# questions

title: tyndall-effect-is-observed-due-to
slug: tyndall-effect-is-observed-due-to-47833
question: <div class="question">Tyndall effect is observed due to</div>
tags: ['Chemistry', 'Surface Chemistry', 'MHT CET', 'MHT CET 2020 (15 Oct Shift 1)']
answer: <div class="solution">No solution</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">neutralization of charge on colloidal particles</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Zig-zag motion of colloidal particles</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">precipitation of colloidal particles</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Scattering of light by 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 answer is:
<span class="option-value">Scattering of light by colloidal particles</span> </div>


title: tyndall-effect-is-observed-when
slug: tyndall-effect-is-observed-when-53689
question: <div class="question">Tyndall effect is observed when :</div>
tags: ['Chemistry', 'Surface Chemistry', 'JEE Main', 'JEE Main 2020 (03 Sep Shift 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The diameter of dispersed particles is much larger than the wavelength of light used.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The diameter of dispersed particles is much smaller than the wavelength of light used</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The refractive index od dispersed phase is greater than that of the dispersion medium.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The diameter of dispersed particles is similar to the wavelength of light used.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">The diameter of dispersed particles is similar to the wavelength of light used.</span> </div>

answer:
<div class="solution">The diameter of the dispersed particles is not much smaller than the wavelength of the lights used. The intensity of scattered light depends on the difference between the refractive indice of the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">P</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">D</mi><mo>.</mo><mi mathvariant="normal">M</mi></math>., In lyophobic colloids, this difference is appreciable and therefore the tyndal effect is quite we ll defined but in lyophilic sols the difference is very small and the tyndal effect is very weak. So, to show Tyndall effect the refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>


tags: ['Physics', 'Kinetic Theory of Gases', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
under-standard-conditions-the-density-of-a-gas-is-13-mg-cm-3-and-the-velocity-of-propagation-of-sound-in-it-is-330-m-s-1-the-number-of-degrees-of-free

slug:
under-standard-conditions-the-density-of-a-gas-is-13-mg-cm-3-and-the-velocity-of-propagation-of-sound-in-it-is-330-m-s-1-the-number-of-degrees-of-free-97458

question:
<div class="question">Under standard conditions, the density of a gas is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1.3</mn><mtext>â</mtext><msup><mi mathvariant="normal">mg cm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></math> and the velocity of propagation of sound, in it, is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>330</mn><mo> </mo><mi mathvariant="normal">m</mi><mo> </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The number of degrees of freedom of gas is</div>

answer:
<div class="solution"><p><math><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>d</mi></mrow></msub><mo>=</mo><msqrt><mfrac><mrow><mi>Î³</mi><mi>P</mi></mrow><mrow><mi>Ï</mi></mrow></mfrac></msqrt></math> and <math><mi>Î³</mi><mo>=</mo><mn>1</mn><mo>+</mo><mfrac><mrow><mn>2</mn></mrow><mrow><mi>f</mi></mrow></mfrac></math><br/><br/><math><mo>â´</mo></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mfrac><mn>2</mn><mi>f</mi></mfrac><mo>=</mo><mfrac><mrow><msubsup><mi>v</mi><mrow><mi>s</mi><mi>o</mi><mi>u</mi><mi>n</mi><mi>d</mi></mrow><mn>2</mn></msubsup><mo>Ã</mo><mi>Ï</mi></mrow><mi>P</mi></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mfrac><mn>2</mn><mi>f</mi></mfrac><mo>=</mo><mfrac><mrow><mo>(</mo><mn>330</mn><msup><mo>)</mo><mn>2</mn></msup><mo>Ã</mo><mo>(</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>)</mo></mrow><mrow><mn>1</mn><mo>.</mo><mn>01</mn><mo>Ã</mo><msup><mn>10</mn><mn>5</mn></msup></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>+</mo><mfrac><mn>2</mn><mi>f</mi></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>40</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>5</mn></math></p></div>


tags: ['Physics', 'Kinetic Theory of Gases', 'AP EAMCET', 'AP EAMCET 2019 (22 Apr Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P3.db
title:
under-standard-conditions-the-density-of-a-gas-is-frac14001089-mathrmkg-mathrm-mathrmm3-and-the-speed-of-sound-propagation-in-it-is-330-mathrmms1-then

slug:
under-standard-conditions-the-density-of-a-gas-is-frac14001089-mathrmkg-mathrm-mathrmm3-and-the-speed-of-sound-propagation-in-it-is-330-mathrmms1-then-28526

question:
<div class="question">Under standard conditions, the density of a gas is \(\frac{1400}{1089} \mathrm{~kg} \mathrm{-} \mathrm{m}^{-3}\) and the speed of sound propagation in it is \(330 \mathrm{~ms}^{-1}\), then the number of degrees of freedom of the gas molecules is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">7</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">3</span> </li> </ul>

answer:
<div class="solution">Given, density of gas, \(\rho=\frac{1400}{1089} \mathrm{~kg} / \mathrm{m}^3\) speed of sound, \(v=330 \mathrm{~m} / \mathrm{s}\) and under standard condition, Pressure of gas, \(p=1 \times 10^5 \mathrm{~N} / \mathrm{m}^2\)<br/>If \(\gamma\) be the ratio of \(C_p\) and \(C_V\) of a gas, then the speed of sound in gas is given by<br/>\(\begin{aligned}<br/>&amp; \qquad v=\sqrt{\frac{\gamma P}{\rho}} \text { or } \frac{\gamma P}{\rho}=v^2 \\<br/>&amp; \quad \gamma=\frac{v^2 \rho}{p}=\frac{330 \times 330}{10^5} \times \frac{1400}{1089} \\<br/>&amp; \quad \gamma=1.4 \\<br/>&amp; \text { So, } \quad \gamma=\frac{C_p}{C_V}=1.4<br/>\end{aligned} \quad\left[\begin{array}{l}<br/>\because \gamma=1+\frac{2}{f} \\<br/>\text { Since, for diatomic gas, the volume of }<br/>\end{array}\right] \begin{aligned}<br/>&amp; \gamma \text { is 1.4. } \\<br/>&amp; \text { Hence, the degree of freedom for }<br/>\end{aligned}\)<br/>So, \(\gamma=\frac{C_p}{C_V}=1.4\)<br/>Since, for diatomic gas, the volume of \(\left[\begin{array}{l}<br/>\because \gamma=1+\frac{2}{f} \\<br/>1.4=1+\frac{2}{f} \\<br/>\therefore f=5<br/>\end{array}\right]\)\(\gamma\) is 1.4.<br/>Hence, the degree of freedom for<br/>diatomic gas is equal to 5.</div>


title: under-what-condition-are-the-two-lines-y-m-x-z-n-x-and-y-m-x-z-n-x-orthogonal
slug: under-what-condition-are-the-two-lines-y-m-x-z-n-x-and-y-m-x-z-n-x-orthogonal-11023
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">Under what condition are the two lines<br/>$\mathrm{y}=\frac{\mathrm{m}}{\ell} \mathrm{x}+\alpha, \mathrm{z}=\frac{\mathrm{n}}{\ell} \mathrm{x}+\beta ;$ and $\mathrm{y}=\frac{\mathrm{m}^{\prime}}{\ell^{\prime}} \mathrm{x}+\alpha^{\prime}, \mathrm{z}=\frac{\mathrm{n}^{\prime}}{\ell^{\prime}} \mathrm{x}+\beta^{\prime}$<br/>orthogonal ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad \ell \ell^{\prime}+\mathrm{mm}^{\prime}+\mathrm{nn}^{\prime}=0$</span> </div>

answer:
<div class="solution">Given two lines are: $\mathrm{y}=\frac{\mathrm{mx}}{\ell}+\alpha, \mathrm{z}=\frac{\mathrm{n}}{\ell} \mathrm{x}+\beta$ and<br/>$\mathrm{y}=\frac{\mathrm{m}^{\prime}}{\ell^{\prime}} \mathrm{x}+\alpha^{\prime}, \mathrm{z}=\frac{\mathrm{n}^{\prime}}{\ell^{\prime}} \mathrm{x}+\beta^{\prime}$<br/>These two lines can be represented as<br/>$\frac{\mathrm{y}-\alpha}{\mathrm{m} / \ell}=\frac{\mathrm{x}-0}{1}=\frac{\mathrm{z}-\beta}{\mathrm{n} / \ell}$ and $\frac{\mathrm{y}-\alpha^{\prime}}{\mathrm{m}^{\prime} / \ell^{\prime}}=\frac{\mathrm{x}-0}{1}=\frac{\mathrm{z}-\beta^{\prime}}{\mathrm{n} 1 / \ell^{\prime}}$<br/>They are orthogonal, if $\frac{\mathrm{m}}{\ell} \times \frac{\mathrm{m}^{\prime}}{\ell^{\prime}}+1 \times 1+\frac{\mathrm{n}}{\ell} \times \frac{\mathrm{n}^{\prime}}{\ell^{\prime}}=-1 \Rightarrow \ell \ell^{\prime}+\mathrm{mm}^{\prime}+\mathrm{nn}^{\prime}=0$</div>


title: under-what-condition-do-2-1-2-1-k-represent-direction-cosines-of-a-line
slug: under-what-condition-do-2-1-2-1-k-represent-direction-cosines-of-a-line-98409
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">Under what condition do $\left\langle\frac{1}{\sqrt{2}}, \frac{1}{2}, \mathrm{~K}\right\rangle$ represent direction cosines of a line?</div>

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

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

answer:
<div class="solution">For $\left(\frac{1}{\sqrt{2}}, \frac{1}{2}, \mathrm{k}\right)$ to represent direction cosines<br/>$\left(\frac{1}{\sqrt{2}}\right)^{2}+\left(\frac{1}{2}\right)^{2}+\mathrm{k}^{2}=1$<br/>or, $\frac{1}{2}+\frac{1}{4}+\mathrm{k}^{2}=1$<br/>$\frac{3}{4}+\mathrm{k}^{2}=1 \Rightarrow \mathrm{k}=\pm \frac{1}{2}$</div>


title: under-what-condition-do-the-planes
slug: under-what-condition-do-the-planes-37055
question: <div class="question">Under what condition do the planes</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a+b+c=\mathbf{0}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a=b=c$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$a l+b m+c n=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$l+m+n=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a l+b m+c n=0$</span> </div>

answer:
<div class="solution">The planes $b x-a y=n, c y-b z=l$ and $a z-c x=m$ intersect in a line, if $a l+b m+c n=0$.</div>


title: under-what-condition-does-a-bc-ab-c-hold-where-a-b-c-are-three-matrices
slug: under-what-condition-does-a-bc-ab-c-hold-where-a-b-c-are-three-matrices-14149
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">Under what condition does $\mathrm{A}(\mathrm{BC})=(\mathrm{AB}) \mathrm{C}$ hold, where $\mathrm{A}$, $\mathrm{B}, \mathrm{C}$ are three matrices?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{AB}$ and $\mathrm{BC}$ both must exist</span> </div>

answer:
<div class="solution">$\mathrm{AB}$ and $\mathrm{BC}$ both must exit, to hold the condition $\mathrm{A}(\mathrm{BC})=(\mathrm{AB}) \mathrm{C}$</div>


title: under-what-condition-does-the-equation-x-2-y-2-z-2-2-ux-2-u-y-2-w-z-d-0-represent-a-real-sphere
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
slug:
under-what-condition-does-the-equation-x-2-y-2-z-2-2-ux-2-u-y-2-w-z-d-0-represent-a-real-sphere-60012

question:
<div class="question">Under what condition does the equation $x^{2}+y^{2}+z^{2}+2 u x+2 u y+2 w z+d=0$ represent a real sphere?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$u^{2}+v^{2}+w^{2}&gt;d$</span> </div>

answer:
<div class="solution">Equation $x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z+d=0$<br/>represent a real sphere if $u^{2}+v^{2}+w^{2}&gt;d$</div>


title: under-what-condition-is-e-cell-0-or-r-g-0-1
slug: under-what-condition-is-e-cell-0-or-r-g-0-1-87118
question: <div class="question">Under what condition is E<sub>Cell</sub>= 0 or â<sub>r</sub>G = 0?</div>
tags: ['Chemistry', 'Electrochemistry', 'NEET']
answer: <div class="solution">Correct Option is : (D)<br/>When the cell reaction reaches equilibrium</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">E<sub>Cell</sub>= 0 when the cell is operating at standard conditions   (25Â°C and 1 atm pressure).</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">E<sub>Cell</sub>= 0 when the cell potential is greater than 1 V.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">E<sub>Cell</sub>= 0 when the concentration of reactants is equal to the concentration of products.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">When the cell reaction reaches equilibrium</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">When the cell reaction reaches equilibrium</span> </div>


title: under-what-condition-will-the-angle-between-two-regression-lines-become-zero
slug: under-what-condition-will-the-angle-between-two-regression-lines-become-zero-26086
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">Under what condition will the angle between two regression lines become zero?</div>

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

answer:
<div class="solution">The angle between two regression lines becomes zero if $\mathrm{r}=\pm 1$</div>


title: under-what-conditions-does-sulphur-dioxide-liquefy-at-room-temperature
slug: under-what-conditions-does-sulphur-dioxide-liquefy-at-room-temperature-28547
question: <div class="question">Under what conditions does sulphur dioxide liquefy at room temperature?</div>
tags: ['Chemistry', 'p Block Elements (Group 15, 16, 17 & 18)', 'NEET']
answer: <div class="solution">Under a pressure of two atmospheres</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Under standard atmospheric pressure</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Under a pressure of two atmospheres</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Under reduced pressure</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Under increased pressure</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Under a pressure of two atmospheres</span> </div>


title: under-what-conditions-is-the-tangent-to-a-given-curve-at-a-point-perpendicular-to-x-axis
slug: under-what-conditions-is-the-tangent-to-a-given-curve-at-a-point-perpendicular-to-x-axis-21273
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">Under what conditions is the tangent to a given curve at a point perpendicular to $\mathrm{x}$ -axis ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{d x}{d y}=0$</span> </div>

answer:
<div class="solution">Tangent to a given curve at a point is perpendicular to<br/>$\mathrm{x}$ -axis gives $\frac{\mathrm{dy}}{\mathrm{dx}}=\tan \frac{\pi}{2}$<br/>$\Rightarrow \quad \frac{\mathrm{dx}}{\mathrm{dy}}=\cot \frac{\pi}{2}=0$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2010 (Phase 2)']
answer: <div class="solution">The given equation represents a circle, if $a=b, h=0$.</div>
source_db: MarksBatch2_P3.db
title:
under-which-of-the-following-conditions-does-a-general-second-degree-equation-a-x-2-2-h-x-y-b-y-2-2-gx-2-f-y-c-0-a-0-represents-a-circle

slug:
under-which-of-the-following-conditions-does-a-general-second-degree-equation-a-x-2-2-h-x-y-b-y-2-2-gx-2-f-y-c-0-a-0-represents-a-circle-27972

question:
<div class="question">Under which of the following conditions does a general second degree equation $a x^{2}+2 h x y+b y^{2}+2 g x+2 f y+c=0$ $(a \neq 0)$ represents a circle?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$h=0, a=\mathrm{b}$</span> </div>


tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2007 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1 or 3</span> </div>
source_db: MarksBatch2_P3.db
title:
under-which-of-the-following-conditions-will-the-matrix-a-0-2-8-0-5-p-q-1-p-be-singular-1-q-0-2-p-0-3-p-20-select-the-correct-answer-using-the-code-gi

slug:
under-which-of-the-following-conditions-will-the-matrix-a-0-2-8-0-5-p-q-1-p-be-singular-1-q-0-2-p-0-3-p-20-select-the-correct-answer-using-the-code-gi-22155

question:
<div class="question">Under which of the following condition(s), will the matrix<br/>$\mathrm{A}=\left[\begin{array}{lll}0 &amp; 0 &amp; \mathrm{q} \\ 2 &amp; 5 &amp; 1 \\ 8 &amp; \mathrm{p} &amp; \mathrm{p}\end{array}\right]$ be singular?<br/>$1. \quad \mathrm{q}=0$<br/>$2. \quad \mathrm{p}=0$<br/>$3. \quad\mathrm{p}=20$<br/>Select the correct answer using the code given below:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 and 2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">3 only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1 and 3</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1 or 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">$\mathrm{A}=\left[\begin{array}{lll}0 &amp; 0 &amp; \mathrm{q} \\ 2 &amp; 5 &amp; 1 \\ 8 &amp; \mathrm{p} &amp; \mathrm{p}\end{array}\right]$<br/>Matrix A will be singular, when $|\mathrm{A}|=0,|\mathrm{~A}|$ will be zero when either one row or one column is zero.<br/>(1) For $\mathrm{q}=0$ $\mathrm{A}=\left[\begin{array}{lll}0 &amp; 0 &amp; 0 \\ 2 &amp; 5 &amp; 1 \\ 8 &amp; \mathrm{p} &amp; \mathrm{p}\end{array}\right]$<br/>$\Rightarrow|\mathrm{A}|=0$<br/>$\therefore$ A is singular.<br/>(2) For $\mathrm{p}=0$ $\mathrm{A}=\left[\begin{array}{lll}0 &amp; 0 &amp; \mathrm{q} \\ 2 &amp; 5 &amp; 5 \\ 8 &amp; 0 &amp; 0\end{array}\right]$<br/>$\Rightarrow|\mathrm{A}|=\mathrm{q}\left|\begin{array}{ll}2 &amp; 5 \\ 8 &amp; 0\end{array}\right|=-40 \mathrm{q}$<br/>$\therefore \quad$ A is not singular.<br/>(3) For $\mathrm{p}=20$<br/>$|\mathrm{A}|=\mathrm{q}\left|\begin{array}{cc}2 &amp; 5 \\ 8 &amp; 20\end{array}\right|=40-40=0$<br/>$\therefore \quad$ A is singular. Thus codes (1) or (3) are correct.</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
under-which-one-of-the-following-condition-does-the-system-of-equations-k-x-y-z-k-1-x-k-y-z-k-1-x-y-k-z-k-1-have-no-solution

slug:
under-which-one-of-the-following-condition-does-the-system-of-equations-k-x-y-z-k-1-x-k-y-z-k-1-x-y-k-z-k-1-have-no-solution-16218

question:
<div class="question">Under which one of the following condition does the system of equations <br/>$\begin{array}{l}<br/>k x+y+z=k-1 \\<br/>x+k y+z=k-1 \\<br/>x+y+k z=k-1<br/>\end{array}$<br/>have no solution?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$k=1$ or $k=-2$</span> </div>

answer:
<div class="solution">The given system of equations are $\mathrm{kx}+\mathrm{y}+\mathrm{z}=\mathrm{k}-1$<br/>$x+k y+z=k-1$<br/>$\mathrm{x}+\mathrm{y}+\mathrm{kz}=\mathrm{k}-1$<br/>$A=\left[\begin{array}{lll}k &amp; 1 &amp; 1 \\ 1 &amp; k &amp; 1 \\ 1 &amp; 1 &amp; k\end{array}\right], B=\left[\begin{array}{l}k-1 \\ k-1 \\ k-1\end{array}\right]$ and $\mathrm{x}=\left[\begin{array}{l}x \\ y \\ z\end{array}\right]$<br/>Now, $|A|=\left|\begin{array}{lll}k &amp; 1 &amp; 1 \\ 1 &amp; k &amp; 1 \\ 1 &amp; 1 &amp; k\end{array}\right|$<br/>$=k\left(k^{2}-1\right)-1(k-1)+1(1-k)$<br/>$=k^{3}-k-k+1+1-k$<br/>$=k^{3}-3 k+2$<br/>The given system of equations has no solution, if<br/>$|A|=0$<br/>$\Rightarrow k^{3}-3 k+2=0$<br/>$\Rightarrow(k-1)^{2}(k+2)=0$<br/>$\Rightarrow k=1$ or $k=-2$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
under-which-one-of-the-following-conditions-are-the-lines-x-a-y-b-z-cy-d-and-x-ey-f-z-g-y-h-perpendicular

