# questions

tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P2.db
title:
during-the-treatment-of-sewage-water-the-chemical-process-is-carried-out-in-which-step-of-water-treatment

slug:
during-the-treatment-of-sewage-water-the-chemical-process-is-carried-out-in-which-step-of-water-treatment-71092

question:
<div class="question">During the treatment of sewage water, the chemical process is carried out in which step of water treatment?</div>

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

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

answer:
<div class="solution">Treatment of sewage water is carried out in three stages: primary treatment is a physical process in which filtration and sedimentation are carried out to remove floating debris and girt. Secondary treatment is a biological treatment in which aerobic heterotrophic microbes are used, which consumes the major part of organic matter present in the effluent. âTertiary treatment: Physiochemical process in which chlorine gas , zirconium, ozone gas, perchlorate salts, UV rays or reverse osmosis etc. are used to remove DDT, pesticides, pathogens and remove turbidity present in wastewater.</div>


title: during-which-stage-of-sewage-treatment-microbes-are-not-used
slug: during-which-stage-of-sewage-treatment-microbes-are-not-used-84278
question: <div class="question">During which stage of sewage treatment microbes are not used?</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary treatment</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Secondary treatment</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary treatment</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Both a and c</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Both a and c</span> </div>

answer:
<div class="solution">Secondary treatment/biological treatment is when the primary effluent is passed into large aeration tanks where it is constantly agitated mechanically and the air is pumped into it. This allows the vigorous growth of useful aerobic microbes into flocs.</div>


title: during-which-stage-of-sewage-treatment-microbes-are-used
slug: during-which-stage-of-sewage-treatment-microbes-are-used-72409
question: <div class="question">During which stage of sewage treatment microbes are used?</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Primary treatment</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Secondary treatment</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Tertiary treatment</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">All of these</span> </li> </ul>

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

answer:
<div class="solution">Primary treatment is a physical process that involves only filtration and sedimentation.<br/><br/>Secondary treatment or Biological treatment: The primary effluent is passed into large aeration tanks where it is constantly agitated mechanically and the air is pumped into it. This allows the vigorous growth of useful aerobic microbes into flocs (masses of bacteria associated with fungal filaments to form mesh-like structures). While growing, these microbes consume the major part of the organic matter in the effluent. This significantly reduces the BOD (biochemical oxygen demand) of the effluent.</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET', 'NEET 2006']
source_db: MarksBatch1_P2.db
title:
e-fe-2-fe-o-0441-v-and-e-fe-3-fe-2-o-0771-v-the-standard-emf-of-the-reaction-fe-2-fe-3-3-fe-2-will-be

slug:
e-fe-2-fe-o-0441-v-and-e-fe-3-fe-2-o-0771-v-the-standard-emf-of-the-reaction-fe-2-fe-3-3-fe-2-will-be-74466

question:
<div class="question">$\mathrm{E}_{\mathrm{Fe} 2+/ \mathrm{Fe}}^{\mathrm{o}}=-0.441 \mathrm{~V}$ and $\mathrm{E}_{\mathrm{Fe}^{3+} \mathrm{Fe}^{2+}}^{\mathrm{O}}=0.771$<br/>$\mathrm{V}$, the standard EMF of the reaction $\mathrm{Fe}$ $+2 \mathrm{Fe}^{3+} \rightarrow 3 \mathrm{Fe}^{2+}$ will be:</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.111 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.330 \mathrm{~V}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.653 \mathrm{~V}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$1.212 \mathrm{~V}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1.212 \mathrm{~V}$</span> </div>

answer:
<div class="solution">For the cell reaction<br/>$$<br/>\begin{aligned}<br/>&amp; \mathrm{Fe}+2 \mathrm{Fe}^{3+} \rightarrow 3 \mathrm{Fe}^{2+} \\<br/>&amp; \text { Anode reaction is } \mathrm{Fe} \rightarrow \mathrm{Fe}^{2+}+2 \mathrm{e}^{-} \\<br/>&amp; \text {Cathode reaction in } 2 \mathrm{Fe}^{3+}+2 \mathrm{e}^{-} \rightarrow \\<br/>&amp; 2 \mathrm{Fe}^{2+} \\<br/>&amp; \mathrm{E}_{\mathrm{Cell}}^{\circ}=\mathrm{E}_{\text {Cathode }}^{\circ}-\mathrm{E}_{\text {Anode }}^{\circ} \\<br/>&amp; =0.771-(-0.441) \\<br/>&amp; \mathrm{E}_{\mathrm{Cell}}^{\circ}=1.212 \mathrm{~V} \\<br/>&amp;<br/>\end{aligned}<br/>$$<br/>Related Theory<br/>If the cell potential is negative, the reaction is reversed. In this case, the electrode of the galvanic cell should be written in a reversed order.<br/>Caution<br/>The positive potential indicates a spontaneous reaction</div>


title: e-of-a-cell-a-a-b-b-c-c-d-d-is
slug: e-of-a-cell-a-a-b-b-c-c-d-d-is-54928
question: <div class="question">$E^{\circ}$ of a cell $a A+b B \rightarrow c C+d D$ is</div>
tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$-\frac{R T}{n F} \log \frac{[C]^c[D]^d}{[A]^a[B]^b}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$-R T \log \frac{[a]^A[b]^B}{[a]^C[d]^D}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$-\frac{R T}{n F} \log \frac{[C]^c[d]^D}{[A]^a[B]^b}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$-\frac{R T}{n F} \log \frac{[C]^c[d]^D}{[a]^A[B]^b}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$-\frac{R T}{n F} \log \frac{[C]^c[D]^d}{[A]^a[B]^b}$</span> </div>

answer:
<div class="solution">The equation for the cell potential of a galvanic cell is (1) $E^{\circ} c e l l=E^{\circ}$ cathode - $E^{\circ}$ anode.<br/>This equation reflects the difference between the standard reduction potentials of the cathode and anode in a galvanic cell. Here's a breakdown of the terms:<br/>- Cell potential ($E^{\circ}$ cell): This is the voltage produced by the cell under standard conditions (specific concentration, temperature, and pressure). A positive cell potential indicates a spontaneous reaction, while a negative cell potential indicates a non-spontaneous reaction.<br/>- Standard reduction potential $\left(E^{\circ}\right)$ : This is the potential of a half-cell reaction measured against a standard hydrogen electrode (SHE) under standard conditions. It represents the tendency of a species in a half-reaction to gain electrons and be reduced. More positive reduction potentials indicate a greater tendency to undergo reduction (gain electrons).<br/>In a galvanic cell, the cathode is the electrode where reduction occurs (electrons are gained) and the anode is the electrode where oxidation occurs (electrons are lost). The standard reduction potential of the cathode is always more positive than the standard reduction potential of the anode. Subtracting the two potentials gives the overall cell potential, $E^{\circ}$ cell.<br/><br/>Therefore, option (1) accurately describes the relationship between the standard reduction potentials of the cathode and anode in determining the cell potential of a galvanic cell.</div>


title: each-of-a-and-b-tosses-two-coins-what-is-the-probability-that-they-get-equal-number-of-heads
slug: each-of-a-and-b-tosses-two-coins-what-is-the-probability-that-they-get-equal-number-of-heads-81056
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Each of $\mathrm{A}$ and $\mathrm{B}$ tosses two coins. What is the probability that they get equal number of heads?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{3}{16}$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\frac{5}{16}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$\frac{4}{16}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{6}{16}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{16}$</span> </div>

answer:
<div class="solution">If both get one head then it is $\frac{1}{4} \times \frac{1}{4}$<br/>and if both get two heads then it is $\frac{1}{2} \times \frac{1}{2}$<br/>$\Rightarrow$ Prob (getting same number of heads) $=\frac{1}{4} \times \frac{1}{4}+\frac{1}{2} \times \frac{1}{2}$<br/>$=\frac{1}{16}+\frac{1}{4}=\frac{5}{16}$</div>


title: each-of-the-following-statements-concerning-testosterone-is-true-except
slug: each-of-the-following-statements-concerning-testosterone-is-true-except-76901
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Each of the following statements concerning testosterone is true, except</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">It is excluded from the adluminal compartment of the seminiferous epithelium.</span> </div>

answer:
<div class="solution">Testosterone is the primary male sex steroid. It is an androgenic steroid synthesized by interstitial Leydig cells in the testes. It is required for spermatogenesis, functional differentiation of the excurrent ducts of the testes and the development of male secondary sexual characteristics. Androgen-binding protein synthesized by Sertoli cells assures that a high concentration of testosterone is present in the adluminal compartment of the seminiferous epithelium.</div>


title: each-of-the-following-statements-concerning-the-seminiferous-epithelium-is-correct-except-1
slug: each-of-the-following-statements-concerning-the-seminiferous-epithelium-is-correct-except-1-36956
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Each of the following statements concerning the seminiferous epithelium is correct except.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Before puberty, it contains spermatids</span> </div>

answer:
<div class="solution">It consists of a population of Sertoli cells and a spermatogenic cell line. Sertoli cells span the thickness of the seminiferous epithelium. Sertoli cell characteristics including the distribution of their intercellular junctions, divide the seminiferous epithelium into a basal compartment containing only spermatogonia and an adluminal compartment containing primary and secondary spermatocytes, spermatids, and spermatozoa. The differentiation of spermatogonia into spermatids does not begin until puberty. Thus, the seminiferous epithelium does not contain spermatids prior to puberty like all epithelial layers, the basal surface of the seminiferous epithelium is bounded by the basement membrane.</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">7</span> </div>
source_db: MarksBatch1_P2.db
title:
each-of-the-two-strings-of-length-51-6-cm-and-49-1-cm-are-equally-tensioned-by-20-n-force-mass-per-unit-length-of-both-the-strings-is-the-same-and-equ

slug:
each-of-the-two-strings-of-length-51-6-cm-and-49-1-cm-are-equally-tensioned-by-20-n-force-mass-per-unit-length-of-both-the-strings-is-the-same-and-equ-34644

question:
<div class="question">Each of the two strings of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>51</mn><mo>.</mo><mn>6</mn><mo> </mo><mi>cm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>49</mn><mo>.</mo><mn>1</mn><mo> </mo><mi>cm</mi></math> are equally  tensioned  by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">N</mi></math> force. Mass per unit length of both the strings is the same and equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">g</mi><mo>/</mo><mi mathvariant="normal">m</mi></math>. When both the strings vibrate simultaneously in fundamental mode the number of beats is--</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">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">B</span> <span class="option-data">8</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">5</span> </li> </ul>

answer:
<div class="solution"><math> <mrow> <msub> <mtext mathvariant="italic">l</mtext> <mn>1</mn> </msub> <mo>=</mo> <mtext>0.516 m</mtext> <mo>,</mo> <msub> <mo mathvariant="italic">l</mo> <mn>2</mn> </msub> <mo>=</mo> <mtext>0. 491 m,</mtext> <mo mathvariant="italic">T</mo> <mo>=</mo> <mtext>20 N</mtext> </mrow> </math>.<br/><br/>Mass per unit length, <math> <mrow> <mi>Î¼</mi> <mo>=</mo> <mtext>0.001 kg/m</mtext> </mrow> </math><br/><br/><math> <mrow> <mtext>Frequency</mtext> <mtext>,</mtext> <mspace width="0.5em"></mspace> <mi></mi><mi></mi><mi>v</mi><mo>â¡</mo> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mi></mi><mi>l</mi><mo>â¡</mo> </mrow> </mfrac> <msqrt> <mfrac> <mrow> <mi></mi><mi>T</mi><mo>â¡</mo> </mrow> <mrow> <mi>Î¼</mi> </mrow> </mfrac> </msqrt> </mrow> </math><br/><br/><math> <mrow> <msub> <mrow> <mi></mi><mi></mi><mi>v</mi><mo>â¡</mo> </mrow> <mn>1</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mo>Ã</mo> <mn>0</mn> <mo>Â·</mo> <mn>51</mn><mn></mn> <mn>6</mn> </mrow> </mfrac> <msqrt> <mfrac> <mrow> <mn>2</mn> <mn>0</mn> </mrow> <mrow> <mn>0</mn> <mo>Â·</mo> <mn>0</mn> <mn>0</mn> <mn>1</mn> </mrow> </mfrac> </msqrt> </mrow> </math><br/><br/><math> <mrow> <msub> <mrow> <mi></mi><mi></mi><mi>v</mi><mo>â¡</mo> </mrow> <mn>2</mn> </msub> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>2</mn> <mo>Ã</mo> <mn>0</mn> <mo>Â·</mo> <mn>4</mn> <mn>9</mn> <mn>1</mn> </mrow> </mfrac> <msqrt> <mfrac> <mrow> <mn>2</mn> <mn>0</mn> </mrow> <mrow> <mn>0</mn> <mo>Â·</mo> <mn>0</mn> <mn>0</mn> <mn>1</mn> </mrow> </mfrac> </msqrt> </mrow> </math><br/><br/>â´  Number of beats <math> <mrow> <mo>=</mo> <msub> <mi>Ï</mi> <mn>1</mn> </msub> <mo>-</mo> <msub> <mi>Ï</mi> <mn>2</mn> </msub> <mo>=</mo> <mn>7</mn> </mrow> </math></div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P2.db
title:
each-of-the-two-strings-of-length-516-cm-and-491-cm-are-tensioned-separately-by-20-n-force-mass-per-unit-length-of-both-the-strings-is-same-and-equal-

slug:
each-of-the-two-strings-of-length-516-cm-and-491-cm-are-tensioned-separately-by-20-n-force-mass-per-unit-length-of-both-the-strings-is-same-and-equal-37026

question:
<div class="question">Each of the two strings of length <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>51.6</mtext><mo> </mo><mi>cm</mi></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>49.1</mtext><mo> </mo><mi>cm</mi></math> are tensioned separately by <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>20</mn><mo> </mo><mi mathvariant="normal">N</mi></math> force. Mass per unit length of both the strings is same and equal to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo> </mo><mi mathvariant="normal">g</mi><mo> </mo><msup><mi mathvariant="normal">m</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. When both the strings vibrate simultaneously in fundamental mode, the number of beats 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>7</mn></math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></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>3</mn></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>5</mn></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>7</mn></math></span> </div>

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mtext>l</mtext><mn>1</mn></msub><mo>=</mo><mtext>0.516 m</mtext><mo>,</mo><msub><mo>l</mo><mn>2</mn></msub><mo>=</mo><mtext>0. 491 m, </mtext><mo>T</mo><mo>=</mo><mtext>20 N</mtext></math><br/><br/>Mass per unit length, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">Î¼</mi><mo>=</mo><msup><mtext>0.001 kg m</mtext><mrow><mo>-</mo><mn>1</mn></mrow></msup></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mtext>Frequency,</mtext><mspace width="0.5em"></mspace><mtext>Ï</mtext><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mi mathvariant="normal">l</mi><mo>â¡</mo></mrow></mfrac><msqrt><mfrac><mrow><mi mathvariant="normal">T</mi><mo>â¡</mo></mrow><mi mathvariant="normal">Î¼</mi></mfrac></msqrt></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Ï</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>Ã</mo><mn>0</mn><mo>Â·</mo><mn>516</mn></mrow></mfrac><msqrt><mfrac><mn>20</mn><mrow><mn>0</mn><mo>Â·</mo><mn>001</mn></mrow></mfrac></msqrt></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Ï</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>1</mn><mrow><mn>2</mn><mo>Ã</mo><mn>0</mn><mo>Â·</mo><mn>491</mn></mrow></mfrac><msqrt><mfrac><mn>20</mn><mrow><mn>0</mn><mo>Â·</mo><mn>001</mn></mrow></mfrac></msqrt></math><br/><br/>â´  Number of beats <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><msub><mi mathvariant="normal">Ï</mi><mn>1</mn></msub><mo>-</mo><msub><mi mathvariant="normal">Ï</mi><mn>2</mn></msub><mo>=</mo><mn>7</mn></math></div>


tags: ['Biology', 'Anatomy of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
each-of-thefollowing-terms-has-some-anatomical-significance-what-do-these-terms-mean-explain-with-the-help-of-line-diagrams-a-plasmodesmata-b-middle-l

slug:
each-of-thefollowing-terms-has-some-anatomical-significance-what-do-these-terms-mean-explain-with-the-help-of-line-diagrams-a-plasmodesmata-b-middle-l-89076

question:
<div class="question">Each of thefollowing terms has some anatomical significance. What do these terms mean? Explain with the help of line diagrams.<br/>(a) Plasmodesmata<br/>(b) Middle Lamella<br/>(c) Secondary wall</div>

answer:
<div class="solution">The given terms and their functions include:<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/-LW0uYeaUUQs1sM--xb-JH6bPAuu4zXxFpLFKMpL_AQ.original.fullsize.png"/><br/></div>


tags: ['Biology', 'Plant Kingdom']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
each-plant-group-of-plants-has-some-phylogenetic-significance-in-relation-to-evolution-cycas-one-of-the-few-living-members-of-gymnosperms-is-called-as

slug:
each-plant-group-of-plants-has-some-phylogenetic-significance-in-relation-to-evolution-cycas-one-of-the-few-living-members-of-gymnosperms-is-called-as-20191

question:
<div class="question">Each plant group of plants has some phylogenetic significance in relation to evolution Cycas, one of the few living members of gymnosperms is called as the 'relic of past'. Can you establish a phylogenetic relationship of $C y$ cas with any other group of plants that justifies the above statement?</div>

answer:
<div class="solution">Cycas is an evergreen plant which resembles palm. It has an unbranched stem and large compound leaves. It exhibits phylogenetic relationship with pteridophyte. Its evolutionary characters include the following:<br/>(i) Growth is redundant.<br/>(ii) Shedding of seed while the embryo is still immature.<br/>(iii) Minimal secondary growth and manoxylic wood.<br/>(iv) Megasporophylls are leaf like.<br/>(v) Sperms are flagellate even when pollen tube is present.<br/>(vi) Leaf bases are persistent.<br/>(vii) Ptysix is circinate.<br/>(viii) Arrangement of microsporangia in well defined archegonia.</div>


title: earths-magnetism-is-due-to
slug: earths-magnetism-is-due-to-18896
question: <div class="question">Earth's magnetism is due to:</div>
tags: ['Physics', 'Magnetic Properties of Matter', 'JEE Main']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Dynamo effect</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Doppler effect</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Solar effect</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Magnus effect</span> </li> </ul>

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

answer:
<div class="solution">The Dynamo effect:<br/>- It is a theory that explains the origin of the Earth's main magnetism in terms of a self-sustaining dynamo.<br/>- In this dynamo mechanism, fluid motion in the Earth's outer core moves conducting material (liquid iron) across an already existing, weak magnetic field and generates an electric current.<br/>- The electric current, in turn, produces a magnetic field that also interacts with the fluid motion to create a secondary magnetic field.<br/>- Together, the two fields are stronger than the original and lie essentially along the axis of the Earth's rotation.</div>


title: ectophloic-siphonostele-is-found-in-1
slug: ectophloic-siphonostele-is-found-in-1-67785
question: <div class="question">Ectophloic siphonostele is found in:</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET', 'NEET 2005']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Osmunda and Equisetum</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Marsilea and Botrychium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Adiantum and Cucurbitaceae</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dicksonia and Maiden hair fern.</span> </li> </ul>

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

answer:
<div class="solution">In Ectophloic siphonostele, the central pith is surrounded successively by xylem, phloem, pericycle, and endodermis. It is found in Osmunda and Equisetum</div>


title: ectophloic-siphonostele-is-found-in-2
slug: ectophloic-siphonostele-is-found-in-2-98518
question: <div class="question">Ectophloic siphonostele is found in</div>
tags: ['Biology', 'Plant Kingdom', 'JIPMER', 'JIPMER 2007']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Adiantum and Cucurbitaceae</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Osmunda and Equisetum</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Marsilea and Botrychium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dicksonia and maiden hair fern</span> </li> </ul>

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

answer:
<div class="solution">In the ectophloic siphonostele the xylem surrounds pith and this xylem is surrounded by phloem, pericycle and endoderm is respectively. e.g., Osmunda and Equisetum.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/jipmer/FN7jBAyGrRnXJ2o5H18IDIMmadK5pywXWAUxbRsd0oQ.original.fullsize.png"/><br/></div>


title: ectophloic-siphonostele-is-found-in
slug: ectophloic-siphonostele-is-found-in-12616
question: <div class="question">Ectophloic siphonostele is found in</div>
tags: ['Biology', 'Anatomy of Flowering Plants', 'AIIMS', 'AIIMS 2008']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">Osmunda and Equisetum</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Marsilea and Botrychium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Adiantum and Cucurbitaceae</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Dicksonia and Maidenhair fern.</span> </li> </ul>

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

answer:
<div class="solution">Stele is a column containing vascular tissues which is surrounded by pericycle and separated from ground tissue by endodermis.<br/>Siphonostele is medullated protostele or protostele with a central non-vascular pith. Leaf gaps are absent. Siphonostele is of two types :<br/>In Ectophloic siphonostele, central pith is surrounded successively by xylem, phloem, pericycle and endodermis. In amphiphloic siphonostele there is a central pith and xylem is surrounded on either side by phloem, pericycle and endodermis. It is found in Osmunda and Equisetum.</div>


title: edible-part-of-mushroom-is
slug: edible-part-of-mushroom-is-93068
question: <div class="question">Edible part of mushroom is</div>
tags: ['Biology', 'Biological Classification', 'JIPMER', 'JIPMER 2009']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">basidiocarp</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">secondary mycelium</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">primary mycelium</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">tertiary mycelium</span> </li> </ul>

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

answer:
<div class="solution">The cap and the stalk together constitute the fruiting body called the <strong>basidiocarp</strong>  or<strong>sporocarp.</strong>  Because of the presence of characteristic gills the members of Agaricaceae family are generally called the gill or gilled fungi. They are generally fleshy and are also known as fleshy fungi. Some of these gilled or<br/>fleshy fungi are edible, ordinarily the edible fleshy (or filled) fungi are called the mushrooms.</div>


tags: ['Chemistry', 'Electrochemistry', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">1.24 V</span> </div>
source_db: MarksBatch1_P2.db
title:
efficiency-of-the-following-cells-is-84-a-s-b-2-a-q-a-2-a-q-b-s-h-285-kj-then-the-standard-electrode-potential-of-the-cell-will-be

slug:
efficiency-of-the-following-cells-is-84-a-s-b-2-a-q-a-2-a-q-b-s-h-285-kj-then-the-standard-electrode-potential-of-the-cell-will-be-27767

question:
<div class="question">Efficiency of the following cells is 84%.<br/> <math><mi mathvariant="normal">A</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo><mo>+</mo><msup><mrow><mi mathvariant="normal">B</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>â</mo><msup><mrow><mi mathvariant="normal">A</mi></mrow><mrow><mn>2</mn><mo>+</mo></mrow></msup><mo>(</mo><mi mathvariant="normal">a</mi><mi mathvariant="normal">q</mi><mo>)</mo><mo>+</mo><mi mathvariant="normal">B</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo></math> ; <math><mi mathvariant="normal">Î</mi><mi mathvariant="normal">H</mi><mo>=</mo><mo>-</mo><mn>285</mn></math> kJ<br/>
Then the standard electrode potential of the cell will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">1.20 V</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">2.40 V</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.10 V</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">1.24 V</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

answer:
<div class="solution">Efficiency <math><mo>=</mo><mfrac><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">G</mi><mo>Â°</mo></mrow><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">H</mi><mo>Â°</mo></mrow></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mi mathvariant="normal">n</mi><mi mathvariant="normal">F</mi><mi mathvariant="normal">E</mi><mo>Â°</mo></mrow><mrow><mi mathvariant="normal">Î</mi><mi mathvariant="normal">H</mi><mo>Â°</mo></mrow></mfrac></math><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.84</mn><mo>=</mo><mfrac><mrow><mo>-</mo><mn>2</mn><mo>Ã</mo><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>Ã</mo><mn>96500</mn></mrow><mrow><mo>-</mo><mn>285</mn><mo>Ã</mo><mn>1000</mn></mrow></mfrac></math><br/><math><mi mathvariant="normal">E</mi><mo>Â°</mo><mo>=</mo><mo>+</mo><mn>1.24</mn><mi mathvariant="normal">V</mi></math> .</div>


tags: ['Mathematics', 'Vector Algebra', 'NDA', 'NDA 2012 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
efgh-is-a-rhombus-such-that-the-angle-efg-is-6-0-the-magnitude-of-vectors-fh-and-m-eg-are-equal-where-m-is-a-scalar-what-is-the-value-of-m

slug:
efgh-is-a-rhombus-such-that-the-angle-efg-is-6-0-the-magnitude-of-vectors-fh-and-m-eg-are-equal-where-m-is-a-scalar-what-is-the-value-of-m-10328

question:
<div class="question">EFGH is a rhombus such that the angle EFG is $60^{\circ}$. The<br/>magnitude of vectors $\overline{\mathrm{FH}}$ and $\{\mathrm{m} \overline{\mathrm{EG}}\}$ are equal where $\mathrm{m}$ is<br/>a scalar. What is the value of $\mathrm{m}$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">3</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$1.5$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\sqrt{2}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\sqrt{3}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/pyq/nda/EMcG95uGwc_ZQP6T_Tp-Tyj70aUZ3t7F5KrtKLSzLj8.original.fullsize.png"/><br/><br/>Rhombus EFGH, $\angle \mathrm{EFG}=60^{\circ}$<br/>$\angle \mathrm{EFH}=30^{\circ}=\angle \mathrm{HFG}$<br/>From parallelogram of forces<br/>$\overrightarrow{\mathrm{FE}}+\overrightarrow{\mathrm{FG}}=\overrightarrow{\mathrm{FH}}$<br/>Given $|\overrightarrow{\mathrm{FE}}|+|\overrightarrow{\mathrm{FG}}|=\mathrm{a}($ say $)$<br/>$\therefore \overrightarrow{\mathrm{FH}}=2 \cdot \frac{\sqrt{3}}{2} \overrightarrow{\mathrm{a}}=\sqrt{3} \overrightarrow{\mathrm{a}}$<br/>$\overrightarrow{\mathrm{EG}}=\overrightarrow{\mathrm{EF}}+\overrightarrow{\mathrm{EH}}$<br/>$=a \sin 30^{\circ}+a \sin 30^{\circ}=a \cdot \frac{1}{2}+a \cdot \frac{1}{2}=a$<br/>Thus, $\frac{\overrightarrow{\mathrm{FH}}}{\overline{\mathrm{EG}}}=\frac{\sqrt{3} \mathrm{a}}{\mathrm{a}}=\sqrt{3}$<br/>So, $\overrightarrow{\mathrm{FH}}=\sqrt{3} \overrightarrow{\mathrm{EG}}$<br/>$\Rightarrow \quad \mathrm{m}=\sqrt{3}$</div>


title: electrolyte-used-in-nicd-cell
slug: electrolyte-used-in-nicd-cell-64689
question: <div class="question">Electrolyte used in Ni-Cd cell</div>
tags: ['Chemistry', 'Electrochemistry', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data"><math><mi>K</mi><mi>O</mi><mi>H</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><msub><mrow><mi>H</mi></mrow><mrow><mn>2</mn></mrow></msub><mi>S</mi><msub><mrow><mi>O</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mi>L</mi><mi>i</mi><mi>O</mi><mi>H</mi></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data"><math><mi>A</mi><msub><mrow><mi>l</mi></mrow><mrow><mn>2</mn></mrow></msub><msub><mrow><mi>O</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span> </li> </ul>

