# questions

tags: ['Chemistry', 'General Organic Chemistry', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-2methyl-pentane-b-22-dimethyl-butane-c-4ethyl23dimethyloctane-d-4lmethylethyl-heptane-how-many-of-them-have-isopropyl-group

slug:
in-a-2methyl-pentane-b-22-dimethyl-butane-c-4ethyl23dimethyloctane-d-4lmethylethyl-heptane-how-many-of-them-have-isopropyl-group-86745

question:
<div class="question">In<br/>(a) 2-Methyl pentane<br/>(b) \( 2,2 \)-Dimethyl butane<br/>(c) 4-Ethyl-2,3-dimethyloctane<br/>(d) 4-(l-Methylethyl) heptane<br/>How many of them have isopropyl group?</div>

answer:
<div class="solution"><blockquote><p>An iso group means a methyl branching on the second carbon.</p><p>(a) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math>-Methyl pentane- It contains a branching on the secondary carbon.</p><p><img height="79" src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/4592dade-803c-48d2-aa78-d0c9bb924cd8-image.png" width="164"/></p><p>(b) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo> </mo><mn>2</mn></math>-Dimethyl butane: There are two substituents on the second carbon, so it is called as neo.</p><p><img height="96" src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/d8f3e391-2a44-447f-806a-d2465d636e6d-image.png" width="138"/></p></blockquote><p> </p><blockquote><p>(c) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>-Ethyl-<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>-</mo></math>dimethyloctane - It contains a branching on the second carbon, so it is an iso group.</p><p><img height="131" src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/dd138067-9e44-48f4-aa2d-d1b30e5942cc-image.png" width="270"/></p><p>(d) <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math>-(<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>-Methyl ethyl) heptane -<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math>-methyl ethyl group is called as an iso group. </p><p><img height="108" src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/39b79549-017d-42bb-9064-894c044e1837-image.png" width="241"/></p><p>A, C, D contain iso group.</p></blockquote></div>


title: in-a-50-gm-living-tissue-what-would-be-the-amount-of-water
slug: in-a-50-gm-living-tissue-what-would-be-the-amount-of-water-93822
question: <div class="question">In a $50 \mathrm{gm}$ living tissue, what would be the amount of water?</div>
tags: ['Biology', 'Transport in Plants', 'AIIMS', 'AIIMS 2011']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$15-25 \mathrm{gm}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$25-30 \mathrm{gm}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$35-45 \mathrm{gm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$70-90 \mathrm{gm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$35-45 \mathrm{gm}$</span> </div>

answer:
<div class="solution">Water is the most abundant chemical compound in living organism. In a cell, water occupies $70-90 \%$ of the cellular mass. So, in 50 $\mathrm{gm}$ of living tissue 35-45 gm of water would be present.</div>


title: in-a-a-bc-a-b-3-1-3-cm-and-a-b-3-1-3-cm-if-angle-a-is-3-0-then-what-is-the-angle-b
slug: in-a-a-bc-a-b-3-1-3-cm-and-a-b-3-1-3-cm-if-angle-a-is-3-0-then-what-is-the-angle-b-13481
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a $\triangle A B C$, $a+b=3(1+\sqrt{3}) \mathrm{cm}$ and $a-b=3(1-\sqrt{3}) \mathrm{cm}$.<br/>If angle $A$ is $30^{\circ}$, then what is the angle $B$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$120^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$90^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$75^{\circ}$</span> </li><li class="correct"> <span class="option-label">D</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> </ul>

answer:
<div class="solution">Given, $a+b=3(1+\sqrt{3}) \ldots \ldots \ldots$. (1)<br/>and $a-b=3(1-\sqrt{3}) \ldots \ldots \ldots .(2)$<br/>By adding (1) and (2) we get<br/>$(a+b)+(a-b)=3+3 \sqrt{3}+3-3 \sqrt{3}$<br/>$\Rightarrow 2 a=6 \Rightarrow a=3$<br/>$\therefore b=3-3+3 \sqrt{3}=3 \sqrt{3}$<br/>By using sine rule, $\Rightarrow \frac{a}{\sin A}=\frac{b}{\sin B}$<br/>Given $\angle A=30 \quad \Rightarrow \frac{3}{\sin 30^{\circ}}=\frac{3 \sqrt{3}}{\sin B}$<br/>$\Rightarrow \sin B=\sqrt{3} \times \frac{1}{2} \Rightarrow \sin B=\sin 60^{\circ}$<br/>$\Rightarrow B=60^{\circ}$</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-abc-angle-b-is-obtuse-and-d-e-f-are-the-middle-points-of-sides-bc-ca-ab-respectively-which-one-of-the-following-vectors-has-the-greatest-magnitud

slug:
in-a-abc-angle-b-is-obtuse-and-d-e-f-are-the-middle-points-of-sides-bc-ca-ab-respectively-which-one-of-the-following-vectors-has-the-greatest-magnitud-15561

question:
<div class="question">In a $\Delta \mathrm{ABC}$, angle $\mathrm{B}$ is obtuse and $\mathrm{D}, \mathrm{E}, \mathrm{F}$ are the middle points of sides $\mathrm{BC}, \mathrm{CA}, \mathrm{AB}$ respectively. Which one of the following vectors has the greatest magnitude?</div>

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

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

answer:
<div class="solution">Since, side opposite to greatest angle is longest and $\angle \mathrm{B}$ is greatest angle in $\Delta \mathrm{ABC}$. Thus, $\overline{\mathrm{CA}}$ has greatest magnitude.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/XdV_DqMP7O16AnRBQMzP9J95FumPmg5VV5RrVF6Yomk.original.fullsize.png"/></div>


title: in-a-abc-if-c-2-a-12-0-a-6-then-what-is-c-equal-to
slug: in-a-abc-if-c-2-a-12-0-a-6-then-what-is-c-equal-to-50327
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a $\triangle \mathrm{ABC}$, if $\mathrm{c}=2, \mathrm{~A}=120^{\circ}, \mathrm{a}=\sqrt{6}$, then what is $\mathrm{C}$ equal<br/>to ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$30^{\circ}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$45^{\circ}$</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">$60^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$75^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$45^{\circ}$</span> </div>

answer:
<div class="solution">Let $c=2, \angle A=120^{\circ}$ and $a=\sqrt{6}$ in $\Delta A B C$,<br/>$\therefore$ By Sine rule, we have<br/>$\begin{aligned} &amp; \frac{a}{\sin A}=\frac{c}{\sin C} \Rightarrow \frac{\sqrt{6}}{\sin 120^{\circ}}=\frac{2}{\sin C} \\ \Rightarrow &amp; \sin C=\frac{2 \times \sqrt{3}}{\sqrt{6} \times 2}=\frac{1}{\sqrt{2}} \\ \Rightarrow \sin C=\sin 45^{\circ} &amp; \Rightarrow \quad \angle C=45^{\circ} \end{aligned}$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-binary-number-system-assume-that-a-00111-and-b-01110-then-in-a-decimal-system-a-b-which-is-equal-to

slug:
in-a-binary-number-system-assume-that-a-00111-and-b-01110-then-in-a-decimal-system-a-b-which-is-equal-to-36822

question:
<div class="question">In a binary number system, assume that $a=00111$ and<br/>$b=01110$, then in a decimal system $\frac{b}{a}$, which is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">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">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution">Let $a=00111=2^{2} \times 1+2^{1} \times 1+2^{0} \times 1$<br/>$\begin{aligned} &amp;=4+2+1=7 \\ \text { Let } b &amp;=01110=2^{3} \times 1+2^{2} \times 1+2^{1} \times 1+2^{0} \times 0 \\ &amp;=8+4+2=14 \end{aligned}$<br/>$\frac{b}{a}=\frac{14}{7}=2$</div>


title: in-a-binomial-distribution-the-mean-is-3-2-and-the-variance-is-9-5-what-is-the-probability-that-x-2
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
slug:
in-a-binomial-distribution-the-mean-is-3-2-and-the-variance-is-9-5-what-is-the-probability-that-x-2-73452

question:
<div class="question">In a binomial distribution, the mean is $\frac{2}{3}$ and the variance<br/>is $\frac{5}{9} .$ What is the probability that $\mathrm{X}=2$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{5}{36}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{25}{36}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{25}{216}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{25}{54}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{25}{216}$</span> </div>

answer:
<div class="solution">Mean $=\frac{2}{3}$, variance $=\frac{5}{9}$<br/>$n p=\frac{2}{3}, n p q=\frac{5}{9}$<br/>$\Rightarrow \frac{2}{3} q=\frac{5}{9} \Rightarrow q=\frac{5}{9} \times \frac{3}{2}=\frac{5}{6}$<br/>So, $\mathrm{p}=1-\frac{5}{6}=\frac{1}{6}$<br/>Now, $\mathrm{np}=\frac{2}{3} \Rightarrow \mathrm{n}\left(\frac{1}{6}\right)=\frac{2}{3} \Rightarrow \mathrm{n}=\frac{2}{3} \times 6=4$<br/>$\therefore \mathrm{p}(\mathrm{x}=2)={ }^{\mathrm{n}} \mathrm{c}_{\mathrm{r}} \cdot \mathrm{p}^{\mathrm{r}} \cdot \mathrm{q}^{\mathrm{n}-\mathrm{r}}={ }^{4} \mathrm{c}_{2} \cdot\left(\frac{1}{6}\right)^{2} \cdot\left(\frac{5}{6}\right)^{4-2}$<br/>$=6 \times \frac{1}{36} \times \frac{25}{36}$<br/>$=\frac{25}{216}$.</div>


title: in-a-binomial-distribution-the-mean-is-4-and-the-variance-is-3-what-is-the-mode
slug: in-a-binomial-distribution-the-mean-is-4-and-the-variance-is-3-what-is-the-mode-55970
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2007 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In a binomial distribution, the mean is 4 and the variance is 3 . What is the mode?</div>

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

answer:
<div class="solution">As give, $n p=4$ and $n p q=3$ [where $\mathrm{p}$ is the probability of success and $\mathrm{q}$ is the probability of failure for an event to occur, and 'n' is the number of trials<br/>$\Rightarrow \mathrm{q}=\frac{\mathrm{npq}}{\mathrm{np}}=\frac{3}{4}$<br/>Also, $\mathrm{p}=1-\mathrm{q}=1-\frac{3}{4}=\frac{1}{4}$<br/>$\mathrm{n}=16$<br/>In a binomial distribution, the value of $\mathrm{r}$ for which $\mathrm{P}(\mathrm{X}=\mathrm{r})$ is maximum is the mode of binomial distribution.<br/>hence, $(\mathrm{n}+1) \mathrm{p}-1 \leq \mathrm{r} \leq(\mathrm{n}+1) \mathrm{p}$<br/>$\Rightarrow \frac{17}{4}-1 \leq \mathrm{r} \leq \frac{17}{4}$<br/>$\Rightarrow \frac{13}{4} \leq \mathrm{r} \leq \frac{17}{4}$<br/>$\Rightarrow 3.25 \leq \mathrm{r} \leq 4.25$<br/>$\Rightarrow \mathrm{r}=4$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">12</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-binomial-distribution-the-occurrence-and-the-nonoccurrence-of-an-event-are-equally-likely-and-the-mean-is-6-the-number-of-trials-required-is

slug:
in-a-binomial-distribution-the-occurrence-and-the-nonoccurrence-of-an-event-are-equally-likely-and-the-mean-is-6-the-number-of-trials-required-is-41686

question:
<div class="question">In a binomial distribution, the occurrence and the nonoccurrence of an event are equally likely and the mean is 6 . The number of trials required is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">15</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">12</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">10</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>

answer:
<div class="solution">$\mathrm{P}=\mathrm{q}=\frac{1}{2}, \mathrm{nP}=6$<br/>$\frac{\mathrm{n}}{2}=6 \Rightarrow \mathrm{n}=12$</div>


tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2002']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$12$</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-binomial-distribution-the-probability-of-getting-success-is-4-1-and-the-standard-deviation-is-3-then-its-mean-is-1

slug:
in-a-binomial-distribution-the-probability-of-getting-success-is-4-1-and-the-standard-deviation-is-3-then-its-mean-is-1-85378

question:
<div class="question">In a binomial distribution the probability of getting success is $\frac{1}{4}$ and the standard deviation is 3 . Then, its mean is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$12$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Given that<br/>$$<br/>\begin{aligned}<br/>p=\frac{1}{4} \text { and } q=1-\frac{1}{4} &amp; =\frac{3}{4} \\<br/>\mathrm{SD}=3 \Rightarrow \sqrt{n p q} &amp; =3 \\<br/>\Rightarrow \quad n p q &amp; =9 \\<br/>\Rightarrow \quad n \cdot \frac{1}{4} \cdot \frac{3}{4} &amp; =9 \\<br/>n &amp; =48 \\<br/>\text { Mean }=n p=48 \times \frac{1}{4} &amp; =12<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Probability', 'TS EAMCET', 'TS EAMCET 2002']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$12$</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-binomial-distribution-the-probability-of-getting-success-is-4-1-and-the-standard-deviation-is-3-then-its-mean-is

slug:
in-a-binomial-distribution-the-probability-of-getting-success-is-4-1-and-the-standard-deviation-is-3-then-its-mean-is-60828

question:
<div class="question">In a binomial distribution the probability of getting success is $\frac{1}{4}$ and the standard deviation is 3 . Then, its mean is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$6$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$8$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$10$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$12$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Given that<br/>$$<br/>\begin{aligned}<br/>p=\frac{1}{4} \text { and } q=1-\frac{1}{4} &amp; =\frac{3}{4} \\<br/>\mathrm{SD}=3 \Rightarrow \sqrt{n p q} &amp; =3 \\<br/>\Rightarrow \quad n p q &amp; =9 \\<br/>\Rightarrow \quad n \cdot \frac{1}{4} \cdot \frac{3}{4} &amp; =9 \\<br/>n &amp; =48 \\<br/>\text { Mean }=n p=48 \times \frac{1}{4} &amp; =12<br/>\end{aligned}<br/>$$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-binominal-distribution-the-mean-is-three-times-its-variance-what-is-the-probability-of-exactly-3-successes-out-of-5-trials

slug:
in-a-binominal-distribution-the-mean-is-three-times-its-variance-what-is-the-probability-of-exactly-3-successes-out-of-5-trials-84037

question:
<div class="question">In a Binominal distribution, the mean is three times its variance. What is the probability of exactly 3 successes out of 5 trials? $\quad$</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{80}{243}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{40}{243}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{20}{243}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{10}{243}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{80}{243}$</span> </div>

answer:
<div class="solution">Mean $=\mathrm{np}$<br/>Variance $=\mathrm{npq}$<br/>Given, $n p=3 n p q$ $\Rightarrow q=\frac{1}{3}, p=\frac{2}{3}$.<br/>Also, Given $n=5$ trials.<br/>$r=3$<br/>we know, $\mathrm{p}(\mathrm{x}=\mathrm{r})={ }^{\mathrm{n}} \mathrm{c}_{\mathrm{r}} \cdot \mathrm{p}^{\mathrm{r}} \cdot \mathrm{q}^{\mathrm{n}-\mathrm{r}}$<br/>$\mathrm{p}(\mathrm{x}=3)={ }^{5} \mathrm{c}_{3}\left(\frac{2}{3}\right)^{3}\left(\frac{1}{3}\right)^{2}$<br/>$=\frac{80}{243} .$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2018 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-bolt-factory-machines-x-y-z-manufacture-bolts-that-are-respectively-25-35-and-40-of-the-factorys-total-output-the-machines-x-y-z-respectively-pro

slug:
in-a-bolt-factory-machines-x-y-z-manufacture-bolts-that-are-respectively-25-35-and-40-of-the-factorys-total-output-the-machines-x-y-z-respectively-pro-87405

question:
<div class="question">In a bolt factory, machines X, Y, Z manufacture bolts that are respectively $25 \%, 35 \%$ and $40 \%$ of the factory's total output. The machines $\mathrm{X}, \mathrm{Y}, \mathrm{Z}$ respectively produce $2 \%, 4 \%$ and $5 \%$ defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine X?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{5}{39}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{11}{39}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{20}{39}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{34}{39}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{39}$</span> </div>

answer:
<div class="solution">Required probability<br/>$=\frac{25 \times 2}{25 \times 2+35 \times 4+40 \times 5}=\frac{5}{39}$</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2019 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-circle-of-diameter-44-cm-the-length-of-a-chord-is-22-cm-what-is-the-length-of-minor-arc-of-the-chord

slug:
in-a-circle-of-diameter-44-cm-the-length-of-a-chord-is-22-cm-what-is-the-length-of-minor-arc-of-the-chord-62056

question:
<div class="question">In a circle of diameter $44 \mathrm{~cm}$, the length of a chord is $22 \mathrm{~cm}$. What is the length of minor arc of the chord?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{484}{21} \mathrm{~cm}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{242}{21} \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{121}{21} \mathrm{~cm}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{44}{7} \mathrm{~cm}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{484}{21} \mathrm{~cm}$</span> </div>

answer:
<div class="solution">Given,<br/>diameter of circle $=44 \mathrm{~cm}$.<br/>radius of circle $=22 \mathrm{~cm}$<br/>Chord of circle $=22 \mathrm{~cm}$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/yXBAHeM6tyw_cfkVDaFWxoPDD-k04pisLKDqpXt01CE.original.fullsize.png"/><br/><br/>In figure $\Delta \mathrm{OAB}$ is equilateral triangle. Angle is $60^{\circ} . \mathrm{So}$.<br/>arc is $\frac{1}{6}$ times circumstance.<br/>Length of arc $=\frac{1}{6} \times 2 \pi r=\frac{1}{6} \times 2 \times \frac{22}{7} \times 22$<br/>$=\frac{484}{21} \mathrm{~cm}$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-1

slug:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-1-48382

question:
<div class="question">In a city, three dailynewspaper $B, C$ are published, $42 \%$ read $A ; 51 \%$ read $B ; 68 \%$ read $C$; $30 \%$ read A and B; $28 \%$ read $B$ and $C$; $36 \%$ read A and $C$; $8 \%$ do read any of the three newspaper<br/>What is the percentage of persons who read only two papers?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$19 \%$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$31 \%$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$44 \%$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">$\quad(30-x)+(36-x)+(28-x)=94-3 x$<br/>$=98-3 \times 25=2$<br/>Hence percentage of people who read only two newspapers $=23 \%$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
answer: <div class="solution">Hence people who read all the three newspapers $=25 \%$</div>
source_db: MarksBatch2_P1.db
title:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-2

slug:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-2-88643

question:
<div class="question">In a city three dailynewspaper $B, C$ are published, $42 \%$ read $A ; 51 \%$ read $B ; 68 \%$ read $C$; $30 \%$ read A and B; $28 \%$ read $B$ and $C$; $36 \%$ read A and $C$; $8 \%$ do read any of the three newspaper<br/> What is the percentage of who read all the three papers?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20 \%$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$25 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$30 \%$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$40 \%$</span> </li> </ul>

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


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-3

slug:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-3-89925

question:
<div class="question">In a city, three dailynewspaper $B, C$ are published, $42 \%$ read $A ; 51 \%$ read $B ; 68 \%$ read $C$; $30 \%$ read A and B; $28 \%$ read $B$ and $C$; $36 \%$ read A and $C$; $8 \%$ do read any of the three newspaper<br/>What is thepercentageof persons who read only one paper?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$38 \%$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$48 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$51 \%$</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">$48 \%$</span> </div>

answer:
<div class="solution">$(x-24)+(x-7)+(x+4)=3 x-27$<br/>$3 \times 25-27=48$<br/>Hence percentage of people who read only one newspaper $=48 \%$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2012 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1 \%$</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th

slug:
in-a-city-three-dailynewspaper-b-c-are-published-42-read-a-51-read-b-68-read-c-30-read-a-and-b-28-read-b-and-c-36-read-a-and-c-8-do-read-any-of-the-th-51502

question:
<div class="question">In a city, three dailynewspaper $B, C$ are published, $42 \%$ read $A ; 51 \%$ read $B ; 68 \%$ read $C$; $30 \%$ read A and B; $28 \%$ read $B$ and $C$; $36 \%$ read A and $C$; $8 \%$ do read any of the three newspaper<br/>What is the percentage of persons who read only A but neither B nor C?</div>