slug:
under-which-one-of-the-following-conditions-are-the-lines-x-a-y-b-z-cy-d-and-x-ey-f-z-g-y-h-perpendicular-40666

question:
<div class="question">Under which one of the following conditions are the lines $\mathrm{x}$ $=a y+b ; z=c y+d$ and $x=e y+f ; z=g y+h$ perpendicular?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{ae}+\mathrm{cg}+1=0$</span> </div>

answer:
<div class="solution">Given, lines $\mathrm{x}=\mathrm{ay}+\mathrm{b}$ and $\mathrm{z}=\mathrm{cy}+\mathrm{d}$ are perpendicular.<br/>$\Rightarrow \frac{x-b}{a}=\frac{y}{1}=\frac{z-d}{c}$<br/>Also, $\mathrm{x}=\mathrm{e} \mathrm{y}+\mathrm{fand} \mathrm{z}=\mathrm{g} \mathrm{y}+\mathrm{h}$ are perpendicular.<br/>$\Rightarrow \frac{x-f}{e}=\frac{y}{1}=\frac{z-h}{g}$<br/>We know, for $\perp^{r}$ lines $a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}=0$<br/>$\Rightarrow \mathrm{ae}+1+\mathrm{cg}=0$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
under-which-one-of-the-following-conditions-does-the-circle-x-2-y-2-2-gx-2-f-y-c-0-meet-the-x-axis-in-two-points-on-opposite-sides-of-the-origin

slug:
under-which-one-of-the-following-conditions-does-the-circle-x-2-y-2-2-gx-2-f-y-c-0-meet-the-x-axis-in-two-points-on-opposite-sides-of-the-origin-40703

question:
<div class="question">Under which one of the following conditions does the circle $x^{2}+y^{2}+2 g x+2 f y+c=0$ meet the $x$ -axis in two points on opposite sides of the origin?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{c}   &lt; 0$</span> </div>

answer:
<div class="solution">For a circle to meet $x$ -axis in two points on the opposite side of the origin its radius $\mathrm{r}$, should be more than the distance of its centre from the origin. Co-ordinate of centre of the circle $x^{2}+y^{2}+2 g x+2 f y$ $+\mathrm{c}=0$ is $(-\mathrm{g},-\mathrm{f})$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/0N3WpHPwVAIr_m8nFK0CDjPjYA34oe81RjS2SUR0F84.original.fullsize.png"/><br/><br/>In the figure shown, $\mathrm{OQ}=\mathrm{OP}=\mathrm{r}$, and distance of centre $\mathrm{C}$, from origin, $\mathrm{O}$ is CO<br/>$\mathrm{r}&gt;\sqrt{\mathrm{OC}}$ i.e. $\mathrm{r}&gt;\sqrt{(-\mathrm{g})^{2}+(-\mathrm{f})^{2}}$<br/>or, $\sqrt{(-\mathrm{g})^{2}+(-\mathrm{f})^{2}-\mathrm{c}}&gt;\sqrt{(-\mathrm{g})^{2}+(-\mathrm{f})^{2}}$<br/>or, $\mathrm{g}^{2}+\mathrm{f}^{2}-\mathrm{c}&gt;\mathrm{g}^{2}+\mathrm{f}^{2}$<br/>or, $-\mathrm{c}&gt;0$<br/>or, $\mathrm{c} &lt; 0$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
under-which-one-of-the-following-conditions-does-the-solution-of-d-x-d-y-cy-d-a-x-b-represent-a-parabola

slug:
under-which-one-of-the-following-conditions-does-the-solution-of-d-x-d-y-cy-d-a-x-b-represent-a-parabola-11040

question:
<div class="question">Under which one of the following conditions does the<br/>solution of $\frac{d y}{d x}=\frac{a x+b}{c y+d}$ represent a parabola?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{a}=0, \mathrm{c} \neq 0, \mathrm{~b} \neq 0$</span> </div>

answer:
<div class="solution">Given: $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{ax}+\mathrm{b}}{\mathrm{cy}+\mathrm{d}}$<br/>or, $\quad(\mathrm{cy}+\mathrm{d}) \mathrm{d} \mathrm{y}=(\mathrm{ax}+\mathrm{b}) \mathrm{d} \mathrm{x}$<br/>Integrating both the sides.<br/>c. $\int \mathrm{ydy}+\mathrm{d} \int \mathrm{dy}=\mathrm{a} \int \mathrm{x} \mathrm{d} \mathrm{x}+\mathrm{b} \int \mathrm{dx}+\mathrm{K}$<br/>$[\mathrm{K}$ is constant<br/>integration]<br/>or, c. $\frac{y^{2}}{2}+d \cdot y=a \frac{x^{2}}{2}+b \cdot x+K$<br/>or, $\mathrm{cy}^{2}+2 \mathrm{~d} . \mathrm{y}=\mathrm{ax}^{2}+2 \mathrm{~b} \cdot \mathrm{x}+2 \mathrm{~K}$<br/>This equation will represent a parabola when either, the coefficient of $\mathrm{x}^{2}$ or the coefficient of $\mathrm{y}^{2}$ is zero, but not both. Thus either $\mathrm{c}=0$ or $\mathrm{a}=0$ but not both. From the choice given, $\mathrm{a}=0, \mathrm{c} \neq 0$ and $\mathrm{b} \neq 0$</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
under-which-one-of-the-following-conditions-will-the-two-planes-x-y-z-7-and-x-y-z-3-be-parallel-but-not-coincident

slug:
under-which-one-of-the-following-conditions-will-the-two-planes-x-y-z-7-and-x-y-z-3-be-parallel-but-not-coincident-63219

question:
<div class="question">Under which one of the following conditions will the two planes $x+y+z=7$ and $\alpha x+\beta y+\gamma z=3$, be parallel (but not coincident)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\alpha=\beta=\gamma=1$ only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\alpha=\beta=\gamma=\frac{3}{7}$ only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\alpha=\beta=\gamma$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\alpha=\beta=\gamma$</span> </div>

answer:
<div class="solution">Given equation of planes are $x+y+z=7$<br/>and $\alpha x+\beta y+\gamma z=3$<br/>For these planes to be parallel, coefficients of $\mathrm{x}, \mathrm{y}$ and $z$ should be same i.e. $\Rightarrow \alpha=\beta=\gamma$</div>


title: unification-of-weak-and-electromagnetic-interactions-was-done-by
slug: unification-of-weak-and-electromagnetic-interactions-was-done-by-96007
question: <div class="question">Unification of weak and electromagnetic interactions was done by</div>
tags: ['Physics', 'Units and Dimensions', 'AP EAMCET', 'AP EAMCET 2021 (23 Aug Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Salam</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Einstein</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Raman</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Salam</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Hubble</span> </li> </ul>

answer:
<div class="solution">As we know that, electromagnetic and weak nuclear forces are fundamental forces, which can be understood as a single interaction, this conclusion was given by three physicists Glashow, Weinberg and Salam.</div>


title: universal-set-u-x-x-5-6-x-4-11-x-3-6-x-2-0-a-x-x-2-5-x-6-0-b-x-x-2-3-x-2-0-what-is-a-b-equal-to
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P3.db
slug:
universal-set-u-x-x-5-6-x-4-11-x-3-6-x-2-0-a-x-x-2-5-x-6-0-b-x-x-2-3-x-2-0-what-is-a-b-equal-to-84365

question:
<div class="question">Universal set, $\mathrm{U}=\left\{\mathrm{x} \mid \mathrm{x}^{5}-6 \mathrm{x}^{4}+11 \mathrm{x}^{3}-6 \mathrm{x}^{2}=0\right\}$<br/>$A=\left\{x \mid x^{2}-5 x+6=0\right\}$<br/>$B=\left\{x \mid x^{2}-3 x+2=0\right\}$<br/>What is $(A \cap B)$ equal to ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\{0,1,3\}$</span> </div>

answer:
<div class="solution">$U=\left\{x: x^{5}-6 x^{4}+11 x^{3}-6 x^{2}=0\right\}$<br/>Solving for values of $\mathrm{x}$, we get $=\{0,1,2,3\}$<br/>$\mathrm{A}=\left\{\mathrm{x}: \mathrm{x}^{2}-5 \mathrm{x}+6=0\right\}$<br/>Solving for values of $\mathrm{x}$, we get $=\{2,3\}$<br/>and $B=\left\{x: x^{2}-3 x+2=0\right\}$<br/>Solving for values of $\mathrm{x}$, we get $=\{2,1\}$<br/>$\mathrm{A} \cap \mathrm{B}=\{2\}$<br/>$(A \cap B)^{\prime}=U-(A \cap B)$<br/>$=\{0,1,2,3\}-\{2\}=\{0,1,3\}$</div>


tags: ['Physics', 'Wave Optics', 'JEE Main', 'JEE Main 2023 (29 Jan Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch2_P3.db
title:
unpolarised-light-is-incident-on-the-boundary-between-two-dielectric-media-whose-dielectric-constants-are-2-8-medium-1-and-6-8-medium-2-respectively-t

slug:
unpolarised-light-is-incident-on-the-boundary-between-two-dielectric-media-whose-dielectric-constants-are-2-8-medium-1-and-6-8-medium-2-respectively-t-77302

question:
<div class="question"><p>Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>.</mo><mn>8</mn></math> (medium –<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>) and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>8</mn></math> (medium – <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>10</mn><mi>θ</mi></mfrac></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math>, the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi></math> is ______.</p><p>(Given for dielectric media, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mi>r</mi></msub><mo>=</mo><mn>1</mn></math>)</p></div>

answer:
<div class="solution"><p>As given in the question, we can write</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mn>1</mn></msub><mo>=</mo><msqrt><msub><mi>ε</mi><mi>r</mi></msub><msub><mi>μ</mi><mi>r</mi></msub></msqrt><mo>=</mo><msqrt><mn>2</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>2</mn><mo>.</mo><mn>8</mn></msqrt></math> and</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mn>2</mn></msub><mo>=</mo><msqrt><msub><mi>ε</mi><mi>r</mi></msub><msub><mi>μ</mi><mi>r</mi></msub></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>.</mo><mn>8</mn><mo>×</mo><mn>1</mn></msqrt><mo>=</mo><msqrt><mn>6</mn><mo>.</mo><mn>8</mn></msqrt></math></p><p>Now applying Snell's law and considering <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mn>90</mn><mo>°</mo><mo>-</mo><mi>i</mi></math>, we get</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>μ</mi><mn>1</mn></msub><mo> </mo><mi>sin</mi><mo> </mo><mi>i</mi><mo>=</mo><msub><mi>μ</mi><mn>2</mn></msub><mo> </mo><mi>cos</mi><mo> </mo><mi>i</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>tan</mi><mo> </mo><mi>i</mi><mo>=</mo><mfrac><msub><mi>μ</mi><mn>2</mn></msub><msub><mi>μ</mi><mn>1</mn></msub></mfrac><mo>=</mo><msqrt><mfrac><mrow><mn>6</mn><mo>.</mo><mn>8</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>8</mn></mrow></mfrac></msqrt></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>tan</mi><mo> </mo><mi>i</mi><mo>=</mo><msup><mfenced><mfrac><mrow><mn>2</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>4</mn></mrow><mrow><mn>2</mn><mo>.</mo><mn>8</mn></mrow></mfrac></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>i</mi><mo>=</mo><msup><mi>tan</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mfenced><mrow><mn>1</mn><mo>+</mo><mfrac><mn>10</mn><mn>7</mn></mfrac></mrow></mfenced><mfrac><mn>1</mn><mn>2</mn></mfrac></msup></math></p><p>Therefore, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>7</mn></math>.</p></div>


tags: ['Chemistry', 'Some Basic Concepts of Chemistry']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
use-the-data-given-in-the-following-table-to-calculate-the-molar-mass-of-naturally-occuring-argon-isotopes-beginarrayllltext-isotope-text-isotopic-mol

slug:
use-the-data-given-in-the-following-table-to-calculate-the-molar-mass-of-naturally-occuring-argon-isotopes-beginarrayllltext-isotope-text-isotopic-mol-42807

question:
<div class="question">Use the data given in the following table to calculate the molar mass of naturally occuring argon isotopes:<br/>\(\begin{array}{lll}\text { Isotope } &amp; \text { Isotopic molar mass } &amp; \text { Abundance } \\ { }^{36} \mathrm{Ar} &amp; 35.96755 \mathrm{~g} \mathrm{~mol}^{-1} &amp; 0.337 \% \\ { }^{38} \mathrm{Ar} &amp; 37.96272 \mathrm{~g} \mathrm{~mol}^{-1} &amp; 0.063 \% \\ { }^{40} \mathrm{Ar} &amp; 39.9624 \mathrm{~g} \mathrm{~mol}^{-1} &amp; 99.600 \%\end{array}\)</div>

answer:
<div class="solution">Molar mass of Ar<br/>\(\begin{aligned}<br/>&amp;=35.96755 \times 0.00337+37.96272 \times 0.00063+39.96924 \\<br/>&amp;\times 0.99600 \\<br/>&amp;=39.948 \mathrm{~g} \mathrm{~mol}^{-1}<br/>\end{aligned}\)</div>


tags: ['Physics', 'Units and Dimensions', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
using-dimensional-analysis-the-resistivity-in-terms-of-fundamental-constants-h-m-e-c-e-0-can-be-expressed-as-1

slug:
using-dimensional-analysis-the-resistivity-in-terms-of-fundamental-constants-h-m-e-c-e-0-can-be-expressed-as-1-48115

question:
<div class="question">Using dimensional analysis the resistivity in terms of fundamental constants $\mathrm{h}, \mathrm{m}_{\mathrm{e}}, \mathrm{c}, \mathrm{e}, \varepsilon_{0}$ can be expressed as</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{h}^{2}}{\mathrm{~m}_{\mathrm{e}} \mathrm{ce}^{2}}$</span> </div>

answer:
<div class="solution">$\rho=\frac{E}{J}$<br/>$E=\left[M L T^{-3} I^{-1}\right]$<br/>$\mathrm{J}=\left[\mathrm{I} \mathrm{L}^{-2}\right]$<br/>$\mathrm{h}=\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-1}$<br/>$\mathrm{~m}_{\mathrm{e}}=\mathrm{M}$<br/>$\mathrm{c}=\mathrm{LT}^{-1}$<br/>$\varepsilon_{0}=\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{I}^{2}$<br/>$\therefore \rho=\frac{\mathrm{h}^{2}}{\mathrm{~m}_{\mathrm{e}} \mathrm{ce}^{2}}$</div>


tags: ['Physics', 'Units and Dimensions', 'KVPY', 'KVPY 2017 (5 Nov SB/SX)']
source_db: MarksBatch2_P3.db
title:
using-dimensional-analysis-the-resistivity-in-terms-of-fundamental-constants-h-m-e-c-e-0-can-be-expressed-as

slug:
using-dimensional-analysis-the-resistivity-in-terms-of-fundamental-constants-h-m-e-c-e-0-can-be-expressed-as-27288

question:
<div class="question">Using dimensional analysis the resistivity in terms of fundamental constants $\mathrm{h}, \mathrm{m}_{\mathrm{e}}, \mathrm{c}, \mathrm{e}, \varepsilon_{0}$ can be expressed as</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\mathrm{h}^{2}}{\mathrm{~m}_{\mathrm{e}} \mathrm{ce}^{2}}$</span> </div>

answer:
<div class="solution">$\rho=\frac{E}{J}$<br/>$E=\left[M L T^{-3} I^{-1}\right]$<br/>$\mathrm{J}=\left[\mathrm{I} \mathrm{L}^{-2}\right]$<br/>$\mathrm{h}=\mathrm{M} \mathrm{L}^{2} \mathrm{~T}^{-1}$<br/>$\mathrm{~m}_{\mathrm{e}}=\mathrm{M}$<br/>$\mathrm{c}=\mathrm{LT}^{-1}$<br/>$\varepsilon_{0}=\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^{4} \mathrm{I}^{2}$<br/>$\therefore \rho=\frac{\mathrm{h}^{2}}{\mathrm{~m}_{\mathrm{e}} \mathrm{ce}^{2}}$</div>


tags: ['Physics', 'Units and Dimensions', 'AIIMS', 'AIIMS 2003']
source_db: MarksBatch2_P3.db
title:
using-mass-m-length-l-time-t-and-current-a-as-fundamental-quantities-the-dimension-of-permeability-is

slug:
using-mass-m-length-l-time-t-and-current-a-as-fundamental-quantities-the-dimension-of-permeability-is-13632

question:
<div class="question">Using mass $(M)$, length $(L)$, time $(T)$ and current $(A)$ as fundamental quantities, the dimension of permeability is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{MLT}^{-2} \mathrm{~A}^{-2}$</span> </div>

answer:
<div class="solution">We know that the force per unit length of a wire carrying current due to another parallel wire carrying current is given by<br/>$$<br/>\begin{gathered}<br/>\frac{d F}{d l}=\frac{\mu_0 i_1 i_2}{2 \pi d} \Rightarrow \mu_0=\frac{2 \pi d}{i_1 i_2} \frac{d F}{d l} \\<br/>\therefore \quad\left[\mu_0\right]=\frac{[\mathrm{L}]}{\left[\mathrm{A}^2\right]} \cdot \frac{\left[\mathrm{MLT}^{-2}\right]}{[\mathrm{L}]} \\<br/>\text { or }\left[\mu_0\right]=\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{A}^{-2}\right]=\left[\mathrm{MLT}^{-2} \mathrm{~A}^{-2}\right] .<br/>\end{gathered}<br/>$$</div>


tags: ['Physics', 'Units and Dimensions', 'AIIMS', 'AIIMS 2004']
source_db: MarksBatch2_P3.db
title:
using-mass-m-length-l-time-t-and-current-a-as-fundamental-quantities-the-dimension-of-permittivity-is

slug:
using-mass-m-length-l-time-t-and-current-a-as-fundamental-quantities-the-dimension-of-permittivity-is-27754

question:
<div class="question">Using mass $(M)$, length $(L)$, time $(T)$ and current $(A)$ as fundamental quantities, the dimension of permittivity is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\mathrm{ML}^{-2} \mathrm{~T}^2 \mathrm{~A}\right]$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right]$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left[\mathrm{MLT}^{-2} \mathrm{~A}\right]$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~A}^2\right]$.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right]$</span> </div>

answer:
<div class="solution">Force of attraction between two charges is given by<br/>$$<br/>\begin{aligned}<br/>F &amp; =\frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_2}{r^2} \\<br/>\Rightarrow \quad \varepsilon_0 &amp; =\frac{1}{4 \pi} \frac{1}{F} \frac{q_1 q_2}{r^2}=\frac{\mathrm{A}^2 \mathrm{~T}^2}{\mathrm{MLT}^{-2} \mathrm{~L}^2} \\<br/>&amp; =\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right] .<br/>\end{aligned}<br/>$$<br/>(where $4 \pi$ is dimensionless)<br/>$=\left[\mathrm{M}^{-1} \mathrm{~L}^{-3} \mathrm{~T}^4 \mathrm{~A}^2\right]$</div>


