# questions

tags: ['Chemistry', 'Thermodynamics (C)', 'BITSAT', 'BITSAT 2022']
source_db: MarksBatch2_P2.db
title:
standard-entropy-of-x-2-y-2-and-x-y-2-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-x-y-3-h-30-kj-to-be-at-equilibrium-the-

slug:
standard-entropy-of-x-2-y-2-and-x-y-2-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-x-y-3-h-30-kj-to-be-at-equilibrium-the-72848

question:
<div class="question">Standard entropy of $X_2, Y_2$ and $X Y_2$ are 60,40 and $50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, respectively. For the reaction, $\frac{1}{2} X_2+\frac{3}{2} Y_2 \longrightarrow X Y_3, \Delta H=-30 \mathrm{~kJ}$, to be at equilibrium, the temperature will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"> <br/>$1250 \mathrm{~K}$
<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"> <br/>$500 \mathrm{~K}$
<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"> <br/>$750 \mathrm{~K}$
<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"> <br/>$1000 \mathrm{~K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"> <br/>$750 \mathrm{~K}$
<br/></span> </div>

answer:
<div class="solution">$\Delta S=S\left(X Y_3\right)-\frac{1}{2} S\left(X_2\right)-\frac{3}{2} S\left(Y_2\right)$
<br/>$=50-30-60=-40 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$
<br/>$\Delta H=-30 \mathrm{~kJ}=-3000 \mathrm{~J}$
<br/>$\Delta G=\Delta H-T \Delta S$
<br/>At equilibrium,
<br/>$\Delta G=0$
<br/>$T=\frac{\Delta H}{\Delta S}=\frac{-3000}{-40}=750 \mathrm{~K}$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main', 'JEE Main 2008']
source_db: MarksBatch2_P2.db
title:
standard-entropy-of-x-2-y-2-and-x-y-3-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-x-y-3-h-30-kj-to-be-at-equilibrium-the-

slug:
standard-entropy-of-x-2-y-2-and-x-y-3-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-x-y-3-h-30-kj-to-be-at-equilibrium-the-41778

question:
<div class="question">Standard entropy of $X_2, Y_2$ and $X Y_3$ are 60,40 and $50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, respectively. For the reaction, $\frac{1}{2} X_2+\frac{3}{2} Y_2 \rightarrow X Y_3, \Delta \mathrm{H}=-30 \mathrm{~kJ}$, to be at equilibrium, the temperature will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$1250 \mathrm{~K}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$500 \mathrm{~K}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$750 \mathrm{~K}$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>$1000 \mathrm{~K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$750 \mathrm{~K}$<br/></span> </div>

answer:
<div class="solution">$$<br/>\begin{aligned}<br/>&amp; \frac{1}{2} X_2+\frac{3}{2} Y_2 \longrightarrow X Y_3 \\<br/>&amp; \Delta S_{\text {reaction }}=50-\left(\frac{3}{2} \times 40+\frac{1}{2} \times 60\right)=-40 \mathrm{Jmol}^{-1} \\<br/>&amp; \Delta G=\Delta H-T \Delta S \\<br/>&amp; \text { at equilibrium } \Delta G=0<br/>\end{aligned}<br/>$$<br/><br/>$$<br/>\begin{aligned}<br/>&amp; \Delta \mathrm{H}=\mathrm{T} \Delta \mathrm{S} \\<br/>&amp; 30 \times 10^3=\mathrm{T} \times 40 \\<br/>&amp; \Rightarrow \mathrm{T}=750 \mathrm{~K}<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'VITEEE', 'VITEEE 2016']
source_db: MarksBatch2_P2.db
title:
standard-entropy-of-x-2-y-2-and-x-y-3-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-xy-3-h-30-kj-to-be-at-equilibrium-the-t

slug:
standard-entropy-of-x-2-y-2-and-x-y-3-are-6040-and-50-jk-1-mol-1-respectively-for-the-reaction-2-1-x-2-2-3-y-2-xy-3-h-30-kj-to-be-at-equilibrium-the-t-16664

question:
<div class="question">Standard entropy of $X_{2}, Y_{2}$ and $X Y_{3}$ are 60,40 and $50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, respectively. For the reaction, $\frac{1}{2} \mathrm{X}_{2}+\frac{3}{2} \mathrm{Y}_{2} \rightarrow \mathrm{XY}_{3}, \Delta \mathrm{H}=-30 \mathrm{~kJ}$, to be at equilibrium, the temperature will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1250 \mathrm{~K}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$500 \mathrm{~K}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$750 \mathrm{~K}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$1000 \mathrm{~K}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$750 \mathrm{~K}$</span> </div>

answer:
<div class="solution">For a reaction to be at equilibrium $\Delta \mathrm{G}=0$. Since $\Delta \mathrm{G}=\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}$ so at equilibrium $\Delta \mathrm{H}-\mathrm{T} \Delta \mathrm{S}=0$
<br/>or $\Delta \mathrm{H}=\mathrm{T} \Delta \mathrm{S}$
<br/>For the reaction
<br/>$$
<br/>\frac{1}{2} \mathrm{X}_{2}+\frac{3}{2} \mathrm{Y}_{2} \longrightarrow \mathrm{XY}_{3} ; \quad \Delta \mathrm{H}=-30 \mathrm{~kJ}
<br/>$$
<br/>(given)
<br/>Calculating $\Delta \mathrm{S}$ for the above reaction, we get
<br/>$$
<br/>\begin{array}{l}
<br/>\Delta S=50-\left[\frac{1}{2} \times 60+\frac{3}{2} \times 40\right] \mathrm{JK}^{-1} \\
<br/>=50-(30+60) \mathrm{JK}^{-1}=-40 \mathrm{JK}^{-1} \\
<br/>\text { At equilibrium, } \mathrm{T} \Delta \mathrm{S}=\Delta \mathrm{H}
<br/>\end{array}
<br/>$$
<br/>$[\because \Delta \mathrm{G}=0]$
<br/>$\therefore \mathrm{T} \times(-40)=-30 \times 1000[\because 1 \mathrm{~kJ}=1000 \mathrm{~J}]$
<br/>or $\quad \mathrm{T}=\frac{-30 \times 1000}{-40}$ or $750 \mathrm{~K}$</div>


tags: ['Chemistry', 'Hydrocarbons', 'NEET', 'NEET 2008 (Screening)']
source_db: MarksBatch2_P2.db
title:
standard-free-energies-of-formation-in-kj-mol-at-298-k-are-2372-3944-and-82-for-h-2-o-l-co-2-g-and-pentane-g-respectively-the-value-of-e-cell-0-for-th

slug:
standard-free-energies-of-formation-in-kj-mol-at-298-k-are-2372-3944-and-82-for-h-2-o-l-co-2-g-and-pentane-g-respectively-the-value-of-e-cell-0-for-th-11946

question:
<div class="question">Standard free energies of formation (in $\mathrm{kJ} / \mathrm{mol}$ ) at $298 \mathrm{~K}$ are $-237.2,-394.4$ and -8.2 for $\mathrm{H}_2 \mathrm{O}(l) \mathrm{CO}_2(g)$ and pentane $(g)$, respectively. The value of $E_{\text {cell }}^0$ for the pentane-oxygen fuel cell is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$1.968 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2.0968 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$1.0968 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.0968 \mathrm{~V}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.0968 \mathrm{~V}$</span> </div>

answer:
<div class="solution">\(\begin{aligned}
<br/>&amp; \mathrm{C}_5 \mathrm{H}_{12(g)}+8 \mathrm{O}_{2(9)} \longrightarrow 5 \mathrm{CO}_{2(g)}+6 \mathrm{H}_2 \mathrm{O}_{(\mathrm{e})} \\
<br/>&amp; \therefore \Delta \mathrm{G}_r=5\left(\Delta \mathrm{G}_r\right)_{\mathrm{CO}_2}+6\left(\Delta \mathrm{G}_{\mathrm{r}}\right)_{\mathrm{H}_2 \mathrm{O}}-\left(\Delta \mathrm{G}_{\mathrm{r}}\right)_{\text {Pentane }} \\
<br/>&amp; =5(-5394.4)+6(-237.2)-(-8.2) \\
<br/>&amp; =-1972-1423.2+8.2 \\
<br/>&amp; \Delta \mathrm{G}_{\mathrm{R}}=-3387 \mathrm{~kJ} / \mathrm{mole} \\
<br/>&amp; \mathrm{C}_5^{\frac{-12}{5}} \mathrm{H}_{12} \longrightarrow 5 \stackrel{4}{\mathrm{C}_2}
<br/>\end{aligned}\)
<br/>For 5 carbon atoms, there is a change of electrons from - 12 to 20
<br/>\(\begin{aligned}
<br/>&amp; \therefore \text { No. of electrons involved }=32 \mathrm{e}^{-} \\
<br/>&amp; \Delta G_r=-3387 \times 10^3=-32 \times E^{\circ} \times 96500 \\
<br/>&amp; E^{\circ}=1.097 V
<br/>\end{aligned}\)</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET', 'NEET 2008 (Mains)']
source_db: MarksBatch2_P2.db
title:
standard-free-energies-of-formation-in-kj-mol-at-298-k-are-2372-3944-and-82-for-h-2-o-l-co-2-g-and-pentane-g-respectively-the-value-of-e-cell-for-the-

slug:
standard-free-energies-of-formation-in-kj-mol-at-298-k-are-2372-3944-and-82-for-h-2-o-l-co-2-g-and-pentane-g-respectively-the-value-of-e-cell-for-the-96840

question:
<div class="question">Standard free energies of formation (in $\mathrm{kJ} / \mathrm{mol}$ ) at $298 \mathrm{~K}$ are $-237.2,-394.4$ and -8.2 for $\mathrm{H}_2 \mathrm{O}(\mathrm{l}), \mathrm{CO}_2(\mathrm{~g})$ and pentane $(\mathrm{g})$ respectively. The value of $\mathrm{E}_{\text {cell }}^{\circ}$ for the pentaneoxygen fuel cell is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.0968 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.968 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.0968 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.0968 \mathrm{~V}$</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.0968 \mathrm{~V}$</span> </div>

answer:
<div class="solution">After calculation $\Delta \mathrm{G}^{\circ}$, use the formula, $\Delta \mathrm{G}^{\circ}=-n F E^{\circ}$<br/>Here, $n=32$ is taken because balanced equation is<br/>$$<br/>\mathrm{C}_5 \mathrm{H}_{12}+8 \mathrm{O}_2 \rightarrow 5 \mathrm{CO}_2+6 \mathrm{H}_2 \mathrm{O}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'AP EAMCET', 'AP EAMCET 2017 (26 Apr Shift 2)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P2.db
title:
standard-gibbs-energy-change-in-kj-mol-1-for-a-galvanic-cell-a-s-b-aq-3-a-aq-3-b-s-that-has-standard-emf-of-05-v-is-f-96500-c-mol-1

slug:
standard-gibbs-energy-change-in-kj-mol-1-for-a-galvanic-cell-a-s-b-aq-3-a-aq-3-b-s-that-has-standard-emf-of-05-v-is-f-96500-c-mol-1-40789

question:
<div class="question">Standard Gibbs energy change in $\mathrm{kJ} \mathrm{mol}^{-1}$ for a galvanic cell<br/>$\mathrm{A}_{(\mathrm{s})}+\mathrm{B}_{(\mathrm{aq})}^{3+} \longrightarrow \mathrm{A}_{(\mathrm{aq})}^{3+}+\mathrm{B}_{(\mathrm{s})}$ that has standard emf of $0.5 \mathrm{~V}$ is : $\left(\mathrm{F}=96500 \mathrm{C} \mathrm{mol}^{-1}\right)$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">-193.50</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">-96.50</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">-144.75</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">-289.50</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">-144.75</span> </div>


title: standard-hydrogen-electrode-she-is-a
slug: standard-hydrogen-electrode-she-is-a-65249
question: <div class="question">Standard hydrogen electrode (SHE) is a</div>
tags: ['Chemistry', 'Electrochemistry', 'MHT CET', 'MHT CET 2019 (Shift 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary reference electrode</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 reference electrode</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Metal â sparingly soluble salt electrode</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Metal â metal ion electrode</span> </li> </ul>

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

answer:
<div class="solution">Standard hydrogen electrode (SHE) is primary reference electrode. SHE is represented by <math><mi>P</mi><mi>t</mi><mfenced separators="|"><mrow><mi>s</mi></mrow></mfenced><mfenced close="|" open="|" separators="|"><mrow><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>g</mi></mrow></mfenced><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup><mfenced separators="|"><mrow><mi>a</mi><mi>q</mi></mrow></mfenced><mo>,</mo></math> is assigned a zero potential at all temperatures corresponding to reaction. <br/><math><msup><mrow><mi>H</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>(</mo><mi>a</mi><mi>q</mi><mo>)</mo><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo></mrow></msup><mo>â</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><mi>g</mi><mo>)</mo></math></div>


tags: ['Chemistry', 'Thermodynamics (C)', 'COMEDK', 'COMEDK 2014']
source_db: MarksBatch2_P2.db
title:
standard-molar-enthalpies-of-formation-of-caco-3-s-cao-s-and-co-2-g-are-120692-kj-mol-1-63509-kj-mol-1-and-39351-kj-mol-1-respectively-the-r-h-for-dec

slug:
standard-molar-enthalpies-of-formation-of-caco-3-s-cao-s-and-co-2-g-are-120692-kj-mol-1-63509-kj-mol-1-and-39351-kj-mol-1-respectively-the-r-h-for-dec-98939

question:
<div class="question">Standard molar enthalpies of formation of $\mathrm{CaCO}_{3}(s), \mathrm{CaO}(s)$ and $\mathrm{CO}_{2}(g)$ are $-1206.92 \mathrm{~kJ} \mathrm{~mol}^{-1},-635.09 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $-393.51 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The $\Delta_{r} H$, for decomposition of $\mathrm{CaCO}_{3}(s)$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$178.3 \mathrm{~kJ} \mathrm{~mol}^{-1} \quad$</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><li class=""> <span class="option-label">B</span> <span class="option-data">$-178.3 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1448.5 \mathrm{~kJ} \mathrm{~mol}^{-1} \quad$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-1448.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$178.3 \mathrm{~kJ} \mathrm{~mol}^{-1} \quad$</span> </div>

answer:
<div class="solution">$\mathrm{CaCO}_{3}(s) \longrightarrow \mathrm{CaO}(s)+\mathrm{CO}_{2}(g)$<br/>$$<br/>\begin{aligned}<br/>\Delta_{r} H^{\circ} &amp;=\Delta_{f} H^{\circ}(\mathrm{CaO})+\Delta_{f} H^{\circ}\left(\mathrm{CO}_{2}\right)-\Delta_{f} H^{\circ}\left(\mathrm{CaCO}_{3}\right) \\<br/>&amp;=-635.09+(-393.51)-(-1206.92) \\<br/>&amp;=178.3 \mathrm{~kJ} \mathrm{~mol}^{-1} .<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P2.db
title:
standard-molar-enthalpy-of-formation-f-h-is-just-a-special-case-of-enthalpy-of-reaction-r-h-is-the-r-h-for-the-following-reaction-same-as-f-h-give-rea

slug:
standard-molar-enthalpy-of-formation-f-h-is-just-a-special-case-of-enthalpy-of-reaction-r-h-is-the-r-h-for-the-following-reaction-same-as-f-h-give-rea-98390

question:
<div class="question">Standard molar enthalpy of formation, â<sub>f</sub>H<sup>â</sup>is just a special case of enthalpy of reaction, â<sub>r</sub>H<sup>â</sup>.   Is the â<sub>r</sub>H<sup>â</sup>for the following reaction same as â<sub>f</sub>H<sup>â</sup>? Give reason for your answer.   CaO(s) + CO<sub>2</sub>(g) â CaCO<sub>3</sub>(s);  â<sub>f</sub>H<sup>â</sup>= â178.3 kJ mol<sup>â1</sup></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Yes,since CaCO<sub>3</sub>has been formed from other compounds and not from its constituent elements.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Yes,since CaO has been formed from other compounds and not from its constituent elements.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">No,since CaCO<sub>3</sub>has been formed from other compounds and not from its constituent elements.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">No,since CaO has been formed from other compounds and not from its constituent elements.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">No,since CaCO<sub>3</sub>has been formed from other compounds and not from its constituent elements.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>No,since CaCO<sub>3</sub>has been formed from other compounds and not from its constituent elements.</div>


title: standard-molar-enthalpy-of-formation-of-c-o-2-is-equal-to
slug: standard-molar-enthalpy-of-formation-of-c-o-2-is-equal-to-58522
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">Standard molar enthalpy of formation of <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> is equal to</div>

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

answer:
<div class="solution">Standard molar enthalpy of formation of <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> is equal to the standard molar enthalpy of combustion of carbon (graphite).</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch2_P2.db
title:
standard-reduction-electrode-potentials-of-three-metals-ab-and-c-are-respectively-05-v-30-v-and-12-v-the-reducing-powers-of-these-metals-are

slug:
standard-reduction-electrode-potentials-of-three-metals-ab-and-c-are-respectively-05-v-30-v-and-12-v-the-reducing-powers-of-these-metals-are-73472

question:
<div class="question">Standard reduction electrode potentials of three metals A,B and C are respectively + 0.5 V, â 3.0 V and â 1.2 V. The reducing powers of these metals are:</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mtext mathvariant="normal">B</mtext><mo>&gt;</mo><mtext>C</mtext><mo>&gt;</mo><mtext>A</mtext></math></span> </div>

answer:
<div class="solution">More the reduction potential, more is the power to get itself reduced or lesser is reducing power or greater is oxidizing power</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2003']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P2.db
title:
standard-reduction-electrode-potentials-of-three-metals-abc-are-respectively-05-v-30-v-12-v-the-reducing-powers-of-these-metals-are

slug:
standard-reduction-electrode-potentials-of-three-metals-abc-are-respectively-05-v-30-v-12-v-the-reducing-powers-of-these-metals-are-16474

question:
<div class="question">Standard reduction electrode potentials of three metals A,B\&amp;C are respectively $+0.5 \mathrm{~V},-3.0 \mathrm{~V} \&amp;-1.2 \mathrm{~V}$. The reducing, powers of these metals are</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$\mathrm{B}&gt;\mathrm{C}&gt;\mathrm{A}$</span> </div>


tags: ['Chemistry', 'Electrochemistry', 'NEET', 'NEET 2012 (Mains)']
source_db: MarksBatch2_P2.db
title:
standard-reduction-potentials-of-the-half-reactions-are-given-below-f-2-g-2-e-2-f-a-q-cl-2-g-2-e-2-cl-a-q-br-2-l-2-e-2-br-a-q-i-2-s-2-e-2-i-a-q-e-285-

slug:
standard-reduction-potentials-of-the-half-reactions-are-given-below-f-2-g-2-e-2-f-a-q-cl-2-g-2-e-2-cl-a-q-br-2-l-2-e-2-br-a-q-i-2-s-2-e-2-i-a-q-e-285-48939

question:
<div class="question">Standard reduction potentials of the half reactions are given below<br/>$$<br/>\begin{array}{ll}<br/>\mathrm{F}_2(g)+2 e^{-} \longrightarrow 2 \mathrm{~F}^{-}(a q) ; &amp; E^{\circ}=+2.85 \mathrm{~V} \\<br/>\mathrm{Cl}_2(g)+2 e^{-} \longrightarrow 2 \mathrm{Cl}^{-}(a q) ; &amp; E^{\circ}=+1.36 \mathrm{~V} \\<br/>\mathrm{Br}_2(l)+2 e^{-} \longrightarrow 2 \mathrm{Br}^{-}(a q) ; &amp; E^{\circ}=+1.06 \mathrm{~V} \\<br/>\mathrm{I}_2(s)+2 e^{-} \longrightarrow 2 \mathrm{I}^{-}(a q) ; &amp; E^{\circ}=+0.53 \mathrm{~V}<br/>\end{array}<br/>$$<br/>The strongest oxidising and reducing agents respectively are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{F}_2$ and $\mathrm{I}^{-}$</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">B</span> <span class="option-data">$\mathrm{Br}_2$ and $\mathrm{Cl}^{-}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{Cl}_2$ and $\mathrm{Br}^{-}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{Cl}_2$ and $\mathrm{I}_2$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{F}_2$ and $\mathrm{I}^{-}$</span> </div>

answer:
<div class="solution">Higher the value of standard reduction potential, stronger will be the oxidising agent. Therefore, $\mathrm{F}_2$ will act as strongest oxidising agent.<br/>Similarly lower the value of standard reduction potential, stronger will be the reducing agent. Therefore, $\mathrm{I}^{-}$will act as strongest reducing agent.</div>


title: state-as-to-why-sodium-is-found-to-be-more-useful-than-potassium
slug: state-as-to-why-sodium-is-found-to-be-more-useful-than-potassium-85042
question: <div class="question">State as to why sodium is found to be more useful than potassium?</div>
tags: ['Chemistry', 's Block Elements', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Sodium is more abundant in nature compared to potassium.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Sodium has a lower ionization energy and is less reactive than potassium.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Sodium forms more stable compounds with common elements than potassium.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Sodium is cheaper and easier to obtain than potassium.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Sodium is cheaper and easier to obtain than potassium.</span> </div>

answer:
<div class="solution">Correct Option is : (D)<br/>Sodium is cheaper and easier to obtain than potassium.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-for-every-chemical-reaction-at-equilibrium-standard-gibbs-energy-of-reaction-is-zero-statement-2-at-constant-temperature-and-pressure-chem

slug:
statement-1-for-every-chemical-reaction-at-equilibrium-standard-gibbs-energy-of-reaction-is-zero-statement-2-at-constant-temperature-and-pressure-chem-12427

question:
<div class="question">Statement 1 For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.<br/>Statement 2 At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement 1 is false, Statement 2 is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">At equilibrium, its free energy change, is zero and for a spontaneous process, $\Delta G &lt; 0$ but at equilibrium standard free energy is not zero.<br/>Analysis of the Paragraph<img src="https://cdn-question-pool.getmarks.app/pyq/jee_advanced/tHsQvv8Onx_VMm13JsbgLaMcMgI1uOlms0UbX1PPBmw.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Current Electricity', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta-1

slug:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta-1-21860

question:
<div class="question">Statement $1 \mathrm{In}$ a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.<br/>and Statement 2 Resistance of a metal increase with increase in temperature.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement 1 is false, Statement 2 is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">With increase in temperature, the value of unknown resistance will increase.<br/>In balanced Wheatstone bridge condition, $\frac{R}{X}=\frac{l_1}{l_2}$<br/>Here, $R=$ value of standard resistance,<br/>$X=$ value of unknown resistance .<br/>To take null point at same point or $\frac{l_1}{l_2}$ to remain unchanged, $\frac{R}{X}$ should also remain unchanged. Therefore, if $X$ is increasing $R$ should also increase.<br/>$\therefore$ correct option is (d).</div>


tags: ['Physics', 'Current Electricity', 'JEE Advanced', 'JEE Advanced 2008 (Paper 1)']
source_db: MarksBatch2_P2.db
title:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta

slug:
statement-1-in-a-meter-bridge-experiment-null-point-for-an-unknown-resistance-is-measured-now-the-unknown-resistance-is-put-inside-an-enclosure-mainta-47628

question:
<div class="question">Statement $1 \mathrm{In}$ a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.<br/>and Statement 2 Resistance of a metal increase with increase in temperature.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is true, Statement 2 is not a correct explanation for Statement 1.<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>Statement 1 is true, Statement 2 is false.<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>Statement 1 is false, Statement 2 is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">With increase in temperature, the value of unknown resistance will increase.<br/>In balanced Wheatstone bridge condition, $\frac{R}{X}=\frac{l_1}{l_2}$<br/>Here, $R=$ value of standard resistance,<br/>$X=$ value of unknown resistance .<br/>To take null point at same point or $\frac{l_1}{l_2}$ to remain unchanged, $\frac{R}{X}$ should also remain unchanged. Therefore, if $X$ is increasing $R$ should also increase.<br/>$\therefore$ correct option is (d).</div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch2_P2.db
title:
statement-a-atherosclerosis-is-a-type-of-coronary-artery-diseases-cad-statement-b-monocytes-are-the-least-abundant-granulocytes

slug:
statement-a-atherosclerosis-is-a-type-of-coronary-artery-diseases-cad-statement-b-monocytes-are-the-least-abundant-granulocytes-65706

question:
<div class="question">Statement A: Atherosclerosis is a type of Coronary Artery Diseases (CAD).<br/> <br/>
Statement B: Monocytes are the least abundant granulocytes.</div>