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

answer:
<div class="solution">$x-24=25-24=1$<br/>Hence percentage of people who read only Newspaper<br/>A but neither $\mathrm{B}$ nor $\mathrm{C}=1 \%$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">125</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-class-54-students-are-good-in-hindi-only-63-students-are-good-in-mathematics-only-and-41-students-are-good-in-english-only-there-are-18-students--1

slug:
in-a-class-54-students-are-good-in-hindi-only-63-students-are-good-in-mathematics-only-and-41-students-are-good-in-english-only-there-are-18-students-1-12591

question:
<div class="question">In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all threesubjects.<br/>What is the number of students who are good in either Hindi or Mathematics but not in English?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">99</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">107</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">125</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">130</span> </li> </ul>

answer:
<div class="solution">Let us represent the given data in Venn diagram as shown<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/TCsGMUK6-S7SSxsKu12Gb_RqAbia7427ElqG2otdye4.original.fullsize.png"/><br/><br/>Number of students who are good in either Hindi or Maths but not in English $=54+18+63=125$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-class-54-students-are-good-in-hindi-only-63-students-are-good-in-mathematics-only-and-41-students-are-good-in-english-only-there-are-18-students-

slug:
in-a-class-54-students-are-good-in-hindi-only-63-students-are-good-in-mathematics-only-and-41-students-are-good-in-english-only-there-are-18-students-22365

question:
<div class="question">In a class, 54 students are good in Hindi only, 63 students are good in Mathematics only and 41 students are good in English only. There are 18 students who are good in both Hindi and Mathematics. 10 students are good in all threesubjects.<br/>What is the number of students who are good in Hindi and Mathematics but not in English?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">18</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">12</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">10</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">8</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">From the same Venn diagram, Number of students whoare good in Hindi and Maths but not English $=8$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2015 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">40</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-class-of-60-students-45-students-like-music-50-students-like-dancing-5-students-like-neither-then-the-number-of-students-in-the-class-who-like-bo

slug:
in-a-class-of-60-students-45-students-like-music-50-students-like-dancing-5-students-like-neither-then-the-number-of-students-in-the-class-who-like-bo-76978

question:
<div class="question">In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">35</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">40</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">50</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/mLVDEkwgwmFTpns8stqjbk7mNlVwM8crDi4fyTmGN_Q.original.fullsize.png"/><br/><br/>Let ' $x$ ' be the number of students wholikes both music<br/>and dance. 5 students likes neither music nor dancing. Hence, total number of remaining students $=60-5=55$<br/>Nowfrom Venn diagram, $45-x+x+$<br/>$\therefore 95-x=55$<br/>$\therefore x=95-55=40$</div>


tags: ['Mathematics', 'Probability', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-class-of-125-students-70-passed-in-mathematics-55-passed-in-statistics-and-30-passed-in-both-what-is-the-probability-that-a-student-selected-at-r-1

slug:
in-a-class-of-125-students-70-passed-in-mathematics-55-passed-in-statistics-and-30-passed-in-both-what-is-the-probability-that-a-student-selected-at-r-1-82993

question:
<div class="question">In a class of 125 students 70 passed in Mathematics, 55 passed in Statistics and 30 passed in both. What is the probability that a student selected at random from the class has passed in only one subject?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$13 / 25$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 / 25$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$17 / 25$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$8 / 25$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$13 / 25$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/e8xLv1Le_Qm0yDs_wqDI-Bmdr48btTb1iKTAHfKTWwU.original.fullsize.png"/><br/><br/>Required probability<br/>$=\frac{40}{125}+\frac{25}{125}=\frac{65}{125}=\frac{13}{25}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-class-of-125-students-70-passed-in-mathematics-55-passed-in-statistics-and-30-passed-in-both-what-is-the-probability-that-a-student-selected-at-r

slug:
in-a-class-of-125-students-70-passed-in-mathematics-55-passed-in-statistics-and-30-passed-in-both-what-is-the-probability-that-a-student-selected-at-r-77993

question:
<div class="question">In a class of 125 students 70 passed in Mathematics, 55 passed in Statistics and 30 passed in both. What is the probability that a student selected at random from the class has passed in only one subject?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$13 / 25$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$3 / 25$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$17 / 25$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$8 / 25$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$13 / 25$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/e8xLv1Le_Qm0yDs_wqDI-Bmdr48btTb1iKTAHfKTWwU.original.fullsize.png"/><br/><br/>Required probability<br/>$=\frac{40}{125}+\frac{25}{125}=\frac{65}{125}=\frac{13}{25}$</div>


tags: ['Physics', 'Waves and Sound', 'JEE Main', 'JEE Main 2024 (30 Jan Shift 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">400</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-closed-organ-pipe-the-frequency-of-fundamental-note-is-30-hz-a-certain-amount-of-water-is-now-poured-in-the-organ-pipe-so-that-the-fundamental-fr

slug:
in-a-closed-organ-pipe-the-frequency-of-fundamental-note-is-30-hz-a-certain-amount-of-water-is-now-poured-in-the-organ-pipe-so-that-the-fundamental-fr-59312

question:
<div class="question">In a closed organ pipe, the frequency of fundamental note is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>Â </mo><mi>Hz</mi></math>. A certain amount of water is now poured in the organ pipe so that the fundamental frequency is increased to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>110</mn><mo>Â </mo><mi>Hz</mi></math>. If the organ pipe has a cross-sectional area of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>Â </mo><msup><mi>cm</mi><mn>2</mn></msup></math>, the amount of water poured in the organ tube is ________<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">g</mi></math>. (Take speed of sound in air is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>330</mn><mo>Â </mo><mi mathvariant="normal">m</mi><mo>Â </mo><msup><mi mathvariant="normal">s</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> )</div>

answer:
<div class="solution"><p>Fundamental frequency for closed organ pipe in the first part:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>V</mi><mrow><mn>4</mn><msub><mi>l</mi><mn>1</mn></msub></mrow></mfrac><mo>=</mo><mn>30</mn><mo>â</mo><msub><mi>l</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>11</mn><mn>4</mn></mfrac><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p>Similarly, for second part:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mi>V</mi><mrow><mn>4</mn><msub><mi>l</mi><mn>2</mn></msub></mrow></mfrac><mo>=</mo><mn>110</mn><mo>â</mo><msub><mi>l</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p>Therefore, change in lengthÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Î</mi><mi>l</mi><mo>=</mo><mn>2</mn><mo>Â </mo><mi mathvariant="normal">m</mi></math></p><p>Change in volumeÂ <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi>AÎ</mi><mi>l</mi><mo>=</mo><mn>400</mn><mo>Â </mo><msup><mi>cm</mi><mn>3</mn></msup></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mn>400</mn><mo>Â </mo><mi mathvariant="normal">g</mi><mo>;</mo><mfenced><mrow><mo>âµ</mo><mi>Ï</mi><mo>=</mo><mn>1</mn><mo>Â </mo><mi mathvariant="normal">g</mi><mo>Â </mo><msup><mi>cm</mi><mrow><mo>-</mo><mn>3</mn></mrow></msup></mrow></mfenced></math></p></div>


title: in-a-complete-study-of-grassland-ecosystem-and-pond-ecosystem-it-may-be-observed-that
slug: in-a-complete-study-of-grassland-ecosystem-and-pond-ecosystem-it-may-be-observed-that-65833
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a complete study of grassland ecosystem and pond ecosystem, it may be observed that</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both biotic and abiotic component are different.</span> </div>

answer:
<div class="solution">Biotic components, or biotic factors, can be described as any living component that affects another organism or shapes the ecosystem. This includes both animals that consume other organisms within their ecosystem. Abiotic factors include all the nonliving things find in nature. They play an important part in the lives of all organisms. The combination of abiotic and biotic factors is different for two different ecosystems. Some examples of abiotic factors include wind, sunlight, soil, temperature, climate, and water.</div>


title: in-a-coordination-entity-what-is-the-lewis-acid
slug: in-a-coordination-entity-what-is-the-lewis-acid-63663
question: <div class="question">In a coordination entity, what is the Lewis acid?</div>
tags: ['Chemistry', 'Coordination Compounds', 'NEET']
answer: <div class="solution">In a coordination entity, the Lewis acid is the central atom/ion.</div>
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">The central atom/ion</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The coordination number</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The counter ions</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">The secondary valence</span> </li> </ul>

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


title: in-a-dicot-root-vascular-cambium-is
slug: in-a-dicot-root-vascular-cambium-is-18410
question: <div class="question">In a dicot root, vascular cambium is</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">completely primary</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">partially primary and partially secondary</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">completely secondary</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">sometimes primary sometimes secondary</span> </li> </ul>

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

answer:
<div class="solution">Dicot plants are sub group of the division Angiosperms which have two cotyledons or embryonic leaves in their seeds. Meristem are a type of tissue found in such plants which can divide indefinitely. These are generally considered undifferentiated as they can give develop into all other tissues and organs of the plant. The meristematic tissues that appear early in plant life and help in formation of the plant body is called primary meristem. The apical and intercalary meristem are included in it. Meristematic tissue occurring between the mature regions of root and shoots of angiosperms are called secondary meristem. These generally form by dedifferentiation of the permanent tissues. The vascular cambium tissues found within the vascular tissues like xylem and phloem are secondary meristem which help in lateral growth of the plant helping in increasing the girth of the root or shoot.</div>


tags: ['Physics', 'Wave Optics', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-o-when-light-of-wavelength-5000-is-incident-on-t-1

slug:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-o-when-light-of-wavelength-5000-is-incident-on-t-1-46606

question:
<div class="question">In a diffraction pattern due to a single slit of width <math> <mrow> <mn>a</mn></mrow> </math> the first minimum is observed at an angle <math><msup><mrow><mn>30</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math> when light of wavelength <math><mn>5000</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Å</mi></math> is incident on the slit. The first secondary maximum is observed at an angle of:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></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><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </div>

answer:
<div class="solution"><p><math><mi mathvariant="normal">a</mi><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mn>30</mn></mrow></mrow><mo>=</mo><mi mathvariant="normal">λ</mi></math><br/><br/><math><mi mathvariant="normal">a</mi><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">λ</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mfrac><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow></mrow><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mn>30</mn></mrow></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi>θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/><math><mi mathvariant="normal">θ</mi><mo>=</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></p></div>


tags: ['Physics', 'Wave Optics', 'NEET', 'NEET 2016 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-o-when-light-of-wavelength-5000-is-incident-on-t

slug:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-o-when-light-of-wavelength-5000-is-incident-on-t-10684

question:
<div class="question">In a diffraction pattern due to a single slit of width <math> <mrow> <mn>a</mn></mrow> </math> the first minimum is observed at an angle <math><msup><mrow><mn>30</mn></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msup></math> when light of wavelength <math><mn>5000</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Å</mi></math> is incident on the slit. The first secondary maximum is observed at an angle of:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></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><mrow><mrow><msup><mrow><mi mathvariant="normal">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </div>

answer:
<div class="solution"><p><math><mi mathvariant="normal">a</mi><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mn>30</mn></mrow></mrow><mo>=</mo><mi mathvariant="normal">λ</mi></math><br/><br/><math><mi mathvariant="normal">a</mi><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mi mathvariant="normal">λ</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mfrac><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow></mrow><mrow><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mn>30</mn></mrow></mrow></mrow></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi mathvariant="normal">θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>×</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></math><br/><br/><math><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mi>θ</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math><br/><br/><math><mi mathvariant="normal">θ</mi><mo>=</mo><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></p></div>


tags: ['Physics', 'Wave Optics', 'AP EAMCET', 'AP EAMCET 2021 (19 Aug Shift 1)']
source_db: MarksBatch2_P1.db
title:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-when-light-of-wavelength-500-nm-is-incident-on-t

slug:
in-a-diffraction-pattern-due-to-a-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-30-when-light-of-wavelength-500-nm-is-incident-on-t-11683

question:
<div class="question">In a diffraction pattern due to a single slit of width <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>'</mo><mi>a</mi><mo>'</mo></math>, the first minimum is observed at an angle <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>°</mo></math> when light of wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi>nm</mi></math> is incident on the slit. The first secondary maximum is observed at an angle of</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></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 xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfrac><mn>1</mn><mn>4</mn></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfrac><mn>3</mn><mn>4</mn></mfrac></math></span> </div>

answer:
<div class="solution"><p>Given that for slit of width <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo></math>the first minimum form at <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><mn>30</mn><mo>°</mo><mo>,</mo><mo> </mo></math>the wavelength of light is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>500</mn><mo> </mo><mi>nm</mi></math></p><p>Using Bragg's law of diffraction, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mi>λ</mi><mo>=</mo><mi>a</mi><mi>sin</mi><mi>θ</mi><mo>,</mo><mo> </mo></math>here <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo> </mo></math>is the whole number and for the first minimum <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>1</mn><mo> </mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfenced><mn>1</mn></mfenced><mi>λ</mi><mo>=</mo><mi>a</mi><mi>sin</mi><mn>30</mn><mo>°</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>a</mi><mo>=</mo><mn>2</mn><mi>λ</mi><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo></math></p><p>For the first secondary maximum, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>n</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mi>λ</mi><mo>=</mo><mi>a</mi><mi>sin</mi><mi>θ</mi><mo>'</mo><mo> </mo></math>where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>1</mn></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>λ</mi><mo>=</mo><mi>a</mi><mi>sin</mi><mi>θ</mi><mo>'</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mfrac><mn>3</mn><mn>2</mn></mfrac><mi>λ</mi><mo>=</mo><mfenced><mrow><mn>2</mn><mi>λ</mi></mrow></mfenced><mi>sin</mi><mi>θ</mi><mo>'</mo><mspace linebreak="newline"></mspace><mo>⇒</mo><mi>θ</mi><mo>'</mo><mo>=</mo><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mfenced><mfrac><mn>3</mn><mn>4</mn></mfrac></mfenced></math></p></div>


tags: ['Physics', 'Wave Optics', 'MHT CET', 'MHT CET 2023 (09 May Shift 1)']
source_db: MarksBatch2_P1.db
title:
in-a-diffraction-pattern-due-to-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-of-3-0-when-the-light-of-wavelength-5400-a-is-inciden

slug:
in-a-diffraction-pattern-due-to-single-slit-of-width-a-the-first-minimum-is-observed-at-an-angle-of-3-0-when-the-light-of-wavelength-5400-a-is-inciden-80110

question:
<div class="question">In a diffraction pattern due to single slit of width 'a', the first minimum is observed at an angle of $30^{\circ}$ when the light of wavelength $5400 Ã$ is incident on the slit. The first secondary maximum is observed at an angle of $\left(\sin 30^{\circ}=\frac{1}{2}\right)$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sin ^{-1}\left(\frac{3}{4}\right)$</span> </div>

answer:
<div class="solution">For $\mathrm{n}^{\text {th }}$ secondary minimum, path difference $=a \sin \theta_{\mathrm{n}}=\mathrm{n} \lambda$ For $\mathrm{n}^{\text {th }}$ secondary maximum, path difference $=a \sin \theta_n=(2 n+1) \frac{\lambda}{2}$<br/>$\therefore \quad$ For $1^{\text {st }}$ minimum, a $\sin 30^{\circ}=\lambda$<br/>For $2^{\text {nd }}$ maximum, a $\sin \theta_{\mathrm{n}}=(2+1) \frac{\lambda}{2}=\frac{3 \lambda}{2}$<br/>$\therefore \quad$ Dividing equation (i) by equation (ii),<br/>$\frac{\left(\frac{1}{2}\right)}{\sin \theta_n}=\frac{2}{3} \Rightarrow \theta_n=\sin ^{-1}\left(\frac{3}{4}\right)$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-factory-there-are-30-men-and-20-women-employees-if-the-average-salary-of-men-is-rs-4050-and-the-average-salary-of-all-the-employees-is-rs-3550-th

slug:
in-a-factory-there-are-30-men-and-20-women-employees-if-the-average-salary-of-men-is-rs-4050-and-the-average-salary-of-all-the-employees-is-rs-3550-th-34462

question:
<div class="question">In a factory, there are 30 men and 20 women employees. If the average salary of men is Rs 4050 and the average salary of all the employees is Rs 3550 , then what is the averago salary of women?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\operatorname{Rs} 3800$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\mathrm{Rs} \underline{3300}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Rs 3000</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Rs 2800</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Rs 2800</span> </div>

answer:
<div class="solution">Let average salary of women be $\mathrm{x}$. According to question, $\Rightarrow 50 \times 3550=30 \times 4050+20 \mathrm{x}$<br/>$\Rightarrow 177500-121500=20 \mathrm{x}$<br/>$\Rightarrow x=2800$<br/>Hence, average salary of women $=\operatorname{Rs} 2800$</div>


title: in-a-fertilised-embryo-sac-the-haploid-diploid-and-triploid-structure-are
slug: in-a-fertilised-embryo-sac-the-haploid-diploid-and-triploid-structure-are-95039
tags: ['Biology', 'Sexual Reproduction in Flowering Plants']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a fertilised embryo sac, the haploid, diploid and triploid structure are:</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><br/>synergid, zygote and primary endosperm nucleus<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/>synergid, antipodal and polar nuclei<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>antipodal, synergid and primary endosperm nucleus<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>synergid, polar nuclei and zygote</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>synergid, zygote and primary endosperm nucleus<br/></span> </div>

answer:
<div class="solution">(i) Synergid - haploid<br/>(ii) Polar nuclei-haploid<br/>(iii) Antipodal-haploid<br/>(iv) Zygote-diploid<br/>(v) Primary Endosperm Nucleus (PEN).<br/>Diploid secondary nucleus fertilises with a haploid male gamete to form a triploid PEN.</div>


tags: ['Mathematics', 'Permutation Combination', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">18</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-football-championship-153-matches-were-played-every-team-played-one-match-with-each-other-team-how-many-teams-participated-in-the-championship

slug:
in-a-football-championship-153-matches-were-played-every-team-played-one-match-with-each-other-team-how-many-teams-participated-in-the-championship-42709

question:
<div class="question">In a football championship 153 matches were played. Every team played one match with each other team. How many teams participated in the championship?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">21</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">18</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">17</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">15</span> </li> </ul>

answer:
<div class="solution">Let total no. of team participated in a championship ben. Since, every team played one match with each other team.<br/>$\therefore{ }^{n} C_{2}=153 \Rightarrow \frac{n !}{2 !(n-2) !}=153$<br/>$\Rightarrow \frac{n(n-1)(n-2) !}{2 !(n-2) !}=153 \Rightarrow \frac{n(n-1)}{2}=153$<br/>$\Rightarrow n(n-1)=306$<br/>$\Rightarrow n^{2}-n-306=0$<br/>$\Rightarrow n^{2}-18 n+17 n-306=0$<br/>$\Rightarrow n(n-18)+17(n-18)=0$<br/>$\Rightarrow n=18,-17$<br/>$n$ cannot be negative $\therefore n \neq-17$<br/>$\Rightarrow n=18</div>


tags: ['Physics', 'Wave Optics', 'MHT CET', 'MHT CET 2022 (10 Aug Shift 2)']
source_db: MarksBatch2_P1.db
title:
in-a-fraunhofer-diffraction-at-a-single-slit-of-width-d-and-incident-light-of-wavelength-5500-a-the-firs-minimum-is-observed-at-an-angle-3-0-the-first

slug:
in-a-fraunhofer-diffraction-at-a-single-slit-of-width-d-and-incident-light-of-wavelength-5500-a-the-firs-minimum-is-observed-at-an-angle-3-0-the-first-27593

question:
<div class="question">In a Fraunhofer diffraction at a single slit of width $d$ and incident light of wavelength $5500 \mathrm{~A}$, the firs minimum is observed at an angle $30^{\circ}$. The first secondary maxima are observed at an angle $\theta=$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sin ^{-1}\left(\frac{3}{4}\right)$</span> </div>

