighter nuclei. Futher, energy will be released in a nuclear process if total binding energy increases. $\therefore$ correct options are (b) and (d).</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
source_db: MarksBatch1_P1.db
title:
assuming-that-hunds-rule-is-violated-the-bond-order-and-magnetic-nature-of-the-diatomic-molecule-b-2-is

slug:
assuming-that-hunds-rule-is-violated-the-bond-order-and-magnetic-nature-of-the-diatomic-molecule-b-2-is-91585

question:
<div class="question">Assuming that Hund's rule is violated, the bond order and magnetic nature of the diatomic molecule $\mathrm{B}_2$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>1 and diamagnetic<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/>0 and diamagnetic<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>1 and paramagnetic<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>0 and paramagnetic</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>1 and diamagnetic<br/></span> </div>

answer:
<div class="solution">$\mathrm{B}_2$ : Total electrons $=10$<br/>Configuration : $\sigma 1 s^2 \sigma^* 1 s^2 \sigma 2 s^2 \sigma^* 2 s^2 \pi 2 p_x^1=\pi 2 p_y^1$<br/>If Hunds rule is violated, then<br/>$$<br/>\sigma 1 s^2 \sigma^* 1 s^2 \sigma 2 s^2 \sigma^* 2 s^2 \quad \pi 2 p_x^2=\pi 2 p_y^0<br/>$$<br/>So, diamagnetic<br/>$$<br/>\text { Bond order }=\frac{6-4}{2}=1<br/>$$<br/>Chemical bonding<br/>Conceptual<br/>II</div>


tags: ['Chemistry', 'States of Matter', '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: MarksBatch1_P1.db
title:
at-400-k-the-root-mean-square-rms-speed-of-a-gas-x-molecular-weight-40-is-equal-to-the-most-probable-speed-of-gas-y-at-60-k-the-molecular-weight-of-th-1

slug:
at-400-k-the-root-mean-square-rms-speed-of-a-gas-x-molecular-weight-40-is-equal-to-the-most-probable-speed-of-gas-y-at-60-k-the-molecular-weight-of-th-1-83755

question:
<div class="question">At $400 \mathrm{~K}$, the root mean square (rms) speed of a gas $X$ (molecular weight $=40$ ) is equal to the most probable speed of gas $Y$ at $60 \mathrm{~K}$. The molecular weight of the gas $Y$ is</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/yBU8f4tzlpEao7J6rrvJegC_Ym8Wh9PTv4aBpNDK5qM.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Alternating Current', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P2.db
title:
at-time-t-0-a-battery-of-10-v-is-connected-across-points-a-and-b-in-the-given-circuit-if-the-capacitors-have-no-charge-initially-at-what-time-in-secon

slug:
at-time-t-0-a-battery-of-10-v-is-connected-across-points-a-and-b-in-the-given-circuit-if-the-capacitors-have-no-charge-initially-at-what-time-in-secon-82615

question:
<div class="question">At time $t=0$, a battery of $10 \mathrm{~V}$ is connected across points $A$ and $B$ in the given circuit. If the capacitors have no charge initially, at what time (in second) does the voltage across them become $4 \mathrm{~V}$ ?<br/>[Take $: \ln 5=1.6, \ln 3=1.1]$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rfEriRiK0xFSvAhxaL1qn9GOEaZY3xS3ePfpc2E2LMM.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Voltage across the capacitors will increase from 0 to $10 \mathrm{~V}$ exponentially. The voltage at time $t$ will be given by<br/>$$<br/>\begin{aligned}<br/>&amp; V=10\left(1-e^{-t / \tau} \mathrm{C}\right) \\<br/>&amp; \text { Here } \tau_c=C_{\text {net }} R_{\text {net }} \\<br/>&amp; =\left(1 \times 10^6\right)\left(4 \times 10^{-6}\right)=4 \mathrm{~s} \\<br/>&amp; \therefore \quad V=10\left(1-e^{-t / 4}\right) \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Substituting $V=4$ volt we have,<br/>$$<br/>4=10\left(1-e^{-t / 4}\right)<br/>$$<br/>Substituting $V=4$ volt we have,<br/>$$<br/>4=10\left(1-e^{-t / 4}\right)<br/>$$<br/>or $e^{-t / 4}=0.6=\frac{3}{5}$<br/>Taking $\log$ both sides we have,<br/>$$<br/>-\frac{t}{4}=\ln 3-\ln 5<br/>$$<br/>or $\quad t=4(\ln 5-\ln 3)=2 \mathrm{~s}$.<br/>Hence, the answer is 2 .</div>


tags: ['Mathematics', 'Parabola', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
axis-of-a-parabola-is-y-x-and-vertex-and-focus-are-at-a-distance-2-and-2-2-respectively-from-the-origin-then-equation-of-the-parabola-is-1

slug:
axis-of-a-parabola-is-y-x-and-vertex-and-focus-are-at-a-distance-2-and-2-2-respectively-from-the-origin-then-equation-of-the-parabola-is-1-74241

question:
<div class="question">Axis of a parabola is $y=x$ and vertex and focus are at a distance $\sqrt{2}$ and $2 \sqrt{2}$ respectively, from the origin. Then, equation of the parabola is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$(x-y)^2=8(x+y-2)$<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/>$(x+y)^2=2(x+y-2)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$(x-y)^2=4(x+y-2)$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$(x+y)^2=2(x-y+2)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$(x-y)^2=8(x+y-2)$<br/></span> </div>

answer:
<div class="solution">As distance of vertex from origin is $\sqrt{2}$ and focus is $2 \sqrt{2}$. $\therefore V(1,1)$ and $F(2,2)$<br/>[i.e. lying on $y=x$ ] where, length of latusrectum<br/>$$<br/>\begin{aligned}<br/>&amp; =4 a, \\<br/>&amp; =4 \sqrt{2}<br/>\end{aligned}<br/>$$<br/>$$<br/>[\because \text { where } a=\sqrt{2}]<br/>$$<br/>$\therefore$ By definition of parabola<br/>$$<br/>P M^2=(4 a)(P N)<br/>$$<br/>where, $P N$ is length of perpendicular upon $x+y-2=0$<br/>[i.e. tangent at vertex]<br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; \frac{(x-y)^2}{2}=4 \sqrt{2}\left(\frac{x+y-2}{\sqrt{2}}\right) \\<br/>\therefore &amp; (x-y)^2=8(x+y-2)<br/>\end{array}<br/>$$<br/>Hence, the equation of parabola is $(x-y)^2=8(x+y-2)$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LTzvcNzfi_9l1vI8uJ56TDZNQEppsHlTrcYn6e3n2TM.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Parabola', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P2.db
title:
axis-of-a-parabola-is-y-x-and-vertex-and-focus-are-at-a-distance-2-and-2-2-respectively-from-the-origin-then-equation-of-the-parabola-is

slug:
axis-of-a-parabola-is-y-x-and-vertex-and-focus-are-at-a-distance-2-and-2-2-respectively-from-the-origin-then-equation-of-the-parabola-is-74624

question:
<div class="question">Axis of a parabola is $y=x$ and vertex and focus are at a distance $\sqrt{2}$ and $2 \sqrt{2}$ respectively, from the origin. Then, equation of the parabola is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>$(x-y)^2=8(x+y-2)$<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/>$(x+y)^2=2(x+y-2)$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$(x-y)^2=4(x+y-2)$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$(x+y)^2=2(x-y+2)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$(x-y)^2=8(x+y-2)$<br/></span> </div>

answer:
<div class="solution">As distance of vertex from origin is $\sqrt{2}$ and focus is $2 \sqrt{2}$. $\therefore V(1,1)$ and $F(2,2)$<br/>[i.e. lying on $y=x$ ] where, length of latusrectum<br/>$$<br/>\begin{aligned}<br/>&amp; =4 a, \\<br/>&amp; =4 \sqrt{2}<br/>\end{aligned}<br/>$$<br/>$$<br/>[\because \text { where } a=\sqrt{2}]<br/>$$<br/>$\therefore$ By definition of parabola<br/>$$<br/>P M^2=(4 a)(P N)<br/>$$<br/>where, $P N$ is length of perpendicular upon $x+y-2=0$<br/>[i.e. tangent at vertex]<br/>$$<br/>\begin{array}{ll}<br/>\Rightarrow &amp; \frac{(x-y)^2}{2}=4 \sqrt{2}\left(\frac{x+y-2}{\sqrt{2}}\right) \\<br/>\therefore &amp; (x-y)^2=8(x+y-2)<br/>\end{array}<br/>$$<br/>Hence, the equation of parabola is $(x-y)^2=8(x+y-2)$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LTzvcNzfi_9l1vI8uJ56TDZNQEppsHlTrcYn6e3n2TM.original.fullsize.png"/><br/></div>


title: b-oh-3-naoh-nabo-2-na-b-oh-4-h-2-o-how-can-this-reaction-is-made-to-proceed-in-forward-direction-1
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Main']
source_db: MarksBatch1_P2.db
slug:
b-oh-3-naoh-nabo-2-na-b-oh-4-h-2-o-how-can-this-reaction-is-made-to-proceed-in-forward-direction-1-71037