tags: ['Chemistry', 'Structure of Atom']
options: None
correct_option: None
answer: <div class="solution">(a) \(1 s\) (b) \(3 p\) (c) \(4 d\) (d) \(4 f\).</div>
source_db: MarksBatch2_P3.db
title:
using-s-p-d-notations-describe-the-orbital-with-the-following-quantum-numbers-beginarraylltext-a-n1-l0-text-b-n3-l1endarray

slug:
using-s-p-d-notations-describe-the-orbital-with-the-following-quantum-numbers-beginarraylltext-a-n1-l0-text-b-n3-l1endarray-13906

question:
<div class="question">Using \(s, p, d\) notations, describe the orbital with the following quantum numbers:<br/>\(\begin{array}{ll}\text { (a) } n=1, l=0 &amp; \text { (b) } n=3, l=1\end{array}\)</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">48</span> </div>
source_db: MarksBatch2_P3.db
title:
using-the-digits-1-2-3-4-and-5-only-once-how-many-numbers-beginarraylltext-greater-than-41000-can-be-formed

slug:
using-the-digits-1-2-3-4-and-5-only-once-how-many-numbers-beginarraylltext-greater-than-41000-can-be-formed-50362

question:
<div class="question">Using the digits $1,2,3,4$ and 5 only once, how many numbers $\begin{array}{ll}\text { greater than } 41000 can be formed?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">41</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">48</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">50</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">55</span> </li> </ul>

answer:
<div class="solution">We have to construct 5 digit numbers which are greater than 41000 . So, we have only 2 ways to choose $5^{\text {th }}$ digit.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/HPR5Pk5ZZZCiyM2QO2p1ZXkbsigivQXL9LJLQhg1aUc.original.fullsize.png"/><br/><br/>$\left[\because\right.$ Only 4 or 5 can come at $5^{\text {th }}$ place $]$ Thus, for $4^{\text {th }}$ place we have 4 ways to choose digits. For $3^{\text {rd }}$ place we have 3 ways. For $2^{\text {nd }}$ place we have 2 ways. and for unit place we have only 1 way. Required number of ways $=2 \times 4 \times 3 \times 2 \times 1=48$</div>


tags: ['Chemistry', 'Electrochemistry', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potential-find-out-the-pair-between-which-redox-reaction-is-not-feasible-e-values-fe-3-fe-2-077-i-2-i-054-cu-2-cu-034-ag-

slug:
using-the-standard-electrode-potential-find-out-the-pair-between-which-redox-reaction-is-not-feasible-e-values-fe-3-fe-2-077-i-2-i-054-cu-2-cu-034-ag-26545

question:
<div class="question">Using the standard electrode potential, find out the pair between which redox reaction is not feasible.
<br/>$E^{\ominus}$ values $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}=+0.77 ; \mathrm{I}_2 / \mathrm{I}^{-}=+054$
<br/>$\mathrm{Cu}^{2+} / \mathrm{Cu}=+0.34 ; \mathrm{Ag}^{+} / \mathrm{Ag}=0.80 \mathrm{~V}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$\mathrm{Fe}^{3+}$ and $\mathrm{I}^{-}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$\mathrm{Ag}^{+}$and $\mathrm{Cu}$
<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"> <br/>$\mathrm{Fe}^{3+}$ and $\mathrm{Cu}$
<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"> <br/>Ag and $\mathrm{Fe}^{3+}$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>Ag and $\mathrm{Fe}^{3+}$</span> </div>

answer:
<div class="solution">(a)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/ok9PLwHyacfw60Pt-I1fhACQVQEJN7EEy9JanOILEpI.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(b)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/nxJ1g2C_J4IFowzBWqJ3kIIwXxWO4-mowicPksj5AwY.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(c)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/uYAzWqaCsCn9jugCPjGq85iTRaQXj2wyeTS2MRGdGo0.original.fullsize.png"/><br/> <br/>This reaction is feasible, since $E_{\text {cell }}^{\circ}$ is positive.
<br/>(d)<img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/rKlHBm3z2AO5UoILkXmMsxRAlIDwTgutH1XzMA8lvbQ.original.fullsize.png"/><br/> <br/>This reaction is not feasible, since $E_{\text {cell }}^{\circ}$ is negative.</div>


tags: ['Chemistry', 'Electrochemistry', 'AP EAMCET', 'AP EAMCET 2018 (22 Apr Shift 2)']
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potentials-given-below-identify-the-correct-statements-from-the-following-fe-2-2-e-fe-e-cu-2-2-e-cu-e-ag-e-ag-e-044-v-034

slug:
using-the-standard-electrode-potentials-given-below-identify-the-correct-statements-from-the-following-fe-2-2-e-fe-e-cu-2-2-e-cu-e-ag-e-ag-e-044-v-034-46611

question:
<div class="question">Using the standard electrode potentials given below identify the correct statements from the following.<br/>$$<br/>\begin{aligned}<br/>\mathrm{Fe}^{2+}+2 e^{-} \longrightarrow \mathrm{Fe} ; E^{\circ} &amp; =-0.44 \mathrm{~V} \\<br/>\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu} ; E^{\circ} &amp; =+0.34 \mathrm{~V} \\<br/>\mathrm{Ag}^{+}+e^{-} \longrightarrow \mathrm{Ag} ; E^{\circ} &amp; =+0.80 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>(i) Copper can displace iron from $\mathrm{FeSO}_4$ solution.<br/>(ii) Iron can displace copper from $\mathrm{CuSO}_4$ solution.<br/>(iii) Silver can displace copper from $\mathrm{CuSO}_4$ solution.<br/>(iv) Iron can displace silver from $\mathrm{AgNO}_3$ solution.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(ii), (iv)</span> </div>

answer:
<div class="solution">$$<br/>\begin{gathered}<br/>\mathrm{Fe}^{2+}+2 e^{-} \longrightarrow \mathrm{Fe} ; E^{\circ}=-0.44 \\<br/>\mathrm{Cu}^{2+}+2 e^{-} \longrightarrow \mathrm{Cu} ; E^{\circ}=+0.34 \\<br/>\mathrm{Ag}+1 e^{-} \longrightarrow \mathrm{Ag} ; E^{\circ}=+0.80<br/>\end{gathered}<br/>$$<br/>If a metal have negative electrode potential than metal easily displace, other metal, i.e. Fe can displace $\mathrm{Cu}$ and $\mathrm{Ag}$.</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potentials-given-below-predict-if-the-reaction-between-the-following-is-feasible-beginarrayl-mathrmemathrmcumathrmredcirc

slug:
using-the-standard-electrode-potentials-given-below-predict-if-the-reaction-between-the-following-is-feasible-beginarrayl-mathrmemathrmcumathrmredcirc-81046

question:
<div class="question">Using the standard electrode potentials given below, predict if the reaction between the following is feasible.<br/>\[<br/>\begin{array}{l}<br/>\mathrm{E}_{\mathrm{Cu}(\mathrm{red})}^{\circ}=0.34 \mathrm{~V} \\<br/>\mathrm{E}_{\mathrm{Ag}(\mathrm{red})}^{\circ}=0.80 \mathrm{~V}<br/>\end{array}<br/>\]<br/>\( \mathrm{Ag}^{+}(\mathrm{aq}), \mathrm{Cu}(\mathrm{s}) \) Report the value of \( \mathrm{E}_{\text {cell }}^{\mathrm{o}} \)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\( +0.46 \mathrm{~V} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( +0.56 \mathrm{~V} \)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( +0.66 \mathrm{~V} \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( +0.76 \mathrm{~V} \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( +0.46 \mathrm{~V} \)</span> </div>

answer:
<div class="solution"><p>The electrode with less SRP will become anode.</p><p>Oxidation half reaction;<br/> <math> <mrow> <mtext>Cu  </mtext><mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mo>⟶</mo> <msup> <mtext>Cu</mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>+</mo> <mn>2</mn> <msup> <mtext>e</mtext> <mo>-</mo> </msup> <mtext> ;</mtext> </mrow> </math>     <math> <mrow> <msup> <mtext>E</mtext> <mtext>o</mtext> </msup> <mo>=</mo> <mo>-</mo> <mn>0</mn> <mtext>.</mtext> <mn>3</mn> <mn>4</mn> <mtext> V</mtext> </mrow> </math><br/>Reduction half reaction;<br/> <math> <mrow> <mn>2</mn> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>+</mo> <mn>2</mn> <msup> <mtext>e</mtext> <mo>-</mo> </msup> <mo>⟶</mo> <mn>2</mn> <mtext>Ag</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mtext> ;</mtext> </mrow> </math>     <math> <mrow> <msup> <mtext>E</mtext> <mtext>o</mtext> </msup> <mo>=</mo> <mo>+</mo> <mn>0</mn> <mtext>.</mtext> <mn>8</mn> <mn>0</mn> <mtext> V</mtext> </mrow> </math><br/>Overall reaction,<br/><math> <mrow> <mtext>Cu</mtext> <mfenced close=")" open="(" separators=","> <mrow> <mtext>s</mtext> </mrow> </mfenced> <mo>+</mo> <mn>2</mn> <msup> <mtext>Ag</mtext> <mo>+</mo> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>⟶</mo> <msup> <mtext>Cu </mtext> <mrow> <mn>2</mn> <mo>+</mo> </mrow> </msup> <mfenced close=")" open="(" separators=","> <mrow> <mtext>aq</mtext> </mrow> </mfenced> <mo>+</mo> <mn>2</mn> <mtext>Ag</mtext> <mtext> ;</mtext> </mrow> </math>      <math> <mrow> <msup> <mtext>E</mtext> <mtext>o</mtext> </msup> <mo>=</mo> <mo>+</mo> <mn>0</mn> <mtext>.</mtext> <mn>4</mn> <mn>6</mn> <mtext> V</mtext> </mrow> </math><br/>Positive emf indicates that the reaction is feasible.</p></div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>Fe<sup>2+</sup>(aq) + I<sub>2</sub>(s)</div>
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potentials-given-in-table-31-predict-if-the-reaction-between-the-following-is-feasible-fe-3-aq-i-aq

slug:
using-the-standard-electrode-potentials-given-in-table-31-predict-if-the-reaction-between-the-following-is-feasible-fe-3-aq-i-aq-19558

question:
<div class="question">Using the standard electrode potentials given in Table 3.1, predict if the   reaction between the following is feasible   Fe<sup>3+</sup>(aq) + I<sup>-</sup>(aq) â <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/wkrOBZQio98VzJKgAcYy2sQiNZVO2KZ3JLlTqK0ZDxvZlVgrNk..png"/><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Fe<sup>2+</sup>(aq) + I<sub>2</sub>(s)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">No Reaction</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Fe(s) + I<sup>3-</sup>(aq)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">FeI<sub>3</sub>(s)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Fe<sup>2+</sup>(aq) + I<sub>2</sub>(s)</span> </div>


tags: ['Chemistry', 'Redox Reactions']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potentials-given-in-table-81-ncert-predict-if-the-reaction-between-the-following-is-feasible-a-mathbff-e3mathrmaq-and-mat

slug:
using-the-standard-electrode-potentials-given-in-table-81-ncert-predict-if-the-reaction-between-the-following-is-feasible-a-mathbff-e3mathrmaq-and-mat-38563

question:
<div class="question">Using the standard electrode potentials given in table \(8.1\) (NCERT), predict if the reaction between the following is feasible:<br/>(a) \(\mathbf{F e}^{3+}(\mathrm{aq})\) and \(\mathrm{I}^{-}(\mathrm{aq})\)<br/>(b) \(\mathbf{A g}^{+}(a q)\) and \(\mathrm{Cu}(\mathrm{s})\)<br/>(c) \(\mathrm{Fe}^{3+}(\mathrm{aq})\) and \(\mathrm{Cu}(\mathrm{s})\)<br/>(d) \(\mathrm{Ag}(\mathrm{s})\) and \(\mathrm{Fe}^{3+}(\mathrm{aq})\)<br/>(e) \(\mathrm{Br}_2(\mathrm{aq})\) and \(\mathrm{Fe}^{2+}(\mathrm{aq})\)</div>

answer:
<div class="solution">A reaction is feasible if E.M.F. of the cell is \(+\) ve.<br/>(a) \(\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^0=+0.77 \mathrm{~V}\) \(\mathrm{E}_{\mathrm{I}_2 / 2 \mathrm{I}^{-}}^{\mathrm{o}}=+0.54 \mathrm{~V}\). Since we have to determine a reaction between \(\mathrm{Fe}^{3+}\) and \(\mathrm{I}^{-}\), the reaction should be \(\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}\) at cathode<br/>\(2 \mathrm{I}^{-} \longrightarrow \mathrm{I}_2+2 \mathrm{e}^{-}\)at anode We know that \(\mathrm{EMF}=\mathrm{E}_{\text {cathode }}^0-\mathrm{E}_{\text {anode }}^0=0.77-0.54\) \(=0.23 \mathrm{~V}\) as it is positive the reaction is feasible and the following reaction would occur.<br/>\(2 \mathrm{Fe}^{3+}+2 \mathrm{I}^{-} \longrightarrow 2 \mathrm{Fe}^{2+}+\mathrm{I}_2\)<br/>(b) \(\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^0=+0.80 \mathrm{~V}\);<br/>\(\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\circ}=+0.34 \mathrm{~V}\). Since we have to determine a reaction between \(\mathrm{Ag}^{+}\)and \(\mathrm{Cu}\), the reaction should be \(\mathrm{Ag}^{+}+\mathrm{e}^{-} \longrightarrow \mathrm{Ag}\) at cathode<br/>\(\mathrm{Cu} \longrightarrow \mathrm{Cu}^{2+}+2 \mathrm{e}^{-}\)at anode.<br/>We know that \(\mathrm{EMF}=\mathrm{E}_{\text {cathode }}^0-\mathrm{E}_{\text {anode }}^0=0.80-0.34\) \(=0.46 \mathrm{~V}\) as it is positive the reaction is feasible and the following reaction would occur.<br/>\(2 \mathrm{Ag}^{+}+\mathrm{Cu} \longrightarrow 2 \mathrm{Ag}+\mathrm{Cu}^{2+}\)<br/>(c) \(\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^{\mathrm{O}}=+0.77 \mathrm{~V}\) \(\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^0=+0.34 \mathrm{~V}\). Since, we have to determine \(\mathrm{a}\) reaction between \(\mathrm{Fe}^{3+}\) and \(\mathrm{Cu}\), the reaction should be \(\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}\) at cathode<br/>\(\mathrm{Cu} \longrightarrow \mathrm{Cu}^{2+}+2 \mathrm{e}^{-}\)at anode . We know that \(\mathrm{EMF}=\mathrm{E}_{\text {cathode }}^0-\mathrm{E}_{\text {anode }}^{\circ}=0.77-0.34\) \(=0.43 \mathrm{~V}\) as it is positive the reaction is feasible and the following reaction would occur.<br/>\(2 \mathrm{Fe}^{3+}+\mathrm{Cu} \longrightarrow 2 \mathrm{Fe}^{2+}+\mathrm{Cu}^{2+}\)<br/>(d) \(\mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^{\mathrm{O}}=+0.77 \mathrm{~V}\)<br/>\(\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^0=+0.80 \mathrm{~V}\). Since we have to determine a reaction between \(\mathrm{Fe}^{3+}\) and \(\mathrm{Ag}\), the reaction should be \(\mathrm{Fe}^{3+}+\mathrm{e}^{-} \longrightarrow \mathrm{Fe}^{2+}\) at cathode<br/>\(\mathrm{Ag} \longrightarrow \mathrm{Ag}^{+}+\mathrm{e}^{-}\)at anode<br/>We know that EMF \(=\mathrm{E}_{\text {cathode }}^0-\mathrm{E}_{\text {anode }}\) a \(=0.77-0.80=-0.03 \mathrm{~V}\) as it is negative the reaction is not feasible.<br/>(e) \(\quad \mathrm{E}_{\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}}^0=+0.77 \mathrm{~V}\)<br/>\(\mathrm{E}_{\mathrm{Br}_2 / 2 \mathrm{Br}^{-}}^{\mathrm{o}}=+1.09 \mathrm{~V}\). Since, we have to determine a reaction between \(\mathrm{Fe}^{2+}\) and \(\mathrm{Br}_2\), the reaction should be \(\mathrm{Fe}^{2+} \longrightarrow \mathrm{Fe}^{3+}+\mathrm{e}^{-}\)at anode<br/>\(\mathrm{Br}_2+2 \mathrm{e}^{-} \longrightarrow 2 \mathrm{Br}^{-}\)at cathode .<br/>We know that EMF \(=\mathrm{E}_{\text {cathode }}^0-\mathrm{E}_{\text {anode }}^0\) \(=1.09-0.77=0.32 \mathrm{~V}\) as it is positive the reaction is feasible and the following reaction would occur.<br/>\(2 \mathrm{Fe}^{2+}+\mathrm{Br}_2 \longrightarrow 2 \mathrm{Fe}^{3+}+2 \mathrm{Br}^{-}\)</div>


tags: ['Chemistry', 'Redox Reactions', 'NEET']
answer: <div class="solution">Correct Option is : (C)<br/>The reaction is feasible</div>
source_db: MarksBatch2_P3.db
title:
using-the-standard-electrode-potentials-given-in-the-table-81-predict-if-the-reaction-between-the-following-is-feasible-using-the-standard-electrode-p

slug:
using-the-standard-electrode-potentials-given-in-the-table-81-predict-if-the-reaction-between-the-following-is-feasible-using-the-standard-electrode-p-95285

question:
<div class="question">Using the standard electrode potentials given in the Table 8.1, predict if the   reaction between the following is feasible: <br/><img src="https://cdn-question-pool.getmarks.app/modules/ncoq/cheas77dtry/SKP19Iw7Rbr4XmC67Cshw2QUPGIKzVKjwIn58nGP1mYdS5Rwcm..png"/><br/>  Using the standard electrode potentials given in the Table 8.1, predict if the reaction between the following is feasible:   FeÂ³âº(aq) and Iâ»(aq)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">FeÂ³âº will reduce Iâ»</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Iâ» will reduce FeÂ³âº</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">The reaction is  feasible</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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 will not react</span> </li> </ul>