answer:
<div class="solution">Slit width $=d$<br/>$\lambda=5500 \AA=5.5 \times 10^{-7} \mathrm{~m}, \theta_1=30^{\circ}$<br/>For first secondary minima, $d \sin \theta_1=\lambda$<br/>$d=\frac{\lambda}{\sin \theta_1}=\frac{5.5 \times 10^{-7}}{\sin 30^{\circ}}=11 \times 10^{-7}$<br/>For first secondary maxima, $d \sin \theta_1=\frac{3 \lambda}{2}$<br/>$\begin{aligned} &amp; \Rightarrow \sin \theta_1=\frac{3 \lambda}{2 d}=\frac{5.5 \times 10^{-7}}{2 \times 11 \times 10^{-7}}=\frac{3}{4} \\ &amp; \theta_1=\sin ^{-1}\left(\frac{3}{4}\right)\end{aligned}$</div>


tags: ['Physics', 'Wave Optics', 'AIIMS', 'AIIMS 2016']
source_db: MarksBatch2_P1.db
title:
in-a-fraunhofer-diffraction-at-single-slit-of-width-d-with-incident-light-of-wavelength-5500-a-the-first-minimum-is-observed-at-angle-3-0-the-first-se

slug:
in-a-fraunhofer-diffraction-at-single-slit-of-width-d-with-incident-light-of-wavelength-5500-a-the-first-minimum-is-observed-at-angle-3-0-the-first-se-64955

question:
<div class="question">In a Fraunhofer diffraction at single slit of width $d$ with incident light of wavelength 5500 $Ã$, the first minimum is observed, at angle $30^{\circ}$. The first secondary maximum is observed at an angle $\theta=$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sin ^{-1} \frac{3}{4}$</span> </div>

answer:
<div class="solution">Slit width $=d$<br/>$\lambda=5500 Ã=5.5 \times 10^{-7} \mathrm{~m}, \theta_n=30^{\circ}$<br/>For first secondary minima, $d \sin \theta_n=\lambda$<br/>$d=\frac{\lambda}{\sin \theta_n}=\frac{5.5 \times 10^{-7}}{\sin 30^{\circ}}=11 \times 10^{-7} \mathrm{~m}$<br/>For first secondary maxima, $d \sin \theta_n=\frac{3 \lambda}{2}$<br/>i. e. $\sin \theta_n=\frac{3 \lambda}{2 d}=\frac{3 \times 5.5 \times 10^{-7}}{2 \times 11 \times 10^{-7}}$<br/>$\sin \theta_n=\frac{3}{4}$ or $\theta_n=\sin ^{-1}(3 / 4)$</div>


tags: ['Physics', 'Wave Optics', 'KCET', 'KCET 2008']
source_db: MarksBatch2_P1.db
title:
in-a-fraunhofer-diffraction-experiment-at-a-single-slit-using-a-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-3-0-the-directio-1

slug:
in-a-fraunhofer-diffraction-experiment-at-a-single-slit-using-a-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-3-0-the-directio-1-49740

question:
<div class="question">In a Fraunhofer diffraction experiment at a single slit using a light of wavelength $400 \mathrm{~nm}$, the first minimum is formed at an angle of $30^{\circ}$. The direction $\theta$ of the first secondary maximum is given by</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\sin ^{-1}\left(\frac{3}{4}\right)$</span> </div>

answer:
<div class="solution">For first diffraction minimum<br/>$$<br/>\Rightarrow \quad \begin{aligned}<br/>a \sin \theta &amp;=\lambda \\<br/>a &amp;=\frac{\lambda}{\sin \theta}<br/>\end{aligned}<br/>$$<br/>For first secondary maximum<br/>$$<br/>a \sin \theta^{\prime}=\frac{3 \lambda}{2}<br/>$$<br/>or $\sin \theta^{\prime}=\frac{3 \lambda}{2} \times \frac{1}{a}=\frac{3 \lambda}{2} \times \frac{\sin \theta}{\lambda}=\frac{3}{2} \times \sin 30^{\circ}=\frac{3}{4}$<br/>or<br/>$$<br/>\theta^{\prime}=\sin ^{-1}\left(\frac{3}{4}\right)<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'COMEDK', 'COMEDK 2018']
source_db: MarksBatch2_P1.db
title:
in-a-fraunhofer-diffraction-experiment-at-a-single-slit-using-a-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-3-0-the-directio

slug:
in-a-fraunhofer-diffraction-experiment-at-a-single-slit-using-a-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-3-0-the-directio-90743

question:
<div class="question">In a Fraunhofer diffraction experiment at a single slit using a light of wavelength $400 \mathrm{~nm}$, the first minimum is formed at an angle of $30^{\circ}$. The direction $\theta$ of the first secondary maximum is given by</div>

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

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

answer:
<div class="solution">Given, wavelength of used light,<br/>$$<br/>\lambda=400 \mathrm{~nm}<br/>$$<br/>For minima in Fraunhofer diffraction,<br/>$\therefore \quad d \sin 30^{\circ}=1 \times 400$<br/>$\Rightarrow \quad d=800 \mathrm{~nm}$<br/>For maxima in diffraction,<br/>$$<br/>d \sin \theta=(2 n+1) \frac{\lambda}{2}<br/>$$<br/>For first maxima $n=0$<br/>$$<br/>\begin{array}{ll}<br/>\therefore &amp; d \sin \theta=(0+1) \frac{\lambda}{2} \\<br/>\Rightarrow &amp; d \sin \theta=\frac{\lambda}{2} \\<br/>\Rightarrow &amp; 800 \sin \theta=\frac{400}{2} \\<br/>\Rightarrow &amp; \sin \theta=\frac{1}{4} \\<br/>\Rightarrow &amp; \theta=\sin ^{-1}\left(\frac{1}{4}\right)<br/>\end{array}<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-fraunhoffer-diffraction-experiment-at-a-single-slit-using-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-30-then-the-direc

slug:
in-a-fraunhoffer-diffraction-experiment-at-a-single-slit-using-light-of-wavelength-400-nm-the-first-minimum-is-formed-at-an-angle-of-30-then-the-direc-81551

question:
<div class="question">In a Fraunhoffer diffraction experiment at a single slit using light of wavelength <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>400</mn><mo> </mo><mi>nm</mi></math> , the first minimum is formed at an angle of <math><mn>30</mn><mo>Â°</mo></math> . Then the direction <math><mi>Î¸</mi></math> of the first secondary maximum is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="italic">tan</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>4</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><msup><mrow><mn>60</mn></mrow><mrow><mi>o</mi></mrow></msup></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math><mrow><mrow><msup><mrow><mi mathvariant="italic">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></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><mrow><mrow><msup><mrow><mi mathvariant="italic">tan</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mrow><mrow><msup><mrow><mi mathvariant="italic">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></span> </div>

answer:
<div class="solution">For first minimum,<br/><br/> <math><mrow><mrow><mi mathvariant="italic">sin</mi></mrow><mo>â¡</mo><mrow><msup><mrow><mn>30</mn></mrow><mrow><mi>o</mi></mrow></msup></mrow></mrow><mo>=</mo><mfrac><mrow><mi>Î»</mi></mrow><mrow><mi>a</mi></mrow></mfrac></math> <br/><br/> <math><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>Î»</mi></mrow><mrow><mi>a</mi></mrow></mfrac></math> <br/><br/> <math><mi>a</mi><mo>=</mo><mn>2</mn><mi>Î»</mi></math> <br/><br/>Now, For 1st secondary maxima<br/><br/> <math><mrow><mrow><mi mathvariant="italic">sin</mi></mrow><mo>â¡</mo><mrow><mi>Î¸</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mi>Î»</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></math> <br/><br/> <math><mrow><mrow><mi mathvariant="italic">sin</mi></mrow><mo>â¡</mo><mrow><mi>Î¸</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn><mi>Î»</mi></mrow><mrow><mn>2</mn><mo>Ã</mo><mn>2</mn><mi>Î»</mi></mrow></mfrac></math> <br/><br/> <math><mrow><mrow><mi mathvariant="italic">sin</mi></mrow><mo>â¡</mo><mrow><mi>Î¸</mi></mrow></mrow><mo>=</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></math> <br/><br/> <math><mi>Î¸</mi><mo>=</mo><mrow><mrow><msup><mrow><mi mathvariant="italic">sin</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced></mrow></mrow></math></div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">97%</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-c-h-3-o-h-l-3-2-o-2-g-c-o-2-g-2-h-2-o-l-at-298-k-standar

slug:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-c-h-3-o-h-l-3-2-o-2-g-c-o-2-g-2-h-2-o-l-at-298-k-standar-93321

question:
<div class="question">In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is<br/> <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced><mo>â</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced><mo>+</mo><mn>2</mn><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced></math><br/>
At 298 K standard Gibbâs energies of formation for <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced><mo>,</mo><mi mathvariant="normal"> </mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced></math> and <math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced></math> are -166.2, -237.2 and -394.4 <math><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal"> </mi><msup><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math> respectively. If standard enthalphy of combustion of methanol is -726 <math> <mrow> <msup> <mrow> <mi mathvariant="normal">kJmol</mi></mrow> <mrow> <mo>â</mo><mn>1</mn></mrow> </msup> </mrow> </math> , efficiency of the fuel cell will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">87%</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">90%</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">97%</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">80%</span> </li> </ul>

answer:
<div class="solution"><math><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced><mo>+</mo><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced><mo>â</mo><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">g</mi></mrow></mfenced><mo>+</mo><mn>2</mn><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">l</mi></mrow></mfenced></math><br/><math><mi mathvariant="normal">Î</mi><mi mathvariant="normal">H</mi><mo>=</mo><mo>-</mo><mn>726</mn><mi mathvariant="normal"></mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>Also <math><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>3</mn></mrow></msub><mi mathvariant="normal">O</mi><mi mathvariant="normal">H</mi><mfenced separators="|"><mrow><mi mathvariant="normal">I</mi></mrow></mfenced><mo>=</mo><mo>-</mo><mn>166.2</mn><mi mathvariant="normal"></mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><math><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><msub><mrow><mi mathvariant="normal">H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi mathvariant="normal">O</mi><mfenced separators="|"><mrow><mi mathvariant="normal">I</mi></mrow></mfenced><mo>=</mo><mo>-</mo><mn>166.2</mn><mi mathvariant="normal"></mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><math><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><mi mathvariant="normal">C</mi><msub><mrow><mi mathvariant="normal">O</mi></mrow><mrow><mn>2</mn></mrow></msub><mfenced separators="|"><mrow><mi mathvariant="normal">I</mi></mrow></mfenced><mo>=</mo><mo>-</mo><mn>394.4</mn><mi mathvariant="normal"></mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><math><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow></mrow></msubsup><mo>=</mo><mo>â</mo><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><mi mathvariant="normal">p</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">s</mi><mo>-</mo><mo>â</mo><mi mathvariant="normal">Î</mi><msubsup><mrow><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">f</mi></mrow><mrow><mi mathvariant="normal">o</mi></mrow></msubsup><mi mathvariant="normal">r</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">s</mi></math><br/><math><mo>=</mo><mo>-</mo><mn>394.4</mn><mo>-</mo><mn>2</mn><mfenced separators="|"><mrow><mn>237.2</mn></mrow></mfenced><mo>+</mo><mn>166.2</mn><mo>=</mo><mn>702.6</mn><mi mathvariant="normal"></mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">J</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><msup><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/>now efficiency of fuel cell<br/><math><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">G</mi></mrow><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">H</mi></mrow></mfrac><mo>Ã</mo><mn>100</mn><mo>=</mo><mfrac><mrow><mn>702.6</mn></mrow><mrow><mn>726</mn></mrow></mfrac><mo>Ã</mo><mn>100</mn><mo>=</mo><mn>97</mn><mi mathvariant="normal">%</mi></math></div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-ch-3-oh-2-3-o-2-g-co-2-g-2-h-2-o-at-298-k-standard-gibbs-1

slug:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-ch-3-oh-2-3-o-2-g-co-2-g-2-h-2-o-at-298-k-standard-gibbs-1-41194

question:
<div class="question">In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_3 \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_3 \mathrm{OH}(\ell), \mathrm{H}_2 \mathrm{O}(\ell)$ and $\mathrm{CO}_2(\mathrm{~g})$ are $-166.2,-237.2$ and $-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, efficiency of the fuel cell will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$80 \%$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$87 \%$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$90 \%$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$97 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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/>$97 \%$</span> </div>

answer:
<div class="solution">$$<br/>\mathrm{CH}_3 \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell) \quad \Delta \mathrm{H}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>$$<br/>Also $\Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{CH}_3 \mathrm{OH}(\ell)=-166.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/>$$<br/>\begin{aligned}<br/>&amp; \Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{H}_2 \mathrm{O}(\ell)=-237.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \\<br/>&amp; \Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{CO}_2(\ell)=-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1} \\<br/>&amp; \because \Delta \mathrm{G}=\Sigma \Delta \mathrm{G}_{\mathrm{f}}^0 \text { products }-\Sigma \Delta \mathrm{G}_{\mathrm{f}}^0 \text { reactants. } \\<br/>&amp; =-394.4-2(237.2)+166.2 \\<br/>&amp; =-702.6 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>\end{aligned}<br/>$$<br/>$$<br/>\begin{aligned}<br/>&amp; \text { now Efficiency of fuel cell }=\frac{\Delta \mathrm{G}}{\Delta \mathrm{H}} \times 100 \\<br/>&amp; =\frac{702.6}{726} \times 100 \\<br/>&amp; =97 \%<br/>\end{aligned}<br/>$$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2009']
source_db: MarksBatch2_P1.db
title:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-ch-3-oh-2-3-o-2-g-co-2-g-2-h-2-o-at-298-k-standard-gibbs

slug:
in-a-fuel-cell-methanol-is-used-as-fuel-and-oxygen-gas-is-used-as-an-oxidizer-the-reaction-is-ch-3-oh-2-3-o-2-g-co-2-g-2-h-2-o-at-298-k-standard-gibbs-40197

question:
<div class="question">In a fuel cell methanol is used as fuel and oxygen gas is used as an oxidizer. The reaction is $\mathrm{CH}_3 \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell)$ At $298 \mathrm{~K}$ standard Gibb's energies of formation for $\mathrm{CH}_3 \mathrm{OH}(\ell), \mathrm{H}_2 \mathrm{O}(\ell)$ and $\mathrm{CO}_2(\mathrm{~g})$ are $-166.2,-237.2$ and $-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. If standard enthalpy of combustion of methanol is $-726 \mathrm{~kJ} \mathrm{~mol}^{-1}$, efficiency of the fuel cell will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$80 \%$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$87 \%$<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$90 \%$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$97 \%$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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/>$97 \%$</span> </div>

answer:
<div class="solution">$$<br/>\mathrm{CH}_3 \mathrm{OH}(\ell)+\frac{3}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{CO}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\ell) \quad \Delta \mathrm{H}=-726 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>$$<br/>Also $\Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{CH}_3 \mathrm{OH}(\ell)=-166.2 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/>$$<br/>\begin{aligned}<br/>&amp; \Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{H}_2 \mathrm{O}(\ell)=-237.2 \mathrm{~kJ} \mathrm{~mol}^{-1} \\<br/>&amp; \Delta \mathrm{G}_{\mathrm{f}}^0 \mathrm{CO}_2(\ell)=-394.4 \mathrm{~kJ} \mathrm{~mol}^{-1} \\<br/>&amp; \because \Delta \mathrm{G}=\Sigma \Delta \mathrm{G}_{\mathrm{f}}^0 \text { products }-\Sigma \Delta \mathrm{G}_{\mathrm{f}}^0 \text { reactants. } \\<br/>&amp; =-394.4-2(237.2)+166.2 \\<br/>&amp; =-702.6 \mathrm{~kJ} \mathrm{~mol}^{-1}<br/>\end{aligned}<br/>$$<br/>$$<br/>\begin{aligned}<br/>&amp; \text { now Efficiency of fuel cell }=\frac{\Delta \mathrm{G}}{\Delta \mathrm{H}} \times 100 \\<br/>&amp; =\frac{702.6}{726} \times 100 \\<br/>&amp; =97 \%<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Semiconductors', 'JEE Main', 'JEE Main 2005']
answer: <div class="solution">frequency $=2$ (frequency of input signal).</div>
source_db: MarksBatch2_P1.db
title:
in-a-full-wave-rectifier-circuit-operating-from-50-hz-mains-frequency-the-fundamental-frequency-in-the-ripple-would-be

slug:
in-a-full-wave-rectifier-circuit-operating-from-50-hz-mains-frequency-the-fundamental-frequency-in-the-ripple-would-be-21906

question:
<div class="question">In a full wave rectifier circuit operating from $50 \mathrm{~Hz}$ mains frequency, the fundamental frequency in the ripple would be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$50 \mathrm{~Hz}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>$25 \mathrm{~Hz}$<br/></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><br/>$100 \mathrm{~Hz}$<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/>$70.7 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$100 \mathrm{~Hz}$<br/></span> </div>


tags: ['Physics', 'Semiconductors', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-fullwave-rectifier-circuit-operating-from-50-hz-mains-frequency-the-fundamental-frequency-in-the-rectifier-wave-would-be

slug:
in-a-fullwave-rectifier-circuit-operating-from-50-hz-mains-frequency-the-fundamental-frequency-in-the-rectifier-wave-would-be-22476

question:
<div class="question">In a full-wave rectifier circuit operating from <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mi>Hz</mi></math> mains frequency, the fundamental frequency in the rectifier wave would be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>Hz</mi><mo> </mo></math>                  <div id="gtx-trans" style="position: absolute; left: 52px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><mn>70.7</mn><mo> </mo><mi>Hz</mi><mo> </mo></math>                  <div id="gtx-trans" style="position: absolute; left: 52px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn><mo> </mo><mi>Hz</mi><mo> </mo></math>                  <div id="gtx-trans" style="position: absolute; left: 52px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi>Hz</mi><mo> </mo></math>                  <div id="gtx-trans" style="position: absolute; left: 52px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn><mo> </mo><mi>Hz</mi><mo> </mo></math>                  <div id="gtx-trans" style="position: absolute; left: 52px; top: -5.77778px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution">Frequency of full wave rectifier = 2 x input frequency <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo> </mo><mn>2</mn><mo> </mo><mo>×</mo><mo> </mo><mn>50</mn><mo> </mo><mo>=</mo><mo> </mo><mn>100</mn><mo> </mo><mi>Hz</mi><mo>.</mo></math></div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-geometric-progression-with-first-term-a-and-common-ratio-r-what-is-the-arithmetic-mean-of-first-five-terms

slug:
in-a-geometric-progression-with-first-term-a-and-common-ratio-r-what-is-the-arithmetic-mean-of-first-five-terms-38060

question:
<div class="question">In a geometric progression with first term $a$ and common ratio $r$, what is the arithmetic mean of first five terms?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$a+2 r$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$a r^{2}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$a\left(r^{5}-1\right) /(r-1)$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$a\left(r^{5}-1\right) /[5(r-1)]$</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>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$a\left(r^{5}-1\right) /[5(r-1)]$</span> </div>

answer:
<div class="solution">Let the Geometric progression be a, ar, ar $^{2}, \mathrm{ar}^{3}, \mathrm{ar}^{4}, \ldots$ First five terms of a geometric progression are $\mathrm{a}, \mathrm{ar}, \mathrm{ar}^{2}$, $\mathrm{ar}^{3}, \mathrm{ar}^{4}$<br/>$\begin{array}{ll}\therefore \quad &amp; \text { Mean }=\frac{a+a r+a r^{2}+a r^{3}+a r^{4}}{5} \\ &amp; =\frac{a\left(r^{5}-1\right)}{5(r-1)} \quad\left(\because \text { Sum of G.P }=\frac{a\left(r^{n}-1\right)}{r-1}\right)\end{array}$</div>


tags: ['Mathematics', 'Sequences and Series', 'NDA', 'NDA 2011 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-gp-of-positive-terms-any-term-is-equal-to-onethird-of-the-sum-of-next-two-terms-what-is-the-common-ratio-of-the-gp

slug:
in-a-gp-of-positive-terms-any-term-is-equal-to-onethird-of-the-sum-of-next-two-terms-what-is-the-common-ratio-of-the-gp-71430

question:
<div class="question">In a GP of positive terms, any term is equal to one-third of the sum of next two terms. What is the common ratio of the GP?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\sqrt{13}+1}{2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\sqrt{13}-1}{2}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\sqrt{13}+1}{3}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\sqrt{13}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{\sqrt{13}-1}{2}$</span> </div>

answer:
<div class="solution">Let a, ar and ar $^{2}$ be three positive terms of G.P.<br/>According to question,<br/>$\mathrm{a}=\frac{1}{3}\left(\mathrm{ar}+\mathrm{ar}^{2}\right)$<br/>$\Rightarrow 3=\mathrm{r}+\mathrm{r}^{2}$<br/>$\Rightarrow \mathrm{r}^{2}+\mathrm{r}-3=0$<br/>$\Rightarrow \mathrm{r}=\frac{-1 \pm \sqrt{1+4 \times 3}}{2}$<br/>$\Rightarrow \mathrm{r}=\frac{-1 \pm \sqrt{13}}{2}=\frac{\sqrt{13}-1}{2},-\left(\frac{1+\sqrt{13}}{2}\right)$<br/>Since, $r$ can not be negative.<br/>$\therefore \quad r=\frac{\sqrt{13}-1}{2}$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">20</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-group-of-50-people-two-tests-were-conducted-one-for-diabetes-and-one-for-blood-pressure-30-people-were-diagnosed-with-diabetes-and-40-people-were

slug:
in-a-group-of-50-people-two-tests-were-conducted-one-for-diabetes-and-one-for-blood-pressure-30-people-were-diagnosed-with-diabetes-and-40-people-were-77685

question:
<div class="question">In a group of 50 people, two tests were conducted, one for diabetes and one for blood pressure. 30 people were diagnosed with diabetes and 40 people were diagnosed with high blood pressure. what is the minimum number of people who were having diabetes and high blood pressure</div>