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

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

answer:
<div class="solution">Coronary Artery Disease (CAD)<br/><br/>- It is often referred to as atherosclerosis, which affects the vessels that supply blood to the heart muscle.<br/><br/>- In this condition, the lumen of arteries gradually becomes narrower due to the deposits of calcium, fat, cholesterol, and fibrous tissues.<br/><br/>Basophils are the least common leukocytes, accounting for less than one percent of the total leukocyte count. </div>


tags: ['Mathematics', 'Inverse Trigonometric Functions', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-if-1-x-0-then-cos-sin-1-x-1-x-2-statement-ii-if-1-x-0-then-sin-cos-1-x-1-x-2-which-one-of-the-following-is-correct-in-respect-of-the-aobve

slug:
statement-i-if-1-x-0-then-cos-sin-1-x-1-x-2-statement-ii-if-1-x-0-then-sin-cos-1-x-1-x-2-which-one-of-the-following-is-correct-in-respect-of-the-aobve-48092

question:
<div class="question">Statement $\mathbf{I}:$ If $-1 \leq x   &lt; 0$, then $\cos \left(\sin ^{-1} x\right)=-\sqrt{1-x^{2}}$<br/>Statement II : If $-1 \leq x &lt; 0$, then $\sin \left(\cos ^{-1} x\right)=\sqrt{1-x^{2}}$<br/>Which one of the following is correct in respect of the aobve statements?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Both statements I and II are independently correct and statement II is the correct explanation of statement I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Both statements I and II are independently correct but statement II is not the correct explanation of statement I</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Statement I is correct but statement II is false.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Statement I is false but statement II is correct.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Statement I is false but statement II is correct.</span> </div>

answer:
<div class="solution">$\quad(\mathrm{I}) \cos \left(\sin ^{-1} x\right)=\cos \left(\cos ^{-1} \sqrt{1-x^{2}}\right)=\sqrt{1-x^{2}}$<br/>$($ II $) \sin \left(\cos ^{-1} x\right)=\sin \left(\sin ^{-1} \sqrt{1-x^{2}}\right)=\sqrt{1-x^{2}}$<br/>Hence, statement I is false and II is true.</div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
title:
statement-i-red-data-book-has-a-record-of-all-animals-statement-ii-exsitu-conservation-is-the-best-method-to-protect-endangered-species

slug:
statement-i-red-data-book-has-a-record-of-all-animals-statement-ii-exsitu-conservation-is-the-best-method-to-protect-endangered-species-99631

question:
<div class="question">Statement I: Red data book has a record of all animals.<br/>
Statement II: Ex-situ conservation is the best method to protect endangered species.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">If both statement I and statement II are true and statement II is a correct explanation of statement I</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">If both statement I and statement II are true but statement II is not a correct explanation of  statement I</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">If statement I is true but statement II is false.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">If statement I is false but statement II is true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">Red data book contains a record of species of an area which are known to be in danger. When there are situations where an animal or plant is endangered or threatened and needs urgent measures to save it from extinction, ex-situ (off-site) conservation is the desirable approach.</div>


tags: ['Mathematics', 'Definite Integration', 'JEE Main', 'JEE Main 2013 (07 Apr)']
source_db: MarksBatch2_P2.db
title:
statement-i-the-value-of-the-integral-6-3-d-x-1-tan-x-is-equal-to-6-statement-ii-a-b-f-x-d-x-a-b-f-a-b-x-d-x

slug:
statement-i-the-value-of-the-integral-6-3-d-x-1-tan-x-is-equal-to-6-statement-ii-a-b-f-x-d-x-a-b-f-a-b-x-d-x-32238

question:
<div class="question"><p><strong>Statement - I : </strong>The value of the integral <math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>tan</mi><mo> </mo><mi>x</mi></msqrt></mrow></mfrac></math> is equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>π</mi><mn>6</mn></mfrac><mo>.</mo></math></p><p><strong>Statement - II : </strong><math xmlns="http://www.w3.org/1998/Math/MathML"><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mi>f</mi><mfenced><mi>x</mi></mfenced><mi>d</mi><mi>x</mi><mo>=</mo><munderover><mo>∫</mo><mi>a</mi><mi>b</mi></munderover><mi>f</mi><mfenced><mrow><mi>a</mi><mo>+</mo><mi>b</mi><mo>-</mo><mi>x</mi></mrow></mfenced><mi>d</mi><mi>x</mi><mo>.</mo></math></p></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> is true; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is false.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> is false; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is true.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> true; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is true; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is a correct explanation for Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math>.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> is true; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is true; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is not a correct explanation for Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math>.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> is false; Statement - <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is true.</span> </div>

answer:
<div class="solution"><p>Statement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>II</mi></math> is a standard property of definite integrals.</p><p>For statement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">I</mi></math> : <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>tan</mi><mo> </mo><mi>x</mi></msqrt></mrow></mfrac><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><mrow><mi>d</mi><mi>x</mi></mrow><mrow><mn>1</mn><mo>+</mo><msqrt><mi>cot</mi><mo> </mo><mi>x</mi></msqrt></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><msqrt><mi>tan</mi><mo> </mo><mi>x</mi></msqrt><mrow><mn>1</mn><mo>+</mo><msqrt><mi>tan</mi><mo> </mo><mi>x</mi></msqrt></mrow></mfrac><mi>d</mi><mi>x</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><mrow><msqrt><mi>sin</mi></msqrt><mi>x</mi></mrow><mrow><msqrt><mi>cos</mi></msqrt><mi>x</mi><mo>+</mo><msqrt><mi>sin</mi><mi>x</mi></msqrt></mrow></mfrac><mi>d</mi><mi>x</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mfrac><mrow><msqrt><mi>cos</mi></msqrt><mi>x</mi></mrow><mrow><msqrt><mi>cos</mi></msqrt><mi>x</mi><mo>+</mo><msqrt><mi>sin</mi><mi>x</mi></msqrt></mrow></mfrac><mi>d</mi><mi>x</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>I</mi><mo>=</mo><munderover><mo>∫</mo><mrow><mi>π</mi><mo>/</mo><mn>6</mn></mrow><mrow><mi>π</mi><mo>/</mo><mn>3</mn></mrow></munderover><mi>d</mi><mi>x</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mi>I</mi><mo>=</mo><mfrac><mi>π</mi><mn>3</mn></mfrac><mo>-</mo><mfrac><mi>π</mi><mn>6</mn></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mo>=</mo><mfrac><mi>π</mi><mrow><mn>1</mn><mn>2</mn></mrow></mfrac></math></p><p>Hence, statement <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi></math> is false.</p></div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
statement-i-y-tan-1-x-1-1-is-an-increasing-function-of-x-statement-ii-d-x-d-y-is-positive-for-all-values-of-x-which-one-of-the-following-is-correct-in

slug:
statement-i-y-tan-1-x-1-1-is-an-increasing-function-of-x-statement-ii-d-x-d-y-is-positive-for-all-values-of-x-which-one-of-the-following-is-correct-in-13229

question:
<div class="question">Statement I : $y=-\tan ^{-1}\left(x^{-1}\right)+1$ is an increasing function of $x$ Statement II : $\frac{d y}{d x}$ is positive for all values of $x$. Which one of the following is correct in respect of the above statements?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Both statements I and II are independently correct and statement II is the correct explanation of statement 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">B</span> <span class="option-data">Both statements I and II are independently correct but statement $\Pi$ is not the correct explanation of statement $\mathrm{I}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Statement I is correct but statement II is false.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Statement I is false but statement II is correct.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both statements I and II are independently correct and statement II is the correct explanation of statement I</span> </div>

answer:
<div class="solution">Let $y=-\tan ^{-1}\left(x^{-1}\right)+1$<br/>$\therefore \quad \frac{d y}{d x}=-\frac{1}{1+x^{-2}}(-1) x^{-2}=\frac{1}{1+x^{2}}$<br/>Since, $\frac{d y}{d x}$ is positive for all values of $x$. Therefore, $y$ is an increasing function of $x$ Hence, option (a) is correct.</div>


tags: ['Biology', 'Plant Kingdom', 'NEET']
source_db: MarksBatch2_P2.db
title:
statementi-the-mesophyll-of-pinus-shows-no-distinction-as-spongy-mesophyll-and-palisade-statementii-parenchymatous-cells-are-present-in-the-mesophyll-

slug:
statementi-the-mesophyll-of-pinus-shows-no-distinction-as-spongy-mesophyll-and-palisade-statementii-parenchymatous-cells-are-present-in-the-mesophyll-52439

question:
<div class="question">Statement-I: The mesophyll of <em>Pinus</em> shows no distinction as spongy mesophyll and palisade.<br/> <br/>
Statement-II: Parenchymatous cells are present in the mesophyll of <em>Pinus</em>.</div>

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

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

answer:
<div class="solution">Within the hypodermis of <em>Pinus</em> leaf is the parenchymatous mesophyll. It is comparted and shows no differentiation into palisade and spongy tissues. It consists of thin-walled cells which contain numerous chloroplasts and abundant starch. The mesophyll thus functions as the chlorophyll bearing tissue which manufactures food for plants.</div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
title:
statementi-tiger-is-not-an-endangered-animal-in-india-statementii-project-tiger-was-launched-to-improve-the-tiger-population

slug:
statementi-tiger-is-not-an-endangered-animal-in-india-statementii-project-tiger-was-launched-to-improve-the-tiger-population-40557

question:
<div class="question">Statement-I: Tiger is not an endangered animal in India.<br/> <br/>
Statement-II: Project Tiger was launched to improve the tiger population.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both the statements are true</span> </div>

answer:
<div class="solution">There are 21 tiger reserves in India. To save the tiger from extinction in India Project Tiger was launched on April 1, 1973. This project planned to create tiger reserves in selected areas of India. Due to this effort considerable improvement has been observed in tiger population.</div>


title: stepup-transformers-are-used-for
slug: stepup-transformers-are-used-for-41469
question: <div class="question">Step-up transformers are used for</div>
tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">increasing electrical power.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">decreasing electrical power.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">decreasing voltage.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">increasing voltage.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">increasing voltage.</span> </div>

answer:
<div class="solution"><blockquote><p>In the step-up transformer, the output (secondary <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi mathvariant="normal">s</mi></msub></math>) voltage is more than the input (primary <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi mathvariant="normal">p</mi></msub></math>) voltage. The ratio of the secondary and primary voltage is given by,</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>V</mi><mi mathvariant="normal">s</mi></msub><msub><mi>V</mi><mi mathvariant="normal">p</mi></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mi mathvariant="normal">s</mi></msub><msub><mi>N</mi><mi mathvariant="normal">p</mi></msub></mfrac></math>; where <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi mathvariant="normal">s</mi></msub></math> number of turns in the secondary coil and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi mathvariant="normal">p</mi></msub></math> is the number of turns in the primary coil.</p><p>In step-up transformer <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>N</mi><mi mathvariant="normal">s</mi></msub><mo>&gt;</mo><msub><mi>N</mi><mi mathvariant="normal">p</mi></msub></math>, hence <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi mathvariant="normal">s</mi></msub><mo>&gt;</mo><msub><mi>V</mi><mi mathvariant="normal">p</mi></msub></math>.</p><p>Thus, step up transformers are used for increasing voltage.</p></blockquote></div>


title: stirredtank-bioreactors-have-been-designed-for-3
slug: stirredtank-bioreactors-have-been-designed-for-3-86777
question: <div class="question">Stirred-tank bioreactors have been designed for:</div>
tags: ['Biology', 'Biotechnology - Principles and Processes', 'NEET', 'NEET 2016 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Purification of product</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Addition of preservatives to the product</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Availability of oxygen throughout the process</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Ensuring anaerobic conditions in the culture vessel</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Availability of oxygen throughout the process</span> </div>

answer:
<div class="solution"><p>Stirred-tank bioreactor is provided with a stirrer for the availability of oxygen throughout the process.</p><p>In stirred tank bioreactors, the air is bubbled through the reactor using a sparger. Air bubbles increase the surface area for transfer of oxygen and result in better mixing.</p><p>The function of the agitation system is to increase mass transfer rates through the bulk liquid and bubble boundary layers by providing proper mixing.</p></div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2011 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$68.0$</span> </div>
source_db: MarksBatch2_P2.db
title:
students-of-three-sections-of-a-class-having-3030-and-40-students-appeared-for-a-test-of-100-marks-the-arithmetic-means-of-the-marks-of-the-three-sect

slug:
students-of-three-sections-of-a-class-having-3030-and-40-students-appeared-for-a-test-of-100-marks-the-arithmetic-means-of-the-marks-of-the-three-sect-69745

question:
<div class="question">Students of three sections of a class, having 30,30 and 40 students appeared for a test of 100 marks. The arithmetic means of the marks of the three sections are $72.2,69.0$ and $64.1$ in that order. What is the arithmetic mean of the marks of all the students of the three sections?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$66.6$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$67.3$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$68.0$</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">$70.6$</span> </li> </ul>

answer:
<div class="solution">Required Arithmetic mean $=\frac{(30 \times 72.2)+(30 \times 69.0)+(40 \times 64.1)}{100}$<br/>$=\frac{6800}{100}=68$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$84.4$</span> </div>
source_db: MarksBatch2_P2.db
title:
students-of-two-schools-appeared-for-a-common-test-carrying-100-marks-the-arithmetic-means-of-their-marks-for-school-i-and-ii-are-82-and-86-respective

slug:
students-of-two-schools-appeared-for-a-common-test-carrying-100-marks-the-arithmetic-means-of-their-marks-for-school-i-and-ii-are-82-and-86-respective-27017

question:
<div class="question">Students of two schools appeared for a common test carrying 100 marks. The arithmetic means of their marks for school I and II are 82 and 86 respectively. If the number of students of school II is $1.5$ times the number of students of school I, what is the arithmetic mean of the marks of all the students of both the schools? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$84.0$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$84.2$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$84.4$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">This cannot be calculated with the given data</span> </li> </ul>

answer:
<div class="solution">Let the number of students of school $I=x$ Number of students of School II $=1.5 \mathrm{x}$ As given Mean of marks for school $I=82$ and mean of marks for school II $=86$<br/>Combined mean $=\frac{x \times 82+1.5 x \times 86}{x+1.5 x}$<br/>$=\frac{\mathrm{x}(82+129)}{2.5 \mathrm{x}}=\frac{211}{2.5}=84.4$</div>


tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch2_P2.db
title:
study-the-following-statements-and-select-the-option-with-correct-statements-i-a-lion-eating-a-deer-and-a-sparrow-feeding-on-grains-are-ecologically-s

slug:
study-the-following-statements-and-select-the-option-with-correct-statements-i-a-lion-eating-a-deer-and-a-sparrow-feeding-on-grains-are-ecologically-s-75223

question:
<div class="question">Study the following statements and select the option with correct statements.<br/> <br/>
(i) A lion eating a deer and a sparrow feeding on grains are ecologically similar in being consumers.<br/> <br/>
(ii) Predator star fish Pisaster helps in maintaining species diversity of some invertebrates.<br/> <br/>
(iii) Predators ultimately lead to the extinction of prey species.<br/> <br/>
(iv) Production of chemicals such as nicotine by the plants are metabolic disorders.</div>

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

answer:
<div class="solution">Predator and prey evolve together. Predators are prudent in nature, they never over exploits there prey as in absence of the prey predator will also become extinct. The prey is part of the predator's environment. Nicotine is an alkaloid found in the night shade family of plants (Solanaceae) that constitutes approximately <math><mn>0.6</mn><mo>â</mo><mn>3.0</mn><mi mathvariant="normal">%</mi></math> of dry weight of tobacco. These are not metabolic disorder products but are secondary metabolites or metabolic wastes.</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'AP EAMCET', 'AP EAMCET 2004']
source_db: MarksBatch2_P2.db
title:
study-the-following-table-beginarrayccc-hline-beginarrayctext-buffer-text-solution-endarray-beginarrayctext-volume-in-mathrmml-text-of-text-0m-weak-ac-1

slug:
study-the-following-table-beginarrayccc-hline-beginarrayctext-buffer-text-solution-endarray-beginarrayctext-volume-in-mathrmml-text-of-text-0m-weak-ac-1-14287

question:
<div class="question">Study the following table:<br/>\begin{array}{c|c|c}<br/>\hline \begin{array}{c}\text { Buffer } \\<br/>\text { Solution }\end{array} &amp; \begin{array}{c}\text { Volume (in } \mathrm{mL} \text { ) of } \\<br/>\text { 0.M Weak acid }\end{array} &amp; \begin{array}{c}\text { Volume (in } \mathrm{mL} \text { ) of } \\<br/>0.1 \mathrm{M} \text { sodium salt of } \\<br/>\text { weak acid }\end{array} \\<br/>\hline I. &amp; 4.0 &amp; 4.0 \\<br/>II. &amp; 4.0 &amp; 40.0 \\<br/>III. &amp; 40.0 &amp; 4.0 \\<br/>IV. &amp; 0.1 &amp; 10.0 \\<br/>\hline<br/>\end{array}<br/>Which of the two sets of butter solutions have least $\mathrm{pH}$ ?</div>

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

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

answer:
<div class="solution">For a buffer solution, $\mathrm{pH}$ is given by Henderson, equation,<br/>$$<br/>\mathrm{pH}=\mathrm{pKa}+\log \frac{[\text { salt }]}{[\text { acid }]}<br/>$$<br/>Hence, $\mathrm{pH}$ is least when concentration of acid is higher than that of salt.</div>


tags: ['Chemistry', 'Ionic Equilibrium', 'TS EAMCET', 'TS EAMCET 2004']
source_db: MarksBatch2_P2.db
title:
study-the-following-table-beginarrayccc-hline-beginarrayctext-buffer-text-solution-endarray-beginarrayctext-volume-in-mathrmml-text-of-text-0m-weak-ac

slug:
study-the-following-table-beginarrayccc-hline-beginarrayctext-buffer-text-solution-endarray-beginarrayctext-volume-in-mathrmml-text-of-text-0m-weak-ac-34238

question:
<div class="question">Study the following table:<br/>\begin{array}{c|c|c}<br/>\hline \begin{array}{c}\text { Buffer } \\<br/>\text { Solution }\end{array} &amp; \begin{array}{c}\text { Volume (in } \mathrm{mL} \text { ) of } \\<br/>\text { 0.M Weak acid }\end{array} &amp; \begin{array}{c}\text { Volume (in } \mathrm{mL} \text { ) of } \\<br/>0.1 \mathrm{M} \text { sodium salt of } \\<br/>\text { weak acid }\end{array} \\<br/>\hline I. &amp; 4.0 &amp; 4.0 \\<br/>II. &amp; 4.0 &amp; 40.0 \\<br/>III. &amp; 40.0 &amp; 4.0 \\<br/>IV. &amp; 0.1 &amp; 10.0 \\<br/>\hline<br/>\end{array}<br/>Which of the two sets of butter solutions have least $\mathrm{pH}$ ?</div>

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

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

answer:
<div class="solution">For a buffer solution, $\mathrm{pH}$ is given by Henderson, equation,<br/>$$<br/>\mathrm{pH}=\mathrm{pKa}+\log \frac{[\text { salt }]}{[\text { acid }]}<br/>$$<br/>Hence, $\mathrm{pH}$ is least when concentration of acid is higher than that of salt.</div>


title: sugar-and-amino-acids-are
slug: sugar-and-amino-acids-are-13064
question: <div class="question">Sugar and amino acids are:</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Primary metabolites</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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 metabolites</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary metabolites</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">Primary metabolites</span> </div>

answer:
<div class="solution">Sugar and amino acids are primary metabolites. Sugars are building blocks of starch, glycogen, etc., while amino acids are the building blocks of proteins.<br/>primary metabolites also referred to as a central metabolite. while secondary metabolite usually has an important ecological function or related function like defence for plants.</div>


title: suggest-a-reagent-for-the-following-conversion
slug: suggest-a-reagent-for-the-following-conversion-36792
tags: ['Chemistry', 'Alcohols Phenols and Ethers']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
question:
<div class="question">Suggest a reagent for the following conversion.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/4RY3TfEm-X9X_h1ffuoo8qjWFSGp39JjuTvfpA2J0TA.original.fullsize.png"/><br/></div>

answer:
<div class="solution">The given reactant is <br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/WW7kE3DfmX0kWs2gsIbo-BknV3syYkGYkg0GLkm-0SQ.original.fullsize.png"/><br/><br/>which is a secondary<br/>alcohol. Secondary alcohol $&gt;\mathrm{CHOH})$ on oxidation by $\mathrm{CrO}_3$ or pyridinium chlorochromate gives ketones without carrying out oxidation at the doule bond.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/_Cy8u_kTYWVLhU36n5L63AdAd8ZmfnCHQbBDS00LKrs.original.fullsize.png"/><br/></div>


tags: ['Biology', 'Reproductive Health']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
suggest-some-important-steps-that-you-would-recommend-to-be-taken-to-improve-the-reproductive-health-standards-in-india

slug:
suggest-some-important-steps-that-you-would-recommend-to-be-taken-to-improve-the-reproductive-health-standards-in-india-39862

question:
<div class="question">Suggest some important steps that you would recommend to be taken to improve the reproductive health standards in India.</div>

answer:
<div class="solution">Following are the measures needed to improve the reproductive health standards in India.<br/>(i) By providing professional expertise and infrastructural facilities to attain reproductive health.<br/>(ii) By educating people about safe and hygienic sexual practices, birth control methods, care of pregnant mothers, importance of breast feeding and safeguard against STDs.<br/>(iii) By introduction of sex education in schools in order to provide proper information to the young minds about sex-related aspects.<br/>(iv) By the help of audio-visual and print media, one should create awareness among people about reproduction related aspects.<br/>(v) Bythe awareness of problems due to population explosion, social evils like sex-abuse and sex-related crimes.<br/>(vi) By statutory ban on amniocentesis to legally check female foeticides.</div>


tags: ['Chemistry', 'Biomolecules', 'AP EAMCET', 'AP EAMCET 2023 (16 May Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">B, D</span> </div>
source_db: MarksBatch2_P2.db
title:
sulphur-containing-amino-acids-of-the-following-are-beginarraycccc-serine-cysteine-lysine-methionine-a-b-c-d-endarray

slug:
sulphur-containing-amino-acids-of-the-following-are-beginarraycccc-serine-cysteine-lysine-methionine-a-b-c-d-endarray-70395

question:
<div class="question">Sulphur containing amino acids of the following are <br/>\begin{array}{cccc} <br/>Serine &amp; Cysteine &amp; Lysine &amp; methionine \\<br/>A &amp; B &amp; C &amp; D<br/>\end{array}</div>