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

answer:
<div class="solution">Electrolyte used in Ni-Cd cell is <math><mi>K</mi><mi>O</mi><mi>H</mi></math> (potassium hydroxide). It is a type of secondary cell. It consists of a cadmium anode and metal grid containing <math><mi>N</mi><mi>i</mi><msub><mrow><mi>O</mi></mrow><mrow><mn>2</mn></mrow></msub></math> as cathode and <math><mi>K</mi><mi>O</mi><mi>H</mi></math> solution is electrolyte. It has longer life than the lead storage cell but more expensive to manufacture.</div>


tags: ['Chemistry', 'Structure of Atom', 'JEE Main', 'JEE Main 2023 (01 Feb Shift 1)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">2</span> </div>
source_db: MarksBatch1_P2.db
title:
electrons-in-a-cathode-ray-tube-have-been-emitted-with-a-velocity-of-1000-ms-1-the-number-of-following-statements-which-isare-true-about-the-emitted-r

slug:
electrons-in-a-cathode-ray-tube-have-been-emitted-with-a-velocity-of-1000-ms-1-the-number-of-following-statements-which-isare-true-about-the-emitted-r-76644

question:
<div class="question"><p>Electrons in a cathode ray tube have been emitted with a velocity of <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1000</mn><mo> </mo><msup><mi>ms</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>. The number of following statements which is/are true about the emitted radiation is</p><p>Given : <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">h</mi><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mi>Js</mi><mo>,</mo><msub><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi></msub><mo>=</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo> </mo><mi>kg</mi></math></p><p>(A ) The deBroglie wavelength of the electron emitted is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>666</mn><mo>.</mo><mn>67</mn><mo> </mo><mi>nm</mi></math></p><p>(B ) The characteristic of electrons emitted depend upon the material of the electrodes of the cathode ray tube.</p><p>(C) The cathode rays start from cathode and move towards anode.</p><p>(D ) The nature of the emitted electrons depends on the nature of the gas present in cathode ray tube..</p></div>

answer:
<div class="solution"><p>(A) <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi></msub><mo>=</mo><mn>1000</mn><mo> </mo><mi mathvariant="normal">m</mi><mo>/</mo><mi mathvariant="normal">s</mi><mo>;</mo><mi mathvariant="normal">h</mi><mo>=</mo><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mi>Js</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi></msub><mo>=</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo> </mo><mi>kg</mi></math><br/>Debroglie wavelength:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⇒</mo><mi mathvariant="normal">λ</mi><mo>=</mo><mfrac><mi mathvariant="normal">h</mi><mi>mv</mi></mfrac><mo>=</mo><mfrac><mrow><mn>6</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></mrow><mrow><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>×</mo><mn>1000</mn></mrow></mfrac><mo>=</mo><mn>666</mn><mo>.</mo><mn>67</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>9</mn></mrow></msup><mo> </mo><mi mathvariant="normal">m</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>666</mn><mo>.</mo><mn>67</mn><mo> </mo><mi>nm</mi></math></p><p>(B) The characteristic of electrons emitted is independent of the material of the electrodes of the cathode ray tube. Electrons are fundamental to all traditional forms of matter.</p><p>(C) The cathode rays start from cathode and move towards anode. It was discovered by Sir J.J. Thompson.</p><p>(D) The nature of the emitted electrons is independent on the nature of the gas present in cathode ray tube. They are fundamental particles.</p></div>


tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2007 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">8</span> </div>
source_db: MarksBatch1_P2.db
title:
elements-of-a-population-are-classified-according-to-the-presence-or-absence-of-each-of-3-attributes-a-b-and-c-what-is-the-number-of-smallest-ultimate

slug:
elements-of-a-population-are-classified-according-to-the-presence-or-absence-of-each-of-3-attributes-a-b-and-c-what-is-the-number-of-smallest-ultimate-57873

question:
<div class="question">Elements of a population are classified according to the presence or absence of each of 3 attributes $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. What is the number of smallest ultimate classes into which the population is divided?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">5</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">6</span> </li><li class="correct"> <span class="option-label">C</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><li class=""> <span class="option-label">D</span> <span class="option-data">9</span> </li> </ul>

answer:
<div class="solution">Elements of a population are classified according to the presence or absence of each of 3 attributes $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$. Then, the smallest number of smallest ultimate classes into which the population is divided, is $2^{3}=8$</div>


title: eliminating-the-arbitrary-constants-b-and-c-in-the-expresion-y-3-c-2-c-x-1-32-b-we-get
slug: eliminating-the-arbitrary-constants-b-and-c-in-the-expresion-y-3-c-2-c-x-1-32-b-we-get-96781
tags: ['Mathematics', 'Differential Equations', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Eliminating the arbitrary constants $\mathrm{B}$ and $\mathrm{C}$ in the expresion<br/>$y=\frac{2}{3 C}(C x-1)^{3 / 2}+B$, we get</div>

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

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

answer:
<div class="solution">$\mathrm{y}=\frac{2}{3 \mathrm{C}}(\mathrm{Cx}-1)^{\frac{3}{2}}+\mathrm{B}$<br/>On differentiating both sides w.r.t. $\mathrm{x}$, we get<br/>$\frac{d y}{d x}=\frac{2}{3 C} \cdot \frac{3}{2}(C x-1)^{\frac{1}{2}} \cdot C+0=(C x-1)^{\frac{1}{2}}$<br/>$\frac{d y}{d x}=(C x-1)^{\frac{1}{2}}$<br/>On squaring both sides, we get<br/>$\left(\frac{d y}{d x}\right)^{2}=C x-1$<br/>$\Rightarrow\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^{2}+1=\mathrm{Cx}$<br/>Now, on differentiating w.r.t. $\mathrm{x}$, we get<br/>$2\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right) \cdot \frac{\mathrm{d}^{2} \mathrm{y}}{\mathrm{dx}^{2}}=\mathrm{C}$<br/>From eq. (i)<br/>$\left(\frac{d y}{d x}\right)^{2}+1=2 x\left(\frac{d y}{d x}\right) \frac{d^{2} y}{d x^{2}}$</div>


title: ellingham-diagram-is-the-plot-of-x-v-s-y-what-are-x-and-y
slug: ellingham-diagram-is-the-plot-of-x-v-s-y-what-are-x-and-y-76581
tags: ['Chemistry', 'Thermodynamics (C)', 'TS EAMCET', 'TS EAMCET 2023 (13 May Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Ellingham diagram is the plot of $\mathrm{X} v s \mathrm{Y}$. what are $\mathrm{X}$ and $\mathrm{Y}$ ?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\Delta \mathrm{G}^{\circ}, \mathrm{T}$</span> </div>

answer:
<div class="solution">Ellingham diagram is a graphical representation of the variation of change in standard gibbs free energy with temperature.<br/>Thus, $\mathrm{X}=\Delta \mathrm{G}^{\circ}, \mathrm{Y}=\mathrm{T}$</div>


title: endemic-species-are
slug: endemic-species-are-19925
question: <div class="question">Endemic species are</div>
tags: ['Biology', 'Biodiversity and its Conservation', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Rare species</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Species localised in a specific region</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Cosmopolitan in distribution</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Critically endangered species</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Species localised in a specific region</span> </div>

answer:
<div class="solution">The two methods used for biodiversity conservation are in-situ conservation and ex-situ conservation. The development of a particular region and conservation of biodiversity can be at times challenging and non feasible. The numbers of species facing danger of extinction are also increasing. In order to overcome this, the species are conserved in those areas where they are found in large numbers. Species which are found localized in a specific area are known as endemic species. These endemic species are confined to that particular region and not found anywhere else. This high degree of endemism makes it easier to conserve these species in their own habitat by creating biodiversity hotspots.</div>


title: endothecium-and-tapetum-in-anther-are-derived-from
slug: endothecium-and-tapetum-in-anther-are-derived-from-82847
question: <div class="question">Endothecium and tapetum in anther are derived from</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">	Primary sporogenous layer </span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Primary parietal layer</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Both primary sporogenous layer and primary parietal layer</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of the above </span> </li> </ul>

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

answer:
<div class="solution">Primary parietal cells divide to form two layers of secondary parietal cells. The outer layer of secondary parietal cells differentiates to form endothecium and the inner layer of secondary parietal cells divide to form two layers, one of which forms the middle layers and the other forms the tapetum.</div>


tags: ['Physics', 'Units and Dimensions', 'NEET']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">zero</span> </div>
source_db: MarksBatch1_P2.db
title:
energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational-cons

slug:
energy-e-angular-momentum-l-and-universal-gravitational-constant-g-are-chosen-as-fundamental-quantities-the-dimensions-of-universal-gravitational-cons-24079

question:
<div class="question">Energy <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">E</mi></mfenced></math>, angular momentum <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">L</mi></mfenced></math> and universal gravitational constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">G</mi></mfenced></math> are chosen as fundamental quantities. The dimensions of universal gravitational constant in the dimensional formula of Planck's constant <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mi mathvariant="normal">h</mi></mfenced></math> is</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">zero</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math><mrow><mfrac linethickness="1"><mn>5</mn><mn>3</mn></mfrac></mrow></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>1</mn></math></span> </li> </ul>

answer:
<div class="solution">h = G<sup>x</sup>L<sup>y</sup>E<sup>z</sup><br/><br/>[M<sup>1</sup> L<sup>2</sup>T<sup>-1</sup>] = [M<sup>-1</sup> L<sup>3</sup>T<sup>-2</sup>] <sup>x </sup>[M<sup>1</sup> L<sup>2</sup>T<sup>-1</sup>]<sup>y </sup>[M<sup>1</sup> L<sup>2</sup>T<sup>-2</sup>]<sup>z</sup> <br/><br/>Comparing the power, we get<br/> <br/>1 = - x + y + z             ... (i)<br/><br/>2 = 3x + 2y + 2z         ... (ii)<br/><br/>-1 = - 2x - y - 2z         ... (iii)<br/> <br/>On solving Eq. (i), (ii) and (iii), we get x = 0</div>


title: energy-storage-at-consumer-level-is-called
slug: energy-storage-at-consumer-level-is-called-67560
question: <div class="question">Energy storage at consumer level is called</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Gross primary productivity</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Secondary productivity</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Net primary productivity</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Net productivity</span> </li> </ul>

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

answer:
<div class="solution">The rate at which the consumers convert the chemical energy of their food into their own biomass is called secondary productivity.</div>


tags: ['Biology', 'Anatomy of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
epidermal-cells-are-often-modified-to-perform-specialised-functions-in-plants-name-some-of-them-and-function-they-perform

slug:
epidermal-cells-are-often-modified-to-perform-specialised-functions-in-plants-name-some-of-them-and-function-they-perform-31597

question:
<div class="question">Epidermal cells are often modified to perform specialised functions in plants. Name some of them and function they perform.</div>

answer:
<div class="solution">The epidermal tissue system comprises of one cell thick layer of epidermal tissue and forms the outer most covering of the whole plant body.<br/>Modification of Epidermal Cells Following are the modifications of the epidermal tissue <br/>(i) root hair<br/>Structure<br/>These unicellular hairs are the extensions of epidermal cell of roots in the root hair zone.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/wSci9VTPSCThn-n0QDT2KGuGh059-ZZAkJ1SXj6fhIk.original.fullsize.png"/><br/><br/>Function<br/>They increase the surface area for absorption of water and minerals.<br/>(ii) Epidermal Appendages<br/>Structure<br/>These are called trichomes and are epidermal cell modifications. There any be unicellular or multicellular.<br/>Appendages of epidermis of leaves<br/>A-Stellate hair of a Alyssum<br/>B-Glandular hair of Pelargonium<br/>C-Short glandular hair of Lavandula<br/>D-Floccose hair of Malva<br/>E-Glandular hair of solanum<br/>F-Urtivating hair of Verbascum<br/>Function<br/>They produce some glandular secretions.</div>


tags: ['Mathematics', 'Circle', 'NDA', 'NDA 2008 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
equation-of-a-circle-passing-through-origin-is-x-2-y-2-6-x-2-y-0-what-is-the-equation-of-one-of-its-diameters

slug:
equation-of-a-circle-passing-through-origin-is-x-2-y-2-6-x-2-y-0-what-is-the-equation-of-one-of-its-diameters-51212

question:
<div class="question">Equation of a circle passing through origin is $\mathrm{x}^{2}+\mathrm{y}^{2}-6 \mathrm{x}$ $+2 \mathrm{y}=0$. What is the equation of one of its diameters?</div>

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

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

answer:
<div class="solution">Equation of the given circle is:<br/>$x^{2}+y^{2}-6 x+2 y=0$<br/>$\Rightarrow x(x-6)+y(y+2)=0$<br/>or, $(x-0)(x-6)+(y-0)(y+2)=0$<br/>This is the equation of circle in diameter form. Here, end points of diameter are $(0,0)$ and $(6,-2)$. Hence, equation of diameter is a line which passes through the points $(0,0)$ and $(6,-2)$ which is<br/>$(y-0)=\frac{-2}{6}(x-0) \Rightarrow x+3 y=0$</div>


title: equation-of-line-passing-through-the-point-12-and-perpendicular-to-the-line-y3-x1
slug: equation-of-line-passing-through-the-point-12-and-perpendicular-to-the-line-y3-x1-99054
tags: ['Mathematics', 'Vector Algebra', 'KCET', 'KCET 2017']
source_db: MarksBatch1_P2.db
question:
<div class="question">Equation of line passing through the point \( (1,2) \) and perpendicular to the line<br/>\( y=3 x-1 \)</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( x+3 y-7=0 \)</span> </div>

answer:
<div class="solution">Given line, $y=3 x-1 \rightarrow(1)$<br/>General equation of line is given by<br/>$y=m x+c$<br/>Here $m=3$ and $c=-1$.<br/>Condition for two perpendicular lines is<br/>$m_{1} \cdot m_{2}=-1$<br/>So, $3 m_{2}=-1 \Rightarrow m_{2}=-\frac{1}{3}$<br/>Standard equation of line passing through point $\left(x_{1}, y_{1}\right)$ is given by $\left(y-y_{1}\right)=m\left(x-x_{1}\right)$<br/>Here $\left(x_{1}, y_{1}\right)=(1,2)$ So,<br/>$(y-2)=-\frac{1}{3}(x-1)$<br/>$\Rightarrow-3 y+6=x-1$<br/>$\Rightarrow x+3 y-7=0$</div>


tags: ['Mathematics', 'Hyperbola', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
equation-of-the-hyperbola-with-eccentricity-32-and-foci-at-2-0-is-5-x-2-4-y-2-k-2-what-is-the-value-of-k

slug:
equation-of-the-hyperbola-with-eccentricity-32-and-foci-at-2-0-is-5-x-2-4-y-2-k-2-what-is-the-value-of-k-86847

question:
<div class="question">Equation of the hyperbola with eccentricity $3 / 2$ and foci at $(\pm 2,0)$ is $5 x^{2}-4 y^{2}=k^{2}$. What is the value of $k$ ?</div>

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

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

answer:
<div class="solution">Given equation of hyperbola $\Rightarrow \frac{x^{2}}{\frac{k^{2}}{5}}-\frac{y^{2}}{\frac{k^{2}}{4}}=1$<br/>$a=\frac{k}{\sqrt{5}}$ and $b=\frac{k}{2}$<br/>The eccentricity $\frac{3}{2}$ and foci at $(\pm 2,0)$ of $5 x^{2}-4 y^{2}=k^{2}$<br/>Then, $e=\frac{3}{2}$ and $\pm a e=2$<br/>$\Rightarrow \frac{k}{\sqrt{5}} \cdot \frac{3}{2}=2 \Rightarrow k=\frac{4}{3} \sqrt{5}$</div>


tags: ['Physics', 'Waves and Sound', 'MHT CET', 'MHT CET 2021 (21 Sep Shift 2)']
source_db: MarksBatch1_P2.db
title:
equation-of-two-simple-harmonic-waves-is-given-by-y-1-2-sin-8-02-t-2-x-m-and-y-2-4-sin-8-016-t-16-x-m-then-both-waves-have

slug:
equation-of-two-simple-harmonic-waves-is-given-by-y-1-2-sin-8-02-t-2-x-m-and-y-2-4-sin-8-016-t-16-x-m-then-both-waves-have-66490

question:
<div class="question">Equation of two simple harmonic waves is given by $\mathrm{Y}_1=2 \sin 8 \pi\left(\frac{\mathrm{t}}{0.2}-\frac{\mathrm{x}}{2}\right) \mathrm{m}$ and $\mathrm{Y}_2=4 \sin 8 \pi\left(\frac{\mathrm{t}}{0.16}-\frac{\mathrm{x}}{1.6}\right) \mathrm{m}$ then both waves have</div>

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

answer:
<div class="solution">The two equations can be written as<br/>$$<br/>\begin{aligned}<br/>&amp; Y_1=2 \sin 2 \pi\left(\frac{4 t}{0.2}-\frac{4 x}{2}\right)=2 \sin 2 \pi\left(\frac{\mathrm{t}}{0.05}-\frac{\mathrm{x}}{0.5}\right) \\<br/>&amp; \text { and } Y_2=4 \sin 2 \pi\left(\frac{4 \mathrm{t}}{0.16}-\frac{4 \mathrm{x}}{1.6}\right)=2 \sin 2 \pi\left(\frac{\mathrm{t}}{0.04}-\frac{\mathrm{x}}{0.4}\right)<br/>\end{aligned}<br/>$$<br/>Comparing with standard equation<br/>$$<br/>\mathrm{Y}=\mathrm{A} \sin 2 \pi\left(\frac{\mathrm{t}}{\mathrm{T}}-\frac{\mathrm{x}}{\lambda}\right)<br/>$$<br/>We get, for the first wave,<br/>$$<br/>\mathrm{T}=0.05 \mathrm{~s} \text { and } \lambda=0.5 \mathrm{~m}<br/>$$<br/>For the second wave,<br/>$$<br/>\mathrm{T}=0.04 \mathrm{~s} \text { and } \lambda=0.4 \mathrm{~m}<br/>$$<br/>Hence their periods (hence frequencies) are not same.<br/>Their wavelength is also not same.<br/>For first wave, velocity $=\frac{\lambda}{\mathrm{T}}=\frac{0.5}{0.05}=10 \mathrm{~m} / \mathrm{s}$<br/>For second wave, velocity $\frac{0.4}{0.04}=10 \mathrm{~m} / \mathrm{s}$<br/>Hence velocity in same</div>


title: estrogen-and-testosterone-are-steroid-hormones-which-most-likely-bind-to
slug: estrogen-and-testosterone-are-steroid-hormones-which-most-likely-bind-to-42467
tags: ['Biology', 'Chemical Coordination and Integration', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Estrogen and testosterone are steroid hormones, which most likely bind to</div>

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

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

answer:
<div class="solution">Hormonal action depends on whether the hormone is Lipid or water soluble. Lipid soluble hormones can cross the target cell membrane easily, get attached to the mobile receptors within the cytoplasm and reach the nucleus to perform their functions. However water soluble hormones are proteinaceous and these include insulin, oxytocin etc. These cannot cross the cell membrane easily. These get attached to the static receptors on the cell membrane. This attachment triggers the formation of secondary messengers that help these hormones to act on cells. Estrogen and Progesterone are steroid hormones that means these are lipid soluble hormones. Hence these attach to receptors within the cytoplasm.</div>


title: ethylene-oxide-when-treated-with-grignard-reagent-yields-1
slug: ethylene-oxide-when-treated-with-grignard-reagent-yields-1-44649
question: <div class="question">Ethylene oxide when treated with Grignard reagent yields:</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET', 'NEET 2006']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary alcohol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">secondary alcohol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">cyclopropyl alcohol</span> </li> </ul>

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

answer:
<div class="solution">Ethylene oxide on treatment with Grignard reagent gives an additive product which on hydrolysis gives primary alcohol.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/neet/8dhFd0I0QhV2_HxeeaPsG7IK_kPXB_SgPpHU415c7k8.original.fullsize.png"/><br/></div>


title: ethylene-oxide-when-treated-with-grignard-reagent-yields
slug: ethylene-oxide-when-treated-with-grignard-reagent-yields-67643
question: <div class="question">Ethylene oxide when treated with Grignard reagent yields</div>
tags: ['Chemistry', 'Alcohols Phenols and Ethers', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">primary alcohol</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">secondary alcohol</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">tertiary alcohol</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">cyclopropyl alcohol</span> </li> </ul>

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

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/b489a030-5f8e-4078-8e83-d12dbe8a871a.png" style="width:4.89375in;height:0.8in"/></div>


title: ethylenediamine-en
slug: ethylenediamine-en-84111
question: <div class="question">Ethylenediamine (en)</div>
tags: ['Chemistry', 'Coordination Compounds', 'TS EAMCET', 'TS EAMCET 2018 (07 May Shift 1)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">monodendate ligand and can occupy one position in coordination polyhedron</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">bidendate ligand and can occupy two positions in coordination polyhedron</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">polydendate ligand</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">tridendate ligand and occupy three positions in coordination polyhedron</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">bidendate ligand and can occupy two positions in coordination polyhedron</span> </div>

answer:
<div class="solution">Ethylenediamine is an organic compound with formula $\mathrm{C}_2 \mathrm{H}_4\left(\mathrm{NH}_2\right)_2$.<br/>$$<br/>\mathrm{H}_2 \text { è- } \mathrm{CH}_2-\mathrm{CH}_2-\mathrm{N}_2<br/>$$<br/>It act as a bidentate ligand due to the presence of lone pair of electrons on nitrogen atoms and can occupy two positions.</div>


title: evaluate-leftbeginarraycccos-15-sin-15-sin-75-cos-75endarrayright
slug: evaluate-leftbeginarraycccos-15-sin-15-sin-75-cos-75endarrayright-66159
tags: ['Mathematics', 'Three Dimensional Geometry', 'KCET', 'KCET 2015']
source_db: MarksBatch1_P2.db
question:
<div class="question">Evaluate \( \left|\begin{array}{cc}\cos 15 &amp; \sin 15 \\ \sin 75 &amp; \cos 75\end{array}\right| \)</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">\( 00 \)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">\( 12 \)</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\( 13 \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 00 \)</span> </div>

answer:
<div class="solution">Given that,<br/>\[<br/>\begin{array}{l}<br/>\left|\begin{array}{l}<br/>\cos 15^{\circ} \sin 15^{\circ} \\<br/>\sin 75^{\circ} \cos 75^{\circ}<br/>\end{array}\right| \\<br/>=\cos 15^{\circ} \cos 75^{\circ}-\sin 15^{\circ} \sin 75^{\circ} \\<br/>=\cos \left(15^{\circ}+75^{\circ}\right)=\cos \left(90^{\circ}\right)=0<br/>\end{array}<br/>\]</div>


title: every-quadratic-equation-a-x-2-b-x-c-0-where-a-b-c-r-a-0-has
slug: every-quadratic-equation-a-x-2-b-x-c-0-where-a-b-c-r-a-0-has-82936
tags: ['Mathematics', 'Quadratic Equation', 'NDA', 'NDA 2014 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Every quadratic equation $a x^{2}+b x+c=0$ where $a, b, c, \in R$ $a \neq 0$ has</div>

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

answer:
<div class="solution">Every quadratic equation<br/>$a x^{2}+b x+c=0$, where $a, b, c \in R, a \neq 0$<br/>has at most two real roots.</div>


title: examples-of-areas-where-secondary-succession-occurs-are
slug: examples-of-areas-where-secondary-succession-occurs-are-29415
question: <div class="question">Examples of areas where secondary succession occurs are</div>
tags: ['Biology', 'Ecosystem', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Abandoned farmlands, newly cooled lava, barerock</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Burned or cut forests, lands that have been flooded</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Bare rock, newly created pond or reservoir</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Newly created pond, lands that have beenflooded</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Burned or cut forests, lands that have been flooded</span> </div>

answer:
<div class="solution">Secondary succession begins in areas where natural biotic communities have been destroyed such as in abandoned farmlands, burned or cut forests, lands that have been flooded. Since some soil or sediment is present, secondary succession is faster than primary succession.</div>


title: examples-of-arithmetic-growth-are
slug: examples-of-arithmetic-growth-are-88688
question: <div class="question">Examples of arithmetic growth are,</div>
tags: ['Biology', 'Plant - Growth and Development', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">root elongation</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">increase in girth</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">both <math><mfenced separators="|"><mrow><mi mathvariant="normal">a</mi></mrow></mfenced><mi mathvariant="normal"> </mi><mi mathvariant="normal">a</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal"> </mi><mfenced separators="|"><mrow><mi mathvariant="normal">b</mi></mrow></mfenced></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">none of these</span> </li> </ul>

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

answer:
<div class="solution">The growth that occurs at a constant rate is known as the arithmetic growth, which is followed by the mitotic cell division. Only one daughter cell continues to divide while the other differentiates and other undergoes maturation. Root elongates at a constant rate thus shows arithmetic growth. An increase in girth of plant shows variable growth and it depends upon the environmental condition and is a secondary growth involving differentiation.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2007 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
examples-of-some-random-variables-are-given-below-1-number-of-sons-among-the-children-of-parents-with-five-children-2-number-of-sundays-in-some-random

slug:
examples-of-some-random-variables-are-given-below-1-number-of-sons-among-the-children-of-parents-with-five-children-2-number-of-sundays-in-some-random-72991

question:
<div class="question">Examples of some random variables are given below<br/>$1.$ Number of sons among the children of parents with five children<br/>$2.$ Number of sundays in some randomly selected months with 30 days<br/>$3.$ Number of apples in some $3 \mathrm{~kg}$ packets, purchased from a retail shop Which of the above is expected to follow binomial distribution?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Variable 1</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Variable 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">Variable 3</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">None of these</span> </li> </ul>