question:
<div class="question">$\mathrm{B}(\mathrm{OH})_3+\mathrm{NaOH} \rightleftharpoons \mathrm{NaBO}_2+\mathrm{Na}\left[\mathrm{B}(\mathrm{OH})_4\right]+\mathrm{H}_2 \mathrm{O}$.<br/>How can this reaction is made to proceed in forward direction?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Addition of cis 1, 2 diol<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/>Addition of borax<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Addition of trans 1, 2 diol<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Addition of $\mathrm{Na}_2 \mathrm{HPO}_4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Addition of cis 1, 2 diol<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/2FNAWz1kMoW_1Cxacm9TeBErG-KHS5AEc7xNT453yjg.original.fullsize.png"/><br/><br/>This reaction is reversible reaction because sodium metaborate, $\mathrm{Na}^{+}\left[\mathrm{B}(\mathrm{OH})_4\right]^{-}$formed by the reaction between $\mathrm{B}(\mathrm{OH})_3$ and $\mathrm{NaOH}$ gets hydrolysed to regenerate $\mathrm{B}(\mathrm{OH})_3$ and $\mathrm{NaOH}$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/HTQ4_yy4c1xOjkvE_9BMrxfhp7VKkCLr5fdyJ0Wx66E.original.fullsize.png"/><br/><br/>If, some quantity of polyhydroxy compound like cis-1, 3-diol, catechol, glycerol etc. is added to the reaction mixture. The $\mathrm{B}(\mathrm{OH})_3$ combines with such polyhydroxy compound to give chelated complex compound. Due to complex compound formation, stability increases and due to higher stability of complex, reaction moves in forward direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/AYuEJLlNLCpXuHv4OFV7V-Q0yw9fQtCkDRYG3LI-2Aw.original.fullsize.png"/><br/></div>


title: b-oh-3-naoh-nabo-2-na-b-oh-4-h-2-o-how-can-this-reaction-is-made-to-proceed-in-forward-direction
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P2.db
slug:
b-oh-3-naoh-nabo-2-na-b-oh-4-h-2-o-how-can-this-reaction-is-made-to-proceed-in-forward-direction-33673

question:
<div class="question">$\mathrm{B}(\mathrm{OH})_3+\mathrm{NaOH} \rightleftharpoons \mathrm{NaBO}_2+\mathrm{Na}\left[\mathrm{B}(\mathrm{OH})_4\right]+\mathrm{H}_2 \mathrm{O}$.<br/>How can this reaction is made to proceed in forward direction?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>Addition of cis 1, 2 diol<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/>Addition of borax<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Addition of trans 1, 2 diol<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>Addition of $\mathrm{Na}_2 \mathrm{HPO}_4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Addition of cis 1, 2 diol<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/2FNAWz1kMoW_1Cxacm9TeBErG-KHS5AEc7xNT453yjg.original.fullsize.png"/><br/><br/>This reaction is reversible reaction because sodium metaborate, $\mathrm{Na}^{+}\left[\mathrm{B}(\mathrm{OH})_4\right]^{-}$formed by the reaction between $\mathrm{B}(\mathrm{OH})_3$ and $\mathrm{NaOH}$ gets hydrolysed to regenerate $\mathrm{B}(\mathrm{OH})_3$ and $\mathrm{NaOH}$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/HTQ4_yy4c1xOjkvE_9BMrxfhp7VKkCLr5fdyJ0Wx66E.original.fullsize.png"/><br/><br/>If, some quantity of polyhydroxy compound like cis-1, 3-diol, catechol, glycerol etc. is added to the reaction mixture. The $\mathrm{B}(\mathrm{OH})_3$ combines with such polyhydroxy compound to give chelated complex compound. Due to complex compound formation, stability increases and due to higher stability of complex, reaction moves in forward direction.<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/AYuEJLlNLCpXuHv4OFV7V-Q0yw9fQtCkDRYG3LI-2Aw.original.fullsize.png"/><br/></div>


title: balanoglossus-has
slug: balanoglossus-has-53404
question: <div class="question">Balanoglossus has</div>
tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">no coelom</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">well developed coelom</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">reduced coelom</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">coelom only in embryonic stage</span> </li> </ul>

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

answer:
<div class="solution">Animals are classified as non-chordates or chordates depending on the absence and presence of notochord. Non-chordates are further divided into many phyla beginning from phylum Porifera to phylum Hemichordates. Phylum Porifera includes the simplest animals while chordates include advanced animals as many features are seen evolving. One such important feature is the presence of body coelom, as the development of organs and organ systems will largely depend on this feature. Porifera, Coelenterate, Ctenophora, Platyhelminthes are acoelomates. Aschelminthes are pseudocoelomates as the coelom is not completely formed. All animals from phylum Annelids to chordates show presence of true coelom and hence are eucoelomates. Thus hemichordates are also eucoelomates and it includes Balanoglossus, Saccoglossus etc.</div>


title: based-on-vsepr-theory-the-number-of-90-degree-f-br-f-angles-in-brf-5-is
slug: based-on-vsepr-theory-the-number-of-90-degree-f-br-f-angles-in-brf-5-is-34052
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">0</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Based on VSEPR theory, the number of 90 degree $\mathrm{F}-\mathrm{Br}-\mathrm{F}$ angles in $\mathrm{BrF}_5$ is</div>

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

answer:
<div class="solution">In $\mathrm{BrF}_5$ number of electrons $=6$ $(1 l p+5 b p)$<br/>So, the structure is supposed to be square pyramidal but will be distorted because of additional lp- $b p$ interaction.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jBK5EAeGKworgMjFPsBPYJn6BCd1lG7jWJ_fjuvI0Js.original.fullsize.png"/><br/><br/>Additional $\quad l p-b p$<br/>interaction reduces the all bond angle and do not let any angle to be $90^{\circ}$.<br/>Chemical bonding<br/>Conceptual<br/>IV</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
bleaching-powder-and-bleach-solution-are-produced-on-a-large-scale-and-used-in-several-household-products-the-effectiveness-of-bleach-solution-is-ofte-1

slug:
bleaching-powder-and-bleach-solution-are-produced-on-a-large-scale-and-used-in-several-household-products-the-effectiveness-of-bleach-solution-is-ofte-1-52597

question:
<div class="question">Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
<br/> <br/><strong> Question:</strong> Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Cl}_{2} \mathrm{O}$</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">$\mathrm{Cl}_{2} \mathrm{O}_{7}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{ClO}_{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Cl}_{2} \mathrm{O}_{6}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Cl}_{2} \mathrm{O}$</span> </div>

answer:
<div class="solution">$\mathrm{Ca}(\mathrm{OCl}) \mathrm{Cl} \longrightarrow \mathrm{Ca}^{2+}+-\mathrm{OCl}+\mathrm{Cl}^{-}$
<br/> <br/>-OCl (Hypochlorite ion) is anion of the acid HOCl which on dehydration gives $\mathrm{Cl}_{2} \mathrm{O}$.
<br/> <br/>$2 \mathrm{HOCl} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{Cl}_{2} \mathrm{O}$</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
bleaching-powder-and-bleach-solution-are-produced-on-a-large-scale-and-used-in-several-household-products-the-effectiveness-of-bleach-solution-is-ofte

slug:
bleaching-powder-and-bleach-solution-are-produced-on-a-large-scale-and-used-in-several-household-products-the-effectiveness-of-bleach-solution-is-ofte-91584

question:
<div class="question">Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.
<br/> <br/><strong> Question:</strong> $25 \mathrm{~mL}$ of household solution was mixed with $30 \mathrm{~mL}$ of $0.50$ M KI and $10 \mathrm{~mL}$ of $4 \mathrm{~N}$ acetic acid. In the titration of the liberated iodine, $48 \mathrm{~mL}$ of $0.25 \mathrm{~N~} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$ was used to reach the end point. The molarity of the household bleach solution is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.48 \mathrm{M}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.96 \mathrm{M}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.24 \mathrm{M}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.024 \mathrm{M}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.24 \mathrm{M}$</span> </div>

answer:
<div class="solution">Bleach $+2 \mathrm{KI} \longrightarrow \mathrm{I}_{2}+$ Products
<br/> <br/>$\mathrm{I}_{2}+2 \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} \longrightarrow \mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}+2 \mathrm{NaI}$
<br/> <br/>Number of millimole of hypo $=0.25 \times 48$
<br/> <br/>$=2 \times$ millimole of $\mathrm{I}_{2}$
<br/> <br/>$\therefore$ Number of millimole of $\mathrm{I}_{2}=\frac{0.25 \times 48}{2}=6$
<br/> <br/>millimole of $\mathrm{I}_{2}=$ millimole of bleach
<br/> <br/>Molarity of bleaching solution
<br/> <br/>$=\frac{\text { Millimoles of bleach }}{\text { Vol.(in } \mathrm{mL} \text { ) of bleach }}=\frac{6}{25}=0.24$</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
bombardment-of-aluminium-by-particle-leads-to-its-artificial-disintegration-in-two-ways-i-and-ii-as-shown-products-x-y-and-z-respectively-are

slug:
bombardment-of-aluminium-by-particle-leads-to-its-artificial-disintegration-in-two-ways-i-and-ii-as-shown-products-x-y-and-z-respectively-are-47667

question:
<div class="question">Bombardment of aluminium by $\alpha$-particle leads to its artificial disintegration in two ways, (i) and (ii) as shown. Products $X, Y$ and $Z$ respectively are<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/NttJfS2pRzHJSAGvhz5rdWwpxT7jPV4BJtMEXjHfsVI.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>proton, neutron, positron<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/>neutron, positron, proton<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>proton, positron, neutron<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>positron, proton, neutron</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>proton, neutron, positron<br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/8N5KwQEz5Jq6ccdlQUbt_fj6SNJIACegYxEAcvQagW4.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
both-ni-co-4-and-ni-cn-4-2-are-diamagnetic-the-hybridisations-of-nickel-in-these-complexes-respectively-are-1

slug:
both-ni-co-4-and-ni-cn-4-2-are-diamagnetic-the-hybridisations-of-nickel-in-these-complexes-respectively-are-1-10145