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

answer:
<div class="solution">S-Containing amino acids $=$ Cysteine, methionine.<br/>$\mathrm{OH}$ - Containing amino acid $=$ Serine<br/>$\mathrm{NH}_2$ - Containing amino acid = Lysine .</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
sum-of-first-n-natural-numbers-is-given-by-2-n-n-1-what-is-the-geometric-mean-of-the-series-1-2-4-8-2-n

slug:
sum-of-first-n-natural-numbers-is-given-by-2-n-n-1-what-is-the-geometric-mean-of-the-series-1-2-4-8-2-n-35751

question:
<div class="question">Sum of first $n$ natural numbers is given by $\frac{n(n+1)}{2} .$ What is the geometric mean of the series $1,2,4,8, \ldots ., 2^{n}$ ?</div>

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

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

answer:
<div class="solution">Geometric mean $=\sqrt[n+1]{1.2 .4 .8 \ldots 2^{n}}$<br/>$\left(\because\right.$ there are $(n+1)$ multiples from $2^{\circ}$ to $\left.2^{n}\right)$<br/>$=\sqrt[n+1]{2^{0} \cdot 2^{1} \cdot 2^{2} \cdot 2^{3} \ldots 2^{n}}$<br/>$=\sqrt[n+1]{2^{1+2+3+\ldots+n}}=\sqrt[n+1]{2 \frac{n(n+1)}{2}}$<br/>$=\left[2^{ \left.\frac{n(n+1)}{2}\right]^{\frac{1}{n+1}}=2^{\frac{n}{2}}}\right.$</div>


title: suppose-1-and-2-are-two-distinct-cube-roots-of-unity-different-from-1-then-what-is-1-2-2-equal-to
tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2016 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">-3</span> </div>
source_db: MarksBatch2_P2.db
slug:
suppose-1-and-2-are-two-distinct-cube-roots-of-unity-different-from-1-then-what-is-1-2-2-equal-to-31639

question:
<div class="question">Suppose $\omega_{1}$ and $\omega_{2}$ are two distinct cube roots of unity<br/>different from 1 . Then what is $\left(\omega_{1}-\omega_{2}\right)^{2}$ equal to?</div>

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

answer:
<div class="solution">Cube root of unity are 1, $-\frac{1}{2} \pm \frac{\sqrt{3}}{2}$ i $\omega_{1}$ and $\omega_{2}$ are two distinct cube roots of unity different from 1 .<br/>$\omega_{1}=-\frac{1}{2}+\frac{\sqrt{3}}{2} i, \omega_{2}=-\frac{1}{2}-\frac{\sqrt{3}}{2} i$<br/>$\left(\omega_{1}-\omega_{2}\right)^{2}=\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i+\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{2}$<br/>$=(\sqrt{3} i)^{2}=3 i^{2}$<br/>$\left(\omega_{1}-\omega_{2}\right)^{2}=-3$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2006']
source_db: MarksBatch2_P2.db
title:
suppose-a-population-a-has-100-observations-101-102-200-and-another-population-b-has-100-observations-151-152-250-if-v-a-and-v-b-represent-the-varianc

slug:
suppose-a-population-a-has-100-observations-101-102-200-and-another-population-b-has-100-observations-151-152-250-if-v-a-and-v-b-represent-the-varianc-28657

question:
<div class="question">Suppose a population $A$ has 100 observations $101,102, \ldots, 200$, and another population $B$ has 100 observations $151,152, \ldots, 250$. If $V_A$ and $V_B$ represent the variances of the two populations, respectively, then $\frac{V_A}{V_B}$ is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>1<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>9/4<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>4/9<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>2/3</span> </li> </ul>

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

answer:
<div class="solution">$\sigma_x^2=\frac{\sum d_1^2}{n}$. (Here deviations are taken from the mean)<br/>Since $A$ and $B$ both has 100 consecutive integers, therefore both have same standard deviation and hence the variance.<br/>$\therefore \frac{V_A}{V_B}=1\left(\right.$ As $\sum d_i^2$ is same in both the cases).</div>


title: suppose-cos-a-is-given-if-only-one-value-of-cos-2-a-is-possible-then-a-must-be
slug: suppose-cos-a-is-given-if-only-one-value-of-cos-2-a-is-possible-then-a-must-be-15304
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">Suppose $\cos \mathrm{A}$ is given. If only one value of $\cos \left(\frac{\mathrm{A}}{2}\right)$ is possible, then A must be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">An odd multiple of $90^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">A multiple of $90^{\circ}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">An odd multiple of $180^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">A multiple of $180^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">An odd multiple of $180^{\circ}$</span> </div>

answer:
<div class="solution">Given, $\cos \frac{\mathrm{A}}{2}$ has only one value.<br/>We know, $\cos A=2 \cos ^{2} \frac{\mathrm{A}}{2}-1$<br/>$\Rightarrow 2 \cos ^{2} \frac{\mathrm{A}}{2}=\cos \mathrm{A}+1 \Rightarrow \cos \frac{\mathrm{A}}{2}=\sqrt{\frac{\cos \mathrm{A}+1}{2}}$<br/>Since, $\cos \frac{\mathrm{A}}{2}$ is single value, $\frac{\cos \mathrm{A}+1}{2}=0$<br/>$\Rightarrow \cos \mathrm{A}=-1$<br/>So, $\mathrm{A}$ is an odd multiple of $180^{\circ}$.</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
suppose-f-mathbbr-rightarrow-mathbbr-be-given-by-fxleftbeginarraycc1-quad-text-if-x1-eleftx101rightx12-sin-frac1x1endarrayright-text-if-x-neq-1-text-t-1

slug:
suppose-f-mathbbr-rightarrow-mathbbr-be-given-by-fxleftbeginarraycc1-quad-text-if-x1-eleftx101rightx12-sin-frac1x1endarrayright-text-if-x-neq-1-text-t-1-26730

question:
<div class="question">Suppose \(f: \mathbb{R} \rightarrow \mathbb{R}\) be given by \(f(x)=\left\{\begin{array}{cc}1, \quad \text { if } x=1 \\ e^{\left(x^{10}-1\right)}+(x-1)^2 \sin \frac{1}{x-1}\end{array}\right., \text { if } x \neq 1 \text { then }\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(f^{\prime}(1)\) does not 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">\(f^{\prime}(1)\) exists and is zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(f^{\prime}(1)\) exist and is 9</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(f^{\prime}(1)\) exists and is 10</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(f^{\prime}(1)\) does not exist</span> </div>

answer:
<div class="solution">Hint: \(f: R \rightarrow R f(x)=\left\{\begin{array}{cc} 1 &amp; \text { if } x=1 &amp; \\  e^{\left(x^{10}-1\right)} &amp;+(x-1)^2  &amp;\cdot \sin \left(\frac{1}{x-1}\right) \text { if } x \neq 1\end{array}\right.\)<br/>\(\begin{aligned}<br/>&amp; f\left(1^{-}\right)=1+0=1 \\<br/>&amp; f\left(1^{+}\right)=1+0=1 \\<br/>&amp; f(1)=1 \\<br/>&amp; \therefore \quad f(x) \text { is continuous at } x=1 \\<br/>&amp; f^{\prime}(x)=\left\{e^{\left(x^{10}-1\right)} \cdot\left(10 x^5\right)+2(x-1) \cdot \sin \left(\frac{1}{x-1}\right)-(x-1)^2 \cdot \cos \left(\frac{1}{x-1}\right) \cdot\left(\frac{1}{x-1}\right)^2\right\}<br/>\end{aligned}\)<br/>which does not exist.</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'WBJEE', 'WBJEE 2023']
source_db: MarksBatch2_P2.db
title:
suppose-f-mathbbr-rightarrow-mathbbr-be-given-by-fxleftbeginarraycc1-quad-text-if-x1-eleftx101rightx12-sin-frac1x1endarrayright-text-if-x-neq-1-text-t

slug:
suppose-f-mathbbr-rightarrow-mathbbr-be-given-by-fxleftbeginarraycc1-quad-text-if-x1-eleftx101rightx12-sin-frac1x1endarrayright-text-if-x-neq-1-text-t-98958

question:
<div class="question">Suppose \(f: \mathbb{R} \rightarrow \mathbb{R}\) be given by \(f(x)=\left\{\begin{array}{cc}1, \quad \text { if } x=1 \\ e^{\left(x^{10}-1\right)}+(x-1)^2 \sin \frac{1}{x-1}\end{array}\right., \text { if } x \neq 1 \text { then }\)</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\(f^{\prime}(1)\) does not 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">\(f^{\prime}(1)\) exists and is zero</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\(f^{\prime}(1)\) exist and is 9</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(f^{\prime}(1)\) exists and is 10</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(f^{\prime}(1)\) does not exist</span> </div>

answer:
<div class="solution">Hint: \(f: R \rightarrow R f(x)=\left\{\begin{array}{cc} 1 &amp; \text { if } x=1 &amp; \\  e^{\left(x^{10}-1\right)} &amp;+(x-1)^2  &amp;\cdot \sin \left(\frac{1}{x-1}\right) \text { if } x \neq 1\end{array}\right.\)<br/>\(\begin{aligned}<br/>&amp; f\left(1^{-}\right)=1+0=1 \\<br/>&amp; f\left(1^{+}\right)=1+0=1 \\<br/>&amp; f(1)=1 \\<br/>&amp; \therefore \quad f(x) \text { is continuous at } x=1 \\<br/>&amp; f^{\prime}(x)=\left\{e^{\left(x^{10}-1\right)} \cdot\left(10 x^5\right)+2(x-1) \cdot \sin \left(\frac{1}{x-1}\right)-(x-1)^2 \cdot \cos \left(\frac{1}{x-1}\right) \cdot\left(\frac{1}{x-1}\right)^2\right\}<br/>\end{aligned}\)<br/>which does not exist.</div>


title: suppose-f-r-r-is-defined-by-f-x-1-x-2-x-2-what-is-the-range-of-the-function
slug: suppose-f-r-r-is-defined-by-f-x-1-x-2-x-2-what-is-the-range-of-the-function-83957
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">Suppose $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ is defined by $\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}^{2}}{1+\mathrm{x}^{2}} .$ What is<br/>the range of the function?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$[0,1)$</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">$[0,1]$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(0,1]$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(0,1)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$[0,1)$</span> </div>

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\frac{\mathrm{x}^{2}}{1+\mathrm{x}^{2}}$<br/>for $\mathrm{x}=0, \mathrm{f}(0)=0$<br/>for $\mathrm{x}=1, \mathrm{f}(1)=\frac{1}{2}=0.5$<br/>So, range is $[0,1)$</div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
suppose-f-x-is-such-a-quadrant-expression-that-it-is-positive-for-all-real-x-if-g-x-f-x-f-x-f-x-then-for-any-real-x-then-for-any-real-x

slug:
suppose-f-x-is-such-a-quadrant-expression-that-it-is-positive-for-all-real-x-if-g-x-f-x-f-x-f-x-then-for-any-real-x-then-for-any-real-x-24502

question:
<div class="question">Suppose $f(x)$ is such a quadrant expression that it is positive for all real $\mathrm{x}$. If $g(x)=f(x)+f^{\prime}(x)+f^{\prime \prime}(x)$, then for any real $x$. Then for any real $\mathrm{x} .$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$g(x)   &lt; 0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$g(x)&gt;0$</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">$g(x)=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{g}(\mathrm{x}) \geq 0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$g(x)&gt;0$</span> </div>

answer:
<div class="solution">Let $f(x)=a x^{2}+b x+c, a&gt;0, b^{2}   &lt; 4 a c \quad(\because f(x)&gt;0)$<br/>Now, $g(x)=a x^{2}+b x+c+2 a x+b+2 a$<br/>$=a x^{2}+(b+2 a) x+2 a+b+c$<br/>Now, $(b+2 a)^{2}-4 a(2 a+b+c)$<br/>$=b^{2}+4 a b+4 a^{2}-8 a^{2}-4 a b-4 a c$<br/>$=b^{2}-4 a c-8 a^{2} &lt; 0$<br/>$\Rightarrow g(x)&gt;0$</div>


tags: ['Mathematics', 'Complex Number', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-is-a-cube-root-of-unity-with-1-suppose-p-and-q-are-the-points-on-the-complex-plane-defined-by-and-2-if-o-is-the-origin-then-what-is-the-angle-

slug:
suppose-is-a-cube-root-of-unity-with-1-suppose-p-and-q-are-the-points-on-the-complex-plane-defined-by-and-2-if-o-is-the-origin-then-what-is-the-angle-84449

question:
<div class="question">Suppose $\omega$ is a cube root of unity with $\omega \neq 1$. Suppose $\mathrm{P}$ and $Q$ are the points on the complex plane defined by $\omega$ and $\omega^{2}$. If $\mathrm{O}$ is the origin, then what is the angle between $\mathrm{OP}$ and $\mathrm{OQ} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$60^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$90^{\circ}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$120^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$150^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$120^{\circ}$</span> </div>

answer:
<div class="solution">$\because \omega=\frac{-1}{2}+i \frac{\sqrt{3}}{2}$<br/>$\&amp; \omega^{2}=\frac{-1}{2}-i \frac{\sqrt{3}}{2}$<br/>$-\frac{1}{2}+\frac{\sqrt{3}}{2} i$ $(\because \omega \neq 1)$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/-8fCaJhGmCLk5juE2zhlWhLo-oZtlyhYKboDLSPnOYM.original.fullsize.png"/><br/><br/>$P$ and $Q$ are points on complex plane. Angle between $O P$ and $O Q$ is<br/>$\theta=\tan ^{-1}\left|\frac{m_{1}-m_{2}}{1+m_{1} m_{2}}\right|$<br/>$m_{1}$ for line $O P, \quad m_{2}$ for line $O Q$<br/>$m_{1}=\frac{\frac{\sqrt{3}}{2}-0}{\frac{-1}{2}-0} \quad m_{2}=\frac{\frac{-\sqrt{3}}{2}-0}{\frac{-1}{2}-0}$<br/>$\Rightarrow m_{1}=-\sqrt{3} \quad \Rightarrow m_{2}=\sqrt{3}$<br/>$\theta=\tan ^{-1}\left[\frac{-\sqrt{3}-\sqrt{3}}{1+(-\sqrt{3})(\sqrt{3})}\right]$<br/>$=\tan ^{-1}\left[\frac{-2 \sqrt{3}}{-2}\right]=\pi-\tan ^{-1} \sqrt{3}=\pi-\tan ^{-1} \tan \frac{\pi}{3}$<br/>$\theta=\pi-\frac{\pi}{3}$<br/>$\theta=120^{\circ}$</div>


tags: ['Mathematics', 'Permutation Combination', 'JEE Main', 'JEE Main 2019 (10 Apr Shift 2)']
source_db: MarksBatch2_P2.db
title:
suppose-that-20-pillars-of-the-same-height-have-been-erected-along-the-boundary-of-circular-stadium-if-the-top-of-each-pillar-has-been-connected-by-be

slug:
suppose-that-20-pillars-of-the-same-height-have-been-erected-along-the-boundary-of-circular-stadium-if-the-top-of-each-pillar-has-been-connected-by-be-64642

question:
<div class="question">Suppose that <math><mn>20</mn></math> pillars of the same height have been erected along the boundary of circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number of beams is:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mn>170</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>180</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>210</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>190</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>170</mn></math></span> </div>

answer:
<div class="solution"><p>Each of the beams connects the top of two non-adjacent pillars, hence we have to find in how many ways we can select the required two pillars which are non-adjacent out of the given <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> pillars.</p><p>As, <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>C</mi><mn>2</mn><none></none><mprescripts></mprescripts><mi> </mi><mn>20</mn></mmultiscripts></math> is the number of beams connecting any two pillars whereas <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn></math> is the number of adjacent beams.</p><p>Thus, the total number of beams <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mmultiscripts><mi>C</mi><mn>2</mn><none></none><mprescripts></mprescripts><mi> </mi><mn>20</mn></mmultiscripts><mo>-</mo><mn>20</mn></math></p><p>Using <math xmlns="http://www.w3.org/1998/Math/MathML"><mmultiscripts><mi>C</mi><mi>r</mi><none></none><mprescripts></mprescripts><none></none><mi>n</mi></mmultiscripts><mo>=</mo><mfrac><mrow><mi>n</mi><mo>!</mo></mrow><mrow><mi>r</mi><mo>!</mo><mfenced><mrow><mi>n</mi><mo>-</mo><mi>r</mi></mrow></mfenced><mo>!</mo></mrow></mfrac><mo>,</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>20</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo><mo>×</mo><mn>18</mn><mo>!</mo></mrow></mfrac><mo>-</mo><mn>20</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>20</mn><mo>×</mo><mn>19</mn><mo>×</mo><mn>18</mn><mo>!</mo></mrow><mrow><mn>2</mn><mo>!</mo><mo>×</mo><mn>18</mn><mo>!</mo></mrow></mfrac><mo>-</mo><mn>20</mn></math></p><p><math><mo>=</mo><mn>190</mn><mo>-</mo><mn>20</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>170</mn><mo>.</mo></math></p></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-that-a-denotes-the-collection-of-all-complexnumbers-whose-square-is-a-negative-real-number-which-one-of-the-following-statements-is-correct

slug:
suppose-that-a-denotes-the-collection-of-all-complexnumbers-whose-square-is-a-negative-real-number-which-one-of-the-following-statements-is-correct-32803

question:
<div class="question">Suppose that A denotes the collection of all complexnumbers whose square is a negative real number. Which one of the  following statements is correct?</div>

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

answer:
<div class="solution">If A denotes the collection of all complex number whose square is a negative real number, then Square of a complex number is a negative real number only if it has no real partand has only imaginary part. Hence, $\mathrm{A}=\{\mathrm{iy}: \mathrm{y} \in \mathrm{R}\}$</div>


tags: ['Physics', 'Electromagnetic Waves']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
suppose-that-the-electric-field-part-of-an-electromagnetic-wave-in-vacuum-is-e-31-n-c-cos-18-rad-m-y-54-1-0-6-rad-s-t-i-a-what-is-the-direction-of-pro

slug:
suppose-that-the-electric-field-part-of-an-electromagnetic-wave-in-vacuum-is-e-31-n-c-cos-18-rad-m-y-54-1-0-6-rad-s-t-i-a-what-is-the-direction-of-pro-16091

question:
<div class="question">Suppose that the electric field part of an electromagnetic wave in vacuum is<br/>$E=\left\{(3.1 \mathrm{~N} / \mathrm{C}) \cos \left[(1.8 \mathrm{rad} / \mathrm{m}) \mathrm{y}+\left(5.4 \times 10^6 \mathrm{rad} / \mathrm{s}\right) t\right]\right\} \hat{\mathrm{i}}$.<br/>(a) What is the direction of propagation?<br/>(b) What is the wavelength $\lambda$ ?<br/>(c) What is the frequency $v$ ?<br/>(d) What is the amplitude of the magnetic field part of the wave?<br/>(e) Write an expression for the magnetic field part of the wave.</div>

answer:
<div class="solution">$\mathrm{E}=\{(3.1 \mathrm{~N} / \mathrm{C}) \cos [1.8 \mathrm{rad} / \mathrm{m}) \mathrm{y}+(1.8 \mathrm{rad} / \mathrm{s}) \mathrm{t}]\} \mathrm{i}$<br/>(a) The waves is propagating in the -ve y-direction.<br/>(b) Comparing eqs.(1) with the standard equation for the e.m. wave. $E=E_0 \sin \left[2 \pi\left(\frac{y}{\lambda}-v t\right)\right]$ we have $\frac{2 \pi}{\lambda}=1.8 \Rightarrow \lambda=\frac{2 \pi}{1.8}=\frac{2 \times 22}{7 \times 1.8}=3.488 \Rightarrow \lambda=3.5 \mathrm{~m}$<br/>(c) Frequency $v=\frac{\mathrm{c}}{\lambda}=\frac{3 \times 10^8}{3.5}=0.85 \times 10^8 \mathrm{~Hz}$ $=8.6 \times 10^7 \mathrm{~Hz}=86 \mathrm{MHz}$<br/>(d) Amplitude of magnetic field<br/>$$<br/>=\mathrm{B}_0=\frac{\mathrm{E}_0}{\mathrm{c}}=\frac{3.1}{3 \times 10^8}=1.03 \times 10^{-8}<br/>$$<br/>$$<br/>\approx 10.3 \times 10^{-9}=10 \mathrm{nT}<br/>$$<br/>(e) Expression for magnetic field<br/>$$<br/>\mathrm{B}=\left[(10 \mathrm{nT}) \cos \left\{(1.8 \mathrm{rad} / \mathrm{m}) \mathrm{y}+\left(5.4 \times 10^6 \mathrm{rad} / \mathrm{s}\right) \mathrm{t}\right\}\right] \hat{\mathrm{k}}<br/>$$</div>


tags: ['Physics', 'Electromagnetic Waves', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
suppose-that-the-electric-field-part-of-an-electromagnetic-wave-in-vacuum-is-eleftleft31-mathrmn-mathrmc1right-cos-leftleft18-mathrmrad-mathrmm1right-

slug:
suppose-that-the-electric-field-part-of-an-electromagnetic-wave-in-vacuum-is-eleftleft31-mathrmn-mathrmc1right-cos-leftleft18-mathrmrad-mathrmm1right-12053

question:
<div class="question">Suppose that the electric field part of an electromagnetic wave in vacuum is<br/>\( E=\left\{\left(3.1 \mathrm{~N} \mathrm{C}^{-1}\right) \cos \left[\left(1.8 \mathrm{rad} \mathrm{m}^{-1}\right) y+\left(5.47 \times 10^{6} \operatorname{rad} \mathrm{s}^{-1}\right) t\right]\right\} \hat{\mathrm{i}} . \)<br/>What is the wavelength \( \lambda \) ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\( 3.5 \mathrm{~m} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( 4.5 \mathrm{~m} \)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( 2.5 \mathrm{~m} \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 3.0 \mathrm{~m} \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 3.5 \mathrm{~m} \)</span> </div>

answer:
<div class="solution">The eletric part of electromagnetic wave in vacuum<br/>E = 3.1 cos (1.8 y + 5.4 × 10<sup>6</sup>t)<math> <mrow> <mover accent="true"> <mtext>i</mtext> <mo>^</mo> </mover> </mrow> </math><br/>Comparing with standard equation E = E<sub>0</sub> cos (Ky + ωt), we get<br/>Angular frequency ω = 5.4 × 10<sup>6</sup> rad/s<br/>Wave number K = 1.8 rad/m<br/>The amplitude of the electric field part of the wave<br/>E<sub>0</sub> = 3.1 N/C<br/><math> <mrow> <mi>λ</mi> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mi>K</mi><mo>â¡</mo> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mi>π</mi> </mrow> <mrow> <mn>1</mn> <mo>·</mo> <mn>8</mn> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mo>·</mo> <mn>4</mn> <mn>9</mn> <mn>2</mn> <mspace width="0.5em"></mspace> <mtext>m</mtext> </mrow> </math><br/>λ = 3.5 m</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2017 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-the-function-f-x-x-n-n-0-is-differentiable-for-all-x-then-n-can-be-any-element-of-the-interval

slug:
suppose-the-function-f-x-x-n-n-0-is-differentiable-for-all-x-then-n-can-be-any-element-of-the-interval-91367

question:
<div class="question">Suppose the function $f(\mathrm{x})=\mathrm{x}^{\mathrm{n}}, \mathrm{n} \neq 0$ is differentiable for all $x$. Then $n$ can be any element of the interval</div>