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

answer:
<div class="solution">Number of Sundays in some randomly selected months with 30 days follow binomial distribution.</div>


title: exoskeleton-of-arthropods-is-composed-of
slug: exoskeleton-of-arthropods-is-composed-of-99379
question: <div class="question">Exoskeleton of arthropods is composed of:</div>
tags: ['Biology', 'Animal Kingdom', 'NEET', 'NEET 2022 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">Chitin</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Cellulose</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Chitin</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Glucosamine</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Cutin</span> </li> </ul>

answer:
<div class="solution"><p>The largest phylum Arthropoda has certain salient features:</p><ul> <li>The body has distinct parts, like head, thorax, abdomen.</li> <li>There is excosketeton made up of chitin.</li> <li>There are jointed appendages.</li> <li>Blood vascular system is open type.</li></ul></div>


title: explain-briefly-i-protonema-ii-antheridium-iii-archegonium-iv-diplontic-v-sporophyll-vi-isogamy
tags: ['Biology', 'Plant Kingdom']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
slug:
explain-briefly-i-protonema-ii-antheridium-iii-archegonium-iv-diplontic-v-sporophyll-vi-isogamy-55918

question:
<div class="question">Explain briefly<br/>(i) Protonema<br/>(ii) Antheridium<br/>(iii) Archegonium<br/>(iv) Diplontic<br/>(v) Sporophyll<br/>(vi) Isogamy</div>

answer:
<div class="solution">(i) Protonema : The predominant stage of moss gametophyte which directly develops from spore is known as protonema.<br/>(ii) Antheridium : The male sex organ in bryophytes, pteridophytes and gymnosperms is called antheridium. It bears male gamete.<br/>(iii) Archegonium : It is the female sex organ found in bryophytes, pteridophytes and gymnosperms. It bears female gamete.<br/>(iv) Diplontic: In the life cycle of plants when their diploid stage is dominant for long time then this is called diplontic.<br/>(v) Sporophyll : The sporophyte bears sporangia that are subtended by leaf like appendages called sporophylls.<br/>(vi) Isogamy : When the gametes involved in sexual reproduction are morphologically similar then this is called isogamy. These gametes are physiologically different.</div>


title: explain-briefly-the-rivet-popper-hypothesis-of-paul-ehrlich
slug: explain-briefly-the-rivet-popper-hypothesis-of-paul-ehrlich-27704
question: <div class="question">Explain briefly the 'rivet popper hypothesis' of Paul Ehrlich.</div>
tags: ['Biology', 'Biodiversity and its Conservation']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">The rivet popper hypothesis was given by ecologist Paul Ehrlich to help in the understanding of the contribution species richness. He compared each species with rivet in the body of an airplane.<br/>(i) This hypothesis considers ecosystem to be an airplane and the species to be the rivets joining all parts together.<br/>(ii) If every passenger travelling in the airplane starts taking rivets home (causing a species to become extinct), initially it may not affect flight safety (proper functioning of ecosystem), but over a period of time the plane becomes weak and dangerous (species become endangered and then gradually extinct).</div>


tags: ['Biology', 'Plant - Growth and Development']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-in-23-lines-each-of-the-following-terms-with-the-help-of-examples-taken-from-different-plant-tissues-a-differentiation-b-dedifferentiation-c-r

slug:
explain-in-23-lines-each-of-the-following-terms-with-the-help-of-examples-taken-from-different-plant-tissues-a-differentiation-b-dedifferentiation-c-r-20652

question:
<div class="question">Explain in 2-3 lines each of the following terms with the help of examples taken from different plant tissues.<br/>(a) Differentiation<br/>(b) De-differentiation<br/>(c) Re-differentiation</div>

answer:
<div class="solution">(a) Differentiation is permanent in composition structure size and function of cells, tissue or organs. For example the meristematic tissues in plants gives rise to new cells which then mature and get differentiated into tissue or an organ of the plant, e.g., cells, distal to root apical meristem form root cap, cell of the periphery form epiblema, followed by cortex, etc.<br/>(b) De-differentiation is the process of regain of differentiated cells so that they again become differentiated and able to divide. e.g., in dicot stem, the cortical cells get de-differentiate and become meristematic to form cambium (interfascicular cambium, and fascicular cambiums).<br/>(c) Re-differentiation The cambium cells thus formed, again re-differentiate to form secondary cortex cells, secondary xylem and phloem elements and phelloderm in case of secondary growth of woody dicot plants.</div>


title: explain-the-bonding-in-coordination-compounds-in-terms-of-werners-postulates
slug: explain-the-bonding-in-coordination-compounds-in-terms-of-werners-postulates-20779
tags: ['Chemistry', 'Coordination Compounds']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Explain the bonding in coordination compounds in terms of Werner's postulates.</div>

answer:
<div class="solution">The main postulates of Werner's theory of coordination compounds are as follows:<br/>(a) Metals possess two types of valencies called<br/>(i) primary valency which are ionisable;<br/>(ii) secondary valency which are nonionisable<br/>(b) Primary valency is satisfied by the negative ions and it is that which a metal exhibits in the formation of its simple salts.<br/>(c) Secondary valencies are satisfied by neutral ligand or negative ligand and are those which metal exercises in the formation of its complex ions. Every cation has a fixed number of secondary valencies which are directed in space about central metal ion in certain fixed directions, e.g., In \(\mathrm{CoCl}_3 \cdot 6 \mathrm{NH}_3\), valencies between \(\mathrm{Co}\) and \(\mathrm{Cl}\) are primary valencies and valencies between \(\mathrm{Co}\) and \(\mathrm{NH}_3\) are secondary. In \(\mathrm{CoCl}_3 \cdot 6 \mathrm{NH}_3\), six ammonia molecules linked to \(\mathrm{Co}\) by secondary valencies are directed to six corners of a regular octahedron and thus account for structure of \(\mathrm{CoCl}_3 \cdot 6 \mathrm{NH}_3\) as follows:<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/PdgG7txbb_SEkitUh1dr0Jph710yX0NFTUNp_IVvdCc.original.fullsize.png"/><br/><br/>In modern theory, it is now referred as coordination number of central metal atom or ion.</div>


tags: ['Chemistry', 'General Principles and Processes of Isolation of Metals', 'NEET']
source_db: MarksBatch1_P2.db
title:
explain-the-following-co-2-is-a-better-reducing-agent-below-710k-whereas-co-is-a-better-reducing-agent-above-710k

slug:
explain-the-following-co-2-is-a-better-reducing-agent-below-710k-whereas-co-is-a-better-reducing-agent-above-710k-54306

question:
<div class="question">Explain the following : CO<sub>2</sub>is a better reducing agent below 710K whereas CO is a better reducing agent above 710K.</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">CO<sub>2</sub>is more stable than CO below 710K.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">CO has a lower bond dissociation energy than CO<sub>2</sub>below 710K.</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">CO<sub>2</sub>is reduced to CO below 710K as per Ellingham diagram.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">CO<sub>2</sub>has a higher standard reduction potential than CO below 710K.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">CO<sub>2</sub>is reduced to CO below 710K as per Ellingham diagram.</span> </div>

answer:
<div class="solution">Correct Option is : (C)<br/>CO<sub>2</sub>is reduced to CO below 710K as per Ellingham diagram.</div>


title: explain-the-following-terms-i-electrophoresis-ii-coagulation-iii-dialysis-iv-tyndall-effect
slug: explain-the-following-terms-i-electrophoresis-ii-coagulation-iii-dialysis-iv-tyndall-effect-53298
tags: ['Chemistry', 'Surface Chemistry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Explain the following terms:<br/>(i) Electrophoresis<br/>(ii) Coagulation<br/>(iii) Dialysis<br/>(iv) Tyndall effect.</div>

answer:
<div class="solution">(i) The colloidal particles are electrically charged, either positive or negative. When an electric current is passed through a colloidal solution, the colloidal particles move towards a positive or a negative terminal. This movement of colloidal particles under applied electric field is known as electrophoresis.<br/>(ii) Coagulation or precipitation: The stability of the lyophobic sols is due to the presence of charge on colloidal particles. If, somehow, the charge is removed, the particles will come nearer to each other to form aggregates (or coagulate) and settle down under the force of gravity. The process of setting down of colloidal particles is called coagulation.<br/>(iii) The process of separating a soluble crystalloid from a colloid is called dialysis. The purification of a colloid by dialysis is based on the fact that colloidal size particles cannot pass through parchment paper or cello phone membrane, whereas small molecules or ions can pass thought it. Thus, when a bag of parchment paper containing a colloidal solution is suspended into pure water, the small molecules and ions pass through the membrane into the pure water and the pure colloidal solution is left behind.<br/>(iv) When a beam of light is passed through a colloidal solution, its path becomes visible. This phenomenon is known as Tyndall effect. It is due to the scattering of light by colloidal particles.</div>


tags: ['Chemistry', 'Alcohols Phenols and Ethers']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-the-following-with-an-example-i-kolbes-reaction-ii-reimer-tiemann-reaction-iii-williamson-ether-synthesis-iv-unsymmetrical-ether

slug:
explain-the-following-with-an-example-i-kolbes-reaction-ii-reimer-tiemann-reaction-iii-williamson-ether-synthesis-iv-unsymmetrical-ether-25400

question:
<div class="question">Explain the following with an example<br/>(i) Kolbe's reaction<br/>(ii) Reimer - Tiemann reaction<br/>(iii) Williamson ether synthesis<br/>(iv) Unsymmetrical ether</div>

answer:
<div class="solution">(i) Kolbe's reaction: Sodium phenoxide when heated with $\mathrm{CO}_2$ at $400 \mathrm{~K}$ under a pressure of 4-7 atmospheres followed by acidification gives 2-hydroxybenzoic acid (salicylic acid) as the major product along with a small amount of 4-hydroxybenzoic acid. This reaction is called Kolbe's reaction.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/giDJCSaaNWbCYXf245VMY0HsWWkvSQDGKzFto72gEa8.original.fullsize.png"/><br/><br/>(ii) Reimer-Tiemann reaction: Treatment of phenol with $\mathrm{CHCl}_3$ in presence of aqueous sodium or potassium hydroxide at $340 \mathrm{~K}$ followed by hydrolysis of the resulting product gives 2-hydroxybenzaldehyde (salicylaldehyde) as the major product. This reaction is called Reimer-Tiemann reaction.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/0HUOEil3ksquPyUxgP0yyDVpa8juKcQN-92ZN76dZl4.original.fullsize.png"/><br/><br/>(iii) Williamson's ether synthesis: It involves the treatment of an alkyl halide with a suitable sodium alkoxide to obtain ethers. The sodium alkoxide needed for the purpose is prepared by the action of sodium on a suitable alcohol. In this reaction alkyl halide should primary. Secondary and tertiary halides will predominantly give an alkene.<img src="https://cdn-question-pool.getmarks.app/modules/cbse/HJFezR0Pd5k2r9GraCrbk0QGuuzm1JBq6TXu9907x-c.original.fullsize.png"/><br/><br/>(iv) Unsymmetrical ether: If the alkyl or aryl groups attached to the oxygen atom are different, ethers are called unsymmetrical ethers. For example, ethylmethylether, methylphenylether, etc.</div>


tags: ['Biology', 'Anatomy of Flowering Plants']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-the-process-of-secondary-growth-in-the-stems-of-woody-angiosperms-with-the-help-of-schematic-diagrams-what-is-its-significance

slug:
explain-the-process-of-secondary-growth-in-the-stems-of-woody-angiosperms-with-the-help-of-schematic-diagrams-what-is-its-significance-30317

question:
<div class="question">Explain the process of secondary growth in the stems of woody angiosperms with the help of schematic diagrams. What is its significance?</div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/modules/cbse/tmCyWee7D0cos85FOBCWo1N7Qa2Nw0SrZXUNguXjxSs.original.fullsize.png"/><br/><br/> Secondary growth in dicot stem: It is "permanent increase in thickness due to the activity of vascular cambium and cork cambium in stelar and extrastelar regions". In dicot stem intra fascicular cambium is present. The cells of medullary ray become meristematic and form interfascicular cambium. These two cambiums unite and make a complete cambial ring. The cells of it divide and produce new cells both on its outer and inner sides. The cells formed on the outer side differentiate into secondary phloem while the cells of inner side form secondary xylem. The epidermis is replaced by a secondary protective tissue by increase in growth of the stem of the plant. It is made of phellogen (cork cambium). It arises from the peripheral cells of cortex. The phellogen forms new cells on the outer side which make phellem (cork) and phelloderm on its inner side also. Significance : Secondary growth increases girth or thickness of plant.<br/>Annual rings of woody angiosperms are very distinct and thus helps in determining the age of plant.</div>


title: explain-the-significance-of-sodium-potassium-magnesium-and-calcium-in-biological-fluids
slug: explain-the-significance-of-sodium-potassium-magnesium-and-calcium-in-biological-fluids-69236
tags: ['Chemistry', 's Block Elements']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Explain the significance of sodium, potassium, magnesium and calcium in biological fluids.</div>

answer:
<div class="solution">Sodium (Na): They are found in our blood plasma and the interstitial fluids around the cells. They help in<br/>(a) Transmission of nerve signals.<br/>(b) They regulate the flow of water across the membranes of the neighbouring cells.<br/>(c) Transport sugars and amino acids from and to cells. Potassium (K): They are found mostly in the cell fluids in greater quantities. They help in<br/>(a) Activating enzymes<br/>(b) Oxidising glucose to form ATP<br/>(c) Transmitting nerve signals.<br/>Magneslum (Mg) and calcium (Ca): They are also called as macro-minerals named so because of their abundance in out body. Mg helps in<br/>(a) Relaxing nerves and muscles<br/>(b) Building and strengthening bones<br/>(c) Maintaining blood circulation in our body Ca helps in<br/>(a) coagulation of blood<br/>(b) Maintaining homeostasis.</div>


title: explain-the-structure-of-middle-and-internal-ear-with-the-help-of-diagram
slug: explain-the-structure-of-middle-and-internal-ear-with-the-help-of-diagram-30562
tags: ['Biology', 'Neural Control and Coordination']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Explain the structure of middle and internal ear with the help of diagram.</div>

answer:
<div class="solution">Ears are a part of statoacoustic organ meant for balancing and hearing the external ear in most mammals is a heap of tissue also called pinna. It is a part of auditory system. The human ear consists of three main parts external ear, middle, ear and internal ear.<br/>Structure of Middle Ear<br/>The middle ear consists of three bones or ossicles-the malleus (hammer), incus (anvil and stapes (stir-up). These bones are attached to one another in a chain-like manner. The malleus is attached to the tympanic membrane and the stapes is attached to the oval window (a membrane beneath the stapes) of cochlea. These three ossicles increase the efficiency of transmission of sound waves to the inner ear. The middle ear also opens into the eustachian tube, which connects with the pharynx and maintains the pressure between the middle ear and the outside atmosphere.<br/>Structure of Internal Ear<br/>The inner ear consists of a labyrinth of chambers filled with fluid within temporal bone of the skull. The labyrinth consists of two parts the bony and membranous labyrinth. The bony labyrinth is a series of channels. Membranous labyrinth lies inside these channels which is surrounded by a fluid called perilymph. The membranous labyrinth is filled with a fluid called endolymph. The coiled portion of the labyrinth is called cochlea.<br/>The cochlea has two large canal separated by a small cochlear duct (scala media). An upper vestibular canal (scala vestibuli) and a lower tympanic canal (scala tympani). The vestibular and tympanic canals contain perilymph and the cochlear duct is filled with endolymph.<br/>The wall of membranous labyrinth comes in contact with the fenestra ovalis at the base of scale vestibuli while the fenestra rotunda.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/MDsBra5DGmyC08Ary90s81NKcwZqP5x-2fkO761Bomw.original.fullsize.png"/><br/></div>


tags: ['Chemistry', 'Biomolecules']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-the-terms-primary-and-secondary-structure-of-proteins-what-is-the-difference-between-helix-and-pleated-sheet-structure-of-proteins

slug:
explain-the-terms-primary-and-secondary-structure-of-proteins-what-is-the-difference-between-helix-and-pleated-sheet-structure-of-proteins-51407

question:
<div class="question">Explain the terms primary and secondary structure of proteins. What is the difference between $\alpha$-helix and $\beta$ pleated sheet structure of proteins?</div>

answer:
<div class="solution">Proteins are made up of one or more polypeptide chains. The specific sequence in which various amino acids are linked with each other to form polypeptide is called its primary structure. Secondary structure refers to the shape which the polypeptide chains assume as a result of<br/>hydrogen bonding between<br/> &lt; smiles&gt;CC(C)=O &lt; /smiles&gt;<br/>and $-\mathrm{NH}-$ groups of the peptide bond. Difference between $\alpha$-helix and $\beta$ pleated sheet structure is as given below:<img src="https://cdn-question-pool.getmarks.app/modules/cbse/GPVV_HcCEO_PdXXoo0z8wU8dIgfDCyWOkV9vytvuVkU.original.fullsize.png"/><br/></div>


tags: ['Physics', 'Units and Dimensions']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-this-statement-clearly-to-call-a-dimensional-quantity-large-or-small-is-meaningless-without-specifying-a-standard-for-comparison-in-view-of-th

slug:
explain-this-statement-clearly-to-call-a-dimensional-quantity-large-or-small-is-meaningless-without-specifying-a-standard-for-comparison-in-view-of-th-68858

question:
<div class="question">Explain this statement clearly :<br/>"To call a dimensional quantity 'large' or 'small' is meaningless without specifying a standard for comparison." In view of this, reframe the following statements wherever necessary:<br/>(a) atoms are very small objects<br/>(b) a jet plane moves with great speed<br/>(c) the mass of Jupiter is very large<br/>(d) the air inside this room contains a large number of molecules<br/>(e) a proton is much more massive than an electron<br/>(f) the speed of sound is much smaller than the speed of light.</div>

answer:
<div class="solution">Physical quantities are called large or small depending on the unit (standard) of measurement. For example, parsec is equal to $3.08 \times 10^{16} \mathrm{~m}$ or $3.08 \times 10^{12} \mathrm{~km}$ is certainly larger than metre or kilometre.<br/>(a) The size of an atom is much smaller than even the sharp tip of a pin.<br/>(b) A Jet plane moves with a speed greater than that of a superfast train.<br/>(c) The mass of Jupiter is very large compared to that of the earth.<br/>(d) The air inside this room contains more number of molecules than in one mole of air.<br/>(e) This is a correct statement.<br/>(f) This is a correct statement.</div>


tags: ['Chemistry', 'Surface Chemistry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-what-is-observed-i-when-a-beam-of-light-is-passed-through-a-colloidal-sol-ii-an-electrolyte-mathrmnacl-is-added-to-hydrated-ferric-oxide-sol-i

slug:
explain-what-is-observed-i-when-a-beam-of-light-is-passed-through-a-colloidal-sol-ii-an-electrolyte-mathrmnacl-is-added-to-hydrated-ferric-oxide-sol-i-85153

question:
<div class="question">Explain what is observed<br/>(i) when a beam of light is passed through a colloidal sol.<br/>(ii) an electrolyte, \(\mathrm{NaCl}\) is added to hydrated ferric oxide sol.<br/>(iii) electric current is passed through a colloidal sol.</div>

answer:
<div class="solution">(i) Scattering of light by the colloidal particles takes place and the path of light becomes visible (Tyndall effect).<br/>(ii) The positively charged colloidal particles of \(\mathrm{Fe}(\mathrm{OH})_3\) get coagulated by the oppositely charged \(\mathrm{Cl}^{-}\)ions provided by \(\mathrm{NaCl}\).<br/>(iii) On passing electric current, colloidal particles move towards the oppositely charged electrode where they lose their charge and get coagulated.</div>


title: explain-why-is-sodium-less-reactive-than-potassium
slug: explain-why-is-sodium-less-reactive-than-potassium-63092
question: <div class="question">Explain why is sodium less reactive than potassium ?</div>
tags: ['Chemistry', 's Block Elements']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">The ionization enthalpy \(\left(\Delta_{\mathrm{i}} \mathrm{H}\right)\) of potassium \(\left(496 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\) is less than that of sodium \(\left(496 \mathrm{~kJ} \mathrm{~mol}^{-1}\right)\) or more precisely the standard electrode potential \(\left(\mathrm{E}^{\circ}\right)\) of potassium \((-2.925 \mathrm{~V})\) is more negative than that of sodium \((-2.714 \mathrm{~V})\) and hence potassium is more reactive than sodium.</div>


tags: ['Physics', 'Waves and Sound']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-why-or-how-a-in-a-sound-wave-a-displacement-node-is-a-pressure-antinode-and-vice-versa-b-bats-can-ascertain-distances-directions-nature-and-si

slug:
explain-why-or-how-a-in-a-sound-wave-a-displacement-node-is-a-pressure-antinode-and-vice-versa-b-bats-can-ascertain-distances-directions-nature-and-si-52942

question:
<div class="question">Explain why (or how):<br/>(a) in a sound wave, a displacement node is a pressure antinode and vice versa,<br/>(b) bats can ascertain distances, directions, nature, and sizes of the obstacles without any "eyes",<br/>(c) a violin note and sitar note may have the same frequency, yet we can distinguish between the two notes,<br/>(d) solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases, and<br/>(e) the shape of a pulse gets distorted during propagation in a dispersive medium.</div>

answer:
<div class="solution">[QUESTION]<br/>(a) As displacement node is a point of zero displacement the pressure variation is maximum at this point.<br/>Hence it is a pressure antinode.<br/>(b) Bats have the ability to produce and detect ultrasonic waves $(v&gt;20 \mathrm{kHz})$ so they can detect the distance of the object by the interval between their producing the waves and receiving the echo. From the intensity of the echo they detect the nature and size of the object and from the small interval between their receiving the echo by their two ears, they can ascertain the direction of the object.<br/>(c) The quality of the sound produced depends on the overtones produced by the instruments. The Sitar and Violin though may have the same fundamental frequency but they produce different overtone which is an integral multiple of fundamental frequency and hence we can differentiate between the sound of the two.<br/>(d) Gases do not have shear elasticity so only the longitudinal waves can travel through them whereas solids have both volume and shear elasticity and hence both longitudinal and tranverse waves can travel through them.<br/>(e) It is the property of a dispersive medium that waves of different wavelength travel with different speeds in different directions or with different velocities. Thus when a sound pulse which is a combination of waves of different wavelengths travels through it gets distorted.</div>


tags: ['Biology', 'Plant Kingdom']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
explain-why-sexual-reproduction-in-angiosperms-is-said-to-take-place-through-double-fertilisation-and-triple-fusion-also-draw-a-labelled-diagram-of-em

slug:
explain-why-sexual-reproduction-in-angiosperms-is-said-to-take-place-through-double-fertilisation-and-triple-fusion-also-draw-a-labelled-diagram-of-em-43735

question:
<div class="question">Explain why sexual reproduction in angiosperms is said to take place through double fertilisation and triple fusion. Also draw a labelled diagram of embryo sac to explain the phenomena.</div>

answer:
<div class="solution">An angiospermic plants reproduces sexually by the formation of male and female gametes. The male gamete is a pollen which contains two male nuclei and the female gamete is an egg cell produced in ovule (female gametophyte).<br/>The pollen grains germinate on the stigma of a flower and the results in growth of pollen through the tissues of stigma and style and reach the egg apparatus. The two male gametes are discharged within the embryo sac. One of the male gamete fuses with the egg cell to form a diploid zygote.<br/>This fusion is known as fertilisation or syngamy. The .second male gamete fuses with the diploid secondary nucleus and forms the triploid Primary Endosperm Nucleus (PEN). This fusion is known as triple fusion.<br/>Because of the involvement of two fusion, this event in angiosperms is termed as double fertilisation. The zygote then develops into embryo and PEN develops into endosperm which provides nourishment to the developing embryo.</div>


title: exponential-growth-in-human-population-is-represented-in
slug: exponential-growth-in-human-population-is-represented-in-68442
question: <div class="question">Exponential growth in human population is represented in</div>
tags: ['Biology', 'Reproductive Health', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Lag phase</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Log phase</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Plateau stage</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">First stage</span> </li> </ul>

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

answer:
<div class="solution">The log phase or exponential phase is the geometrical increase in population size owing to the abundance of food and other favourable conditions.</div>


title: exponential-growth-occurs-when-there-is
slug: exponential-growth-occurs-when-there-is-92078
question: <div class="question">Exponential growth occurs when there is</div>
tags: ['Biology', 'Organisms and Populations', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">a great environmental resistance</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">no environmental resistance</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">no biotic potential</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">a fixed carrying capacity</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">no environmental resistance</span> </div>

answer:
<div class="solution">Exponential growth in a population occurs when the resources are abundant in the environment and organism is not faced by any resistance from the environment like calamities.</div>


title: extrusion-of-second-polar-body-from-egg-nucleus-occurs-1
slug: extrusion-of-second-polar-body-from-egg-nucleus-occurs-1-15070
question: <div class="question">Extrusion of second polar body from egg nucleus occurs</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">after entry of sperm, before completion of fertilization</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">after completion of fertilization</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">before the entry of sperm</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">has no relation with sperm entry</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">after entry of sperm, before completion of fertilization</span> </div>

answer:
<div class="solution">In oogenesis the primary oocyte forms secondary oocyte just before ovulation. This secondary oocyte as formed starts Meiosis 2 but this is arrested at metaphase 2 and is ovulated at this stage. It enters the oviduct and remains viable for one day and then sheds in the form of menstruation alongwith the endometrial lining. Thus secondary oocyte sheds in the arrested phase only. When in the oviduct if the sperm enters there are chances of fertilization. The sperm swims the vagina, cervix and uterus are enters the oviduct where it approaches the ovum membrane. As the sperm touches the membrane the MAF (Metaphase arrested factor) disappears and thus Meiosis 2 completes following this, syngamy i.e. fusion of nuclei takes place and thus fertilization is completed.</div>


title: extrusion-of-second-polar-body-from-egg-nucleus-occurs-2
slug: extrusion-of-second-polar-body-from-egg-nucleus-occurs-2-17722
question: <div class="question">Extrusion of second polar body from egg nucleus occurs</div>
tags: ['Biology', 'Human Reproduction', 'NEET', 'NEET 2019 (All India)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">after entry of sperm but before fertilization.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">after fertilization.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">before entry of sperm into ovum.</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">simultaneously with first cleavage.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">after entry of sperm but before fertilization.</span> </div>

answer:
<div class="solution">The sperm entry stimulates the secondary oocyte to undergo a meiotic II division, which produces the ovum and the second polar body. This event occurs before fertilization. </div>


title: extrusion-of-second-polar-body-from-egg-nucleus-occurs
slug: extrusion-of-second-polar-body-from-egg-nucleus-occurs-48417
question: <div class="question">Extrusion of second polar body from egg nucleus occurs:</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">After the entry of sperm, before the completion of fertilization</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">After the completion of fertilization</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Before the entry of sperm</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Has no relation to sperm entry.</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">After the entry of sperm, before the completion of fertilization</span> </div>

answer:
<div class="solution">The entry of sperm stimulates the secondary oocyte to resume and complete the suspended meiosis II.  This produces a haploid mature ovum and a second polar body. The second polar body immediately degenerates and sperm tail as well.</div>


title: f-1-2-3-4-5-is-not-a-function-if-it-is-defined-by-which-one-of-the-following
slug: f-1-2-3-4-5-is-not-a-function-if-it-is-defined-by-which-one-of-the-following-62703
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">$f:\{1,2,3\} \rightarrow\{4,5\}$ is not a function if it is defined by which one of the following?</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\{(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)\}$</span> </div>

answer:
<div class="solution">If the relation is defined by option (d), then each 1,2 and 3 has two images. $\mathrm{So}$, it is not a function.</div>


title: f-a-is-a-finite-set-having-n-elements-then-the-number-of-relations-which-can-be-defined-in-a-is
tags: ['Mathematics', 'Sets and Relations', 'NDA', 'NDA 2013 (Phase 2)']
source_db: MarksBatch1_P2.db
slug:
f-a-is-a-finite-set-having-n-elements-then-the-number-of-relations-which-can-be-defined-in-a-is-57406

question:
<div class="question">f $A$ is a finite set having $n$ elements, then the number of relations which can be defined in $A$ is</div>

