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JgwzjfiWPQwOGEFm | physics | atoms-and-nuclei | nucleus-and-radioactivity | The energy spectrum of $$\beta $$-particles [ number $$N(E)$$ as a function of $$\beta $$-energy $$E$$ ] emitted from a radioactive source is | [{"identifier": "A", "content": "<img class=\"question-image\" src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734265018/exam_images/j6cjai4rrvt2apgdba3j.webp\" loading=\"lazy\" alt=\"AIEEE 2006 Physics - Atoms and Nuclei Question 210 English Option 1\"> "}, {"identifier": "B", "content": "<img class=\"questi... | ["C"] | null | The range of energy of $$\beta $$-particles is from zero to some maximum value. | mcq | aieee-2006 | 9,172 |
kHqs3QBgfq1sxHkG | physics | atoms-and-nuclei | nucleus-and-radioactivity | In gamma ray emission from a nucleus | [{"identifier": "A", "content": "only the proton number changes "}, {"identifier": "B", "content": "both the neutron number and the proton number change "}, {"identifier": "C", "content": "there is no change in the proton number and the neutron number "}, {"identifier": "D", "content": "only the neutron number changes ... | ["C"] | null | There is no change in the proton number and the neutron number as the $$\gamma $$ - emission takes place as a result of excitation or de-excitation of nuclei. $$\gamma $$-rays have no charge or mass. | mcq | aieee-2007 | 9,173 |
xFdm9vHuxpcBCazi | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive nucleus (initial mass number $$A$$ and atomic number $$Z$$ emits $$3\,\alpha $$- particles and $$2$$ positrons. The ratio of number of neutrons to that of protons in the final nucleus will be | [{"identifier": "A", "content": "$${{A - Z - 8} \\over {Z - 4}}$$ "}, {"identifier": "B", "content": "$${{A - Z - 4} \\over {Z - 8}}$$ "}, {"identifier": "C", "content": "$${{A - Z - 12} \\over {Z - 4}}$$ "}, {"identifier": "D", "content": "$${{A - Z - 4} \\over {Z - 2}}$$ "}] | ["B"] | null | $${}_Z^AX\mathop \to \limits^{A - 12} {}_{Z - 8}Y + 3{}_2^4{X_e} + {}_t^0e$$
<br><br>Number of protons, N<sub>p</sub> = Z - 8
<br><br>Number of neutrons, N<sub>n</sub> = $$A - 12 - \left( {Z - 8} \right)$$
<br><br>$$\therefore$$ Required ratio $$ = {{A - Z - 4} \over {Z - 8}}$$ | mcq | aieee-2010 | 9,175 |
xvat97DTKRC07MRS | physics | atoms-and-nuclei | nucleus-and-radioactivity | The half life of a radioactive substance is $$20$$ minutes. The approximate time interval $$\left( {{t_2} - {t_1}} \right)$$ between the time $${{t_2}}$$ when $${2 \over 3}$$ of it had decayed and time $${{t_1}}$$ when $${1 \over 3}$$ of it had decayed is : | [{"identifier": "A", "content": "$$14$$ min "}, {"identifier": "B", "content": "$$20$$ min "}, {"identifier": "C", "content": "$$28$$ min "}, {"identifier": "D", "content": "$$7$$ min "}] | ["B"] | null | Number of undecayed atom after time $${t_2};$$
<br><br>$${{{N_0}} \over 3} = {N_0}{e^{ - \lambda {t_2}}}\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( i \right)$$
<br><br>Number of undecayed atom after time $${t_1};$$
<br><br>$${{2{N_0}} \over 3} = {N_0}{e^{ - \lambda {t_1}}}\,\,\,\,\,\,\,\,\,\,\,\,\,...\left( {ii} \right)$$
<br>... | mcq | aieee-2011 | 9,176 |
tKd2dCc3kT7LtJzy | physics | atoms-and-nuclei | nucleus-and-radioactivity | Half-lives of two radioactive elements $$A$$ and $$B$$ are $$20$$ minutes and $$40$$ minutes, respectively. Initially, the samples have equal number of nuclei. After $$80$$ minutes, the ratio of decayed number of $$A$$ and $$B$$ nuclei will be: | [{"identifier": "A", "content": "$$1:4$$ "}, {"identifier": "B", "content": "$$5:4$$ "}, {"identifier": "C", "content": "$$1:16$$ "}, {"identifier": "D", "content": "$$4:1$$ "}] | ["B"] | null | For $${A_{t{\raise0.5ex\hbox{$\scriptstyle 1$}
\kern-0.1em/\kern-0.15em
\lower0.25ex\hbox{$\scriptstyle 2$}}}} = 20\,\,$$ min, $$t=80$$ min, number of half lifes $$n=4$$
<br><br>$$\therefore$$ Nuclei remaining $$ = {{{N_0}} \over {{2^4}}}.$$ Therefore nuclei decayed
<br><br>$$ = {N_0} - {{{N_0}} \over {{2^4}}}$$
<br><b... | mcq | jee-main-2016-offline | 9,177 |
9udS0dofmfXrIqDe | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by : | [{"identifier": "A", "content": "$$t = {T \\over {\\log (1.3)}}$$ "}, {"identifier": "B", "content": "$$t = T\\log (1.3)$$ "}, {"identifier": "C", "content": "$$t = {T \\over 2}{{\\log 2} \\over {\\log 1.3}}$$ "}, {"identifier": "D", "content": "$$t = T{{\\log 1.3} \\over {\\log 2}}$$ "}] | ["D"] | null | Let initially there are total N<sub>0</sub> number of nuclei.