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

answer:
<div class="solution">$\mathrm{f}(\mathrm{x})=\mathrm{x}^{\mathrm{n}}, \mathrm{n} \neq 0$ This function is differentiable for all values of $\mathrm{n}$, except 0 . Hence $\mathrm{n} \in(1, \infty)$</div>


tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-the-system-of-equations-a-1-x-b-1-y-c-1-z-d-1-a-2-x-b-2-y-c-2-z-d-2-a-3-x-b-3-y-c-3-z-d-3-has-a-unique-solution-x-0-y-0-z-0-if-x-0-0-then-whic

slug:
suppose-the-system-of-equations-a-1-x-b-1-y-c-1-z-d-1-a-2-x-b-2-y-c-2-z-d-2-a-3-x-b-3-y-c-3-z-d-3-has-a-unique-solution-x-0-y-0-z-0-if-x-0-0-then-whic-30287

question:
<div class="question">Suppose the system of equations<br/>$\begin{array}{l}<br/>a_{1} x+b_{1} y+c_{1} z=d_{1} \\<br/>a_{2} x+b_{2} y+c_{2} z=d_{2} \\<br/>a_{3} x+b_{3} y+c_{3} z=d_{3}<br/>\end{array}$<br/>has a unique solution $\left(x_{0}, y_{0}, z_{0}\right)$. If $x_{0}=0$, then which one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left|\begin{array}{lll}\mathrm{a}_{1} &amp; \mathrm{~b}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{a}_{2} &amp; \mathrm{~b}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{a}_{3} &amp; \mathrm{~b}_{3} &amp; \mathrm{c}_{3}\end{array}\right|=0$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left|\begin{array}{lll}\mathrm{d}_{1} &amp; \mathrm{~b}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{~d}_{2} &amp; \mathrm{~b}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{~d}_{3} &amp; \mathrm{~b}_{3} &amp; \mathrm{c}_{3}\end{array}\right|=0$</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">$\left|\begin{array}{lll}\mathrm{d}_{1} &amp; \mathrm{a}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{~d}_{2} &amp; \mathrm{a}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{~d}_{3} &amp; \mathrm{a}_{3} &amp; \mathrm{c}_{3}\end{array}\right|=0$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left|\begin{array}{lll}\mathrm{d}_{1} &amp; \mathrm{a}_{1} &amp; \mathrm{~b}_{1} \\ \mathrm{~d}_{2} &amp; \mathrm{a}_{2} &amp; \mathrm{~b}_{2} \\ \mathrm{~d}_{3} &amp; \mathrm{a}_{3} &amp; \mathrm{~b}_{3}\end{array}\right|=0$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left|\begin{array}{lll}\mathrm{d}_{1} &amp; \mathrm{~b}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{~d}_{2} &amp; \mathrm{~b}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{~d}_{3} &amp; \mathrm{~b}_{3} &amp; \mathrm{c}_{3}\end{array}\right|=0$</span> </div>

answer:
<div class="solution">The given system of equations is<br/>$\mathrm{a}_{1} \mathrm{x}+\mathrm{b}_{1} \mathrm{y}+\mathrm{c}_{1} \mathrm{z}=\mathrm{d}_{1}$<br/>$a_{2} x+b_{2} y+c_{2} z=d_{2}$<br/>and $\mathrm{a}_{3} \mathrm{x}+\mathrm{b}_{3} \mathrm{y}+\mathrm{c}_{3} \mathrm{z}=\mathrm{d}_{3}$<br/>Let $\Delta=\left|\begin{array}{lll}\mathrm{a}_{1} &amp; \mathrm{~b}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{a}_{2} &amp; \mathrm{~b}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{a}_{3} &amp; \mathrm{~b}_{3} &amp; \mathrm{c}_{3}\end{array}\right|$<br/>This system has a unique solution $x_{0}, y_{0}, z_{0}$ if $\Delta \neq 0$<br/>and $x_{0}=\frac{\Delta x}{\Delta}=0 \Rightarrow \Delta x=0$<br/>$\Rightarrow\left|\begin{array}{lll}\mathrm{d}_{1} &amp; \mathrm{~b}_{1} &amp; \mathrm{c}_{1} \\ \mathrm{~d}_{2} &amp; \mathrm{~b}_{2} &amp; \mathrm{c}_{2} \\ \mathrm{~d}_{3} &amp; \mathrm{~b}_{3} &amp; \mathrm{c}_{3}\end{array}\right|=0$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2016 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-there-is-a-relation-between-the-positive-numbers-x-and-y-given-by-x-y-if-and-only-if-x-y-2-then-which-one-of-the-following-is-correct

slug:
suppose-there-is-a-relation-between-the-positive-numbers-x-and-y-given-by-x-y-if-and-only-if-x-y-2-then-which-one-of-the-following-is-correct-68604

question:
<div class="question">Suppose there is a relation $*$ between the positive numbers<br/>$x$ and $y$ given by $x * y$ if and only if $x \leq y^{2}$. Then which one of the following is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$*$ is reflexive but not transitive and symmetric</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$*$ is transitive but not reflexive and symmetric</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">*is symmetric and reflexive but not tran sitive</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$*$ is symmetric and but not reflexive and transitive</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$*$ is reflexive but not transitive and symmetric</span> </div>

answer:
<div class="solution">$x$ and $y$ are positive numbers.<br/>$x \leq v^{2}$<br/>Reflexive-<br/>$x \leq x^{2} \forall$ positive numbers. Hence relation is reflexive. Transitive $-$ $x \leq y^{2} \quad y \leq z^{2}$<br/>Let $x=5, y=3, z=2$<br/>$5 \leq(3)^{2} \quad(3) \leq(2)^{2}$<br/>but $5 \pm(2)^{2}$<br/>Hence, $x \leq y^{2} \quad y \leq z^{2}$<br/>but $x \leq z^{2}$<br/>Thusrelation is not transitive. Symmetric<br/>$1 \leq(2)^{2}$ while $2 \pm(1)^{2}$<br/>Hence relation is not symmetric.<br/>Thus $x \leq y^{2} \forall$ positivenumbersis reflexive, but not transitive and symmetric.</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
suppose-x-1-2-3-4-and-r-is-a-relation-on-x-if-r-1-1-2-2-3-3-1-2-2-1-2-3-3-2-then-which-one-of-the-following-is-correct

slug:
suppose-x-1-2-3-4-and-r-is-a-relation-on-x-if-r-1-1-2-2-3-3-1-2-2-1-2-3-3-2-then-which-one-of-the-following-is-correct-43875

question:
<div class="question">Suppose $\mathrm{X}=\{1,2,3,4\}$ and $\mathrm{R}$ is a relation on $\mathrm{X}$. If $\mathrm{R}=\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3) \cdot(3,2)\}$, then which<br/>one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{R}$ is reflexive and symmetric, but not transitive</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{R}$ is symmetric and transitive, but not reflexive</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{R}$ is reflexiveand transitive, but not symmetric</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{R}$ is neither reflexive nor transitive, but symmetric</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\mathrm{R}$ is neither reflexive nor transitive, but symmetric</span> </div>

answer:
<div class="solution">Given,<br/>$x=\{1,2,3,4\}$ $\mathrm{R}=\{(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2)\}$<br/>$\mathrm{R}$ is reflexive, if aRa for all $\mathrm{a} \in \mathrm{x}$ $(4,4) \notin \mathrm{R}$<br/>$\therefore \mathrm{R}$ is not reflexive ...(1)<br/>$\mathrm{R}$ is transitive, if $\mathrm{R} \mathrm{R} \mathrm{b}, \mathrm{b} \mathrm{R} \mathrm{c} \Rightarrow \mathrm{aR} \mathrm{C}$ for all $\mathrm{a}, \mathrm{b}, \mathrm{c} \in \mathrm{x}(1,2)$<br/>$(2,3), \in \mathrm{R}$, but $(1,3) \notin \mathrm{R}$<br/>$\therefore \mathrm{R}$ is not transitive...(2) <br/>$\mathrm{R}$ is symmetric, if $\mathrm{a} \mathrm{R} \mathrm{b} \Rightarrow \mathrm{b} \mathrm{R} \mathrm{a}$, for all $\mathrm{a}, \mathrm{b} \in \mathrm{x}$<br/>$\therefore \mathrm{R}$ is symmetric...(3)<br/>(3) From $(1),(2),(3)$ we can say, $\mathrm{R}$, is neither reflexivenor transitive, but symmetric.</div>


title: sweet-potato-is-a-modified-root-potato-is-a-modified-stem-both-these-plants-are-classified-in-order
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P2.db
slug:
sweet-potato-is-a-modified-root-potato-is-a-modified-stem-both-these-plants-are-classified-in-order-95201

question:
<div class="question">Sweet potato is a modified root. Potato is a modified stem. Both these plants are classified in order</div>

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

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

answer:
<div class="solution"><em>Ipomoea batatas</em> or sweet potato is a plant which belongs to the family Convolvulaceae. It is also called the Morning glory Family. Potato belongs to the family Solanaceae. Both are included in the order Polymoniales.<br/><br/>Generally, order and other higher taxonomic categories are identified based on the aggregates of characters. Order is an assemblage of families that exhibit a few similar characters. The similar characters are less in number as compared to different genera included in a family. Plant families like Convolvulaceae, Solanaceae are included in the order polymoniales mainly based on the floral characters.</div>


tags: ['Biology', 'Morphology of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch2_P2.db
title:
take-one-flower-each-of-the-families-fabaceae-and-solanaceae-and-write-its-semitechnical-description-also-draw-their-floral-diagram-after-studying-the

slug:
take-one-flower-each-of-the-families-fabaceae-and-solanaceae-and-write-its-semitechnical-description-also-draw-their-floral-diagram-after-studying-the-40649

question:
<div class="question">Take one flower each of the families Fabaceae and Solanaceae and write its semi-technical description. Also draw their floral diagram after studying them.</div>

answer:
<div class="solution">Fabaceae: This family was earlier called papilionoidae, a subfamily of family Leguminosae. It is distributed all over the world.<br/>Example: Pisum sativum<br/>Semi technical descritpion of $P$ isum sativum are as follows:<br/>Vegetative characters :<br/>Habit : An annual herb.<br/>Root: Nodulated tap root.<br/>Stem : Climber, leaflet tendrils<br/>Leaves: Alternate, pinnately compound or simple; leaf base, pulvinate, stipulate, venation reticulate.<br/>Floral characters :<br/>Inflorescence : Racemose<br/>Flower: Bisexual, zygomorphic, complete, irregular, hypogynous Calyx : Sepal 5, gamosepalous, valvate aestivation.<br/>Corolla : Petals 5, polypetalous, papilionaceous consisting of a posterior standard, two lateral wings, two anterior ones forming a keel. Thus, flower becomes zygomorphic, with descending imbricate aestivation i.e. vexillary aestivation. Androecium : Stamen 10, diadelphous $[1+(9)]$, anther dithecous, introrse.<br/>Gynoecium: Ovary superior, monocarpellary, unilocular with many ovules, marginal placentation.<br/>Fruit : Legume<br/>Seed : One to many, non-endospermic.<br/>Economic importance<br/>Many plants belonging to the family are sources of pulses (gram, arhar, sem, moong, soyabean, edible oil (soyabean, groundnut); fibres (sunhemp); fodder (Sesbania, Trifolium), ornamentals (lupin, sweet pea); medicine (muliathi).<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/JbKE9XgQyFPZbqQG7FfKEo1S3U6jJzi2Wvrb3Rs4Pug.original.fullsize.png"/><br/><br/>Solanaceae :<br/>It is large family, commonly called as the potato family. It is widely distributed in tropics, subtropics and temperate zones.<br/>Example: Datura<br/>Semi technical description of Solanum nigrum.<br/>Vegetative characters :<br/>Habit : Annual herb<br/>Stem : Erect, cylindrical, hairy, slightly fistular.<br/>Leaves : Alternate, simple, petiolate, ovate with acute apex, venation reticulate.<br/>Floral characters :<br/>Inflorescence : Solitary, axillary<br/>Flower : Ebracteate, actinomorphic, hypogynous<br/>Calyx : Sepals 5, gamosepalous, persistent, valvate astivation.<br/>Corolla : Petals 5 , gamopetalous, valvate aestivation<br/>Androecium : Stamen 5, epipetalous<br/>Gynoecium : Bicarpellary, syncarpous, ovary superior, bilocular but four celled by formation of false septum, placenta swollen with many ovules.<br/>Fruit: Spinous capsule with septifragal dehiscence.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/uct2oeK-jgNZM-qRxjetVfVLfLYbB7AqubN3oIYdVO4.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/hJQlFg9jrj25ed68eaXo_xDQTU4b5XKQoyJRGFPlFQE.original.fullsize.png"/><br/></div>


title: tan-5-4-can-be-expressed-as
slug: tan-5-4-can-be-expressed-as-41663
question: <div class="question">$\tan 54^{\circ}$ can be expressed as</div>
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sin 9^{\circ}+\cos 9^{\circ}}{\sin 9^{\circ}-\cos 9^{\circ}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{\sin 9^{\circ}-\cos 9^{\circ}}{\sin 9^{\circ}+\cos 9^{\circ}}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\sin 36^{\circ}}{\cos 36^{\circ}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\cos 9^{\circ}+\sin 9^{\circ}}{\cos 9^{\circ}-\sin 9^{\circ}}$</span> </div>

answer:
<div class="solution">\tan 54^{\circ}=\tan \left(45^{\circ}+9^{\circ}\right) \\=&amp; \frac{\tan 45^{\circ}+\tan 9^{\circ}}{1-\tan 45^{\circ} \cdot \tan 9^{\circ}}=\frac{1+\tan 9^{\circ}}{1-\tan 9^{\circ}} \\</div>


title: taxonomic-studies-consider-a-group-of-individual-organisms-with-fundamental-similarities-as-a
slug: taxonomic-studies-consider-a-group-of-individual-organisms-with-fundamental-similarities-as-a-98624
tags: ['Biology', 'The Living World', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">Taxonomic studies consider a group of individual organisms with fundamental similarities as a</div>

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

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

answer:
<div class="solution">The classification of all living organism has been done by dividing them into different levels based on their features and characteristics. There is a hierarchy in this classification and each step represents a rank or category known as taxonomic category. There are around seven main taxonomic ranks or categories - species, genus, family, order, class, phylum/division and kingdom. Group of individuals having similar fundamental qualities are called species. When the group of related species have more common characters among them they are referred to as genus. Families which exhibit few similar characters are placed under the same Order. All the fishes, amphibians, reptiles, birds along with mammals constitute the taxonomic level phylum.</div>


tags: ['Chemistry', 'States of Matter', 'TS EAMCET', 'TS EAMCET 2022 (20 Jul Shift 2)']
source_db: MarksBatch2_P2.db
title:
text-1-l-closed-flask-contains-a-mixture-of-4-mathrmg-text-of-methane-and-44-mathrmg-text-of-carbon-dioxide-the-pressure-inside-the-flask-at-endarray-

slug:
text-1-l-closed-flask-contains-a-mixture-of-4-mathrmg-text-of-methane-and-44-mathrmg-text-of-carbon-dioxide-the-pressure-inside-the-flask-at-endarray-46835

question:
<div class="question">\text { 1 L closed flask contains a mixture of } 4 \mathrm{~g} \text { of methane and } \\ 4.4 \mathrm{~g} \text { of carbon dioxide. The pressure inside the flask at }\end{array}$<br/>$27^{\circ} \mathrm{C}$ is [Assume ideal behaviour of gases]</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$8.6 \mathrm{~atm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$2.2 \mathrm{~atm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4.2 \mathrm{~atm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$6.1 \mathrm{~atm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$8.6 \mathrm{~atm}$</span> </div>

answer:
<div class="solution">no. of moles of $\mathrm{CH}_4\left(\mathrm{n}_1\right)=4 / 16=0.25 \mathrm{~mol}$<br/>no. of moles of $\mathrm{CO}_2\left(\mathrm{n}_2\right)=4.4 / 44=0.1 \mathrm{~mol}$<br/>Total no. of moles $\left(\mathrm{n}_{\mathrm{T}}\right)=\mathrm{n}_1+\mathrm{n}_2=0.35 \mathrm{~mol}$<br/>$\therefore \quad \mathrm{P}=\frac{0.35 \times 0.082 \times 300}{1}=8.6 \mathrm{~atm}$</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'KCET', 'KCET 2014']
source_db: MarksBatch2_P2.db
title:
text-if-fxleftbeginarraycc-frac3-sin-pi-x5-x-x-neq-0-2-k-x0-endarrayright-is-continuous-at-x0-then-the-value-of-k-is

slug:
text-if-fxleftbeginarraycc-frac3-sin-pi-x5-x-x-neq-0-2-k-x0-endarrayright-is-continuous-at-x0-then-the-value-of-k-is-43626

question:
<div class="question">\[<br/>\text { If } f(x)=\left\{\begin{array}{cc}<br/>\frac{3 \sin \Pi x}{5 x} ; &amp; x \neq 0 \\<br/>2 K ; &amp; x=0<br/>\end{array}\right.<br/>\]<br/>is continuous at \( x=0 \), then the value of \( K \) is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\( \frac{3 \pi}{10} \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( \frac{3 \pi}{5} \)</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( \frac{\Pi}{10} \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( \frac{3 \pi}{2} \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( \frac{3 \pi}{10} \)</span> </div>

answer:
<div class="solution">Given that \( f(x)=\left\{\begin{array}{cl}\frac{3 \sin \pi x}{5 x} &amp; x \neq 0 \\ 2 K &amp; x=0\end{array}\right. \)<br/>Now,<br/>\[<br/>\begin{array}{l}<br/>\lim _{x \rightarrow 0}\left(\frac{3 \sin \pi x}{5 x}\right)=2 K \\<br/>\Rightarrow \frac{3 \pi}{5} \lim _{x \rightarrow 0} \frac{\sin \pi x}{x I I}=2 K \\<br/>\Rightarrow \frac{3 \Pi}{5} \times 1=2 K \Rightarrow K=\frac{3 \Pi}{10}<br/>\end{array}<br/>\]</div>


title: text-what-is-the-value-of-tan-75circcot-75circ
slug: text-what-is-the-value-of-tan-75circcot-75circ-24100
question: <div class="question">\text { What is the value of } \tan 75^{\circ}+\cot 75^{\circ} ?</div>
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
answer: <div class="solution">$\tan 75^{\circ}+\cot 75^{\circ}=2+\sqrt{3}+2-\sqrt{3}=4$</div>
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">4</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2 \sqrt{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \sqrt{3}$</span> </li> </ul>


title: the-59-th-term-of-an-ap-is-449-and-the-449-th-term-is-59-which-term-is-equal-to-0-zero
slug: the-59-th-term-of-an-ap-is-449-and-the-449-th-term-is-59-which-term-is-equal-to-0-zero-34465
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The 59 th term of an $\mathrm{AP}$ is 449 and the 449 th term is 59 . Which term is equal to 0 (zero)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$501^{\text {st }}$ term</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$502^{\text {nd }}$ term</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$508^{\text {th }}$ term</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$509^{\text {th }}$ term</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$508^{\text {th }}$ term</span> </div>

answer:
<div class="solution">Let a and $\mathrm{d}$ be the first term and common difference of an AP respectively<br/>$\therefore \quad a+58 d=449$ and $a+448 d=59$<br/>On solving Eqs. (i) and (ii), we get<br/>$a=507$ and $d=-1$<br/>$\mathrm{n}^{\text {th }}$ term of $\mathrm{AP}$ is $\mathrm{a}+(\mathrm{n}-1) \mathrm{d}$<br/>Let us assume that $\mathrm{n}^{\text {th }}$ term will be zero.<br/>$\therefore \quad a+(n-1) d=0$<br/>$\Rightarrow 0=507+(n-1)(-1)$<br/>$\Rightarrow 507=n-1 \Rightarrow n=508$<br/>Hence, $508^{\text {th }}$ term will be zero.</div>


title: the-abundantly-distributed-enzyme-in-germinating-seeds-and-adipocytes-is
slug: the-abundantly-distributed-enzyme-in-germinating-seeds-and-adipocytes-is-95248
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch2_P2.db
question:
<div class="question">The abundantly distributed enzyme in germinating seeds and adipocytes is</div>

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

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

answer:
<div class="solution">The germinating seeds and adipocytes contain fat as reserved food materials and while metabolic reactions in order to release the free fatty acids and glycerol the lipases acts on the stored lipids.</div>


title: the-acidic-oxide-from-the-following-is
slug: the-acidic-oxide-from-the-following-is-17096
question: <div class="question">The acidic oxide from the following is</div>
tags: ['Chemistry', 'p Block Elements (Group 13 & 14)', 'TS EAMCET', 'TS EAMCET 2022 (19 Jul Shift 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{SnO}_2$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{SiO}_2$</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">$\mathrm{PbO}_2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{SnO}$</span> </li> </ul>

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

answer:
<div class="solution">On moving down the group, the tendancy to lose<br/>electron increases due to which basic character of oxides<br/>increases and acidic character decreases. Hence, $\mathrm{SiO}_2$<br/>form acidic oxide.</div>


title: the-acromion-process-is-a-part-of-the
slug: the-acromion-process-is-a-part-of-the-70443
question: <div class="question">The acromion process is a part of the</div>
tags: ['Biology', 'Locomotion and Movement', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">humerus</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">sternum</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">clavicle</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">scapula</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">scapula</span> </div>

answer:
<div class="solution">Human skeleton system is divided into Axial and Appendicular. Axial skeleton consists of 80 bones and Appendicular skeleton consists of 126 bones. It includes the bones of girdles and bones of appendages. Pectoral girdle is the upper girdle. It consists of two scapulae and two clavicles. Scapula is also known as shoulder blade. It articulates with the clavicle on one side and with the humerus on the other side. It shows the presence of two processes: Acromion process and Coracoid process. Acromion process articulates with the clavicle and coracoid process with the ligament.</div>


title: the-activation-energy-of-a-chemical-reaction-can-be-determined-by
slug: the-activation-energy-of-a-chemical-reaction-can-be-determined-by-53088
question: <div class="question">The activation energy of a chemical reaction can be determined by,</div>
tags: ['Chemistry', 'Chemical Kinetics', 'KCET', 'KCET 2016']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">evaluating rate constants at two different temperatures.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">O changing the concentration of reactants.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">evaluating the concentration of reactants at two different temperatures.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">evaluating rate constant at standard temperature,</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">evaluating rate constants at two different temperatures.</span> </div>

answer:
<div class="solution">Activation energy of a chemical reaction can be determined by measuring the values of rate constant at two<br/>differenttemperatures<br/>Let \( k_{1} \) and \( k_{2} \) are the rate constant for the reaction at two different temperature, that is, \( T_{1} \) and \( T_{2} \) respectively.<br/>\( \log k_{1}=\log A-\frac{E_{a}}{2.303 R T_{1}} \rightarrow(1) \) \( \log k_{2}=\log A-\frac{E_{a}}{2.303 R T_{2}} \rightarrow(2) \)<br/>Subtract Eq. (1) from Eq. (2), we get<br/>\[<br/>\begin{array}{l}<br/>\log k_{2}-\log k_{1}=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \\<br/>\log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{1}{T_{1}}-\frac{1}{T_{2}}\right] \\<br/>\log \frac{k_{2}}{k_{1}}=\frac{E_{a}}{2.303 R}\left[\frac{T_{2}-T_{1}}{T_{1} T_{2}}\right] \\<br/>E_{a}=2.303 R \log \frac{k_{2}}{k_{1}} \times\left[\frac{T_{1} T_{2}}{T_{2}-T_{1}}\right]<br/>\end{array}<br/>\]</div>


title: the-actual-3d-structure-of-trna-molecule-appears-as
slug: the-actual-3d-structure-of-trna-molecule-appears-as-87023
question: <div class="question">The actual 3D structure of tRNA molecule appears as</div>
tags: ['Biology', 'Molecular Basis of Inheritance', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">L-shaped</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">E-shaped</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Y-shaped</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">S-shaped</span> </li> </ul>