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

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

answer:
<div class="solution">If A is a finite set having $n$ elements, then the number of relations which can be defined in A set is<br/>$2^{n \times n}=2^{n^{2}}$</div>


tags: ['Mathematics', 'Continuity and Differentiability', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
f-x-3-x-2-12-x-1-37-x-1-x-2-2-x-3-which-of-the-following-statements-are-correct-1-f-x-is-continuous-at-x-2-2-f-x-attains-greatest-value-at-x-2-3-f-x-i

slug:
f-x-3-x-2-12-x-1-37-x-1-x-2-2-x-3-which-of-the-following-statements-are-correct-1-f-x-is-continuous-at-x-2-2-f-x-attains-greatest-value-at-x-2-3-f-x-i-45289

question:
<div class="question">$f(\mathrm{x})=\left\{\begin{array}{ll}3 x^{2}+12 x-1 &amp; -1 \leq x \leq 2 \\ 37-x, &amp; 2   &lt; x \leq 3\end{array}\right.$<br/>Which of the following statements are correct?<br/>1- $\mathrm{f}(\mathrm{x})$ is continuous at $\mathrm{x}=2$.<br/>2- $\mathrm{f}(\mathrm{x})$ attains greatest value at $\mathrm{x}=2$.<br/>3- $\mathrm{f}(\mathrm{x})$ is differentiable at $\mathrm{x}=2$. Select the correct answer using the code given below:</div>

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

answer:
<div class="solution">For continuity at $x=2$. RHL<br/>$\lim _{x \rightarrow 2^{+}} f(x)=\lim _{x \rightarrow 2^{+}} 37-x=37-2=3 \sigma$<br/>LHL<br/>$\lim _{x \rightarrow 2^{-}} f(x)=\lim _{x \rightarrow 2^{-}} 3 x^{2}+12 x-1$<br/>$=3(2)^{2}+12 \times 2-1=12+24-1=35 .$<br/>$f(2)=3 \times 4+12 \times 2-1=12+24-1=35$<br/>So. $\mathrm{RHL}=\mathrm{LHL}$<br/>$\Rightarrow f(x)$ is continuous at $x=2$. For differentiability at $x=2$.<br/>$\mathrm{LHD}=\lim _{x \rightarrow 2^{-}} \frac{f(x)-f(2)}{x-2}=\lim _{h \rightarrow 0} \frac{f(2-h)-f(2)}{2-h-2}$<br/>$=\lim _{h \rightarrow 0} \frac{3(2-h)^{2}+12(2-h)-(12+24-1)}{-h}$<br/>$=\lim _{h \rightarrow 0} \frac{3 h^{2}-24 h}{-h}=\lim _{h \rightarrow 0} 24-3 h=24$<br/>$\mathrm{RHD}=\lim _{x \rightarrow 2^{+}} \frac{f(x)-f(2)}{x-2}=\lim _{h \rightarrow 0} \frac{f(2+h)-f(2)}{2+h-2}$<br/>$=\lim _{h \rightarrow 0} \frac{37-2-h-35}{h}=-1$<br/>$\mathrm{LHD} \neq \mathrm{RHD}$<br/>$\Rightarrow f(x)$ is not differentiable at $x=2$.<br/>To check 2 .<br/>For $x=2$. $f(x)=3 x^{2}+12 x-1$<br/>$=3\left(x^{2}+4 x-\frac{1}{3}\right)=3\left((x+2)^{2}-\frac{13}{3}\right)$<br/>On putting $x=2$<br/>$f(x)=3\left(16-\frac{13}{3}\right)=35$<br/>On putting $x=1$<br/>$f(1)=3\left((1+2)^{2}-\frac{13}{3}\right)=3\left(9-\frac{13}{3}\right)=14$<br/>So $f(x)$ attains greatest value at $x=2$.</div>


tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
f-x-3-x-2-12-x-1-37-x-1-x-2-2-x-3-which-of-the-following-statements-isare-correct-1-f-x-is-increasing-in-the-interval-1-2-2-f-x-is-decreasing-in-the-i

slug:
f-x-3-x-2-12-x-1-37-x-1-x-2-2-x-3-which-of-the-following-statements-isare-correct-1-f-x-is-increasing-in-the-interval-1-2-2-f-x-is-decreasing-in-the-i-25146

question:
<div class="question">$f(\mathrm{x})=\left\{\begin{array}{ll}3 x^{2}+12 x-1 &amp; -1 \leq x \leq 2 \\ 37-x, &amp; 2   &lt; x \leq 3\end{array}\right.$<br/>Which of the following statements is/are correct?<br/>1- $\quad \mathrm{f}(\mathrm{x})$ is increasing in the interval $[-1,2]$.<br/>2- $\mathrm{f}(\mathrm{x})$ is decreasing in the interval $(2,3]$. Select the correct answer using the code given below:</div>

answer:
<div class="solution">For $-1 \leq x \leq 2$<br/>$f(x)=3 x^{2}+12 x-1$<br/>$f^{\prime}(x)=6 x+12$<br/>If we take any point in the interval $[-1,2]$ then<br/>$f^{\prime}(1)=6 \times 1+12=18&gt;0$<br/>$\Rightarrow f(x)$ is increasing in the interval $[-1,2]$.<br/>For $2   &lt; x \leq 3$<br/>$f(x)=37-x$<br/>$f^{\prime}(x)=-1 &lt; 0$<br/>$\Rightarrow f(x)$ is decreasing in the interval $(2,3]$</div>


title: f-x-cos-x-is-monotonic-decreasing-under-which-one-of-the-following-conditions
slug: f-x-cos-x-is-monotonic-decreasing-under-which-one-of-the-following-conditions-30462
tags: ['Mathematics', 'Application of Derivatives', 'NDA', 'NDA 2008 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">$f(x)=\cos x$ is monotonic decreasing under which one of the following conditions? $\quad$</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\quad 0   &lt; x &lt; \pi$</span> </div>

answer:
<div class="solution">Given, $f(x)=\cos x$,<br/>$\Rightarrow f^{\prime}(x)=-\sin x$<br/>Now $f^{\prime}(x)=0$<br/>$\Rightarrow-\sin x=0$<br/>$\Rightarrow \sin x=\sin (0)$<br/>$\Rightarrow x=n \pi$<br/>Clearly, $f^{\prime}(x)   &lt; 0$, when $0 &lt; x &lt; _{x}$<br/>Hence $f(x)$ is decreasing when $0 &lt; x &lt; \pi$</div>


title: f-xy-f-x-f-y-is-true-for-all
slug: f-xy-f-x-f-y-is-true-for-all-73377
tags: ['Mathematics', 'Functions', 'NDA', 'NDA 2015 (Phase 2)']
source_db: MarksBatch1_P2.db
question:
<div class="question">$\mathrm{f}(\mathrm{xy})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})$ is true for all</div>

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

answer:
<div class="solution">Let $f(x)=\log x$<br/>$\therefore f(y)=\log y$<br/>$\&amp; f(x y)=\log (x y)=\log x+\log y$<br/>$\Rightarrow \mathrm{f}(\mathrm{xy})=\mathrm{f}(\mathrm{x})+\mathrm{f}(\mathrm{y})$</div>


title: fertilization-membrane-in-ovum-prevents
slug: fertilization-membrane-in-ovum-prevents-15804
question: <div class="question">Fertilization membrane in ovum prevents</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Meiosis-II</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Polyspermy</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Meiosis-I</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Phase of Multiplication</span> </li> </ul>

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

answer:
<div class="solution">Process of Fertilisation :<br/><br/>I. Entry of a sperm induces changes in the zona pellucida layer of the ovum and blocks the entry of other sperms preventing polyspermy.<br/><br/>II. Acrosomal secretions (including enzymes) help the sperm to enter into the cytoplasm of the ovum through the zona pellucida.<br/><br/>III. Secondary oocyte undergoes completion of meiosis -II, resulting in formation of a ovum (n) and a Second polar body (n).<br/><br/>IV. Nuclei of both gametes fuse to form a zygote.</div>


tags: ['Physics', 'Oscillations']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
figure-a-shows-a-spring-of-force-constant-k-clamped-rigidly-at-one-end-and-a-mass-m-attached-to-its-free-end-a-force-f-applied-at-the-free-end-stretch

slug:
figure-a-shows-a-spring-of-force-constant-k-clamped-rigidly-at-one-end-and-a-mass-m-attached-to-its-free-end-a-force-f-applied-at-the-free-end-stretch-73529

question:
<div class="question">Figure (a) shows a spring of force constant $k$ clamped rigidly at one end and a mass $m$ attached to its free end. A force $\boldsymbol{F}$ applied at the free end stretches the spring. Figure (b) shows the same spring with both ends free and attached to a mass $m$ at either end. Each end of the spring in Fig. (b) is stretched by the same force $F$.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/zv46zqa4t3PApbO43KeU2w9QeV4UyExr8XQH97KqBv0.original.fullsize.png"/><br/><br/>(a) What is the maximum extension of the spring in the two cases?<br/>(b) If the mass in Fig. (a) and the two masses in Fig.<br/>(b) are released, what is the peried of oscillation in each case?</div>

answer:
<div class="solution">(a) Let $y$ be the maximum extension produced in the spring in Fig. (a)<br/>Then $F=k y$ (in magnitude) $\therefore y=\frac{F}{k}$<br/>In Fig. (b), the force on one mass acts as the force of reaction due to the force on the other mass.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/I81iqS_wFndASzzxFwDo5Aa9ORTjb1XGBUfxChqbScg.original.fullsize.png"/><br/><br/>Therefore, each mass behaves as if it is fixed with respect to the other.<br/>Therefore, $F=k y \Rightarrow y=\frac{F}{k}$<br/>(b) In Fig. (a), $F=-k y$<br/>$$<br/>\begin{aligned}<br/>&amp;\Rightarrow m a=-k y \Rightarrow a=-\frac{k}{m} y \\<br/>&amp;\therefore \omega^2=\frac{k}{m} \text { i.e., } \omega=\sqrt{\frac{k}{m}}\left[\because a=\omega^2 y\right]<br/>\end{aligned}<br/>$$<br/>Therefore, period $T=\frac{2 \pi}{\omega}=2 \pi \sqrt{\frac{m}{k}}$<br/>In Fig. (b), we may consider that the centre of the system is $\mathrm{O}$ and there are two springs each of length $\frac{l}{2}$ attached to the two masses, each $m$, so that $K^{\prime}$ is the spring factor of each of the springs.<br/>Then, $K^{\prime}=2 k$<br/>$$<br/>\therefore T=2 \pi \sqrt{\frac{m}{K^{\prime}}}=2 \pi \sqrt{\frac{m}{2 k}}<br/>$$</div>


tags: ['Physics', 'Current Electricity']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
figure-shows-a-potentiometer-circuit-for-comparison-of-two-resistances-the-balance-point-with-a-standard-resistor-r-100-is-found-to-be-583-cm-while-th

slug:
figure-shows-a-potentiometer-circuit-for-comparison-of-two-resistances-the-balance-point-with-a-standard-resistor-r-100-is-found-to-be-583-cm-while-th-42893

question:
<div class="question">Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor $\mathrm{R}=10.0 \Omega$ is found to be $58.3 \mathrm{~cm}$, while that with the unknown resistance $X$ is $68.5 \mathrm{~cm}$. Determine the value of $X$. What might you do if you failed to find a balance point with the given cell of emf $E$ ?<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/XsZrZbiOelgII-LiIkX_pmxV1ciS-tVSHlG4ODVTdLE.original.fullsize.png"/><br/></div>

answer:
<div class="solution">In this case, $\frac{R}{X}=\frac{l_1}{l_2}$<br/>or $\quad X=R \frac{l_2}{l_1}=\frac{10 \times 68.5}{58.3}=11.75 \Omega$<br/>In case of failure, a high resistance is put in series with the cell $\mathrm{E}$. This will reduce current through $\mathrm{R}$ and $\mathrm{X}$ and potential difference across them will be reduced to values lower than the potential difference across wire $\mathrm{AB}$.</div>


tags: ['Physics', 'Current Electricity']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
figure-shows-a-potentiometer-with-a-cell-of-20-v-and-internal-resistance-040-maintaining-a-potential-drop-across-the-resistor-wire-ab-a-standard-cell-

slug:
figure-shows-a-potentiometer-with-a-cell-of-20-v-and-internal-resistance-040-maintaining-a-potential-drop-across-the-resistor-wire-ab-a-standard-cell-22664

question:
<div class="question">Figure shows a potentiometer with a cell of $2.0 \mathrm{~V}$ and internal resistance $0.40 \Omega$ maintaining a potential drop across the resistor wire AB. A standard cell which maintains a constant emf of $1.02 \mathrm{~V}$ (for very moderate currents upto a few $\mathrm{mA}$ ) gives a balance point at $67.3$ cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance<br/>of $600 \mathrm{k} \Omega$ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown emf $E$ and the balance point found similarly, turns out to be at $82.3 \mathrm{~cm}$ length of the wire.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/lSrrrKY-WT248mp-3R-QyrPYaU_kmDjl60jFxBq_-MA.original.fullsize.png"/><br/><br/>(a) What is the value of $E$ ?<br/>(b) What purpose does the high resistance of $600 \mathrm{k} \Omega$ have?<br/>(c) Is the balance point affected by this high resistance?<br/>(d) Is the balance point affected by the internal resistance of the driver cell?<br/>(e) Would the method work in the above situation if the driver cell of the potentiometer had an emf of $1.0 \mathrm{~V}$ instead of $2.0 \mathrm{~V}$ ?<br/>(f) Would the circuit work well for determining an extremely small emf, say of the order of a few mV (such as the typical emf of the thermo-couple)? If not, how will you modify the circuit?</div>

answer:
<div class="solution">(a) By formula, $\frac{\mathrm{E}}{\mathrm{E}_{\text {standard }}}=\frac{l}{l_{\text {standard }}}$ $\Rightarrow \mathrm{E}=\frac{l \times \mathrm{E}_{\text {standard }}}{l_{\text {standard }}}=\frac{82.3 \times 1.02}{67.3}=1.2474 \mathrm{~V}$<br/>(b) To reduce current through the galvanometer when the movable contact is far from the balance point.<br/>(c) No.<br/>(d) No.<br/>(e) No. If E is greater than the emf of the drive cell of the potentiometer, there will be no balance point on the wire $A B$.<br/>(f) The circuit, as it is, would be unsuitable because the balance point (for $\varepsilon$ of the order a few $\mathrm{mV}$ ) will be very close to the end $\mathrm{A}$ and the percentage error in measurement will be very large. The circuit is modified by putting a suitable resistor $\mathrm{R}$ in series with the wire $\mathrm{AB}$ so that potential drop across $\mathrm{AB}$ is only slightly greater than the emf to be measured. Then the balance point will be at larger length of the wire and the percentage error will be much smaller.</div>


tags: ['Physics', 'Wave Optics']
source_db: MarksBatch1_P2.db
title:
figure-shows-a-standard-two-slit-arrangement-witn-slits-s-1-s-2-p-1-p-2-are-the-two-minima-points-on-either-side-of-p-figure-at-p-2-on-the-screen-ther

slug:
figure-shows-a-standard-two-slit-arrangement-witn-slits-s-1-s-2-p-1-p-2-are-the-two-minima-points-on-either-side-of-p-figure-at-p-2-on-the-screen-ther-11639

question:
<div class="question">Figure shows a standard two slit arrangement witn slits $\mathrm{S}_1, \mathrm{~S}_2, \mathrm{P}_1, \mathrm{P}_2$ are the two minima points on either side of $\mathrm{P}$ (figure).<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/id8Ol81SNGIP4hTTDVIMPF4PkZGlxexvSwmyPFtzG6c.original.fullsize.png"/><br/><br/>At $\mathrm{P}_2$ on the screen, there is a hole and behind $\mathrm{P}_2$ is a second 2-slit arrangement with slits $\mathrm{S}_3, \mathrm{~S}_4$ and a second screen behind them.</div>

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

answer:
<div class="solution">Consider the given figure there is a hole at point $\mathbf{P}_2$. By Huygen's principle, wave will propagates from the sources $S_1$ and $S_2$. Each point on the screen will acts as sources of secondary wavelets. Wavefront starting from $\mathrm{P}_2$ reaches at $\mathrm{S}_3$ and $\mathrm{S}_4$ which will again act as two monochromatic or coherent sources.<br/>Hence, there will be always a regular two slit pattern on the second screen.</div>


tags: ['Biology', 'Human Health and Diseases', 'NEET']
source_db: MarksBatch1_P2.db
title:
fill-in-the-blanks-i-the-a-lymphoid-organs-provide-the-sites-for-interaction-of-lymphocytes-with-antigen-which-then-proliferate-to-become-b-ii-the-thy

slug:
fill-in-the-blanks-i-the-a-lymphoid-organs-provide-the-sites-for-interaction-of-lymphocytes-with-antigen-which-then-proliferate-to-become-b-ii-the-thy-30722

question:
<div class="question">Fill in the blanks:<br/> <br/>
(i) The <math><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">a</mi><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo></math> lymphoid organs provide the sites for interaction of lymphocytes with antigen, which then proliferate to become <math><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">b</mi><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mo>_.</mo></math><br/> <br/>
(ii) The thymus is a lobed organ located near the heart and beneath the <math><mo>_</mo><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">c</mi><mo>_</mo><mo>_</mo><mo>_</mo><mo>_.</mo></math><br/> <br/>
(iii) Spleen has a large reservoir of <math><mo>_</mo><mo>_</mo><mo>_</mo><mi mathvariant="normal">d</mi><mo>_</mo><mo>_</mo><mo>_.</mo></math></div>

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

answer:
<div class="solution">Lymphoid organs can be primary or secondary. Primary organs are those organs that form and mature the lymphocytes. These are bone marrow and thymus. Bone marrow forms B and T lymphocytes while thymus helps in maturing T lymphocytes.Secondary organs provide the sites for interaction of formed lymphocytes and thus these form effector cells. These organs are spleen, lymph nodes, peyer's patches etc. Thymus is also known as 'throne of immunity' and is located in the chest region located near the heart and beneath the breastbone. Spleen is known as the graveyard of red blood cells and thus is a reservoir of it.</div>


tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P2.db
title:
find-beat-frequency-if-the-motion-of-two-particles-is-given-by-y-1-025-sin-310-t-y-2-025-sin-316-t-1

slug:
find-beat-frequency-if-the-motion-of-two-particles-is-given-by-y-1-025-sin-310-t-y-2-025-sin-316-t-1-97969

question:
<div class="question">Find beat frequency if the motion of two particles is given by<br/> <math><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>310</mn><mi>t</mi></mrow></mfenced></mrow></mrow></math><br/> <math><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>316</mn><mi>t</mi></mrow></mfenced></mrow></mrow></math></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</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><mfrac><mrow><mn>3</mn></mrow><mrow><mi>Ï</mi></mrow></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><mfrac><mrow><mn>6</mn></mrow><mrow><mi>Ï</mi></mrow></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"><mn>6</mn></math></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>3</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac></math></span> </div>

answer:
<div class="solution">The given equations of waves be written as<br/><br/><math><msub><mrow><mi mathvariant="normal">y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mn>310</mn><mi mathvariant="normal">t</mi></mrow></mfenced></mrow></mrow><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mrow><mi mathvariant="normal">i</mi></mrow></mfenced></math><br/><br/>And <math><msub><mrow><mi mathvariant="normal">y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mn>316</mn><mi mathvariant="normal">t</mi></mrow></mfenced></mrow></mrow><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi></mrow></mfenced></math><br/><br/>Comparing Eqs. (i) and (ii) with the standard wave equation, written as<br/><br/><math><mi mathvariant="normal">y</mi><mo>=</mo><mi mathvariant="normal">a</mi><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>⁡</mo><mrow><mfenced separators="|"><mrow><mi mathvariant="normal">ω</mi><mi mathvariant="normal">t</mi></mrow></mfenced></mrow></mrow><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi></mrow></mfenced></math><br/><br/>We have, <math><msub><mrow><mi mathvariant="normal">ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>310</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⟹</mo><msub><mi>ν</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>310</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo> </mo><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math><br/><br/>And <math><msub><mrow><mi mathvariant="normal">ω</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>316</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⟹</mo><msub><mi>ν</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>316</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo> </mo><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math><br/><br/>Hence, beat frequency=<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>ν</mi><mn>2</mn></msub><mo>-</mo><msub><mi>ν</mi><mn>1</mn></msub></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>316</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo>-</mo><mfrac><mn>310</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mi mathvariant="normal">π</mi></mfrac><mi mathvariant="normal"> </mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math></div>


title: find-beat-frequency-if-the-motion-of-two-particles-is-given-by-y-1-025-sin-310-t-y-2-025-sin-316-t
tags: ['Physics', 'Waves and Sound', 'NEET']
source_db: MarksBatch1_P2.db
slug:
find-beat-frequency-if-the-motion-of-two-particles-is-given-by-y-1-025-sin-310-t-y-2-025-sin-316-t-88522

question:
<div class="question">Find beat frequency if the motion of two particles is given by<br/> <math><msub><mrow><mi>y</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>310</mn><mi>t</mi></mrow></mfenced></mrow></mrow></math><br/> <math><msub><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>0.25</mn><mrow><mrow><mi mathvariant="normal">sin</mi></mrow><mo>â¡</mo><mrow><mfenced separators="|"><mrow><mn>316</mn><mi>t</mi></mrow></mfenced></mrow></mrow></math></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</mn></math></span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data"><math><mfrac><mrow><mn>3</mn></mrow><mrow><mi>Ï</mi></mrow></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><mfrac><mrow><mn>6</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac></math></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">6</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><math><mfrac><mrow><mn>3</mn></mrow><mrow><mi>Ï</mi></mrow></mfrac></math></span> </div>

answer:
<div class="solution">The given equations of waves be written as<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>y</mi><mn>1</mn></msub><mo>=</mo><mn>0.25</mn><mi>sin</mi><mo>⁡</mo><mfenced separators="|"><mrow><mn>310</mn><mi>t</mi></mrow></mfenced><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mi mathvariant="normal">i</mi></mfenced></math><br/><br/>And <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>y</mi><mn>2</mn></msub><mo>=</mo><mn>0.25</mn><mi>sin</mi><mo>⁡</mo><mfenced separators="|"><mrow><mn>316</mn><mi>t</mi></mrow></mfenced><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi></mrow></mfenced></math><br/><br/>Comparing Eqs. (i) and (ii) with the standard wave equation, written as<br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi mathvariant="normal">a</mi><mi>sin</mi><mo>⁡</mo><mfenced separators="|"><mrow><mi mathvariant="normal">ω</mi><mi>t</mi></mrow></mfenced><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mi mathvariant="normal"> </mi><mo>…</mo><mfenced separators="|"><mrow><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">i</mi></mrow></mfenced></math><br/><br/>We have, <math><msub><mrow><mi mathvariant="normal">ω</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>310</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⟹</mo><msub><mi>v</mi><mn>1</mn></msub><mo>=</mo><mfrac><mn>310</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo> </mo><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math><br/><br/>And <math><msub><mrow><mi mathvariant="normal">ω</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>=</mo><mn>316</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>⟹</mo><msub><mi>v</mi><mn>2</mn></msub><mo>=</mo><mfrac><mn>316</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo> </mo><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math><br/><br/>Hence, beat frequency=<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>v</mi><mn>2</mn></msub><mo>-</mo><msub><mi>v</mi><mn>1</mn></msub></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mfrac><mn>316</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo>-</mo><mfrac><mn>310</mn><mrow><mn>2</mn><mi mathvariant="normal">π</mi></mrow></mfrac><mo>=</mo><mfrac><mn>3</mn><mi>π</mi></mfrac><mi mathvariant="normal"> </mi><mi mathvariant="normal">u</mi><mi mathvariant="normal">n</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">t</mi></math></div>


title: find-incorrect-statement-wrt-pollen-grains
slug: find-incorrect-statement-wrt-pollen-grains-37281
question: <div class="question">Find incorrect statement w.r.t. pollen grains.</div>
tags: ['Biology', 'Sexual Reproduction in Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Generally spherical measuring about 25-50 micro meters</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Exineless areas in pollen wall are called germ pore</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">The vegetative cell is bigger, has abundant food reserves and a large irregularly shaped nucleus.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">The generative cell has abundant cytoplasm and an irregular shaped nucleus</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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 generative cell has abundant cytoplasm and an irregular shaped nucleus</span> </div>

answer:
<div class="solution">The generative cell is small and floats in the cytoplasm of the vegetative cell. It is spindle-shaped with dense cytoplasm and a nucleus.</div>


tags: ['Mathematics', 'Vector Algebra', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 2)']
source_db: MarksBatch1_P2.db
title:
find-lambda-if-mathbfa-mathbfb-mathbfc-are-three-noncoplanar-vectors-such-that-leftbeginarrayccc-4-a3-bc-4-a3-b2-c-quad-a4-bc-endarrayright-leftlambda

slug:
find-lambda-if-mathbfa-mathbfb-mathbfc-are-three-noncoplanar-vectors-such-that-leftbeginarrayccc-4-a3-bc-4-a3-b2-c-quad-a4-bc-endarrayright-leftlambda-12499