<br><br>At time t $${{{N_B}} \over {{N_A}}}$$ = 0.3 (given)
<br><br>$$ \Rightarrow $$ $${{N_B}}$$ = 0.3$${{N_A}}$$
<br><br>N<sub>0</sub> = N<sub>A</sub> + N<sub>B</sub> = N<sub>A</sub> + 0.3N<sub>A</sub>
<br><br>$$ \therefore $$ N<sub>A</sub> = $${{{N_0}} \o... | mcq | jee-main-2017-offline | 9,178 |
klyqpQNdPaWCYJRWhONTr | physics | atoms-and-nuclei | nucleus-and-radioactivity | A solution containing active cobalt $${^{60}_{27}}Co$$ having activity of $$0.8$$ $$\mu Ci$$ and decay constant $$\lambda $$ is injected in an animal's body. If $$1\,c{m^3}$$ of blood is drawn from the animal's body after $$10$$ hrs of injection, the activity found was $$300$$ decays per minute What is the volume of bl... | [{"identifier": "A", "content": "$$6$$ liters"}, {"identifier": "B", "content": "$$7$$ liters"}, {"identifier": "C", "content": "$$4$$ liters"}, {"identifier": "D", "content": "$$5$$ liters"}] | ["D"] | null | Initial activity, N<sub>o</sub> = 0.8 $$\mu $$<sup>Ci</sup>
<br><br>Activity at time t, N = N<sub>0</sub> e<sup>$$-$$$$\lambda $$t</sup>
<br><br>Activity in 1 cm<sup>3</sup> blood after 10 hr, n = 300 decays per minute
<br><br>= $${{300} \over {60}}\,dps$$
<br><br>= 5 dps.
<br><br>Activity in whole blood after to hr =... | mcq | jee-main-2018-online-15th-april-morning-slot | 9,179 |
0uhgHoPX8uRa15yU1mKaY | physics | atoms-and-nuclei | nucleus-and-radioactivity | An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is : | [{"identifier": "A", "content": "8 : 27"}, {"identifier": "B", "content": "4 : 9"}, {"identifier": "C", "content": "3 : 2"}, {"identifier": "D", "content": "2 : 3"}] | ["C"] | null | <p>The two nuclei have velocity in ratio 8 : 27. By conservation of momentum, we have</p>
<p>$${m_1}{v_1} = {m_2}{v_2} \Rightarrow {{{v_1}} \over {{v_2}}} = {{{m_2}} \over {{m_1}}} \Rightarrow {{{m_2}} \over {{m_1}}} = {8 \over {27}}$$</p>
<p>Now, since $$m = \rho {4 \over 3}\pi {r^3}$$</p>
<p>Therefore, $${{{m_2}} \ov... | mcq | jee-main-2018-online-15th-april-evening-slot | 9,180 |
ufB55eRLFOuOWldW8U3rsa0w2w9jx7grwdi | physics | atoms-and-nuclei | nucleus-and-radioactivity | Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :
| [{"identifier": "A", "content": "9 : 8"}, {"identifier": "B", "content": "1 : 8"}, {"identifier": "C", "content": "8 : 1"}, {"identifier": "D", "content": "3 : 8"}] | ["A"] | null | N<sub>A</sub> = N<sub>0</sub>$${\left( {{1 \over 2}} \right)^{{t \over {{T_{{1 \over 2}}}}}}}$$
<br>= N<sub>0</sub>$${\left( {{1 \over 2}} \right)^{{{60} \over {10}}}}$$
<br>= N<sub>0</sub>$${\left( {{1 \over 2}} \right)^6}$$
<br><br>N<sub>B</sub> = N<sub>0</sub>$${\left( {{1 \over 2}} \right)^{{t \over {{T_{{1 \over... | mcq | jee-main-2019-online-12th-april-evening-slot | 9,182 |
NlbbE5WpPNAY4GRkyN3rsa0w2w9jwzipjr0 | physics | atoms-and-nuclei | nucleus-and-radioactivity | Two radioactive substances A and B have decay constants 5$$\lambda $$ and $$\lambda $$ respectively. At t = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $${\left( {{1 \over e}} \right)^2}$$
will be : | [{"identifier": "A", "content": "$${2 \\over \\lambda }$$"}, {"identifier": "B", "content": "$${1 \\over {4\\lambda }}$$"}, {"identifier": "C", "content": "$${1 \\over {2\\lambda }}$$"}, {"identifier": "D", "content": "$${1 \\over {\\lambda }}$$"}] | ["C"] | null | N<sub>x</sub>(at t) = N<sub>0</sub>e<sup>–5$$\lambda $$t</sup><br><br>
N<sub>y</sub>(at t) = N<sub>0</sub>e<sup>–$$\lambda $$t</sup><br><br>
$${{{N_x}} \over {{N_y}}} = {1 \over {{e^2}}} = {e^{ - 4\lambda t}}$$<br><br>