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


tags: ['Chemistry', 's Block Elements', 'AP EAMCET', 'AP EAMCET 2017 (25 Apr Shift 1)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P3.db
title:
using-the-standard-reduction-potentials-of-the-electrodes-li-zn-mg-ni-as-305-076-236-025-v-respectively-identify-the-correct-statement

slug:
using-the-standard-reduction-potentials-of-the-electrodes-li-zn-mg-ni-as-305-076-236-025-v-respectively-identify-the-correct-statement-27491

question:
<div class="question">Using the standard reduction potentials of the electrodes $\mathrm{Li}, \mathrm{Zn}, \mathrm{Mg}, \mathrm{Ni}$ as $-3.05,-0.76$, $-2.36,-0.25 \mathrm{~V}$ respectively, identify the correct statement.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{Mg}$, displaces $\mathrm{Zn}$ from its 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">$\mathrm{Ni}$, reduces $\mathrm{Zn}^{2+}$ to $\mathrm{Zn}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Mg}$, reduces $\mathrm{Li}^{+}$to $\mathrm{Li}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Zn}$, reduces $\mathrm{Mg}^{2+}$ to $\mathrm{Mg}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{Mg}$, displaces $\mathrm{Zn}$ from its solution.</span> </div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
value-of-standard-electrode-potential-for-the-oxidation-of-cl-ions-is-more-positive-than-that-of-water-even-then-in-the-electrolysis-of-aqueous-sodium-1

slug:
value-of-standard-electrode-potential-for-the-oxidation-of-cl-ions-is-more-positive-than-that-of-water-even-then-in-the-electrolysis-of-aqueous-sodium-1-66579

question:
<div class="question">Value of standard electrode potential for the oxidation of Cl<sup>â</sup>ions is more positive than that of water, even then in the electrolysis of aqueous sodium chloride, why is Cl<sup>â</sup>oxidized at anode instead of water?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Under the conditions of electrolysis of aqueous sodium chloride, oxidation of water at anode requires overpotential hence Cl<sup>â</sup>is oxidized instead of water</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>Under the conditions of electrolysis of aqueous sodium chloride, oxidation of water at anode requires overpotential hence Cl<sup>â</sup>is oxidized instead of water</div>


tags: ['Chemistry', 'Electrochemistry']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
value-of-standard-electrode-potential-for-the-oxidation-of-cl-ions-is-more-positive-than-that-of-water-even-then-in-the-electrolysis-of-aqueous-sodium

slug:
value-of-standard-electrode-potential-for-the-oxidation-of-cl-ions-is-more-positive-than-that-of-water-even-then-in-the-electrolysis-of-aqueous-sodium-30403

question:
<div class="question">Value of standard electrode potential for the oxidation of $\mathrm{Cl}^{-}$ions is more positive than that of water, even then in the electrolysis of aqueous sodium chloride, why is $\mathrm{Cl}^{-}$ oxidised at anode instead of water?</div>

answer:
<div class="solution">Under the condition of electrolysis of aqueous sodium chloride, oxidation of water at anode requires over potential. So, $\mathrm{Cl}^{-}$is oxidized at anode instead of water. Possible oxidation half cell reactions occurring at anode are<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{Cl}^{-}(a q) \longrightarrow \frac{1}{2} \mathrm{Cl}_2(g)+e^{-} ; \mathrm{E}_{\text {Cell }}^{\circ}=1.36 \mathrm{~V} \\<br/>&amp;2 \mathrm{H}_2 \mathrm{O}(l) \longrightarrow \mathrm{O}_2(g)+4 \mathrm{H}^{+}(a q)+4 e^{-} ; \mathrm{E}_{\text {Cell }}^{\circ}=1.23 \mathrm{~V}<br/>\end{aligned}<br/>$$<br/>Species having lower $\mathrm{E}_{\text {Cell }}^{\circ}$ undergo oxidation first than the higher value but oxidation of $\mathrm{H}_2 \mathrm{O}$ to $\mathrm{O}_2$ is kinetically so slow that it needs some overvoltage.</div>


tags: ['Chemistry', 'Chemical Kinetics', 'NEET']
source_db: MarksBatch2_P3.db
title:
vant-hoffs-equation-for-a-chemical-reaction-under-equilibrium-is-given-by-standard-reaction-enthalpy-at-temperature-t-and-k-is-the-equilibrium-constan

slug:
vant-hoffs-equation-for-a-chemical-reaction-under-equilibrium-is-given-by-standard-reaction-enthalpy-at-temperature-t-and-k-is-the-equilibrium-constan-51619

question:
<div class="question">Van't Hoff's equation for a chemical reaction under equilibrium is given by standard reaction enthalpy at temperature T and K is the equilibrium constant. Predict how K will vary with temperature for an exothermic reaction.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">K decreases as the temperature rises</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">K remain unchanged</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">K increases as the temperature rise</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Information is not sufficient</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">K decreases as the temperature rises</span> </div>

answer:
<div class="solution">Here K decreases as the temperature rises as K <math><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mi mathvariant="normal">T</mi></mrow></mfrac></math> .</div>


title: variance-is-always-independent-of-the-change-of
slug: variance-is-always-independent-of-the-change-of-95117
question: <div class="question">Variance is always independent of the change of</div>
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2013 (Phase 1)']
answer: <div class="solution">Variance is always independent of change of the origin but not scale</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">origin but not scale</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">scale only</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both origin and scale</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

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


title: vascular-bundles-in-a-dicot-stem-are
slug: vascular-bundles-in-a-dicot-stem-are-50679
question: <div class="question">Vascular bundles in a dicot stem are</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Closed, collateral, endarch</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Open, collateral, endarch</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Closed, collateral, exarch</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Open, collateral, exarch</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Open, collateral, endarch</span> </div>

answer:
<div class="solution">In dicot stem, vascular bundles are conjoint, collateral in which xylem is present towards inner side and phloem towards the center. Xylem is endarch as protoxylem is present towards center and metaxylem towards the periphery.</div>


title: vascular-cambium-and-cork-cambium-are-the-examples-of
slug: vascular-cambium-and-cork-cambium-are-the-examples-of-66186
question: <div class="question">Vascular cambium and cork cambium are the examples of ______.</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">apical meristem</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">lateral meristem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">intercalary meristem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">promeristem</span> </li> </ul>

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

answer:
<div class="solution">Growth in the plant is of two types i.e.primary and secondary growth. Primary growth mainly occurs in the primary meristem. They help in increasing the length of the plant because they present on the axis of it. On the lateral side of it, axillary buds are present that form branches. Secondary meristem is of two types i.e. vascular cambium and cork cambium. Vascular cambium is present in between vascular tissue that helps in the secondary growth of the plants and increases the girth of the plants by the addition of cells in the lateral direction. Similarly, cork cambium also helps in the addition of cells in the cortex. So the correct answer is  <math><mi mathvariant="normal">B</mi></math> .</div>


title: vascular-tissues-in-flowering-plants-develop-from-1
slug: vascular-tissues-in-flowering-plants-develop-from-1-68952
question: <div class="question">Vascular tissues in flowering plants develop from</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2008 (Screening)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phellogen</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">plerome</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">periblem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">dermatogen</span> </li> </ul>

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

answer:
<div class="solution">Histogen theory for shoot apical meristem has been proposed by Hanstein (1870). It advocates that there are three distinct meristematic zones (layers) called dermatogen periblem and plerome. The dermatogen is the outermost histogen giving rise to epidermis, periblem is the middle one producing the cortex and plerome is the innermost resulting in central cylinder (ie, vascular tissue).<br/>Cork cambium (phellogen) is the secondary lateral meristem found in outer cortical region. Its cells divide periclinally cutting off cells towards the outside (forming cork or phellem) and inside (forming secondary cortex or phelloderm).</div>


title: vascular-tissues-in-flowering-plants-develop-from-2
slug: vascular-tissues-in-flowering-plants-develop-from-2-20873
question: <div class="question">Vascular tissues in flowering plants develop from</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'JIPMER', 'JIPMER 2012']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">phellogen</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">plerome</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">periblem</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">dermatogen</span> </li> </ul>

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

answer:
<div class="solution">Histogen theory for shoot apical meristem has been proposed by Hanstein (1870). It advocates that there are three distinct meristematic zones (layers) called dermatogen periblem and plerome. The dermatogen is the outermost histogen giving rise to epidermis, periblem is the middle on producing the cortex and plerome is the innermost resulting in central cylinder (i.e., vascular tissue).<br/>Cork cambium (phellogen) is the secondary lateral meristem found in outer cortical region. Its cells divide periclinally cutting off cells towards the outside (forming cork or phellem) and inside (forming secondary cortex or phelloderm).</div>


tags: ['Biology', 'Ecosystem', 'NEET', 'NEET 2015 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
vertical-distribution-of-different-species-occupying-different-levels-in-a-biotic-community-is-known-as

slug:
vertical-distribution-of-different-species-occupying-different-levels-in-a-biotic-community-is-known-as-10821

question:
<div class="question">Vertical distribution of different species occupying different levels in a biotic community is known as:</div>

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

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

answer:
<div class="solution"><p style="text-align: justify;">By the definition of stratification, it is the distribution of a community in different levels by various socioeconomic means. The different growth form (trees, shrubs, under shrubs, herbs) determines the structure of a plant community. Stratification is based on mode of arrangement of various growth forms.</p><p style="text-align: justify;">In the deep lake, zonation or stratification may be according to the need of light. There are three types of zones differentiated is a deep lake - </p><ul> <li style="text-align: justify;">Littoral Zone</li> <li style="text-align: justify;">Limnetic zone</li> <li style="text-align: justify;">Profundal zone</li></ul><p style="text-align: justify;">The clear stratification (vertical arrangement) in various growths from plants according to the need for light is any dense forest.</p><p style="text-align: justify;">Surface dwellers <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>→</mo></math>  Herbs <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>→</mo></math>  under shrubs <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>→</mo></math> Shrubs <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>→</mo></math> Trees<br/> </p></div>


title: vessels-in-xylem-are-found-in
slug: vessels-in-xylem-are-found-in-67229
question: <div class="question">Vessels in xylem are found in</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2018 (27 May)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">all angiosperms and gymnosperms</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">most of angiosperms and few gymnosperms</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">few angiosperms, all gymnosperms and some pteridophytes</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">all pteridophytes.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">most of angiosperms and few gymnosperms</span> </div>

answer:
<div class="solution">Vessels occur in the wood (both primary and secondary xylem) of almost all angiosperms. But in some angiosperms like Dracaena, Yucca etc., they are absent. Vessels are also absent in the wood of most gymnosperms (except Gnetales) and pteridophytes.</div>


title: vexillary-aestivation-is-seen-in
slug: vexillary-aestivation-is-seen-in-58609
question: <div class="question">Vexillary aestivation is seen in</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Bean</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">China rose</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Bean</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Gulmohur</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cotton</span> </li> </ul>

answer:
<div class="solution">In pea and bean flowers, there are five petals, the largest (standard) overlaps the two lateral petals (wings) which in turn overlap the two smallest anterior petals (keel); this type of aestivation is known as vexillary or papilionaceous.</div>


title: viable-material-of-endangered-species-can-be-preserved-by
slug: viable-material-of-endangered-species-can-be-preserved-by-74643
question: <div class="question">Viable material of endangered species can be preserved by</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">gene bank.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">gene library.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">herbarium.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">gene pool.</span> </li> </ul>

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

answer:
<div class="solution">Viable material of endangered species can be preserved by the gene bank. Gene bank is an institute that maintains stocks of viable seeds (seed banks), live growing plants (orchards), tissue culture and frozen germplasm with the whole range of genetic variability.</div>


title: viral-infection-is-usually-absent-in
slug: viral-infection-is-usually-absent-in-98230
question: <div class="question">Viral infection is usually absent in</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Phloem cells</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Xylem cells</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Pith cells</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Apical meristem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Apical meristem</span> </div>

answer:
<div class="solution">The apical meristems are present in the apices of primary and secondary shoots and roots of the plant. The cells of apical meristem are in an active stage of division, have dense cytoplasm, thin cell wall, and remain virus-free. Due to this reason, meristematic culture is carried out to obtain virus-free plants.</div>


title: viruses-that-infect-bacteria-multiply-and-cause-their-lysis-are-called
slug: viruses-that-infect-bacteria-multiply-and-cause-their-lysis-are-called-27132
tags: ['Biology', 'Biological Classification', 'NEET', 'NEET 2004']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">lytic</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">Viruses that infect bacteria multiply and cause their lysis, are called:</div>

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

answer:
<div class="solution">Bacteriophage is a kind of virus that can infect bacteria and start replicating inside the bacterial cell because the lysis represents the lytic cycle. Lysogenic cycle allows the host cell to continue to survive and reproduce, the virus is reproduced in all of the cell's offspring. Any hormone (such as epinephrine, glucagon, and cortisol) that promotes release of free fatty acids from fat tissue is known as lypolytic. Lysozyme is a naturally occurring enzyme found in bodily secretions such as tears, saliva, and milk and act as an antimicrobial agent<br/>Related Theory<br/>Human lysozyme act as physiological barrier in immune system against some bacteria. It is found in abundance in tears, saliva and mucous.</div>


title: voltage-in-the-secondary-coil-of-a-transformer-does-not-depend-upon
slug: voltage-in-the-secondary-coil-of-a-transformer-does-not-depend-upon-94022
question: <div class="question">Voltage in the secondary coil of a transformer does not depend upon</div>
tags: ['Physics', 'Alternating Current', 'JIPMER', 'JIPMER 2011']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">frequency of the source</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">voltage in the primary coil</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">ratio of number of turns in the two coils</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Both (b) and (c)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">frequency of the source</span> </div>

answer:
<div class="solution">The voltage in primary and secondary coil is related as:<br/>$\Rightarrow \frac{\mathrm{V}_{\mathrm{S}}}{\mathrm{V}_{\mathrm{P}}}=\frac{\text { no. of turns in secondary coil }\left(\mathrm{N}_{\mathrm{s}}\right)}{\text { no. of turns in primary coil }\left(\mathrm{N}_{\mathrm{p}}\right)}$<br/>Clearly, voltage in secondary coil depends on voltage in primary coil and number of turns in primary and secondary coil. It is independent of frequency of the source.<br/>Hence, option 1 is correct.</div>


title: water-in-plants-is-transported-by
slug: water-in-plants-is-transported-by-21003
question: <div class="question">Water in plants is transported by :</div>
tags: ['Biology', 'Transport in Plants', 'JIPMER', 'JIPMER 2006']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">xylem</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">cambium</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">phloem</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">xylem</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">epidermis</span> </li> </ul>

answer:
<div class="solution">The water absorbed by root hairs is transported to other parts of the plant through xylem. Phloem transfers food prepared in leaves to the other parts. Cambium is responsible for secondary growth while epidermis is the outermost protective layer of cells.</div>


title: water-potential-is-equal-to
slug: water-potential-is-equal-to-47259
question: <div class="question">Water potential is equal to</div>
tags: ['Biology', 'Transport in Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ψ<sub>s</sub> + O.P.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">ψ<sub>s</sub> + T.P.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">ψ<sub>p</sub> + ψ<sub>w</sub></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Ï<sub>s</sub> + Ï<sub>p</sub></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Ï<sub>s</sub> + Ï<sub>p</sub></span> </div>

answer:
<div class="solution">Water potential is defined as the difference between the chemical potential of water at any point in a system and that of pure water under standard conditions. The unit of measurement of water potential is the pascal, Pa (1 megapascal, Mpa = 10 bars). It is represented by greek letter PSi (Ï). Water potential has two components solute potential which is always negative and pressure potential which is usually positive. Therefore, water potential Ï<sub>w</sub> is expressed as Ï<sub>w</sub> = Ï<sub>s</sub> + Ï<sub>p.</sub></div>


title: water-potential-of-pure-water-at-standard-temperature-is-equal-to
slug: water-potential-of-pure-water-at-standard-temperature-is-equal-to-71410
question: <div class="question">Water potential of pure water at standard temperature is equal to</div>
tags: ['Biology', 'Transport in Plants']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>10<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>20<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>zero<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/>None of these</span> </li> </ul>

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

answer:
<div class="solution">Water potential of pure water at standard temperature is zero. It is the highest value of water potential.</div>


tags: ['Physics', 'Communication System', 'JEE Main', 'JEE Main 2022 (27 Jun Shift 2)']
source_db: MarksBatch2_P3.db
title:
we-do-not-transmit-low-frequency-signal-to-long-distances-because-a-the-size-of-the-antenna-should-be-comparable-to-signal-wavelength-which-is-unreal-

slug:
we-do-not-transmit-low-frequency-signal-to-long-distances-because-a-the-size-of-the-antenna-should-be-comparable-to-signal-wavelength-which-is-unreal-86053

question:
<div class="question"><p>We do not transmit low frequency signal to long distances because<br/>(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.<br/>(b) Effective power radiated by a long wavelength baseband signal would be high.<br/>(c) We want to avoid mixing up signals transmitted by different transmitter simultaneously.<br/>(d) Low frequency signal can be sent to long distances by superimposing with a high frequency wave as well.</p><p>Therefore, the most suitable option will be :</p></div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">(a), (c) and (d) are true only</span> </div>

answer:
<div class="solution"><p>For longer wavelength, size of antenna would increase. The size of the antennas should be atleast <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>λ</mi><mn>4</mn></mfrac></math> for high efficiency of signal radiation. </p><p>The effective power radiated by an antenna is inversely proportional to the square of the wavelength, so, for the same antenna length, the power radiated increases with decreasing wavelength or increasing frequency.Hence, the effective power radiated by a long-wavelength baseband signal would be small.</p><p>Also, mixing of signals needs to be avoided, as all the signals get mixed together and a receiver can not separate them from each other.  Also, we can use modulation to send low frequency signal by superimposing them with high frequency signals. Electrical audio signals are superimposed on a high frequency wave called the carrier wave. The carrier wave is generated from radio-frequency oscillators and is undamped in nature.</p></div>


title: wha-t-i-s-sin-a-cos-a-tan-a-cos-a-sin-acota-equal-to
slug: wha-t-i-s-sin-a-cos-a-tan-a-cos-a-sin-acota-equal-to-68981
question: <div class="question">$ What is $\sin A \cos A \tan A+$ cos $A$ sin AcotA equal to?</div>
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\sin \mathrm{A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\cos \mathrm{A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\tan \mathrm{A}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Given expression<br/>$\begin{aligned}=&amp; \sin A \cos A \cdot \frac{\sin A}{\cos A}+\cos A \sin A \frac{\cos A}{\sin A} \\=&amp; \sin ^{2} A+\cos ^{2} A=1 \end{aligned}$</div>


title: what-0-2-x-2-1-dx-equal-to
slug: what-0-2-x-2-1-dx-equal-to-61338
question: <div class="question">What $\int_{0}^{2} \frac{\mathrm{dx}}{\mathrm{x}^{2}+1}$ equal to ?</div>
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\pi}{8}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\pi}{8}$</span> </div>

answer:
<div class="solution">Let $\mathrm{I}=\int_{0}^{2} \frac{\mathrm{dx}}{\mathrm{x}^{2}+4}=\int_{0}^{2} \frac{\mathrm{dx}}{\mathrm{x}^{2}+(2)^{2}}$<br/>$=\frac{1}{2}\left[\tan ^{-1} \frac{\mathrm{x}}{2}\right]_{0}^{-2}=\frac{1}{2}\left[\tan ^{-1}(1)-\tan ^{-1}(0)\right]$<br/>$=\frac{1}{2}\left[\frac{\pi}{4}-0\right]=\frac{\pi}{8}$</div>


title: what-advantage-do-the-fuel-cells-have-over-primary-and-secondary-batteries-1
slug: what-advantage-do-the-fuel-cells-have-over-primary-and-secondary-batteries-1-32767
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What advantage do the fuel cells have over primary and secondary batteries?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Fuel cells have higher energy density.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Fuel cells produce fewer environmental pollutants.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Fuel cells are smaller and more portable.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Primary batteries contain a limited amount of reactants and are discharged when the reactants have been consumed. Secondary batteries can be recharged but take a long time to recharge. Fuel cell runs continuously as long as the reactants are supplied to it and products are removed continuously.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Primary batteries contain a limited amount of reactants and are discharged when the reactants have been consumed. Secondary batteries can be recharged but take a long time to recharge. Fuel cell runs continuously as long as the reactants are supplied to it and products are removed continuously.</span> </div>

answer:
<div class="solution">Correct Option is : (D)<br/>Primary batteries contain a limited amount of reactants and are discharged when the reactants have been consumed. Secondary batteries can be recharged but take a long time to recharge. Fuel cell runs continuously as long as the reactants are supplied to it and products are removed continuously.</div>


title: what-advantage-do-the-fuel-cells-have-over-primary-and-secondary-batteries
slug: what-advantage-do-the-fuel-cells-have-over-primary-and-secondary-batteries-34364
tags: ['Chemistry', 'Electrochemistry']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
question:
<div class="question">What advantage do the fuel cells have over primary and secondary batteries?</div>

answer:
<div class="solution">Reaction occuring in Daniel cell is as following:<br/>$$<br/>\mathrm{Zn}+\mathrm{Cu}^{2+} \longrightarrow \mathrm{Zn}^{2+}+\mathrm{Cu}<br/>$$<br/><br/><br/>Nernst equation for Daniel cell is given as following:<br/>$$<br/>\begin{aligned}<br/>&amp;\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\circ}-\frac{0.0591}{2} \log \left[\frac{\mathrm{Zn}^{2+}}{\mathrm{Cu}^{2+}}\right] \\<br/>&amp;\mathrm{E}_{\text {cell }}=\mathrm{E}_{\text {cell }}^{\circ}+\frac{0.0591}{2} \log \left[\frac{\mathrm{Cu}^{2+}}{\mathrm{Zn}^{2+}}\right]<br/>\end{aligned}<br/>$$<br/>According to this equation $E_{\text {cell }}$ is directly dependent on concentration of $\mathrm{Cu}^{2+}$ and inversely dependent upon concentration of $\mathrm{Zn}^{2+}$ ions.<br/><br/>Therefore, $E_{\text {cell }}$ decreases when concentration of $\mathrm{Zn}^{2+}$ ions is increased.</div>


title: what-angle-does-the-line-segment-joining-5-2-and-6-15-subtend-at-00
slug: what-angle-does-the-line-segment-joining-5-2-and-6-15-subtend-at-00-27319
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What angle does the line segment joining $(5,2)$ and $(6,-15)$ subtend at $(0,0) ?</div>