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

answer:
<div class="solution">In actual or primary structure, the tRNA is a compact molecule which looks like inverted L-shaped structure. Kim et al., (1973) suggested the 3D, L-shaped model of t-RNA by X-Ray diffraction analysis. The secondary structure of tRNA is the clover-leaf structure. </div>


tags: ['Physics', 'Current Electricity', 'JEE Main', 'JEE Main 2019 (10 Jan Shift 2)']
source_db: MarksBatch2_P2.db
title:
the-actual-value-of-resistance-r-shown-in-the-figure-is-30-this-is-measured-in-an-experiment-as-shown-using-the-standard-formula-r-v-i-where-v-and-i-a

slug:
the-actual-value-of-resistance-r-shown-in-the-figure-is-30-this-is-measured-in-an-experiment-as-shown-using-the-standard-formula-r-v-i-where-v-and-i-a-19861

question:
<div class="question">The actual value of resistance <math><mi>R</mi></math> , shown in the figure is <math><mn>30</mn><mi>Ω</mi><mo>.</mo></math> This is measured in an experiment as shown using the standard formula <math><mi>R</mi><mo>=</mo><mfrac><mrow><mi>V</mi></mrow><mrow><mi>I</mi></mrow></mfrac></math> , where <math><mi>V</mi></math> and <math><mi>I</mi></math> are the readings of the voltmeter and ammeter, respectively. If the measured value of <math><mi>R</mi></math> is <math><mn>5</mn><mi>%</mi></math> less, then the internal resistance of the voltmeter is:<br/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/463a009e-db76-4f86-8f1b-698f0c0c9b2e-image.png" style="width: 400px; height: 260px;"/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>35</mn><mi mathvariant="normal">Î©</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>600</mn><mi mathvariant="normal">Î©</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mn>570</mn><mi mathvariant="normal">Î©</mi></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mn>350</mn><mi mathvariant="normal">Î©</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>570</mn><mi mathvariant="normal">Î©</mi></math></span> </div>

answer:
<div class="solution"><p>Measured value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mn>5</mn><mo>%</mo></math> less than<br/>actual value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> i.e., <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mo>'</mo></msup><mo>=</mo><mn>30</mn><mo>-</mo><mo>(</mo><mn>5</mn><mo>%</mo></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>)</mo><mo>=</mo><mn>30</mn><mo>-</mo><mfrac><mn>5</mn><mn>100</mn></mfrac><mo>×</mo><mn>30</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mo>'</mo></msup><mo>=</mo><mn>28</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mi mathvariant="normal">i</mi></mfenced></math></p><p><img src="https://cdn-question-pool.getmarks.app/pyq/jee_main/f1d29977-3dd1-4ef4-88ec-6b78d9dac75d-image.png" style="width: 193px; height: 184px;"/></p><p>Now, let us assume that internal resistance of voltmeter <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>V</mi></msub></math>. Replacing voltmeter with its internal resistance, we get following circuit.</p><p>It is clear that the measured value, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mo>'</mo></msup></math> should be equal to parallel combination of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>V</mi></msub></math>. Mathematically,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>R</mi><mo>'</mo></msup><mo>=</mo><mfrac><mrow><mi>R</mi><mo>×</mo><msub><mi>R</mi><mi>V</mi></msub></mrow><mrow><mi>R</mi><mo>+</mo><msub><mi>R</mi><mi>V</mi></msub></mrow></mfrac><mo>=</mo><mn>28</mn><mo>.</mo><mn>5</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p>Given. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mn>30</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mfrac><mrow><mn>30</mn><mo> </mo><msub><mi>R</mi><mi>V</mi></msub></mrow><mrow><mn>30</mn><mo>+</mo><msub><mi>R</mi><mi>V</mi></msub></mrow></mfrac><mo>=</mo><mn>28</mn><mo>.</mo><mn>5</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>30</mn><mo> </mo><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mfenced><mrow><mn>28</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>30</mn></mrow></mfenced><mo>+</mo><mn>28</mn><mo>.</mo><mn>5</mn><mo> </mo><msub><mi>R</mi><mi>V</mi></msub></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>5</mn><mo> </mo><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mn>28</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>30</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mfrac><mrow><mn>28</mn><mo>.</mo><mn>5</mn><mo>×</mo><mn>30</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mn>19</mn><mo>×</mo><mn>30</mn></math></p><p>or <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>R</mi><mi>V</mi></msub><mo>=</mo><mn>570</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></p></div>


title: the-acute-angle-which-the-perpendicular-from-origin-on-the-line-7-x-3-y-4-makes-with-the-x-axis-is
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P2.db
slug:
the-acute-angle-which-the-perpendicular-from-origin-on-the-line-7-x-3-y-4-makes-with-the-x-axis-is-98598

question:
<div class="question">The acute angle which the perpendicular from origin on the line $7 x-3 y=4$ makes with the $x$ -axis is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">zero</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">positive but not $\pi / 4$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">negative</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\pi / 4$</span> </li> </ul>

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

answer:
<div class="solution">Given line, $7 x-3 y=4$ $\Rightarrow \quad 3 y=7 x-4$<br/>$\Rightarrow \quad y=\left(\frac{7}{3}\right) x-\left(\frac{4}{3}\right)$<br/>$\therefore \quad$ Slope $=\frac{7}{3}$<br/>The slope of the line perpendicular to $7 \mathrm{x}-3 \mathrm{y}=4$ is $\left(\frac{-3}{7}\right)$<br/>If $^{\prime} \theta$ ' is the angle between the perpendicular line with<br/>slope $\frac{-3}{7}$ and $\mathrm{x}$ -axis, then $\frac{-3}{7}=\tan \theta \Rightarrow \theta$ is negative</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-adjacent-sides-ab-and-ac-of-a-triangle-abc-are-represented-by-the-vectors-2-i-3-j-2-k-and-4-i-5-j-2-k-respectively-the-area-of-the-triangle-abc-is

slug:
the-adjacent-sides-ab-and-ac-of-a-triangle-abc-are-represented-by-the-vectors-2-i-3-j-2-k-and-4-i-5-j-2-k-respectively-the-area-of-the-triangle-abc-is-14861

question:
<div class="question">The adjacent sides $\mathrm{AB}$ and $\mathrm{AC}$ of a triangle $\mathrm{ABC}$ are represented by the vectors $-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-4 \hat{i}+5 \hat{j}+2 \hat{k}$ respectively. The area of the triangle $\mathrm{ABC}$ is</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">3 square units</span> </div>

answer:
<div class="solution">Area of $\Delta \mathrm{ABC}=\frac{1}{2}(\overrightarrow{\mathrm{AB}} \times \overrightarrow{\mathrm{AC}})$<br/>$=\frac{1}{2}\left|\begin{array}{ccc}\hat{\mathrm{i}} &amp; \hat{\mathrm{j}} &amp; \hat{\mathrm{k}} \\ -2 &amp; 3 &amp; 2 \\ -4 &amp; 5 &amp; 2\end{array}\right|$<br/>$=\frac{1}{2}[\hat{\mathrm{i}}(6-10)-\hat{\mathrm{j}}(-4+8)+\hat{\mathrm{k}}(-10+12)]$<br/>$=\frac{1}{2}[-4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}+2 \hat{\mathrm{k}}]$<br/>$=\frac{1}{2} \sqrt{16+16+4}=\frac{1}{2} \sqrt{36}=\frac{1}{2} \times 6$<br/>$=3$ square units<br/>$\therefore \quad$ Option (d) is correct.</div>


title: the-adjoint-of-the-matrix-a-1-2-0-0-1-3-2-0-1-is
slug: the-adjoint-of-the-matrix-a-1-2-0-0-1-3-2-0-1-is-44975
tags: ['Mathematics', 'Matrices', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The adjoint of the matrix $\mathrm{A}=\left[\begin{array}{lll}1 &amp; 0 &amp; 2 \\ 2 &amp; 1 &amp; 0 \\ 0 &amp; 3 &amp; 1\end{array}\right]$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left[\begin{array}{ccc}-1 &amp; 6 &amp; 2 \\ -2 &amp; 1 &amp; -4 \\ 6 &amp; 3 &amp; 1\end{array}\right]$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\left[\begin{array}{ccc}1 &amp; 6 &amp; -2 \\ -2 &amp; 1 &amp; 4 \\ 6 &amp; -3 &amp; 1\end{array}\right]$</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">$\left[\begin{array}{rrr}6 &amp; 1 &amp; 2 \\ 4 &amp; -1 &amp; 2 \\ 6 &amp; 3 &amp; -1\end{array}\right]$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\left[\begin{array}{ccc}-6 &amp; 2 &amp; 1 \\ 4 &amp; -2 &amp; 1 \\ 3 &amp; 1 &amp; -6\end{array}\right]$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left[\begin{array}{ccc}1 &amp; 6 &amp; -2 \\ -2 &amp; 1 &amp; 4 \\ 6 &amp; -3 &amp; 1\end{array}\right]$</span> </div>

answer:
<div class="solution">$\mathrm{A}=\left[\begin{array}{lll}1 &amp; 0 &amp; 2 \\ 2 &amp; 1 &amp; 0 \\ 0 &amp; 3 &amp; 1\end{array}\right]$<br/>$A_{11}=1-0=1 ; A_{12}=-(2-0)=-2 ; A_{13}=6-0=6$<br/>$A_{21}=-(0-6)=6 ; A_{22}=1-0=1 ; A_{23}=-3-0=-3$<br/>$A_{31}=0-2=-2 ; A_{32}=-(0-4)=4 ; A_{33}=1-0=1$<br/>$\therefore \operatorname{Adj} A=\left[\begin{array}{ccc}1 &amp; 6 &amp; -2 \\ -2 &amp; 1 &amp; 4 \\ 6 &amp; -3 &amp; 1\end{array}\right]$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2020 (14 Oct Shift 2)']
answer: <div class="solution">Theory question</div>
source_db: MarksBatch2_P2.db
title:
the-air-column-in-an-organ-pipe-closed-at-one-end-is-made-to-vibrate-so-that-there-are-2-nodes-and-antinodes-each-the-mode-of-vibration-is-called

slug:
the-air-column-in-an-organ-pipe-closed-at-one-end-is-made-to-vibrate-so-that-there-are-2-nodes-and-antinodes-each-the-mode-of-vibration-is-called-82113

question:
<div class="question">The air column in an organ pipe closed at one end is made to vibrate so that there are<br/>2 nodes and antinodes each. The mode of vibration is called</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">1st overtone</span> </div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'VITEEE', 'VITEEE 2011']
source_db: MarksBatch2_P2.db
title:
the-alcohol-having-molecular-formula-c-4-h-9-oh-when-shaken-with-a-mixture-of-anhydrous-zncl-2-and-conc-hcl-gives-an-oily-layer-product-after-five-min

slug:
the-alcohol-having-molecular-formula-c-4-h-9-oh-when-shaken-with-a-mixture-of-anhydrous-zncl-2-and-conc-hcl-gives-an-oily-layer-product-after-five-min-79416

question:
<div class="question">The alcohol having molecular formula $\mathrm{C}_{4} \mathrm{H}_{9} \mathrm{OH}$, when shaken with a mixture of anhydrous $\mathrm{ZnCl}_{2}$ and conc. HCl gives an oily layer product after five minutes. The alcohol is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{H}_{3} \mathrm{C}-\left(\mathrm{CH}_{2}\right)_{3}-\mathrm{OH}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{CH}-\mathrm{CH}_{2} \mathrm{OH}_{1}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\left(\mathrm{CH}_{3}\right)_{3} \mathrm{C}-\mathrm{OH}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2}-\mathrm{CH}_{3}$</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">$\mathrm{H}_{3} \mathrm{C}-\mathrm{CH}(\mathrm{OH}) \mathrm{CH}_{2}-\mathrm{CH}_{3}$</span> </div>

answer:
<div class="solution">Secondary alcohol, when shaken with a mixture of anthydrous $\mathrm{ZnCl}_{2}$ and conc. $\mathrm{HCl}$ (Lucas regent) gives an oily layer product after five minutes.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/viteee/XPhIBC5Z1CIjdKh9irdXTdXUAgT3Yf4ZjnOg-9SBVZA.original.fullsize.png"/><br/><br/>oily layer product after $5 \mathrm{~min}$.<br/>The amines in which amino group is directly attached to benzene ring undergo diazot isat ion reaction.</div>


title: the-alcohol-that-produces-turbidity-immediately-with-zncl-2-conc-hcl-at-room-temperature
slug: the-alcohol-that-produces-turbidity-immediately-with-zncl-2-conc-hcl-at-room-temperature-36566
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'MHT CET', 'MHT CET 2008']
source_db: MarksBatch2_P2.db
question:
<div class="question">The alcohol that produces turbidity immediately with $\mathrm{ZnCl}_{2} /$ conc. HCl at room temperature</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2-hydroxy-2-methyl propane</span> </div>

answer:
<div class="solution">Mixture of anhydrous $\mathrm{ZnCl}_{2}$ and conc. HCl is known as Lucas reagent. Lucas test is used for the distinction between primary, secondary and tertiary alcohols. The tertiary alcohol reacts immediately with Lucas reagent producing turbidity. The secondary alcohol gives turbidity within 5-10 min and primary alcohol do not give turbidity at all at room temperature. In the given alternates, 2 -hydroxy-2-methyl propane is $3^{\circ}$ alcohol, so it is more reactive.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2012 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">30,1</span> </div>
source_db: MarksBatch2_P2.db
title:
the-algebraic-sum-of-the-deviations-of-20-observations-measured-from-30-is-2-what-would-be-the-mean-of-the-observations

slug:
the-algebraic-sum-of-the-deviations-of-20-observations-measured-from-30-is-2-what-would-be-the-mean-of-the-observations-56496

question:
<div class="question">The algebraic sum of the deviations of 20 observations measured from 30 is 2 . What would be the mean of the $\begin{array}{ll}\text { observations? } &amp; {}\end{array}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\quad 30$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">32</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$30.2$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">30,1</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 $\sum_{i=1}^{20}\left(x_{i}-30\right)=2$<br/>$\Rightarrow \sum_{i=1}^{20} x_{i}-\sum_{i=1}^{20} 30=2$<br/>$\Rightarrow \sum_{i=1}^{20} x_{1}=2+\sum_{i=1}^{20} 30=2+30 \times 20=602$<br/>Now, mean $=\frac{\sum_{i=1}^{20} x_{i}}{20}$<br/>$\therefore \quad$ Mean $=\frac{602}{20}=30.1$</div>


tags: ['Chemistry', 'Electrochemistry', 'TS EAMCET', 'TS EAMCET 2023 (14 May Shift 1)']
source_db: MarksBatch2_P2.db
title:
the-alkali-metal-with-lowest-e-m-m-v-is-x-and-the-alkali-metal-with-highest-e-m-m-v-is-y-then-x-and-y-are-respectively

slug:
the-alkali-metal-with-lowest-e-m-m-v-is-x-and-the-alkali-metal-with-highest-e-m-m-v-is-y-then-x-and-y-are-respectively-64295

question:
<div class="question">The alkali metal with lowest $\mathrm{E}_{\mathrm{M}^{+} / \mathrm{M}}(\mathrm{V})$ is $\mathrm{X}$ and the alkali metal with highest $\mathrm{E}_{\mathrm{M}^{+} / \mathrm{M}}^{\circ}(\mathrm{V})$ is $\mathrm{Y}$. Then $\mathrm{X}$ and Y are respectively</div>

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

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

answer:
<div class="solution">The standard reduction potential of $\mathrm{Li}^{+}$is lowest because of its exceptionally small size and high chargeto-mass ratio. It is highest for $\mathrm{Na}^{+}$to $\mathrm{Na}$ due to its size, electropositivity and hydration enthalpy.</div>


title: the-alternating-emf-induced-in-the-secondary-coil-of-a-transformer-is-mainly-due-to
slug: the-alternating-emf-induced-in-the-secondary-coil-of-a-transformer-is-mainly-due-to-63644
tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2023 (14 May Shift 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The alternating e.m.f. induced in the secondary coil of a transformer is mainly due to</div>

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

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

answer:
<div class="solution">The secondary coil experiences an emf as a result of the changing magnetic field. Therefore, a changing magnetic field is primarily responsible for the transformer voltage that is induced in a transformer's secondary coil.</div>


title: the-amine-a-when-treated-with-nitrous-acid-gives-a-yellow-oily-substance-the-amine-a-is-1
slug: the-amine-a-when-treated-with-nitrous-acid-gives-a-yellow-oily-substance-the-amine-a-is-1-34521
tags: ['Chemistry', 'Amines', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question">The amine 'A', when treated with nitrous acid, gives a yellow oily substance. The amine A is</div>

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

answer:
<div class="solution"><math><mrow><mrow><msup><mrow><mn>2</mn></mrow><mrow><mi>o</mi></mrow></msup></mrow><mo>/</mo><mrow><mi> </mi></mrow></mrow></math> Secondary amines <math><mover accent="false"><mo>â</mo><mrow><mi mathvariant="normal">N</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">s</mi><mi> </mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi></mrow></mover></math> Yellow oily substance.<br/>Out of these given four options, only methyl phenylamine is a secondary amine.</div>


title: the-amine-that-reacts-will-hinsbergs-reagent-to-give-an-alkali-insoluble-product-is
slug: the-amine-that-reacts-will-hinsbergs-reagent-to-give-an-alkali-insoluble-product-is-38085
tags: ['Chemistry', 'Amines', 'NEET', 'NEET 2019 (Odisha)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The amine that reacts will Hinsberg's reagent to give an alkali insoluble product is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/g-VJIGgUivFeHbY_9XG-i47X0iQt2-jOGblW07UX2qY.original.fullsize.png"/><br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/R535U7HKKi7fPU1IIA8P5bd6ftLEZlgIIz7yEmWZIks.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/X_5KT2vLri6HJVqlKDubKvNI9D61iX8NZRH1g6o_izM.original.fullsize.png"/><br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/GlSzhjrQ5xRG92GOZIiYNFNv9IxODtoLklb2KGDBB6A.original.fullsize.png"/><br/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/g-VJIGgUivFeHbY_9XG-i47X0iQt2-jOGblW07UX2qY.original.fullsize.png"/><br/></span> </div>

answer:
<div class="solution">Secondary amines on reaction with Hinsberg's reagent (benzene sulphonyl chloride) forms $\mathrm{N}, \mathrm{N}$-dialkyl benzene sulphonamide. The product formed is not acidic as no $\mathrm{H}$-atom is attached to $\mathrm{N}$ thus it is insoluble in alkali.<br/>The reaction of $2^{\circ}$ amine given in option (1) takes place as follows:<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/badhYXKX3jH_UPxIRCJ49xW7iiAqJVC7RzoGkoLBRJQ.original.fullsize.png"/><br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/3zv_67fhVQOnMK19T6A1vDZ3CGCsCvfHhVdazPXx-6A.original.fullsize.png"/><br/><br/>On the other hand, $1^{\circ}$ amines react with Hinsberg's reagent to yield $\mathrm{N}$-alkyl benzene sulphonamide which is soluble in alkali and $3^{\circ}$ amines do not react with $\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}$. The remaining options contain $1^{\circ}$ and $3^{\circ}$ amines.<img src="https://cdn-question-pool.getmarks.app/pyq/neet/4G5GQRwUDaQ2U2jT4aR-VDldjAa9riTYF9TW3TOni_c.original.fullsize.png"/><br/><br/>Thus, option (1) is correct.</div>


title: the-amine-which-can-react-with-c-6-h-5-so-2-cl-to-form-a-product-insoluble-in-alkali-shall-be
slug: the-amine-which-can-react-with-c-6-h-5-so-2-cl-to-form-a-product-insoluble-in-alkali-shall-be-45797
tags: ['Chemistry', 'Amines', 'JEE Main']
source_db: MarksBatch2_P2.db
question:
<div class="question">The amine which can react with $\mathrm{C}_6 \mathrm{H}_5-\mathrm{SO}_2-\mathrm{Cl}$ to form a product insoluble in alkali shall be</div>

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

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

answer:
<div class="solution">$\mathrm{C}_6 \mathrm{H}_5 \mathrm{SO}_2 \mathrm{Cl}$ is called Hinsberg's reagent; they react with secondary amine to form a product that is soluble in alkalies. This reaction used to separate $1^{\circ}, 2^{\circ}$ and $3^{\circ}$ amine from their mixture.</div>


title: the-amine-which-does-not-react-with-chloroform-and-ethanolic-potassium-hydroxide-is-1
slug: the-amine-which-does-not-react-with-chloroform-and-ethanolic-potassium-hydroxide-is-1-54182
tags: ['Chemistry', 'Amines', 'AP EAMCET', 'AP EAMCET 2018 (25 Apr Shift 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The amine which does not react with chloroform and ethanolic potassium hydroxide is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/e9e16e71-3ccd-435b-a253-37ebbbd7d019-image.png" style="width: 158px; height: 62px;"/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">C</mi><mn>6</mn></msub><msub><mi mathvariant="normal">H</mi><mn>5</mn></msub><mo>-</mo><msub><mi>NH</mi><mn>2</mn></msub></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/5faf56e7-0b6d-4234-8a8c-6f53def33b0b-image.png" style="width: 79px; height: 109px;"/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/4ebb93d3-be7b-49dd-9cc2-ac24efbf7f62-image.png" style="width: 117px; height: 61px;"/></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/e9e16e71-3ccd-435b-a253-37ebbbd7d019-image.png" style="width: 158px; height: 62px;"/></span> </div>

answer:
<div class="solution"><p>The carbylamine reaction (also known as Hoffmann isocyanide synthesis) is a synthesis of an isocyanide by the reaction of a primary amine, chloroform and a base (ethanolic potassium hydroxide). If a primary amine is present, the isocyanide is formed, which are foul-smelling substances.</p><p>Only primary amines give<b> </b>carbylamine test and secondary, tertiary amines do not give this test.</p></div>


title: the-amine-which-will-not-liberate-nitrogen-with-nitrous-acid-is
slug: the-amine-which-will-not-liberate-nitrogen-with-nitrous-acid-is-80706
question: <div class="question">The amine which will not liberate nitrogen with nitrous acid is</div>
tags: ['Chemistry', 'Amines', 'COMEDK', 'COMEDK 2012']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">ethyl amine</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">methyl amine</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">dimethyl amine</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">2-amino propane</span> </li> </ul>

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

answer:
<div class="solution">Only aliphatic primary amines react with nitrous acid to give alcohols with the evolution of $N_{2}$ gas.<br/>$$<br/>R-\mathrm{NH}_{2}+\mathrm{HONO} \stackrel{273-278 \mathrm{~K}}{\longrightarrow} R-\mathrm{OH}+\mathrm{N}_{2}+\mathrm{H}_{2} \mathrm{O}<br/>$$<br/>$\because$ Dimethyl amine is a secondary amine, it will not give $\mathrm{N}_{2}$ gas.</div>


tags: ['Biology', 'Ecosystem', 'NEET', 'NEET 2022 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-amount-of-biomass-or-organic-matter-produced-per-unit-area-over-a-time-period-by-plants-during-photosynthesis-is-called

slug:
the-amount-of-biomass-or-organic-matter-produced-per-unit-area-over-a-time-period-by-plants-during-photosynthesis-is-called-34040

question:
<div class="question">The amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis is called:</div>