question:
<div class="question">Both $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ and $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are diamagnetic. The hybridisations of nickel in these complexes, respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$s p^3, s p^3$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$s p^3, d s p^2$<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/>$d s p^2, s p^3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$d s p^2, d s p^2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$s p^3, d s p^2$<br/></span> </div>

answer:
<div class="solution">In $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$, the oxidation state of $\mathrm{Ni}$ is zero $(0)$.<br/>$$<br/>\mathrm{Ni}(28)[\mathrm{Ar}] 4 \mathrm{~s}^2, 3 d^8<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oIC9d-0NGOX_srClo0QKbVyDCeYchWJctGF5_WjTIKc.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{CO} \text { is a strong ligand, causes coupling, thus }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bcHe7j1ZtsEEcvl2tYnvbMRRu2Vy865vuDkB_Vp4YYA.original.fullsize.png"/><br/><br/>In $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$, the oxidation state of $\mathrm{Ni}$ is $+2$ $\mathrm{Ni}^{2+}=[\mathrm{Ar}] 3 d^8, 4 s^0$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Qxu23mVkSmprXu3Qvb1lZMHlQxEsu9BBH9KMNo2mQhU.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{CN}^{-} \text {is strong ligand causes coupling. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/_C01Xet0X6H59uhNAeFOMLo4VnQ9HC0JJPA0XUQ9RM0.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Coordination Compounds', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
both-ni-co-4-and-ni-cn-4-2-are-diamagnetic-the-hybridisations-of-nickel-in-these-complexes-respectively-are

slug:
both-ni-co-4-and-ni-cn-4-2-are-diamagnetic-the-hybridisations-of-nickel-in-these-complexes-respectively-are-19742

question:
<div class="question">Both $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$ and $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$ are diamagnetic. The hybridisations of nickel in these complexes, respectively, are</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$s p^3, s p^3$<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$s p^3, d s p^2$<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/>$d s p^2, s p^3$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$d s p^2, d s p^2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$s p^3, d s p^2$<br/></span> </div>

answer:
<div class="solution">In $\left[\mathrm{Ni}(\mathrm{CO})_4\right]$, the oxidation state of $\mathrm{Ni}$ is zero $(0)$.<br/>$$<br/>\mathrm{Ni}(28)[\mathrm{Ar}] 4 \mathrm{~s}^2, 3 d^8<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/oIC9d-0NGOX_srClo0QKbVyDCeYchWJctGF5_WjTIKc.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{CO} \text { is a strong ligand, causes coupling, thus }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/bcHe7j1ZtsEEcvl2tYnvbMRRu2Vy865vuDkB_Vp4YYA.original.fullsize.png"/><br/><br/>In $\left[\mathrm{Ni}(\mathrm{CN})_4\right]^{2-}$, the oxidation state of $\mathrm{Ni}$ is $+2$ $\mathrm{Ni}^{2+}=[\mathrm{Ar}] 3 d^8, 4 s^0$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Qxu23mVkSmprXu3Qvb1lZMHlQxEsu9BBH9KMNo2mQhU.original.fullsize.png"/><br/><br/>$$<br/>\mathrm{CN}^{-} \text {is strong ligand causes coupling. }<br/>$$<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/_C01Xet0X6H59uhNAeFOMLo4VnQ9HC0JJPA0XUQ9RM0.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Kinetic Theory of Gases', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
c-v-and-c-p-denote-the-molar-specific-heat-capacities-of-a-gas-at-constant-volume-and-constant-pressure-respectively-then-1

slug:
c-v-and-c-p-denote-the-molar-specific-heat-capacities-of-a-gas-at-constant-volume-and-constant-pressure-respectively-then-1-60996

question:
<div class="question">$C_V$ and $C_p$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$C_p-C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>$C_p+C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.<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/>$\frac{C_p}{C_V}$ is larger for a diatomic ideal gas than for a monoatomic ideal gas<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$C_p \cdot C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas</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/>$C_p+C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas.<br/>, <br/>$C_p \cdot C_V$ is larger for a diatomic ideal gas than for a monoatomic ideal gas</span> </div>

answer:
<div class="solution">For monoatomic gas,<br/>$$<br/>C_p=\frac{5}{2} R \text { and } C_V=\frac{3}{2} R<br/>$$<br/><br/>For diatomic gas,<br/>$$<br/>C_p=\frac{7}{2} R \text { and } C_V=\frac{5}{2} R<br/>$$</div>


tags: ['Chemistry', 'Biomolecules', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
cellulose-upon-acetylation-with-excess-acetic-anhydride-h-2-so-4-catalytic-gives-cellulose-triacetate-whose-structures-is

slug:
cellulose-upon-acetylation-with-excess-acetic-anhydride-h-2-so-4-catalytic-gives-cellulose-triacetate-whose-structures-is-99253

question:
<div class="question">Cellulose upon acetylation with excess acetic anhydride $/ \mathrm{H}_2 \mathrm{SO}_4$ (catalytic) gives cellulose triacetate whose structures is</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/vcZWeiwKU2Vq9yUSu_12xota-a4MELVx4tBB_R7Mtyk.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/cFjjhfJ5MqUjhtPAANFIh657CBYwMmJ4ppRqLkx8-k8.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/-8XI9mYzYOXsJOA9AWUyO1eA4Mb45HNpMzM9Fgor0-E.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/i0fyHXTqCwabq19fcj15yW5CyfeHsUF7SYB_85zK-AA.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/vcZWeiwKU2Vq9yUSu_12xota-a4MELVx4tBB_R7Mtyk.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Cellulose is a straight chain polysaccharide composed of D-glucose units, which are joined by $\beta$-glycosidic linkages between $\mathrm{C}-1$ of one glucose and C-4 of the next glucose. In one, unit only three hydroxy groups are free to form acetate, that's why called cellulose triacetate</div>


title: ch-3-ch-ch-2-nocl-p-identify-the-adduct-1
slug: ch-3-ch-ch-2-nocl-p-identify-the-adduct-1-95065
tags: ['Chemistry', 'Aldehydes and Ketones', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}_2+\mathrm{NOCl} \longrightarrow \mathrm{P}$ Identify the adduct</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/hBDjHuTrjg1pzC7KcJJZmnLq3gj3MPGYTnq3ajXXnhI.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/Q2JShttJbmx1vQpBM-c9ziq9WvyFYSYvyh8NsWTz8W8.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/aln0mwlee8prVyom8E-6aBx0nwJ19ijU3LAO9Ddy8Mw.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/zu49wLBARvCCgvY-9CHzliwWng_jWXSHPwlwNTiJDfg.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/hBDjHuTrjg1pzC7KcJJZmnLq3gj3MPGYTnq3ajXXnhI.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/fWmQ1u9Zb29tpL0UaRDVHMIGOgF0yPYER4UMMEG9V34.original.fullsize.png"/><br/><br/>This reaction is an example of electrophilic addition reaction and in it addition takes place according to Markownikoff's rule.<br/>("Negative part of additive reagent adds less hydrogenated or more substituted carbon atom of double bond of unsymmetrical alkane").<br/>It is also represented in form of following mechanism<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/RIBOhB3sHm1HWFo7FAHgSRCJh1ncRQmVKenACml5K2c.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/LxfQmQ0RPqlVzeM86opqZyIw-btmJ47G1FcxQvaIsmE.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/mv1dP53C1NwTMZQbBeNPkb_F233kh6Sl3FEgguWHdxU.original.fullsize.png"/><br/></div>


title: ch-3-nh-2-chcl-3-koh-nitrogen-containing-compound-kcl-h-2-o-nitrogen-containing-compound-is
slug: ch-3-nh-2-chcl-3-koh-nitrogen-containing-compound-kcl-h-2-o-nitrogen-containing-compound-is-47891
tags: ['Chemistry', 'Amines', 'JEE Advanced', 'JEE Advanced 2006']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\mathrm{CH}_3 \mathrm{NH}_2+\mathrm{CHCl}_3+\mathrm{KOH} \rightarrow$ Nitrogen containing compound $+\mathrm{KCl}+\mathrm{H}_2 \mathrm{O}$. Nitrogen containing compound 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/A_1q5aGunq7DPFBBiriEIrJRuKWB6MM1Gmr_iTQTi40.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/SnKyxqtkwcHky7_hoLsc7piAoHmpbYECE7ke4-moDUI.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/BlpAWdMlMVe06WBukkkUJtiXPvvYJHs-7mVWhElMUWg.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/5-QWyE3ce6q4seY-y3iZrqY6MBAJ2KAnD2fKv0G2h1w.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> </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/5-QWyE3ce6q4seY-y3iZrqY6MBAJ2KAnD2fKv0G2h1w.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">$\mathrm{CH}_3 \mathrm{NH}_2+\mathrm{CHCl}_3+3 \mathrm{KOH} \rightarrow \mathrm{CH}_3 \mathrm{NC}+3 \mathrm{KCl}+3 \mathrm{H}_2 \mathrm{O}$ $\mathrm{CH}_3 \mathrm{NC}$ or $\mathrm{CH}_3-\mathrm{N}^{+} \equiv \overline{\mathrm{C}}$ Methyl isocyanide or Methyl carbyl amine This reaction is an example of carbyl amine reaction and its is used for the distinction of $p$-amines with $s$ - and $t$-amines or identification of $p$-amino group.</div>


title: choose-the-correct-reasons-for-the-stability-of-the-lyophobic-colloidal-particles
slug: choose-the-correct-reasons-for-the-stability-of-the-lyophobic-colloidal-particles-98542
tags: ['Chemistry', 'Surface Chemistry', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Choose the correct reason(s) for the stability of the lyophobic colloidal particles.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Preferential adsorption of ions on their surface from the solution.</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">Preferential adsorption of solvent on their surface from the solution.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Attraction between different particles having opposite charges on their surface.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles.</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">Preferential adsorption of ions on their surface from the solution., Potential difference between the fixed layer and the diffused layer of opposite charges around the colloidal particles.</span> </div>