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

answer:
<div class="solution">Slope of line joining $(5,2)$ and $(0,0)$<br/>$\tan \mathrm{A}=\mathrm{m}_{1}=\frac{2-0}{5-0}=\frac{2}{5}$<br/>Slope of line joining $(6,-15)$ and $(0,0)$<br/>$\tan \mathrm{B}=\mathrm{m}_{2}=\frac{-15}{6}=\frac{-5}{2}$<br/>Now, $\mathrm{m}_{1} \cdot \mathrm{m}_{2}=\frac{2}{5}\left(-\frac{5}{2}\right)=-1$<br/>Hence, both lines are perpendicular. and than angle<br/>between them $=\frac{\pi}{2}$</div>


title: what-are-animals-that-feed-on-herbivores-called
slug: what-are-animals-that-feed-on-herbivores-called-84346
question: <div class="question">What are animals that feed on herbivores called?</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary carnivores</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Secondary carnivores</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary carnivores</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Herbivores</span> </li> </ul>

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

answer:
<div class="solution">The consumers that feed on herbivores are carnivores, or more correctly, primary carnivores.</div>


title: what-are-coordinates-of-the-point-equidistant-from-the-points-a-0-0-0-a-0-0-0-a-and-0-0-0
slug: what-are-coordinates-of-the-point-equidistant-from-the-points-a-0-0-0-a-0-0-0-a-and-0-0-0-73612
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are coordinates of the point equidistant from the points $(a, 0,0),(0, a, 0),(0,0, a)$ and $(0,0,0) ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(\frac{\mathrm{a}}{2}, \frac{\mathrm{a}}{2}, \frac{\mathrm{a}}{2}\right)$</span> </div>

answer:
<div class="solution">Let the point $\mathrm{A}(\mathrm{x}, \mathrm{y}, \mathrm{z})$ is equidistant from the points $\begin{aligned} &amp; \mathrm{B}(\mathrm{a}, 0,0), \mathrm{C}(0, \mathrm{a}, 0), \mathrm{D}(0,0, \mathrm{a}) \text { and } \mathrm{E}(0,0,0) . \\ &amp; \text { Hence, }(\mathrm{x}-\mathrm{a})^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}=\mathrm{x}^{2}+(\mathrm{y}-\mathrm{a})^{2}+\mathrm{z}^{2} \\ &amp;=\mathrm{x}^{2}+\mathrm{y}^{2}+(\mathrm{z}-\mathrm{a})^{2} \\ &amp;=\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{z}^{2} \\ \Rightarrow &amp;(\mathrm{x}-\mathrm{a})^{2}+\mathrm{y}^{2}+\mathrm{z}^{2}=\mathrm{x}^{2}+(\mathrm{y}-\mathrm{a})^{2}+\mathrm{z}^{2} \\ \Rightarrow &amp; \mathrm{x}^{2}+\mathrm{a}^{2}-2 \mathrm{ax}+\mathrm{y}^{2}+\mathrm{z}^{2}=\mathrm{x}^{2}+\mathrm{y}^{2}+\mathrm{a}^{2}-2 \mathrm{ay}+\mathrm{z}^{2} \\ \Rightarrow &amp;-2 \mathrm{ax}=-2 \mathrm{ay} \\ \Rightarrow &amp; \mathrm{ax}=\mathrm{ay} \Rightarrow \mathrm{x}=\mathrm{y} \\ &amp; \text { Similarly, ay }=\mathrm{az} \Rightarrow \mathrm{y}=\mathrm{z} \end{aligned}$<br/>$\Rightarrow x=y=z$<br/>$(x-a)^{2}+x^{2}+x^{2}=x^{2}+x^{2}+x^{2}$<br/>$\Rightarrow x^{2}+a^{2}-2 a x+x^{2}+x^{2}=3 x^{2}$<br/>$\Rightarrow \mathrm{a}^{2}=2 \mathrm{ax} \Rightarrow \mathrm{x}=\frac{\mathrm{a}}{2}$<br/>$\therefore$ Point is $\left(\frac{\mathrm{a}}{2}, \frac{\mathrm{a}}{2}, \frac{\mathrm{a}}{2}\right)$</div>


title: what-are-sacred-groves-and-their-role-in-biodiversity-conservation
slug: what-are-sacred-groves-and-their-role-in-biodiversity-conservation-89003
question: <div class="question">What are sacred groves and their role in biodiversity conservation?</div>
tags: ['Biology', 'Biodiversity and its Conservation']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
answer:
<div class="solution">Sacred tracts which are held in high esteem by local communities are sacred groves. The sacred groves are dedicated to local deities or ancestral spirits. They are protected by local communities through social traditions and taboos that incorporate spiritual as well as ecological values.<br/>A native vegetation in a natural or near natural state is represented by sacred groves and are thus, rich in biodiversity and harbour many rare species of plants and animals.<br/>sacred groves as such are found in Meghalaya (Khasi and Jaintia hills), Aravalli hills of Rajasthan, Western Ghats, regions of Karnataka and Maharashtra and Madhya Pradesh (Bastar. Chanda and Sarguia region).</div>


title: what-are-secondary-medullary-rays
slug: what-are-secondary-medullary-rays-35247
question: <div class="question">What are secondary medullary rays?</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Narrow band of parenchyma</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Arranged transversely</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Dead and lignified</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Formed by primary cambium</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Narrow band of parenchyma</span> </div>

answer:
<div class="solution">During secondary growth, at some places, the cambium forms a narrow band of parenchyma, which passes through the secondary xylem and the secondary phloem in the radial directions. These are the secondary medullary rays.</div>


title: what-are-side-reactions
slug: what-are-side-reactions-57384
question: <div class="question">What are side reactions?</div>
tags: ['Chemistry', 'Chemical Kinetics', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Reactions that occur on the side of a reaction vessel.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Reactions that produce unexpected products alongside the main reaction.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Reactions that are unrelated to the main reaction.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Reactions that involve secondary reactants.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Reactions that produce unexpected products alongside the main reaction.</span> </div>

answer:
<div class="solution">Side reactions are reactions that produce unexpected products alongside the main reaction.</div>


title: what-are-some-examples-of-secondary-metabolites-that-are-useful-to-human-welfare
slug: what-are-some-examples-of-secondary-metabolites-that-are-useful-to-human-welfare-31595
tags: ['Biology', 'Biomolecules (B)', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are some examples of secondary metabolites that are useful to human welfare?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Rubber, drugs, spices, scents and pigments</span> </div>

answer:
<div class="solution">Many secondary metabolites are useful to human welfare, including rubber, drugs, spices, scents and pigments.</div>


tags: ['Biology', 'The Living World']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
what-are-taxonomical-aids-give-the-importance-of-herbaria-and-museums-how-are-botanical-gardens-and-zoological-parks-useful-in-conserving-biodiversity

slug:
what-are-taxonomical-aids-give-the-importance-of-herbaria-and-museums-how-are-botanical-gardens-and-zoological-parks-useful-in-conserving-biodiversity-79443

question:
<div class="question">What are taxonomical aids? Give the importance of herbaria and museums. How are Botanical gardens and Zoological parks useful in conserving biodiversity?</div>

answer:
<div class="solution">The aids which help in identification, classification and naming of a newly discovered organisms (plant or animal) the taxonomic aids.<br/>It could be in the form of a preserved document like herbaria or specimen kept at museums or scientific institutions. Other aids include written document like monography, taxonomic keys, couplets, etc.<br/>A new organism found can be studied while comparing it with living plants and animals living in protected areas like Botanical gardens, Zoological parks, etc.<br/>Botanical gardens helps in conservation of plants by<br/>(i) Plant species growing important local and keeping record of them.<br/>(ii) Growing and maintaining species that rare are and endangered.<br/>(iii) Supplying seeds for different aspects of botanical research.<br/>Zoological parks contribute in conserving biodiversity by<br/>(i) Providing natural environment and open space to animals.<br/>(ii) Providing home to different native and exotic wild animals.<br/>(iii) Rescue of endangered species.<br/>(iv) Facilitating breeding animal and releasing them free.<br/>Thus, both botanical gardens and zoological parks play an important role in conservation of biodiversity.</div>


title: what-are-the-actions-of-estrogens-in-female-individuals
slug: what-are-the-actions-of-estrogens-in-female-individuals-45620
question: <div class="question">What are the actions of estrogens in female individuals?</div>
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Stimulation of male secondary sex organs</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Development of male secondary sex characters</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Stimulation of growth and activities of female secondary sex organs</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Stimulation of alveoli formation</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Stimulation of growth and activities of female secondary sex organs</span> </div>

answer:
<div class="solution">Estrogens produce wide ranging actions such as stimulation of growth and activities of female secondary sex organs, development of growing ovarian follicles, appearance of female secondary sex characters, mammary gland development, and regulation of female sexual behaviour.</div>


tags: ['Biology', 'Human Reproduction']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
what-are-the-changes-in-the-oogonia-during-the-transition-of-a-primary-follicle-to-graafian-follicle

slug:
what-are-the-changes-in-the-oogonia-during-the-transition-of-a-primary-follicle-to-graafian-follicle-85935

question:
<div class="question">What are the changes in the oogonia during the transition of a primary follicle to Graafian follicle?</div>

answer:
<div class="solution">After the repeated division of the germinal epithelial cells many diploid oogonia are formed. The oogonia grow further to form primary oocytes, which then gets surrounded by a layer of granulosa cells called the primary follicles.<br/>When more layers of granulosa cells surrounds primary follicles. It forms secondary follicles. The secondary follicle soon transforms into a tertiary follicle which is characterised by a fluid filled cavity called antrum.<br/>In primary oocyte within the tertiary follicle meiotic division occurs to become a secondary oocyte and a first polar body (haploid). The tertiary follicle further changes into the mature follicle or Graafian follicle that ruptures and releases the secondary oocyte (ovum) from the ovary by the process called ovulation.</div>


title: what-are-the-characteristics-of-the-leafy-stage-in-mosses
slug: what-are-the-characteristics-of-the-leafy-stage-in-mosses-57023
question: <div class="question">What are the characteristics of the leafy stage in mosses?</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Upright, slender axes bearing spirally arranged leaves</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Creeping, green, branched and filamentous</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Multicellular and branched rhizoids</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Upright, slender axes bearing spirally arranged leaves</span> </div>

answer:
<div class="solution">The leafy stage in mosses develops from the secondary protonema as a lateral bud. They consist of upright, slender axes bearing spirally arranged leaves.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-are-the-coefficients-a-and-b-in-the-equation-for-calculating-the-enthalpy-change-using-standard-enthalpies-of-formation

slug:
what-are-the-coefficients-a-and-b-in-the-equation-for-calculating-the-enthalpy-change-using-standard-enthalpies-of-formation-38383

question:
<div class="question">What are the coefficients 'a' and 'b' in the equation for calculating the enthalpy change using standard enthalpies of formation?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">'a' represents the coefficients of the products, and 'b' represents the coefficients of the reactants.</span> </div>

answer:
<div class="solution">In the equation for calculating the enthalpy change using standard enthalpies of formation, 'a' represents the coefficients of the products, and 'b' represents the coefficients of the reactants in the balanced chemical equation.</div>


title: what-are-the-common-types-of-secondary-structure-of-proteins-1
slug: what-are-the-common-types-of-secondary-structure-of-proteins-1-81413
question: <div class="question">What are the common types of secondary structure of proteins?</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The common types of secondary structure of proteins include primary and tertiary structures.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">The common types of secondary structure of proteins are alpha helix and beta sheets.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The common types of secondary structure of proteins are globular and fibrous.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The common types of secondary structure of proteins are hydrophobic and hydrophilic regions.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The common types of secondary structure of proteins are alpha helix and beta sheets.</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>The common types of secondary structure of proteins are alpha helix and beta sheets.</div>


title: what-are-the-common-types-of-secondary-structure-of-proteins
slug: what-are-the-common-types-of-secondary-structure-of-proteins-45780
question: <div class="question">What are the common types of secondary structure of proteins?</div>
tags: ['Chemistry', 'Biomolecules']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
answer:
<div class="solution">The conformation which the polypeptide chains assume as a result of hydrogen bonding is called secondary structure of the proteins. The two types of secondary structures are \(\alpha\)-helix and \(\beta\)-pleated sheet structure.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
what-are-the-coordinates-of-the-foot-of-the-perpendicular-drawn-from-the-point-3-5-4-on-the-plane-z-0

slug:
what-are-the-coordinates-of-the-foot-of-the-perpendicular-drawn-from-the-point-3-5-4-on-the-plane-z-0-64358

question:
<div class="question">What are the co-ordinates of the foot of the perpendicular drawn from the point $(3,5,4)$ on the plane $\mathrm{z}=0$ ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad(3,5,0) \quad$</span> </div>

answer:
<div class="solution">Plane z $=0$ is simply xy plane, so z quadrant value will be zero.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/4e1QHwIfRvgt5HWWKYhqoGuhjW2PP1VGZW5AstIo_Yk.original.fullsize.png"/><br/><br/>So, options (b) is correct option.</div>


title: what-are-the-coordinates-of-the-foot-of-the-perpendicular-from-the-point-2-3-on-the-line-x-y-11-0
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
slug:
what-are-the-coordinates-of-the-foot-of-the-perpendicular-from-the-point-2-3-on-the-line-x-y-11-0-10607

question:
<div class="question">What are the co-ordinates of the foot of the perpendicular from the point $(2,3)$ on the line $x+y-11=0 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(2,9)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$(5,6)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(-5,6)$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(6,5)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(5,6)$</span> </div>

answer:
<div class="solution">Let B be the foot of perpendicular $\mathrm{AB}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/vJsdvSHyxQJdUQCU6GQtTfdJyBe5chIhZix0DpzrvkY.original.fullsize.png"/><br/><br/>Now, $x+y-11=0$<br/>$\Rightarrow \mathrm{y}=-\mathrm{x}+11$ ...(1)<br/>$\Rightarrow$ Slope $=-1$ ...(2)<br/>Since, $A B$ is perpendicular to $x+y-11=0$ product of their slopes $=-1$ $\Rightarrow-1+$ Slope of $A B=-1$<br/>$\Rightarrow$ Slope of $\mathrm{AB}=1$<br/>Now, equation of $\mathrm{AB}$ is given as $y-3=1(x-2) \quad$ (using slope point form) $\Rightarrow y-x=1$ ...(3)<br/>Now, foot of perpendicular<br/>$=$ Point of intersection of line $A B$ and $x+y-11=0$ So, on solving equation (1) and (2) we get $x=5, y=6$. <br/>Hence, $B=(5,6)$.</div>


title: what-are-the-coordinates-of-the-point-equidistant-from-the-four-points-0-0-0-2-0-0-0-4-0-0-0-6
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
slug:
what-are-the-coordinates-of-the-point-equidistant-from-the-four-points-0-0-0-2-0-0-0-4-0-0-0-6-17910

question:
<div class="question">What are the coordinates of the point equidistant from the four points $(0,0,0),(2,0,0),(0,4,0),(0,0,6) ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1,2,3)$</span> </div>

answer:
<div class="solution">The equation of sphere passing through the given points is<br/>$x^{2}+y^{2}+z^{2}+2 u x+2 v y+2 w z+d=0$<br/>$\therefore(0)^{2}+(0)^{2}+(0)^{2}+2 u(0)+2 v(0)+2 w(0)+d=0$<br/>$\Rightarrow d=0$<br/>$(2)^{2}+(0)^{2}+(0)^{2}+2 u(2)+2 v(0)+2 u(0)+0=0$<br/>$\Rightarrow u=-1$<br/>$(0)^{2}+(4)^{2}+(0)^{2}+2 u(0)+2 v(4)+2 u(0)+0=0$<br/>$\Rightarrow v=-2$<br/>$(0)^{2}+(0)^{2}+(6)^{2}+2 u(0)+2 v(0)+2 w(6)+0=0$<br/>$\Rightarrow w=-3$<br/>$\therefore$ The centre of sphere $=(1,2,3)$<br/>It will be the point equidistant from the four points $(0,0,0),(2,0,0),(0,4,0)$ and $(0,0,6)$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2009 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,1</span> </div>
source_db: MarksBatch2_P3.db
title:
what-are-the-degree-and-order-respectively-of-differential-equation-of-the-family-of-rectangular-hyperbolas-whose-axis-of-symmetry-are-the-coordinate-

slug:
what-are-the-degree-and-order-respectively-of-differential-equation-of-the-family-of-rectangular-hyperbolas-whose-axis-of-symmetry-are-the-coordinate-54987

question:
<div class="question">What are the degree and order respectively of differential equation of the family of rectangular hyperbolas whose axis of symmetry are the coordinate axis?</div>