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

answer:
<div class="solution">$\mathrm{n}(\mathrm{T})=50$<br/>$\mathrm{n}(\mathrm{D})=30$<br/>$\mathrm{n}(\mathrm{H})=40$<br/>$\mathrm{n}(\mathrm{T})=\mathrm{n}(\mathrm{D})+\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{DnH})$<br/>$50=30+40-\mathrm{n}(\mathrm{D} \cap \mathrm{H})$<br/>$\mathrm{n}(\mathrm{D} \cap \mathrm{H})=70-50=20$<br/>Number of people having diabetes and high blood pressure $=20$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">300</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-group-of-500-students-there-are-475-students-who-can-speak-hindi-and-200-can-speak-bengali-what-is-the-number-of-students-who-can-speak-hindi-onl

slug:
in-a-group-of-500-students-there-are-475-students-who-can-speak-hindi-and-200-can-speak-bengali-what-is-the-number-of-students-who-can-speak-hindi-onl-39838

question:
<div class="question">In a group of 500 students, there are 475 students who can speak Hindi and 200 can speak Bengali. What is the number of students who can speak Hindi only ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">275</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">300</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">325</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">350</span> </li> </ul>

answer:
<div class="solution">Total number of students $=500$ Let $\mathrm{H}$ be the set showing number of students who can speak Hindi $=475$ and $\mathrm{B}$ be the set showing number of students who can speak Ben gali $=200$ So, $\mathrm{n}(\mathrm{H})=475$ and $\mathrm{n}(\mathrm{B})=200$ and given that $\mathrm{n}(\mathrm{B} \cup$<br/>$\mathrm{H})=500$<br/>we have $n(B \cup H)=n(B)+n(H)-n(B \cap H)$<br/>$\Rightarrow 500=200+475-n(B \cap H)$<br/>$0, \mathrm{n}(\mathrm{B} \cap \mathrm{H})=175$<br/>Hence, persons who speak Hindi only $=\mathrm{n}(\mathrm{H})-\mathrm{n}(\mathrm{B} \cap \mathrm{H})$<br/>$=475-175=300$</div>


tags: ['Physics', 'Semiconductors', 'TS EAMCET', 'TS EAMCET 2015']
source_db: MarksBatch2_P1.db
title:
in-a-half-wave-rectifier-the-ac-input-source-of-frequency-50-hz-is-used-the-fundamental-frequency-of-the-output-is

slug:
in-a-half-wave-rectifier-the-ac-input-source-of-frequency-50-hz-is-used-the-fundamental-frequency-of-the-output-is-67604

question:
<div class="question">In a half wave rectifier, the AC input source of frequency $50 \mathrm{~Hz}$ is used. The fundamental frequency of the output is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$50 \mathrm{~Hz}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$150 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$200 \mathrm{~Hz}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$75 \mathrm{~Hz}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$50 \mathrm{~Hz}$</span> </div>

answer:
<div class="solution">In half wave rectifier frequency remain unchanged.<br/>$\therefore$ Fundamental frequency of the output is $50 \mathrm{~Hz}$.</div>


tags: ['Mathematics', 'Hyperbola', 'AP EAMCET', 'AP EAMCET 2021 (23 Aug Shift 2)']
source_db: MarksBatch2_P1.db
title:
in-a-hyperbola-if-the-length-of-transverse-axis-is-twice-that-of-the-conjugate-axis-then-the-distance-between-its-directrices-is-units

slug:
in-a-hyperbola-if-the-length-of-transverse-axis-is-twice-that-of-the-conjugate-axis-then-the-distance-between-its-directrices-is-units-31154

question:
<div class="question">In a hyperbola, if the length of transverse axis is twice that of the conjugate axis, then the distance between its directrices is..... units.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$\frac{8 b}{\sqrt{5}}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{8 a}{\sqrt{5}}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{2 a}{\sqrt{5}}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{2 b}{\sqrt{5}}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{8 b}{\sqrt{5}}$</span> </div>

answer:
<div class="solution">Given, in a hyperbola, the length of transverse axis is twice that of the conjugate axis. The equation of standard hyperbola is<br/>$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$<br/>$\because$ Length of transverse axis $=2 \times$ length of conjugate axis<br/>$2 a=2 \times 2 b$<br/>$\begin{array}{lll}\Rightarrow &amp; a &amp; =2 b \\ \because &amp; b^2 &amp; =a^2\left(e^2-1\right)\end{array}$<br/>$\begin{array}{ll}\Rightarrow &amp; \frac{a^2}{4}=a^2\left(e^2-1\right) \\ \Rightarrow &amp; e^2=1+\frac{1}{4}=\frac{5}{4}\end{array}$<br/>$\Rightarrow \quad e=\frac{\sqrt{5}}{2}$<br/>$\therefore$ Distance between its directrix $=\frac{2 a}{e}=\frac{2(2 b)}{\sqrt{5} / 2}$<br/>$=\frac{8 b}{\sqrt{5}}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-lottery-16-tickets-are-sold-and-4-prizes-are-awarded-if-a-person-buys-4-ticketswhat-is-the-probability-of-his-winning-a-prize

slug:
in-a-lottery-16-tickets-are-sold-and-4-prizes-are-awarded-if-a-person-buys-4-ticketswhat-is-the-probability-of-his-winning-a-prize-82242

question:
<div class="question">In a lottery, 16 tickets are sold and 4 prizes are awarded. If a person buys 4 tickets,what is the probability of his winning a prize?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{4}{16^{4}}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{175}{256}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{1}{4}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{81}{256}$</span> </li> </ul>

answer:
<div class="solution">$16$ tickets are sold and 4 prizes are awarded. A person<br/>buys 4 tickets, then required probability $=\frac{4}{16}=\frac{1}{4}$</div>


title: in-a-manufacture-of-readymade-garments-which-average-is-used-to-find-the-most-frequent-size
slug: in-a-manufacture-of-readymade-garments-which-average-is-used-to-find-the-most-frequent-size-68742
tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Mode</span> </div>
answer: <div class="solution">Mode is most suitable for this.</div>
source_db: MarksBatch2_P1.db
question:
<div class="question">In a manufacture of ready-made garments, which average is used to find the most frequent size ?</div>

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


tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-mature-7celled-or-8nucleate-embryo-sac-the-ploidy-level-of-the-secondary-nucleus-is-the-same-as-that-of-the

slug:
in-a-mature-7celled-or-8nucleate-embryo-sac-the-ploidy-level-of-the-secondary-nucleus-is-the-same-as-that-of-the-73298

question:
<div class="question">In a mature 7-celled or 8-nucleate embryo sac, the ploidy level of the secondary nucleus is the same as that of the:</div>

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

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

answer:
<div class="solution">The embryo sac is the mature female gametophyte of the angiosperm which is a 7 celled 8 nuclei structure. In it, at the chalazal end there are cells called antipodal cells which act as nutritional centre. Female gamete is surrounded by two synergid cells which help in the fertilization process and present at the micropylar end of the sac. In the centre of the sac, polar nuclei is found which is a cell with two nuclei. The ploidy level of synergids, antipodal cells and female gamete 'n' but the polar nuclei is '2n'. It is similar to the nucellus (2n) tissue cells which have not participated in the megasporogenesis process.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-mature-dicot-stem-which-has-undergone-secondary-growth-the-youngest-layer-of-secondary-xylem-is-situated

slug:
in-a-mature-dicot-stem-which-has-undergone-secondary-growth-the-youngest-layer-of-secondary-xylem-is-situated-30094

question:
<div class="question">In a mature dicot stem which has undergone secondary growth, the youngest layer of secondary xylem is situated ________________.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">just inner to the vascular cambium</span> </div>

answer:
<div class="solution">Dicot plants are sub group of the division Angiosperms which have two cotyledons or embryonic leaves in their seeds. Meristematic tissue occurring between the mature regions of root and shoots of angiosperms are called secondary meristem. These generally form by dedifferentiation of the permanent tissues. The vascular cambium tissues found within the vascular tissues like xylem and phloem are secondary meristem which help in lateral growth of the plant helping in increasing the girth of the stem. The cambium cells between the xylem and phloem is called as intra fascicular cambium. The new cambium cells that form towards the pith and mature into secondary xylem that is inner to the vascular cambium and the cells forming towards the periphery on the outer side is called secondary phloem. The younger cambium cells that will develop into xylem grow towards the central or inner side of the stem.</div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-meter-bridge-experiment-with-a-standard-resistance-in-the-right-gap-and-a-resistance-coil-dipped-in-water-in-a-beaker-in-the-left-gap-the-balanci

slug:
in-a-meter-bridge-experiment-with-a-standard-resistance-in-the-right-gap-and-a-resistance-coil-dipped-in-water-in-a-beaker-in-the-left-gap-the-balanci-81390

question:
<div class="question">In a meter bridge experiment, with a standard resistance in the right gap and a resistance coil dipped in water (in a beaker) in the left gap, the balancing length obtained is <math><mi>l</mi></math>. If the temperature of the water is increased, the new balancing length</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math> <mrow> <mo>&lt;</mo><mi>l</mi></mrow></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math> <mrow> <mo>&gt;</mo><mi>l</mi></mrow> </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><mo>=</mo><mn>0</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math> <mrow> <mo>=</mo><mi>l</mi></mrow></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math> <mrow> <mo>&gt;</mo><mi>l</mi></mrow> </math></span> </div>

answer:
<div class="solution">According to the question,<br/><br/><math><mfrac><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">k</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">w</mi><mi mathvariant="normal">n</mi></mrow></msub></mrow><mrow><msub><mrow><mi>R</mi></mrow><mrow><mi mathvariant="normal">s</mi><mi mathvariant="normal">t</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">r</mi><mi mathvariant="normal">d</mi></mrow></msub></mrow></mfrac><mo>=</mo><mfrac><mrow><mi>l</mi></mrow><mrow><mfenced separators="|"><mrow><mn>1</mn><mo>-</mo><mi>l</mi></mrow></mfenced></mrow></mfrac></math><br/><br/>If temperature increases than resistance increases. Hence the new balancing is greater than <math><mi>l</mi></math></div>


tags: ['Physics', 'Current Electricity', 'TS EAMCET', 'TS EAMCET 2020 (14 Sep Shift 2)']
source_db: MarksBatch2_P1.db
title:
in-a-meter-bridge-the-balancing-length-from-the-left-end-is-found-to-be-25-cm-the-value-of-the-unknown-resistance-is-assume-standard-resistance-of-1-i

slug:
in-a-meter-bridge-the-balancing-length-from-the-left-end-is-found-to-be-25-cm-the-value-of-the-unknown-resistance-is-assume-standard-resistance-of-1-i-28136

question:
<div class="question">In a meter bridge the balancing length from the left end is found to be $25 \mathrm{~cm}$. The value of the unknown resistance is (assume, standard resistance of $1 \Omega$ is in the right gap)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.25 \Omega$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$0.33 \Omega$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.20 \Omega$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$0.50 \Omega$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$0.33 \Omega$</span> </div>

answer:
<div class="solution">According to given situation, circuit diagram of meter bridge is given as<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ts_eamcet/xAGdRBlQiOevVxipb3urSFyOPrOLVCCl68ueRp0ZHyE.original.fullsize.png"/><br/><br/>At balance condition of meter bridge,<br/>$\frac{S}{R}=\frac{25}{(100-25)} \Rightarrow \frac{S}{1}=\frac{25}{75} \Rightarrow S=\frac{1}{3} \Omega=0.33 \Omega$</div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-metrebridge-the-balancing-length-from-the-left-end-when-a-standard-resistance-of-1-is-in-the-right-gap-is-found-to-be-20-cm-the-value-of-the-unkn

slug:
in-a-metrebridge-the-balancing-length-from-the-left-end-when-a-standard-resistance-of-1-is-in-the-right-gap-is-found-to-be-20-cm-the-value-of-the-unkn-35964

question:
<div class="question">In a metre-bridge, the balancing length from the left end when a standard resistance of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">Î©</mi></math> is in the right gap is found to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi>cm</mi></math>. The value of the unknown resistance is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0.4</mtext><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>0.5</mtext><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi mathvariant="normal">Ω</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.25</mn><mo> </mo><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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.25</mn><mo> </mo><mi mathvariant="normal">Î©</mi></math></span> </div>

answer:
<div class="solution">Let the unknown resistance be <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">X</mi></math></em>. Then the condition of Wheatstone's bridge gives <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mtext>X</mtext><mtext>R</mtext></mfrac><mo>=</mo><mfrac><mrow><mn>20</mn><mtext>r</mtext></mrow><mtext>80r</mtext></mfrac></math>, where <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">r</mi></math> is the resistance of wire per <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cm</mi></math>.<br/><br/><style type="text/css"><!--		@page { margin: 2cm }		P { margin-bottom: 0.21cm }	--></style><p style="margin-bottom: 0cm"><img alt="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/content_1937.png" style="width: 517px; height: 428px;"/><br/> </p><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>â´</mo><mtext>X</mtext><mo>=</mo><mfrac><mn>20</mn><mn>80</mn></mfrac><mo>Ã</mo><mtext>R</mtext><mo>=</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>Ã</mo><mn>1</mn><mo>=</mo><mtext>0.25 </mtext><mi mathvariant="normal">Î©</mi><mo> </mo></math></div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-multiplechoice-test-an-examinee-either-knows-the-correct-answer-with-probability-p-or-guesses-with-probability-1-p-the-probability-of-answering-a

slug:
in-a-multiplechoice-test-an-examinee-either-knows-the-correct-answer-with-probability-p-or-guesses-with-probability-1-p-the-probability-of-answering-a-69915

question:
<div class="question">In a multiple-choice test, an examinee either knows the correct answer with probability $\mathrm{p}$, or guesses with probability $1-\mathrm{p}$. The probability of answering a question<br/>correctly is $\frac{1}{\mathrm{~m}}$, if he or she merely guesses. If the examinee<br/>answers a question correctly, the probability that he or she really knows the answer is</div>

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

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

answer:
<div class="solution">Probability of knowing correct answer $=\mathrm{p}$ Probability to guess correct answer $=(1-\mathrm{p})\left(\frac{1}{\mathrm{~m}}\right)$<br/>Probability to answer correctly $=\mathrm{p}+\frac{1-\mathrm{p}}{\mathrm{m}}$<br/>So, required probability $=\frac{p}{p+\frac{1-p}{m}}=\frac{m p}{m p+1-p}$.<br/>$=\frac{\mathrm{mp}}{1+\mathrm{p}(\mathrm{m}-1)}$</div>


title: in-a-nonleap-year-the-probability-of-getting-53-sunday-or-53-tuesday-or-53-thursday-is
slug: in-a-nonleap-year-the-probability-of-getting-53-sunday-or-53-tuesday-or-53-thursday-is-95411
tags: ['Mathematics', 'Probability', 'TS EAMCET', 'TS EAMCET 2023 (12 May Shift 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a non-leap year, the probability of getting 53 Sunday or 53 Tuesday or 53 Thursday is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac {1}{7}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac {2}{7}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac {3}{7}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac {4}{7}$</span> </li> </ul>

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

answer:
<div class="solution">In non-leap year, there are 365 days i.e. 52 complete weeks and $1$ extra day.<br/>That day can be any of 7 days.<br/>$\therefore \quad P(53 \text { Sunday })=P(\text { Last } 1 \text { day Sunday })=\frac{1}{7}$<br/>Similarly, $P(53$ Tuesday $)=\frac{1}{7}$<br/>$\begin{aligned} &amp; P(53 \text { Thursday })=\frac{1}{7} \\ &amp; \therefore \quad \text { Probability }=\frac{1}{7}+\frac{1}{7}+\frac{1}{7}=\frac{3}{7} .\end{aligned}$</div>


tags: ['Biology', 'Morphology of Flowering Plants', 'NEET', 'NEET 2023 (Manipur)']
source_db: MarksBatch2_P1.db
title:
in-a-pea-flower-five-petals-are-arranged-in-a-specialized-manner-with-one-posterior-two-lateral-and-two-anterior-these-are-named-as-and-respectively

slug:
in-a-pea-flower-five-petals-are-arranged-in-a-specialized-manner-with-one-posterior-two-lateral-and-two-anterior-these-are-named-as-and-respectively-48427

question:
<div class="question">In a pea flower, five petals are arranged in a specialized manner with one posterior, two lateral and two anterior. These are named as ___________,  ___________ and  ___________ respectively.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Standard, Wings and Keel</span> </div>

answer:
<div class="solution">In pea flowers, vexillary aestivation is found. In this aestivation, the largest petal, i.e., standard overlaps the two smaller lateral petals that are wings which in turn overlap. The two smallest anterior petals are keel.</div>


tags: ['Physics', 'Nuclear Physics']
options: None
correct_option: None
source_db: MarksBatch2_P1.db
title:
in-a-periodic-table-the-average-atomic-mass-of-magnesium-is-given-as-24312-u-the-average-value-is-based-on-their-relative-natural-abundance-on-earth-t

slug:
in-a-periodic-table-the-average-atomic-mass-of-magnesium-is-given-as-24312-u-the-average-value-is-based-on-their-relative-natural-abundance-on-earth-t-99090

question:
<div class="question">In a periodic table the average atomic mass of magnesium is given as $24.312 \mathrm{u}$. The average value is based on their relative natural abundance on earth. The three isotopes and their masses are ${ }_{12}^{24} \mathrm{Mg}(\mathbf{2 3 . 9 8 5 0 4 \mathrm { u } ) \text { , }}$ ${ }_{12}^{25} \mathrm{Mg}(\mathbf{2 4 . 9 8 5 8 4 u})$ and ${ }_{12}^{26} \mathrm{Mg}(\mathbf{2 5 . 9 8 2 5 9} \mathrm{u})$. The natural abundance of ${ }_{12}^{24} \mathrm{Mg}$ is $78.99 \%$ by mass. Calculate the abundances of other two isotopes.</div>

answer:
<div class="solution">Let the abundance of ${ }_{12}^{25} \mathrm{Mg}$ be $\mathrm{x} \%$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad &amp; \text { Abundance of }{ }_{12}^{26} \mathrm{Mg} \\<br/>&amp;=\left(100-\text { abundance of }{ }_{12}^{24} \mathrm{Mg}-\mathrm{x}\right) \\<br/>&amp;=100-8.99-\mathrm{x}=(21.01-\mathrm{x}) \%<br/>\end{aligned}<br/>$$<br/>Average atomic mass $=24.312 \mathrm{u}$<br/>$$<br/>\begin{aligned}<br/>=&amp; \frac{23.98504 \times 78.99+24.98584 \times x+25.98259(21.01-x)}{100} \\<br/>\Rightarrow &amp; 24.312=\frac{1894.578+24.98584 x+545.89-25.98259 x}{100} \\<br/>\Rightarrow &amp; 2431.2=2440.47-0.9967 x \\<br/>\Rightarrow &amp; x=\frac{2440.47-2431.2}{0.9967}=\frac{9.270}{0.9967}=9.3 \% \\<br/>\therefore \quad &amp; \% \text { of }{ }_{12}^{25} \mathrm{Mg}=9.3 \% \\<br/>&amp; \% \text { of }{ }_{12}^{26} \mathrm{Mg}=21.01-9.3=11.71 \%<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2022 (06 Aug Shift 1)']
source_db: MarksBatch2_P1.db
title:
in-a-pipe-closed-at-one-end-air-column-is-vibrating-in-the-fourth-overtone-so-the-vibrating-air-column-has

slug:
in-a-pipe-closed-at-one-end-air-column-is-vibrating-in-the-fourth-overtone-so-the-vibrating-air-column-has-11350

question:
<div class="question">In a pipe closed at one end, air column is vibrating in the fourth overtone, so the vibrating air column has</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">5 nodes and 5 antinodes.</span> </div>

answer:
<div class="solution">For a pipe with one closed end:<br/>Fundamental mode has one node and one antinode.<br/>First overtone has two nodes and two antinodes.<br/>Second overtone has three nodes and three antinodes.<br/>So, the fifth overtone has five nodes and five antinodes.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2004']
source_db: MarksBatch2_P1.db
title:
in-a-plant-organ-which-is-covered-by-periderm-and-in-which-the-stomata-are-absent-some-gaseous-exchange-still-takes-place-through

slug:
in-a-plant-organ-which-is-covered-by-periderm-and-in-which-the-stomata-are-absent-some-gaseous-exchange-still-takes-place-through-74425

question:
<div class="question">In a plant organ which is covered by periderm and in which the stomata are absent, some gaseous exchange still takes place through</div>