answer:
<div class="solution">(a) When two or more ions are present in the dispersion medium, preferential adsorption of the ion common to the colloidal particle takes place.
<br/> <br/>(d) This is called zeta potential which helps in increasing the stability of the lyophobic sol.</div>


tags: ['Physics', 'Thermodynamics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
column-i-contains-a-list-of-processes-involving-expansion-of-an-ideal-gas-match-this-with-column-ii-describing-the-thermodynamic-change-during-this-pr-1

slug:
column-i-contains-a-list-of-processes-involving-expansion-of-an-ideal-gas-match-this-with-column-ii-describing-the-thermodynamic-change-during-this-pr-1-61397

question:
<div class="question">Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/s0ugJepkebnu1flVpkDdt7wUA4Ooz2bTodMr_eXYBLg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>(A) q, (B) p,q, (C) p,s, (D) q,s<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/>(A) q,r, (B) p,q, (C) s, (D) q<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p, (B) q, (C) p,r, (D) q,s<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,q, (B) q, (C) p,q, (D) q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) q, (B) p,q, (C) p,s, (D) q,s<br/></span> </div>

answer:
<div class="solution">(A) : In case of free expansion under adiabatic conditions, change in internal energy $\Delta U=0$.<br/>$\therefore$ Internal energy and temperature will remain constant.<br/>(B) $p \propto \frac{1}{v^2}$<br/><br/>$$<br/>\begin{array}{rrrr} <br/>&amp; \therefore &amp; p V^2 &amp; =\text { constant } \\<br/>&amp; \text { or } &amp; \left(\frac{n R T}{V}\right) V^2=\text { constant } \\<br/>&amp; \therefore &amp; T \propto \frac{1}{V}<br/>\end{array}<br/>$$<br/>If volume is doubled, temperature will decrease as per Eq. (ii). Further, molar heat capacity in process $p V^x=$ constant is<br/>$$<br/>C=C_V+\frac{R}{1-x}<br/>$$<br/>From Eq. (i), $x=2$<br/>$$<br/>\therefore \quad C=\frac{3}{2} R+\frac{R}{1-2}=+\frac{R}{2}<br/>$$<br/>Since molar heat capacity is positive, according to $Q=n C \Delta T, Q$ will be negative it $\Delta T$ is negative. Or gas loses heat if temperature is decreasing.<br/>(C) :<br/>$$<br/>\begin{aligned}<br/>p &amp; \propto \frac{1}{V^{1 / 3}} \\<br/>P V^{4 / 3} &amp; =\text { constant } \\<br/>\left(\frac{n R T}{V}\right) V^{4 / 3} &amp; =\text { constant } \\<br/>T &amp; \propto \frac{1}{V^{1 / 3}}<br/>\end{aligned}<br/>$$<br/>Further, with increase in volume temperature will decrease.<br/>Here,<br/>$$<br/>\begin{array}{lc}<br/>\text { Here, } &amp; x=4 / 3 \\<br/>\therefore &amp; C=\frac{3}{2} R+\frac{R}{1-4 / 3}=-1.5 R<br/>\end{array}<br/>$$<br/>As molar heat capacity is negative, $Q$ will be positive, if $\Delta T$ is negative or gas gains heat with decrease in temperature.<br/>(D) $T \propto p V$<br/>In expansion from $V_1$ or $2 V_1$, product of $p V$ is increasing. Therefore, temperature will increase or $\Delta U=+$ ve.<br/>Further, in expansion work done is also positive.<br/>Hence, $Q=W+\Delta U=+$ ve<br/>or gas gains heat.</div>


tags: ['Physics', 'Thermodynamics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-contains-a-list-of-processes-involving-expansion-of-an-ideal-gas-match-this-with-column-ii-describing-the-thermodynamic-change-during-this-pr

slug:
column-i-contains-a-list-of-processes-involving-expansion-of-an-ideal-gas-match-this-with-column-ii-describing-the-thermodynamic-change-during-this-pr-98922

question:
<div class="question">Column I contains a list of processes involving expansion of an ideal gas. Match this with Column II describing the thermodynamic change during this process. Indicate your answer by darkening the appropriate bubbles of the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/s0ugJepkebnu1flVpkDdt7wUA4Ooz2bTodMr_eXYBLg.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>(A) q, (B) p,q, (C) p,s, (D) q,s<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/>(A) q,r, (B) p,q, (C) s, (D) q<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p, (B) q, (C) p,r, (D) q,s<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,q, (B) q, (C) p,q, (D) q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) q, (B) p,q, (C) p,s, (D) q,s<br/></span> </div>

answer:
<div class="solution">(A) : In case of free expansion under adiabatic conditions, change in internal energy $\Delta U=0$.<br/>$\therefore$ Internal energy and temperature will remain constant.<br/>(B) $p \propto \frac{1}{v^2}$<br/><br/>$$<br/>\begin{array}{rrrr} <br/>&amp; \therefore &amp; p V^2 &amp; =\text { constant } \\<br/>&amp; \text { or } &amp; \left(\frac{n R T}{V}\right) V^2=\text { constant } \\<br/>&amp; \therefore &amp; T \propto \frac{1}{V}<br/>\end{array}<br/>$$<br/>If volume is doubled, temperature will decrease as per Eq. (ii). Further, molar heat capacity in process $p V^x=$ constant is<br/>$$<br/>C=C_V+\frac{R}{1-x}<br/>$$<br/>From Eq. (i), $x=2$<br/>$$<br/>\therefore \quad C=\frac{3}{2} R+\frac{R}{1-2}=+\frac{R}{2}<br/>$$<br/>Since molar heat capacity is positive, according to $Q=n C \Delta T, Q$ will be negative it $\Delta T$ is negative. Or gas loses heat if temperature is decreasing.<br/>(C) :<br/>$$<br/>\begin{aligned}<br/>p &amp; \propto \frac{1}{V^{1 / 3}} \\<br/>P V^{4 / 3} &amp; =\text { constant } \\<br/>\left(\frac{n R T}{V}\right) V^{4 / 3} &amp; =\text { constant } \\<br/>T &amp; \propto \frac{1}{V^{1 / 3}}<br/>\end{aligned}<br/>$$<br/>Further, with increase in volume temperature will decrease.<br/>Here,<br/>$$<br/>\begin{array}{lc}<br/>\text { Here, } &amp; x=4 / 3 \\<br/>\therefore &amp; C=\frac{3}{2} R+\frac{R}{1-4 / 3}=-1.5 R<br/>\end{array}<br/>$$<br/>As molar heat capacity is negative, $Q$ will be positive, if $\Delta T$ is negative or gas gains heat with decrease in temperature.<br/>(D) $T \propto p V$<br/>In expansion from $V_1$ or $2 V_1$, product of $p V$ is increasing. Therefore, temperature will increase or $\Delta U=+$ ve.<br/>Further, in expansion work done is also positive.<br/>Hence, $Q=W+\Delta U=+$ ve<br/>or gas gains heat.</div>


tags: ['Physics', 'Oscillations', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
column-i-describes-some-situations-in-which-a-small-object-moves-column-ii-describes-some-characteristics-of-these-motions-match-the-situations-in-col

slug:
column-i-describes-some-situations-in-which-a-small-object-moves-column-ii-describes-some-characteristics-of-these-motions-match-the-situations-in-col-69144

question:
<div class="question">Column I describes some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situations in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/r-gAAZvz8yPUnIXR2inQDq09yI4uh7JKQ1NdLpZ0wDQ.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>A-p; B-q; C-p; D-q, r<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/>A-p; B-r; C-r, s; D-p, q<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>A-s; B-p; C-p; D-q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-p; B-r; C-p, q; D-r</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-p; B-q; C-p; D-q, r<br/></span> </div>


tags: ['Physics', 'Experimental Physics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-gives-a-list-of-possible-set-of-parameters-measured-in-some-experiments-the-variations-of-the-parameters-in-the-form-of-graphs-are-shown-in-c

slug:
column-i-gives-a-list-of-possible-set-of-parameters-measured-in-some-experiments-the-variations-of-the-parameters-in-the-form-of-graphs-are-shown-in-c-86940

question:
<div class="question">Column I gives a list of possible set of parameters measured in some experiments. The variations of the parameters in the form of graphs are shown in Column II. Match the set of parameters given in Column I with the graphs given in Column II. Indicate your answer by darkening the appropriate bubble of the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kKOnEC0VsHIYxeGj56aR3d6HdmJGw3KZd3eJoq8bRzU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) q, (B) p,q, (C) p,s, (D) q,s<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) q,r, (B) p,q, (C) s, (D) q<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>(A) p, (B) q,s, (C) s, (D) q<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/>(A) p,q, (B) q, (C) p,q, (D) q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p, (B) q,s, (C) s, (D) q<br/></span> </div>

answer:
<div class="solution">(A) Potential energy is minimum at mean position.<br/>(B) For $a=0, s=v t \longrightarrow$ option $(q)$<br/>or $\quad s=s_0+v t \longrightarrow$ option $(r)$<br/>For $a=$ constant,<br/>$$<br/>s=u t+\frac{1}{2} a t^2 \longrightarrow \text { option }(s)<br/>$$<br/>(C) $R=\frac{v^2 \sin 2 \theta}{g} \therefore R \propto v^2 \longrightarrow$ option (s)<br/>(D) $T=2 \pi \sqrt{\frac{l}{g}} \therefore T^2 \propto l \longrightarrow$ option $(q)$</div>