question:
<div class="question">Find ' \(\lambda\) ' if \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) are three non-coplanar vectors such that<br/>\(\left[\begin{array}{ccc}<br/>4 a+3 b-c &amp; 4 a+3 b+2 c \quad a-4 b-c<br/>\end{array}\right]\)<br/>\(=\left(\lambda^2+\lambda+1\right)\left[\begin{array}{lll}a &amp; b &amp; c\end{array}\right]\)</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(-7,8\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(-7,-6\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(7,-8\)</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">\(-7,-8\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(7,-8\)</span> </div>

answer:
<div class="solution">\(\begin{array}{rlrl}<br/>\left|\begin{array}{ccc}<br/>4 &amp; 3 &amp; -1 \\<br/>4 &amp; 3 &amp; 2 \\<br/>1 &amp; -4 &amp; -1<br/>\end{array}\right|[\bar{a} \bar{b} \bar{c}] &amp; =\left(\lambda^2+\lambda+1\right)[\bar{a} \bar{b} \bar{c}] \\<br/>4(5)-3(-6)-1(-19) &amp; =\lambda^2+\lambda+1 \\<br/>57 &amp; =\lambda^2+\lambda+1 \\<br/>\Rightarrow &amp; &amp; \lambda^2+\lambda-56 &amp; =0 \\<br/>\Rightarrow &amp; &amp; (\lambda-7)(\lambda+8) &amp; =0 \\<br/>\Rightarrow &amp; &amp; \lambda &amp; =7 \text { (or) }-8<br/>\end{array}\)<br/>Hence, option (c) is correct.</div>


tags: ['Mathematics', 'Matrices', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
find-number-of-possible-triplets-alpha-beta-gamma-if-aleftbeginarrayccc0-alpha-alpha-2-beta-beta-beta-gamma-gamma-gammaendarrayright-is-an-orthogonal-

slug:
find-number-of-possible-triplets-alpha-beta-gamma-if-aleftbeginarrayccc0-alpha-alpha-2-beta-beta-beta-gamma-gamma-gammaendarrayright-is-an-orthogonal-24892

question:
<div class="question">Find number of possible triplets \( (\alpha, \beta, \gamma) \),if \( A=\left|\begin{array}{ccc}0 &amp; \alpha &amp; \alpha \\ 2 \beta &amp; \beta &amp; -\beta \\ \gamma &amp; -\gamma &amp; \gamma\end{array}\right| \) is an orthogonal matrix.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</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><li class=""> <span class="option-label">B</span> <span class="option-data">\( 6 \)</span> </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">\( 2 \)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( 8 \)</span> </div>

answer:
<div class="solution"><math><mi>A</mi><msup><mrow><mi>A</mi></mrow><mrow><mi>T</mi></mrow></msup><mo>=</mo><mi>I</mi></math> <br/> <math><mfenced close="|" open="|" separators="|"><mrow><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mi>Î±</mi></mtd><mtd><mi>Î±</mi></mtd></mtr><mtr><mtd><mn>2</mn><mi>Î²</mi></mtd><mtd><mi>Î²</mi></mtd><mtd><mo>-</mo><mi>Î²</mi></mtd></mtr><mtr><mtd><mi>Î³</mi></mtd><mtd><mo>-</mo><mi>Î³</mi></mtd><mtd><mi>Î³</mi></mtd></mtr></mtable></mrow></mfenced><mfenced close="|" open="|" separators="|"><mrow><mtable><mtr><mtd><mn>0</mn></mtd><mtd><mn>2</mn><mi>Î²</mi></mtd><mtd><mi>Î³</mi></mtd></mtr><mtr><mtd><mi>Î±</mi></mtd><mtd><mi>Î²</mi></mtd><mtd><mo>-</mo><mi>Î³</mi></mtd></mtr><mtr><mtd><mi>Î±</mi></mtd><mtd><mo>-</mo><mi>Î²</mi></mtd><mtd><mi>Î³</mi></mtd></mtr></mtable></mrow></mfenced><mo>=</mo><mfenced close="|" open="|" separators="|"><mrow><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></mfenced></math> <br/> <math><mo>â</mo><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Â </mi><mfenced close="|" open="|" separators="|"><mrow><mtable><mtr><mtd><mn>2</mn><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup></mtd><mtd><mi>Î±</mi></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>6</mn><msup><mrow><mi>Î²</mi></mrow><mrow><mn>2</mn></mrow></msup></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>3</mn><msup><mrow><mi>Î³</mi></mrow><mrow><mn>2</mn></mrow></msup></mtd></mtr></mtable></mrow></mfenced><mo>=</mo><mfenced close="|" open="|" separators="|"><mrow><mtable><mtr><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd><mtd><mn>0</mn></mtd></mtr><mtr><mtd><mn>0</mn></mtd><mtd><mn>0</mn></mtd><mtd><mn>1</mn></mtd></mtr></mtable></mrow></mfenced></math> <br/> <math><mo>â</mo><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Â </mi><mn>2</mn><msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>,</mo><mi>Â </mi><mn>6</mn><msup><mrow><mi>Î²</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn><mo>,</mo><mi>Â </mi><mn>3</mn><msup><mrow><mi>Î³</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><mn>1</mn></math> <br/> <math><mo>â´</mo><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Â </mi><mi>Î±</mi><mo>Â±</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>2</mn></msqrt></mrow></mfrac><mo>,</mo><mi>Â </mi><mi>Î²</mi><mo>=</mo><mo>Â±</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>6</mn></msqrt></mrow></mfrac><mo>,</mo><mi>Â </mi><mi>Î³</mi><mo>=</mo><mo>Â±</mo><mfrac><mrow><mn>1</mn></mrow><mrow><msqrt><mn>3</mn></msqrt></mrow></mfrac></math></div>


tags: ['Physics', 'Gravitation', 'AIIMS', 'AIIMS 2012']
source_db: MarksBatch1_P2.db
title:
find-out-the-correct-relation-for-the-dependance-of-change-in-acceleration-due-to-gravity-on-the-angle-at-the-latitude-due-to-rotation-of-earth

slug:
find-out-the-correct-relation-for-the-dependance-of-change-in-acceleration-due-to-gravity-on-the-angle-at-the-latitude-due-to-rotation-of-earth-70106

question:
<div class="question">Find out the correct relation for the dependance of change in acceleration due to gravity on the angle at the latitude, due to rotation of earth</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$d g \propto \cos ^2 \phi$</span> </div>

answer:
<div class="solution">Effective acceleration due to gravity due to rotation earth is given as<br/>$\begin{aligned} &amp; g^{\prime}=g-R \omega^2 \cos ^2 \phi \\ \therefore &amp; \text { Change in acceleration, } d g=R \omega^2 \cos ^2 \phi \\ \therefore &amp; d g \propto \cos ^2 \phi\end{aligned}$</div>


title: find-out-the-correct-statement-1
slug: find-out-the-correct-statement-1-97949
question: <div class="question">Find out the correct statement.</div>
tags: ['Biology', 'Organisms and Populations', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Totally unrelated species could also compete for the same resources.</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Resources need not to be limiting for competition to occur.</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">In interference competition, feed efficiency of one species might be reduced due to the interfering and inhibitory presence of the other species, even if resources are abundant.</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">All are true</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">In some shallow South American lakes, visiting flamingoes and resident fishes compete for the same resource: the food zooplanktons present in the lakes. Resources need not be limiting for competition to occur. In interference competition, the feeding efficiency of one species might be reduced due to the interfering and inhibitory presence of the other species.</div>


tags: ['Biology', 'Biological Classification', 'NEET']
source_db: MarksBatch1_P2.db
title:
find-out-the-incorrect-statements-1-bluegreen-alga-is-a-prokaryotic-cell-2-wbc-is-ameboid-in-shape-3-mycoplasma-is-the-largest-cell-4-microbodies-are-

slug:
find-out-the-incorrect-statements-1-bluegreen-alga-is-a-prokaryotic-cell-2-wbc-is-ameboid-in-shape-3-mycoplasma-is-the-largest-cell-4-microbodies-are-22874

question:
<div class="question">Find out the incorrect statements:<br/> <math><mo>(</mo><mn>1</mn><mo>)</mo></math> Blue-green alga is a prokaryotic cell.<br/> <math><mo>(</mo><mn>2</mn><mo>)</mo></math> WBC is ameboid in shape.<br/> <math><mo>(</mo><mn>3</mn><mo>)</mo></math> Mycoplasma is the largest cell.<br/> <math><mo>(</mo><mn>4</mn><mo>)</mo></math> Microbodies are cell organelles.<br/> <math><mo>(</mo><mn>5</mn><mo>)</mo></math> Prokaryotes do not exhibit a wide variety of shapes.</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">3 and 5 only</span> </div>

answer:
<div class="solution">Mycoplasma is the smallest cell, they are 0.3 microns in diameter. The organization of the prokaryotic cell is fundamentally similar even though prokaryotes exhibits a wide variety of shape and function. The four basic shapes of bacteria are bacilli (rod-like), coccus (spherical), vibrio (comma-shaped) and spirillum (spiral). </div>


title: find-out-the-mismatched-pair
slug: find-out-the-mismatched-pair-24965
question: <div class="question">Find out the MISMATCHED pair.</div>
tags: ['Biology', 'Principles of Inheritance and Variation', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Haemophilia - Sex linked recessive</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Cystic fibrosis - Autosomal dominant</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Down's syndrome - Trisomy 21</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Turner's syndrome - X-linked</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Cystic fibrosis - Autosomal dominant</span> </div>

answer:
<div class="solution">The chromosomal disorder occurs when there is an addition or deletion of the chromosome in the individual. In the case of trisomy of the 21st chromosome causes Down's syndrome. Turner's syndrome is a type of chromosomal disorder occurring due to loss of one X chromosome resulting in the genotype as 44+X or 44+XO. Such females are characterized by stunted height and webbed-neck. They are sterile as ovaries are rudimentary and lack secondary sexual characteristics.<br/><br/>Haemophilia is an X-linked recessive blood disorder. In it, the individual has delayed clotting time for blood which can be fatal. X-lined disorders are inherent disorders due to mutation in the X-chromosome which causes the phenotype to be always expressed in male and in female only in homozygous condition.<br/><br/>Cystic fibrosis is a hereditary genetic autosomal recessive disorder of the respiratory system. It is caused due to mutation in the CFTR gene. This condition occurs in an individual when both the alleles for CFTR are affected.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'NEET']
answer: <div class="solution">Correct Option is : (A)<br/>2.4 Ã 10<sup>2</sup></div>
source_db: MarksBatch1_P2.db
title:
find-out-the-value-of-equilibrium-constant-for-the-following-reaction-at-298-k-2nh-3-g-co-2-g-nh-2-conh-2-aq-h-2-ol-standard-gibbs-energy-change-r-g-a

slug:
find-out-the-value-of-equilibrium-constant-for-the-following-reaction-at-298-k-2nh-3-g-co-2-g-nh-2-conh-2-aq-h-2-ol-standard-gibbs-energy-change-r-g-a-10013

question:
<div class="question">Find out the value of equilibrium constant for the following reaction at 298 K -   2NH<sub>3</sub>(g) + CO<sub>2</sub>(g) â NH<sub>2</sub>CONH<sub>2</sub>(aq) + H<sub>2</sub>O(l)   Standard Gibbs energy change, â<sub>r</sub>G at the given temperature is â13.6 kJ mol<sup>â1</sup>.</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">2.4 Ã 10<sup>2</sup></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">3.6 Ã 10<sup>2</sup></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">1.2 Ã 10<sup>2</sup></span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4.8 Ã 10<sup>2</sup></span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">2.4 Ã 10<sup>2</sup></span> </div>


title: find-out-the-wrongly-matched-pair
slug: find-out-the-wrongly-matched-pair-16696
question: <div class="question">Find out the wrongly matched pair.</div>
tags: ['Chemistry', 'Biomolecules', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Secondary metabolite â Anthocyanin</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Protein – Insulin</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Chitin – Polysaccharide</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">Cellulose – Heteropolymer</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">Cellulose – Heteropolymer</span> </div>

answer:
<div class="solution">Cellulose is the most important structural component of the cell wall of plants. It is a linear polymer of <math> <mrow> <mtext>β</mtext> <mo>-</mo> <mtext>D</mtext> </mrow> </math> glucose units connected through <math> <mrow> <mtext>β</mtext> <mo>-</mo> <mn>1</mn> </mrow> </math>, 4-glycosidic linkage. The linear chains form microfibrillae or bundles of parallel chains held together by hydrogen bonds.</div>


title: find-the-area-of-the-region-bounded-by-the-curves-y-x-2-2-y-x-x-0-and-x-3
slug: find-the-area-of-the-region-bounded-by-the-curves-y-x-2-2-y-x-x-0-and-x-3-88316
tags: ['Mathematics', 'Area Under Curves']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the area of the region bounded by the curves $y=x^2+2, y=x, x=0$ and $x=3$.</div>

answer:
<div class="solution">Equation of the parabola is<br/>$$<br/>y=x^2+2 \text { or } x^2=(y-2)<br/>$$<br/>Its vertrx is $(0,2)$ axis is $y$-axis.<br/>Boundary lines are $\mathrm{y}=\mathrm{x}$, $x=0, x=3$. Graphs of the<br/>curve and lines have been<br/>shown in the figure.<br/>Area of the region $\mathrm{PQRO}$<br/>$=$ Area of the region $\mathrm{OAQR}$ - Area of region $\mathrm{OAP}$<br/>$$<br/>=\int_0^3\left(x^2+2\right) d x-\int_0^3 x d x=\left[\frac{x^3}{3}+2 x\right]_0^3-\left[\frac{x^2}{2}\right]_0^3<br/>$$<br/>$=\left[\left(\frac{27}{3}+6\right)-0\right]-\left(\frac{9}{2}-0\right)=\frac{21}{2}$ sq. units.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/yM6O3vyCDPUHiv1RbNXR2d_Todtc15kyf8wWnYyvf2g.original.fullsize.png"/><br/></div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-9-y-2-27-x-2-1

slug:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-9-y-2-27-x-2-1-32927

question:
<div class="question">Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola<br/>$\frac{y^2}{9}-\frac{x^2}{27}=1$</div>

answer:
<div class="solution">Comparing the equation $\frac{y^2}{9}-\frac{x^2}{27}=1$ with the standard equation.<br/>we have, $a=3, b=3 \sqrt{3}$<br/>and $c=\sqrt{a^2+b^2}=\sqrt{9+27}=\sqrt{36}=6$<br/>Therefore, the coordinates of the foci are $(0, \pm 6)$ and that of vertices are $(0, \pm 3)$. Also, the eccentricity $e=\frac{c}{a}=\frac{5}{4}$ and the length of latus rectum $=\frac{2 b^2}{a}=\frac{2(3 \sqrt{3})^2}{3}=\frac{54}{3}=18$ units</div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-16-x-2-9-y-2-1

slug:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-16-x-2-9-y-2-1-36782

question:
<div class="question">Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbola<br/>$\frac{x^2}{16}-\frac{y^2}{9}=1$</div>

answer:
<div class="solution">Comparing the equation $\frac{x^2}{16}-\frac{y^2}{9}=1$ with the standard equation $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, we have, $a=4, b=3$ and $c=\sqrt{a^2+b^2}=\sqrt{16+9}=\sqrt{25}=5$ Therefore, the coordinates of the foci are $(\pm 5,0)$ and that of vertices are $(\pm 4,0)$.<br/>Also, the eccentricity $e=\frac{c}{a}=\frac{5}{4}$ and the length of latus rectum $=\frac{2 b^2}{a}=\frac{2(3)^2}{4}=\frac{9}{2}$ units.</div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-49-y-2-16-x-2-784

slug:
find-the-coordinates-of-the-foci-and-the-vertices-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-hyperbola-49-y-2-16-x-2-784-39222

question:
<div class="question">Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola<br/>$49 y^2-16 x^2=784$</div>

answer:
<div class="solution">Dividing the equation by 784 on both sides, we have<br/>$\frac{49 y^2}{a}-\frac{16 x^2}{784}=1 \Rightarrow \frac{y^2}{16}-\frac{x^2}{49}=1$<br/>Comparing the equation with the standard equation $\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$, we find that $a=4, b=7$ and $c=\sqrt{a^2+b^2}=\sqrt{16+49}=\sqrt{65}$<br/>Therefore the coordinates of the foci are $(0, \pm \sqrt{65})$ and that of vertices are $(0, \pm 4)$. Also the eccentricity $e=\frac{c}{a}=\frac{\sqrt{65}}{4}$ and the length of latus rectum is $\frac{2 b^2}{a}=\frac{2(7)^2}{4}=\frac{49}{2}$ units.</div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-1

slug:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-1-67730

question:
<div class="question">Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.<br/>$36 x^2+4 y^2=144$</div>

answer:
<div class="solution">The given equation of the ellipse can be written if standard form as<br/>$\frac{36 x^2}{144}+\frac{4 y^2}{144}=1 \text { or } \frac{x^2}{4}+\frac{y^2}{36}=1$<br/>Since the denominator of $x^2 &lt; $ denominator of $y^2$, the major axis is along the $y$-axis. Comparing the given equation with the standard equation<br/>$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1,$<br/>we have $b=2$ and $a=6$.<br/>Also, $c=\sqrt{a^2-b^2}=\sqrt{36-4}=\sqrt{32}=4 \sqrt{2}$<br/>and $e=\frac{c}{a}=\frac{\sqrt{34}}{6}=\frac{4 \sqrt{2}}{6}=\frac{2 \sqrt{2}}{3}$<br/>Hence, the foci, are $(0,4 \sqrt{2})$ and $(0,-4 \sqrt{2})$. Vertices, are $(0,6)$ and $(0,-6)$; the length of the major axis, $2 a$ is 12 units, the length of the minor axis, $2 b$ is 4 units and the eccentricity of the ellipse, $e$ is $\frac{2 \sqrt{2}}{3}$.<br/>The length of latus rectum,<br/>$\frac{2 b^2}{a}$ is $\frac{2\left(2^2\right)}{6}=\frac{4}{3}$ units.</div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-3

slug:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-3-42821

question:
<div class="question">Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.<br/>$4 x^2+9 y^2=36$</div>

answer:
<div class="solution">The given equation of the ellipse can be written in standard form as<br/>$\frac{4 x^2}{36}+\frac{9 y^2}{36}=\frac{36}{36} \Rightarrow \frac{x^2}{9}+\frac{y^2}{4}=1$<br/>Since the denominator of $x^2&gt;$ denominator of $y^2$, the major axis is along the $x$-axis. Comparing the given equation with the standard equation<br/>$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$<br/>We have $a=3$ and $b=2$.<br/>Also, $c=\sqrt{a^2-b^2}=\sqrt{9-4}=\sqrt{5}$<br/>and $e=\frac{c}{a}=\frac{\sqrt{5}}{3}$<br/>Hence, the foci, are $(\sqrt{5}, 0)$ and $(-\sqrt{5}, 0)$. vertices, are $(3,0)$ and $(-3,0)$; the length of the major axis, $2 a$ is 6 units, the length of the minor axis, $2 b$ is 4 units and the eccentricity of the ellipse, $e$ is $\frac{\sqrt{5}}{3}$.<br/>The length of latus rectum<br/>$=\frac{2 b^2}{a}=\frac{2\left(2^2\right)}{3}=\frac{8}{3} \text { units. }$</div>


tags: ['Mathematics', 'Conic Sections']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-7

slug:
find-the-coordinates-of-the-foci-the-vertices-the-length-of-major-axis-the-minor-axis-the-eccentricity-and-the-length-of-the-latus-rectum-of-the-ellip-7-16738

question:
<div class="question">Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.<br/>$\frac{x^2}{4}+\frac{y^2}{25}=1$</div>

answer:
<div class="solution">Since the denominator of $y^2$ is larger than the denominator of $x^2$, the major axis is along the $y$-axis. Comparing the given equation with the standard equation<br/>$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$<br/>We have $b=2$ and $a=5$<br/>Also $c=\sqrt{a^2-b^2}=\sqrt{25-4}=\sqrt{21}$ and $e=\frac{c}{a}=\frac{\sqrt{21}}{5}$<br/>Hence, the foci, $(0, c)$ and $(0,-c)$ are $(0, \sqrt{21})$ and $(0,-\sqrt{21})$; the vertices are $(0,5)$ and $(0,-5)$; length of the major axis, $2 a$ is 10 units, the length of the minor axis, $2 b$ is 4 units and the eccentricity of the ellipse, $e$ is $\frac{\sqrt{21}}{5}$. The length of latus rectum $=\frac{2 b^2}{a}=\frac{8}{5}$ units.</div>


title: find-the-current-through-the-primary-coil-p-of-the-transformer-shown-below
slug: find-the-current-through-the-primary-coil-p-of-the-transformer-shown-below-44541
tags: ['Physics', 'Alternating Current', 'AP EAMCET', 'AP EAMCET 2020 (21 Sep Shift 1)']
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the current through the primary coil \((P)\) of the transformer shown below.<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/lS2yZ7PZy3gUyO5xGrdhwjWfBBYq3mA-tzmdmDoqgUw.original.fullsize.png"/><br/></div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">\(0.08 \mathrm{~A}\)</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">\(0.04 \mathrm{~A}\)</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">\(0.02 \mathrm{~A}\)</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><li class=""> <span class="option-label">D</span> <span class="option-data">\(0.01 \mathrm{~A}\)</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\(0.02 \mathrm{~A}\)</span> </div>

answer:
<div class="solution">The given situation is shown in the figure<br/><img src="https://cdn-question-pool.getmarks.app/pyq/ap_eamcet/Ad7FywoYIPxP76oI0Q0hPgtYCoPewO2OLPL9dRtNRLA.original.fullsize.png"/><br/><br/>For the given transformer,<br/>\(\begin{aligned}<br/>&amp; V_p=230 \mathrm{~V} \\<br/>&amp; V_S=23 \mathrm{~V} \\<br/>&amp; R_S=115 \Omega<br/>\end{aligned}\)<br/>Currrent in secondary coil,<br/>\(I_S=\frac{V_S}{R_S}=\frac{23}{115}=0.2 \mathrm{~A}\)<br/>We know that, in a transformer<br/>\(\begin{aligned}<br/>\frac{V_S}{V_P} &amp; =\frac{I_P}{I_S} \\<br/>\Rightarrow \quad &amp; I_P=\frac{V_S I_S}{V_P}=\frac{23 \times 0.2}{230}=0.02 \mathrm{~A}<br/>\end{aligned}\)</div>


tags: ['Mathematics', 'Parabola', 'AP EAMCET', 'AP EAMCET 2021 (19 Aug Shift 2)']
source_db: MarksBatch1_P2.db
title:
find-the-equation-of-the-parabola-which-passes-through-6-2-has-its-vertex-at-the-origin-and-its-axis-along-the-y-axis

slug:
find-the-equation-of-the-parabola-which-passes-through-6-2-has-its-vertex-at-the-origin-and-its-axis-along-the-y-axis-79418

question:
<div class="question">Find the equation of the parabola which passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>)</mo></math>, has its vertex at the origin and its axis along the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo></math>axis.</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>y</mi><mn>2</mn></msup><mo>=</mo><mn>18</mn><mi>x</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"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mn>18</mn><mi>y</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>y</mi><mn>2</mn></msup><mo>=</mo><mo>−</mo><mn>18</mn><mi>x</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"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>−</mo><mn>18</mn><mi>y</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"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>−</mo><mn>18</mn><mi>y</mi></math></span> </div>

answer:
<div class="solution"><p>As given, the vertex of the parabola is origin and it's axis is along the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo></math>axis,</p><p>So, the standard equation of the parabola with given conditions is, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>4</mn><mi>a</mi><mi>y</mi><mo> </mo><mo> </mo><mo>.</mo><mo>.</mo><mo>.</mo><mfenced><mn>1</mn></mfenced></math>, as it passes through <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>6</mn><mo>,</mo><mo> </mo><mo>-</mo><mn>2</mn></mrow></mfenced></math></p><p>Hence, <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>4</mn><mi>a</mi><mi>y</mi><mo> </mo><mo>⇒</mo><mo> </mo><msup><mfenced><mn>6</mn></mfenced><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>4</mn><mo>×</mo><mi>a</mi><mo>×</mo><mfenced><mrow><mo>-</mo><mn>2</mn></mrow></mfenced><mo> </mo><mo>⇒</mo><mo> </mo><mi>a</mi><mo>=</mo><mfrac><mn>36</mn><mn>8</mn></mfrac><mo>=</mo><mfrac><mn>9</mn><mn>2</mn></mfrac></math></p><p>So, substituting the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> in equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mn>1</mn></mfenced></math></p><p>The equation is <math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>2</mn></msup><mo>=</mo><mo>-</mo><mn>18</mn><mi>y</mi></math></p></div>


title: find-the-incorrect-statement-about-human-reproduction
slug: find-the-incorrect-statement-about-human-reproduction-86137
question: <div class="question">Find the INCORRECT statement about human reproduction.</div>
tags: ['Biology', 'Human Reproduction', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Hormonal contraceptives are effective with lesser side effects and well accepted by females</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">Primary oocyte completes meiosis-I when sperm enters the cytoplasm of the primary oocyte</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">Spermatogenesis and oogenesis require different temperature</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Spermatogenesis takes place in seminiferous tubules of testes</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">Primary oocyte completes meiosis-I when sperm enters the cytoplasm of the primary oocyte</span> </div>

answer:
<div class="solution">The primary oocyte completes the first reduction division in the tertiary follicle and results in the formation of the secondary oocyte. The completion of the meiotic division in the secondary oocyte takes place when the sperm enters the cytoplasm of the ovum. The second meiotic division which is unequal results in the formation of a second polar body and an ootid(haploid ovum).</div>


title: find-the-mean-and-standard-deviation-for-the-following-data-1
slug: find-the-mean-and-standard-deviation-for-the-following-data-1-98804
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the mean and standard deviation for the following data:<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/VuMnWQekx1PXeJ2m6q_JDhpF3yStYMPLrDqpVGesPdE.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Calculation for Standard Deviation<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/BO2ZKfVmU7BzQYnIcv02cCWn_X2NH69S0g1fMkEsN3s.original.fullsize.png"/><br/><br/>Mean $=A+\frac{\Sigma f_i d_i}{N}=98+\frac{44}{22}=100$<br/>Standard Deviation $=\sqrt{\frac{\Sigma f_i d_i^2}{N}-\left(\frac{\Sigma f_i d_i}{N}\right)^2}$<br/>$\begin{aligned}<br/>&amp;=\sqrt{\frac{728}{22}-\left(\frac{44}{22}\right)^2}=\sqrt{33.0909-4} \\<br/>&amp;=\sqrt{29.0909}=5.09<br/>\end{aligned}$<br/>Hence $\bar{x}=100$, S.D. $=5.09$.</div>