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

answer:
<div class="solution">The equation of family of rectangular hyperbola is $\mathrm{xy}=\mathrm{c}^{2}$<br/>On differentiating w.r.t. $\mathrm{x}$, we get<br/>$$<br/>y+x \frac{d y}{d x}=0<br/>$$<br/>Thus, the order and degree of differential equation are 1 and 1 respectively.</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2016 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,1</span> </div>
source_db: MarksBatch2_P3.db
title:
what-are-the-degree-and-order-respectively-of-the-differential-equation-satisfying-e-y-1-x-2-x-1-y-2-ce-x-where-c-0-x-1-y-1

slug:
what-are-the-degree-and-order-respectively-of-the-differential-equation-satisfying-e-y-1-x-2-x-1-y-2-ce-x-where-c-0-x-1-y-1-58632

question:
<div class="question">What are the degree and order respectively of the differential<br/>equation satisfying $\mathrm{e}^{\mathrm{y} \sqrt{1-\mathrm{x}^{2}}+\mathrm{x} \sqrt{1-\mathrm{y}^{2}}}=\mathrm{ce}^{\mathrm{x}}$,<br/>$($ where $c&gt;0,|x|   &lt; 1,|y| &lt; 1) ? \quad$</div>

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

answer:
<div class="solution">$\begin{aligned} &amp; \mathrm{e}^{\mathrm{y}\left(\sqrt{1-\mathrm{x}^{2}}+\mathrm{x} \sqrt{1-\mathrm{y}^{2}}\right)-\mathrm{s}-\mathrm{c}} \\ &amp; \Rightarrow \mathrm{y} \sqrt{1-\mathrm{x}^{2}}+\mathrm{x} \sqrt{1-\mathrm{y}^{2}}-\mathrm{x}=\log \mathrm{c} \\ &amp; \Rightarrow \frac{\mathrm{dy}}{\mathrm{d} \mathrm{x}} \sqrt{1-\mathrm{x}^{2}}+\mathrm{y} \cdot \frac{1}{\not 2 \sqrt{1-\mathrm{x}^{2}}}(-\not{2} \mathrm{x})+\sqrt{1-\mathrm{y}^{2}} \\ &amp; &amp; \\+\mathrm{x} \cdot \frac{1}{\not{2} \sqrt{1-\mathrm{y}^{2}}}(-\not{2} \mathrm{y}) \cdot \frac{\mathrm{dy}}{\mathrm{dx}}-1=0 \\ \Rightarrow &amp; \frac{\mathrm{dy}}{\mathrm{d} \mathrm{x}} \sqrt{1-\mathrm{x}^{2}}-\frac{\mathrm{x} \mathrm{y}}{\sqrt{1-\mathrm{x}^{2}}}+\sqrt{1-\mathrm{y}^{2}}-\frac{\mathrm{xy}}{\sqrt{1-\mathrm{y}^{2}}} \cdot \frac{\mathrm{dy}}{\mathrm{dx}}=1 \\ &amp; \text { Degree }=1, \text { order }=1 \end{aligned}$</div>


title: what-are-the-degree-and-order-respectively-of-the-differential-equation-y-x-dx-dy-2-dy-dx-2
slug: what-are-the-degree-and-order-respectively-of-the-differential-equation-y-x-dx-dy-2-dy-dx-2-95154
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2017 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4,1</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the degree and order respectively of the<br/>differential equation $\mathrm{y}=\mathrm{x}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+\left(\frac{\mathrm{dx}}{\mathrm{dy}}\right)^{2} ? \quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1,2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2,1</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1,4</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">4,1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$y=x\left(\frac{d y}{d x}\right)^{2}+\left(\frac{d x}{d y}\right)^{2}$<br/>$=\mathrm{x}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{-2}$<br/>$\Rightarrow \mathrm{y}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}=\mathrm{x} \cdot\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{4}+1$<br/>So, degree $=4$, order $=1$</div>


tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-are-the-difficulties-that-one-would-face-in-classification-of-animals-if-common-fundamental-features-are-not-taken-into-account

slug:
what-are-the-difficulties-that-one-would-face-in-classification-of-animals-if-common-fundamental-features-are-not-taken-into-account-22821

question:
<div class="question">What are the difficulties that one would face in classification of animals, if common fundamental features are not taken into account?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">It is impossible to add new species detected every day without common features</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">No difficulties are faced</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Cannot be defined</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It is impossible to add new species detected every day without common features</span> </div>

answer:
<div class="solution">Without common features, it is very difficult to treat each organism individually. It is impossible to add new species detected every day without common features. To study diversity in animals, classification must be based on common basic features.</div>


tags: ['Biology', 'Animal Kingdom']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
what-are-the-difficulties-that-you-would-face-in-classification-of-animals-if-common-fundamental-features-are-not-taken-into-account

slug:
what-are-the-difficulties-that-you-would-face-in-classification-of-animals-if-common-fundamental-features-are-not-taken-into-account-97685

question:
<div class="question">What are the difficulties that you would face in classification of animals, if common fundamental features are not taken into account?</div>

answer:
<div class="solution">If fundamental characters are not taken into account then the classification of animals is difficult due to difference in characters in different animals which are as following :<br/>(i) Grade of organisation<br/>(ii) Symmetry<br/>(iii) Coelom<br/>(iv) Segmentation<br/>(v) Notochord<br/>Common fundamental features help in grouping animals in certain categories or sub-categories. For examples, all birds have fore-limbs modified to assist in flying. This gives us one clue to categorise a particular animals among aves.</div>


tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
what-are-the-direction-cosines-of-a-line-which-is-equally-inclined-to-the-positive-directions-of-the-axes

slug:
what-are-the-direction-cosines-of-a-line-which-is-equally-inclined-to-the-positive-directions-of-the-axes-61546

question:
<div class="question">What are the direction cosines of a line which is equally inclined to the positive directions of the axes?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left\langle\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right\rangle$</span> </div>

answer:
<div class="solution">Let $\ell, \mathrm{m}, \mathrm{n}$ are the dc's of a line that is inclined equally at $\alpha$ to the $+$ ve direction of axes.<br/>Now, $\begin{aligned} \ell &amp;=\cos \alpha \\ \mathrm{m} &amp;=\cos \alpha \\ \mathrm{n} &amp;=\cos \alpha . \end{aligned}$<br/>Also, $\ell^{2}+\mathrm{m}^{2}+\mathrm{n}^{2}=1$<br/>$3 \cos ^{2} \alpha=1$<br/>$\cos \alpha=\frac{1}{\sqrt{3}}$<br/>$\therefore \quad$ dc's of the line are : $\left\langle\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\right\rangle$</div>


title: what-are-the-direction-cosines-of-the-line-represented-by-3-x-y-2-z-7-x-2-y-3-z-5
slug: what-are-the-direction-cosines-of-the-line-represented-by-3-x-y-2-z-7-x-2-y-3-z-5-88202
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the direction cosines of the line represented<br/>by $3 x+y+2 z=7, x+2 y+3 z=5 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(-1,-7,5)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(-1,7,5)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left(-\frac{1}{\sqrt{75}},-\frac{7}{\sqrt{75}}, \frac{5}{\sqrt{75}}\right)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left(-\frac{1}{\sqrt{75}}, \frac{7}{\sqrt{75}}, \frac{5}{\sqrt{75}}\right)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left(-\frac{1}{\sqrt{75}},-\frac{7}{\sqrt{75}}, \frac{5}{\sqrt{75}}\right)$</span> </div>

answer:
<div class="solution">Let the direction ratio of the line be, $\mathrm{a}, \mathrm{b}, \mathrm{c}$<br/>This line is contained by both plane,<br/>$3 x+y+2 z=7$ and $x+2 y+3 z=5$<br/>$\Rightarrow 3 \mathrm{a}+\mathrm{b}+2 \mathrm{c}=0$<br/>and $a+2 b+3 c=0$<br/>Solving these two equations<br/>$\frac{a}{\left|\begin{array}{ll}1 &amp; 2 \\ 2 &amp; 3\end{array}\right|}=\frac{-b}{\left|\begin{array}{ll}3 &amp; 2 \\ 1 &amp; 3\end{array}\right|}=\frac{c}{\left|\begin{array}{ll}3 &amp; 1 \\ 1 &amp; 2\end{array}\right|}=k$<br/>Let<br/>$\Rightarrow \frac{\mathrm{a}}{-1}=\frac{-\mathrm{b}}{7}=\frac{\mathrm{c}}{5}=\mathrm{k}$<br/>$\mathrm{a}=-\mathrm{k}, \mathrm{b}=-7 \mathrm{k}, \mathrm{c}=5 \mathrm{k}$<br/>Direction cosines are<br/>$\frac{a}{\sqrt{a^{2}+b^{2}+c^{2}}}, \frac{b}{\sqrt{a^{2}+b^{2}+c^{2}}}, \frac{c}{\sqrt{a^{2}+b^{2}+c^{2}}}$<br/>$\sqrt{a^{2}+b^{2}+c^{2}}=\sqrt{(-k)^{2}+(-7 k)^{2}+(5 k)^{2}}$<br/>$=\sqrt{\mathrm{k}^{2}+49 \mathrm{k}^{2}+25^{2}}=\mathrm{k} \sqrt{75}$<br/>So, Direction cosines are $\left(\frac{-\mathrm{k}}{\mathrm{k} \sqrt{75}}, \frac{-7 \mathrm{k}}{\mathrm{k} \sqrt{75}}, \frac{5 \mathrm{k}}{\mathrm{k} \sqrt{75}}\right)$<br/>$=\left(-\frac{1}{\sqrt{75}},-\frac{7}{\sqrt{75}}, \frac{5}{\sqrt{75}}\right)$</div>


title: what-are-the-direction-cosines-of-z-axis
slug: what-are-the-direction-cosines-of-z-axis-84208
question: <div class="question">What are the direction cosines of $z$ -axis?</div>
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2019 (Phase 1)']
answer: <div class="solution">No Solution</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$   &lt; 1,1,1&gt;$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$   &lt; 1, \underline{0,0}&gt;$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$   &lt; 0,1,0&gt;$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$   &lt; 0,0,1&gt;$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$   &lt; 0,0,1&gt;$</span> </div>


title: what-are-the-direction-ratios-of-normal-to-the-plane-2-x-y-2-z-1-0
slug: what-are-the-direction-ratios-of-normal-to-the-plane-2-x-y-2-z-1-0-30988
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the direction ratios of normal to the plane $2 \mathrm{x}-\mathrm{y}+2 \mathrm{z}+1=0 \quad$</div>

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

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

answer:
<div class="solution">Given equation of plane is $2 \mathrm{x}-\mathrm{y}+2 \mathrm{z}+1=0$ $\Rightarrow a=2, b=-1, c=2$<br/>Hence d.R $\langle 2,-1,2\rangle$ i.e., $\left\langle 1,-\frac{1}{2}, 1\right\rangle$</div>


title: what-are-the-direction-ratios-of-the-line-determined-by-the-planes-x-y-2-z-1-and-x-y-z-3
slug: what-are-the-direction-ratios-of-the-line-determined-by-the-planes-x-y-2-z-1-and-x-y-z-3-73723
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the direction ratios of the line determined by the planes $x-y+2 z=1$ and $x+y-z=3 ? \quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(-1,3,2)$</span> </div>

answer:
<div class="solution">The intersection of given plane is $x-y+2 z-1+\lambda(x+y-z-3)=0$<br/>$\Rightarrow x(1+\lambda)+y(\lambda-1)+z(2-\lambda)-3 \lambda-1=0$<br/>DR's of normal to the above plane is $(1+\lambda, \lambda-1,2-\lambda)$<br/>By taking option (a) $-1(1+\lambda)+3(\lambda-1)+2(2-\lambda)=0$<br/>$\Rightarrow-1-\lambda+3 \lambda-3+4-2 \lambda=0$<br/>$\Rightarrow 0=0$ which is true.<br/>Hence, option (a) is correct.</div>


title: what-are-the-direction-ratios-of-the-line-of-intersection-of-the-planes-x-3-z-4-and-y-2-z-3
slug: what-are-the-direction-ratios-of-the-line-of-intersection-of-the-planes-x-3-z-4-and-y-2-z-3-90571
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the direction ratios of the line of intersection of the planes $x=3 z+4$ and $y=2 z-3 ?$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\langle 3,2,1\rangle$</span> </div>

answer:
<div class="solution">Let $P_{1}: x-3 z-4=0$ and $P_{2}: y-2 z+3=0$ be two planes Let $a x+b y+c z=d$ be the equation of line. Since, the line of intersection will be perpendicular to the normal of both the planes $\therefore \quad a(1)+b(0)+c(-3)=0$<br/>$\Rightarrow \mathrm{a}-3 \mathrm{c}=0$<br/>and $a(0)+b(1)+c(-2)=0$<br/>$\Rightarrow \mathrm{b}-2 \mathrm{c}=0$<br/>(ii) From (1) and (2) we have<br/>$$<br/>\frac{\mathrm{a}}{3}=\frac{\mathrm{b}}{2}=\frac{\mathrm{c}}{1}<br/>$$<br/>Hence, $\mathrm{d} \cdot \mathrm{Rs}=   &lt; 3,2,1&gt;$</div>


title: what-are-the-effects-of-androgens-on-male-individuals
slug: what-are-the-effects-of-androgens-on-male-individuals-75654
question: <div class="question">What are the effects of androgens on male individuals?</div>
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Stimulation of female secondary sex organs</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Stimulation of muscular growth</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Stimulation of spermatozoa formation</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Stimulation of mammary gland development</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Stimulation of muscular growth</span> </div>

answer:
<div class="solution">Androgens regulate the development, maturation and functions of the male accessory sex organs and stimulate muscular growth, growth of facial and axillary hair, aggressiveness, low pitch of voice, and influence the male sexual behaviour (libido). They also produce anabolic effects on protein and carbohydrate metabolism.</div>


title: what-are-the-equations-of-the-directrices-of-the-ellipse-25-x-2-16-y-2-400
slug: what-are-the-equations-of-the-directrices-of-the-ellipse-25-x-2-16-y-2-400-51525
tags: ['Mathematics', 'Ellipse', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the equations of the directrices of the ellipse $25 x^{2}+16 y^{2}=400 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad 3 x \pm 25=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$3 y \pm 25=0$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$x \pm 15=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$y \pm 25=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 y \pm 25=0$</span> </div>

answer:
<div class="solution">Given equation of ellipse is $25 x^{2}+16 y^{2}=400$ which can be rewritten as<br/>$\frac{x^{2}}{16}+\frac{y^{2}}{25}=1$<br/>We know standard equation of ellipse is<br/>$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$<br/>On comparing given equation with standard equation, we get $a=4$ and $b=5(b&gt;a)$ Equations of the directrices are<br/>$y=\pm \frac{b}{e}=\pm \frac{5}{\sqrt{1-\frac{16}{25}}}=\pm \frac{25}{3} \quad\left(\because e=\sqrt{1-\frac{a^{2}}{b^{2}}}\right)$<br/>$\Rightarrow 3 y \pm 25=0$</div>


tags: ['Biology', 'Human Reproduction']
options: None
correct_option: None
source_db: MarksBatch2_P3.db
title:
what-are-the-events-that-take-place-in-the-ovary-an-uterus-during-follicular-phase-of-the-menstrual-cycle

slug:
what-are-the-events-that-take-place-in-the-ovary-an-uterus-during-follicular-phase-of-the-menstrual-cycle-76264

question:
<div class="question">What are the events that take place in the ovary an uterus during follicular phase of the menstrual cycle.</div>

answer:
<div class="solution">The events involved in the menstrual cycle are menstrual phase, follilcular phase, ovulatory phase and luteal phase. In follicular please there is development of follicles in ovary This phase is also called as proliferative phase as there is proliferation of endometrium in uterus. It last for about 14 days. Lining of the uterus and fallopian tubes proliferates.<br/>A graafian follicle grows, matures and secretes oestrogen. It ruptures to release its egg (secondary oocyte) after about 14 days. The secretion of gonadotropins (LH and FSH) increases gradually during the follicular phase, and stimulates follicular development as well as secretion of estrogens by the growing follicles.<br/>Both LH and FSH attain a peak level in the middle of cycle (about 14th day). Rapid secretion of LH leading to its maximum level during the mid-cycle called LH surge that induces rupture of Graafian follicle and thereby the release of ovum (ovulation). The follicular phase ends with ovulation.</div>


title: what-are-the-fundamental-properties-of-an-element
slug: what-are-the-fundamental-properties-of-an-element-48515
question: <div class="question">What are the fundamental properties of an element?</div>
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Atomic number and mass</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Atomic and ionic radii, ionization enthalpy, electron gain enthalpy, and valence</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Chemical reactivity and metallic character</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Transition metals and main group elements</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Atomic and ionic radii, ionization enthalpy, electron gain enthalpy, and valence</span> </div>

answer:
<div class="solution">The fundamental properties are atomic and ionic radii, ionization enthalpy, electron gain enthalpy, and valence.</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-are-the-individual-numbers-of-primary-secondary-and-tertiary-bromide-across-all-the-structural-isomers-of-c-5-h-11-br

slug:
what-are-the-individual-numbers-of-primary-secondary-and-tertiary-bromide-across-all-the-structural-isomers-of-c-5-h-11-br-36821

question:
<div class="question">What are the individual numbers of  primary, secondary and tertiary bromide across all the structural isomers of C<sub>5</sub>H<sub>11</sub>Br?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">4 primary , 3 secondary and 3 tertiary bromides</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4 primary , 3 secondary and 1 tertiary bromides</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">4 primary , 2 secondary and 2 tertiary bromides</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5 primary , 4 secondary and 2 tertiary bromides</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">4 primary , 3 secondary and 1 tertiary bromides</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>4 primary , 3 secondary and 1 tertiary bromides</div>


title: what-are-the-last-two-digits-of-the-number-9-200
slug: what-are-the-last-two-digits-of-the-number-9-200-85417
question: <div class="question">What are the last two digits of the number $9^{200}$ ?</div>
tags: ['Mathematics', 'Binomial Theorem', 'NDA', 'NDA 2006 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1</span> </div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">19</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">21</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">41</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Using binomial theorem $9^{200}=(1+8)^{200}$<br/>$=1+8.200+\frac{200 \times 199}{2 !} \times 8^{2}+\ldots$<br/>$=1+1600+1273600+\ldots$<br/>From above, it is clear that the last two digits of the number $9^{200}$ are 01 .</div>


title: what-are-the-main-components-of-the-epidermal-tissue-system
slug: what-are-the-main-components-of-the-epidermal-tissue-system-45162
question: <div class="question">What are the main components of the epidermal tissue system?</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Epidermal cells</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Stomata</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Epidermal appendages</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">The epidermal tissue system is made up of epidermal cells, stomata, and the epidermal appendages, which include trichomes and hairs. All three components work together to protect the plant and regulate water loss through the stomata.</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2008 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4,2</span> </div>
source_db: MarksBatch2_P3.db
title:
what-are-the-order-and-degree-respectively-of-the-differential-equation-d-4-y-d-x-4-3-23-7-x-d-3-y-d-x-3-2-8

slug:
what-are-the-order-and-degree-respectively-of-the-differential-equation-d-4-y-d-x-4-3-23-7-x-d-3-y-d-x-3-2-8-50875

question:
<div class="question">What are the order and degree respectively of the differential<br/>equation<br/>$\left.\left(d^{4} y / d x^{4}\right)^{3}\right\}^{2 / 3}-7 x\left(d^{3} y / d x^{3}\right)^{2}=8 ? \quad$</div>