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

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

answer:
<div class="solution">Productivity is the total amount of biomass or organic matter produced per unit area. Over a period of time by plants. This is also called Primary production.<br/>$\rightarrow$ Productivity of consumer is called Secondary production.</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-amount-of-biomass-or-organic-matter-produced-per-unit-area-over-a-time-period-by-the-plants-during-photosynthesis-is-called

slug:
the-amount-of-biomass-or-organic-matter-produced-per-unit-area-over-a-time-period-by-the-plants-during-photosynthesis-is-called-84138

question:
<div class="question">The amount of biomass or organic matter produced per unit area over a time period by the plants during photosynthesis is called</div>

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

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

answer:
<div class="solution">Each trophic level has a certain mass of living material at a particular time called as the standing crop. The standing crop is measured as the mass of living organism (biomass) or the number in a unit area. The biomass of a species is expressed in terms of fresh weight or dry weight. Measurement of biomass in terms of dry weight is more accurate.<br/> Primary production is defined as the amount of biomass or organic matter produced per unit area over a time period by plants during photosynthesis.</div>


tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P2.db
title:
the-amount-of-organic-matter-or-biomass-that-is-generated-by-producers-per-unit-area-over-a-span-of-time-is-called

slug:
the-amount-of-organic-matter-or-biomass-that-is-generated-by-producers-per-unit-area-over-a-span-of-time-is-called-88855

question:
<div class="question">The amount of organic matter or biomass that is generated by producers per unit area over a span of time is called ___</div>

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

answer:
<div class="solution">The amount of organic matter or biomass that is generated by producers per unit area over a span of time is called primary productivity.</div>


tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-a-lies-in-the-third-quadrant-and-it-satisfies-the-equation-4-sin-2-x-cos-x-1-what-is-the-measure-of-the-beginarraylltext-angle-a

slug:
the-angle-a-lies-in-the-third-quadrant-and-it-satisfies-the-equation-4-sin-2-x-cos-x-1-what-is-the-measure-of-the-beginarraylltext-angle-a-81870

question:
<div class="question">The angle $A$ lies in the third quadrant and it satisfies the equation $4\left(\sin ^{2} x+\cos x\right)=1$. What is the measure of the $\begin{array}{ll}\text { angle } A ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$225^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$240^{\circ}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$210^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$210^{\circ}$</span> </div>

answer:
<div class="solution">Given equation is $4\left(\sin ^{2} x+\cos x\right)=1$<br/>$\Rightarrow 4 \sin ^{2} x+4 \cos x=1$<br/>$\Rightarrow 4 \sin ^{2} x+4 \cos x-1=0$<br/>$\Rightarrow 4\left(1-\cos ^{2} x\right)+4 \cos x-1=0$<br/>$\Rightarrow 4-4 \cos ^{2} x+4 \cos x-1=0$<br/>$\Rightarrow-4 \cos ^{2} x+4 \cos x+3=0$<br/>$\Rightarrow 4 \cos ^{2} x-4 \cos x-3=0$<br/>This is the quadratic in $\cos x$. $\Rightarrow 4 \cos ^{2} x-6 \cos x+2 \cos x-3=0$<br/>$\Rightarrow(2 \cos x-3)(2 \cos x+1)=0$<br/>$\Rightarrow \cos x=\frac{3}{2}$ and $\cos x=-\frac{1}{2}$<br/>$\cos x=\frac{3}{2}$ is not possible therefore $\cos x=-\frac{1}{2}$<br/>$\Rightarrow \cos A=-\frac{1}{2}=\cos 210^{\circ}$<br/>$\Rightarrow A=210^{\circ}$</div>


title: the-angle-between-lines-represented-by-sin-2-y-2-2-x-y-cos-2-cos-2-1-x-2-0-is
slug: the-angle-between-lines-represented-by-sin-2-y-2-2-x-y-cos-2-cos-2-1-x-2-0-is-89433
tags: ['Mathematics', 'Pair of Lines', 'AP EAMCET', 'AP EAMCET 2021 (24 Aug Shift 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angle between lines represented by $\left(\sin ^2 \alpha\right) y^2-2 x y\left(\cos ^2 \alpha\right)+\left(\cos ^2 \alpha-1\right) x^2=0$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$2 \alpha$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\alpha$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$90^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$45^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$90^{\circ}$</span> </div>

answer:
<div class="solution">Pair of straight lines<br/>$$<br/>\left(\sin ^2 \alpha\right) y^2-2 x y \cos ^2 \alpha+\left(\cos ^2 \alpha-1\right) x^2=0<br/>$$<br/>Standard form<br/>$$<br/>\begin{aligned}<br/>&amp; a x^2+2 h x y+b y^2=0 \\<br/>&amp; \therefore \quad \begin{array}{l}<br/>a=\cos ^2 \alpha-1 \\<br/>h=-\cos ^2 \alpha \\<br/>b=\sin ^2 \alpha<br/>\end{array} \\<br/>&amp; \because \tan \theta=\left|\frac{2 \sqrt{h^2-a b}}{a+b}\right|<br/>\end{aligned}<br/>$$<br/>$\begin{gathered}\tan \theta=\left|\frac{2 \sqrt{\cos ^4 \alpha-\left(\cos ^2 \alpha-1\right) \sin ^2 \alpha}}{\cos ^2 \alpha-1+\sin ^2 \alpha}\right| \\ \because \sin ^2 \alpha+\cos ^2 \alpha=1 \\ \therefore \quad \tan \theta=\left|\frac{2 \sqrt{\cos ^4 \alpha+\sin ^4 \alpha}}{0}\right| \\ \tan \theta=\infty \Rightarrow \theta=90^{\circ}\end{gathered}$</div>


title: the-angle-between-the-curves-y-sin-x-and-y-cos-x-0-x-2-is
slug: the-angle-between-the-curves-y-sin-x-and-y-cos-x-0-x-2-is-79942
tags: ['Mathematics', 'Area Under Curves', 'MHT CET', 'MHT CET 2022 (07 Aug Shift 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angle between the curves $y=\sin x$ and $y=\cos x 0<x is=""> <div class="tags" data-pagefind-ignore=""> <span class="tag">Mathematics</span><span class="tag">Area Under Curves</span><span class="tag">MHT CET</span><span class="tag">MHT CET 2022 (07 Aug Shift 2)</span> </div> <span class="label">Options:</span>
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\tan ^{-1}(\sqrt{2})$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}(3 \sqrt{2})$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\tan ^{-1}(2 \sqrt{2})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\tan ^{-1}(3 \sqrt{3})$</span> </li> </ul> <!-- /Question --> <!-- Solution --> <section class="solution-container" id="accepted-answer"> <div class="solution-header"> <span class="label">Solution:</span> <div class="badges-container" data-pagefind-ignore=""> <span class="badge upvotes-count"> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.625 5.0075C14.4842 4.84795 14.3111 4.72019 14.1171 4.63269C13.9231 4.54519 13.7128 4.49996 13.5 4.5H10V3.5C10 2.83696 9.73661 2.20107 9.26777 1.73223C8.79893 1.26339 8.16304 1 7.5 1C7.40711 0.999934 7.31604 1.02574 7.237 1.07454C7.15795 1.12333 7.09407 1.19318 7.0525 1.27625L4.69125 6H2C1.73478 6 1.48043 6.10536 1.29289 6.29289C1.10536 6.48043 1 6.73478 1 7V12.5C1 12.7652 1.10536 13.0196 1.29289 13.2071C1.48043 13.3946 1.73478 13.5 2 13.5H12.75C13.1154 13.5001 13.4684 13.3668 13.7425 13.1252C14.0166 12.8835 14.1931 12.5501 14.2388 12.1875L14.9888 6.1875C15.0153 5.97626 14.9966 5.76179 14.9339 5.55833C14.8712 5.35488 14.7659 5.16711 14.625 5.0075ZM2 7H4.5V12.5H2V7Z" fill="#014A82"></path> </svg> 1233 Upvotes
</span> <span class="badge expert-verification-badge" data-pagefind-ignore=""> <svg fill="none" height="16" viewbox="0 0 16 16" width="16" xmlns="http://www.w3.org/2000/svg"> <path d="M14.1163 6.42625C13.8806 6.18 13.6369 5.92625 13.545 5.70312C13.46 5.49875 13.455 5.16 13.45 4.83187C13.4406 4.22187 13.4306 3.53062 12.95 3.05C12.4694 2.56937 11.7781 2.55937 11.1681 2.55C10.84 2.545 10.5012 2.54 10.2969 2.455C10.0744 2.36312 9.82 2.11937 9.57375 1.88375C9.1425 1.46937 8.6525 1 8 1C7.3475 1 6.85812 1.46937 6.42625 1.88375C6.18 2.11937 5.92625 2.36312 5.70312 2.455C5.5 2.54 5.16 2.545 4.83187 2.55C4.22187 2.55937 3.53062 2.56937 3.05 3.05C2.56937 3.53062 2.5625 4.22187 2.55 4.83187C2.545 5.16 2.54 5.49875 2.455 5.70312C2.36312 5.92562 2.11937 6.18 1.88375 6.42625C1.46937 6.8575 1 7.3475 1 8C1 8.6525 1.46937 9.14187 1.88375 9.57375C2.11937 9.82 2.36312 10.0738 2.455 10.2969C2.54 10.5012 2.545 10.84 2.55 11.1681C2.55937 11.7781 2.56937 12.4694 3.05 12.95C3.53062 13.4306 4.22187 13.4406 4.83187 13.45C5.16 13.455 5.49875 13.46 5.70312 13.545C5.92562 13.6369 6.18 13.8806 6.42625 14.1163C6.8575 14.5306 7.3475 15 8 15C8.6525 15 9.14187 14.5306 9.57375 14.1163C9.82 13.8806 10.0738 13.6369 10.2969 13.545C10.5012 13.46 10.84 13.455 11.1681 13.45C11.7781 13.4406 12.4694 13.4306 12.95 12.95C13.4306 12.4694 13.4406 11.7781 13.45 11.1681C13.455 10.84 13.46 10.5012 13.545 10.2969C13.6369 10.0744 13.8806 9.82 14.1163 9.57375C14.5306 9.1425 15 8.6525 15 8C15 7.3475 14.5306 6.85812 14.1163 6.42625ZM10.8538 6.85375L7.35375 10.3538C7.30731 10.4002 7.25217 10.4371 7.19147 10.4623C7.13077 10.4874 7.06571 10.5004 7 10.5004C6.93429 10.5004 6.86923 10.4874 6.80853 10.4623C6.74783 10.4371 6.69269 10.4002 6.64625 10.3538L5.14625 8.85375C5.05243 8.75993 4.99972 8.63268 4.99972 8.5C4.99972 8.36732 5.05243 8.24007 5.14625 8.14625C5.24007 8.05243 5.36732 7.99972 5.5 7.99972C5.63268 7.99972 5.75993 8.05243 5.85375 8.14625L7 9.29313L10.1462 6.14625C10.1927 6.09979 10.2479 6.06294 10.3086 6.0378C10.3692 6.01266 10.4343 5.99972 10.5 5.99972C10.5657 5.99972 10.6308 6.01266 10.6914 6.0378C10.7521 6.06294 10.8073 6.09979 10.8538 6.14625C10.9002 6.1927 10.9371 6.24786 10.9622 6.30855C10.9873 6.36925 11.0003 6.4343 11.0003 6.5C11.0003 6.5657 10.9873 6.63075 10.9622 6.69145C10.9371 6.75214 10.9002 6.8073 10.8538 6.85375Z" fill="#00672E"></path> </svg>
Verified Answer
</span> </div> </div> <div class="correct-answer">
The correct answer is:
<span class="option-value">$\tan ^{-1}(2 \sqrt{2})$</span> </div> <div class="solution">$y=\sin x$ and $y=\cos x$ intersects at $x=\frac{\pi}{4}$<br/>$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\text {for first curve at } x=\frac{\pi}{4}}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}$<br/>$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\text {for second curve at } x=\frac{\pi}{4}}=-\sin \frac{\pi}{4}=-\frac{1}{\sqrt{2}}$<br/>Required angle $=\theta=\tan ^{-1}\left\{\frac{\frac{1}{\sqrt{2}}-\left(-\frac{1}{\sqrt{2}}\right)}{1+\left(\frac{1}{\sqrt{2}}\right)\left(-\frac{1}{\sqrt{2}}\right)}\right\}=\tan ^{-1}\left(\frac{\sqrt{2}}{\frac{1}{2}}\right)$<br/>$=\tan ^{-1}(2 \sqrt{2})$</div> </section> <!-- /Solution --> <!-- Call to Action --> <section class="call-to-action" data-pagefind-ignore=""> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\tan ^{-1}(\sqrt{2})$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\tan ^{-1}(3 \sqrt{2})$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\tan ^{-1}(2 \sqrt{2})$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\tan ^{-1}(3 \sqrt{3})$</span> </li> </ul>

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

answer:
<div class="solution">$y=\sin x$ and $y=\cos x$ intersects at $x=\frac{\pi}{4}$<br/>$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\text {for first curve at } x=\frac{\pi}{4}}=\cos \frac{\pi}{4}=\frac{1}{\sqrt{2}}$<br/>$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{\text {for second curve at } x=\frac{\pi}{4}}=-\sin \frac{\pi}{4}=-\frac{1}{\sqrt{2}}$<br/>Required angle $=\theta=\tan ^{-1}\left\{\frac{\frac{1}{\sqrt{2}}-\left(-\frac{1}{\sqrt{2}}\right)}{1+\left(\frac{1}{\sqrt{2}}\right)\left(-\frac{1}{\sqrt{2}}\right)}\right\}=\tan ^{-1}\left(\frac{\sqrt{2}}{\frac{1}{2}}\right)$<br/>$=\tan ^{-1}(2 \sqrt{2})$</div>


title: the-angle-between-the-lines-with-direction-ratios-1-0-cos-is-6-0-what-is-the-value-of
slug: the-angle-between-the-lines-with-direction-ratios-1-0-cos-is-6-0-what-is-the-value-of-60576
tags: ['Mathematics', 'Three Dimensional Geometry', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angle between the lines with direction ratios $(1,0, \pm \cos \alpha)$ is $60^{\circ} .$ What is the value of ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\cos ^{-1}(1 / \sqrt{3})$</span> </div>

answer:
<div class="solution">Let the angle between two lines whose direction ratios are $a_{1}, b_{1}, c_{1}$ and $a_{2}, b_{2}, c_{2}$ respectively is 0 .<br/>Then, $\cos \theta=\frac{a_{1} a_{2}+b_{1} b_{2}+c_{1} c_{2}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}} \sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}$<br/>$\cos 60^{\circ}=\frac{1 \times 1+0 \times 0+(\cos \alpha)(-\cos \alpha)}{\sqrt{1^{2}+(0)^{2}+\cos ^{2} \alpha} \sqrt{1^{2}+(0)^{2}+(-\cos \alpha)^{2}}}$<br/>$\Rightarrow \frac{1}{2}=\frac{1-\cos ^{2} \alpha}{\sqrt{1+\cos ^{2}} \alpha \sqrt{1+\cos ^{2} \alpha}}$<br/>$\Rightarrow \frac{1}{2}=\frac{1-\cos ^{2} \alpha}{1+\cos ^{2} \alpha} \Rightarrow \frac{1+2}{1-2}=\frac{2}{-2 \cos ^{2} \alpha}$<br/>$\Rightarrow \frac{3}{-1}=\frac{1}{-\cos ^{2} \alpha}$<br/>$\Rightarrow \cos \alpha=\frac{1}{\sqrt{3}} \Rightarrow \alpha=\cos ^{-1}\left(\frac{1}{\sqrt{3}}\right)$</div>


tags: ['Mathematics', 'Pair of Lines', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angle-between-the-lines-x-y-3-0-and-x-y-3-0-is-and-the-acute-angle-between-the-lines-x-3-y-2-3-0-and-3-x-y-1-0-is-which-one-of-the-following-is-co

slug:
the-angle-between-the-lines-x-y-3-0-and-x-y-3-0-is-and-the-acute-angle-between-the-lines-x-3-y-2-3-0-and-3-x-y-1-0-is-which-one-of-the-following-is-co-41819

question:
<div class="question">The angle between the lines $x+y-3=0$ and $x-y+3=0$ is $\alpha$ and the acute angle between the lines<br/>$\mathrm{x}-\sqrt{3} \mathrm{y}+2 \sqrt{3}=0$ and $\sqrt{3} \mathrm{x}-\mathrm{y}+1=0$ is $\beta .$ Which one of<br/>the following is correct?</div>

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

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

answer:
<div class="solution">$\quad$ The slope of line $x+y-3=0$ is $-1$ The slope of line $x-y+3=0$ is 1 So, these are perpendicular lines and so angle between them is $90^{\circ}$.<br/>$\therefore \alpha=90^{\circ}$<br/>The slope of line $x-\sqrt{3} y+2 \sqrt{3}=0$ is $m_{1}=\frac{1}{\sqrt{3}}$<br/>The slope of line $\sqrt{3} \mathrm{x}-\mathrm{y}+1=0$ is $\mathrm{m}_{2}=\sqrt{3}$.<br/>$\therefore \tan \beta=\left|\frac{\sqrt{3}-\frac{1}{\sqrt{3}}}{1+(\sqrt{3})\left(\frac{1}{\sqrt{3}}\right)}\right|=\left|\frac{2}{2 \sqrt{3}}\right|=\frac{1}{\sqrt{3}} \therefore \beta=30^{\circ}$<br/>$\therefore \alpha&gt;\beta$</div>


title: the-angle-between-the-two-lines-1-x-my-n-0-and-1-x-m-y-n-0-is-given-by-tan-1-what-equal-to
slug: the-angle-between-the-two-lines-1-x-my-n-0-and-1-x-m-y-n-0-is-given-by-tan-1-what-equal-to-60232
tags: ['Mathematics', 'Straight Lines', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angle between the two lines $1 \mathrm{x}+\mathrm{my}+\mathrm{n}=0$ and $1^{\prime} x+m^{\prime} y+n^{\prime}=0$ is given by $\tan ^{-1} \theta .$ What $\theta$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\left|\frac{\ell \mathrm{m}^{\prime}-\ell^{\prime} \mathrm{m}}{\ell \ell^{\prime}-\mathrm{mm}^{\prime}}\right|$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\left|\frac{\ell \mathrm{m}^{\prime}+\ell^{\prime} \mathrm{m}}{\ell \ell^{\prime}+\mathrm{mm}^{\prime}}\right|$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\left|\frac{\varepsilon \mathrm{m}^{\prime}-\ell^{\prime} \mathrm{m}}{\ell \ell^{\prime}+\mathrm{mm}^{\prime}}\right|$</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">$\left|\frac{\ell \mathrm{m}^{\prime}+\ell^{\prime} \mathrm{m}}{\ell \ell^{\prime}-\mathrm{mm}^{\prime}}\right|$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\left|\frac{\varepsilon \mathrm{m}^{\prime}-\ell^{\prime} \mathrm{m}}{\ell \ell^{\prime}+\mathrm{mm}^{\prime}}\right|$</span> </div>

answer:
<div class="solution">$\tan ^{-1}(\theta)=\tan ^{-1}\left|\frac{\ell m^{\prime}-\ell^{\prime} m}{\ell \ell^{\prime}+m m^{\prime}}\right|$<br/>$\Rightarrow \theta=\left|\frac{\ell m^{\prime}-\ell^{\prime} m}{\ell \ell^{\prime}+m m^{\prime}}\right|$</div>


title: the-angle-between-velocity-and-acceleration-of-a-particle-describing-uniform-circular-motion-is
tags: ['Physics', 'Laws of Motion', 'NEET']
source_db: MarksBatch2_P2.db
slug:
the-angle-between-velocity-and-acceleration-of-a-particle-describing-uniform-circular-motion-is-52605

question:
<div class="question">The angle between velocity and acceleration of a particle describing uniform circular motion is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><msup><mrow><mn>180</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><msup><mrow><mn>90</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><msup><mrow><mn>45</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><msup><mrow><mn>60</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msup><mrow><mn>90</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> </div>

answer:
<div class="solution">When an object follows a circular path at a constant speed, the motion of object is called uniform circular motion.<br/><br/>Although the speed does not vary the particle is accelerating because the velocity changes its direction at every point on circular track.<br/><br/> <img call-to-action="" data-pagefind-ignore="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/yawadzpgcwjwjgndwhezufmtskkmijpxlgvewhtqcnrqystlrm.jpeg" style="max-width:100%; object-fit:contain /&gt; &lt;br/&gt;&lt;br/&gt;The acceleration is centripetal, which is perpendicular to motion at every point and acts along the radius and directed towards the centre of the curved circular path.&lt;/div&gt; &lt;/section&gt; &lt;!-- /Solution --&gt; &lt;!-- Call to Action --&gt; &lt;section class="/> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-from-a-point-on-the-bank-of-ariver-of-the-top-of-a-temple-on-the-other-bank-is-4-5-retreating-50-m-the-observer-finds-the-new-a

slug:
the-angle-of-elevation-from-a-point-on-the-bank-of-ariver-of-the-top-of-a-temple-on-the-other-bank-is-4-5-retreating-50-m-the-observer-finds-the-new-a-84000

question:
<div class="question">The angle of elevation from a point on the bank of ariver of the top of a temple on the other bank is $45^{\circ}$. Retreating $50 \mathrm{~m}$, the observer finds the new angle of elevation as $30^{\circ} .$ What is the width of the river? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$50 \sqrt{3} \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$50 /(\sqrt{3}-1) \mathrm{m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 /(\sqrt{3}-1) \mathrm{m}$</span> </div>

answer:
<div class="solution">$\operatorname{In} \Delta \mathrm{ABC}, \tan 45^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/Tjl4lwyliSmFefknY7CY0WQ7ILqaYLZ-n6jy4H0_mmk.original.fullsize.png"/><br/><br/>$\Rightarrow 1=\frac{h}{x}$<br/>$\Rightarrow h=x$<br/>Now, in $\triangle \mathrm{ABD}$.<br/>$\tan 30^{\circ}=\frac{A B}{B D}$<br/>$\Rightarrow \frac{1}{\sqrt{3}}=\frac{h}{x+50}$<br/>$\Rightarrow x+50=h \sqrt{3}$<br/>$\Rightarrow h+50=h \sqrt{3}$<br/>[fom Eq. (i)]<br/>$\Rightarrow h=\frac{50}{\sqrt{3}-1} m$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-a-stationary-cloud-from-a-point-25-m-above-a-lake-is-1-5-and-the-angle-of-depression-of-its-image-in-the-lake-is-4-5-the-hei

slug:
the-angle-of-elevation-of-a-stationary-cloud-from-a-point-25-m-above-a-lake-is-1-5-and-the-angle-of-depression-of-its-image-in-the-lake-is-4-5-the-hei-26545

question:
<div class="question">The angle of elevation of a stationary cloud from a point $25 \mathrm{~m}$ above a lake is $15^{\circ}$ and the angle of depression of its image in the lake is $45^{\circ} .$ The height of the cloud above the lake level is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$25 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$25 \sqrt{3} \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$50 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$50 \sqrt{3} \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$25 \sqrt{3} \mathrm{~m}$</span> </div>