title: find-the-mean-and-standard-deviation-for-the-following-data
slug: find-the-mean-and-standard-deviation-for-the-following-data-90724
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the mean and standard deviation for the following data :<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/YAJU-DIHo4DshDTq1Td8WkaCsXfOhBfez1f8oORrREs.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Calculation for Mean and Standard Deviation<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/L4IBkgGFQPY0DZDzndM-gMq9l3ZgJok115UP7QSBrSc.original.fullsize.png"/><br/><br/>$\text { Mean }=\frac{\Sigma f_i x_i}{\Sigma f_i}=\frac{760}{40}=19$<br/>$\begin{aligned}<br/>\text { S.D. } &amp;=\sqrt{\frac{\Sigma f_i x_i^2}{\Sigma f_i}-\left(\frac{\Sigma f_i x_i}{\Sigma f_i}\right)^2}=\sqrt{\frac{16176}{40}-\left(\frac{760}{40}\right)^2} \\<br/>&amp;=\sqrt{404.4-361}=\sqrt{43.4}=6.59 .<br/>\end{aligned}$<br/>Hence, Mean $=19$, S.D. $=6.59$.</div>


title: find-the-mean-and-standard-deviation-using-shortcut-method
slug: find-the-mean-and-standard-deviation-using-shortcut-method-24530
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the mean and standard deviation using shortcut method<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/86w4-PBaE9FuMbS9xbmju8_sUyam8N81NweTsIBI_RE.original.fullsize.png"/><br/></div>

answer:
<div class="solution">Let $y_i=\frac{x_i-\mathrm{A}}{i}=\frac{x_i-64}{1}$<br/>$[\because i=1$ and $\mathrm{A}$ is assumed to be 64$]$<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/7GQY8z-0YoiBwJMubeLjSJiUM39L0hiwPP_xa9AA47s.original.fullsize.png"/><br/><br/>$\operatorname{Mean} \bar{x}=\mathrm{A}+i \bar{y}=64+\frac{\sum f_i y_i}{\sum f_i}=64$<br/>Variance, $\sigma^2=\frac{1}{\sum f_i}\left[\sum f_i y_i^2-n \bar{y}^2\right]$<br/>$=\frac{1}{100}[286]=2.86$<br/>$\therefore \quad \sigma=\sqrt{2.86}=1.69$</div>


title: find-the-mean-variance-and-standard-deviation-using-short-cut-method
slug: find-the-mean-variance-and-standard-deviation-using-short-cut-method-62332
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the mean, variance and standard deviation using short cut method.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/b_qBdNb5s8bT8NvMV0IshRO9ZwF7LePEaaVIa2NVPbY.original.fullsize.png"/><br/></div>

answer:
<div class="solution"><img src="https://cdn-question-pool.getmarks.app/modules/cbse/ZH7lpU80IcKBcXF3BQ37mempSQ2cfayQnu-cms89F44.original.fullsize.png"/><br/><br/>$\begin{aligned} y_i &amp;=\frac{x_i-92.5}{5} \quad \because h=5, A=92.5 \\ \therefore \bar{x} &amp;=A+\frac{\sum f_i y_i}{\sum f_i} \times h \\ &amp;=92.5+\frac{6}{60} \times 5=93 \end{aligned}$<br/>$\begin{aligned}<br/>&amp;\text { Variance }=\sigma^2=\frac{h^2}{N^2}\left[N \sum f_i y_i^2-\left(\sum f_i y_i\right)^2\right] \\<br/>&amp;=\frac{25}{3600}\left[60 \times 254-(6)^2\right]=105.58<br/>\end{aligned}$<br/>Standard deviation $\sigma=\sqrt{105.58}=10.27$</div>


title: find-the-standard-deviation-of-the-first-n-natural-numbers
slug: find-the-standard-deviation-of-the-first-n-natural-numbers-70686
question: <div class="question">Find the standard deviation of the first $n$ natural numbers.</div>
tags: ['Mathematics', 'Statistics']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
answer:
<div class="solution">We have $x=\mathrm{i}$, where $\mathrm{i}=1,2, \ldots ., \mathrm{n}$. Let $x$ be the mean and $\sigma$ be the S.D. Then,<br/>$\overline{\mathrm{x}}=\frac{1}{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}=\frac{1}{\mathrm{n}} \sum_{\mathrm{i}-1}^{\mathrm{n}}$ (i)<br/>$=\frac{1}{n}(1+2+3+\ldots .+n)=\frac{n(n+1)}{2 n}=\frac{n+1}{2}$<br/>$=$ Again, variance $\sigma^2=\frac{1}{n}\left(\sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}^2\right)-\left(\frac{1}{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{n}} \mathrm{x}_{\mathrm{i}}\right)^2$<br/>$=\frac{1}{n}\left(1^2+2^2+\ldots n^2\right)-\left(\frac{n+1}{2}\right)^2$<br/>$=\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{(\mathrm{n})(6)}-\frac{(\mathrm{n}+1)^2}{4}$<br/>$=\frac{(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}-\frac{(\mathrm{n}+1)^2}{4}$<br/>$=\frac{2\left(2 n^2+3 n+1\right)-3\left(n^2+2 n+1\right)}{12}=\frac{n^2-1}{12}$<br/><br/>$$<br/>\begin{aligned}<br/>&amp;\Rightarrow \text { Variance }=\frac{\mathrm{n}^2-1}{12} \\<br/>&amp;\Rightarrow \text { S.D. }=\sqrt{\frac{\mathrm{n}^2-1}{12}}<br/>\end{aligned}<br/>$$</div>


tags: ['Physics', 'Oscillations']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-time-period-of-mass-m-when-displaced-from-its-equilibrium-position-and-then-released-for-the-system-shown-in-figure

slug:
find-the-time-period-of-mass-m-when-displaced-from-its-equilibrium-position-and-then-released-for-the-system-shown-in-figure-79252

question:
<div class="question">Find the time period of mass $M$ when displaced from its equilibrium position and then released for the system shown in figure.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/PVtWT-tJefku8yeFTcKHOYGrZxTkVU9OM9C3nEP7rHo.original.fullsize.png"/><br/></div>

answer:
<div class="solution">When mass $(M)$ is pulled and released then the mass $(M)$ oscillates up-down along with pulley.<br/>In this situation we will neglect gravity because it is constant throughout and will not effect the net restoring force.<br/>Let in the equilibrium position, the spring has extended by an amount $x_0$.<br/><img src="https://cdn-question-pool.getmarks.app/modules/cbse/sIYdGYthH9VdgzcLAfoAhHGOrsDvECiE4s6pdYScXzo.original.fullsize.png"/><br/><br/>Now, if the mass is given a further displacement downwards by an amount $x$. The string and spring both should increase in length by $x$.<br/>But, string is inextensible, hence the spring alone will contribute the total extension $x+x=2 x$, to lower the mass down by $x$ from initial equilibrium mean position $x_0$. So, total extension in spring $h=\left(2 x+x_0\right)$<br/>When pulled downward by $x, T=k\left(x_0+2 x\right)$<br/>The extension and compression of string from initial postion is larger and smaller respectively.<br/>Now force on the mass before bulling (in the $x_0$ extension case)<br/>$$<br/>F=2 T<br/>$$<br/>When no pulling, $T=k x_0$<br/>(where $k$ is spring constant)<br/>$F=2 T \Rightarrow F=2 k x_0$<br/>When the mass is lowered down further by $x$,<br/>$$<br/>F^{\prime}=2 T^{\prime} \quad \because T^{\prime}=k\left(x_0+2 x\right)<br/>$$<br/>So, $F^{\prime}=2 k\left(2 x+x_0\right)$<br/>Restoring force on the system.<br/>$$<br/>F_{\text {restoring }}=-\left[F^{\prime}-F\right]<br/>$$<img src="https://cdn-question-pool.getmarks.app/modules/cbse/1RFxhvnuBhkp4miX8r5mf1phFrNjFgEmXC8nBoRxeRY.original.fullsize.png"/><br/><br/>From Eqs. (i) and (ii), then,<br/>$$<br/>\begin{aligned}<br/>&amp;\begin{aligned}<br/>F_{\text {restoring }} &amp;=-\left[2 k\left(2 x+x_0\right)-2 k x_0\right] \\<br/>&amp;=-\left[2 \times 2 k x+2 k x_0-2 k x_0\right]<br/>\end{aligned} \\<br/>&amp;\begin{aligned}<br/>F_{\text {restoring }} &amp;=-4 k x \\<br/>\text { or } M a &amp;=-4 k x \quad \quad\left(\text { As, } F_{\text {res. }}=m a\right)<br/>\end{aligned}<br/>\end{aligned}<br/>$$<br/>The Acceleration is, $a=-\left(\frac{4 k}{M}\right) x$<br/>$k, M$ being constant.<br/>$$<br/>\therefore a \propto-x<br/>$$<br/>Hence, motion is SHM.<br/>Comparing the above acceleration expression with standard SHM equation $a=-\omega^2 x$, we get<br/>$$<br/>\begin{aligned}<br/>&amp;\omega^2=\frac{+4 k}{M} \Rightarrow \omega=\sqrt{\frac{4 k}{M}} \\<br/>&amp;\therefore \text { Time period } T=\frac{2 \pi}{\omega}=\frac{2 \pi}{\sqrt{\frac{4 k}{M}}} \\<br/>&amp;=2 \pi \sqrt{\frac{M}{4 k}} \\<br/>&amp;T=\pi \sqrt{\frac{M}{k}}<br/>\end{aligned}<br/>$$</div>


title: find-the-value-of-k-if-leftbeginarrayccc-k2-2-k3-3-k4-k4-2-k9-3-k16-k8-2-k27-3-k64-endarrayright0
tags: ['Mathematics', 'Determinants', 'AP EAMCET', 'AP EAMCET 2020 (18 Sep Shift 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">4</span> </div>
source_db: MarksBatch1_P2.db
slug:
find-the-value-of-k-if-leftbeginarrayccc-k2-2-k3-3-k4-k4-2-k9-3-k16-k8-2-k27-3-k64-endarrayright0-18240

question:
<div class="question">Find the value of ' \(k\) ', if<br/>\(\left|\begin{array}{ccc}<br/>k-2 &amp; 2 k-3 &amp; 3 k-4 \\<br/>k-4 &amp; 2 k-9 &amp; 3 k-16 \\<br/>k-8 &amp; 2 k-27 &amp; 3 k-64<br/>\end{array}\right|=0\)</div>

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

answer:
<div class="solution">It is given that,<br/>\(\left|\begin{array}{ccc}<br/>k-2 &amp; 2 k-3 &amp; 3 k-4 \\<br/>k-4 &amp; 2 k-9 &amp; 3 k-16 \\<br/>k-8 &amp; 2 k-27 &amp; 3 k-64<br/>\end{array}\right|=0\)<br/>On applying, \(R_2 \longrightarrow R_2-R_1\) and \(R_3 \longrightarrow R_3-R_1\), we get<br/>\(\begin{aligned}<br/>&amp; \Rightarrow \quad\left|\begin{array}{ccc}<br/>k-2 &amp; 2 k-3 &amp; 3 k-4 \\<br/>-2 &amp; -6 &amp; -12 \\<br/>-6 &amp; -24 &amp; -60<br/>\end{array}\right|=0 \\<br/>&amp; \Rightarrow \quad\left|\begin{array}{ccc}<br/>k-2 &amp; 2 k-3 &amp; 3 k-4 \\<br/>1 &amp; 3 &amp; 6 \\<br/>1 &amp; 4 &amp; 10<br/>\end{array}\right|=0 \\<br/>&amp; \Rightarrow \quad(k-2)[30-24]-(2 k-3)[10-6]+(3 k-4)[4-3]=0 \\<br/>&amp; \Rightarrow \quad 6 k-12-8 k+12+3 k-4=0 \Rightarrow k=4<br/>\end{aligned}\)</div>


title: find-the-value-of-k-in-which-the-system-of-equations-k-x-2-y-5-and-3-x-y-1-has-no-solution
slug: find-the-value-of-k-in-which-the-system-of-equations-k-x-2-y-5-and-3-x-y-1-has-no-solution-99223
tags: ['Mathematics', 'Determinants', 'NDA', 'NDA 2011 (Phase 1)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">6</span> </div>
source_db: MarksBatch1_P2.db
question:
<div class="question">Find the value of $k$ in which the system of equations $k x+2 y=5$ and $3 x+y=1$ has no solution?</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">3</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">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">15</span> </li> </ul>

answer:
<div class="solution">We know,<br/>System of a pair of linear equations in two variables are given as<br/>$a_{1} x+b_{1} y+c_{1}=0$ ...(i)<br/>and $a_{2} x+b_{2} y+c_{2}=0$ ...(ii)<br/>This system has no solution if<br/>$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}} \neq \frac{c_{1}}{c_{2}}$<br/>Now, on comparing given equations with (i) and (ii), we get<br/>$a_{1}=k, a_{2}=3, b_{1}=2, b_{2}=1, c_{1}=-5, c_{2}=-1$<br/>For no solution,<br/>$\frac{k}{3}=\frac{2}{1} \Rightarrow k=6$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'TS EAMCET', 'TS EAMCET 2020 (11 Sep Shift 1)']
source_db: MarksBatch1_P2.db
title:
find-the-value-of-the-equilibrium-constant-k-of-a-reaction-at-300-k-when-standard-gibbs-free-energy-change-is-25-kj-mol-1-consider-r-833-jmol-1-k-1

slug:
find-the-value-of-the-equilibrium-constant-k-of-a-reaction-at-300-k-when-standard-gibbs-free-energy-change-is-25-kj-mol-1-consider-r-833-jmol-1-k-1-56570

question:
<div class="question">Find the value of the equilibrium constant $(K)$ of a reaction at $300 \mathrm{~K}$, when standard Gibbs free energy change is $-25 \mathrm{~kJ} \mathrm{~mol}^{-1}$ ? (Consider $R=8.33 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$e^8$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$e^9$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$e^{10}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$e^{11}$</span> </li> </ul>

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

answer:
<div class="solution">Given,<br/>Gibbs free energy $=-25 \mathrm{~kJ} \mathrm{~mol}^{-1}$<br/>Temperature $=300 \mathrm{~K}$<br/>Equilibrium constant $(K)=$ ?<br/>$\Delta G^{\circ}=-R T \ln K$<br/>$-25 \mathrm{~kJ} \mathrm{~mol}^{-1}=\left(-8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \times 300 \mathrm{~K}\right) \ln k$<br/>$\ln K=\left(-\frac{25 \mathrm{~kJ} \mathrm{~mol}^{-1}}{8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \times 300 \mathrm{~K}}\right)$<br/>$=\frac{25 \times 10^3 \mathrm{~J} \mathrm{~mol}^{-1}}{8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \times 300 \mathrm{~K}}$<br/>$\ln K=-10.02, K=e^{10.02}$</div>


tags: ['Mathematics', 'Three Dimensional Geometry']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
find-the-values-of-p-so-that-the-lines-3-1-x-2-p-7-y-14-2-z-3-and-3-p-7-7-x-1-y-5-5-6-z-are-at-right-angles

slug:
find-the-values-of-p-so-that-the-lines-3-1-x-2-p-7-y-14-2-z-3-and-3-p-7-7-x-1-y-5-5-6-z-are-at-right-angles-73700

question:
<div class="question">Find the values of $p$ so that the lines $\frac{1-x}{3}=\frac{7 y-14}{2 p}=\frac{z-3}{2}$ and $\frac{7-7 x}{3 p}=\frac{y-5}{1}=\frac{6-z}{5}$ are at right angles.</div>

answer:
<div class="solution">The given equation are not in the standard form. The equation of the given lines<br/>$$<br/>\frac{x-1}{-3}=\frac{y-2}{2 p / 7}=\frac{z-3}{2}<br/>$$<br/>and $\frac{x-1}{3 p /-7}=\frac{y-5}{1}=\frac{z-6}{-5}$<br/>The direction ratios of the given lines are $-3, \frac{2 \mathrm{P}}{7}, 2$ and $\frac{-3 \mathrm{P}}{7}, 1,-5$.<br/>The lines are perpendicualr to each other<br/>$$<br/>\therefore(-3)\left(\frac{-3 \mathrm{P}}{7}\right)+\left(\frac{2 \mathrm{P}}{7}\right)(1)+2(-5)=0 \Rightarrow \mathrm{P}=\frac{70}{11}<br/>$$</div>


tags: ['Physics', 'Wave Optics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
first-secondary-minima-in-case-of-diffraction-due-to-single-slit-is-obtained-at-a-distance-x-from-central-maximum-position-then

slug:
first-secondary-minima-in-case-of-diffraction-due-to-single-slit-is-obtained-at-a-distance-x-from-central-maximum-position-then-86698

question:
<div class="question">First secondary minima in case of diffraction due to single slit is obtained at a distance \( x \) from central maximum position,<br/>then</div>

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

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">\( x=\frac{\lambda D}{a} \)</span> </div>

answer:
<div class="solution"><blockquote><p>In the case of Fraunhofer single slit diffraction, </p><p><img src="https://cdn-question-pool.getmarks.app/modules/tq5/jee_main/e7562f72-5999-4613-830d-95a140bfca3c-image.png" style="width: 300px; height: 208px;"/></p><p>Condition for the minimum, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>asin</mi><mi>θ</mi><mo>=</mo><mi>m</mi><mi>λ</mi></math>. </p><p>Since, <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mi>sin</mi><mi>θ</mi><mo>≃</mo><mi>tan</mi><mi>θ</mi></mrow></mfenced></math> and from the figure <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tan</mi><mi>θ</mi><mo>=</mo><mfrac><mi>x</mi><mi>D</mi></mfrac></math>, thus <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mi>λ</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mi>x</mi></mrow><mi>D</mi></mfrac><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><mfenced><mn>1</mn></mfenced></math>, here <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>.</mo><mo>.</mo></math>, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>λ</mi></math> is wavelength, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math> is width of slit and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi></math> is the distance between slit and screen.</p><p>Now, for the first secondary minima from the central maximum position, the path difference is an integral number of wavelengths.</p><p>Thus, for first secondary minima, <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>1</mn></math> and <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>sin</mi><mi>θ</mi><mo>=</mo><mi>m</mi><mi>λ</mi></math>.</p><p>From equation <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mn>1</mn></mfenced></math>, we get <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>a</mi><mi>x</mi></mrow><mi>D</mi></mfrac><mo>=</mo><mi>λ</mi><mo>⇒</mo></math><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mfrac><mrow><mi>λ</mi><mi>D</mi></mrow><mi>a</mi></mfrac></math></p></blockquote></div>


title: fishes-in-eutrophic-lake-die-due-to
slug: fishes-in-eutrophic-lake-die-due-to-23334
question: <div class="question">Fishes in eutrophic lake die due to</div>
tags: ['Biology', 'Strategies for Enhancement in Food Production', 'AIIMS', 'AIIMS 2018 (27 May)']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">lack of oxygen</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">nutrient enrichment</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{CO}_2$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">none of these.</span> </li> </ul>

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

answer:
<div class="solution">Eutrophic lakes have high levels of biological productivity due to the rich nutrient constituents, especially nitrogen and phosphorus. An abundance of plants are supported in this lake. Initially, eutrophic lakes accelerate multiplication and growth of lake fauna. Plants and/ or algal blooms overcrowd the lake, they later die and decomposition of dead organic matter starts which leads to decrease in dissolved oxygen content. Decrease in dissolved oxygen suffocats lake fauna, e.g., fishes to death.</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
five-coins-whose-faces-are-marked-23-are-thrown-what-is-the-probability-of-obtainining-a-total-of-12

slug:
five-coins-whose-faces-are-marked-23-are-thrown-what-is-the-probability-of-obtainining-a-total-of-12-16292

question:
<div class="question">Five coins whose faces are marked 2,3 are thrown. What is the probability of obtainining a total of $12 ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{1}{16}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{3}{16}$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$\frac{5}{16} \quad$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\frac{7}{16}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\frac{5}{16} \quad$</span> </div>

answer:
<div class="solution">Let $\mathrm{E}$ be the event of total of 12 . $\mathrm{E}=(2,2,2,3,3),(2,2,3,3,2),(2,3,3,2,2)$,<br/>$(3,3,2,2,2),(3,2,3,2,2),(3,2,2,3,2)$,<br/>$(3,2,2,2,3),(2,3,2,3,2),(2,3,2,2,3)$,<br/>$(2,2,3,2,3)$<br/>$\mathrm{n}(\mathrm{E})=10$<br/>Sample sapce contain total possibility $=2^{5}=32$ Hence, $n(s)=32$<br/>So, $\mathrm{P}(\mathrm{E})=\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}=\frac{10}{32}=\frac{5}{16}$</div>


tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2017 (Phase 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$0.3$</span> </div>
source_db: MarksBatch1_P2.db
title:
five-sticks-of-length-1-3-5-7-and-9-feet-are-given-three-of-these-sticks-are-selected-at-random-what-is-the-probability-that-the-selected-sticks-can-f

slug:
five-sticks-of-length-1-3-5-7-and-9-feet-are-given-three-of-these-sticks-are-selected-at-random-what-is-the-probability-that-the-selected-sticks-can-f-12969

question:
<div class="question">Five sticks of length $1,3,5,7$ and 9 feet are given. Three of these sticks are selected at random. What is the probability that the selected sticks can from a triangle?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.5$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$0.4$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$0.3$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">0</span> </li> </ul>

answer:
<div class="solution">$3$ sticks can be selected from 5 sticks in ${ }^{5} \mathrm{c}_{3}$ ways<br/>${ }^{5} \mathrm{c}_{3}=10$.<br/>Probability that selected sticks from a triangle is<br/>$\mathrm{n}(\mathrm{E})={ }^{4} \mathrm{c}_{3}-1=\frac{4 \times 3 \times 2 \times 1}{3 \times 2 \times 1}-1=4-1=3$<br/>$\therefore \mathrm{p}(\mathrm{E})=\frac{3}{10}=0.3$</div>


title: flocs-produced-in-the-secondary-treatment-plant-of-the-sewage-comprises-of
slug: flocs-produced-in-the-secondary-treatment-plant-of-the-sewage-comprises-of-90819
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Flocs produced in the secondary treatment plant of the sewage comprises of,</div>

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

answer:
<div class="solution">The primary effluent was passed into large aeration tanks with constant agitation and the air was pumped into it. This allowed the vigorous growth of useful aerobic microbes like bacteria and fungi to form mesh-like flocs. The microbes consumes a significant part of the organic matter in the effluent and reduced its BOD.</div>


title: flocs-which-are-used-in-the-secondary-treatment-of-sewage-are
slug: flocs-which-are-used-in-the-secondary-treatment-of-sewage-are-11241
question: <div class="question">Flocs, which are used in the secondary treatment of sewage, are:</div>
tags: ['Biology', 'Microbes in Human Welfare', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">masses of bacteria in symbiosis with algae</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">foliose lichens</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">masses of fungi associated with algae</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">masses of bacteria associated with fungal filaments forming mesh like structures</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">masses of bacteria associated with fungal filaments forming mesh like structures</span> </div>

answer:
<div class="solution">Flocs are aerobic masses of bacteria associated with fungal filaments forming mesh like structures. These microbes consume the major part of the organic matter in the effluent reducing its biological oxygen demand.</div>


title: flower-in-angiosperms
slug: flower-in-angiosperms-38981
question: <div class="question">Flower in angiosperms:</div>
tags: ['Biology', 'Morphology of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">Is a modified reproductive shoot</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">Possess different floral appendages at successive nodes</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">Have floral appendages which are modified leaves</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">More than one option is correct</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution">Flower is defined as modified dwarf shoot which is meant for sexual reproduction. It is characteristic feature of angiosperm.<br/><br/>The flowers are termed pedicellate if they possess stalks and sessile if they lack them. The flower may be described as complete if it bears all the floral parts and incomplete, when one or more floral parts are absent. Flowers are called bisexual if they bear both androecium and gynoecium. The unisexual flowers have either androecium or gynoecium. The unisexual flowers may be male flowers or female flowers. The male flower are also called staminate flowers as they have stamens only.<br/><br/>The female flowers have only the carpels and hence called pistillate flowers. Flowers with sterile sex organs are described as neutral flowers. According to the distribution of male, female and bisexual flowers, various patterns are recognized.</div>


title: fluoride-pollution-mainly-affects
slug: fluoride-pollution-mainly-affects-18374
question: <div class="question">Fluoride pollution mainly affects:</div>
tags: ['Biology', 'Environmental Issues', 'NEET', 'NEET 2003']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">teeth</span> </div>
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">brain</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">heart</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">teeth</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">kidney</span> </li> </ul>

answer:
<div class="solution">Fluoride is a mineral found in bones, teeth, the thyroid gland, and the skin. It is important for the optimal formation of dental enamel and bone mineralization. However, in abundance, it has negative effects on the joints, bones and causes fluorosis in the teeth.<br/>Related Theory<br/>- Teeth are affected by fluoride immediately. Since it results in tooth decay and decolouration quite quickly. it gets distributed into the contaminated water: great caution must be taken. Knock knee syndrome is caused by Fluoride pollution.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2009 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
folloming-table-gives-the-mean-and-variance-of-monthly-demand-for-four-products-a-b-c-and-d-in-a-supermarket-beginarraylcccc-hline-multicolumn1c-produ

slug:
folloming-table-gives-the-mean-and-variance-of-monthly-demand-for-four-products-a-b-c-and-d-in-a-supermarket-beginarraylcccc-hline-multicolumn1c-produ-84093

question:
<div class="question">Folloming table gives the mean and variance of monthly demand for four products $A, B, C$ and $D$ in a supermarket \begin{array}{|l|c|c|c|c|}<br/>\hline \multicolumn{1}{|c|} { Product } &amp; A &amp; B &amp; C &amp; D \\<br/>\hline Mcan demand &amp; 60 &amp; 90 &amp; 80 &amp; 120 \\<br/>\hline Variance &amp; 12 &amp; 25 &amp; 36 &amp; 16 \\<br/>\hline For which nmduct the demand is cnncictent? &amp; 77000-II<br/>\end{array}</div>