$$ \Rightarrow 4\lambda t = 2$$ <br><br>
$$ \Rightarrow t = {2 \over {4\lambda }} = \left( {{1 \over ... | mcq | jee-main-2019-online-10th-april-evening-slot | 9,183 |
FjcX4DtArwI1Qn68wl18hoxe66ijvztgcko | physics | atoms-and-nuclei | nucleus-and-radioactivity | Two radioactive materials A and B have decay
constants 10$$\lambda $$ and $$\lambda $$, respectively. It initially
they have the same number of nuclei, then the
ratio of the number of nuclei of A to that of B
will be 1/e after a time : | [{"identifier": "A", "content": "1/9$$\\lambda $$"}, {"identifier": "B", "content": "11/10$$\\lambda $$"}, {"identifier": "C", "content": "1/10$$\\lambda $$"}, {"identifier": "D", "content": "1/11$$\\lambda $$"}] | ["A"] | null | N<sub>1</sub> = N<sub>0</sub>e<sup>–10$$\lambda $$t</sup>
; N<sub>2</sub> = N<sub>0</sub>e<sup>–$$\lambda $$t</sup><br><br>
$${1 \over e} = {{{N_1}} \over {{N_2}}} = {e^{ - 9\lambda t}}$$<br><br>
$$ \Rightarrow 9\lambda t = 1$$<br><br>
$$ \Rightarrow t = {1 \over {9\lambda }}$$ | mcq | jee-main-2019-online-10th-april-morning-slot | 9,185 |
YZoXYcmEfMUcCC1WKrRjE | physics | atoms-and-nuclei | nucleus-and-radioactivity | In a radioactive decay chain, the initial nucleus is $${}_{90}^{232}$$Th. At the end there are 6 $$\alpha $$-particles and 4 $$\beta $$-particles which are emitted. If the end nucleus is $${}_Z^A$$X, A and Z are given by : | [{"identifier": "A", "content": "A = 208; Z = 80"}, {"identifier": "B", "content": "A = 208; Z = 82"}, {"identifier": "C", "content": "A = 200; Z = 81 "}, {"identifier": "D", "content": "A = 202; Z = 80"}] | ["B"] | null | $${}_{90}^{232}$$Th $$\buildrel \, \over
\longrightarrow $$ $${}_{78}^{208}$$Y + $${}_2^4$$He
<br><br>$${}_{78}^{208}$$Y $$\buildrel \, \over
\longrightarrow $$ $${}_{82}^{208}$$ X + 4$$\beta $$ | mcq | jee-main-2019-online-12th-january-evening-slot | 9,186 |
UrX1dBuDzRM0r7lAhAEbf | physics | atoms-and-nuclei | nucleus-and-radioactivity | At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio $${{{R_B}} \over {{R_A}}}$$ of their activities after time t itself decays with time t as e<sup>$$-$$3t</sup>. If the half-life of A is ln<sup>2</sup>, the half-life of B is : | [{"identifier": "A", "content": "4ln2"}, {"identifier": "B", "content": "$${{\\ln 2} \\over 2}$$"}, {"identifier": "C", "content": "$${{\\ln 2} \\over 4}$$"}, {"identifier": "D", "content": "2ln2"}] | ["C"] | null | We know,
<br><br>Activity (R) = R<sub>0</sub> e<sup>$$-$$$$\lambda $$t</sup>
<br><br>Given that,
<br><br>at t = 0
<br><br>R<sub>A</sub> = R<sub>B</sub>
<br><br>$$ \Rightarrow $$ R<sub>0A</sub> e<sup>$$-$$$$\lambda $$<sub>A</sub>x0</sup> = R<sub>0</sub><sub>B</sub> e<sup>$$-$$ $$\lambda $$<sub>B</sub>x... | mcq | jee-main-2019-online-9th-january-evening-slot | 9,187 |
160d07KInIQ2dmyL1Ykxm | physics | atoms-and-nuclei | nucleus-and-radioactivity | A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 $$ \times $$ 10<sup>10</sup> decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct choices for half-lives of A and B would then be respectively : | [{"identifier": "A", "content": "5 days and 10 days"}, {"identifier": "B", "content": "10 days and 40 days"}, {"identifier": "C", "content": "20 days and 5 days"}, {"identifier": "D", "content": "20 days and 10 days"}] | ["C"] | null | Let number of nuclei present in material A is N<sub>A</sub> and in meterial B is N<sub>B</sub> According to question,
<br><br>N<sub>A</sub> = 2N<sub>B</sub>
<br><br>We know, activity (A) = $$\lambda $$N.