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

answer:
<div class="solution">$\left\{\left(\frac{d^{4} y}{d x^{4}}\right)^{3}\right\}^{\frac{2}{3}}-7 x\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=8$<br/>$\Rightarrow\left(\frac{d^{4} y}{d x^{4}}\right)^{2}-7 x\left(\frac{d^{3} y}{d x^{3}}\right)^{2}=8$<br/>- The order and degree of the given differential equation are 4 and 2 respectively.</div>


title: what-are-the-order-and-degree-respectively-of-the-differential-equation-dx-2-d-2-y-56-dx-dy-13-3
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2008 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2,5</span> </div>
source_db: MarksBatch2_P3.db
slug:
what-are-the-order-and-degree-respectively-of-the-differential-equation-dx-2-d-2-y-56-dx-dy-13-3-25722

question:
<div class="question">What are the order and degree, respectively of the differential<br/>equation $\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3} ?$3</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2,1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">2,5</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2, \frac{5}{6} \quad$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1, \frac{1}{3} \quad$</span> </li> </ul>

answer:
<div class="solution">Given differential equation is:<br/>$\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5 / 6}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{1 / 3}$<br/>Raising both the side to power of 6 , to make it a polynomial of derivatives.<br/>$\Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{6 / 3} \Rightarrow\left(\frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{d} \mathrm{x}^{2}}\right)^{5}=\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}$<br/>Highest derivative has power of $5 .$ So, the order and degree of given differential equation are 2 and 5 respectively.</div>


title: what-are-the-order-and-degree-respectively-of-the-differential-equation-dx-3-d-3-y-2-y-4-dx-dy-5
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3,2</span> </div>
source_db: MarksBatch2_P3.db
slug:
what-are-the-order-and-degree-respectively-of-the-differential-equation-dx-3-d-3-y-2-y-4-dx-dy-5-63811

question:
<div class="question">What are the order and degree, respectively, of the differential<br/>equation $\left(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}\right)^{2}=\mathrm{y}^{4}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{5} ?$</div>

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

answer:
<div class="solution">$\left(\frac{\mathrm{d}^{3} \mathrm{y}}{\mathrm{dx}^{3}}\right)^{2}=\mathrm{y}^{4}+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{5}$<br/>order $=3$, degree $=2$</div>


tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,4</span> </div>
source_db: MarksBatch2_P3.db
title:
what-are-the-order-and-degree-respectively-of-the-differential-equation-whose-solution-is-y-cx-c-2-3-c-32-2-where-c-is-a-parameter

slug:
what-are-the-order-and-degree-respectively-of-the-differential-equation-whose-solution-is-y-cx-c-2-3-c-32-2-where-c-is-a-parameter-42496

question:
<div class="question">What are the order and degree respectively of the differential equation whose solution is $\mathrm{y}=\mathrm{cx}+\mathrm{c}^{2}-3 \mathrm{c}^{3 / 2}+2$, where $\mathrm{c}$ is a parameter?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1,2</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2,2</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1,3</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1,4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Given:<br/>Solution of differential equation is<br/>$$<br/>y=c x+c^{2}-3 c^{\frac{3}{2}}+2<br/>$$<br/>To find order and degree of differential equation, we will find differential equation first. Now differentiating equation (1) w.r.t. $x$ and putting value of $c$ to remove it, we get<br/>$$<br/>\begin{array}{l}<br/>\frac{d y}{d x}=c \\<br/>y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{2}-3\left(\frac{d y}{d x}\right)^{\frac{3}{2}}+2 \\<br/>\Rightarrow(y-2)^{2}+\left(\frac{d y}{d x}\right)^{4}+(2 x-9)\left(\frac{d y}{d x}\right)^{3}<br/>\end{array}<br/>$$<br/>$$<br/>+\left(x^{2}-2 y+4\right)\left(\frac{d y}{d x}\right)^{2}+(-2 x y+4 x) \frac{d y}{d x}=0<br/>$$<br/>Hence order of differential equation is 1 and degree is $4 .$</div>


title: what-are-the-order-and-degree-respectively-of-the-differential-equation-y-x-dx-dy-dy-dx
slug: what-are-the-order-and-degree-respectively-of-the-differential-equation-y-x-dx-dy-dy-dx-76598
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2006 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1,2</span> </div>
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the order and degree respectively of the<br/>differential equation $\mathrm{y}=\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\frac{\mathrm{dx}}{\mathrm{dy}} ?$</div>

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

answer:
<div class="solution">The given differential equation is<br/>$\mathrm{y}=\mathrm{x} \frac{\mathrm{dy}}{\mathrm{dx}}+\frac{\mathrm{dx}}{\mathrm{dy}}$<br/>Multiplying both the sides by $\frac{\mathrm{dy}}{\mathrm{dx}}$<br/>We get $\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) \mathrm{y}=\mathrm{x}\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+1$<br/>$\Rightarrow \quad x\left(\frac{d y}{d x}\right)^{2}-y\left(\frac{d y}{d x}\right)+1=0$<br/>Hence, order and degree of differential equation are 1 and 2.</div>


title: what-are-the-paired-appendages-of-vertebrates
slug: what-are-the-paired-appendages-of-vertebrates-12298
question: <div class="question">What are the paired appendages of Vertebrates?</div>
tags: ['Biology', 'Animal Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Fins</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Limbs</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Both A) and B)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both A) and B)</span> </div>

answer:
<div class="solution">Vertebrates have paired appendages which may be fins or limbs, Fish have fins and Tetrapods have limbs.</div>


title: what-are-the-points-of-intersection-of-the-curve-4-x-2-9-y-2-1-with-its-conjugate-axis
slug: what-are-the-points-of-intersection-of-the-curve-4-x-2-9-y-2-1-with-its-conjugate-axis-43013
tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the points of intersection of the curve $4 \mathrm{x}^{2}-9 y^{2}=1$ with its conjugate axis?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(1 / 2,0)$ and $(-1 / 2,0)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(0,2)$ and $(0,-2)$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(0,3)$ and $(0,-3)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">No such point exists</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">No such point exists</span> </div>

answer:
<div class="solution">The given equation of curve is $4 x^{2}-9 y^{2}=1$<br/>$\Rightarrow \quad \frac{x^{2}}{1 / 4}-\frac{y^{2}}{1 / 9}=1$<br/>This is an equation of a hyperbola which does not<br/>inter sect with conjugate Hence, no point of inter section exists</div>


title: what-are-the-points-on-the-curve-x-2-y-2-2-x-3-0-where-the-tangents-are-parallel-toxaxis
slug: what-are-the-points-on-the-curve-x-2-y-2-2-x-3-0-where-the-tangents-are-parallel-toxaxis-54016
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the points on the curve $x^{2}+y^{2}-2 x-3=0$ where the tangents are parallel tox-axis?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(1,2)$ and $(1,-2)$</span> </div>

answer:
<div class="solution">Given equation curve is $x^{2}+y^{2}-2 x-3=0$<br/>On differentiating we get<br/>$2 x+2 y \frac{d y}{d x}-2=0$<br/>$\Rightarrow y \frac{d y}{d x}=-x+1$<br/>$\Rightarrow \frac{d y}{d x}=-\frac{x+1}{y}$<br/>Since, tangent is parallel to $x$ -axis<br/>$\therefore \frac{d y}{d x}=0 \Rightarrow-\frac{x+1}{y}=0 \Rightarrow x=1$<br/>From equation (1), we have $1+y^{2}-2-3=0 \Rightarrow y=\pm 2$<br/>Hence, required points are $(1,2)$ and $(1,-2)$.</div>


tags: ['Chemistry', 'Aldehydes, Ketones and Carboxylic Acids', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-are-the-products-of-the-reduction-of-aldehydes-and-ketones-by-sodium-borohydride-nabh-4-or-lithium-aluminium-hydride-lialh-4

slug:
what-are-the-products-of-the-reduction-of-aldehydes-and-ketones-by-sodium-borohydride-nabh-4-or-lithium-aluminium-hydride-lialh-4-86695

question:
<div class="question">What are the products of the reduction of aldehydes and ketones by sodium borohydride (NaBH<sub>4</sub>) or lithium aluminium hydride (LiAlH<sub>4</sub>)?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary and secondary alcohols</span> </div>

answer:
<div class="solution">Aldehydes are reduced to primary alcohols, and ketones are reduced to secondary alcohols by sodium borohydride (NaBH<sub>4</sub>) or lithium aluminium hydride (LiAlH<sub>4</sub>).</div>


title: what-are-the-roots-of-the-equation-2-y-2-2-5-y-2-12
slug: what-are-the-roots-of-the-equation-2-y-2-2-5-y-2-12-67187
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the roots of the equation $2(\mathrm{y}+2)^{2}-5(\mathrm{y}+2)=12 ?$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$-7 / 2,2$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-3 / 2,4$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-5 / 3$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$3 / 2,4$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-7 / 2,2$</span> </div>

answer:
<div class="solution">Given equation is $2(y+2)^{2}-5(y+2)=12$ Let $y+2=a$ So, quadratic equation can be rewritten as $2 a^{2}-5 a-12=0$<br/>$\Rightarrow 2 a^{2}-8 a+3 a-12=0$<br/>$\Rightarrow 2 a(a-4)+3(a-4)=0$<br/>$\Rightarrow(2 a+3)(a-4)=0$<br/>$\Rightarrow 2 a+3=0$ or $a-4=0$<br/>$\Rightarrow a=\frac{-3}{2}$ or $a=4$<br/>$\Rightarrow y+2=\frac{-3}{2}$ or $y+2=4$<br/>$\Rightarrow y=\frac{-3}{2}-2$ or $y=2$<br/>$\Rightarrow y=\frac{-7}{2}$ or 2 (Required roots)</div>


title: what-are-the-roots-of-the-equation-x-2-x-6-x-2
slug: what-are-the-roots-of-the-equation-x-2-x-6-x-2-54460
question: <div class="question">What are the roots of the equation $\left|x^{2}-x-6\right|=x+2 ?$</div>
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$-2,1,4$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0,2,4$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0,1,4$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$-2,2,4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-2,2,4$</span> </div>

answer:
<div class="solution">Given, $\left|x^{2}-x-6\right|=x+2$ $\therefore \mathrm{x}^{2}-\mathrm{x}-6=\mathrm{x}+2$ and $\mathrm{x}^{2}-\mathrm{x}-6=-(\mathrm{x}+2)$<br/>$\Rightarrow \mathrm{x}^{2}-2 \mathrm{x}-8=0$<br/>$\Rightarrow \mathrm{x}^{2}=\mathrm{X}=6=-\mathrm{X}=2$<br/>$\Rightarrow \mathrm{x}^{2}-4 \mathrm{x}+2 \mathrm{x}-8=0$<br/>$\Rightarrow \mathrm{x}^{2}=4$<br/>$\Rightarrow \mathrm{x}(\mathrm{x}-4)+2(\mathrm{x}-4)=0$<br/>$\Rightarrow \mathrm{x}-+2,-2$<br/>$\Rightarrow \mathrm{x}=4,-2$<br/>$\therefore \mathrm{x}=-2,2,4$</div>


title: what-are-the-square-roots-of-2-i-i-1
slug: what-are-the-square-roots-of-2-i-i-1-42277
question: <div class="question">What are the square roots of -2 i ? $(i=\sqrt{-1})$</div>
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\pm(1+i)$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\pm(1-i)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pm i$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pm 1$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pm(1-i)$</span> </div>

answer:
<div class="solution">Let $Z=x+i y=-2 i$<br/>Let square root of $z$ be $a+i b$.<br/>Then $\sqrt{x+i y}=a+i b$<br/>$\Rightarrow x+i y=(a+i b)^{2}=\left(a^{2}-b^{2}\right)+(2 a b) i$<br/>$\Rightarrow-2 i=\left(a^{2}-b^{2}\right)+i(2 a b)$<br/>Equating real and imaginary part, we get $a^{2}-b^{2}=0$ and $2 a b=-2 \quad \Rightarrow a b=-1$<br/>Since, $a b   &lt; 0$ therefore<br/>$\sqrt{x+i y}=\pm\left[\sqrt{\frac{\sqrt{x^{2}+y^{2}}+x}{2}}-i \sqrt{\frac{\sqrt{x^{2}+y^{2}}-x}{2}}\right]$<br/>$=\pm\left[\sqrt{\frac{\sqrt{4}+0}{2}}-i \sqrt{\frac{\sqrt{4}-0}{2}}\right]$<br/>$=\pm\left[\sqrt{\frac{2}{2}}-i \sqrt{\frac{2}{2}}\right]=\pm[1-i]$</div>


title: what-are-the-structures-that-subtend-the-sporangia-in-pteridophytes
slug: what-are-the-structures-that-subtend-the-sporangia-in-pteridophytes-72332
question: <div class="question">What are the structures that subtend the sporangia in pteridophytes?</div>
tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Stems</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Roots</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Sporophylls</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Rhizomes</span> </li> </ul>

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

answer:
<div class="solution">The sporangia in pteridophytes are subtended by leaf-like appendages called sporophylls.</div>


title: what-are-the-two-broad-categories-into-which-unit-cells-can-be-divided
slug: what-are-the-two-broad-categories-into-which-unit-cells-can-be-divided-91188
question: <div class="question">What are the two broad categories into which unit cells can be divided?</div>
tags: ['Chemistry', 'Solid State', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary and secondary unit cells</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Simple and complex unit cells</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Primitive and centred unit cells</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Hexagonal and cubic unit cells</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primitive and centred unit cells</span> </div>

answer:
<div class="solution">Unit cells can be broadly divided into two categories: primitive and centred unit cells, as mentioned in the paragraph.</div>


title: what-are-the-two-functions-of-testes
slug: what-are-the-two-functions-of-testes-29128
question: <div class="question">What are the two functions of testes?</div>
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary sex organ and endocrine gland</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Secondary sex organ and endocrine gland</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Primary sex organ and digestive gland</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Secondary sex organ and digestive gland</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary sex organ and endocrine gland</span> </div>

answer:
<div class="solution">Testes performs dual functions as a primary sex organ as well as an endocrine glanD)</div>


tags: ['Biology', 'Human Health and Diseases', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-are-the-two-types-of-lymphocytes-present-in-our-blood-that-carry-out-primary-and-secondary-immune-responses

slug:
what-are-the-two-types-of-lymphocytes-present-in-our-blood-that-carry-out-primary-and-secondary-immune-responses-39017

question:
<div class="question">What are the two types of lymphocytes present in our blood that carry out primary and secondary immune responses?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">B-lymphocytes and T-lymphocytes</span> </div>

answer:
<div class="solution">The primary and secondary immune responses are carried out with the help of two special types of lymphocytes present in our blood, i.e., B-lymphocytes and T-lymphocytes.</div>


title: what-are-the-unit-vectors-parallel-to-x-y-plane-and-perpendicular-to-the-vector-4-i-3-j-k
slug: what-are-the-unit-vectors-parallel-to-x-y-plane-and-perpendicular-to-the-vector-4-i-3-j-k-41923
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the unit vectors parallel to $x y$ -plane and perpendicular to the vector $4 \hat{i}-3 \hat{j}+\hat{k}$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\pm(3 \hat{i}+4 \hat{j}) / 5$</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">$\pm(4 \hat{i}+3 \hat{j}) / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\pm(3 \hat{i}-4 \hat{j}) / 5$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\pm(4 \hat{i}-3 \hat{j}) / 5$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\pm(3 \hat{i}+4 \hat{j}) / 5$</span> </div>

answer:
<div class="solution">A vector whose dot product with the vector $4 \hat{i}-3 \hat{j}+\hat{k}$ is zero and magnitude is 1 , will be the<br/>required vectors. By taking option (a)<br/>$\pm \frac{(3 \hat{i}+4 \hat{j})}{5} \cdot(4 \hat{i}-3 \hat{j}+\hat{k})=\frac{1}{5}(12-12)=0$<br/>Hence, the vector given in option 'a' is the required vector.</div>


title: what-are-the-units-of-standard-enthalpy-change-r-h
slug: what-are-the-units-of-standard-enthalpy-change-r-h-93036
question: <div class="question">What are the units of standard enthalpy change, â<sub>r</sub> H?</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">kJ</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">kJ molâ1</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">kJ/mol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">J</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">kJ molâ1</span> </div>

answer:
<div class="solution">Standard enthalpy  change, â<sub>r</sub>H, is typically expressed in units of kJ molâ1, representing the enthalpy change per mole of substances specified by the equation.</div>


title: what-are-the-values-of-p-which-satisfy-the-equation-0-p-3-x-2-4-x-5-d-x-p-3-2
slug: what-are-the-values-of-p-which-satisfy-the-equation-0-p-3-x-2-4-x-5-d-x-p-3-2-37935
tags: ['Mathematics', 'Definite Integration', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What are the values of $p$ which satisfy the equation $\int_{0}^{P}\left(3 x^{2}+4 x-5\right) d x=p^{3}-2 ? \quad$</div>

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

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

answer:
<div class="solution">Given equation,<br/>$\int_{0}^{p}\left(3 x^{2}+4 x-5\right) d x=p^{3}-2$<br/>$\Rightarrow\left[\frac{3 x^{3}}{3}+\frac{4 x^{2}}{2}-5 x\right]_{0}^{p}=p^{3}-2$<br/>$\Rightarrow p^{3}+2 p^{2}-5 p=p^{3}-2$<br/>$\Rightarrow 2 p^{2}-5 p+2=0$<br/>$\Rightarrow 2 p^{2}-4 p-p+2=0$<br/>$\Rightarrow 2 p(p-2)-1(p-2)=0$<br/>$\Rightarrow(p-2)(2 p-1)=0$<br/>$\Rightarrow p-2=0,2 p-1=0$<br/>Hence the values of $p$ are $\frac{1}{2}$ and 2 .</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
what-are-the-values-of-x-for-which-the-two-vectors-x-2-1-i-x-2-j-x-2-k-and-2-i-x-j-3-k-are-orthogonal

slug:
what-are-the-values-of-x-for-which-the-two-vectors-x-2-1-i-x-2-j-x-2-k-and-2-i-x-j-3-k-are-orthogonal-92568

question:
<div class="question">What are the values of $x$ for which the two vectors<br/>$\left(\mathrm{x}^{2}-1\right) \hat{\mathrm{i}}+(\mathrm{x}+2) \hat{\mathrm{j}}+\mathrm{x}^{2} \hat{\mathrm{k}}$ and $2 \hat{\mathrm{i}}-\mathrm{x} \hat{\mathrm{j}}+3 \hat{\mathrm{k}}$ are orthogonal?</div>

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

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

answer:
<div class="solution">Ifvectors $\left(x^{2}-1\right) \hat{i}+(x+2) \hat{j}+x^{2} \hat{k}$ and $2 \hat{i}-x \hat{j}+3 \hat{k}$ are<br/>orthogonal, then $2\left(x^{2}-1\right)-x(x+2)+3 x^{2}=0$<br/>$\Rightarrow 2 x^{2}-2-x^{2}-2 x+3 x^{2}=0$<br/>$\Rightarrow 4 \mathrm{x}^{2}-2 \mathrm{x}-2=0$<br/>$\Rightarrow\left(2 \mathrm{x}^{2}-\mathrm{x}-1\right)=0$<br/>$\Rightarrow(2 x+1)(x-1)=0$<br/>$\Rightarrow \mathrm{x}=-\frac{1}{2}$ and $\mathrm{x}=1$</div>


tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P3.db
title:
what-are-the-values-of-x-y-satisfying-the-simultaneous-equations-sin-1-x-sin-1-y-3-2-and-cos-1-x-cos-1-y-3

slug:
what-are-the-values-of-x-y-satisfying-the-simultaneous-equations-sin-1-x-sin-1-y-3-2-and-cos-1-x-cos-1-y-3-65443

question:
<div class="question">What are the values of $(\mathrm{x}, \mathrm{y})$ satisfying the simultaneous<br/>equations $\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}$ and $\cos ^{-1} x-\cos ^{-1} y=\frac{\pi}{3} ?$</div>