answer:
<div class="solution">PQ is the lake and $\mathrm{A}$ is the point of observation. Given, $\mathrm{AP}=25 \mathrm{~m}, \angle \mathrm{BAD}=15^{\circ}$ and $\angle \mathrm{DAC}=45^{\circ}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/vGm-hk0lnOGN5xTVRRI3Wf2bUa0vfX4vh8w3nu6ckCo.original.fullsize.png"/><br/><br/>Let $\mathrm{BD}=\mathrm{x}$<br/>Then, $\mathrm{DQ}=\mathrm{AP}=25 \mathrm{~m}$ and $\mathrm{QC}=\mathrm{BD}+\mathrm{DQ}=\mathrm{x}+25$<br/>Also, $\mathrm{DC}=\mathrm{DQ}+\mathrm{QC}=25+\mathrm{x}+25=\mathrm{x}+50$<br/>In $\triangle \mathrm{ADC}$<br/>$\tan 45^{\circ}=\frac{\mathrm{DC}}{\mathrm{AD}}=\frac{\mathrm{x}+50}{\mathrm{AD}}$<br/>$\Rightarrow 1=\frac{\mathrm{x}+50}{\mathrm{AD}} \Rightarrow \mathrm{AD}=\mathrm{x}+50$<br/>Also, $\tan 15^{\circ}=\frac{\sqrt{3}-1}{\sqrt{3}+1}$.<br/>In $\Delta \mathrm{ABD}, \tan 15^{\circ}=\frac{\mathrm{BD}}{\mathrm{AD}}$<br/>$\Rightarrow \frac{\sqrt{3}-1}{\sqrt{3}+1}=\frac{x}{x+50} \quad($ from $(1))$<br/>$\Rightarrow(x+50)(\sqrt{3}-1)=x(\sqrt{3}+1)$<br/>$\Rightarrow \sqrt{3} x-x+50 \sqrt{3}-50=\sqrt{3} x+x$<br/>$\Rightarrow 2 \mathrm{x}=50 \sqrt{3}-50=50(\sqrt{3}-1)$<br/>$\Rightarrow x=25(\sqrt{3}-1)$<br/>Now, $B Q=B D+D Q=x+25$<br/>$=25(\sqrt{3}-1)+25$<br/>$=25 \sqrt{3}-25+25$<br/>$=25 \sqrt{3}$<br/>$\therefore$ Height of the cloud above the lake $=25 \sqrt{3} \mathrm{~m}$.</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-a-tower-at-a-level-ground-is-3-0-the-angle-of-elevation-becomes-when-10-m-moved-towards-the-tower-if-the-height-of-tower-is-

slug:
the-angle-of-elevation-of-a-tower-at-a-level-ground-is-3-0-the-angle-of-elevation-becomes-when-10-m-moved-towards-the-tower-if-the-height-of-tower-is-28888

question:
<div class="question">The angle of elevation of a tower at a level ground is $30^{\circ}$. The angle of elevation becomes $\theta$ when $10 \mathrm{~m}$ moved towards the tower. If the height of tower is $5 \sqrt{3} \mathrm{~m}$, then what is $\theta$ equal to? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$45^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$60^{\circ}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$75^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above</span> </li> </ul>

answer:
<div class="solution">Let $\mathrm{BC}$ be the tower of height $5 \sqrt{3} \mathrm{~m}$ Let $\mathrm{AD}=10 \mathrm{~m}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/XMEeJrXnfTyi0IZgKBVUWOC4JWzAB1IJ08yjHGSvfWU.original.fullsize.png"/><br/><br/>In $\Delta \mathrm{ABC}$<br/>$\frac{\mathrm{BC}}{\mathrm{AB}}=\tan 30^{\circ}$<br/>$\Rightarrow A B=\frac{B C}{\tan 30^{\circ}}=\frac{5 \sqrt{3}}{1 / \sqrt{3}}=15$<br/>Given $\mathrm{AD}=10 \mathrm{~m}$<br/>$\therefore \mathrm{DB}=(15-10) \mathrm{m}=5 \mathrm{~m}$<br/>In $\Delta \mathrm{BCD}$<br/>$\frac{\mathrm{BC}}{\mathrm{BD}}=\tan \theta$<br/>$\frac{5 \sqrt{3}}{5}=\tan \theta \Rightarrow \tan \theta=\sqrt{3}$<br/>$\Rightarrow \theta=60^{\circ}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-a-tower-of-height-h-from-a-point-a-due-south-of-it-is-x-and-from-a-point-b-due-east-of-a-is-y-if-ab-z-then-which-one-of-the-

slug:
the-angle-of-elevation-of-a-tower-of-height-h-from-a-point-a-due-south-of-it-is-x-and-from-a-point-b-due-east-of-a-is-y-if-ab-z-then-which-one-of-the-26627

question:
<div class="question">The angle of elevation of a tower of height h from a point $A$ due South of it is $\mathrm{x}$ and from a point $\mathrm{B}$ due East of $\mathrm{A}$ is $\mathrm{y}$. If $\mathrm{AB}=\mathrm{z}$, then which one of the following is correct?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\mathrm{h}^{2}\left(\cot ^{2} \mathrm{y}-\cot ^{2} \mathrm{x}\right)=\mathrm{z}^{2}$</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">$z^{2}\left(\cot ^{2} y-\cot ^{2} x\right)=h^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$h^{2}\left(\tan ^{2} y-\tan ^{2} x\right)=z^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$z^{2}\left(\tan ^{2} y-\tan ^{2} x\right)=h^{2}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{h}^{2}\left(\cot ^{2} \mathrm{y}-\cot ^{2} \mathrm{x}\right)=\mathrm{z}^{2}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/uUzNmqy8nixim70ntM0niR7DX061vnWTQQKtwdyuj2I.original.fullsize.png"/><br/><br/>from figure (iii), $\mathrm{h}^{2} \cot ^{2} \mathrm{y}=\mathrm{z}^{2}+\mathrm{h}^{2} \cot ^{2} \mathrm{x}$<br/>$\Rightarrow \mathrm{z}^{2}=\mathrm{h}^{2}\left(\cot ^{2} \mathrm{y}-\cot ^{2} \mathrm{x}\right)$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-tip-of-a-flag-staff-from-a-point-10-m-due-south-of-its-base-is-6-0-what-is-the-height-of-the-flag-staff-correct-to-the-n

slug:
the-angle-of-elevation-of-the-tip-of-a-flag-staff-from-a-point-10-m-due-south-of-its-base-is-6-0-what-is-the-height-of-the-flag-staff-correct-to-the-n-43940

question:
<div class="question">The angle of elevation of the tip of a flag staff from a point 10 $\mathrm{m}$ due South of its base is $60^{\circ}$. What is the height of the flag staff correct to the nearest meter? $\quad$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$16 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$17 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$18 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$17 \mathrm{~m}$</span> </div>

answer:
<div class="solution">Let ' $\mathrm{A}$ ' be the top of the flag staff. Let ' $\mathrm{x}$ ' be the height of the flag staff<br/>$\operatorname{In} \Delta \mathrm{ABC}, \tan 60^{\circ}=\frac{\mathrm{x}}{10}$<br/>$\sqrt{3}=\frac{\mathrm{x}}{10}$<br/>$\mathrm{x}=10 \sqrt{3}=10 \times 1.732$<br/>$=17.32 \cong 17$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/eEcn71fILLKnzRKYWo84GmNf9OacTc8fjnMJtaQocjk.original.fullsize.png"/></div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-flag-post-from-a-point-5-m-away-fromits-base-is-7-5-what-is-the-approximate-height-of-the-flag-post

slug:
the-angle-of-elevation-of-the-top-of-a-flag-post-from-a-point-5-m-away-fromits-base-is-7-5-what-is-the-approximate-height-of-the-flag-post-21350

question:
<div class="question">The angle of elevation of the top of a flag post from a point 5 m away fromits base is $75^{\circ}$. What is the approximate height of the flag post?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$17 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$19 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$21 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$19 \mathrm{~m}$</span> </div>

answer:
<div class="solution">Let $h$ be the height of the flag post where $\mathrm{BC}$ is the base. In $\Delta \mathrm{ABC}$<br/>$\tan 75^{\circ}=\frac{A B}{B C}=\frac{h}{5}$<br/>$\Rightarrow \tan \left(45^{\circ}+30^{\circ}\right)=\frac{h}{5}$<br/>$\Rightarrow \frac{\tan 45^{\circ}+\tan 30^{\circ}}{1-\tan 45^{\circ} \tan 30^{\circ}}=\frac{h}{5}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/K-RdNkdiyuL0wIvbSssC8wQsoc7uvjQz0ljTKsxQ1WQ.original.fullsize.png"/><br/><br/>$\begin{aligned}(\because \tan (A+B)=&amp; \left.\frac{\tan A+\tan B}{1-\tan A \tan B}\right) \\ \Rightarrow \frac{\sqrt{3}+1}{\sqrt{3}-1}=\frac{h}{5} \Rightarrow h=\frac{(\sqrt{3}+1)^{2}}{(\sqrt{3})^{2}-(1)^{2}} \times 5 \\ \Rightarrow \quad h=5\left(\frac{3+1+2 \sqrt{3}}{3-1}\right)=5(2+\sqrt{3}) \\=5 \times 3.732=18.660 \end{aligned}$<br/>$=19 \mathrm{~m}$ (approx.)</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-pillar-of-height-h-at-a-point-on-the-ground-at-a-distance-x-from-the-pillar-is-3-0-on-walking-a-distanced-towar

slug:
the-angle-of-elevation-of-the-top-of-a-pillar-of-height-h-at-a-point-on-the-ground-at-a-distance-x-from-the-pillar-is-3-0-on-walking-a-distanced-towar-49178

question:
<div class="question">The angle of elevation of the top of a pillar of height $\mathrm{h}$ at a point on the ground at a distance $\mathrm{x}$ from the pillar is $30^{\circ} . \mathrm{On}$ walking a distance'd towards the pillar the angle of elevation becomes $60^{\circ}$. Then, which one of the following is correct?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{x}=\mathrm{d}+\mathrm{h}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$x=\frac{3 d}{2}$</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">$\mathrm{x}=\frac{5 \mathrm{~d}}{4} \quad$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{x}=2 \mathrm{~d} \quad\mathrm{}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$x=\frac{3 d}{2}$</span> </div>

answer:
<div class="solution">Let DC be the pillar of height $\mathrm{h}$ and $\mathrm{A}$ be the point at a distance $\mathrm{x}$ from pillar such that $\angle \mathrm{CAD}=30^{\circ} .$ On walking a distance $\mathrm{d}$ towards pillar (point B) $\angle \mathrm{CBD}$ $=60^{\circ} .$ So, in $\Delta \mathrm{BCD}$<br/>$\tan 60^{\circ}=\frac{\mathrm{CD}}{\mathrm{BC}}$<br/>$\Rightarrow \sqrt{3}=\frac{\mathrm{h}}{\mathrm{x}-\mathrm{d}}$<br/>$\Rightarrow \mathrm{h}=\sqrt{3}(\mathrm{x}-\mathrm{d})$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/9HK3A0VuFyze5a9_1xxtzGLLhuOUYByaz680QNTQAmw.original.fullsize.png"/><br/><br/>and in $\triangle \mathrm{ACD}$,<br/>$$<br/>\begin{array}{l}<br/>\tan 30^{\circ}=\frac{\mathrm{CD}}{\mathrm{AC}} \\<br/>\Rightarrow \frac{1}{\sqrt{3}}=\frac{\mathrm{h}}{\mathrm{x}} \\<br/>\Rightarrow \mathrm{x}=\mathrm{h} \sqrt{3} \\<br/>\Rightarrow \mathrm{x}=3(\mathrm{x}-\mathrm{d})<br/>\end{array}<br/>$$<br/>(using Eq. (i))<br/>$$<br/>\Rightarrow x=3 x-3 d<br/>$$<br/>$$<br/>\begin{array}{l}<br/>\Rightarrow 2 \mathrm{x}=3 \mathrm{~d} \\<br/>\Rightarrow \mathrm{x}=\frac{3 \mathrm{~d}}{2}<br/>\end{array}<br/>$$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-tower-ef-f-being-the-foot-of-the-tower-as-seen-from-a-point-a-which-is-on-the-same-level-as-f-is-on-advancing-t

slug:
the-angle-of-elevation-of-the-top-of-a-tower-ef-f-being-the-foot-of-the-tower-as-seen-from-a-point-a-which-is-on-the-same-level-as-f-is-on-advancing-t-48611

question:
<div class="question">The angle of elevation of the top of a tower EF (F being the foot of the tower) as seen from a point $A$ which is on the same level as $\mathrm{F}$, is $\alpha$. On advancing towards the foot of the tower the angle of elevation of the top of the tower as seen from a point $B$ such that $A B=x$, is $\beta .$ If $B F=y$, his the height of the tower and $\alpha+\beta=\frac{\pi}{2}$, then which one of the following is correct?</div>

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

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

answer:
<div class="solution">Let EF be the height of the tower, and $\mathrm{FB}=\mathrm{Y}, \mathrm{AB}=\mathrm{x}$ and $\mathrm{EF}=\mathrm{h}$.<br/>$\operatorname{In} \Delta \mathrm{BEF}$,<br/>$$<br/>\begin{array}{l}<br/>\tan \beta=\frac{\mathrm{EF}}{\mathrm{BF}} \\<br/>\tan \beta=\frac{\mathrm{h}}{\mathrm{y}}<br/>\end{array}<br/>$$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/bGoem7r3JA9gre8WecvHQ7kbgZqpNMznP7-fkZzObr8.original.fullsize.png"/><br/><br/>and in $\triangle \mathrm{AFE}$,<br/>$\begin{aligned} &amp; \tan \alpha=\frac{E F}{A F} \\ \Rightarrow &amp; \tan \alpha=\frac{\mathrm{h}}{\mathrm{x}+\mathrm{y}}, \\ \Rightarrow &amp; \tan \left(\frac{\pi}{2}-\beta\right)=\frac{\mathrm{h}}{\mathrm{x}+\mathrm{y}} \quad\left(\text { Given that } \alpha+\beta=\frac{\pi}{2}\right) \\ \Rightarrow &amp; \cot \beta=\frac{\mathrm{h}}{\mathrm{x}+\mathrm{y}} \end{aligned}$<br/>From Eqs. (i) and (ii), we get<br/>$\begin{aligned} &amp; \tan \beta \cdot \cot \beta=\frac{\mathrm{h}}{\mathrm{y}} \cdot \frac{\mathrm{h}}{(\mathrm{x}+\mathrm{y})} \quad(\because \tan \beta \cdot \cot \beta=1) \\ \Rightarrow \mathrm{xy}+\mathrm{y}^{2}=\mathrm{h}^{2} \end{aligned}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-tower-from-a-point-20-m-away-from-its-base-is-4-5-what-is-the-height-of-the-tower

slug:
the-angle-of-elevation-of-the-top-of-a-tower-from-a-point-20-m-away-from-its-base-is-4-5-what-is-the-height-of-the-tower-31641

question:
<div class="question">The angle of elevation of the top of a tower from a point $20 \mathrm{~m}$ away from its base is $45^{\circ}$. What is the height of the tower?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$10 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$20 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$30 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$40 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$20 \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\operatorname{In} \Delta \mathrm{ABC}$,<br/>$\mathrm{AB}=\mathrm{h}$<br/>$\mathrm{BC}=20 \mathrm{~m}$<br/>$\angle \mathrm{C}=45^{\circ}$<br/>$\therefore \quad \tan 45^{\circ}=\frac{\mathrm{AB}}{\mathrm{BC}}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/tHlXDGfSHMQV301Lq2yVJmWV_11w3V8rTJGX4HHPu2A.original.fullsize.png"/><br/><br/>$1=\frac{\mathrm{h}}{20}$<br/>$\mathrm{h}=20 \mathrm{~m}$<br/>$\therefore \quad$ Height of the tower $=20 \mathrm{~m}$<br/>$\therefore$ Option (b) is correct.</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-tower-from-two-places-situated-at-distances-21-m-and-x-m-from-the-base-of-the-tower-are-4-5-and-6-0-respectivel

slug:
the-angle-of-elevation-of-the-top-of-a-tower-from-two-places-situated-at-distances-21-m-and-x-m-from-the-base-of-the-tower-are-4-5-and-6-0-respectivel-58066

question:
<div class="question">The angle of elevation of the top of a tower from two places situated at distances $21 \mathrm{~m}$. and $x \mathrm{~m}$. from the base of the tower are $45^{\circ}$ and $60^{\circ}$ respectively. What is the value of $x$ ?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$7 \sqrt{3}$</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">$7-\sqrt{3}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$7+\sqrt{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">14</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$7 \sqrt{3}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/02YEAtI6ViPPK2P1A8jcR3WjYWiL2ENi0ZuesURunvQ.original.fullsize.png"/><br/><br/>$\operatorname{In} \triangle \mathrm{ADB}, \tan 45^{\circ}=\frac{\mathrm{AD}}{\mathrm{BD}}=\frac{\mathrm{AD}}{21}$<br/>$\mathrm{AD}=21 \mathrm{~m}$<br/>$\operatorname{In} \triangle \mathrm{ADC}, \tan 60^{\circ}=\frac{\mathrm{AD}}{\mathrm{x}}$<br/>$\mathrm{x}=\frac{21}{\sqrt{3}}=7 \sqrt{3} \mathrm{~m}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angle-of-elevation-of-the-top-of-a-tower-of-height-h-from-the-foot-of-another-tower-in-the-same-plane-is-6-0-and-the-angle-of-elevation-of-the-top

slug:
the-angle-of-elevation-of-the-top-of-a-tower-of-height-h-from-the-foot-of-another-tower-in-the-same-plane-is-6-0-and-the-angle-of-elevation-of-the-top-17634

question:
<div class="question">The angle of elevation of the top of a tower of height $\mathrm{H}$ from the foot of another tower in the same plane is $60^{\circ}$ and the angle of elevation of the top of the second tower from the foot of the first tower is $30^{\circ}$. If $\mathrm{h}$ is the height of the other tower, then which one of the following is correct?</div>

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

answer:
<div class="solution">Let $\mathrm{AB}$ be the tower of height $\mathrm{H}$. Let $\mathrm{CD}$ be the tower of height $\mathrm{h}$. Let $\mathrm{x}$ be the distance between the $\mathrm{AB}$ and $\mathrm{CD}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/eQUWG4N902bwC7aD0u6i6AKf0GgkrctiAI8utbOyvvw.original.fullsize.png"/><br/><br/>from $\Delta \mathrm{ABC}, \frac{\mathrm{H}}{\mathrm{x}}=\sqrt{3}$ and from $\Delta \mathrm{ACD}, \frac{\mathrm{h}}{\mathrm{x}}=\frac{1}{\sqrt{3}}$<br/>$\Rightarrow \frac{\mathrm{H}}{\mathrm{h}}=3 \Rightarrow \mathrm{H}=3 \mathrm{~h} .$</div>


title: the-angle-subtended-at-the-centre-of-a-circle-of-radius-3-cm-by-an-arc-of-length-1-cm-is
slug: the-angle-subtended-at-the-centre-of-a-circle-of-radius-3-cm-by-an-arc-of-length-1-cm-is-87635
tags: ['Mathematics', 'Trigonometric Ratios & Identities', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angle subtended at the centre of a circle of radius $3 \mathrm{~cm}$ by an arc of length $1 \mathrm{~cm}$ is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{30^{\circ}}{\pi}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{60^{\circ}}{\pi}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$60^{\circ}$</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">$\frac{60^{\circ}}{\pi}$</span> </div>

answer:
<div class="solution">Let $\theta$ be the required angle<br/>$\therefore \quad \theta=\frac{\operatorname{arc}}{\text { radius }}=\frac{1}{3}$ radians<br/>Now, 1 radian $=\frac{180^{\circ}}{\pi}$<br/>$\therefore \quad \frac{1}{3}$ radian $=\frac{180^{\circ}}{\pi} \times \frac{1}{3}=\frac{60^{\circ}}{\pi}$<br/>Hence, Required angle $=\theta=\frac{60^{\circ}}{\pi}$</div>


title: the-angles-a-b-c-of-a-triangle-are-in-the-ratio-2-5-5-what-is-the-value-of-tan-b-tan-c
slug: the-angles-a-b-c-of-a-triangle-are-in-the-ratio-2-5-5-what-is-the-value-of-tan-b-tan-c-54054
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2006 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The angles $\mathrm{A}, \mathrm{B}, \mathrm{C}$ of a triangle are in the ratio $2: 5: 5$. What is the value of $\tan \mathrm{B} \tan \mathrm{C} ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$4+\sqrt{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$4+2 \sqrt{3}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$7+4 \sqrt{3}$</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">$3+3 \sqrt{3}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$7+4 \sqrt{3}$</span> </div>

answer:
<div class="solution">Let the angles $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ of a triangle are $2 \mathrm{x}, 5 \mathrm{x}$ and $5 \mathrm{x}$, respectively So, $2 x+5 x+5 x=180^{\circ}$<br/>$\Rightarrow \mathrm{x}=\frac{180^{\circ}}{12}=15^{\circ}$<br/>Angles are $30^{\circ}, 75^{\circ}, 75^{\circ}$<br/>$\angle \mathrm{B}=75^{\circ}$ and $\angle \mathrm{C}=75^{\circ}$<br/>$\tan B \tan C=\left(\tan 75^{\circ}\right)^{2}=\left(\tan \left(45^{\circ}+30^{\circ}\right)\right)^{2}$<br/>$=\left(\frac{\tan 45^{\circ}+\tan 30^{\circ}}{1-\tan 45^{\circ} \tan 30^{\circ}}\right)^{2}=\left(\frac{1+\frac{1}{\sqrt{3}}}{1-\frac{1}{\sqrt{3}}}\right)^{2}=\left(\frac{\sqrt{3}+1}{\sqrt{3}-1}\right)^{2}$<br/>$=\left(\frac{(\sqrt{3}+1)^{2}}{3-1}\right)^{2}=\frac{1}{4}[3+1+2 \sqrt{3}]^{2}$<br/>$=\frac{1}{4}[4+2 \sqrt{3}]^{2}=\frac{1}{4}[16+12+16 \sqrt{3}]$<br/>$=\frac{1}{4}[28+16 \sqrt{3}]=7+4 \sqrt{3}$</div>


title: the-angles-of-a-triangle-are-in-ap-and-the-least-angle-is-3-0-what-is-the-greatest-angle-in-radian
tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch2_P2.db
slug:
the-angles-of-a-triangle-are-in-ap-and-the-least-angle-is-3-0-what-is-the-greatest-angle-in-radian-98820

question:
<div class="question">The angles of a triangle are in AP and the least angle is $30^{\circ}$. What is the greatest angle (in radian)?</div>