<br><br>$$ \therefore $$ $$\lambda $$<sub>A</sub>N<sub>A</sub> = 10 . . . . . . (1)
<br><br>a... | mcq | jee-main-2019-online-9th-january-morning-slot | 9,188 |
8ujCIhDzis1vgjc8Puefo | physics | atoms-and-nuclei | nucleus-and-radioactivity | The ratio of mass densities of nuclei of <sup>40</sup>Ca
and <sup>16</sup>O is close to :- | [{"identifier": "A", "content": "1"}, {"identifier": "B", "content": "5"}, {"identifier": "C", "content": "0.1"}, {"identifier": "D", "content": "2"}] | ["A"] | null | Densities of nucleus happens to be constant,
irrespective of mass number. | mcq | jee-main-2019-online-8th-april-evening-slot | 9,189 |
HiECt2eLjPlGBJY7Gs7k9k2k5f4r8b3 | physics | atoms-and-nuclei | nucleus-and-radioactivity | The activity of a radioactive sample falls from 700 s<sup>–1</sup> to 500 s<sup>–1</sup> in 30 minutes. Its half life is close
to:
| [{"identifier": "A", "content": "62 min"}, {"identifier": "B", "content": "66 min"}, {"identifier": "C", "content": "72 min"}, {"identifier": "D", "content": "52 min"}] | ["A"] | null | A = A<sub>0</sub> e<sup>-$$\lambda $$t</sup>
<br><br>$$ \Rightarrow $$ 500 = 700 e<sup>-$$\lambda $$$$ \times $$30</sup>
<br><br>$$ \Rightarrow $$ $$\ln {7 \over 5}$$ = $$\lambda $$$$ \times $$30
<br><br>Also T<sub>1/2</sub> = $${{\ln 2} \over \lambda }$$ = $${{\ln 2} \over {\ln {7 \over 5}}} \times 30$$
<br><br>$$ \Ri... | mcq | jee-main-2020-online-7th-january-evening-slot | 9,190 |
0Zn1aBpQemDUqte27djgy2xukf15vama | physics | atoms-and-nuclei | nucleus-and-radioactivity | In a radioactive material, fraction of active
material remaining after time t is 9/16. The
fraction that was remaining after t/2 is
| [{"identifier": "A", "content": "$${3 \\over 4}$$"}, {"identifier": "B", "content": "$${4 \\over 5}$$"}, {"identifier": "C", "content": "$${3 \\over 5}$$"}, {"identifier": "D", "content": "$${7 \\over 8}$$"}] | ["A"] | null | First order decay
<br><br>N(t) = N<sub>0</sub>e<sup>-$$\lambda $$t</sup>
<br><br>Given $${{N\left( t \right)} \over {{N_0}}} = {9 \over {16}} = $$ e<sup>-$$\lambda $$t</sup>
<br><br>N(t/2) = N<sub>0</sub>e<sup>-$$\lambda $$(t/2)</sup>
<br><br>$${{N\left( {t/2} \right)} \over {{N_0}}} = \sqrt {{e^{ - \lambda t}}} $$ = $... | mcq | jee-main-2020-online-3rd-september-morning-slot | 9,191 |
UDljbalqZMZ4U44li4jgy2xukf3uo6t9 | physics | atoms-and-nuclei | nucleus-and-radioactivity | The radius R of a nucleus of mass number A can be estimated by the formula<br/> R = (1.3 $$ \times $$ 10<sup>–15</sup>)A<sup>1/3</sup> m.