tags: ['Physics', 'Electrostatics', 'JEE Main']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
column-i-gives-certain-situations-in-which-a-straight-metallic-wire-of-resistance-r-is-used-and-column-ii-gives-some-resulting-effects-match-the-state-1

slug:
column-i-gives-certain-situations-in-which-a-straight-metallic-wire-of-resistance-r-is-used-and-column-ii-gives-some-resulting-effects-match-the-state-1-37440

question:
<div class="question">Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XbJRAPqV9FDyICAzYRczTAx0JuPw0KdH9oX8LjpfT_c.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-r; C-q; D-p, q<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>A-p; B-s; C-s; D-p, q<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>A-q; B-r, s; C-s; D-p, q, r<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/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-q; B-r, s; C-s; D-p, q, r<br/></span> </div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
column-i-gives-certain-situations-in-which-a-straight-metallic-wire-of-resistance-r-is-used-and-column-ii-gives-some-resulting-effects-match-the-state

slug:
column-i-gives-certain-situations-in-which-a-straight-metallic-wire-of-resistance-r-is-used-and-column-ii-gives-some-resulting-effects-match-the-state-39624

question:
<div class="question">Column I gives certain situations in which a straight metallic wire of resistance $R$ is used and Column II gives some resulting effects. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/XbJRAPqV9FDyICAzYRczTAx0JuPw0KdH9oX8LjpfT_c.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>A-p, r; B-r; C-q; D-p, q<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>A-p; B-s; C-s; D-p, q<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>A-q; B-r, s; C-s; D-p, q, r<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/>A-r, s; B-q; C-p; D-p, q, s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-q; B-r, s; C-s; D-p, q, r<br/></span> </div>


tags: ['Physics', 'Thermal Properties of Matter', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
column-i-gives-some-devices-and-column-ii-gives-some-processes-on-which-the-functioning-of-these-devices-depend-match-the-devices-in-column-i-with-the

slug:
column-i-gives-some-devices-and-column-ii-gives-some-processes-on-which-the-functioning-of-these-devices-depend-match-the-devices-in-column-i-with-the-57529

question:
<div class="question">Column I gives some devices and Column II gives some processes on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $4 \times 4$ matrix given in the ORS.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/3ApZB5GHsSU_-qwfqXns5dFJm436CWuGQKaMFbn4T_Y.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>A-s; B-q; C-p, q; D-q<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/>A-p; B-r; C-r, s; D-p<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>A-s; B-p; C-p; D-q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>A-p; B-r; C-p, q; D-p</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>A-s; B-q; C-p, q; D-q<br/></span> </div>


tags: ['Physics', 'Waves and Sound', 'JEE Advanced', 'JEE Advanced 2011 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-showns-four-systems-each-of-the-same-length-l-for-producing-standing-waves-the-lowest-possible-natural-frequency-of-a-system-is-called-its-fu

slug:
column-i-showns-four-systems-each-of-the-same-length-l-for-producing-standing-waves-the-lowest-possible-natural-frequency-of-a-system-is-called-its-fu-39105

question:
<div class="question">Column I showns four systems, each of the same length $L$, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $\lambda_f$. Match each system with statements given in Column II describing the nature and wave length of the standing waves.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/EUOQt3ki7T6dLYxfsmw5td75JLfbZKiLRorgXFDB8DU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>(A) p,t, (B) p,s, (C) q,s, (D) q,r<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/>(A) p,q,t, (B) p,r, (C) q,r, (D) q,s<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,s, (B) p,r, (C) q,s, (D) q,r<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,q,r,t, (B) p,s, (C) q,r, (D) q,s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,t, (B) p,s, (C) q,s, (D) q,r<br/></span> </div>

answer:
<div class="solution">In organ pipes, longitudinal waves are formed. In string, transverse waves are formed. Open end of pipe is displacement antinode and closed end is displacement node. In case of string fixed end of a string is node.<br/>Further, least distance between a node and an antinode is $\frac{\lambda}{4}$ and between two nodes is $\frac{\lambda}{2}$. Keeping these points in mind answer to this question is as under;<br/>$(\mathrm{A}) \rightarrow(\mathrm{p}, \mathrm{t})$<br/>(B) $\rightarrow(\mathrm{p}, \mathrm{s})$<br/>$(\mathrm{C}) \rightarrow(\mathrm{q}, \mathrm{s})$<br/>(D) $\rightarrow$ (q, r)<br/>Analysis of Question<br/>(i) Unlike the previous years's few match the column problems, this question seems to be more logical. If you know the subject, you can select correct matching without confusion.<br/>(ii) In option (d) of column I, string is fixed from centre, therefore at lowest frequency two loops will be formed as shown below.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/rnGnEFAsnZpkoHbpmxp9dlFR16LVSlCab_-rSfbpjs4.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Wave Optics', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
column-i-shows-four-situations-of-standard-youngs-double-slit-arrangement-with-the-screen-placed-far-away-from-the-slits-s-1-and-s-2-in-each-of-these-

slug:
column-i-shows-four-situations-of-standard-youngs-double-slit-arrangement-with-the-screen-placed-far-away-from-the-slits-s-1-and-s-2-in-each-of-these-26081

question:
<div class="question">Column I shows four situations of standard Young's double slit arrangement with the screen placed far away from the slits $S_1$ and $S_2$. In each of these cases $S_1 P_0=S_2 P_0$, $S_1 P_1-S_2 P_1=\frac{\lambda}{4}$ and $S_1 P_2-S_2 P_2=\frac{\lambda}{3}$, where $\lambda$ is the wavelength of the light used. In the cases $\mathrm{B}, \mathrm{C}$ and $\mathrm{D}$, a transparent sheet of refractive index $\mu$ and thickness $t$ is pasted on slit $S_2$. The thickness of the sheets are different in different cases. The phase difference between the light waves reaching a point $P$ on the screen from the two slits is denoted by $\delta(P)$ and the intensity by $I(P)$. Match each situation given in Column-I with the statement(s) in Column-II valid for that situation.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/WB06TwRxOzqpnbZ5VrecHzPxESIeLecOdphK0motYWQ.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) q,t, (B) q, (C) t, (D) r,s,t<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>(A) q,r,s, (B) r, (C) q,r, (D) q,s,t<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,s, (B) r, (C) q,t, (D) r,s<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,s, (B) q, (C) t, (D) r,s,t</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,s, (B) q, (C) t, (D) r,s,t</span> </div>

answer:
<div class="solution">(A) $\rightarrow(\mathrm{p}, \mathrm{s}) \rightarrow$ Intensity at $P_0$ is maximum. It will continuously decrease from $P_0$ towards $P_2$.<br/>$(B) \rightarrow(q) \rightarrow$ Path difference due to slap will be compensated by geometrical path difference. Hence, $\delta\left(P_1\right)=0$.<br/>$(\mathrm{C}) \rightarrow(\mathrm{t}) \rightarrow \delta\left(P_0\right)=\frac{\lambda}{2}, \delta\left(P_1\right)=\frac{\lambda}{2}-\frac{\lambda}{4}=\frac{\lambda}{4}$ and $\delta\left(P_2\right)=\frac{\lambda}{2}-\frac{\lambda}{3}=\frac{\lambda}{6}$. When path difference increases from 0 to $\frac{\lambda}{2}$, intensity will decrease from maximum to zero. Hence, in this case,<br/>$$<br/>I\left(P_2\right)&gt;I\left(P_1\right)&gt;I\left(P_0\right)<br/>$$<br/>$(\mathrm{D}) \rightarrow(\mathrm{r}, \mathrm{s}, \mathrm{t})$<br/>$$<br/>\delta\left(P_0\right)=\frac{3 \lambda}{4}, \delta\left(P_1\right)=\frac{3 \lambda}{4}-\frac{\lambda}{4}=\frac{\lambda}{2}<br/>$$<br/>and $\delta\left(P_2\right)=\frac{3 \lambda}{4}-\frac{\lambda}{3}=\frac{5 \lambda}{12}$<br/>In this case $I\left(P_1\right)=0$</div>


tags: ['Physics', 'Work Power Energy', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
column-ii-shows-five-systems-in-which-two-objects-are-labelled-as-x-and-y-also-in-each-case-a-point-p-is-shown-columni-gives-some-statements-about-x-a-1

slug:
column-ii-shows-five-systems-in-which-two-objects-are-labelled-as-x-and-y-also-in-each-case-a-point-p-is-shown-columni-gives-some-statements-about-x-a-1-45439

question:
<div class="question">Column II shows five systems in which two objects are labelled as $X$ and $Y$. Also in each case a point $P$ is shown. Column-I gives some statements about $X$ and/or $Y$. Match these statements to the appropriate system(s) from Column-II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Nmjp-6aDDAiZbMGB3BfCFqOpbccuBbUIpfhDHt9E9zY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>(A) p,t, (B) q,s,t, (C) p,r,t, (D) r,q,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">B</span> <span class="option-data"><br/>(A) q,t, (B) q,s, (C) p,r, (D) r,q,t<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,t, (B) q,s,t, (C) r,t, (D) r,q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,r, (B) q,s, (C) p,r,t, (D) r,q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,t, (B) q,s,t, (C) p,r,t, (D) r,q,t<br/></span> </div>

answer:
<div class="solution">$(\mathrm{A}) \rightarrow(\mathrm{p}, \mathrm{t}) \rightarrow$ Net force on $Y$ is ero.<br/>(B) $\rightarrow(\mathrm{q}, \mathrm{s}, \mathrm{t}) \rightarrow \ln (\mathrm{s})$ and $(\mathrm{t})$ gravitational potential energy of $Y$ is decreasing and that of $X$ is increasing.<br/>(C) $\rightarrow(\mathrm{p}, \mathrm{r}, \mathrm{t}) \rightarrow \operatorname{In}(\mathrm{t}), \mathrm{Y}$ is moving with constant speed.<br/>(D) $\rightarrow$ (q) $\rightarrow$ No explanation is required</div>