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

answer:
<div class="solution">Due to continued formation of secondary tissues in the older stem and roots however the epidermis gets stressed and ultimately tends to rupture and followed by death of epidermal cells and outer tissues, and a new protective layer is developed called periderm. Structurally it consists of three parts Phellogen or Cork cambium, phellem or cork and phelloderm.<br/>Usually in the periderm of most plants, certain areas with loosely arranged cells have been found, which possess more or less raised and corky spots where the underneath tissues break through the epidermis. Such areas are universally found in the stems of woody plants. These broken areas are called lenticels, which perform the function of exchange of gases in the absence of stomata.</div>


tags: ['Mathematics', 'Probability', 'TS EAMCET', 'TS EAMCET 2021 (06 Aug Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-poisson-distribution-if-p-x-2-is-twice-p-x-1-then-the-standard-deviation-of-the-distribution-is

slug:
in-a-poisson-distribution-if-p-x-2-is-twice-p-x-1-then-the-standard-deviation-of-the-distribution-is-50227

question:
<div class="question">In a poisson distribution, If P (X) = 2 is twice<br/>P (X), = 1 then the standard deviation of the<br/>distribution is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">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">4</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">8</span> </li> </ul>

answer:
<div class="solution">$\begin{aligned} &amp; \text { } P(x=2)=2 P(x=1) \\ &amp; P(X=x)=\frac{e^{-\lambda} \cdot \lambda^x}{x !} \Rightarrow \frac{e^{-x} \cdot \lambda^2}{2 !}=2 \times \frac{e^{-x} \cdot \lambda^1}{1 !} \\ &amp; \Rightarrow \quad \frac{\lambda}{2}=2 \Rightarrow \lambda=4 \\ &amp; \because \quad \mu=n p=\lambda \Rightarrow \mu=4 \\ &amp; \text { So, } \quad \sigma=\sqrt{\mu}=\sqrt{4}=2 \\ &amp; \end{aligned}$</div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-potentiometer-experiment-a-cell-in-the-secondary-circuit-gives-null-point-at-25-m-when-the-length-of-the-potentiometer-wire-is-10-m-if-the-length

slug:
in-a-potentiometer-experiment-a-cell-in-the-secondary-circuit-gives-null-point-at-25-m-when-the-length-of-the-potentiometer-wire-is-10-m-if-the-length-91860

question:
<div class="question">In a potentiometer experiment, a cell in the secondary circuit gives null point at <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>2.5</mtext><mo> </mo><mi mathvariant="normal">m</mi></math> when the length of the potentiometer wire is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi mathvariant="normal">m.</mi></math> If the length of the potentiometer wire is increased by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math> without changing the cell in the primary circuit, then the position of the null point will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.5</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.75</mn><mo> </mo><mi mathvariant="normal">m</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 xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2.75</mn><mo> </mo><mi mathvariant="normal">m</mi></math></span> </div>

answer:
<div class="solution">The resistance of a potentiometer wire is given as,<br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>=</mo><mi mathvariant="normal">Ï</mi><mo>Ã</mo><mfrac><mi mathvariant="normal">l</mi><mi mathvariant="normal">A</mi></mfrac></math><br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">R</mi><mo>'</mo></msup><mo>=</mo><mfrac linethickness="1"><mrow><mn>2</mn><mo>.5</mo><mi mathvariant="normal">Ï</mi></mrow><mrow><mi mathvariant="normal">A</mi><mo>Ã</mo><mn>10</mn></mrow></mfrac></math><br/> <br/>Potential <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">V</mi><mo>'</mo><mo>=</mo><mi mathvariant="normal">I</mi><mo>Ã</mo><mi mathvariant="normal">R</mi><mo>'</mo></math>,<br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mi mathvariant="normal">I</mi><mo>â¡</mo><mfenced close="}" open="{"><mfrac><mrow><mtext>2.5</mtext><mi mathvariant="normal">Ï</mi></mrow><mrow><mi mathvariant="normal">A</mi><mo>â¡</mo><mo>Ã</mo><mn>10</mn></mrow></mfrac></mfenced></math><br/> <br/>Now, again the length of potentiometer wire is increased by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">m</mi></math>, then the resistance of null position wire.<br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi mathvariant="normal">R</mi><mrow><mo>'</mo><mo>'</mo></mrow></msup><mo>=</mo><mfrac linethickness="1"><mrow><mi mathvariant="normal">Ï</mi><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><mn>11</mn><mo>Ã</mo><mi mathvariant="normal">A</mi></mrow></mfrac></math><br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">V</mi><mo>"</mo><mo>=</mo><mi>IR</mi><mo>"</mo></math><br/> <br/>and, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">V</mi><mo>'</mo><mo>=</mo><mi mathvariant="normal">V</mi><mo>"</mo></math><br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac linethickness="1"><mrow><mi mathvariant="normal">I</mi><mo>Ã</mo><mn>2</mn><mo>.5</mo><mi mathvariant="normal">Ï</mi></mrow><mrow><mi mathvariant="normal">A</mi><mo>Ã</mo><mn>10</mn></mrow></mfrac><mo>=</mo><mfrac linethickness="1"><mrow><mi mathvariant="normal">I</mi><mo>Ã</mo><mi mathvariant="normal">Ï</mi><mo>Ã</mo><mi mathvariant="normal">l</mi></mrow><mrow><mn>11</mn><mo>Ã</mo><mi mathvariant="normal">A</mi></mrow></mfrac></math><br/> <br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac linethickness="1"><mrow><mn>2</mn><mo>.5</mo><mo>Ã</mo><mn>11</mn></mrow><mn>10</mn></mfrac><mo>=</mo><mi mathvariant="normal">l</mi><mo>=</mo><mtext>2.75</mtext><mo> </mo><mi mathvariant="normal">m</mi></math></div>


tags: ['Physics', 'Current Electricity', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-potentiometer-experiment-a-cell-of-emf-15-v-connected-in-the-secondary-circuit-gives-a-balancing-length-of-165-c-m-of-the-wire-if-a-resistance-of

slug:
in-a-potentiometer-experiment-a-cell-of-emf-15-v-connected-in-the-secondary-circuit-gives-a-balancing-length-of-165-c-m-of-the-wire-if-a-resistance-of-92682

question:
<div class="question">In a potentiometer experiment a cell of e.m.f <math><mn>1.5</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">V</mi></math> connected in the secondary circuit gives a balancing length of <math><mn>165</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> of the wire. If a resistance of <math><mn>5</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">Î©</mi></math> is connected in parallel to the cell, the balancing length of the wire is <math><mn>150</mn><mi mathvariant="normal"> </mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">m</mi></math> . The internal resistance of the cell is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>1.5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>1</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mn>0.5</mn><mi mathvariant="normal">Â </mi><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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>0.5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></span> </div>

answer:
<div class="solution">In a potentiometer experiment internal resistance is given by,<br/><br/> <math><mi mathvariant="normal">r</mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow><mrow><msub><mrow><mi mathvariant="normal">l</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac><mo>â</mo><mn>1</mn></mrow></mfenced><mi mathvariant="normal">R</mi></math> <br/><br/> <math><mi mathvariant="normal">r</mi><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>165</mn></mrow><mrow><mn>150</mn></mrow></mfrac><mo>â</mo><mn>1</mn></mrow></mfenced><mo>Ã</mo><mn>5</mn></math> <br/><br/> <math><mi mathvariant="normal">r</mi><mo>=</mo><mn>0.5</mn><mi mathvariant="normal">Â </mi><mi mathvariant="normal">Î©</mi></math></div>


tags: ['Physics', 'Current Electricity', 'AP EAMCET', 'AP EAMCET 2017 (24 Apr Shift 1)']
answer: <div class="solution">No solution. Refer to answer key.</div>
source_db: MarksBatch2_P1.db
title:
in-a-potentiometer-experiment-when-a-cell-in-the-secondary-circuit-is-shunted-by-a-resistance-r-balancing-length-is-l-1-on-doubling-the-shunt-resistan

slug:
in-a-potentiometer-experiment-when-a-cell-in-the-secondary-circuit-is-shunted-by-a-resistance-r-balancing-length-is-l-1-on-doubling-the-shunt-resistan-89603

question:
<div class="question">In a potentiometer experiment, when a cell in the secondary circuit is shunted by a resistance ' $R$ ', balancing length is ' $L_1$ '. On doubling the shunt resistance, balancing length increases to ' $L_2$ '. Internal resistance of the cell is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{2 \mathrm{R}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{\mathrm{L}_1-2 \mathrm{~L}_2}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{2 \mathrm{R}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{\left(2 \mathrm{~L}_1-\mathrm{L}_2\right)}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{\mathrm{R}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{\mathrm{L}_1-2 \mathrm{~L}_2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{R}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{\left(2 \mathrm{~L}_1-\mathrm{L}_2\right)}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{2 \mathrm{R}\left(\mathrm{L}_2-\mathrm{L}_1\right)}{\left(2 \mathrm{~L}_1-\mathrm{L}_2\right)}$</span> </div>


tags: ['Physics', 'Current Electricity', 'AP EAMCET', 'AP EAMCET 2021 (19 Aug Shift 2)']
source_db: MarksBatch2_P1.db
title:
in-a-potentiometer-of-10-wires-the-balance-point-is-obtained-on-the-6-th-wire-to-shift-the-balance-point-to-8-th-wire-we-should

slug:
in-a-potentiometer-of-10-wires-the-balance-point-is-obtained-on-the-6-th-wire-to-shift-the-balance-point-to-8-th-wire-we-should-84974

question:
<div class="question">In a potentiometer of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn></math> wires, the balance point is obtained on the <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>6</mn><mtext>th </mtext></msup></math> wire. To shift the balance point to <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mn>8</mn><mtext>th </mtext></msup></math> wire, we should</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Increase resistance in the main circuit</span> </div>

answer:
<div class="solution"><p>By increasing resistance in the primary circuit the P.G of the  wire decreases thereby it requires more length to measure the emf of secondary cell.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo></math>By increasing the resistance in series  circuit we can move balancing point from sixth to eight wire.</p></div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-random-arrangement-of-the-letters-of-the-word-university-what-is-the-probability-that-two-is-do-not-come-together

slug:
in-a-random-arrangement-of-the-letters-of-the-word-university-what-is-the-probability-that-two-is-do-not-come-together-69339

question:
<div class="question">In a random arrangement of the letters of the word 'UNIVERSITY', what is the probability that two I's do not come together?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$4 / 5$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1 / 5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1 / 10$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$9 / 10$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 / 5$</span> </div>

answer:
<div class="solution">Total number of words formed byletters of UNIVERSITY<br/>$=\frac{10 !}{2 !} \quad(\because \mathrm{I}$ is repeated $)$<br/>Taking two $\mathrm{I}_{\mathrm{s}}$ together, number of ways to arrange letters of UNIVERSITY $=9 !$ $\therefore$ Probability of two $\mathrm{I}_{\mathrm{s}}$ coming together<br/>$=\frac{9 !}{\frac{10 !}{2 !}}=\frac{9 ! \times 2 !}{10 !}=\frac{2}{10}=\frac{1}{5}$<br/>$\therefore$ Probability of two $\mathrm{I}_{\mathrm{s}}$ not coming together<br/>$=1-\frac{1}{5}=\frac{4}{5}$</div>


title: in-a-reflecting-telescope-a-secondary-mirror-is-used-to-1
slug: in-a-reflecting-telescope-a-secondary-mirror-is-used-to-1-44659
question: <div class="question">In a reflecting telescope, a secondary mirror is used to:</div>
tags: ['Physics', 'Ray Optics', 'BITSAT', 'BITSAT 2023 (Memory Based Paper 1)']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">reduce the problem of mechanical support</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">remove spherical aberration</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">make chromatic aberration zero</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">move the eyepiece outside the telescopic tube</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">move the eyepiece outside the telescopic tube</span> </div>

answer:
<div class="solution">(d) To redirect the light that enters the telescope to the eyepiece or camera. The primary mirror of a reflecting telescopes gathers the light and reflects towards the secondary mirror which then reflect the light towards the eyepiece allowing the observer to see image.<br/>It has advantage of a large focal length in a short telescope.</div>


title: in-a-reflecting-telescope-a-secondary-mirror-is-used-to
slug: in-a-reflecting-telescope-a-secondary-mirror-is-used-to-10763
question: <div class="question"><p>In a reflecting telescope, a secondary mirror is used to:</p></div>
tags: ['Physics', 'Ray Optics', 'JEE Main', 'JEE Main 2023 (08 Apr Shift 1)']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">reduce the problem of mechanical support</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">make chromatic aberration zero</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">move the eyepiece outside the telescopic tube</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">remove spherical aberration</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">move the eyepiece outside the telescopic tube</span> </div>

answer:
<div class="solution"><blockquote><p>Mirrors are used in reflecting telescopes, which allow astronomers to see distant objects in space more clearly.</p><p>A mirror forms an image by gathering light from spatial objects. A second mirror receives the picture that was reflected by the first mirror, which may be rather wide. The light is reflected by this tiny mirror onto an eyepiece lens, which magnifies or enlarges the image of the object.</p><p>Hence, the secondary mirror is used to move the eyepiece outside the telescopic tube.</p></blockquote></div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-relayrace-there-are-six-teams-a-b-c-d-e-and-f-what-is-the-probability-that-a-b-c-finish-first-second-third-respectively

slug:
in-a-relayrace-there-are-six-teams-a-b-c-d-e-and-f-what-is-the-probability-that-a-b-c-finish-first-second-third-respectively-89293

question:
<div class="question">In a relayrace, there are six teams $A, B, C, D, E$ and $F$. What is the probability that $A, B, C$ finish first, second, third respectively?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{2}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{1}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{60}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{120}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\frac{1}{120}$</span> </div>

answer:
<div class="solution">Probability of $\mathrm{A}=\frac{1}{6}$ Probability of $\mathrm{B}=\frac{1}{5}$ Probability of $\mathrm{C}=\frac{1}{4}$ Hence, required probability $=\frac{1}{6} \times \frac{1}{5} \times \frac{1}{4}=\frac{1}{120}$</div>


title: in-a-rightangled-triangle-abc-if-the-hypotenuse-ab-p-then-what-is-ab-ac-bc-ba-ca-cb-equal-to
slug: in-a-rightangled-triangle-abc-if-the-hypotenuse-ab-p-then-what-is-ab-ac-bc-ba-ca-cb-equal-to-64030
tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a right-angled triangle $\mathrm{ABC}$, if the hypotenuse $\mathrm{AB}=\mathrm{p}$, then what is $\overrightarrow{\mathrm{AB}}$. $\overrightarrow{\mathrm{AC}}+\overrightarrow{\mathrm{BC}} . \overrightarrow{\mathrm{BA}}+\overrightarrow{\mathrm{CA}} \cdot \overrightarrow{\mathrm{CB}}$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{p}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{p}^{2}$</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">$2 \mathrm{p}^{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\mathrm{p}^{2}}{2}$</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/vCJ_rjPrvD85YgmkI2J8GSPlGP_2dGb-d1eP6yBwchs.original.fullsize.png"/><br/><br/>$\begin{aligned} \overrightarrow{A B} \cdot \overrightarrow{A C}+\overrightarrow{B C} \cdot \overrightarrow{B A}+\overrightarrow{C A} \cdot \overrightarrow{C B} \\=&amp;(A B \cdot A C \cdot \cos \theta)+(B C \cdot B A \cdot \cos (90-\theta)) \\ &amp; \quad+(C A \cdot C B \cdot \cos 90) \\=&amp;(p \cdot x \cdot \cos \theta)+(y \cdot p \cdot \sin \theta)+0 \\=&amp; p[x \cos \theta+y \sin \theta] \end{aligned}$<br/>By projection formula :<br/>$p=x \cos \theta+y \cos (90-\theta)$<br/>$=x \cos \theta+y \sin \theta$<br/>$\therefore \quad p[x \cos \theta+y \sin \theta]=p \times p=p^{2} .$</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'NEET', 'NEET 2008 (Screening)']
source_db: MarksBatch2_P1.db
title:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate-1

slug:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate-1-13449

question:
<div class="question">In a $S_{\mathrm{N}} 2$ substitution reaction of the type $\mathrm{R}-\mathrm{Br}+\mathrm{Cl}^{-} \stackrel{\mathrm{DMF}}{\longrightarrow} \mathrm{R}-\mathrm{Cl}+\mathrm{Br}^{-}$, which one of the following has the highest relative rate?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_3-\mathrm{CH}_2-\mathrm{CH}_2 \mathrm{Br}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/neet/o4K3RCV9-I8IuFCDUIo2_D7SLsK07YzFJ_rT2o0DbPY.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/kF2DGHJzhxGDedUNyZIeTqW_Z8gSTF0SoGk4gv6UHjE.original.fullsize.png"/><br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">Key Idea: The relative reactivity of alkyl halides towards $\mathrm{S}_{\mathrm{N}} 2$ reactions is as follows:<br/>Primary $&gt;$ Secondary $&gt;$ Tertiary<br/>However, if the primary alkyl halide or the nucleophile/base is sterically hindered the nucleophile will have difficulty to getting the back side of the $\alpha$-carbon as a result of this, the elimination product will be predominant. Here $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}$ is the least hindered, hence it has the highest relative rate towards $\mathrm{S}_{\mathrm{N}} 2$ reaction.</div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate-2