<br/>It follows that the mass density of a nucleus is of the order of :
<br/><br/>(M<sub>prot.</sub> $$ \cong $$ M<sub>neut</sub> $$ \simeq $$ 1.67 $$ \times $$ 10<sup>–27</sup> kg) | [{"identifier": "A", "content": "10<sup>24</sup> kg m<sup>\u20133</sup>"}, {"identifier": "B", "content": "10<sup>10</sup> kg m<sup>\u20133</sup>"}, {"identifier": "C", "content": "10<sup>17</sup> kg m<sup>\u20133</sup>"}, {"identifier": "D", "content": "10<sup>3</sup> kg m<sup>\u20133</sup>"}] | ["C"] | null | $$R = (1.3 \times {10^{ - 15}}){A^{{1 \over 3}}}$$<br><br>We know, $$m = pV$$<br><br>$$ \Rightarrow $$ $$p = {m \over V}$$<br><br>$$ \Rightarrow $$ $$p = {{{m_p}A} \over {{4 \over 3}\pi {R^3}}}$$<br><br>$$p = {{{m_p}A} \over {{4 \over 3}\pi \times {{(1.3 \times {{10}^{ - 15}})}^3}A}}$$<br><br>$$p \approx {10^{17}}kg/m... | mcq | jee-main-2020-online-3rd-september-evening-slot | 9,192 |
0emef2jIkxyeI8ZQyXjgy2xukfl37s3m | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive nucleus decays by two different
processes. The half life for the first process is
10 s and that for the second is 100 s. The
effective half life of the nucleus is close to : | [{"identifier": "A", "content": "12 sec"}, {"identifier": "B", "content": "9 sec"}, {"identifier": "C", "content": "55 sec"}, {"identifier": "D", "content": "6 sec"}] | ["B"] | null | T<sub>1</sub> = 10 sec
<br><br>$$\lambda $$<sub>1</sub> = $${{\ln 2} \over {{T_1}}}$$
<br><br>T<sub>2</sub> = 100 sec
<br><br>$$\lambda $$<sub>2</sub> = $${{\ln 2} \over {{T_2}}}$$
<br><br>$$\lambda $$<sub>eq</sub> = $${{\ln 2} \over {{T_{eq}}}}$$
<br><br>We know,
<br><br>$$\lambda $$<sub>eq</sub> = $$\lambda $$<sub>1<... | mcq | jee-main-2020-online-5th-september-evening-slot | 9,194 |
MPH3hdGxfeQZjSoDxxjgy2xukg0i5sfh | physics | atoms-and-nuclei | nucleus-and-radioactivity | Given the masses of various atomic particles
<br/>m<sub>p</sub> = 1.0072 u, m<sub>n</sub> = 1.0087 u, m<sub>e</sub> = 0.000548 u,
<br/>$${m_{\overline v }}$$ = 0, m<sub>d</sub> = 2.0141 u, where p $$ \equiv $$ proton,
n $$ \equiv $$ neutron, <br/>e $$ \equiv $$ electron, $$\overline v $$ $$ \equiv $$ antineutrino and
d... | [{"identifier": "A", "content": "n + n $$ \\to $$ deuterium atom\n<br>(electron bound to the nucleus)"}, {"identifier": "B", "content": "n + p $$ \\to $$ d + $$\\gamma $$"}, {"identifier": "C", "content": "p $$ \\to $$ n + e<sup>+</sup> + $$\\overline v $$"}, {"identifier": "D", "content": "e<sup>+</sup> + e<sup>-</sup... | ["B"] | null | n + n $$ \to $$ deuterium atom (This is incorrect)
<br><br>Correct is n + p $$ \to $$ d + $$\gamma $$
<br><br>p $$ \to $$ n + e<sup>+</sup> + $$\overline v $$ <br>(This is incorrect as mass is increasing)
<br><br>e<sup>+</sup> + e<sup>-</sup> $$ \to $$ $$\gamma $$ (This is incorrect)
<br><br>Correct is e<sup>+</sup> + ... | mcq | jee-main-2020-online-6th-september-evening-slot | 9,195 |