tags: ['Physics', 'Work Power Energy', 'JEE Advanced', 'JEE Advanced 2009 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
column-ii-shows-five-systems-in-which-two-objects-are-labelled-as-x-and-y-also-in-each-case-a-point-p-is-shown-columni-gives-some-statements-about-x-a

slug:
column-ii-shows-five-systems-in-which-two-objects-are-labelled-as-x-and-y-also-in-each-case-a-point-p-is-shown-columni-gives-some-statements-about-x-a-53317

question:
<div class="question">Column II shows five systems in which two objects are labelled as $X$ and $Y$. Also in each case a point $P$ is shown. Column-I gives some statements about $X$ and/or $Y$. Match these statements to the appropriate system(s) from Column-II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/Nmjp-6aDDAiZbMGB3BfCFqOpbccuBbUIpfhDHt9E9zY.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>(A) p,t, (B) q,s,t, (C) p,r,t, (D) r,q,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">B</span> <span class="option-data"><br/>(A) q,t, (B) q,s, (C) p,r, (D) r,q,t<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>(A) p,t, (B) q,s,t, (C) r,t, (D) r,q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,r, (B) q,s, (C) p,r,t, (D) r,q</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,t, (B) q,s,t, (C) p,r,t, (D) r,q,t<br/></span> </div>

answer:
<div class="solution">$(\mathrm{A}) \rightarrow(\mathrm{p}, \mathrm{t}) \rightarrow$ Net force on $Y$ is ero.<br/>(B) $\rightarrow(\mathrm{q}, \mathrm{s}, \mathrm{t}) \rightarrow \ln (\mathrm{s})$ and $(\mathrm{t})$ gravitational potential energy of $Y$ is decreasing and that of $X$ is increasing.<br/>(C) $\rightarrow(\mathrm{p}, \mathrm{r}, \mathrm{t}) \rightarrow \operatorname{In}(\mathrm{t}), \mathrm{Y}$ is moving with constant speed.<br/>(D) $\rightarrow$ (q) $\rightarrow$ No explanation is required</div>


tags: ['Physics', 'Work Power Energy', 'JEE Advanced', 'JEE Advanced 2009 (Paper 2)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch1_P2.db
title:
columnii-gives-certain-systems-undergoing-a-process-columni-suggests-changes-in-some-of-the-parameters-related-to-the-system-match-the-statements-in-c

slug:
columnii-gives-certain-systems-undergoing-a-process-columni-suggests-changes-in-some-of-the-parameters-related-to-the-system-match-the-statements-in-c-54726

question:
<div class="question">Column-II gives certain systems undergoing a process. Column-I suggests changes in some of the parameters related to the system. Match the statements in Column-I to the appropriate process (es) from Column-II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/G_QqC-7_pg_NzGDr82H8KAsvaf0LgQidVsnjc4WmM3E.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) q,t, (B) r, (C) t, (D) r<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>(A) p,q,s,t, (B) q, (C) s, (D) s<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/>(A) p,s, (B) r, (C) s, (D) r<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) p,q,s,t, (B) q, (C) t, (D) s</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p,q,s,t, (B) q, (C) s, (D) s<br/></span> </div>


tags: ['Mathematics', 'Hyperbola', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-branch-of-the-hyperbola-x-2-2-y-2-2-2-x-4-2-y-6-0-with-vertex-at-the-point-a-let-b-be-one-of-the-end-points-of-its-latus-rectum-if-c-is-the

slug:
consider-a-branch-of-the-hyperbola-x-2-2-y-2-2-2-x-4-2-y-6-0-with-vertex-at-the-point-a-let-b-be-one-of-the-end-points-of-its-latus-rectum-if-c-is-the-36102

question:
<div class="question">Consider a branch of the hyperbola $x^2-2 y^2-2 \sqrt{2} x-4 \sqrt{2} y-6=0$ with vertex at the point $A$. Let $B$ be one of the end points of its latus rectum. If $C$ is the focus of the hyperbola nearest to the point $A$, then the area of the $\triangle A B C$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\sqrt{\frac{3}{2}}-1$ sq unit<br/></span> </div>

answer:
<div class="solution">The given equation can be rewritten as $\frac{(x-\sqrt{2})^2}{1}-\frac{(y+\sqrt{2})^2}{2}=1$ for $A(x, y)$,<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/kJiDAgQz4cB8Ql-009_N5DDom8WjagEpxMaE9lZAfMg.original.fullsize.png"/><br/><br/>$$<br/>\begin{aligned}<br/>&amp; e=\sqrt{1+\frac{2}{4}}=\sqrt{\frac{3}{2}} \\<br/>&amp; \therefore x-\sqrt{2}=2 \Rightarrow x=2+\sqrt{2} \\<br/>&amp; \text { For } C(x, y), x-\sqrt{2}=a e=\sqrt{6} \\<br/>&amp; \Rightarrow \quad x=\sqrt{6}+\sqrt{2} \\<br/>&amp; \text { Now, } A C=\sqrt{6}+\sqrt{2}-2-\sqrt{2}=\sqrt{6}-2 \\<br/>&amp; \qquad B C=\frac{b^2}{a}=\frac{2}{2}=1 \\<br/>&amp; \text { Area of } \Delta A B C=\frac{1}{2} \times(\sqrt{6}-2) \times B C \\<br/>&amp; =\frac{1}{2} \times(\sqrt{6}-2) \times 1=\sqrt{\frac{3}{2}}-1<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Rotational Motion', 'JEE Advanced', 'JEE Advanced 2012 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-disc-rotating-in-the-horizontal-plane-with-a-constant-angular-speed-about-its-centre-o-the-disc-has-a-shaded-region-on-one-side-of-the-diam

slug:
consider-a-disc-rotating-in-the-horizontal-plane-with-a-constant-angular-speed-about-its-centre-o-the-disc-has-a-shaded-region-on-one-side-of-the-diam-85336

question:
<div class="question">Consider a disc rotating in the horizontal plane with a constant angular speed $\omega$ about its centre $\mathrm{O}$. The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure. When the disc is in the orientation as shown, two pebbles $P$ and $Q$ are simultaneously projected at an angle towards $R$. The velocity of projection is in the $y$ - $z$ plane and is same for both pebbles with respect to the disc. Assume that (i) they land back on the disc before the disc has completed $1 / 8$ rotation, (ii) their range is less than half the disc radius, and (iii) $\omega$ remains constant throughout. Then
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/4Z-V_5_KytE90rgAnNsqUdyYITXRjOw-3D1XemNP20Y.original.fullsize.png"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$P$ lands in the shaded region and $Q$ in the unshaded region.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$P$ lands in the unshaded region and $Q$ in the shaded region.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both $P$ and $Q$ land in the unshaded region.</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">Both $P$ and $Q$ land in the shaded region.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both $P$ and $Q$ land in the unshaded region.</span> </div>

answer:
<div class="solution">For $\frac{1}{8}$ of rotation of disc,
<br/> <br/>$\begin{aligned}
<br/> <br/>t=\frac{1}{8} \times \frac{2 \pi}{\omega}=\frac{\pi}{4 \omega} &amp; \\
<br/> <br/>x \text {-coordinate of } P &amp;=\omega R T \\
<br/> <br/>&amp;=\frac{\pi R}{4}&gt;R \sin 45^{\circ}
<br/> <br/>\end{aligned}$
<br/> <br/>To reach the unshaded part, particle$P$ needs to travel horizontal range $&gt;$ $R \sin 45^{\circ} \simeq 0.7 \mathrm{R}$
<br/> <br/>But its range is less than $\mathrm{R} / 2$ so it will land on shaded part. $Q$ is near the origin, its velocity will be nearly along QR so it will land in unshaded part.
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/nNaoB62ZECYr2P82saF5y7BuBNr7sgHYC9XoG5Dyi1o.original.fullsize.png"/></div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-neutral-conducting-sphere-a-positive-point-charge-is-placed-outside-the-sphere-the-net-charge-on-the-sphere-is-then

slug:
consider-a-neutral-conducting-sphere-a-positive-point-charge-is-placed-outside-the-sphere-the-net-charge-on-the-sphere-is-then-92668

question:
<div class="question">Consider a neutral conducting sphere. A positive point charge is placed outside the sphere. The net charge on the sphere is then</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>negative and distributed uniformly over the surface of the sphere<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>negative and appears only at the point on the sphere closest to the point charge<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>negative and distributed non-uniformly over the entire surface of the sphere<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">$$<br/>\text { Charge will be induced in the conducting sphere, but net charge on it will be zero. }<br/>$$<br/><br/>$$<br/>\therefore \text { Option (d) is correct. }<br/>$$</div>


tags: ['Chemistry', 'Chemical Kinetics', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value"><br/>3</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-a-reaction-a-g-b-h-products-when-concentration-of-both-the-reactants-g-and-h-is-doubled-the-rate-increases-by-eight-times-however-when-concen-1

slug:
consider-a-reaction-a-g-b-h-products-when-concentration-of-both-the-reactants-g-and-h-is-doubled-the-rate-increases-by-eight-times-however-when-concen-1-44566