slug:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate-2-98343

question:
<div class="question">In a $\mathrm{S}_{\mathrm{N}} 2$ substitution reaction of the type $\mathrm{R}-\mathrm{Br}+\mathrm{Cl}^{-} \stackrel{\mathrm{DMF}}{\longrightarrow} \mathrm{R}-\mathrm{Cl}+\mathrm{Br}^{-}$
<br/> <br/>which one of the following has the highest relative rate?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2} \mathrm{Br}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d1XsGBHA2CzZm0OetNdOJst_dlnO_s2lcVzKm3XRcQI.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/SRpALsUieGgskOCrw7D3Le2-4ZWmZcF-ctXhDUrKOOQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}$</span> </div>

answer:
<div class="solution">$\mathrm{S}_{\mathrm{N}} 2$ mechanism is followed in case of primary and secondary halides i.e., $\mathrm{S}_{\mathrm{N}}^{2}$ reaction is favoured by small groups on the carbon atom attached to halogens so
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/UxGpTB0zlK2tNKPe8q7QtZVHOXwWyjcPieTaY2aLHc4.original.fullsize.png"/></div>


tags: ['Chemistry', 'Haloalkanes and Haloarenes', 'BITSAT', 'BITSAT 2013']
source_db: MarksBatch2_P1.db
title:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate

slug:
in-a-s-n-2-substitution-reaction-of-the-type-r-br-cl-dmf-r-cl-br-which-one-of-the-following-has-the-highest-relative-rate-51959

question:
<div class="question">In a $\mathrm{S}_{\mathrm{N}} 2$ substitution reaction of the type $\mathrm{R}-\mathrm{Br}+\mathrm{Cl}^{-} \stackrel{\mathrm{DMF}}{\longrightarrow} \mathrm{R}-\mathrm{Cl}+\mathrm{Br}^{-}$
<br/> <br/>which one of the following has the highest relative rate?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2} \mathrm{Br}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/d1XsGBHA2CzZm0OetNdOJst_dlnO_s2lcVzKm3XRcQI.original.fullsize.png"/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/SRpALsUieGgskOCrw7D3Le2-4ZWmZcF-ctXhDUrKOOQ.original.fullsize.png"/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Br}$</span> </div>

answer:
<div class="solution">$\mathrm{S}_{\mathrm{N}} 2$ mechanism is followed in case of primary and secondary halides i.e., $\mathrm{S}_{\mathrm{N}}^{2}$ reaction is favoured by small groups on the carbon atom attached to halogens so
<br/> <br/><img src="https://cdn-question-pool.getmarks.app/pyq/bitsat/UxGpTB0zlK2tNKPe8q7QtZVHOXwWyjcPieTaY2aLHc4.original.fullsize.png"/></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">111</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-school-all-the-students-play-at-least-one-of-three-indoor-games-chess-carrom-and-table-tennis-60-play-chess-50-play-table-tennis-48-play-carrom-1-1

slug:
in-a-school-all-the-students-play-at-least-one-of-three-indoor-games-chess-carrom-and-table-tennis-60-play-chess-50-play-table-tennis-48-play-carrom-1-1-27922

question:
<div class="question">In a school, all the students play at least one of three indoor games - chess, carrom and table tennis, 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.<br/>What can be the minimum number of students in the school?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">123</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">111</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">95</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">63</span> </li> </ul>

answer:
<div class="solution">Number of students who play chess, $\mathrm{n}(\mathrm{A})=60$ Number of students who play tennis, $\mathrm{n}(\mathrm{B})=50$ Number of students who play carrom, $\mathrm{n}(\mathrm{C})=48$ Given, $n(A \cap B)=20$<br/>$n(B \cap C)=15$<br/>$n(A \cap C)=12$<br/>$\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=\mathrm{n}(\mathrm{A})+\mathrm{n}(\mathrm{B})+\mathrm{n}(\mathrm{C})-\mathrm{n}(\mathrm{A} \cap \mathrm{B})-\mathrm{n}(\mathrm{B} \cap$<br/>C) $-n(A \cap C)+n(A \cap B \cap C)$<br/>$=60+50+48-20-15-12+n(A \cap B \cap C)$<br/>$=111+\mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})$<br/>So, minimum number of students $=111$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2019 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">123</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-school-all-the-students-play-at-least-one-of-three-indoor-games-chess-carrom-and-table-tennis-60-play-chess-50-play-table-tennis-48-play-carrom-1

slug:
in-a-school-all-the-students-play-at-least-one-of-three-indoor-games-chess-carrom-and-table-tennis-60-play-chess-50-play-table-tennis-48-play-carrom-1-97404

question:
<div class="question">In a school, all the students play at least one of three indoor games - chess, carrom and table tennis, 60 play chess, 50 play table tennis, 48 play carrom, 12 play chess and carrom, 15 play carrom and table tennis, 20 play table tennis and chess.<br/>What can be the maximum number of students in the school?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">111</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">123</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">125</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">135</span> </li> </ul>

answer:
<div class="solution">$\mathrm{n}(\mathrm{A} \cup \mathrm{B} \cup \mathrm{C})=111+\mathrm{n}(\mathrm{A} \cap \mathrm{B} \cap \mathrm{C})$<br/>Maximum number of students $=111+12=123$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-school-there-are-40-science-students-and-the-remaining-60-are-arts-students-it-is-known-that-5-of-the-science-students-are-girls-and-10-of-the-ar

slug:
in-a-school-there-are-40-science-students-and-the-remaining-60-are-arts-students-it-is-known-that-5-of-the-science-students-are-girls-and-10-of-the-ar-15734

question:
<div class="question">In a school there are $40 \%$ science students and the remaining $60 \%$ are arts students. It is known that $5 \%$ of the science students are girls and $10 \%$ of the arts students are girls. One student selected at random is a girl. What is the probability that she is an arts student?</div>

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

answer:
<div class="solution">Let there be 100 students. So, there are 40 students of science and 60 students of<br/>arts.<br/>$5 \%$ of $40=2$ science students (girls) $10 \%$ of $60=6$ science students (girls) Total girls students $=8$ If a girl is chosed then<br/>$\mathrm{P}(\mathrm{arts})=\frac{6}{8}=\frac{3}{4}$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-series-of-2-n-observations-half-of-them-are-equal-to-a-2-and-the-remaining-half-are-equal-to-a-2-if-the-standard-deviation-of-the-observations-is

slug:
in-a-series-of-2-n-observations-half-of-them-are-equal-to-a-2-and-the-remaining-half-are-equal-to-a-2-if-the-standard-deviation-of-the-observations-is-46928

question:
<div class="question">In a series of <math><mn>2</mn><mi>n</mi></math> observations, half of them are equal to <math><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></math> and the remaining half are equal to <math><mo>â</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>.</mo></math> If the standard deviation of the observations is <math><mn>2</mn><mo>,</mo></math> then <math><mfenced close="|" open="|" separators="|"><mrow><mi>a</mi></mrow></mfenced></math> is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mfrac><mrow><mn>1</mn></mrow><mrow><mi>n</mi></mrow></mfrac></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><msqrt><mn>2</mn></msqrt></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><mn>2</mn></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mfrac><mrow><msqrt><mn>2</mn></msqrt></mrow><mrow><mi>n</mi></mrow></mfrac></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><msqrt><mn>2</mn></msqrt></math></span> </div>

answer:
<div class="solution"><math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></math> for <math><mi>i</mi><mo>=</mo><mn>1,2</mn><mo>,.</mo><mo>.</mo><mo>,</mo><mi>n</mi></math> and <math><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mo>-</mo><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></math> for <math><mi>i</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn><mo>,...</mo><mn>2</mn><mi>n</mi></math><br/><math><mi mathvariant="normal">S</mi><mo>.</mo><mi mathvariant="normal">D</mi><mo>=</mo><msqrt><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></mfrac><mrow><msubsup><mo stretchy="false">â</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msubsup><mrow><msup><mrow><mfenced separators="|"><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>-</mo><mover accent="true"><mrow><mi>x</mi></mrow><mo>-</mo></mover></mrow></mfenced></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></msqrt></math><br/><math><mo>â</mo><mn>2</mn><mo>=</mo><msqrt><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></mfrac><mrow><msubsup><mo stretchy="false">â</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msubsup><mrow><msubsup><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msubsup></mrow></mrow></msqrt><mfenced separators="|"><mrow><mi mathvariant="normal">S</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">c</mi><mi mathvariant="normal">e</mi><mi></mi><mrow><msubsup><mo stretchy="false">â</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mn>2</mn><mi>n</mi></mrow></msubsup><mrow><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>=</mo><mn>0</mn></mrow></mrow></mrow></mfenced></math><br/><math> <mrow> <mo>â</mo><mn>2</mn><mo>=</mo><msqrt> <mrow> <mfrac> <mn>1</mn> <mrow> <mn>2</mn><mi>n</mi></mrow> </mfrac> <mo>â</mo><mn>2</mn><mi>n</mi><msup> <mi>a</mi> <mn>4</mn> </msup> </mrow> </msqrt> <mo>â</mo><mfenced close="|" open="|"> <mi>a</mi> </mfenced><mo>=</mo><msqrt> <mn>2</mn> </msqrt> </mrow> </math><br/> </div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2004']
source_db: MarksBatch2_P1.db
title:
in-a-series-of-2-n-observations-half-of-them-equal-a-and-remaining-half-equal-a-if-the-standard-deviation-of-the-observations-is-2-then-a-equals

slug:
in-a-series-of-2-n-observations-half-of-them-equal-a-and-remaining-half-equal-a-if-the-standard-deviation-of-the-observations-is-2-then-a-equals-73334

question:
<div class="question">In a series of $2 n$ observations, half of them equal a and remaining half equal $-a$. If the standard deviation of the observations is 2 , then $|a|$ equals</div>

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

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

answer:
<div class="solution">$x_i=a$ for $i=1,2, \ldots, n$ and $x_i=-a$ for $i=n, \ldots ., 2 n$<br/>S.D. $=\sqrt{\frac{1}{2 n} \sum_{i=1}^{2 n}\left(x_i-\bar{x}\right)^2} \Rightarrow 2=\sqrt{\frac{1}{2 n} \sum_{i=1}^{2 n} x_i^2} \quad\left(\right.$ Since $\left.\sum_{i=1}^{2 n} x_i=0\right) \Rightarrow 2=\sqrt{\frac{1}{2 n} \cdot 2 n a^2} \Rightarrow|a|=2$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-series-of-3-oneday-cricket-matches-between-teams-a-and-b-of-a-college-the-probability-of-team-a-winning-or-drawing-are-13-and-16-respectively-if-

slug:
in-a-series-of-3-oneday-cricket-matches-between-teams-a-and-b-of-a-college-the-probability-of-team-a-winning-or-drawing-are-13-and-16-respectively-if-14931

question:
<div class="question">In a series of 3 one-day cricket matches between teams A and $\mathrm{B}$ of a college, the probability of team A winning or drawing are $1 / 3$ and $1 / 6$ respectively. If a win, loss or draw gives 2,0 and 1 point respectively, then what is the probability that team A will score 5 points in the series?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{17}{18}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{11}{12}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{1}{12}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{1}{18}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\frac{1}{18}$</span> </div>

answer:
<div class="solution">$\begin{array}{l}\text { Req. Prob. }=\mathrm{P}(5 \text { points })=\mathrm{P}(\text { two wins and one draw) } \\ = &amp; \mathrm{P}(\mathrm{WWD})+\mathrm{P}(\mathrm{WDW})+\mathrm{P}(\mathrm{DWW}) \\ = &amp; \frac{1}{3} \times \frac{1}{3} \times \frac{1}{6}+\frac{1}{3} \times \frac{1}{6} \times \frac{1}{3}+\frac{1}{6} \times \frac{1}{3} \times \frac{1}{3} \\ = &amp; \frac{1}{18}\end{array}$</div>


tags: ['Mathematics', 'Statistics', 'JEE Main', 'JEE Main 2013 (25 Apr Online)']
source_db: MarksBatch2_P1.db
title:
in-a-set-of-2-n-observations-half-of-them-are-equal-to-a-and-the-remaining-hall-are-equal-to-a-if-the-standard-deviation-of-all-the-observations-is-2-

slug:
in-a-set-of-2-n-observations-half-of-them-are-equal-to-a-and-the-remaining-hall-are-equal-to-a-if-the-standard-deviation-of-all-the-observations-is-2-53206

question:
<div class="question">In a set of $2 n$ observations, half of them are equal to ' $\mathrm{a}$ ' and the remaining hall are equal to ' $-\mathrm{a}^{\prime}$ '. If the standard deviation of all the observations is 2 ; then the value of $|a|$ is :</div>

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

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

answer:
<div class="solution">Clearly mean $\mathrm{A}=0$<br/>Now, standard deviation $\sigma=\sqrt{\frac{\Sigma(x-\mathrm{A})^2}{2 n}}$<br/>$$<br/>\begin{aligned}<br/>2=&amp; \sqrt{\frac{(a-0)^2+(a-0)^2+\ldots \ldots+(0-a)^2+\ldots . .}{2 n}} \\<br/>&amp;=\sqrt{\frac{a^2 \cdot 2 n}{2 n}}=|a|<br/>\end{aligned}<br/>$$<br/>Hence, $|a|=2$</div>


tags: ['Physics', 'Wave Optics', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-singleslit-diffraction-pattern-the-position-of-first-secondary-maximum-is-at-3-0-then-what-will-be-the-angular-position-of-second-minima

slug:
in-a-singleslit-diffraction-pattern-the-position-of-first-secondary-maximum-is-at-3-0-then-what-will-be-the-angular-position-of-second-minima-87480

question:
<div class="question">In a single-slit diffraction pattern, the position of first secondary maximum is at <math><mn>3</mn><msup><mrow><mn>0</mn></mrow><mrow><mo>â</mo></mrow></msup></math>, then what will be the angular position of second minima?</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mi> </mi><mfenced separators="|"><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></mfenced></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 xmlns="http://www.w3.org/1998/Math/MathML"><mrow><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mo>(</mo></mrow><mn>1</mn><mo>)</mo><mi> </mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>⁡</mo><mfenced separators="|"><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mi> </mi><mfenced separators="|"><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></mfenced></math></span> </div>

answer:
<div class="solution"><p>For first secondary maxima,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><msub><mi>θ</mi><mn>1</mn></msub><mo>=</mo><mfenced separators="|"><mrow><mn>1</mn><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mfrac><mi>λ</mi><mi>a</mi></mfrac><mo>=</mo><mfrac><mrow><mn>3</mn><mi>λ</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi>sin</mi><mn>3</mn><msup><mn>0</mn><mi>o</mi></msup><mo>=</mo><mfrac><mrow><mn>3</mn><mi>λ</mi></mrow><mrow><mn>2</mn><mi>a</mi></mrow></mfrac></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mfrac><mi>λ</mi><mi>a</mi></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac></math><br/><br/>For second minima,<br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sin</mi><mo>⁡</mo><mi>θ</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>λ</mi></mrow><mi>a</mi></mfrac><mo>=</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math> or <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>θ</mi><mo>=</mo><msup><mi>sin</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mi> </mi><mfenced separators="|"><mrow><mn>2</mn><mo>/</mo><mn>3</mn></mrow></mfenced></math></p></div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET', 'NEET 2009 (Screening)']
source_db: MarksBatch2_P1.db
title:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-representation-of-the-respective-activity-of-the-human-heart-1

slug:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-representation-of-the-respective-activity-of-the-human-heart-1-35138

question:
<div class="question">In a standard ECG, which one of the following alphabets is the correct representation of the respective activity of the human heart?</div>

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

answer:
<div class="solution">In ECG, P-wave indicates impulse of contraction generated by SA-node and it spreads in atria causing atrial depolarisation.<br/>T-wave is the most constant and conspicuous wave having the tallest amplitude. It is the first positive deflection during ventricular depolarisation.<br/>S-wave is the next downward deflection constant but often inconspicuous.<br/>T-wave is repolarisation wave of ventricular relaxation.</div>


tags: ['Biology', 'Body Fluids and Circulation', 'AIIMS', 'AIIMS 2014']
source_db: MarksBatch2_P1.db
title:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-representation-of-the-respective-activity-of-the-human-heart

slug:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-representation-of-the-respective-activity-of-the-human-heart-27017

question:
<div class="question">In a standard ECG which one of the following alphabets is the correct representation of the respective activity of the human heart?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">P - depolarisation of the atria</span> </div>

answer:
<div class="solution">A normal electrogram (ECG) is composed of a P wave, a QRS wave (complex) and a $\mathrm{T}$ wave. The P-wave represents the electrical excitation or depolarisation of the atria. The QRS complex represents the depolarisation of the ventricles which initiates the ventricular contraction. The contraction starts shortly after Q and marks the beginning of the systole. The T-wave represents the repolarisation of ventricles. The end of the T-wave marks the end of systole.</div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET', 'NEET 2009 (Mains)']
answer: <div class="solution">No Solution Available</div>
source_db: MarksBatch2_P1.db
title:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-represention-of-the-respective-activity-of-the-human-heart

slug:
in-a-standard-ecg-which-one-of-the-following-alphabets-is-the-correct-represention-of-the-respective-activity-of-the-human-heart-15472

question:
<div class="question">In a standard ECG which one of the following alphabets is the correct represention of the respective activity of the human heart?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">P-depolarisation of the atria</span> </div>


tags: ['Biology', 'Body Fluids and Circulation', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-standard-ecg-which-one-of-the-following-is-the-correct-representation-of-the-respective-activity-of-the-human-heart

slug:
in-a-standard-ecg-which-one-of-the-following-is-the-correct-representation-of-the-respective-activity-of-the-human-heart-50859

question:
<div class="question">In a standard ECG, which one of the following is the correct representation of the respective activity of the human heart?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">P - depolarisation of the atria</span> </div>

answer:
<div class="solution">In a standard ECG, the P-wave is a small upward wave that indicates the depolarization of the atria. This is caused by the activation of the SA node.<br/><br/><img alt="" object-fit:contain="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/ECG.png" style="max-width:"/></div>


tags: ['Physics', 'Wave Optics', 'JEE Main']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">5</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-standard-youngs-doubleslit-experiment-how-many-maxima-can-be-obtained-on-a-screen-including-central-maxima-if-the-distance-between-the-silts-is-d

slug:
in-a-standard-youngs-doubleslit-experiment-how-many-maxima-can-be-obtained-on-a-screen-including-central-maxima-if-the-distance-between-the-silts-is-d-52434

question:
<div class="question">In a standard Young's double-slit experiment, how many maxima can be obtained on a screen (including central maxima), if the distance between the silts is <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext mathvariant="italic">d</mtext><mo>=</mo><mfrac><mrow><mn>5</mn><mi>Î»</mi></mrow><mn>2</mn></mfrac></math> (where <math><mrow><mi>Î»</mi> </mrow> </math> is the wavelength of light)?</div>

answer:
<div class="solution"><p>In YDSE, path difference, <math> <mrow> <mo>Î</mo> <mtext>x</mtext> <mo>=</mo> <mtext>d sin</mtext> <mi>Î¸</mi> </mrow> </math><br/><br/>For maxima, <math> <mrow> <mo>Î</mo> <mtext>x</mtext> <mo>=</mo> <mtext>n</mtext> <mi>Î»</mi> </mrow> </math>, where <math> <mrow> <mtext>n</mtext> <mo>=</mo> <mn>0</mn> <mtext>, </mtext> <mo>Â±</mo> <mn>1</mn> <mtext>, </mtext> <mo>Â±</mo> <mn>2</mn> <mtext>....</mtext> </mrow> </math><br/><br/><math> <mrow> <mfrac> <mrow> <mn>5</mn> <mi>Î»</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mtext>sin</mtext> <mi>Î¸</mi> <mo>=</mo> <mtext>n</mtext> <mi>Î»</mi> </mrow> </math>  (given that <math> <mrow> <mtext>d</mtext> <mo>=</mo> <mfrac> <mrow> <mn>5</mn> <mi>Î»</mi> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math>)</p><p><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable columnalign="left"><mtr><mtd><mo>â</mo><mi>sin</mi><mi>Î¸</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mi>n</mi></mrow><mn>5</mn></mfrac><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mo>(</mo><mi>i</mi><mo>)</mo></mtd></mtr></mtable></math><br/><br/><mtr><mtd><mo>Since,</mo><mtext> </mtext><mtext> </mtext><mo>â</mo><mn>1</mn><mo>â¤</mo><mi>sin</mi><mi>Î¸</mi><mo>â¤</mo><mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mi>F</mi><mi>r</mi><mi>o</mi><mi>m</mi><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo stretchy="false">(</mo><mi>i</mi><mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> </mtr> <mtr> <mtd> <mo>â</mo><mo>â</mo><mn>1</mn><mo>â¤</mo><mfrac> <mrow> <mn>2</mn><mi>n/</mi></mrow><mn>5</mn> </mfrac> <mo>â¤</mo><mn>1</mn> </mtd> </mtr><br/><math><mrow></mrow> </math><br/><br/>So, <math> <mrow> <mo>-</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> <mo>â¤</mo> <mtext>n</mtext> <mo>â¤</mo> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math><br/><br/>So, possible values of n are -2, -1, 0, 1, 2 Thus a total of 5 maximas will be obtained.</p></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-1