6qKuSPF2JCosrabfIb1klrxavxo | physics | atoms-and-nuclei | nucleus-and-radioactivity | Two radioactive substances X and Y originally have N<sub>1</sub> and N<sub>2</sub> nuclei respectively. Half life of X is half of the half life of Y. After three half lives of Y, number of nuclei of both are equal. The ratio $${{{N_1}} \over {{N_2}}}$$ will be equal to : | [{"identifier": "A", "content": "$${1 \\over 8}$$"}, {"identifier": "B", "content": "$${3 \\over 1}$$"}, {"identifier": "C", "content": "$${1 \\over 3}$$"}, {"identifier": "D", "content": "$${8 \\over 1}$$"}] | ["D"] | null | Let Half life of x = t<br><br>then half life of y = 2t<br><br>when 3 half life of y is completed then 6 half life of x is completed.<br><br>$$ \therefore $$ Now x have = $${{{N_1}} \over {{2^6}}}$$ nuclei<br><br>and y have = $${{{N_2}} \over {{2^3}}}$$ nuclei<br><br>From question, <br><br>$${{{N_1}} \over {{2^6}}} = {{... | mcq | jee-main-2021-online-25th-february-morning-slot | 9,196 |
VCwfDV3vYMGiyFF62d1klukkixr | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive sample is undergoing $$\alpha$$ decay. At any time t<sub>1</sub>, its activity is A and another time t<sub>2</sub>, the activity is $${A \over 5}$$. What is the average life time for the sample? | [{"identifier": "A", "content": "$${{\\ln 5} \\over {{t_2} - {t_1}}}$$"}, {"identifier": "B", "content": "$${{\\ln ({t_2} + {t_1})} \\over 2}$$"}, {"identifier": "C", "content": "$${{{t_1} - {t_2}} \\over {\\ln 5}}$$"}, {"identifier": "D", "content": "$${{{t_2} - {t_1}} \\over {\\ln 5}}$$"}] | ["D"] | null | Let initial activity be A<sub>0</sub><br><br>A = A<sub>0</sub> e<sup>$$-$$$$\lambda$$t<sub>1</sub></sup> ........(i)<br><br>$${A \over 5}$$ = A<sub>0</sub> e<sup>$$-$$$$\lambda$$t<sub>2</sub></sup> .......(ii)<br><br>(i) $$ \div $$ (ii)<br><br>5 = e<sup>$$\lambda$$(t<sub>2</sub> $$-$$ t<sub>1</sub>)</sup><br><br>$$\lam... | mcq | jee-main-2021-online-26th-february-evening-slot | 9,197 |
KXzo19ctsrQF7crqVk1kmip3ifx | physics | atoms-and-nuclei | nucleus-and-radioactivity | The half-life of Au<sup>198</sup> is 2.7 days. The activity of 1.50 mg of Au<sup>198</sup> if its atomic weight is 198 g mol<sup>$$-$$1</sup> is, (N<sub>a</sub> = 6 $$\times$$ 10<sup>23</sup>/mol). | [{"identifier": "A", "content": "240 Ci"}, {"identifier": "B", "content": "357 Ci"}, {"identifier": "C", "content": "252 Ci"}, {"identifier": "D", "content": "535 Ci"}] | ["B"] | null | Activity, $$A = \lambda N$$<br><br>Where, $$N = n{N_A}$$<br><br>$${N_A} = 6 \times {10^{23}}$$/mol<br><br>$$ = {{6 \times {{10}^{23}}} \over {3.7 \times {{10}^{10}}}}$$ Ci<br><br>Here, $${A_0} = \lambda {N_0}$$<br><br>We know, <br><br>$${T_{1/2}} = {{\ln (2)} \over \lambda }$$<br><br>$$ \Rightarrow \lambda = {{\ln (2)... | mcq | jee-main-2021-online-16th-march-evening-shift | 9,199 |
guiz8db8Hl7p2nGFw71kmlvyl3v | physics | atoms-and-nuclei | nucleus-and-radioactivity | The decay of a proton to neutron is : | [{"identifier": "A", "content": "always possible as it is associated only with $$\\beta$$<sup>+</sup> decay"}, {"identifier": "B", "content": "possible only inside the nucleus"}, {"identifier": "C", "content": "not possible as proton mass is less than the neutron mass"}, {"identifier": "D", "content": "not possible but... | ["B"] | null | Positron emission or Beta plus decay is a subtype of radioactive decay called Beta decay, in which a proton inside a nucleus is converted into a neutron while releasing a positron and an electron neutrino.