question:
<div class="question">Consider a reaction $a G+b H \rightarrow$ products. When concentration of both the reactants $G$ and $H$ is doubled, the rate increases by eight times. However, when concentration of $G$ is doubled keeping the concentration of $H$ fixed, the rate is doubled. The overall order of the reaction is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>0<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>1<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>2<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>3</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$a G+b H \longrightarrow$ Product<br/>Suppose order of reaction $=n$<br/>When concentration of both $G$ and $H$ is double than rate increase by eight times.<br/>$$<br/>\begin{aligned}<br/>\text { rate } &amp; =k(\text { reactants })^n \\<br/>(2)^8 &amp; =k(2)^n \\<br/>(2)^3 &amp; =k(2)^n \\<br/>n &amp; =3<br/>\end{aligned}<br/>$$<br/>when concentration of $G$ is doubled than concentration $H$ is fixed, the rate is double.<br/>than $\quad$ rate $\propto[G]^1[H]^2$</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-a-system-of-three-charges-3-q-3-q-and-3-2-q-placed-at-points-a-b-and-c-respectively-as-shown-in-the-figure-take-o-to-be-the-centre-of-the-cir

slug:
consider-a-system-of-three-charges-3-q-3-q-and-3-2-q-placed-at-points-a-b-and-c-respectively-as-shown-in-the-figure-take-o-to-be-the-centre-of-the-cir-81349

question:
<div class="question">Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $-\frac{2 q}{3}$ placed at points $A, B$ and $C$, respectively, as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $C A B=60^{\circ}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/h78g_hb3-iGHvg7H2ZK6jg55DjbqxES3XJLSjyLzlNQ.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>The electric field at point $O$ is $\frac{q}{8 \pi \varepsilon_0 R^2}$ directed along the negative $x$-axis<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>The potential energy of the system is zero<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>The magnitude of the force between the charges at $C$ and $B$ is $\frac{q^2}{54 \pi \varepsilon_0 R^2}$<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">D</span> <span class="option-data"><br/>The potential at point $O$ is $\frac{q}{12 \pi \varepsilon_0 R}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>The magnitude of the force between the charges at $C$ and $B$ is $\frac{q^2}{54 \pi \varepsilon_0 R^2}$<br/></span> </div>

answer:
<div class="solution">Distance $B C=A B \sin 60^{\circ}=(2 R) \frac{\sqrt{3}}{2}=\sqrt{3} R$<br/>$\therefore \quad\left|F_{B C}\right|=\frac{1}{4 \pi \varepsilon_0} \frac{(q / 3)(2 q / 3)}{(\sqrt{3} R)^2}=\frac{q^2}{54 \pi \varepsilon_0 R^2}$<br/>$\therefore$ correct option is (c).</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2012 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-thin-spherical-shell-of-radius-r-with-centre-at-the-origin-carrying-uniform-positive-surface-charge-density-the-variation-of-the-magnitude-

slug:
consider-a-thin-spherical-shell-of-radius-r-with-centre-at-the-origin-carrying-uniform-positive-surface-charge-density-the-variation-of-the-magnitude-45909

question:
<div class="question">Consider a thin spherical shell of radius $R$ with centre at the origin, carrying uniform positive surface charge density. The variation of the magnitude of the electric field $|\vec{E}(r)|$ and the electric potential $V(r)$ with the distance $r$ from the centre, is best represented by which graph?</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/E3m10uZEbKDsryfNH6apC8lG9tonBECzbJDocju9JQk.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ZUWR2PHmFvOetGpbNJ5XeSiX4S1xKyQltlV82kwjSIw.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/etr6C3Rn7FUxZjqQnTXzGHWVwuP02jk7HEZLe3ddo1A.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/ikjTnp-ZIgcQMIDCC4C-yNMcYCNlesQGvAePbfXQpaM.original.fullsize.png"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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/ikjTnp-ZIgcQMIDCC4C-yNMcYCNlesQGvAePbfXQpaM.original.fullsize.png"/></span> </div>

answer:
<div class="solution">For a thin uniformly positive charged spherical shell
<br/> <br/>(i) Inside the shell at any point
<br/> <br/>$E=O$ and $V=\frac{1}{4 \pi \in_{0}} \quad \frac{q}{R}=$ constt.
<br/> <br/>where $q=$ charge on sphere
<br/> <br/>$R=$ Radius of sphere
<br/> <br/>(ii) Outside the shell at any point at any distance $r$ from
<br/> <br/>the centre $E \propto \frac{1}{r^{2}}$ and $V \propto \frac{1}{r}$</div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-a-thin-square-sheet-of-side-l-and-thickness-t-made-of-a-material-of-resistivity-the-resistance-between-two-opposite-faces-shown-by-the-shaded-1

slug:
consider-a-thin-square-sheet-of-side-l-and-thickness-t-made-of-a-material-of-resistivity-the-resistance-between-two-opposite-faces-shown-by-the-shaded-1-30679

question:
<div class="question">Consider a thin square sheet of side $L$ and thickness $t$, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded areas in the figure is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jQWT8TUcKYNLj76kfHeUfDLbThIKMquc23PlGL0NDCw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>directly proportional to $L$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>directly proportional to $t$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>independent of $L$<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/>independent of $t$</span> </li> </ul>

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

answer:
<div class="solution">$R=\frac{\rho(L)}{A}=\frac{\rho L}{t L}=\frac{\rho}{t}$ ie, $R$ is independent of $L$. Hence the correct option is (c).</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2010 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
consider-a-thin-square-sheet-of-side-l-and-thickness-t-made-of-a-material-of-resistivity-the-resistance-between-two-opposite-faces-shown-by-the-shaded

slug:
consider-a-thin-square-sheet-of-side-l-and-thickness-t-made-of-a-material-of-resistivity-the-resistance-between-two-opposite-faces-shown-by-the-shaded-33624

question:
<div class="question">Consider a thin square sheet of side $L$ and thickness $t$, made of a material of resistivity $\rho$. The resistance between two opposite faces, shown by the shaded areas in the figure is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/jQWT8TUcKYNLj76kfHeUfDLbThIKMquc23PlGL0NDCw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>directly proportional to $L$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>directly proportional to $t$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>independent of $L$<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/>independent of $t$</span> </li> </ul>

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

answer:
<div class="solution">$R=\frac{\rho(L)}{A}=\frac{\rho L}{t L}=\frac{\rho}{t}$ ie, $R$ is independent of $L$. Hence the correct option is (c).</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Advanced', 'JEE Advanced 2007 (Paper 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value"><br/>6</span> </div>
answer: <div class="solution">Mole ratio is reverse of $x$-factor ratio.</div>
source_db: MarksBatch1_P2.db
title:
consider-a-titration-of-potassium-dichromate-solution-with-acidified-mohrs-salt-solution-using-diphenylamine-as-indicator-the-number-of-moles-of-mohrs

slug:
consider-a-titration-of-potassium-dichromate-solution-with-acidified-mohrs-salt-solution-using-diphenylamine-as-indicator-the-number-of-moles-of-mohrs-29351

question:
<div class="question">Consider a titration of potassium dichromate solution with acidified Mohr's salt solution using diphenylamine as indicator. The number of moles of Mohr's salt required per mole of dichromate is</div>

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=""> <span class="option-label">C</span> <span class="option-data"><br/>5<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>6</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


tags: ['Mathematics', 'Properties of Triangles', 'JEE Advanced', 'JEE Advanced 2010 (Paper 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P2.db
title:
consider-a-triangle-a-bc-and-let-a-b-and-c-denote-the-lengths-of-the-sides-opposite-to-vertices-a-b-and-c-respectively-suppose-a-6-b-10-and-the-area-o

slug:
consider-a-triangle-a-bc-and-let-a-b-and-c-denote-the-lengths-of-the-sides-opposite-to-vertices-a-b-and-c-respectively-suppose-a-6-b-10-and-the-area-o-24899

question:
<div class="question">Consider a triangle $A B C$ and let $a, b$ and $c$ denote the lengths of the sides opposite to vertices $A, B$ and $C$ respectively. Suppose $a=6, b=10$ and the area of the triangle is $15 \sqrt{3}$. If $\angle A C B$ is obtuse and if $r$ denotes the radius of the incircle of the triangle, then $r^2$ is equal to</div>

answer:
<div class="solution">$\sin C=\frac{\sqrt{3}}{2}$ and $C$ is given to be obtuse<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \Rightarrow \quad C=\frac{2 \pi}{3}=\sqrt{a^2+b^2-2 a b \cos C} \\<br/>&amp; =\sqrt{6^2+10^2-2 \times 6 \times 10 \times \cos \frac{2 \pi}{3}}=14 \\<br/>&amp; \therefore \quad r=\frac{\Delta}{s} \Rightarrow r^2=\frac{225 \times 3}{\left(\frac{6+10+14}{2}\right)^2}=3<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
consider-all-possible-permutations-of-the-letters-of-the-word-endeanoel-match-the-statementsexpressions-in-column-i-with-the-statementsexpressions-in--1

slug:
consider-all-possible-permutations-of-the-letters-of-the-word-endeanoel-match-the-statementsexpressions-in-column-i-with-the-statementsexpressions-in-1-15009

question:
<div class="question">Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1Oj7xgNtMlSTH_bJ2EXv-IV_L6I5OltoIjA2nwL0Yr0.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) r, (B) q, (C) s, (D) p<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>(A) p, (B) s, (C) q, (D) q<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/>(A) p, (B) r, (C) s, (D) q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) r, (B) s, (C) r, (D) p</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p, (B) s, (C) q, (D) q<br/></span> </div>