slug:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-1-60127

question:
<div class="question">In a state with a population of $75 \times 10^{\circ}, 45 \%$ of them know Hindi, $22 \%$ know English, $18 \%$ know Sanskrit, $12 \%$ know Hindi and English, $8 \%$ know English and Sanskrit, $10 \%$ know Hindi and Sanskrit and $5 \%$ knowall the three languages.<br/>What is the number of people who know only one language</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$3 \times 10^{6}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$4 \times 10^{6}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$3 \times 10^{7}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$4 \times 10^{7}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$4 \times 10^{6}$</span> </div>

answer:
<div class="solution">Number of people who know only one language $=a+b+c=21 \times 10^{6}+5.25 \times 10^{6}+3.75 \times 10^{6}$<br/>$=30 \times 10^{6}=3 \times 10^{7} .$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 1)']
source_db: MarksBatch2_P1.db
title:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-2

slug:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-2-24992

question:
<div class="question">In a state with a population of $75 \times 10^{\circ}, 45 \%$ of them know Hindi, $22 \%$ know English, $18 \%$ know Sanskrit, $12 \%$ know Hindi and English, $8 \%$ know English and Sanskrit, $10 \%$ know Hindi and Sanskrit and $5 \%$ knowall the three languages.<br/>What is the number of people who know only two $\begin{array}{ll}\text { languages ? } \end{array}$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$11.25 \times 10^{3}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$11.25 \times 10^{6}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$12 \times 10^{5}$</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">$12.5 \times 10^{5}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$12 \times 10^{5}$</span> </div>

answer:
<div class="solution">Number of people who know only two language $=\mathrm{d}+\mathrm{e}+\mathrm{f}=3.75 \times 10^{6}+2.25 \times 10^{6}+5.25 \times 10^{6}$<br/>$=11.25 \times 10^{6}$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 1)']
answer: <div class="solution">Number of people who knowonly Hindi=a $=21 \times 10^{6}$</div>
source_db: MarksBatch2_P1.db
title:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-3

slug:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-3-78074

question:
<div class="question">In a state with a population of $75 \times 10^{\circ}, 45 \%$ of them know Hindi, $22 \%$ know English, $18 \%$ know Sanskrit, $12 \%$ know Hindi and English, $8 \%$ know English and Sanskrit, $10 \%$ know Hindi and Sanskrit and $5 \%$ knowall the three languages.<br/>What is the number of people who know Hindi only?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$21 \times 10^{6}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$25 \times 10^{6}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$28 \times 10^{6}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$3 \times 10$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$3 \times 10$</span> </div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 1)']
answer: <div class="solution">Number of people who know only English $=5.25 \times 10^{6}$</div>
source_db: MarksBatch2_P1.db
title:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-4

slug:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-4-63907

question:
<div class="question">In a state with a population of $75 \times 10^{\circ}, 45 \%$ of them know Hindi, $22 \%$ know English, $18 \%$ know Sanskrit, $12 \%$ know Hindi and English, $8 \%$ know English and Sanskrit, $10 \%$ know Hindi and Sanskrit and $5 \%$ knowall the three languages.<br/>What is the number of people who know English only?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \times 10^{6}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$45 \times 10^{5}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$4 \times 10^{6}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">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">$4 \times 10^{6}$</span> </div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 1)']
answer: <div class="solution">Number of people who knowonly Sanskrit $\mathrm{c}=3.75 \times 10^{6}$</div>
source_db: MarksBatch2_P1.db
title:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10

slug:
in-a-state-with-a-population-of-75-1-0-45-of-them-know-hindi-22-know-english-18-know-sanskrit-12-know-hindi-and-english-8-know-english-and-sanskrit-10-53029

question:
<div class="question">In a state with a population of $75 \times 10^{\circ}, 45 \%$ of them know Hindi, $22 \%$ know English, $18 \%$ know Sanskrit, $12 \%$ know Hindi and English, $8 \%$ know English and Sanskrit, $10 \%$ know Hindi and Sanskrit and $5 \%$ knowall the three languages.<br/>What is the number of people who know Sanskrit only?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$5 \times 10^{6}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$45 \times 10^{5}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$4 \times 10^{6}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">None of the above</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>


title: in-a-step-up-transformer-which-one-of-the-following-statements-is-correct
slug: in-a-step-up-transformer-which-one-of-the-following-statements-is-correct-40286
tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2021 (21 Sep Shift 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a step up transformer, 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">Number of turns in the secondary coil is less than in primary coil</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Voltage in secondary coil is less than in primary coil</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">Current in the primary coil is more than current in the secondary coil</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Current in the primary coil is equal to current in the secondary coil</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Current in the primary coil is more than current in the secondary coil</span> </div>

answer:
<div class="solution">In a step-up transformer, the current in the secondary is less than the current in the primary.</div>


title: in-a-stepdown-transformer-the-number-of-turns-in
slug: in-a-stepdown-transformer-the-number-of-turns-in-59580
question: <div class="question">In a step-down transformer, the number of turns in</div>
tags: ['Physics', 'Alternating Current', 'MHT CET', 'MHT CET 2012']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">primary are less</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">primary are more</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">primary and secondary are equal</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">secondary are infinite</span> </li> </ul>

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

answer:
<div class="solution">In a step-down transformer, the number of turns of the primary coil are more than the number of turns of the secondary.</div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-stepup-transformer-the-ratio-of-turns-of-primary-to-secondary-is-1-10-and-the-primary-voltage-is-230-v-if-the-load-current-is-2-a-then-the-curren

slug:
in-a-stepup-transformer-the-ratio-of-turns-of-primary-to-secondary-is-1-10-and-the-primary-voltage-is-230-v-if-the-load-current-is-2-a-then-the-curren-13025

question:
<div class="question">In a step-up transformer, the ratio of turns of primary to secondary is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>:</mo><mn>10</mn></math> and the primary voltage is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>230</mn><mo> </mo><mi mathvariant="normal">V</mi></math>. If the load current is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">A</mi></math>, then the current in the primary is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 65px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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"><mn>10</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 65px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 65px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 65px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi></math><div id="gtx-trans" style="position: absolute; left: 65px; top: 37.6667px;"><div class="gtx-trans-icon"> </div></div></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>N</mi><mtext>p</mtext></msub><msub><mi>N</mi><mtext>s</mtext></msub></mfrac><mo>=</mo><mfrac><mn>1</mn><mrow><mn>1</mn><mn>0</mn></mrow></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>V</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mo> </mo><mn>230</mn><mo> </mo><mi mathvariant="normal">V</mi><mo>,</mo><mo> </mo><msub><mi>I</mi><mi mathvariant="italic">s</mi></msub><mo> </mo><mo>=</mo><mo> </mo><mn>2</mn><mo> </mo><mi mathvariant="normal">A</mi><mo>,</mo></math><br/><br/>            <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mtext>p</mtext></msub><msub><mi>I</mi><mtext>s</mtext></msub></mfrac><mo>=</mo><mfrac><msub><mi>N</mi><mtext>s</mtext></msub><msub><mi>N</mi><mtext>p</mtext></msub></mfrac></math><br/><br/>            <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi>I</mi><mtext>p</mtext></msub><mn>2</mn></mfrac><mo>=</mo><mfrac><mrow><mn>1</mn><mn>0</mn></mrow><mn>1</mn></mfrac></math><br/><br/><math><mrow><mn>⇒   </mn></mrow></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><msub><mi>I</mi><mi mathvariant="normal">p</mi></msub><mo>=</mo><mn>20</mn><mo> </mo><mi mathvariant="normal">A</mi><mo>​</mo></math><div id="gtx-trans" style="position: absolute; left: 36px; top: 248.753px;"><div class="gtx-trans-icon"> </div></div></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-stepup-transformer-the-voltage-in-the-primary-is-220-v-and-the-current-is-5-a-the-secondary-voltage-is-found-to-be-22000-v-the-current-in-the-sec

slug:
in-a-stepup-transformer-the-voltage-in-the-primary-is-220-v-and-the-current-is-5-a-the-secondary-voltage-is-found-to-be-22000-v-the-current-in-the-sec-55383

question:
<div class="question">In a step-up transformer, the voltage in the primary is <math><mn>220</mn><mi> </mi><mn>V</mn></math> and the current is <math><mn>5</mn><mi> </mi><mn>A</mn><mo>.</mo></math> The secondary voltage is found to be <math><mn>22000</mn><mi> </mi><mn>V</mn><mo>.</mo></math> The current in the secondary coil (neglect losses) is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math><mn>5</mn><mi> A</mi></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math><mn>50</mn><mi> A</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mn>500</mn><mi> A</mi></math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math><mn>0.05</mn><mi> A</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> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mn>0.05</mn><mi> A</mi></math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">s</mi></msub><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">p</mi></msub></mfrac><mo>=</mo><mfrac><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">p</mi></msub><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">s</mi></msub></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mo> </mo><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">s</mi></msub><mo>=</mo><msub><mi mathvariant="normal">I</mi><mi mathvariant="normal">p</mi></msub><mo>×</mo><mfrac><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">p</mi></msub><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">s</mi></msub></mfrac></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5</mn><mo>×</mo><mfrac><mn>220</mn><mn>22000</mn></mfrac><mo>=</mo><mn>0</mn><mo>.05</mo><mo> </mo><mi mathvariant="normal">A</mi></math></div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch2_P1.db
title:
in-a-study-of-two-groups-the-following-results-wer-obtained-b-beginarraylcc-hline-group-group-hline-mathbfa-mathbfb-sample-size-20-25-sample-mean-22-2

slug:
in-a-study-of-two-groups-the-following-results-wer-obtained-b-beginarraylcc-hline-group-group-hline-mathbfa-mathbfb-sample-size-20-25-sample-mean-22-2-36261

question:
<div class="question">In a study of two groups, the following results wer obtained $b$ \begin{array}{lcc}<br/>\hline &amp; Group &amp; Group \\<br/>\hline &amp; \mathbf{A} &amp; \mathbf{B} \\<br/>Sample Size &amp; 20 &amp; 25 \\<br/>Sample mean &amp; 22 &amp; 23 \\<br/>Sample standard deviation &amp; 10 &amp; 12 \\<br/>\hline<br/>\end{array} Which of the following statements is correct?</div>

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

answer:
<div class="solution">For Group A:<br/>Coefficient of variation<br/>$C V_{A}=\frac{\text { S.D. }}{\text { Mean }}=\frac{10}{22}=0.4545$<br/>For Group B:<br/>$C V_{B}=\frac{12}{23}=0.522$<br/>$\Rightarrow$ Group $\mathrm{A}$ is less variable.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-study-on-the-relationship-between-investment-x-and-profit-y-the-following-two-regression-equations-were-beained-hased-on-the-data-on-x-and-y-3-x-

slug:
in-a-study-on-the-relationship-between-investment-x-and-profit-y-the-following-two-regression-equations-were-beained-hased-on-the-data-on-x-and-y-3-x-92689

question:
<div class="question">In a study on the relationship between investment $(X)$ and profit $(Y)$, the following two regression equations were beained hased on the data on $X$ and $Y$ $3 X+Y-12=0$<br/>$X+2 Y-14=0$<br/>What is the mean $\bar{X}$ ?</div>

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

answer:
<div class="solution">Given lines of regression are $3 X+Y-12=0$ and $X+2 Y-14=0$<br/>Since, lines of regression passes through $(\bar{X}, \bar{Y})$.<br/>therefore $(\bar{X}, \bar{Y})$ satisfies the given equations.<br/>$\therefore 3 \bar{X}+\bar{Y}-12=0$<br/>and $\bar{X}+2 \bar{Y}-14=0$<br/>Multiply equation (ii) by 3 and subtract from (i), we get<br/>$(3 \bar{X}+\bar{Y}-12)-(3 \bar{X}+6 \bar{Y}-42)=0$<br/>$\Rightarrow 5 \bar{Y}+30=0 \Rightarrow \bar{Y}=6$<br/>Thus, $\bar{X}=14-2 \bar{Y}=14-12=2$<br/>Hence, mean, $\mathrm{X}=2$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2 only</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem-1

slug:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem-1-37854

question:
<div class="question">In a survey of 25 students, it was found that 15 had taker Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.<br/>onsider the following statements<br/> 1.The number of students who had taken only one<br/>subject is equal to the number of students who had taken only two subjects<br/>2.The number of students who had taken at least two subjects is four times the number of students who had taken all the three subjects<br/>Which of the above statements is/are correct?</div>

answer:
<div class="solution">Statement 1:<br/>Students, who had taken only one subject $=2+5+4=11$<br/>Students, who had taken only two subjects $=6+2+1=9$<br/>$1 \neq 9$<br/>State me nt $2:$<br/>Students who had taken atleast two subject $=1+2+6+3=12$<br/>Students who had taken all three subjects<br/>$4 \times 3=12$</div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">9</span> </div>
answer: <div class="solution">Only two subjects $=6+2+1=9$ 99</div>
source_db: MarksBatch2_P1.db
title:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem-2

slug:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem-2-21376

question:
<div class="question">In a survey of 25 students, it was found that 15 had taker Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.<br/>The number of students who had taken only two subjects<br/>IS</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">7</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">8</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">9</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">10</span> </li> </ul>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2014 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
answer: <div class="solution">Only Physics $=12-(1+3+6)=2$ 198</div>
source_db: MarksBatch2_P1.db
title:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem

slug:
in-a-survey-of-25-students-it-was-found-that-15-had-taker-mathematics-12-had-taken-physics-and-11-had-taken-chemistry-5-had-taken-mathematics-and-chem-30172

question:
<div class="question">In a survey of 25 students, it was found that 15 had taker Mathematics, 12 had taken Physics and 11 had taken Chemistry, 5 had taken Mathematics and Chemistry, 9 had taken Mathematics and Physics, 4 had taken Physics and Chemistry and 3 had taken all the three subjects.<br/>The number of students who had taken only physics is</div>

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


tags: ['Physics', 'Units and Dimensions', 'JIPMER', 'JIPMER 2006']
source_db: MarksBatch2_P1.db
title:
in-a-system-of-units-if-force-f-acceleration-a-and-time-t-are-taken-as-fundamental-units-then-the-dimensional-formula-of-energy-is

slug:
in-a-system-of-units-if-force-f-acceleration-a-and-time-t-are-taken-as-fundamental-units-then-the-dimensional-formula-of-energy-is-25068

question:
<div class="question">In a system of units if force $(F)$, acceleration $(A)$, and time ( $T$ ) are taken as fundamental units, then the dimensional formula of energy is :</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$F A^2 T$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$F A T^2$</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">$F^2 A T$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">FAT</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$F A T^2$</span> </div>

answer:
<div class="solution">Let energy $E=F^x A^y T^3$<br/>Writing the dimensions on both sides<br/>$\begin{aligned} &amp; {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]=\left[\mathrm{MLT}^{-2}\right]^x\left[\mathrm{LT}^{-2}\right]^y[\mathrm{~T}]^2} \\ &amp; {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]=\left[\mathrm{M}^x \mathrm{~L}^{x+y} \mathrm{~T}^{-2 x-2 y+z}\right]}\end{aligned}$<br/>On comparing both sides<br/>$\begin{aligned} &amp; x=1 \\ &amp; x+y=2 \\ &amp; \Rightarrow \quad y=2-x=2-1=1 \\ &amp; \text { and } \quad-2 x-2 y+z=-2 \\ &amp; \Rightarrow-2 \times 1-2 \times 1+z=-2 \\ &amp; \Rightarrow \quad z=-2+2+2 \\ &amp; =2 \\ &amp; \end{aligned}$<br/>$\therefore$ Dimensional formula of energy<br/>$=F A T^2$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2018 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">36</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-test-in-mathematics-20-of-the-students-obtained-first-class-if-the-data-are-represented-by-a-piechart-what-is-the-central-angle-corresponding-to-

slug:
in-a-test-in-mathematics-20-of-the-students-obtained-first-class-if-the-data-are-represented-by-a-piechart-what-is-the-central-angle-corresponding-to-74171

question:
<div class="question">In a test in Mathematics, $20 \%$ of the students obtained "first class". If the data are represented by a Pie-Chart, what is the central angle corresponding to "first class"</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$20^{\circ}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$72^{\circ}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">36</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">144</span> </li> </ul>

answer:
<div class="solution">Central angle $=20 \%$ of $360^{\circ}$<br/>$=\frac{20 \times 60}{100}$<br/>$=72^{\circ}$</div>


title: in-a-thermochemical-equation-what-does-the-standard-state-refer-to
slug: in-a-thermochemical-equation-what-does-the-standard-state-refer-to-52021
question: <div class="question">In a thermochemical equation, what does the standard state refer to?</div>
tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
source_db: MarksBatch2_P1.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">The state of matter when a substance is in its liquid phase.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">The state of matter when a substance is in its gaseous phase.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The pure form of a substance at 0Â°C.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The most stable state of a substance at a specified temperature and pressure.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">The most stable state of a substance at a specified temperature and pressure.</span> </div>

answer:
<div class="solution">The standard state in a thermochemical equation refers to the most stable state of a substance under specific conditions of temperature and pressure.</div>


tags: ['Chemistry', 'Redox Reactions', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-titration-experiment-10-ml-of-an-fecl-2-solution-consumed-25-ml-of-a-standard-k-2-cr-2-o-7-solution-to-reach-the-equivalent-point-the-standard-k--1

slug:
in-a-titration-experiment-10-ml-of-an-fecl-2-solution-consumed-25-ml-of-a-standard-k-2-cr-2-o-7-solution-to-reach-the-equivalent-point-the-standard-k-1-14222

question:
<div class="question"><p>In a titration experiment, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi>mL</mi></math> of an <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math> solution consumed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi>mL</mi></math> of a standard <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> solution to reach the equivalent point. The standard <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> solution is prepared by dissolving <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>225</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>250</mn><mo> </mo><mi>mL</mi></math> water. The concentration of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math> solution is closest to</p><br/><br/><p>[Given : molecular weight of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub><mo>=</mo><mn>294</mn><mo> </mo><mi mathvariant="normal">g</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>]</p><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>50</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>04</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </div>