<br><br>So, decay of a proton to neutron is possible only inside the nucleus. Free proton cannot decay to neutron ... | mcq | jee-main-2021-online-18th-march-evening-shift | 9,201 |
mSwUCZDhHNAgD0SsqN1krpmvvl6 | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains ? (Take ln 3 = 1.1) | [{"identifier": "A", "content": "740 years"}, {"identifier": "B", "content": "1110 years"}, {"identifier": "C", "content": "700 years"}, {"identifier": "D", "content": "340 years"}] | ["A"] | null | The given situation can be shown as<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1kxpz7lve/098683e2-ad9d-4fbe-b0a9-a193566a87fa/4322eda0-67ca-11ec-9473-1365722e3eb6/file-1kxpz7lvf.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1kxpz7lve/098683e2-ad9d-4fbe-b0a9-a193566a8... | mcq | jee-main-2021-online-20th-july-morning-shift | 9,202 |
1krqcwf30 | physics | atoms-and-nuclei | nucleus-and-radioactivity | For a certain radioactive process the graph between In R and t(sec) is obtained as shown in the figure. Then the value of half life for the unknown radioactive material is approximately :<br/><img src="data:image/png;base64,UklGRrgRAABXRUJQVlA4IKwRAABQcQCdASppAVYBPm02l0ikIqIhIpJpyIANiWlu/HyZN+tQ0P0U/kv5AeCH9r/qX7I+ff4n... | [{"identifier": "A", "content": "9.15 sec"}, {"identifier": "B", "content": "6.93 sec"}, {"identifier": "C", "content": "2.62 sec"}, {"identifier": "D", "content": "4.62 sec"}] | ["D"] | null | R = R<sub>0</sub>e<sup>$$-$$$$\lambda$$t</sup><br><br>lnR = lnR<sub>0</sub> $$-$$ $$\lambda$$t<br><br>$$-$$$$\lambda$$ is slope of straight line<br><br>$$\lambda$$ = $${3 \over {20}}$$<br><br>$${t_{1/2}} = {{\ln 2} \over \lambda } = 4.62$$ | mcq | jee-main-2021-online-20th-july-evening-shift | 9,203 |
1krqg0plb | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive substance decays to $${\left( {{1 \over {16}}} \right)^{th}}$$ of its initial activity in 80 days. The half life of the radioactive substance expressed in days is ____________. | [] | null | 20 | $${N_0}\buildrel {{{{t_1}} \over 2}} \over
\longrightarrow {{{N_0}} \over 2}\buildrel {{{{t_1}} \over 2}} \over
\longrightarrow {{{N_0}} \over 4}\buildrel {{{{t_1}} \over 2}} \over
\longrightarrow {{{N_0}} \over 8}\buildrel {{{{t_1}} \over 2}} \over
\longrightarrow {{{N_0}} \over {16}}$$<br><br>$$4 \times {t_{1/2}}... | integer | jee-main-2021-online-20th-july-evening-shift | 9,204 |
1krueyi4t | physics | atoms-and-nuclei | nucleus-and-radioactivity | Some nuclei of a radioactive material are undergoing radioactive decay. The time gap between the instances when a quarter of the nuclei have decayed and when half of the nuclei have decayed is given as :<br/><br/>(where $$\lambda$$ is the decay constant) | [{"identifier": "A", "content": "$${1 \\over 2}{{\\ln 2} \\over \\lambda }$$"}, {"identifier": "B", "content": "$${{\\ln 2} \\over \\lambda }$$"}, {"identifier": "C", "content": "$${{2\\ln 2} \\over \\lambda }$$"}, {"identifier": "D", "content": "$${{\\ln {3 \\over 2}} \\over \\lambda }$$"}] | ["D"] | null | $${{3{N_0}} \over 4} = {N_0}{e^{ - \lambda {t_1}}}$$<br><br>$${{{N_0}} \over 2} = {N_0}{e^{ - \lambda {t_2}}}$$<br><br>$$\ln (3/4) = - \lambda {t_1}$$ ..... (i)<br><br>$$\ln (1/2) = - \lambda {t_2}$$ ..... (i)<br><br>$$\ln (3/4) - \ln (1/2) = \lambda ({t_2} - {t_1})$$ ....(i)<br><br>$$\Delta t = {{\ln (3 /2)} \over \... | mcq | jee-main-2021-online-25th-july-morning-shift | 9,205 |
1krukk6c4 | physics | atoms-and-nuclei | nucleus-and-radioactivity | The half-life of $${}^{198}Au$$ is 3 days. If atomic weight of $${}^{198}Au$$ is 198 g/mol then the activity of 2 mg of $${}^{198}Au$$ is [in disintegration/second] : | [{"identifier": "A", "content": "2.67 $$\\times$$ 10<sup>12</sup>"}, {"identifier": "B", "content": "6.06 $$\\times$$ 10<sup>18</sup>"}, {"identifier": "C", "content": "32.36 $$\\times$$ 10<sup>12</sup>"}, {"identifier": "D", "content": "16.18 $$\\times$$ 10<sup>12</sup>"}] | ["D"] | null | A = $$\lambda$$N<br><br>$$\lambda = {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over {3 \times 24 \times 60 \times 60}}$$sec<sup>$$-$$1</sup> = 2.67 $$\times$$ 10<sup>$$-$$6</sup> sec<sup>$$-$$1</sup><br><br>N = Number of atoms in 2 mg Au<br><br>$$ = {{2 \times {{10}^{ - 3}}} \over {198}} \times 6 \times {10^{23}}$$ = 6.0... | mcq | jee-main-2021-online-25th-july-morning-shift | 9,206 |