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

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

answer:
<div class="solution">To find the consistent demand we will calculate coeff of variance.<br/>We know coefficient of variance $=\frac{\sqrt{\mathrm{SD}}}{\text { mean }}$<br/>Also, we know, $\mathrm{S.D}=\sqrt{\text { variance }}$<br/>Coefficient of variance of $A=\frac{\sqrt{12}}{60}=\frac{3.46}{60}=0.057$<br/>Coefficient of variance of $B=\frac{\sqrt{25}}{90}=\frac{5}{90}=0.055$<br/>Coefficient of variance of $C=\frac{\sqrt{36}}{80}=\frac{6}{80}=0.075$<br/>Coefficient of variance of $D=\frac{\sqrt{16}}{120}=\frac{4}{120}=0.033$ We see that minimum coefficient of variance is of $D$. hence product $D$ is consistent.</div>


tags: ['Biology', 'Anatomy of Flowering Plants', 'NEET']
source_db: MarksBatch1_P2.db
title:
following-are-the-differences-between-monocot-and-dicot-stem-which-ones-are-correct-property-monocot-stem-dicot-stem-i-hypodermis-sclerenchymatous-col

slug:
following-are-the-differences-between-monocot-and-dicot-stem-which-ones-are-correct-property-monocot-stem-dicot-stem-i-hypodermis-sclerenchymatous-col-29821

question:
<div class="question">Following are the differences between monocot and dicot stem. Which ones are correct?<br/>
 
<table border="1"> <tbody> <tr> <td> </td> <td>Property</td> <td>Monocot stem</td> <td>Dicot stem</td> </tr> <tr> <td>(i)</td> <td>Hypodermis</td> <td>Sclerenchymatous</td> <td>Collenchymatous</td> </tr> <tr> <td>(ii)</td> <td>Xylem</td> <td>Exarch</td> <td>Endarch</td> </tr> <tr> <td>(iii)</td> <td>Pith</td> <td>Absent</td> <td>Present</td> </tr> <tr> <td>(iv)</td> <td>Bundle Sheath</td> <td>Sclerenchymatous</td> <td>Parenchymatous</td> </tr> </tbody> </table> </div>

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

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

answer:
<div class="solution">In dicot stem, hypodermis consists of a few layers of collenchymatous cells just below the epidermis, which provide mechanical strength to the young stem. The monocot stem has a sclerenchymatous hypodermis.<br/><br/>In stems (monocots and dicots), the protoxylem lies towards the centre (pith) and the metaxylem lies towards the periphery of the organ. This type of primary xylem is called endarch. In roots (monocots and dicots), the protoxylem lies towards periphery and metaxylem lies towards the centre. Such arrangement of primary xylem is called exarch. In dicot stem, a large number of vascular bundles are arranged in a ring. It also has a large number of rounded, parenchymatous cells with large intercellular spaces which occupy the central portion of the stem which constitute the pith. Moncot stems have a large number of scattered vascular bundles, hence pith is absent. In monocot stem each vascular bundle is surrounded by a sclerenchymatous bundle sheath. Bundle sheaths are absent in dicot stem</div>


tags: ['Mathematics', 'Statistics', 'MHT CET', 'MHT CET 2021 (22 Sep Shift 2)']
source_db: MarksBatch1_P2.db
title:
following-data-shows-the-information-about-marks-obtained-in-physics-chemistry-mathematics-and-biology-by-100-students-in-a-class-then-subject-shows-t

slug:
following-data-shows-the-information-about-marks-obtained-in-physics-chemistry-mathematics-and-biology-by-100-students-in-a-class-then-subject-shows-t-94056

question:
<div class="question">Following data shows the information about marks obtained in Physics, Chemistry, Mathematics and Biology by 100 students in a class. Then <img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/Mz1pvcT-s_x_OAStfTQafUsm0Wzkq9rKwVC3hGOPlHI.original.fullsize.png"/><br/>subject shows the highest variability in marks<img src="https://cdn-question-pool.getmarks.app/pyq/mht_cet/Fy3JzEYDO62lr4UneS5F7bcRNFaETgVjyzoirTdt-4s.original.fullsize.png"/><br/></div>

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

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

answer:
<div class="solution">$\begin{aligned} &amp; \text { We know that Coefficient of Variation }=\frac{\text { Standard Deviation }}{\text { mean }} \\ &amp; \therefore \quad(\text { C.V. })_{\text {Physics }}=\frac{3}{20}=0.15 \text { and }(\text { C.V. })_{\text {Chemistry }}=\frac{2}{25}=0.08 \\ &amp; \left.\text { (C.V. })_{\text {Mathematics }}=\frac{4}{23}=0.174 \text { and (C.V. }\right)_{\text {Biology }}=\frac{5}{27}=0.185\end{aligned}$</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2006 (Phase 1)']
source_db: MarksBatch1_P2.db
title:
following-is-the-frequency-distribution-oflife-length-in-hours-of-100-electric-bulbs-beginarrayccccccc-hline-life-length-of-bulbs-in-hrs-85135-135185-

slug:
following-is-the-frequency-distribution-oflife-length-in-hours-of-100-electric-bulbs-beginarrayccccccc-hline-life-length-of-bulbs-in-hrs-85135-135185-18076

question:
<div class="question">Following is the frequency distribution oflife length in hours of 100 electric bulbs:<br/>\begin{array}{|c|c|c|c|c|c|c|}<br/>\hline Life length of bulbs (in hrs) &amp; 8.5-13.5 &amp; 13.5-18.5 &amp; 18.5-23.5 &amp; 23.5-28.5 &amp; 28.5-33.5 &amp; 33.5-38.5 \\<br/>\hline No. of bulbs &amp; 7 &amp; \mathrm{x} &amp; 40 &amp; \mathrm{y} &amp; 10 &amp; 2 \\<br/>\hline<br/>\end{array} If the median of life length is 20 hours, then what are the missing frequencies $(\mathrm{x}, \mathrm{y})$ ?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(28,13)$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(23,18)$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$(31,10)$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$(25,16)$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$(31,10)$</span> </div>

answer:
<div class="solution">Let $x=31$ and $y=10$ C.I. $\quad \mathrm{x} \quad \mathrm{f} \quad \mathrm{cf}$<br/>$8.5-13.5$<br/>$\begin{array}{lll}\mathrm{x} &amp; \mathrm{f} \\ 11 &amp; 7\end{array}$<br/>$\begin{array}{rrrr}13.5-18.5 &amp; 16 &amp; 31 &amp; 38 \\ 18.5-23.5 &amp; 21 &amp; 40 &amp; 78\end{array}$<br/>$\begin{array}{llll}23.5-28.5 &amp; 26 &amp; 10 &amp; 88\end{array}$<br/>$\begin{array}{llll}28.5-33.5 &amp; 31 &amp; 10 &amp; 98\end{array}$<br/>$\begin{array}{llll}33.5-38.5 &amp; 36 &amp; 2 &amp; 100\end{array}$<br/>$\mathrm{N}=100, \therefore \frac{\mathrm{N}}{2}=50$<br/>Median group is $18.5-23.5$<br/>$\mathrm{~L}_{1}=18.5, \mathrm{~L}_{2}=23.5, \mathrm{C}=38, \mathrm{~h}=5, \mathrm{f}=40$<br/>Median $=\mathrm{L}_{1}+\frac{\left(\frac{\mathrm{N}}{2}-\mathrm{C}\right)}{\mathrm{f}} \times \mathrm{h}$<br/>$=18.5+\frac{50-38}{40} \times 5=18.5+\frac{12 \times 5}{40}=18.5+1.5=20$<br/>Thus, our assumption is correct. Therefore missing numbers are 31 and 10 respectively.</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'TS EAMCET', 'TS EAMCET 2019 (03 May Shift 2)']
source_db: MarksBatch1_P2.db
title:
following-lists-contain-reactions-and-their-corresponding-equilibrium-constants-at-different-temperatures-list-i-reaction-list-ii-k-p-2-so-2-g-o-2-g-2

slug:
following-lists-contain-reactions-and-their-corresponding-equilibrium-constants-at-different-temperatures-list-i-reaction-list-ii-k-p-2-so-2-g-o-2-g-2-84315

question:
<div class="question"><p>Following lists contain reactions and their corresponding equilibrium constants at different temperatures:</p><table border="1" cellpadding="1" cellspacing="1" style="width: 500px;"> <tbody> <tr> <td>List - I (Reaction)</td> <td>List - II <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><msub><mi mathvariant="normal">K</mi><mi mathvariant="normal">p</mi></msub></mfenced></math></td> </tr> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msub><mi>SO</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>+</mo><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>⇌</mo><mn>2</mn><msub><mi>SO</mi><mn>3</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mtext> at </mtext><mn>298</mn><mo> </mo><mi mathvariant="normal">K</mi></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>24</mn></msup></math></td> </tr> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msub><mi>SO</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>+</mo><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>⇌</mo><mn>2</mn><msub><mi>SO</mi><mn>3</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mtext> at </mtext><mn>700</mn><mo> </mo><mi mathvariant="normal">K</mi></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>4</mn></msup></math></td> </tr> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>⇌</mo><mn>2</mn><msub><mi>NO</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mtext> at </mtext><mn>298</mn><mo> </mo><mi mathvariant="normal">K</mi></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>98</mn></math></td> </tr> <tr> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mo>⇌</mo><mn>2</mn><msub><mi>NO</mi><mn>2</mn></msub><mo>(</mo><mo> </mo><mi mathvariant="normal">g</mi><mo>)</mo><mtext> at </mtext><mn>500</mn><mo> </mo><mi mathvariant="normal">K</mi></math></td> <td><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1700</mn></math></td> </tr> </tbody></table><p>If <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup></math> are the standard enthalpies for the reactions <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><msub><mi>SO</mi><mn>2</mn></msub><mo> </mo><mo>+</mo><mo> </mo><msub><mi mathvariant="normal">O</mi><mn>2</mn></msub><mo> </mo><mo>⇌</mo><mo> </mo><mn>2</mn><msub><mi>SO</mi><mn>3</mn></msub><mo> </mo><mi>and</mi><mo> </mo><msub><mi mathvariant="normal">N</mi><mn>2</mn></msub><msub><mi mathvariant="normal">O</mi><mn>4</mn></msub><mo> </mo><mo>⇌</mo><mo> </mo><mn>2</mn><msub><mi>NO</mi><mn>2</mn></msub></math>  respectively, then: </p></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"><mi>Both</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup><mo> </mo><mi>are</mi><mo> </mo><mi>negative</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"><mi>Both</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><mpadded lspace="-1px"><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup><mo> </mo><mi>are</mi><mo> </mo><mi>positive</mi></mpadded></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"><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>negative</mi><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>positive</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"><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>positive</mi><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>negative</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"><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>1</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>negative</mi><mo> </mo><mi>and</mi><mo> </mo><mo>∆</mo><msubsup><mi mathvariant="normal">H</mi><mn>2</mn><mn>0</mn></msubsup><mo> </mo><mi>is</mi><mo> </mo><mi>positive</mi></math></span> </div>

answer:
<div class="solution"><p>From thermodynamics of equilibria, we have:</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ln</mi><mo> </mo><msub><mi mathvariant="normal">K</mi><mi>ep</mi></msub><mo> </mo><mo>=</mo><mo> </mo><mi>ln</mi><mo> </mo><mi mathvariant="normal">A</mi><mo> </mo><mo>-</mo><mo> </mo><mfrac><mrow><mo>∆</mo><msup><mi mathvariant="normal">H</mi><mn>0</mn></msup></mrow><mi>RT</mi></mfrac></math></p><p>For endothermic reaction, the equilibrium constant increases with temperature while for the exothermic reaction, the equilibrium constant decreases when temperature is raised.</p></div>


title: following-process-is-known-as-h-v-e-e
slug: following-process-is-known-as-h-v-e-e-64900
tags: ['Physics', 'Nuclear Physics', 'NEET']
source_db: MarksBatch1_P2.db
question:
<div class="question">Following process is known as<br/> <br/> <math><mi>h</mi><mi>v</mi><mo>â</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>+</mo></mrow></msup><mo>+</mo><msup><mrow><mi>e</mi></mrow><mrow><mo>-</mo></mrow></msup></math></div>

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

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

answer:
<div class="solution">Pair production refers to the creation of an elementary particle and its anti-particle usually from a photon (or another neutral boson). This is allowed, provided these is enough energy available to created the pair.<br/><br/> <img call-to-action="" data-pagefind-ignore="" src="https://cdn-question-pool.getmarks.app/nta_abhyas/neet/images/qwvbutienpvqofhnbhfkystuarkaitcfgwbnpqsesyubguqqdr.jpeg" style="max-width:100%; object-fit:contain /&gt;&lt;/div&gt; &lt;/section&gt; &lt;!-- /Solution --&gt; &lt;!-- Call to Action --&gt; &lt;section class="/> <div class="call-to-action-header"> <svg fill="none" height="24" viewbox="0 0 25 24" width="25" xmlns="http://www.w3.org/2000/svg"> <path d="M19.9999 13.5C20.0018 13.8058 19.9089 14.1047 19.734 14.3555C19.559 14.6063 19.3107 14.7968 19.023 14.9006L14.1874 16.6875L12.4062 21.5269C12.3007 21.8134 12.1098 22.0608 11.8594 22.2355C11.6089 22.4101 11.3109 22.5038 11.0055 22.5038C10.7002 22.5038 10.4022 22.4101 10.1517 22.2355C9.90124 22.0608 9.71039 21.8134 9.60491 21.5269L7.8124 16.6875L2.97303 14.9062C2.68646 14.8008 2.43915 14.6099 2.26445 14.3595C2.08976 14.109 1.99609 13.811 1.99609 13.5056C1.99609 13.2003 2.08976 12.9022 2.26445 12.6518C2.43915 12.4013 2.68646 12.2105 2.97303 12.105L7.8124 10.3125L9.59366 5.47313C9.69914 5.18656 9.88998 4.93924 10.1404 4.76455C10.3909 4.58985 10.6889 4.49619 10.9943 4.49619C11.2996 4.49619 11.5977 4.58985 11.8481 4.76455C12.0986 4.93924 12.2894 5.18656 12.3949 5.47313L14.1874 10.3125L19.0268 12.0938C19.3146 12.1986 19.5628 12.3901 19.7371 12.642C19.9114 12.8939 20.0033 13.1937 19.9999 13.5ZM14.7499 4.5H16.2499V6C16.2499 6.19891 16.3289 6.38968 16.4696 6.53033C16.6102 6.67098 16.801 6.75 16.9999 6.75C17.1988 6.75 17.3896 6.67098 17.5302 6.53033C17.6709 6.38968 17.7499 6.19891 17.7499 6V4.5H19.2499C19.4488 4.5 19.6396 4.42098 19.7802 4.28033C19.9209 4.13968 19.9999 3.94891 19.9999 3.75C19.9999 3.55109 19.9209 3.36032 19.7802 3.21967C19.6396 3.07902 19.4488 3 19.2499 3H17.7499V1.5C17.7499 1.30109 17.6709 1.11032 17.5302 0.96967C17.3896 0.829018 17.1988 0.75 16.9999 0.75C16.801 0.75 16.6102 0.829018 16.4696 0.96967C16.3289 1.11032 16.2499 1.30109 16.2499 1.5V3H14.7499C14.551 3 14.3602 3.07902 14.2196 3.21967C14.0789 3.36032 13.9999 3.55109 13.9999 3.75C13.9999 3.94891 14.0789 4.13968 14.2196 4.28033C14.3602 4.42098 14.551 4.5 14.7499 4.5ZM22.9999 7.5H22.2499V6.75C22.2499 6.55109 22.1709 6.36032 22.0302 6.21967C21.8896 6.07902 21.6988 6 21.4999 6C21.301 6 21.1102 6.07902 20.9696 6.21967C20.8289 6.36032 20.7499 6.55109 20.7499 6.75V7.5H19.9999C19.801 7.5 19.6102 7.57902 19.4696 7.71967C19.3289 7.86032 19.2499 8.05109 19.2499 8.25C19.2499 8.44891 19.3289 8.63968 19.4696 8.78033C19.6102 8.92098 19.801 9 19.9999 9H20.7499V9.75C20.7499 9.94891 20.8289 10.1397 20.9696 10.2803C21.1102 10.421 21.301 10.5 21.4999 10.5C21.6988 10.5 21.8896 10.421 22.0302 10.2803C22.1709 10.1397 22.2499 9.94891 22.2499 9.75V9H22.9999C23.1988 9 23.3896 8.92098 23.5302 8.78033C23.6709 8.63968 23.7499 8.44891 23.7499 8.25C23.7499 8.05109 23.6709 7.86032 23.5302 7.71967C23.3896 7.57902 23.1988 7.5 22.9999 7.5Z" fill="#1589EE"></path> </svg> <h3>Looking for more such questions to practice?</h3> </div> <p>
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tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
for-2n1-observations-x-1-x-1-x-2-x-2-x-n-x-n-and-0-where-x-s-are-all-distinct-let-sd-and-md-denote-the-standard-deviation-and-median-respectively-then

slug:
for-2n1-observations-x-1-x-1-x-2-x-2-x-n-x-n-and-0-where-x-s-are-all-distinct-let-sd-and-md-denote-the-standard-deviation-and-median-respectively-then-84639

question:
<div class="question">For (2n+1) observations $x_1,-x_1, x_2,-x_2, \ldots \ldots x_n,-x_n$ and 0 where $x$ 's are all distinct. Let S.D. and M.D. denote the standard deviation and median respectively. Then which of the following is always true</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">S.D. $ \lt $ M.D.</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">S.D. $\gt$ M.D.</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$S.D. = M.D.$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">Nothing can he said in general about the relationship</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">S.D. $\gt$ M.D.</span> </div>

answer:
<div class="solution">On arranging the given observations in ascending order, we get<br/>All negative terms $\underbrace{O}_{(n+1)^n t e r m}$ All positive terms<br/>The median of given observations $=(n+1)^{\text {th }}$ term $=0$ $\therefore \mathrm{S} . \mathrm{D} .\gt\mathrm{M}$ D.</div>


tags: ['Mathematics', 'Statistics', 'NDA', 'NDA 2016 (Phase 2)']
source_db: MarksBatch1_P2.db
title:
for-10-observations-on-price-x-and-supply-y-the-following-data-was-obtained-x-130-y-220-x-2-2288-y-2-5506-and-xy-3467-what-is-line-of-regression-of-y-

slug:
for-10-observations-on-price-x-and-supply-y-the-following-data-was-obtained-x-130-y-220-x-2-2288-y-2-5506-and-xy-3467-what-is-line-of-regression-of-y-62989

question:
<div class="question">For 10 observations on price $(\mathrm{x})$ and supply (y), the following data was obtained :<br/>$\sum \mathrm{x}=130, \sum \mathrm{y}=220$<br/>$\sum \mathrm{x}^{2}=2288, \sum \mathrm{y}^{2}=5506$ and $\sum \mathrm{xy}=3467$.<br/>What is line of regression of $y$ on $x ?$</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\mathrm{y}=0.91 \mathrm{x}+8.74$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$\mathrm{y}=1.02 \mathrm{x}+8.74$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\mathrm{y}=1.02 \mathrm{x}-7.02$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$\mathrm{y}=0.91 \mathrm{x}-7.02$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$\mathrm{y}=1.02 \mathrm{x}+8.74$</span> </div>

answer:
<div class="solution">Line of regression of $y$ on $x$ is:<br/>$y-\bar{y}=b_{y x}(x-\bar{x})$<br/>$\bar{y}=\frac{\Sigma y}{n} ; \bar{x}=\frac{\Sigma x}{n} \Rightarrow \bar{y}=\frac{220}{10}=22 ; \bar{x}=\frac{130}{10}=13$<br/>$b_{y x}=\mathbf{r} \cdot \frac{\sigma_{y}}{\sigma_{x}}$<br/>$\mathrm{r}=\frac{n \Sigma x y-(\Sigma x)(\Sigma y)}{\sqrt{\left[n \Sigma x^{2}-(\Sigma x)^{2}\right]\left[n \Sigma y^{2}-(\Sigma y)^{2}\right]}}$<br/>$=\frac{10(3467)-(130)(220)}{\sqrt{\left[(10 \times 2288)-130^{2}\right]\left[(10 \times 5506)-\left(220^{2}\right)\right]}}$<br/>$r=0.962$<br/>$\sigma_{y}=\sqrt{\frac{\Sigma y^{2}}{n}-\left(\frac{\Sigma y}{n}\right)^{2}} \Rightarrow \sigma_{y}=8.2 ; \sigma_{x}=7.73$<br/>$\Rightarrow b_{y x}=0.962 \times \frac{8.2}{7.73}=1.02$<br/>$\Rightarrow$ Line of regression of $y$ on $x$ is<br/>$y-22=1.02(x-13)$<br/>$\Rightarrow y=1.02 x+8.74$</div>


tags: ['Mathematics', 'Statistics', 'MHT CET', 'MHT CET 2023 (12 May Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$2$</span> </div>
source_db: MarksBatch1_P2.db
title:
for-20-observations-of-variable-x-if-x-i-2-20-and-x-i-2-2-100-then-the-standard-deviation-of-variable-x-is

slug:
for-20-observations-of-variable-x-if-x-i-2-20-and-x-i-2-2-100-then-the-standard-deviation-of-variable-x-is-21041

question:
<div class="question">For 20 observations of variable $x$, if $\sum\left(x_{\mathrm{i}}-2\right)=20$ and $\sum\left(x_{\mathrm{i}}-2\right)^2=100$, then the standard deviation of variable $x$ 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">$4$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$9$</span> </li> </ul>

answer:
<div class="solution">Note that standard derivation is independent of change of origin.<br/>$\therefore \quad$ S.D. of $x_{\mathrm{i}}=$ S.D. of $\left(x_{\mathrm{i}}-2\right)$<br/>$$<br/>\begin{aligned}<br/>\therefore \quad \text { S.D. of }\left(x_{\mathrm{i}}-2\right) &amp; =\sqrt{\frac{1}{\mathrm{n}} \sum_{\mathrm{i}}^{20}\left(x_{\mathrm{i}}-2\right)^2-\left[\frac{\sum\left(x_{\mathrm{i}}-2\right)}{\mathrm{n}}\right]^2} \\<br/>&amp; =\sqrt{\frac{100}{20}-(1)^2} \\<br/>&amp; =2 \\<br/>\Rightarrow \text { Required S.D } &amp; =2<br/>\end{aligned}<br/>$$</div>


title: for-a-binomial-distribution-b-n-p-mean-200-standard-deviation-10-then-n-2-p-2-1-q-2-1-is-equal-to
tags: ['Mathematics', 'Probability', 'AP EAMCET', 'AP EAMCET 2021 (24 Aug Shift 2)']
source_db: MarksBatch1_P2.db
slug:
for-a-binomial-distribution-b-n-p-mean-200-standard-deviation-10-then-n-2-p-2-1-q-2-1-is-equal-to-26514

question:
<div class="question">For a binomial distribution $B(n, p)$ mean $=200$, standard deviation $=10$, then $n^2+\frac{1}{p^2}+\frac{1}{q^2}$ is equal to</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$160004$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$160006$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$160008$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 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">$160002$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$160008$</span> </div>

answer:
<div class="solution">In binomial distribution mean $=n p$ and<br/>standard deviation $=\sqrt{n p q}$<br/>$\therefore \quad 200=n p$ and $10=\sqrt{n p q}$<br/>$200=n p$ ...(i)<br/>$100=n p q$ ...(ii)<br/>From Eqs. (i) and (ii), we get<br/>$q=\frac{1}{2}, n=400$ and $p=\frac{1}{2}$<br/>$\therefore \quad n^2+\frac{1}{p^2}+\frac{1}{q^2}$<br/>$(400)^2+(2)^2+(2)^2$<br/>$=160000+4+4=160008$</div>


title: for-a-binomial-distribution-b-n-p-p-4-and-variance-n-pq-43-what-is-the-probability-p-x-5-equal-to
tags: ['Mathematics', 'Probability', 'NDA', 'NDA 2009 (Phase 1)']
source_db: MarksBatch1_P2.db
slug:
for-a-binomial-distribution-b-n-p-p-4-and-variance-n-pq-43-what-is-the-probability-p-x-5-equal-to-18426

question:
<div class="question">For a binomial distribution $B(n, p), \eta p=4$ and variance $n p q$ $=4 / 3 .$ What is the probability $P(x \geq 5)$ equal to?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$(2 / 3)^{6}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$(1 / 3)^{6}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$(1 / 3)^{6}$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$Q^{8} / 3^{6} y$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$Q^{8} / 3^{6} y$</span> </div>

answer:
<div class="solution">Given, $n p=4$ and $n p q=\frac{4}{3}$<br/>$\therefore \quad 4 q=\frac{4}{3} \Rightarrow q=\frac{1}{3}$<br/>$\therefore \quad p=1-\frac{1}{3}=\frac{2}{3}$<br/>$\Rightarrow \quad n=\frac{4 \times 3}{2}=6$<br/>Now, $P(X \geq 5)={ }^{6} C_{5}(p)^{5}(q)^{1}+{ }^{6} C_{6} p^{6} q^{0}$<br/>$={ }^{6} C_{5}\left(\frac{2}{3}\right)^{5}\left(\frac{1}{3}\right)+{ }^{6} C_{6}\left(\frac{2}{3}\right)^{6}$<br/>$=\frac{6 \times 32}{3^{6}}+\frac{64}{3^{6}}=\frac{256}{3^{6}}=\frac{2^{8}}{3^{6}}$</div>


tags: ['Chemistry', 'Electrochemistry', 'COMEDK', 'COMEDK 2023']
source_db: MarksBatch1_P2.db
title:
for-a-cell-reaction-a-s-b-2-a-q-a-2-a-q-b-s-the-standard-emf-of-the-cell-is-0295-v-at-2-5-c-the-equilibrium-constant-at-2-5-c-will-be

slug:
for-a-cell-reaction-a-s-b-2-a-q-a-2-a-q-b-s-the-standard-emf-of-the-cell-is-0295-v-at-2-5-c-the-equilibrium-constant-at-2-5-c-will-be-54611

question:
<div class="question">For a cell reaction,<br/>$A(s)+B^{2+}(a q) \longrightarrow A^{2+}(a q)+B(s)$; the<br/>standard emf of the cell is $0.295 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$. The equilibrium constant at $25^{\circ} \mathrm{C}$ will be</div>

options:
<ul class="options"> <li class="correct"> <span class="option-label">A</span> <span class="option-data">$1 \times 10^{10}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">B</span> <span class="option-data">10</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$2.95 \times 10^{-2}$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2.95 \times 10^{-10}$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$1 \times 10^{10}$</span> </div>

answer:
<div class="solution">For this given reaction, $n=2$. At $25^{\circ} \mathrm{C}$,<br/>$\begin{aligned}<br/>\therefore \quad K &amp; =\text { antilog }\left[\frac{n E^{\circ}}{0.059}\right]=\operatorname{antilog}\left[\frac{2 \times(-0.295)}{0.059}\right] \\<br/>K &amp; =1 \times 10^{10}<br/>\end{aligned}$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
for-a-cell-reaction-involving-a-twoelectron-change-the-standard-emf-of-the-cell-is-found-to-be-0295-v-at-2-5-c-the-equilibrium-constant-of-the-reactio-1

slug:
for-a-cell-reaction-involving-a-twoelectron-change-the-standard-emf-of-the-cell-is-found-to-be-0295-v-at-2-5-c-the-equilibrium-constant-of-the-reactio-1-56477

question:
<div class="question">For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be $0.295 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$. The equilibrium constant of the reaction at $25^{\circ} \mathrm{C}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$29.5 \times 10^{-2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>10<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$1 \times 10^{10}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$1 \times 10^{-10}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1 \times 10^{-10}$</span> </div>

answer:
<div class="solution">The equilibrium constant is related to the standard emf of cell by the expression<br/>$\log K=E_{\text {cell }}^0 \times \frac{n}{0.059}=0.295 \times \frac{2}{0.059}$<br/>$\log \mathrm{K}=\frac{590}{59}=10$ or $\mathrm{K}=1 \times 10^{-10}$</div>


tags: ['Chemistry', 'Electrochemistry', 'JEE Main', 'JEE Main 2003']
source_db: MarksBatch1_P2.db
title:
for-a-cell-reaction-involving-a-twoelectron-change-the-standard-emf-of-the-cell-is-found-to-be-0295-v-at-2-5-c-the-equilibrium-constant-of-the-reactio

slug:
for-a-cell-reaction-involving-a-twoelectron-change-the-standard-emf-of-the-cell-is-found-to-be-0295-v-at-2-5-c-the-equilibrium-constant-of-the-reactio-83552

question:
<div class="question">For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be $0.295 \mathrm{~V}$ at $25^{\circ} \mathrm{C}$. The equilibrium constant of the reaction at $25^{\circ} \mathrm{C}$ will be</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><br/>$29.5 \times 10^{-2}$<br/></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><br/>10<br/></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><br/>$1 \times 10^{10}$<br/></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><br/>$1 \times 10^{-10}$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value"><br/>$1 \times 10^{-10}$</span> </div>

answer:
<div class="solution">The equilibrium constant is related to the standard emf of cell by the expression<br/>$\log K=E_{\text {cell }}^0 \times \frac{n}{0.059}=0.295 \times \frac{2}{0.059}$<br/>$\log \mathrm{K}=\frac{590}{59}=10$ or $\mathrm{K}=1 \times 10^{-10}$</div>


title: for-a-cell-reaction-to-be-spontaneous-the-standard-free-energy-change-of-the-reaction-must-be
slug: for-a-cell-reaction-to-be-spontaneous-the-standard-free-energy-change-of-the-reaction-must-be-48988
tags: ['Chemistry', 'Electrochemistry', 'VITEEE', 'VITEEE 2006']
source_db: MarksBatch1_P2.db
question:
<div class="question">For a cell reaction to be spontaneous, the standard free energy change of the reaction must be</div>