answer:
<div class="solution"><p>In titration at equivalence point, number of equivalents of both reactants must be same.</p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msub><mi mathvariant="normal">N</mi><mn>1</mn></msub><msub><mi mathvariant="normal">V</mi><mn>1</mn></msub><mo>=</mo><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">V</mi><mn>2</mn></msub></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math> (normality) of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mfenced><mrow><mi mathvariant="normal">N</mi><mo>×</mo><mi mathvariant="normal">V</mi></mrow></mfenced><mo> </mo><mi>of</mi><mo> </mo><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></mrow><mrow><mi mathvariant="normal">V</mi><mo> </mo><mi>of</mi><mo> </mo><msub><mi>FeCl</mi><mn>2</mn></msub></mrow></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math> (normality) of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub><mo>=</mo><mfrac><mrow><mo> </mo><mi>Mass</mi><mo> </mo><mo>×</mo><mn>1000</mn></mrow><mrow><mo> </mo><mi>Equivalent</mi><mo> </mo><mi>mass</mi><mo> </mo><mo>×</mo><mo> </mo><mi>Volume</mi><mo> </mo><mi>of</mi><mo> </mo><mi>solution</mi><mo> </mo><mi>prepared</mi></mrow></mfrac></math></p><br/><br/><p>Equivalent mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo> </mo><mi>Molar</mi><mo> </mo><mi>mass</mi><mo> </mo></mrow><mrow><mi mathvariant="normal">n</mi><mo> </mo><mi>factor</mi><mo> </mo></mrow></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>294</mn><mn>6</mn></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>49</mn><mo> </mo><mi mathvariant="normal">g</mi><mo>/</mo><mi>equi</mi><mo>.</mo></math></p><br/><br/><p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> as oxidising agent is reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>Cr</mi><mrow><mn>3</mn><mo>+</mo></mrow></msup></math>).</p><br/><br/><p>Oxidation state of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cr</mi></math> atoms change from <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>6</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>3</mn></math>.</p><br/><br/><p>Total change is<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><mn>2</mn><mo>=</mo><mn>6</mn></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal">n</mi></math>-factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn></math>)</p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">N</mi></math> (of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1225</mn><mo>×</mo><mn>1000</mn></mrow><mrow><mn>49</mn><mo>×</mo><mn>250</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mi mathvariant="normal">N</mi></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">N</mi></math> (of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>25</mn></mrow><mn>10</mn></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p><br/></div>


tags: ['Chemistry', 'Redox Reactions', 'KVPY', 'KVPY 2019 (SB/SX)']
source_db: MarksBatch2_P1.db
title:
in-a-titration-experiment-10-ml-of-an-fecl-2-solution-consumed-25-ml-of-a-standard-k-2-cr-2-o-7-solution-to-reach-the-equivalent-point-the-standard-k-

slug:
in-a-titration-experiment-10-ml-of-an-fecl-2-solution-consumed-25-ml-of-a-standard-k-2-cr-2-o-7-solution-to-reach-the-equivalent-point-the-standard-k-16001

question:
<div class="question"><p>In a titration experiment, <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo> </mo><mi>mL</mi></math> of an <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math> solution consumed <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo> </mo><mi>mL</mi></math> of a standard <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> solution to reach the equivalent point. The standard <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> solution is prepared by dissolving <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mn>225</mn><mo> </mo><mi mathvariant="normal">g</mi></math> of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> in <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>250</mn><mo> </mo><mi>mL</mi></math> water. The concentration of the <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math> solution is closest to</p><br/><br/><p>[Given : molecular weight of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub><mo>=</mo><mn>294</mn><mo> </mo><mi mathvariant="normal">g</mi><mo> </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>]</p><br/></div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</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">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>50</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>10</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>04</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</mi></math></span> </div>

answer:
<div class="solution"><p>In titration at equivalence point, number of equivalents of both reactants must be same.</p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><msub><mi mathvariant="normal">N</mi><mn>1</mn></msub><msub><mi mathvariant="normal">V</mi><mn>1</mn></msub><mo>=</mo><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">V</mi><mn>2</mn></msub></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math> (normality) of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub><mo>=</mo><mfrac><mrow><mfenced><mrow><mi mathvariant="normal">N</mi><mo>×</mo><mi mathvariant="normal">V</mi></mrow></mfenced><mo> </mo><mi>of</mi><mo> </mo><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></mrow><mrow><mi mathvariant="normal">V</mi><mo> </mo><mi>of</mi><mo> </mo><msub><mi>FeCl</mi><mn>2</mn></msub></mrow></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">N</mi></math> (normality) of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub><mo>=</mo><mfrac><mrow><mo> </mo><mi>Mass</mi><mo> </mo><mo>×</mo><mn>1000</mn></mrow><mrow><mo> </mo><mi>Equivalent</mi><mo> </mo><mi>mass</mi><mo> </mo><mo>×</mo><mo> </mo><mi>Volume</mi><mo> </mo><mi>of</mi><mo> </mo><mi>solution</mi><mo> </mo><mi>prepared</mi></mrow></mfrac></math></p><br/><br/><p>Equivalent mass <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mo> </mo><mi>Molar</mi><mo> </mo><mi>mass</mi><mo> </mo></mrow><mrow><mi mathvariant="normal">n</mi><mo> </mo><mi>factor</mi><mo> </mo></mrow></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>294</mn><mn>6</mn></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>49</mn><mo> </mo><mi mathvariant="normal">g</mi><mo>/</mo><mi>equi</mi><mo>.</mo></math></p><br/><br/><p>(<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math> as oxidising agent is reduced to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msup><mi>Cr</mi><mrow><mn>3</mn><mo>+</mo></mrow></msup></math>).</p><br/><br/><p>Oxidation state of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Cr</mi></math> atoms change from <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>6</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>+</mo><mn>3</mn></math>.</p><br/><br/><p>Total change is<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>×</mo><mn>2</mn><mo>=</mo><mn>6</mn></math>, (<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mi mathvariant="normal">n</mi></math>-factor <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>6</mn></math>)</p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">N</mi></math> (of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">K</mi><mn>2</mn></msub><msub><mi>Cr</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>7</mn></msub></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>1225</mn><mo>×</mo><mn>1000</mn></mrow><mrow><mn>49</mn><mo>×</mo><mn>250</mn></mrow></mfrac><mo>=</mo><mn>0</mn><mo>.</mo><mn>1</mn><mi mathvariant="normal">N</mi></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∴</mo><mo> </mo><mi mathvariant="normal">N</mi></math> (of <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>FeCl</mi><mn>2</mn></msub></math>) <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>1</mn><mo>×</mo><mn>25</mn></mrow><mn>10</mn></mfrac></math></p><br/><br/><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>25</mn><mo> </mo><mi mathvariant="normal">N</mi></math></p><br/></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2009 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1460</span> </div>
source_db: MarksBatch2_P1.db
title:
in-a-town-354-of-the-people-are-not-literates-27-have-education-up-to-primary-school-186-have-education-up-to-middle-school-the-people-with-education-

slug:
in-a-town-354-of-the-people-are-not-literates-27-have-education-up-to-primary-school-186-have-education-up-to-middle-school-the-people-with-education-17800

question:
<div class="question">In a town $35.4 \%$ of the people are not literates, $27 \%$ have education up to primary school, $18.6 \%$ have education up to middle school. The people with education up to high school are twice the number of people with education up to Pre-University. Of the remaining, 660 are graduates. If the population of the town is 15000 , then what is the number of people with education up to high school?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3120</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">1560</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">1460</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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>

answer:
<div class="solution">No. of people whoare illiterates $=15000 \times \frac{34.5}{100}=5175$ No. of people who have education up to primaryschool<br/>$=15000 \times \frac{27}{100}=4050$<br/>Similarly, No. of peoplewho have education upto middle school $=2790$ Let the no. of people who have education upto high school $=x$ $\therefore$ According to the question. No. of people who have education upto pre-university<br/>$=\frac{x}{2}$<br/>So, Total no. of people who are not graduates<br/>$=5175+4050+2790+x+\frac{x}{2}=12150+x+\frac{x}{2}$<br/>Since, 660 are graduates, therefore<br/>$15000-\left(12150+x+\frac{x}{2}\right)=660$<br/>$\Rightarrow 15000-660=12150+\frac{3 x}{2}$<br/>$\Rightarrow 2(15000-660)=24300+3 x$<br/>$\Rightarrow 28680-24300=3 x$<br/>$\Rightarrow \frac{4380}{3}=x \Rightarrow x=1460$<br/>Hence, 1460 students have education upto high school.</div>


tags: ['Physics', 'Alternating Current', 'AIIMS', 'AIIMS 2019 (25 May)']
source_db: MarksBatch2_P1.db
title:
in-a-transformer-number-of-turns-in-primary-circuit-is-500-and-in-secondary-circuit-number-of-turns-is-10-the-load-resistance-is-10-and-voltage-of-sec

slug:
in-a-transformer-number-of-turns-in-primary-circuit-is-500-and-in-secondary-circuit-number-of-turns-is-10-the-load-resistance-is-10-and-voltage-of-sec-73586

question:
<div class="question">In a transformer number of turns in primary circuit is 500 and in secondary circuit number of turns is 10 . The load resistance is $10 \Omega$ and voltage of secondary coil is $50 \mathrm{~V}$. Then find the current in primary circuit.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.2 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.3 \mathrm{~A}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$0.4 \mathrm{~A}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$0.1 \mathrm{~A}$</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">$0.1 \mathrm{~A}$</span> </div>

answer:
<div class="solution">Given, $N_1=500, N_2=10, R_L=10 \Omega$<br/>$V_2=50 \mathrm{~V}$<br/>Current in the secondary circuit is<br/>$\begin{aligned} &amp; i_2=\frac{V_2}{R_L}=\frac{50}{10}=5 \mathrm{~A} \\ &amp; \frac{i_1}{i_2}=\frac{N_2}{N_1} \Rightarrow \frac{i_1}{5}=\frac{10}{500} \Rightarrow i_1=0.1 \mathrm{~A}\end{aligned}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main', 'JEE Main 2002']
source_db: MarksBatch2_P1.db
title:
in-a-transformer-number-of-turns-in-the-primary-coil-are-140-and-that-in-the-secondary-coil-are-280-if-current-in-primary-coil-is-4-a-then-that-in-the

slug:
in-a-transformer-number-of-turns-in-the-primary-coil-are-140-and-that-in-the-secondary-coil-are-280-if-current-in-primary-coil-is-4-a-then-that-in-the-64566

question:
<div class="question">In a transformer, number of turns in the primary coil are 140 and that in the secondary coil are 280. If current in primary coil is $4 \mathrm{~A}$, then that in the secondary coil is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>4 A<br/></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><br/>2 A<br/></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>6 A<br/></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><br/>10 A</span> </li> </ul>

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

answer:
<div class="solution">$I_1 N_1=I_2 N_2 \Rightarrow I_2=\frac{4 \times 140}{280}=2 \mathrm{~A}$</div>


tags: ['Physics', 'Alternating Current', 'JEE Main']
source_db: MarksBatch2_P1.db
title:
in-a-transformer-the-number-of-primary-turns-is-four-times-that-of-the-secondary-turns-its-primary-is-connected-to-an-ac-source-of-voltage-v-then

slug:
in-a-transformer-the-number-of-primary-turns-is-four-times-that-of-the-secondary-turns-its-primary-is-connected-to-an-ac-source-of-voltage-v-then-97223

question:
<div class="question">In a transformer the number of primary turns is four times that of the secondary turns. Its primary is connected to an AC  source of voltage <math><mi>V</mi><mo>.</mo></math> Then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">current through its secondary is about four times that of the current through its primary.</span> </div>

answer:
<div class="solution">In a transformer the primary and secondary currents are related by<br/><br/><math><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac></mrow></mfenced><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></math><br/><br/>And the voltage are related by<br/><br/><math><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow></mfrac></mrow></mfenced><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub></math><br/><br/>Where subscripts p and s refer to the primary and secondary of the transformer.<br/><br/>Here, <math><msub><mrow><mi>V</mi></mrow><mrow><mi>p</mi></mrow></msub><mo>=</mo><mi>V</mi><mo>,</mo><mtext>â</mtext><mfrac><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>p</mi></mrow></msub></mrow><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>s</mi></mrow></msub></mrow></mfrac><mo>=</mo><mn>4</mn></math><br/><br/><math><mo>â´</mo><msub><mrow><mi>I</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mn>4</mn><msub><mrow><mi>I</mi></mrow><mrow><mi>p</mi></mrow></msub></math><br/><br/>And <math><msub><mrow><mi>V</mi></mrow><mrow><mi>s</mi></mrow></msub><mo>=</mo><mfenced separators="|"><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac></mrow></mfenced><mi>V</mi><mo>=</mo><mfrac><mrow><mi>V</mi></mrow><mrow><mn>4</mn></mrow></mfrac></math></div>


tags: ['Physics', 'Alternating Current', 'NEET']
source_db: MarksBatch2_P1.db
title:
in-a-transformer-the-number-of-turns-in-the-primary-coil-is-140-and-that-in-the-secondary-coil-is-280-if-the-current-in-the-primary-coil-is-4-a-then-t

slug:
in-a-transformer-the-number-of-turns-in-the-primary-coil-is-140-and-that-in-the-secondary-coil-is-280-if-the-current-in-the-primary-coil-is-4-a-then-t-25184

question:
<div class="question">In a transformer, the number of turns in the primary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>140</mn></math> and that in the secondary coil is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>280</mn></math>. If the current in the primary coil is <math> <mrow> <mn>4</mn> <mtext> A</mtext></mrow></math>, then that in the secondary coil is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math> <mrow> <mn>4</mn> <mtext> A</mtext> </mrow> </math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math> <mrow> <mn>2</mn> <mtext> A</mtext> </mrow> </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> <mrow> <mn>6</mn> <mtext> A</mtext> </mrow> </math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math> <mrow> <mn>10</mn> <mtext> A</mtext> </mrow> </math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math> <mrow> <mn>2</mn> <mtext> A</mtext> </mrow> </math></span> </div>

answer:
<div class="solution"><math> <mrow> <msub> <mtext mathvariant="italic">I</mtext> <mn>2</mn> </msub> <msub> <mtext mathvariant="italic">N</mtext> <mn>2</mn> </msub> <mo>=</mo> <msub> <mtext mathvariant="italic">I</mtext> <mn>1</mn> </msub> <msub> <mtext mathvariant="italic">N</mtext> <mn>1</mn> </msub> </mrow> </math><br/><br/><math> <mrow> <mo>∴</mo> </mrow> </math>  <math> <mrow> <msub> <mtext mathvariant="italic">I</mtext> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mtext mathvariant="italic">I</mtext> <mn>1</mn> </msub> <msub> <mtext mathvariant="italic">N</mtext> <mn>1</mn> </msub> </mrow> <mrow> <msub> <mtext mathvariant="italic">N</mtext> <mn>2</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mo>×</mo> <mtext>140</mtext> </mrow> <mrow> <mtext>280</mtext> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <mtext> A.</mtext> </mrow> </math> </div>


title: in-a-triangle-a-bc-a-1-3-cm-b-2-cm-and-angle-c-6-0-then-the-other-two-angles-are
slug: in-a-triangle-a-bc-a-1-3-cm-b-2-cm-and-angle-c-6-0-then-the-other-two-angles-are-33129
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2015 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a triangle $A B C, a=(1+\sqrt{3}) \mathrm{cm}, b=2 \mathrm{~cm}$ and angle $C=60^{\circ} .$ Then the other two angles are</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$45^{\circ}$ and $75^{\circ}$</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">B</span> <span class="option-data">$30^{\circ}$ and $90^{\circ}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$105^{\circ}$ and $15^{\circ}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$100^{\circ}$ and $20^{\circ}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$45^{\circ}$ and $75^{\circ}$</span> </div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/RBx4qXouOI_RfEaiLzD-pxi8vRAIruSVCroxiZpjcZU.original.fullsize.png"/><br/><br/>Now as a $&gt;$ b $\angle \mathrm{A}&gt;\angle \mathrm{B}$<br/>Now from Sine Rule, $\frac{\sin A}{a}=\frac{\sin B}{b}$<br/>$\frac{\sin A}{1+\sqrt{3}}=\frac{\sin B}{2}$<br/>From option<br/>(a) $\frac{\sin 75}{1+\sqrt{3}}=\frac{\sin 45}{2}$<br/>$\frac{\sqrt{6}+\sqrt{2}}{4(1+\sqrt{3})}=\frac{1}{2 \sqrt{2}}$<br/>$2 \sqrt{12}+4=4+4 \sqrt{3}$<br/>$4+4 \sqrt{3}=4+4 \sqrt{3}$<br/>$\therefore \quad$ Option (a) is correct.</div>


title: in-a-triangle-a-bc-bc-39-a-c-5-and-a-b-7-what-is-the-measure-of-the-angle-a
slug: in-a-triangle-a-bc-bc-39-a-c-5-and-a-b-7-what-is-the-measure-of-the-angle-a-61402
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2010 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a triangle $A B C, B C=\sqrt{39}, A C=5$ and $A B=7$. What is the measure of the angle $A ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{\pi}{4}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{\pi}{3}$</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">$\frac{\pi}{2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{\pi}{6}$</span> </li> </ul>

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

answer:
<div class="solution">Let $\mathrm{a}, \mathrm{b}, \mathrm{c}$ be the sides of $\Delta A B C$ and $\angle A=\theta$<br/><img src="https://cdn-question-pool.getmarks.app/pyq/nda/U6vX5AGJHNH72QjgN58cAJ1oiSdlaHHHnvWsd9CWFK4.original.fullsize.png"/><br/><br/>$\therefore \quad a=\sqrt{39}, b=5$ and $c=7$<br/>and $\cos A=\frac{b^{2}+c^{2}-a^{2}}{2 b c}=\frac{25+49-39}{2 \times 5 \times 7}$<br/>$=\frac{1}{2}=\cos \frac{\pi}{3}$<br/>$\Rightarrow \quad A=\frac{\pi}{3}$</div>


title: in-a-triangle-a-bc-if-a-tan-1-2-and-b-tan-1-3-then-c-is-equal-to
slug: in-a-triangle-a-bc-if-a-tan-1-2-and-b-tan-1-3-then-c-is-equal-to-98036
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2011 (Phase 2)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a triangle $A B C$, if $A=\tan ^{-1} 2$ and $\mathrm{B}=\tan ^{-1} 3$, then $\mathrm{C}$ is equal to</div>

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

answer:
<div class="solution">We have $A=\tan ^{-1} 2 \Rightarrow \tan A=2$<br/>and $B=\tan ^{-1} 3 \Rightarrow \tan B=3$.<br/>Since, $A, B, C$ are angles of a triangle $\therefore A+B+C=\pi$<br/>$\Rightarrow C=\pi-(A+B)$ ...(1)<br/>Now, $A+B=\tan ^{-1} 2+\tan ^{-1} 3$<br/>$=\pi+\tan ^{-1}\left(\frac{2+3}{1-2.3}\right)$<br/>$\left[\because \tan ^{-1} x+\tan ^{-1} y=\pi+\tan ^{-1} \frac{x+y}{1-x y}\right]$<br/>$=\pi+\tan ^{-1}(-1)=\pi-\tan ^{-1}(1)$<br/>$=\pi-\frac{\pi}{4}=\frac{3 \pi}{4}$<br/>$\therefore$ from $(1), C=\pi-\frac{3 \pi}{4}=\frac{\pi}{4}$</div>


title: in-a-triangle-abc-a-2-b-and-a-3-b-which-one-of-the-following-is-correct
slug: in-a-triangle-abc-a-2-b-and-a-3-b-which-one-of-the-following-is-correct-56186
tags: ['Mathematics', 'Properties of Triangles', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch2_P1.db
question:
<div class="question">In a triangle $\mathrm{ABC}, \mathrm{a}=2 \mathrm{~b}$ and $\angle \mathrm{A}=3 \angle \mathrm{B}$. Which one of the following is correct?</div>

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

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

answer:
<div class="solution">From properties of triangle we know that<br/>$\frac{\mathrm{a}}{\sin \mathrm{A}}=\frac{\mathrm{b}}{\sin \mathrm{B}}=\frac{\mathrm{c}}{\sin \mathrm{C}}$<br/>Given that $\mathrm{a}=2 \mathrm{~b}$ and $\mathrm{A}=3 \mathrm{~B}$.<br/>We get $\frac{2 b}{\sin 3 B}=\frac{b}{\sin B}$<br/>$\Rightarrow \frac{\sin 3 B}{\sin B}=2 \Rightarrow \frac{3 \sin B-4 \sin ^{3} B}{\sin B}=2$<br/>$\Rightarrow 3-4 \sin ^{2} B=2$<br/>$\Rightarrow \sin ^{2} B=\left(\frac{1}{2}\right)^{2} \Rightarrow \sin B=\frac{1}{2}=\sin \frac{\pi}{6}$<br/>$\Rightarrow B=\frac{\pi}{6}$ since $A=3 B$<br/>So, $\angle A=\frac{\pi}{2}$<br/>Thus, triangle is right angled triangle.</div>