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

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

answer:
<div class="solution">Given that<br/>$\sin ^{-1} x+\sin ^{-1} y=\frac{2 \pi}{3}$ ...(i)<br/>and $\cos ^{-1} x-\cos ^{-1} y=\frac{\pi}{3}$<br/>$\Rightarrow \frac{\pi}{2}-\sin ^{-1} x-\frac{\pi}{2}+\sin ^{-1} y=\frac{\pi}{3}$<br/>$\left[\right.$ since $\left.\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}\right]$<br/>$\Rightarrow-\sin ^{-1} x+\sin ^{-1} y=\frac{\pi}{3}$ ...(ii)<br/>On solving eq. (i) and (ii), we get<br/>$2 \sin ^{-1} \mathrm{y}=\pi$ and $2 \sin ^{-1} \mathrm{x}=\frac{\pi}{3}$<br/>$\Rightarrow \sin ^{-1} \mathrm{y}=\frac{\pi}{2}$ and $\sin ^{-1} \mathrm{x}=\frac{\pi}{6}$<br/>Hence, $\mathrm{y}=\sin \frac{\pi}{2}$ and $\mathrm{x}=\sin \frac{\pi}{6}$<br/>$\Rightarrow \mathrm{x}=\frac{1}{2}$ and $\mathrm{y}=1$</div>


tags: ['Chemistry', 'Hydrocarbons', 'AP EAMCET', 'AP EAMCET 2018 (22 Apr Shift 1)']
source_db: MarksBatch2_P3.db
title:
what-are-x-and-y-in-the-following-reaction-pent2ene-ii-zn-n-h-2-o-i-o-3-x-y-beginarrayllmulticolumn1cx-multicolumn1cy-endarray

slug:
what-are-x-and-y-in-the-following-reaction-pent2ene-ii-zn-n-h-2-o-i-o-3-x-y-beginarrayllmulticolumn1cx-multicolumn1cy-endarray-34540

question:
<div class="question">What are $X$ and $Y$ in the following reaction?<br/>Pent-2-ene $\underset{\text { (ii) } \mathrm{Zn}_{\mathrm{n} / \mathrm{H}_2 \mathrm{O}}}{\stackrel{\text { (i) } \mathrm{O}_3}{\longrightarrow}} X+Y$<br/>\begin{array}{ll}\multicolumn{1}{c}{X} &amp; \multicolumn{1}{c}{Y}<br/>\end{array}</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_3 \mathrm{CHO}$  $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$  $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CH}_3 \mathrm{CHO}$  $\left(\mathrm{CH}_3\right)_2 \mathrm{CO}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_3 \mathrm{CHO}$ $\mathrm{CH}_3 \mathrm{CHO}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_3 \mathrm{CHO}$  $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CHO}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/sPu9NfLxpFSTT9thE-pAE02N-X46rxZDKzhTd1jGgIY.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-characteristic-feature-describes-the-spatial-arrangement-of-ionsgroups-bound-by-secondary-linkages-in-coordination-compounds

slug:
what-characteristic-feature-describes-the-spatial-arrangement-of-ionsgroups-bound-by-secondary-linkages-in-coordination-compounds-18012

question:
<div class="question">What characteristic feature describes the spatial arrangement of ions/groups bound by secondary linkages in coordination compounds?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It corresponds to different coordination numbers</span> </div>

answer:
<div class="solution">According to Werner's theory, the characteristic spatial arrangement of ions/groups bound by secondary linkages corresponds to different coordination numbers.</div>


title: what-concept-did-alfred-werner-propose-for-metal-ions-in-coordination-compounds
slug: what-concept-did-alfred-werner-propose-for-metal-ions-in-coordination-compounds-55864
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What concept did Alfred Werner propose for metal ions in coordination compounds?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary valence and secondary valence</span> </div>

answer:
<div class="solution">Alfred Werner proposed the concept of primary valence and secondary valence for metal ions in coordination compounds.</div>


tags: ['Chemistry', 'Surface Chemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-conditions-are-necessary-for-the-observation-of-the-tyndall-effect-as-mentioned-in-the-paragraph

slug:
what-conditions-are-necessary-for-the-observation-of-the-tyndall-effect-as-mentioned-in-the-paragraph-39008

question:
<div class="question">What conditions are necessary for the observation of the Tyndall effect, as mentioned in the paragraph?</div>

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

answer:
<div class="solution">According to the paragraph, the Tyndall effect is observed when the refractive indices of the dispersed phase and dispersion medium differ greatly in magnitude.</div>


tags: ['Chemistry', 'Environmental Chemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-could-be-a-possible-reason-for-the-sudden-fish-kill-in-the-lake-with-an-abundance-of-phytoplankton

slug:
what-could-be-a-possible-reason-for-the-sudden-fish-kill-in-the-lake-with-an-abundance-of-phytoplankton-48795

question:
<div class="question">What could be a possible reason for the sudden fish kill in the lake with an abundance of phytoplankton?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The phytoplankton depleted the oxygen in the water.</span> </div>

answer:
<div class="solution">Correct Option is : (B)<br/>The phytoplankton depleted the oxygen in the water.</div>


title: what-defines-minerals-suitable-for-metal-extraction
slug: what-defines-minerals-suitable-for-metal-extraction-75201
question: <div class="question">What defines minerals suitable for metal extraction?</div>
tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'NEET']
answer: <div class="solution">Only a few minerals, termed ores, are viable for extracting metals.</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Abundance</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Viability as ores</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Color</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Hardness</span> </li> </ul>

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


title: what-determines-the-spatial-arrangement-of-ionsgroups-bound-by-secondary-linkages
slug: what-determines-the-spatial-arrangement-of-ionsgroups-bound-by-secondary-linkages-99802
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What determines the spatial arrangement of ions/groups bound by secondary linkages?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It corresponds to different coordination numbers</span> </div>

answer:
<div class="solution">The spatial arrangement of ions/groups bound by secondary linkages corresponds to different coordination numbers in Werner's theory.</div>


title: what-did-henry-moseleys-work-demonstrate-about-atomic-number-and-atomic-mass
slug: what-did-henry-moseleys-work-demonstrate-about-atomic-number-and-atomic-mass-21881
tags: ['Chemistry', 'Classification of Elements and Periodicity in Properties', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What did Henry Moseley's work demonstrate about atomic number and atomic mass?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Atomic number is a more fundamental property than atomic mass.</span> </div>

answer:
<div class="solution">Henry Moseley showed that the atomic number is a more fundamental property of an element than its atomic mass.A plot of âv (where v is frequency of X-rays emitted) against atomic number (Z) gave a straight line and not the plot of vs atomic mass. He thereby showed that the atomic number is a more fundamental property of an element than its atomic mass</div>


title: what-distinction-did-avogadro-make-between-atoms-and-molecules-in-his-proposal
slug: what-distinction-did-avogadro-make-between-atoms-and-molecules-in-his-proposal-34505
tags: ['Chemistry', 'Some Basic Concepts of Chemistry', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What distinction did Avogadro make between atoms and molecules in his proposal?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Atoms and molecules are the same.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Atoms cannot be combined.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Atoms are larger than molecules.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Atoms are smaller than molecules.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Atoms and molecules are the same.</span> </div>

answer:
<div class="solution">Avogadro made a distinction between atoms and molecules, which is now understandable, implying that he recognized that atoms and molecules are the same.</div>


title: what-distinguishes-an-open-system-from-a-closed-system-in-thermodynamics
slug: what-distinguishes-an-open-system-from-a-closed-system-in-thermodynamics-60437
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What distinguishes an open system from a closed system in thermodynamics?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">An open system has no boundaries, while a closed system has boundaries.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">An open system allows energy exchange, while a closed system does not.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">An open system allows both energy and matter exchange, while a closed system allows only energy exchange.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">An open system has fixed boundaries, while a closed system has flexible boundaries.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">An open system allows both energy and matter exchange, while a closed system allows only energy exchange.</span> </div>

answer:
<div class="solution">The key distinction between open and closed systems is that open systems allow both energy and matter exchange with the surroundings, while closed systems only allow energy exchange.</div>


title: what-does-100-volume-hydrogen-peroxide-mean-in-terms-of-its-oxygen-production-at-stp
slug: what-does-100-volume-hydrogen-peroxide-mean-in-terms-of-its-oxygen-production-at-stp-51389
tags: ['Chemistry', 'Hydrogen', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does "100 volume" hydrogen peroxide mean in terms of its oxygen production at STP?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">One milliliter of solution gives 100 mL of oxygen at STP</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">One milliliter of solution gives 10 mL of oxygen at STP</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">One milliliter of solution gives 50 mL of oxygen at STP</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">One milliliter of solution gives 200 mL of oxygen at STP</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">One milliliter of solution gives 100 mL of oxygen at STP</span> </div>

answer:
<div class="solution">"100 volume" hydrogen peroxide means that one milliliter of the solution will give 100 mL of oxygen at standard temperature and pressure (STP).</div>


title: what-does-a-positive-value-of-standard-electrode-potential-indicate
slug: what-does-a-positive-value-of-standard-electrode-potential-indicate-76089
question: <div class="question">What does a positive value of standard electrode potential indicate?</div>
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The species on the right is more stable than hydrogen 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><li class=""> <span class="option-label">B</span> <span class="option-data">The species on the left is more stable than hydrogen gas.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The species on the right is less stable than hydrogen gas.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The species on the left is less stable than hydrogen gas.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The species on the right is more stable than hydrogen gas.</span> </div>

answer:
<div class="solution">If the standard electrode potential of an electrode is greater than zero (or positive) then its reduced form is more stable compared to hydrogen gas.</div>


tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P3.db
title:
what-does-an-equation-of-the-first-degree-containing-one-arbitrary-parameter-passing-through-a-fixed-point-represent

slug:
what-does-an-equation-of-the-first-degree-containing-one-arbitrary-parameter-passing-through-a-fixed-point-represent-37880

question:
<div class="question">What does an equation of the first degree containing one arbitrary parameter passing through a fixed point represent?</div>

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

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

answer:
<div class="solution">From the given information, we have an equation of the first degree which contains one arbitraryparameter. Therefore the required equation represents a straight line</div>


title: what-does-any-deviation-from-the-standard-shape-of-ecg-indicate
slug: what-does-any-deviation-from-the-standard-shape-of-ecg-indicate-49009
question: <div class="question">What does any deviation from the standard shape of ECG indicate?</div>
tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Normalcy</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Abnormality or disease</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Heart rate</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cardiac cycle</span> </li> </ul>

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

answer:
<div class="solution">Since ECGs obtained from different individuals have roughly the same shape for a given lead configuration, any deviation from this shape indicates a possible abnormality or disease.</div>


title: what-does-e-cell-eo-cell-2303rt-2f-log-k-c-provide-a-relationship-between
slug: what-does-e-cell-eo-cell-2303rt-2f-log-k-c-provide-a-relationship-between-70561
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does E<sub>(cell)</sub> = Eo<sub>(cell)</sub> - 2.303RT / 2F log K<sub>c</sub> provide a relationship between?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Equilibrium constant and standard potential of the cell</span> </div>

answer:
<div class="solution">E<sub>(cell)</sub> = Eo<sub>(cell)</sub> - 2.303RT / 2F log K<sub>c</sub>provides a relationship between equilibrium constant and standard potential of the cell, as mentioned in the paragraph.</div>


title: what-does-eo-cell-represent
slug: what-does-eo-cell-represent-22808
question: <div class="question">What does Eo<sub>(cell)</sub> represent?</div>
tags: ['Chemistry', 'Electrochemistry', 'NEET']
answer: <div class="solution">Eo<sub>(cell)</sub> is the cell's electromotive force.</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The cell's electromotive force</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">The cell's equilibrium constant</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The cell's standard Gibbs energy</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The cell's charge passed</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The cell's electromotive force</span> </div>


title: what-does-iupac-stand-for-in-the-context-of-coordination-chemistry-nomenclature
slug: what-does-iupac-stand-for-in-the-context-of-coordination-chemistry-nomenclature-89882
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does IUPAC stand for in the context of Coordination Chemistry nomenclature?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">International Union of Pure and Applied Chemistry</span> </div>

answer:
<div class="solution">IUPAC stands for the International Union of Pure and Applied Chemistry, which provides recommendations for coordination chemistry nomenclature.</div>


title: what-does-knowledge-of-molecular-structure-help-in-understanding-and-predicting
slug: what-does-knowledge-of-molecular-structure-help-in-understanding-and-predicting-88295
tags: ['Chemistry', 'General Organic Chemistry', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does knowledge of molecular structure help in understanding and predicting?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Properties of organic compounds</span> </div>

answer:
<div class="solution">Knowledge of fundamental concepts of molecular structure helps in understanding and predicting the properties of organic compounds.</div>


title: what-does-nernsts-equation-represent-for-the-electrode-reaction-involving-mnaq-and-ms
slug: what-does-nernsts-equation-represent-for-the-electrode-reaction-involving-mnaq-and-ms-68235
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does Nernst's equation represent for the electrode reaction involving Mn+(aq) and M(s)?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The standard hydrogen electrode potential for the reaction</span> </div>

answer:
<div class="solution">Nernst's equation represents the electrode potential at any concentration measured with respect to the standard hydrogen electrode for the electrode reaction involving Mn+(aq) and M(s).</div>


title: what-does-stp-stand-for-in-the-context-of-gases
slug: what-does-stp-stand-for-in-the-context-of-gases-91206
question: <div class="question">What does STP stand for in the context of gases?</div>
tags: ['Chemistry', 'States of Matter', 'NEET']
answer: <div class="solution">STP stands for Standard Temperature and Pressure.</div>
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Standard Test Parameters</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Standard Temperature and Pressure</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">Specific Thermal Properties</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Standard Testing Procedures</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Standard Temperature and Pressure</span> </div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P3.db
title:
what-does-the-decreasing-standard-electrode-potential-imply-as-we-go-from-top-to-bottom-in-the-series

slug:
what-does-the-decreasing-standard-electrode-potential-imply-as-we-go-from-top-to-bottom-in-the-series-94740

question:
<div class="question">What does the decreasing standard electrode potential imply as we go from top to bottom in the series?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The reducing power of the species on the left increases.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The oxidizing power of the species on the left increases.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The reducing power of the species on the right increases.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Both B and 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">Both B and C</span> </div>

answer:
<div class="solution">The paragraph explains that as we go from top to bottom in the series, the standard electrode potential decreases and with this, decreases the oxidising power of the species on the left and increases the reducing power of the species on the right hand side of the reaction.</div>


title: what-does-the-differential-equation-y-d-x-d-y-x-a-where-a-is-a-constant-represent
slug: what-does-the-differential-equation-y-d-x-d-y-x-a-where-a-is-a-constant-represent-46702
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does the differential equation $y \frac{d y}{d x}+x=a$ (where $a$ is a constant) represent? $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A set of circles having centre on the $X$ -axis</span> </div>

answer:
<div class="solution">Given differential equation is<br/>$\frac{y d y}{d x}+x=a$<br/>$\Rightarrow \quad y d y+x d x=a d x$<br/>Integrate on both sides, we get<br/>$$<br/>\int y d y+\int x d x=\int a d x<br/>$$<br/>$\Rightarrow \quad \frac{y^{2}}{2}+\frac{x^{2}}{2}=a x+c$<br/>where $c$ is a constant of integration. $\Rightarrow \quad y^{2}+x^{2}-2 a x=c$<br/>This represents a circle whose centre is on the $X$ -axis.</div>


title: what-does-the-differential-equation-y-d-x-d-y-x-k-where-k-is-a-constant-represents
slug: what-does-the-differential-equation-y-d-x-d-y-x-k-where-k-is-a-constant-represents-62050
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2010 (Phase 2)']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does the differential equation $y \frac{d y}{d x}+x=k$ (where k<br/>is a constant) represents?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A family of circles having centre on the $\mathrm{x}$ -axis.</span> </div>

answer:
<div class="solution">Given differential equation is $\mathrm{y} \frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{x}=\mathrm{k}$<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow \quad y \frac{d y}{d x}=k-x \\<br/>\Rightarrow \quad y d y=(k-x) d x<br/>\end{array}<br/>$$<br/>Integrate on both side, we get<br/>$$<br/>\int \mathrm{ydy}=\int(\mathrm{k}-\mathrm{x}) \mathrm{d} \mathrm{x}<br/>$$<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow \quad \frac{\mathrm{y}^{2}}{2}=\mathrm{kx}-\frac{\mathrm{x}^{2}}{2}+\mathrm{c} \\<br/>\Rightarrow \mathrm{x}^{2}+\mathrm{y}^{2}-2 \mathrm{kx}-\mathrm{c}=0<br/>\end{array}<br/>$$<br/>Which represents a family of circles whose centre lies on the $\mathrm{x}$ -axis.</div>


title: what-does-the-equation-the-universe-the-system-the-surroundings-represent
slug: what-does-the-equation-the-universe-the-system-the-surroundings-represent-16655
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P3.db
question:
<div class="question">What does the equation "The universe = The system + The surroundings" represent?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The relationship between the universe, system, and surroundings</span> </div>

answer:
<div class="solution">This equation represents the relationship between the universe, system, and surroundings in thermodynamics.</div>


title: what-does-the-equation-x-3-y-x-y-3-x-y-0-represent
slug: what-does-the-equation-x-3-y-x-y-3-x-y-0-represent-87739
question: <div class="question">What does the equation $x^{3} y+x y^{3}-x y=0$ represent?</div>
tags: ['Mathematics', 'Pair of Lines', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A pair of straight lines only</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">A pair of straight lines and a circle</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 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">A rectangular hyperbola only</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A rectangular hyperbola and a circle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">A pair of straight lines and a circle</span> </div>

answer:
<div class="solution">$\begin{array}{ll}\text { Given equation } \\ x^{3} y+x y^{3}-x y &amp; =0\end{array}$<br/>$\Rightarrow x y\left(x^{2}+y^{2}\right)=x y$<br/>$\Rightarrow x y\left(x^{2}+y^{2}-1\right)=0$<br/>$\Rightarrow x^{2}+y^{2}=1, x y=0$<br/>Above equations represent a pair of straight lines and a circle.</div>


title: what-does-the-equation-x-d-y-y-d-x-represent
slug: what-does-the-equation-x-d-y-y-d-x-represent-19075
question: <div class="question">What does the equation $x d y=y d x$ represent?</div>
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P3.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">A family of circles</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A family of parabolas</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">A family of hyperbolas</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">A family of straight lines</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">A family of straight lines</span> </div>

answer:
<div class="solution">Given equation is $x d y=y d x$ By separating the variable we get <br/>$\frac{d y}{y}=\frac{d x}{x}$<br/>On integrating both sides, we get<br/>$\int \frac{d y}{y}=\int \frac{d x}{x}$<br/>$\Rightarrow \log y=\log x+\log c$<br/>$\Rightarrow y=c x$<br/>It represents a family of straight lines.</div>