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

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

answer:
<div class="solution">For spontaneous reaction free energy change is negative.<br/>$\Delta \mathrm{G}=-\mathrm{nFE}$</div>


tags: ['Physics', 'Waves and Sound', 'AP EAMCET', 'AP EAMCET 2016']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">$1\ m$</span> </div>
source_db: MarksBatch1_P2.db
title:
for-a-certain-organ-pipe-three-successive-resonance-frequencies-are-observed-at-425595-and-765-hz-respectively-the-length-of-the-pipe-is-speed-of-soun

slug:
for-a-certain-organ-pipe-three-successive-resonance-frequencies-are-observed-at-425595-and-765-hz-respectively-the-length-of-the-pipe-is-speed-of-soun-27169

question:
<div class="question">For a certain organ pipe, three successive resonance frequencies are observed at 425,595 and $765 \mathrm{~Hz}$, respectively. The length of the pipe is (speed of sound in air $=340 \mathrm{~ms}^{-1}$ )</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$0.5\ m$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$1\ m$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$1.5\ m$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$2\ m$</span> </li> </ul>

answer:
<div class="solution">For closed organ pipe only odd harmonies are possible.<br/>$\therefore$ Fundamental frequency<br/>Fundamental frequency for a closed organ pipe<br/>$\begin{aligned}<br/>&amp; v_0=\frac{v_0}{4 l} \Rightarrow 85=\frac{340}{4 \times l} \\<br/>&amp; {\left[\because v_0=\frac{595-425}{2}=\frac{765-595}{2}=85 \mathrm{~Hz}\right]} \\<br/>&amp; l=\frac{340}{4 \times 85}=1 \mathrm{~m}<br/>\end{aligned}$</div>


tags: ['Chemistry', 'Thermodynamics (C)', 'JEE Main', 'JEE Main 2024 (01 Feb Shift 2)']
options: None
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">57</span> </div>
source_db: MarksBatch1_P2.db
title:
for-a-certain-reaction-at-300-k-k-10-then-g-for-the-same-reaction-is-10-1-kj-mol-1-given-r-8-314-jk-1-mol-1

slug:
for-a-certain-reaction-at-300-k-k-10-then-g-for-the-same-reaction-is-10-1-kj-mol-1-given-r-8-314-jk-1-mol-1-60742

question:
<div class="question"><p>For a certain reaction at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>300</mn><mo>Â </mo><mi mathvariant="normal">K</mi><mo>,</mo><mo>Â </mo><mi mathvariant="normal">K</mi><mo>=</mo><mn>10</mn><mo>,</mo></math>Â then <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ÎG</mi><mo>Â°</mo></math> for the same reaction is â ________Â <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>Â </mo><mi>kJ</mi><mo>Â </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>.</mo></math>Â <math xmlns="http://www.w3.org/1998/Math/MathML"></math> (Given <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">R</mi><mo>=</mo><mn>8</mn><mo>.</mo><mn>314</mn><msup><mi>JK</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>Â </mo><msup><mi>mol</mi><mrow><mo>-</mo><mn>1</mn></mrow></msup></math>)</p></div>

answer:
<div class="solution"><p>The standard Gibbs free energy of the formation of a compound is basically the change of Gibbs free energy that is followed by the formation of oneÂ Â mole of that substance from its component element available at their standard states or the most stable form of the element which is at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn><mo>Â </mo><mo>Â°</mo></math>C and <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>100</mn></math> kPa. Its symbol is <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi mathvariant="normal">Î</mi><mi mathvariant="normal">f</mi></msub><mi mathvariant="normal">G</mi><mo>Ë</mo></math>.</p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ÎG</mi><mo>Â°</mo><mo>=</mo><mo>-</mo><mi>RTânK</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mo>-</mo><mn>8</mn><mo>.</mo><mn>314</mn><mo>Ã</mo><mn>300</mn><mi>ln</mi><mo>(</mo><mn>10</mn><mo>)</mo></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>5744</mn><mo>.</mo><mn>14</mn><mo>Â </mo><mi mathvariant="normal">J</mi><mo>/</mo><mi>mole</mi></math></p><p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>57</mn><mo>.</mo><mn>44</mn><mo>Ã</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>1</mn></mrow></msup><mo>Â </mo><mi>kJ</mi><mo>/</mo><mi>mole</mi></math></p></div>


tags: ['Chemistry', 'Thermodynamics (C)', 'TS EAMCET', 'TS EAMCET 2019 (04 May Shift 1)']
source_db: MarksBatch1_P2.db
title:
for-a-chemical-reaction-the-standard-gibbs-energy-change-g-is-764-1-0-4-j-mol-1-what-is-the-value-of-equilibrium-constant-k

slug:
for-a-chemical-reaction-the-standard-gibbs-energy-change-g-is-764-1-0-4-j-mol-1-what-is-the-value-of-equilibrium-constant-k-95352

question:
<div class="question">For a chemical reaction, the standard Gibbs energy change, $\Delta G^{\circ}$ is $-7.64 \times 10^4 \mathrm{~J} \mathrm{~mol}^1$. What is the value of equilibrium constant (K)?</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$K=1$</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">$k&gt;1$</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">C</span> <span class="option-data">$K &lt; 1$</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$K=0$</span> </li> </ul>

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

answer:
<div class="solution">Standard Gibbs free energy,<br/>$$<br/>\Delta G^{\circ}=-2.303 R T \log K<br/>$$<br/>Given, $\Delta G^{\circ}=-7.64 \times 10^4 \mathrm{~J} / \mathrm{mol}$<br/>$$<br/>\begin{aligned}<br/>\log K &amp; =-\frac{\Delta G^{\circ}}{2.303 R T} \\<br/>K &amp; =\operatorname{antilog}-\left(\frac{\Delta G^{\circ}}{2.303 R T}\right) \\<br/>K &amp; =\text { antilog }-\left(\frac{(-) 7.64 \times 10^4}{2.303 \times 8.314 \times 298}\right)<br/>\end{aligned}<br/>$$<br/>Here, $K$ is greater than one.<br/>Thus, option (2) is correct.</div>


tags: ['Physics', 'Magnetic Effects of Current']
options: None
correct_option: None
source_db: MarksBatch1_P2.db
title:
for-a-circular-coil-of-radius-r-and-n-turns-carrying-current-i-the-magnitude-of-the-magnetic-field-at-a-point-on-its-axis-at-a-distance-x-from-its-cen

slug:
for-a-circular-coil-of-radius-r-and-n-turns-carrying-current-i-the-magnitude-of-the-magnetic-field-at-a-point-on-its-axis-at-a-distance-x-from-its-cen-75762

question:
<div class="question">For a circular coil of radius $R$ and $N$ turns carrying current $I$, the magnitude of the magnetic field at a point on its axis at a distance $\mathbf{x}$ from its centre is given by,<br/>$$<br/>\mathbf{B}=\frac{\mu_0 \mathrm{IR}^2 \mathrm{~N}}{2\left(\mathrm{x}^2+\mathrm{R}^2\right)^{3 / 2}}<br/>$$<br/>(a) Show that this reduces to the familiar result for field at the centre of the coil.<br/>(b) Consider two parallel co-axial circular coils of equal radius $R$, and number of turns $N$, carrying equal currents in the same direction, and separated by a distance R. Show that the field on the axis around the mid-point between the coils is uniform over a distance that is small as compared to $R$, and is given by, $\mathbf{B}=0.72 \frac{\mu_0 \mathrm{NI}}{\mathrm{R}}$, approximately.<br/>(Such an arrangement to produce a nearly uniform magnetic field over a small region is known as Helmholtz coils.)</div>

answer:
<div class="solution">(a) $\mathrm{B}=\frac{\mu_0 \mathrm{IR}^2 \mathrm{~N}}{2\left(\mathrm{x}^2+\mathrm{R}^2\right)^{3 / 2}}$<br/>At the centre of the coil $x=0$<br/>$B=\frac{\mu_0 I^2 \mathrm{~N}}{2 \mathrm{R}^3}=\frac{\mu_0 \mathrm{IN}}{2 \mathrm{R}}$-which is same standard result.<br/>(b) In a small region of length $2 \mathrm{~d}$ about the mid-point between the coils,<br/>$$<br/>\begin{gathered}<br/>\mathrm{B}=\frac{\mu_0 \mathrm{IR}^2 \mathrm{~N}}{2} \times\left[\left\{\left(\frac{\mathrm{R}}{2}+\mathrm{d}\right)^2+\mathrm{R}^2\right\}^{-3 / 2}\right. \\<br/>\left.+\left\{\left(\frac{\mathrm{R}}{2}-\mathrm{d}\right)^2+\mathrm{R}^2\right\}^{-3 / 2}\right] \\<br/>=\frac{\mu_0 \mathrm{IR}^2 \mathrm{~N}}{2} \times\left(\frac{5 \mathrm{R}^2}{4}\right)^{3 / 2} \\<br/>\left.\approx \frac{\mu_0 \mathrm{IR}^2 \mathrm{~N}}{2 \mathrm{R}^3} \times\left(\frac{4}{5}\right)^{-3 / 2} \times\left[1-\frac{4 \mathrm{~d}}{5 \mathrm{R}}\right)^{-3 / 2}+\left(1-\frac{3 \mathrm{~d}}{5 \mathrm{R}}\right)^{-3 / 2}\right]<br/>\end{gathered}<br/>$$<br/>(Neglecting term with $\mathrm{d}^2 / \mathrm{R}^2$ and higher powers of $\mathrm{d} / \mathrm{R}$ since $\mathrm{d} / \mathrm{R}&lt; &lt; 1$ ).<br/>$$<br/>\therefore \quad \mathrm{B}=\left(\frac{4}{5}\right)^{3 / 2} \frac{\mu_0 \mathrm{IN}}{\mathrm{R}} \approx 0.72 \frac{\mu_0 \mathrm{IN}}{\mathrm{R}}<br/>$$</div>


title: for-a-continuous-series-the-mode-is-computed-by-the-formula
slug: for-a-continuous-series-the-mode-is-computed-by-the-formula-24537
question: <div class="question">For a continuous series the mode is computed by the formula</div>
tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$l+\frac{f_{m-1}}{f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\left(\frac{f_1}{f_m-f_1-f_2}\right) \times i$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$l=\frac{f_m-f_{m-1}}{f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\frac{f_m-f_1}{f_m-f_1-f_2} \times i$</span> </li><li class="correct"> <span class="option-label">C</span> <span class="option-data">$l+\frac{f_m-f_{m-1}}{2 f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\frac{f_m-f_1}{2 f_m-f_1-f_2} \times i$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li><li class=""> <span class="option-label">D</span> <span class="option-data">$l+\frac{2 f_m-f_{m-1}}{f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\frac{2 f_m-f_1}{f_m-f_1-f_2} \times i$</span> </li> </ul>

correct_option:
<div class="correct-answer">
The correct answer is:
<span class="option-value">$l+\frac{f_m-f_{m-1}}{2 f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\frac{f_m-f_1}{2 f_m-f_1-f_2} \times i$</span> </div>

answer:
<div class="solution">$l+\frac{f_m-f_{m-1}}{2 f_m-f_{m-1}-f_{m+1}} \times C$ or $l+\left(\frac{f_m-f_1}{2 f_m-f_1-f_2}\right)$<br/>$\mathrm{I}=$ lower boundary of the modal class<br/>$\mathrm{C}$ or $\mathrm{i}=$ size of the modal class<br/>$f_m=a$ frequency corresponding to the modal<br/>class<br/>$f_{m-1} / f_1=a$ frequency of preceding to the modal class<br/>$f_{m+1} / f_2=$ a frequency next to the modal class</div>


title: for-a-critical-study-of-secondary-growth-in-plants-which-one-of-the-following-pairs-is-suitable
tags: ['Biology', 'Organisms and Populations', 'NEET', 'NEET 2007']
source_db: MarksBatch1_P2.db
slug:
for-a-critical-study-of-secondary-growth-in-plants-which-one-of-the-following-pairs-is-suitable-25918

question:
<div class="question">For a critical study of secondary growth in plants, which one of the following pairs is suitable?</div>

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

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

answer:
<div class="solution">Teak and pine is most suitable for the study of critical secondary growth because in secondary growth, secondary tissues are formed from lateral meristem which is well developed in these two cases andsecondary growth occurs in gymnosperms and dicots. Wheat, sugarcane are monocots, maiden hair fern and fern are pteridophytes, deodar and sunflower are dicots.</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
for-a-given-distribution-of-marks-mean-is-3516-and-its-standard-deviation-is-1976-the-coefficient-of-variation-is

slug:
for-a-given-distribution-of-marks-mean-is-3516-and-its-standard-deviation-is-1976-the-coefficient-of-variation-is-21076

question:
<div class="question">For a given distribution of marks mean is 35.16 and its standard deviation is $19.76$. The co-efficient of variation is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">$\frac{35.16}{19.76}$</span> </li><li class=""> <span class="option-label">B</span> <span class="option-data">$\frac{19.76}{35.16}$</span> </li><li class=""> <span class="option-label">C</span> <span class="option-data">$\frac{35.16}{19.76} \times 100$</span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data">$\frac{19.76}{35.16} \times 100$</span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 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">$\frac{19.76}{35.16} \times 100$</span> </div>

answer:
<div class="solution">Coefficient of variation $=\frac{\text { S.D. }}{\text { Mean }} \times 100=\frac{19.76}{35.16} \times 100$.</div>


tags: ['Mathematics', 'Statistics', 'JEE Main']
source_db: MarksBatch1_P2.db
title:
for-a-group-of-50-male-workers-the-mean-and-the-standard-deviation-of-their-daily-wages-are-rs-630-and-rs-90-respectively-and-for-a-group-of-40-female

slug:
for-a-group-of-50-male-workers-the-mean-and-the-standard-deviation-of-their-daily-wages-are-rs-630-and-rs-90-respectively-and-for-a-group-of-40-female-82583

question:
<div class="question">For a group of <math> <mn>50</mn> </math> male workers, the mean and the standard deviation of their daily wages are <math> <mtext>Rs</mtext><mo>.</mo><mtext> </mtext><mn>630</mn> </math> and <math> <mtext>Rs</mtext><mo>.</mo><mtext> </mtext><mn>90</mn> </math> respectively and for a group of <math> <mn>40</mn> </math> female workers these are <math> <mtext>Rs</mtext><mo>.</mo><mtext> </mtext><mn>540</mn> </math> and <math> <mtext>Rs</mtext><mo>.</mo><mtext> </mtext><mn>60</mn> </math> respectively. Then, the standard deviation of all these <math> <mn>90</mn> </math> workers is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data"><math> <mn>60</mn></math></span> </li><li class=""> <span class="option-label">B</span> <span class="option-data"><math> <mn>70</mn></math></span> </li><li class=""> <span class="option-label">C</span> <span class="option-data"><math> <mn>80</mn> </math></span> </li><li class="correct"> <span class="option-label">D</span> <span class="option-data"><math> <mn>90</mn> </math></span> <svg fill="none" height="24" viewbox="0 0 24 24" width="24" xmlns="http://www.w3.org/2000/svg"> <path d="M12 2.25C10.0716 2.25 8.18657 2.82183 6.58319 3.89317C4.97982 4.96452 3.73013 6.48726 2.99218 8.26884C2.25422 10.0504 2.06114 12.0108 2.43735 13.9021C2.81355 15.7934 3.74215 17.5307 5.10571 18.8943C6.46928 20.2579 8.20656 21.1865 10.0979 21.5627C11.9892 21.9389 13.9496 21.7458 15.7312 21.0078C17.5127 20.2699 19.0355 19.0202 20.1068 17.4168C21.1782 15.8134 21.75 13.9284 21.75 12C21.7473 9.41498 20.7192 6.93661 18.8913 5.10872C17.0634 3.28084 14.585 2.25273 12 2.25ZM16.2806 10.2806L11.0306 15.5306C10.961 15.6004 10.8783 15.6557 10.7872 15.6934C10.6962 15.7312 10.5986 15.7506 10.5 15.7506C10.4014 15.7506 10.3038 15.7312 10.2128 15.6934C10.1218 15.6557 10.039 15.6004 9.96938 15.5306L7.71938 13.2806C7.57865 13.1399 7.49959 12.949 7.49959 12.75C7.49959 12.551 7.57865 12.3601 7.71938 12.2194C7.86011 12.0786 8.05098 11.9996 8.25 11.9996C8.44903 11.9996 8.6399 12.0786 8.78063 12.2194L10.5 13.9397L15.2194 9.21937C15.2891 9.14969 15.3718 9.09442 15.4628 9.0567C15.5539 9.01899 15.6515 8.99958 15.75 8.99958C15.8486 8.99958 15.9461 9.01899 16.0372 9.0567C16.1282 9.09442 16.2109 9.14969 16.2806 9.21937C16.3503 9.28906 16.4056 9.37178 16.4433 9.46283C16.481 9.55387 16.5004 9.65145 16.5004 9.75C16.5004 9.84855 16.481 9.94613 16.4433 10.0372C16.4056 10.1282 16.3503 10.2109 16.2806 10.2806Z" fill="#24A865"></path> </svg> </li> </ul>

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

answer:
<div class="solution"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>1</mn></msub><mo>=</mo><mn>50</mn><mo>,</mo><mo> </mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>=</mo><mn>630</mn><mo>,</mo><mo> </mo><msub><mi>σ</mi><mn>1</mn></msub><mo>=</mo><mn>90</mn></math><br/><br/><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>n</mi><mn>2</mn></msub><mo>=</mo><mn>40</mn><mo>,</mo><mo> </mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>2</mn></msub><mo>=</mo><mn>540</mn><mo>,</mo><mo> </mo><msub><mi>σ</mi><mn>2</mn></msub><mo>=</mo><mn>60</mn></math><br/><br/><math> <mover accent="true"> <mi>x</mi> <mo>¯</mo> </mover> <mo>=</mo><mfrac> <mrow> <mn>50</mn><mo>×</mo><mn>630</mn><mo>+</mo><mn>40</mn><mo>×</mo><mn>540</mn> </mrow> <mrow> <mn>50</mn><mo>+</mo><mn>40</mn> </mrow> </mfrac> <mo>=</mo><mfrac> <mrow> <mn>3150</mn><mo>+</mo><mn>2160</mn> </mrow> <mn>9</mn> </mfrac> </math><br/><br/><math> <mtext> </mtext><mtext> </mtext><mtext> </mtext><mtext> </mtext><mo>=</mo><mfrac> <mrow> <mn>5310</mn> </mrow> <mn>9</mn> </mfrac> <mo>=</mo><mn>590</mn> </math><br/><br/>Now, <math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>d</mi><mn>1</mn></msub><mo>=</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>1</mn></msub><mo>−</mo><mover><mi>x</mi><mo>¯</mo></mover><mo>,</mo><mo> </mo><msub><mi>d</mi><mn>2</mn></msub><mo>=</mo><msub><mover><mi>x</mi><mo>¯</mo></mover><mn>2</mn></msub><mo>−</mo><mover><mi>x</mi><mo>¯</mo></mover></math><br/><br/><math> <msub> <mi>d</mi> <mn>1</mn> </msub> <mo>=</mo><mn>630</mn><mo>−</mo><mn>590</mn><mo>=</mo><mn>40</mn> </math><br/><br/><math> <msub> <mi>d</mi> <mn>2</mn> </msub> <mo>=</mo><mn>540</mn><mo>−</mo><mn>590</mn><mo>=</mo><mo>−</mo><mn>50</mn> </math><br/><br/>S.D. of the <math> <mrow> <mn>90</mn> </mrow> </math> workers<br/><br/><math> <mo>=</mo> </math> <math><msqrt><mfrac><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>(</mo><msubsup><mrow><mi>σ</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo><mo>+</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>(</mo><msubsup><mrow><mi>σ</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>+</mo><msubsup><mrow><mi>d</mi></mrow><mrow><mn>2</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>)</mo></mrow><mrow><msub><mrow><mi>n</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>n</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></mfrac></msqrt></math><br/><br/><math> <mo>=</mo> </math><math><mfrac><mrow><msqrt><mn>50</mn><mo>(</mo><mn>8100</mn><mo>+</mo><mn>1600</mn><mo>)</mo><mo>+</mo><mn>40</mn><mo>(</mo><mn>3600</mn><mo>+</mo><mn>2500</mn><mo>)</mo></msqrt></mrow><mrow><mn>90</mn></mrow></mfrac></math><br/><br/><math> <mo>=</mo> </math> <math><mfrac><mrow><msqrt><mn>5</mn><mo>(</mo><mn>9700</mn><mo>)</mo><mo>+</mo><mn>4</mn><mo>(</mo><mn>6100</mn><mo>)</mo></msqrt></mrow><mrow><mn>9</mn></mrow></mfrac></math><br/><br/><math> <mo>=</mo> </math><math><mfrac><mrow><msqrt><mn>48500</mn><mo>+</mo><mn>24400</mn></msqrt></mrow><mrow><mn>9</mn></mrow></mfrac></math><br/><br/><math> <mo>=</mo> </math> <math><msqrt><mfrac><mrow><mn>72900</mn></mrow><mrow><mn>9</mn></mrow></mfrac></msqrt><mo>=</mo><msqrt><mn>8100</mn></msqrt><mo>=</mo><mn>90</mn></math></div>


tags: ['Mathematics', 'Statistics', 'TS EAMCET', 'TS EAMCET 2019 (04 May Shift 2)']
correct_option: <div class="correct-answer"> The correct answer is: <span class="option-value">3</span> </div>
source_db: MarksBatch1_P2.db
title:
for-a-group-of-100-observations-the-arithmetic-mean-and-standard-deviation-are-8-and-105-respectively-the-mean-and-standard-deviation-of-50-items-sele

slug:
for-a-group-of-100-observations-the-arithmetic-mean-and-standard-deviation-are-8-and-105-respectively-the-mean-and-standard-deviation-of-50-items-sele-75289

question:
<div class="question">For a group of 100 observations, the arithmetic mean and standard deviation are 8 and $\sqrt{10.5}$ respectively. The mean and standard deviation of 50 items selected from these 100 observations are 10 and 2 respectively. Then the standard deviation of the remaining 50 observation is</div>

options:
<ul class="options"> <li class=""> <span class="option-label">A</span> <span class="option-data">2</span> </li><li class="correct"> <span class="option-label">B</span> <span class="option-data">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">3.5</span> </li><li class=""> <span class="option-label">D</span> <span class="option-data">4</span> </li> </ul>

answer:
<div class="solution">Let $\sigma_1$ and $\bar{x}_1$ are the standard deviation and mean of 50 observation and $\sigma_2$ and $\bar{x}_2$ are standard deviation one mean of another 50 observation respectively<br/>$$<br/>\begin{gathered}<br/>\bar{x}_1=10, \sigma_1=2, n_1=50 \\<br/>\bar{x}=\text { Mean of } 100 \text { observation }=8 \\<br/>\sigma=\text { SD of } 100 \text { observation }=\sqrt{10.5} \\<br/>\bar{x}=\frac{50 \bar{x}_1+50 \bar{x}_2}{50+50} \\<br/>800=500+50 \bar{x}_2 \\<br/>\bar{x}=6 \\<br/>\sigma^2=\frac{n_1\left(\sigma_1\right)^2+n_2\left(\sigma_2\right)^2}{n_1+n_2}+\frac{n_1 n_2\left(\bar{x}_1-\bar{x}_2\right)^2}{\left(n_1+n_2\right)^2} \\<br/>10.5=\frac{50(4)+50\left(\sigma_2\right)^2}{100}+\frac{2500(10-6)^2}{(100)^2} \\<br/>10.5=\frac{200+50\left(\sigma_2\right)^2}{100}+\frac{25 \times 16}{100} \\<br/>\Rightarrow \quad 1050=600+50\left(\sigma_2\right)^2 \\<br/>\Rightarrow \quad \sigma_2^2=\frac{1050-600}{50}=9 \Rightarrow \sigma_2=3<br/>\end{gathered}<br/>$$</div>