answer:
<div class="solution">(A) If ENDEA is fixed word, then assume this as a single letter.<br/>Total number of letters $=5$ and total number of arrangements $=5$ ! .<br/>(B) If $E$ is at first and last places, then total number of permutations<br/>$$<br/>\frac{7 !}{2 !}=21 \times 5 !<br/>$$<br/>(C) If $\mathrm{D}, \mathrm{L}, \mathrm{N}$ are not in last five positions<br/>$$<br/>\leftarrow \mathrm{D}, \mathrm{L}, \mathrm{N}, \mathrm{N} \rightarrow \leftarrow \text { E, E, E, A, O } \rightarrow<br/>$$<br/>Total number of permutations $=\frac{4 !}{2 !} \times \frac{5 !}{3 !}=2 \times 5$ ! .<br/>(D) Total number of odd positions $=5$<br/>Permutations of AEEEO are $\frac{5 !}{3 !}$<br/>Total number of even positions $=4$<br/>Number of permutations of $\mathrm{N}, \mathrm{N}, \mathrm{D}, \mathrm{L}=\frac{4 !}{2 !}$<br/>Hence, total number of permutations $=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !$.</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-all-possible-permutations-of-the-letters-of-the-word-endeanoel-match-the-statementsexpressions-in-column-i-with-the-statementsexpressions-in-

slug:
consider-all-possible-permutations-of-the-letters-of-the-word-endeanoel-match-the-statementsexpressions-in-column-i-with-the-statementsexpressions-in-37165

question:
<div class="question">Consider all possible permutations of the letters of the word ENDEANOEL. Match the Statements/Expressions in Column I with the Statements/Expressions in Column II.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/1Oj7xgNtMlSTH_bJ2EXv-IV_L6I5OltoIjA2nwL0Yr0.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>(A) r, (B) q, (C) s, (D) p<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>(A) p, (B) s, (C) q, (D) q<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/>(A) p, (B) r, (C) s, (D) q<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>(A) r, (B) s, (C) r, (D) p</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>(A) p, (B) s, (C) q, (D) q<br/></span> </div>

answer:
<div class="solution">(A) If ENDEA is fixed word, then assume this as a single letter.<br/>Total number of letters $=5$ and total number of arrangements $=5$ ! .<br/>(B) If $E$ is at first and last places, then total number of permutations<br/>$$<br/>\frac{7 !}{2 !}=21 \times 5 !<br/>$$<br/>(C) If $\mathrm{D}, \mathrm{L}, \mathrm{N}$ are not in last five positions<br/>$$<br/>\leftarrow \mathrm{D}, \mathrm{L}, \mathrm{N}, \mathrm{N} \rightarrow \leftarrow \text { E, E, E, A, O } \rightarrow<br/>$$<br/>Total number of permutations $=\frac{4 !}{2 !} \times \frac{5 !}{3 !}=2 \times 5$ ! .<br/>(D) Total number of odd positions $=5$<br/>Permutations of AEEEO are $\frac{5 !}{3 !}$<br/>Total number of even positions $=4$<br/>Number of permutations of $\mathrm{N}, \mathrm{N}, \mathrm{D}, \mathrm{L}=\frac{4 !}{2 !}$<br/>Hence, total number of permutations $=\frac{5 !}{3 !} \times \frac{4 !}{2 !}=2 \times 5 !$.</div>


tags: ['Physics', 'Electrostatics', 'JEE Advanced', 'JEE Advanced 2011 (Paper 1)']
source_db: MarksBatch1_P2.db
title:
consider-an-electric-field-e-e-0-x-where-e-0-is-a-constant-the-flux-through-the-shaded-area-as-shown-in-the-figure-due-to-this-field-is

slug:
consider-an-electric-field-e-e-0-x-where-e-0-is-a-constant-the-flux-through-the-shaded-area-as-shown-in-the-figure-due-to-this-field-is-28226

question:
<div class="question">Consider an electric field $\mathbf{E}=E_0 \hat{\mathbf{x}}$ where $\bar{E}_0$ is a constant. The flux through the shaded area ( as shown in the figure) due to this field is<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/E8rJdxbxJvoMYCbK6XQXC69Eq6GFBN_dcj0grzJMvrU.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$2 E_0 a^2$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$\sqrt{2} E_0 a^2$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$E_0 a^2$<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">D</span> <span class="option-data"><br/>$\frac{E_0 a^2}{\sqrt{2}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$E_0 a^2$<br/></span> </div>

answer:
<div class="solution">Electric flux, $\mathbf{E} \cdot \mathbf{S}$, or $\phi=E S \cos \theta$ Here, $\theta$ is the angle between $\mathbf{E}$ and $\mathbf{S}$. In this question $\theta=45^{\circ}$, because $\mathbf{S}$ is perpendicular to the surface.<br/>$$<br/>\begin{gathered}<br/>E=E_0 \\<br/>\Rightarrow \quad S=(\sqrt{2 a})(a)=\sqrt{2} a^2 \\<br/>\therefore \phi=\left(E_0\right)\left(\sqrt{2} a^2\right) \cos 45^{\circ}=E_0 a^2<br/>\end{gathered}<br/>$$<br/>$\therefore$ Correct option is (c).<br/>Analysis of Question<br/>(i) Question is moderately tough.<br/>(ii) The given shaded area is a rectangle not a square. One side of this rectangle is $a$ and other side is $\sqrt{2} a$.<br/>(iii) Electric field is uniform, whose magnitude is $E_0$ and direction is positive $x$. In uniform electric field we can use, $\phi=E S \cos \theta$</div>


tags: ['Physics', 'Units and Dimensions', 'JEE Advanced', 'JEE Advanced 2017 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-an-expanding-sphere-of-instantaneous-radius-r-whose-total-mass-remains-constant-the-expansion-is-such-that-the-instantaneous-density-remains--1

slug:
consider-an-expanding-sphere-of-instantaneous-radius-r-whose-total-mass-remains-constant-the-expansion-is-such-that-the-instantaneous-density-remains-1-43548

question:
<div class="question">Consider an expanding sphere of instantaneous radius <math> <mi>R</mi> </math> whose total mass remains constant. The expansion is such that the instantaneous density <math><mi>Ï</mi></math> remains uniform throughout the volume. The rate of fractional change in density <math><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac><mfrac><mrow><mi>d</mi><mi>Ï</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></mrow></mfenced></math> is constant. The velocity <math><mi>v</mi></math> of any point on the surface of the expanding sphere is proportional to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>R</mi></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mi>R</mi></math></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"><math><msup><mrow><mi>R</mi></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></math></span> </li> </ul>

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

answer:
<div class="solution"><p>Density of sphere is <math><mi>ρ</mi><mo>=</mo><mfrac><mrow><mi>m</mi></mrow><mrow><mi>v</mi></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>m</mi></mrow><mrow><mn>4</mn><mi>π</mi><msup><mrow><mi>R</mi></mrow><mrow><mn>3</mn></mrow></msup></mrow></mfrac></math></p><p><math><mo>⇒</mo><mi> </mi><mi> </mi><mi> </mi><mi> </mi><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ρ</mi></mrow></mfrac><mfrac><mrow><mi>d</mi><mi>ρ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mo>=</mo><mi> </mi><mo>-</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mi>R</mi></mrow></mfrac><mi> </mi><mfrac><mrow><mi>d</mi><mi>R</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math></p><p>Since  <math><mo>⇒</mo><mi> </mi><mi> </mi><mfrac><mrow><mn>1</mn></mrow><mrow><mi>ρ</mi></mrow></mfrac><mfrac><mrow><mi>d</mi><mi>ρ</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac></math>  is constant</p><p><math><mo>∴</mo><mi> </mi><mi> </mi><mi> </mi><mfrac><mrow><mi>d</mi><mi>R</mi></mrow><mrow><mi>d</mi><mi>t</mi></mrow></mfrac><mi> </mi><mo>∝</mo><mi>R</mi></math></p></div>


tags: ['Mathematics', 'Straight Lines', 'JEE Advanced', 'JEE Advanced 2008 (Paper 2)']
source_db: MarksBatch1_P2.db
title:
consider-l-1-2-x-3-y-p-3-0-l-2-2-x-3-y-p-3-0-where-p-is-a-real-number-and-c-x-2-y-2-6-x-10-y-30-0-statement-1-if-line-l-1-is-a-chord-of-circle-c-then-

slug:
consider-l-1-2-x-3-y-p-3-0-l-2-2-x-3-y-p-3-0-where-p-is-a-real-number-and-c-x-2-y-2-6-x-10-y-30-0-statement-1-if-line-l-1-is-a-chord-of-circle-c-then-73070

question:
<div class="question">Consider $L_1: 2 x+3 y+p-3=0 ; L_2: 2 x+3 y+p+3=0$ where $p$ is a real number and $C: x^2+y^2+6 x-10 y+30=0$.<br/>Statement 1 If line $L_1$ is a chord of circle $C$, then line $L_2$ is not always a diameter of circle $C$.<br/>Statement 2 If line $L_1$ is a diameter of circle $C$, then line $L_2$ is not a chord of circle $C$.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 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 1 is false, Statement 2 is true</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </div>

answer:
<div class="solution">Equation of circle $C$ is<br/>$$<br/>\begin{aligned}<br/>(x+3)^2+(y-5)^2 &amp; =9+25-30=4 \\<br/>\Rightarrow \quad \quad(x+3)^2+(y-5)^2 &amp; =2^2 \\<br/>\text { Centre } &amp; =(3,-5)<br/>\end{aligned}<br/>$$<br/><br/>If $L_1$ is diameter, then $2(3)+3(-5)+p-3=0 \Rightarrow p=12$<br/>$\therefore \quad L_1$ is $2 x+3 y+9=0$<br/>and<br/>$L_2$ is $2 x+3 y+15=0$<br/>Distance of centre of circle from $L_2=\left|\frac{2(3)+3(-5)+15}{\sqrt{2^2+3^2}}\right|=\frac{6}{\sqrt{13}} &lt; 2 \quad$ [radius of circle]<br/>$\therefore L_2$ is a chord of circle $C$.<br/>Statement 2 is false.</div>