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

answer:
<div class="solution">We have, $\mathrm{a}=30^{\circ}, \mathrm{n}=3$,<br/>$\mathrm{S}_{3}=180^{\circ}$<br/>$\mathrm{S}_{3}=\frac{3}{2}\left[2 \times 30^{\circ}+(3-1) \mathrm{d}\right]$<br/>$180=\frac{3}{2}[60+2 \mathrm{~d}]$<br/>$180=3[30+\mathrm{d}]$<br/>$30+d=60$<br/>$\mathrm{d}=30$<br/>Now, largest angle $=\mathrm{a}+2 \mathrm{~d}=30+60=90^{\circ}=\frac{\pi}{2}$</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
title:
the-angles-of-elevation-of-the-top-of-a-tower-from-the-top-and-foot-of-a-pole-are-respectively-3-0-and-4-5-if-h-t-is-the-height-of-the-tower-and-h-p-i

slug:
the-angles-of-elevation-of-the-top-of-a-tower-from-the-top-and-foot-of-a-pole-are-respectively-3-0-and-4-5-if-h-t-is-the-height-of-the-tower-and-h-p-i-74557

question:
<div class="question">The angles of elevation of the top of a tower from the top and foot of a pole are respectively $30^{\circ}$ and $45^{\circ} .$ If $\mathrm{h}_{\mathrm{T}}$ is the height of the tower and $\mathrm{h}_{\mathrm{p}}$ is the height of the pole, then which of the following are correct? <br/>1.$\quad \frac{2 \mathrm{~h}_{\mathrm{P}} \mathrm{h}_{\mathrm{T}}}{3+\sqrt{3}}=\mathrm{h}_{\mathrm{P}}^{2} \quad$ <br/>2.$\quad \frac{\mathrm{h}_{\mathrm{T}}-\mathrm{h}_{\mathrm{P}}}{\sqrt{3}+1}=\frac{\mathrm{h}_{\mathrm{P}}}{2}$<br/>3.$\quad \frac{2\left(\mathrm{hp}+\mathrm{h}_{\mathrm{T}}\right)}{\mathrm{h}_{\mathrm{P}}}=4+\sqrt{3}$<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 3 only</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2 and 3 only</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1 and 2 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">1,2 and 3</span> </li> </ul>

answer:
<div class="solution">Let the distance between tower and pole be ' $\mathrm{x}$.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/0DjKR-lTpw_9fwj8s8wD_UQ6xNQxeezMUjVHcfV13GQ.original.fullsize.png"/><br/><br/>$\tan 45^{\circ}=\frac{\mathrm{h}_{\mathrm{t}}}{\mathrm{x}} \Rightarrow \frac{\mathrm{h}_{\mathrm{t}}}{\mathrm{x}}=1$<br/>$\Rightarrow \mathrm{h}_{\mathrm{t}}=\mathrm{x}$<br/>Now, $\tan 30^{\circ}=\frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\mathrm{x}} \Rightarrow \frac{1}{\sqrt{3}}=\frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\mathrm{x}}$<br/>$\Rightarrow \frac{1}{\sqrt{3}}=\frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\mathrm{h}_{\mathrm{t}}}$<br/>$\Rightarrow \frac{1}{\sqrt{3}-1}=\frac{h_{t}-h_{p}}{h_{t}-\left(h_{t}-h_{p}\right)}$<br/>$\Rightarrow \frac{\sqrt{3}+1}{2}=\frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\mathrm{h}_{\mathrm{p}}} \Rightarrow \frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\sqrt{3}+1}=\frac{\mathrm{h}_{\mathrm{p}}}{2}$<br/>So, statement ' 2 ' is correct.<br/>Now, $\frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}}{\mathrm{h}_{\mathrm{p}}}=\frac{\sqrt{3}+1}{2} \Rightarrow \frac{\mathrm{h}_{\mathrm{t}}-\mathrm{h}_{\mathrm{p}}+2 \mathrm{~h}_{\mathrm{p}}}{\mathrm{h}_{\mathrm{p}}}=\frac{\sqrt{3}+1+4}{2}$<br/>$\Rightarrow \frac{\mathrm{h}_{\mathrm{t}}+\mathrm{h}_{\mathrm{p}}}{\mathrm{h}_{\mathrm{p}}}=\frac{5+\sqrt{3}}{2}$<br/>So, statement ' 3 ' is incorrect.</div>


tags: ['Mathematics', 'Heights and Distances', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-angles-of-elevation-of-the-top-of-a-tower-standing-on-a-horizontal-plane-from-two-points-on-a-line-passing-through-the-foot-of-the-tower-at-distan

slug:
the-angles-of-elevation-of-the-top-of-a-tower-standing-on-a-horizontal-plane-from-two-points-on-a-line-passing-through-the-foot-of-the-tower-at-distan-76673

question:
<div class="question">The angles of elevation of the top of a tower standing on a horizontal plane from two points on a line passing through the foot of the tower at distances $49 \mathrm{~m}$ and $36 \mathrm{~m}$ are $43^{\circ}$ and $47^{\circ}$ respectively. What is the height of the tower?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$40 \mathrm{~m}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$42 \mathrm{~m}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$45 \mathrm{~m}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$47 \mathrm{~m}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$42 \mathrm{~m}$</span> </div>

answer:
<div class="solution">$\mathrm{AB}=\mathrm{h}$ (height of the tower $\mathrm{BD}=36 \mathrm{~m}$<br/>$\mathrm{BC}=49 \mathrm{~m}$<br/>$\angle \mathrm{D}=47^{\circ}$<br/>$\angle \mathrm{C}=43^{\circ}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/wlYF5daRaJTDK_rY06BMGHuHx9chNSsJSRlpMTatuyI.original.fullsize.png"/><br/><br/>Now, in $\triangle \mathrm{ABD}$,<br/>$\tan 47^{\circ}=\frac{\mathrm{h}}{36 \mathrm{~m}}$<br/>and in $\triangle \mathrm{ABC}$,<br/>$\tan 43^{\circ}=\frac{\mathrm{h}}{49 \mathrm{~m}}$<br/>$\tan \left(90^{\circ}-47^{\circ}\right)=\frac{\mathrm{h}}{49}$<br/>$\therefore \quad \cot 47^{\circ}=\frac{\mathrm{h}}{49}$<br/>Multiplying equations (i) and (ii)<br/>$\tan 47^{\circ} \cdot \cot 47^{\circ}=\frac{\mathrm{h}}{36} \times \frac{\mathrm{h}}{49}=1=\frac{\mathrm{h}^{2}}{36 \times 49}$<br/>$\mathrm{h}=6 \times 7=42 \mathrm{~m}$<br/>$\therefore \quad$ Option (b) is correct</div>


tags: ['Physics', 'Oscillations', 'JEE Main', 'JEE Main 2014 (11 Apr Online)']
source_db: MarksBatch2_P2.db
title:
the-angular-frequency-of-the-damped-oscillator-is-given-by-m-k-4-m-2-r-2-where-k-is-the-spring-constant-m-is-the-mass-of-the-oscillator-and-r-is-the-d

slug:
the-angular-frequency-of-the-damped-oscillator-is-given-by-m-k-4-m-2-r-2-where-k-is-the-spring-constant-m-is-the-mass-of-the-oscillator-and-r-is-the-d-65554

question:
<div class="question">The angular frequency of the damped oscillator is given by, $\omega=\sqrt{\left(\frac{\mathrm{k}}{\mathrm{m}}-\frac{\mathrm{r}^2}{4 \mathrm{~m}^2}\right)}$ where $\mathrm{k}$ is the spring constant, $\mathrm{m}$ is the mass of the oscillator and $r$ is the damping constant. If the ratio $\frac{r^2}{\mathrm{mk}}$ is $8 \%$, the change in time period compared to the undamped oscillator is approximately as follows:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>increases by $1 \%$<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>increases by $8 \%$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>decreases by $1 \%$<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>decreases by $8 \%$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>increases by $1 \%$<br/></span> </div>

answer:
<div class="solution">The change in time period compared to the undamped oscillator increases by $1 \%$.</div>


title: the-antrum-is
slug: the-antrum-is-85786
question: <div class="question">The antrum is</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Fluid filled cavity of Graffian follicle</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">An inner theca interna</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The secondary follicle</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Fluid filled cavity of primary follicle</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Fluid filled cavity of Graffian follicle</span> </div>

answer:
<div class="solution">The antrum is the fluid-filled space found in antral or Graafian follicles; also called the follicular cavity.</div>


title: the-area-bounded-by-the-coordinate-axes-and-the-curve-x-y-1-is
slug: the-area-bounded-by-the-coordinate-axes-and-the-curve-x-y-1-is-70462
tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The area bounded by the coordinate axes and the curve $\sqrt{\mathrm{x}}+\sqrt{\mathrm{y}}=1$, is</div>

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

answer:
<div class="solution">$\begin{aligned} \text { Area }=\int y d x \\=&amp; \int_{0}^{1}(1-\sqrt{x})^{2} d x \end{aligned}$<br/>$[\because$ curve makes the intercept of 1 on both axes] $=\int_{0}^{1}(1+x-2 \sqrt{x}) d x$<br/>$=[\mathrm{x}]_{0}^{1}+\frac{1}{2}\left[\mathrm{x}^{2}\right]_{0}^{1}-\frac{4}{3}\left[\mathrm{x}^{\frac{3}{2}}\right]_{0}^{1}$<br/>$=1+\frac{1}{2}-\frac{4}{3}=\frac{3}{2}-\frac{4}{3}=\frac{1}{6} \mathrm{sq}$ unit</div>


title: the-area-bounded-by-the-curve-x-f-y-the-y-axis-and-the-two-lines-y-a-and-y-b-is-equal-to
slug: the-area-bounded-by-the-curve-x-f-y-the-y-axis-and-the-two-lines-y-a-and-y-b-is-equal-to-28662
tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The area bounded by the curve $x=\mathrm{f}[\mathrm{y}]$, the $\mathrm{y}$ -axis and the two lines $\mathrm{y}=\mathrm{a}$ and $\mathrm{y}=\mathrm{b}$ is equal to: $\quad\mathrm{}$</div>

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

answer:
<div class="solution">Required Area $=\int_{\mathrm{y}=\mathrm{a}}^{\mathrm{b}} \mathrm{f}(\mathrm{y}) \mathrm{d} \mathrm{y}=\int_{\mathrm{a}}^{\mathrm{b}} \mathrm{x} \mathrm{dy}$</div>


title: the-area-bounded-by-the-curve-x-y-1-is
slug: the-area-bounded-by-the-curve-x-y-1-is-37412
question: <div class="question">The area bounded by the curve $|\mathrm{x}|+|\mathrm{y}|=1$ is</div>
tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1 square unit</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$2 \sqrt{2}$ square units</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">2 square units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2 \sqrt{3}$ square units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2 square units</span> </div>

answer:
<div class="solution">$|\mathrm{x}|+|\mathrm{y}|=1$<br/>We know, $|x|=\left\{\begin{array}{l}x, x \geq 0 \\ -x, x   &lt; 0\end{array}\right.$<br/>$\therefore|x|+|y|=1$ is<br/>$\left\{\begin{array}{cc}x+y=1 &amp; \text { for } x&gt;0, y&gt;0 \\ -x+y=1 &amp; \text { for } x &lt; 0, y&gt;0 \\ x-y=1 &amp; \text { for } x&gt;0, y &lt; 0 \\ -x-y=1 &amp; \text { for } x &lt; 0, y &lt; 0\end{array}\right.$<br/>If we plot graphs of these equations, we get<img src="https://cdn-question-pool.getmarks.app/pyq/nda/e54_e7Cw2SZE_qS2FPE9hi7nJxh9F2RkL82f-2rLwk4.original.fullsize.png"/><br/><br/>The curve is symmetrical about $\mathrm{x}$ any $\mathrm{y}$ -axis. $\therefore$ Area $=4 \times$ Area of $A O D$<br/>$=4 \times \int_{0}^{1} \mathrm{ydx}=4 \times \int_{0}^{1}(1-\mathrm{x}) \mathrm{d} \mathrm{x}=4\left[\mathrm{x}-\frac{\mathrm{x}^{2}}{2}\right]_{0}^{1}$<br/>$=4\left[1-\frac{1^{2}}{2}-\left(0-\frac{0^{2}}{2}\right)\right]$<br/>$=4\left(1-\frac{1}{2}\right)=4 \times \frac{1}{2}=2$</div>


title: the-area-bounded-by-the-curve-y-x-2-xaxis-x-1-and-x-4-is
slug: the-area-bounded-by-the-curve-y-x-2-xaxis-x-1-and-x-4-is-32907
question: <div class="question">The area bounded by the curve, $y=-x^2$, x-axis, $x=1$ and $x=4$, is</div>
tags: ['Mathematics', 'Area Under Curves', 'MHT CET', 'MHT CET 2022 (08 Aug Shift 1)']
source_db: MarksBatch2_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">21 sq. units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">10 sq. units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">20 sq. units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{21}{2}$ sq. units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">21 sq. units</span> </div>

answer:
<div class="solution">$-\int_1^4\left(-x^2\right) \mathrm{d} x=\left[\frac{x^3}{3}\right]_1^4=\frac{64}{3}-\frac{1}{3}=21$ sq. units<br/><img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/MjTIzhV5Cvi15Nkg4jfQAwKNANC9NDAuoMih5yyv4-k.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P2.db
title:
the-area-of-a-rectangle-whose-length-is-five-more-than-twice-its-width-is-75-square-unit-the-length-is

slug:
the-area-of-a-rectangle-whose-length-is-five-more-than-twice-its-width-is-75-square-unit-the-length-is-16833

question:
<div class="question">The area of a rectangle whose length is five more than twice its width is 75 square unit. The length is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5 unit</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">10 unit</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">15 unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">20 unit</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">15 unit</span> </div>

answer:
<div class="solution">Letwidth of the rectangle $=\mathrm{x}$ so, length $=2 \mathrm{x}+5$<br/>Given, Area of rectangle $=75$ $\Rightarrow x(2 x+5)=75 \Rightarrow 2 x^{2}+5 x-75=0$<br/>$\Rightarrow 2 x^{2}+15 x-10 x-75=0$<br/>$\Rightarrow(x-5)(2 x+15)=0$<br/>$\Rightarrow \quad x=5,-\frac{15}{2}$<br/>Since, width can not be negative.<br/>$\mathrm{x}=5$<br/>length $=2 \mathrm{x}+5=15$ unit</div>


tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P2.db
title:
the-area-of-a-triangle-whose-vertices-are-3-4-5-2-and-the-point-of-intersection-of-the-lines-x-a-and-y-5-is-3-square-units-what-is-the-value-of-a

slug:
the-area-of-a-triangle-whose-vertices-are-3-4-5-2-and-the-point-of-intersection-of-the-lines-x-a-and-y-5-is-3-square-units-what-is-the-value-of-a-17755

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

answer:
<div class="solution">Area of $\Delta \mathrm{ABC}=3 \mathrm{sq}$. unit<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/q24OWgnBh1TOQLiRbSBFGZX-XFnsFCaKXsiJkY3qWeo.original.fullsize.png"/><br/><br/>$\therefore \quad \frac{1}{2}\left|\begin{array}{lll}3 &amp; 4 &amp; 1 \\ 5 &amp; 2 &amp; 1 \\ \mathrm{a} &amp; 5 &amp; 1\end{array}\right|=3$<br/>$\therefore\left|\begin{array}{lll}3 &amp; 4 &amp; 1 \\ 5 &amp; 2 &amp; 1 \\ \mathrm{a} &amp; 5 &amp; 1\end{array}\right|=6$<br/>$\begin{array}{ll}\therefore &amp; 3(2-5)-4(5-a)+1(25-2 a)=6 \\ &amp; -9-20+4 a+25-2 a=6 \\ &amp; 2 a=10 \\ &amp; a=5\end{array}$<br/>Option (d) is correct</div>


tags: ['Mathematics', 'Area Under Curves', 'JEE Main']
source_db: MarksBatch2_P2.db
title:
the-area-of-the-closed-figure-bounded-by-x1-x2-and-yleftbeginarrayclx22-x-leq-1-2-x1-x1endarrayright-and-the-x-axis-is

slug:
the-area-of-the-closed-figure-bounded-by-x1-x2-and-yleftbeginarrayclx22-x-leq-1-2-x1-x1endarrayright-and-the-x-axis-is-73093

question:
<div class="question">The area of the closed figure bounded by \( x=-1, x=2 \) and \( y=\left\{\begin{array}{cl}-x^{2}+2, &amp; x \leq 1 \\ 2 x-1, &amp; x&gt;1\end{array}\right. \) and the \( x \)-axis is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">\( \frac{16}{3} \) sq. units</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\( \frac{10}{3} \) sq. units</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">\( \frac{13}{3} \) sq. units</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( \frac{7}{3} \) sq. units</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( \frac{16}{3} \) sq. units</span> </div>

answer:
<div class="solution"><blockquote><p><img src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/7fb2f827-7481-46a9-896a-6933914676c9-image.png" style="width: 300px; height: 399px;"/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><msubsup><mo>∫</mo><mrow><mo>-</mo><mn>1</mn></mrow><mn>1</mn></msubsup><mfenced><mrow><mo>-</mo><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><mn>2</mn></mrow></mfenced><mi>d</mi><mi>x</mi><mo>+</mo><msubsup><mo>∫</mo><mn>1</mn><mn>2</mn></msubsup><mfenced><mrow><mn>2</mn><mi>x</mi><mo>-</mo><mn>1</mn></mrow></mfenced><mi>d</mi><mi>x</mi></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msubsup><mfenced><mrow><mo>-</mo><mfrac><msup><mi>x</mi><mn>3</mn></msup><mn>3</mn></mfrac><mo>+</mo><mn>2</mn><mi>x</mi></mrow></mfenced><mrow><mo>-</mo><mn>1</mn></mrow><mn>1</mn></msubsup><mo>+</mo><msup><mfenced><mrow><msup><mi>x</mi><mn>2</mn></msup><mo>-</mo><mi>x</mi></mrow></mfenced><mn>2</mn></msup></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>16</mn><mn>3</mn></mfrac><mi mathvariant="normal"> </mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">q</mi><mo>.</mo><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">s</mi></math></p></blockquote></div>


title: the-area-of-the-figure-formed-by-the-lines-a-x-b-y-c-0-a-x-b-y-c-0-a-x-b-y-c-0-and-a-x-b-y-c-0-is
tags: ['Mathematics', 'Area Under Curves', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
slug:
the-area-of-the-figure-formed-by-the-lines-a-x-b-y-c-0-a-x-b-y-c-0-a-x-b-y-c-0-and-a-x-b-y-c-0-is-66860

question:
<div class="question">The area of the figure formed by the lines $a x+b y+c=0$, $a x-b y+c=0, a x+b y-c=0$ and $a x-b y-c=0$ is</div>

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

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

answer:
<div class="solution">Area of triangle<br/>$\Delta \mathrm{AOB}=\frac{1}{2} \times \frac{\mathrm{c}}{\mathrm{b}} \times \frac{\mathrm{c}}{\mathrm{a}}=\frac{\mathrm{c}^{2}}{2 \mathrm{ab}}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/oZG7nITyp_38zG0dj6h-Knlc0U0-gA5OCUL-WYCnDGk.original.fullsize.png"/><br/><br/>Total area $=4 \times$ area $\triangle \mathrm{AOB}$<br/>$=4 \times \frac{\mathrm{c}^{2}}{2 \mathrm{ab}}$<br/>$=\frac{2 c^{2}}{a b}$</div>


title: the-area-of-the-square-one-of-whose-diagonals-is-3-i-4-j-is
slug: the-area-of-the-square-one-of-whose-diagonals-is-3-i-4-j-is-19260
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The area of the square, one of whose diagonals is $3 \hat{i}+4 \hat{j}$ is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">12 square unit</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$12.5$ square unit</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">25 square unit</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$156.25$ square unit</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12.5$ square unit</span> </div>

answer:
<div class="solution">Length of diagonal<br/>$=\mathrm{D}=\sqrt{3^{2}+4^{2}}$<br/>$\Rightarrow \mathrm{D}=5$<br/>$\therefore$ Area $=\frac{1}{2}(\mathrm{D})^{2}=\frac{25}{2}$<br/>$=12.5$ units</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">31.5</span> </div>
source_db: MarksBatch2_P2.db
title:
the-arithmetic-mean-and-standard-deviation-of-a-data-of-nine-numbers-are-13-and-5-respectively-if-3-is-included-as-the-10th-item-of-the-data-then-the--1

slug:
the-arithmetic-mean-and-standard-deviation-of-a-data-of-nine-numbers-are-13-and-5-respectively-if-3-is-included-as-the-10th-item-of-the-data-then-the-1-17291

question:
<div class="question">The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10th item of the data, then the variance of the data of ten number is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">23.5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">21.5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">31.5</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">27</span> </li> </ul>

answer:
<div class="solution">$\because \frac{\sum_{i=1}^9 x_i}{9}=13 \Rightarrow \sum_{i=1}^9 x_i=117$.<br/>$\begin{array}{rlrl} &amp; &amp; &amp; \\ \text { and } &amp; &amp; \sigma^2=25=\frac{\sum_{i=1}^9 x_i^2}{9}-(13)^2 \\ \Rightarrow &amp; \quad \sum_{i=1}^9 x_i^2=9[25+169]\end{array}$<br/>Now, after including $10^{\text {th }}$ item as ' 3 '<br/>$$<br/>\begin{gathered}<br/>\text { New mean } \bar{y}=\frac{\sum_{i=1}^9 x_i+3}{10}=\frac{117+3}{10}=12 \\<br/>\text { and new variance }=\frac{\left(\sum_{i=1}^9 x_i^2+9\right)}{10}-(12)^2 \\<br/>=\frac{(169+25+1) 9}{10}-144=\frac{1755-1440}{10}=31.5<br/>\end{gathered}<br/>$$</div>


tags: ['Mathematics', 'Statistics', 'AP EAMCET', 'AP EAMCET 2018 (22 Apr Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">31.5</span> </div>
source_db: MarksBatch2_P2.db
title:
the-arithmetic-mean-and-standard-deviation-of-a-data-of-nine-numbers-are-13-and-5-respectively-if-3-is-included-as-the-10th-item-of-the-data-then-the-

slug:
the-arithmetic-mean-and-standard-deviation-of-a-data-of-nine-numbers-are-13-and-5-respectively-if-3-is-included-as-the-10th-item-of-the-data-then-the-89039

question:
<div class="question">The arithmetic mean and standard deviation of a data of nine numbers are 13 and 5 respectively. If 3 is included as the 10th item of the data, then the variance of the data of ten number is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">23.5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">21.5</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">31.5</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">27</span> </li> </ul>

answer:
<div class="solution">$\because \frac{\sum_{i=1}^9 x_i}{9}=13 \Rightarrow \sum_{i=1}^9 x_i=117$.<br/>$\begin{array}{rlrl} &amp; &amp; &amp; \\ \text { and } &amp; &amp; \sigma^2=25=\frac{\sum_{i=1}^9 x_i^2}{9}-(13)^2 \\ \Rightarrow &amp; \quad \sum_{i=1}^9 x_i^2=9[25+169]\end{array}$<br/>Now, after including $10^{\text {th }}$ item as ' 3 '<br/>$$<br/>\begin{gathered}<br/>\text { New mean } \bar{y}=\frac{\sum_{i=1}^9 x_i+3}{10}=\frac{117+3}{10}=12 \\<br/>\text { and new variance }=\frac{\left(\sum_{i=1}^9 x_i^2+9\right)}{10}-(12)^2 \\<br/>=\frac{(169+25+1) 9}{10}-144=\frac{1755-1440}{10}=31.5<br/>\end{gathered}<br/>$$</div>


title: the-arithmetic-mean-of-1-8-27-64-up-ton-terms-is-given-by
slug: the-arithmetic-mean-of-1-8-27-64-up-ton-terms-is-given-by-25214
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch2_P2.db
question:
<div class="question">The arithmetic mean of $1,8,27,64, \ldots . .$ up ton terms is given<br/>by</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{n(n+1)^{2}}{2}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{n(n+1)^{2}}{4}$</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><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{n}^{2}(\mathrm{n}+1)^{2}}{4}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{n(n+1)^{2}}{4}$</span> </div>

answer:
<div class="solution">Sum of the given terms $=1+8+27+64 \ldots \ldots .+$ upton terms<br/>Sum $=1^{3}+2^{3}+3^{3}+4^{3}+\ldots \ldots .+$ upto $n$ terms<br/>Sum $=\left(\frac{n(n+1)}{2}\right)^{2}=\frac{n^{2}(n+1)^{2}}{4}$<br/>$\mathrm{AM}=\frac{\mathrm{n}^{2}(\mathrm{n}+1)^{2}}{4} \times \frac{1}{\mathrm{n}}=\frac{\mathrm{n}(\mathrm{n}+1)^{2}}{4}$</div>