1krwcyk48 | physics | atoms-and-nuclei | nucleus-and-radioactivity | The nuclear activity of a radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years. The half-life of radioactive element is _____________ years. | [] | null | 10 | We know, $$A = {A_0}{e^{ - \lambda t}}$$
<br><br>For half life
<br><br>$${{{A_0}} \over 2} = {e^{ - \lambda {t_{1/2}}}}$$
<br><br>$$ \Rightarrow $$ $${\lambda {t_{1/2}}}$$ = ln 2 .....(1)
<br><br>And when radioactive element becomes $${\left( {{1 \over 8}} \right)^{th}}$$ of its initial value in 30 years
<br><br>$${{{... | integer | jee-main-2021-online-25th-july-evening-shift | 9,207 |
1krywmd9h | physics | atoms-and-nuclei | nucleus-and-radioactivity | If 'f' denotes the ratio of the number of nuclei decayed (N<sub>d</sub>) to the number of nuclei at t = 0 (N<sub>0</sub>) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as :<br/><br/>[$$\lambda$$ is the radioactive decay constant] | [{"identifier": "A", "content": "$$-$$ $$\\lambda$$ (1 $$-$$ e<sup>$$-$$$$\\lambda$$t</sup>)"}, {"identifier": "B", "content": "$$\\lambda$$ (1 $$-$$ e<sup>$$-$$$$\\lambda$$t</sup>)"}, {"identifier": "C", "content": "$$\\lambda$$e<sup>$$-$$$$\\lambda$$t</sup>"}, {"identifier": "D", "content": "$$-$$ $$\\lambda$$e<sup>$... | ["C"] | null | N = N<sub>0</sub>e<sup>$$-$$$$\lambda$$t</sup><br><br>N<sub>d</sub> = N<sub>0</sub> $$-$$ N<br><br>N<sub>d</sub> = N<sub>0</sub> (1 $$-$$ e<sup>$$-$$$$\lambda$$t</sup>)<br><br>$${{{N_d}} \over {{N_0}}} = f = 1 - {e^{ - \lambda t}}$$<br><br>$$ \Rightarrow $$ $${{df} \over {dt}} = \lambda {e^{ - \lambda t}}$$ | mcq | jee-main-2021-online-27th-july-morning-shift | 9,208 |
1kryyegjk | physics | atoms-and-nuclei | nucleus-and-radioactivity | A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 $$\mu$$F is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be _____________ $$\Omeg... | [] | null | 150 | T<sub>m</sub> =30 ms<br><br>C = 200 $$\mu$$F<br><br>$${q \over N} = {{{Q_0}{e^{ - t/RC}}} \over {{N_0}{e^{ - \lambda t}}}} = {{{Q_0}} \over {{N_0}}}{e^{t\left( {\lambda - {1 \over {RC}}} \right)}}$$<br><br>Since q/N is constant hence<br><br>$$\lambda ={1 \over {RC}}$$<br><br>$$R = {1 \over {\lambda C}} = {{{T_m}} \ov... | integer | jee-main-2021-online-27th-july-morning-shift | 9,209 |
1ks18m3oj | physics | atoms-and-nuclei | nucleus-and-radioactivity | Consider the following statements :<br/><br/>A. Atoms of each element emit characteristics spectrum.<br/><br/>B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.<br/><br/>C. The density of nuclear matter depends on the size of the nucleus.<br/><br/>D. A free neutron... | [{"identifier": "A", "content": "A, B, C, D and E"}, {"identifier": "B", "content": "A, B and E only"}, {"identifier": "C", "content": "B and D only"}, {"identifier": "D", "content": "A, C and E only"}] | ["B"] | null | (A) True, atom of each element emits characteristic spectrum.<br><br>(B) True, according to Bohr's postulates $$mvr = {{nh} \over {2\pi }}$$ and hence electron resides into orbits of specific radius called stationary orbits.<br><br>(C) False, density of nucleus is constant.<br><br>(D) False, A free neutron is unstable ... | mcq | jee-main-2021-online-27th-july-evening-shift | 9,210 |
1ktbqe7cv | physics | atoms-and-nuclei | nucleus-and-radioactivity | At time t = 0, a material is composed of two radioactive atoms A and B, where N<sub>A</sub>(0) = 2N<sub>B</sub>(0). The decay constant of both kind of radioactive atoms is $$\lambda$$. However, A disintegrates to B and B disintegrates to C. Which of the following figures represents the evolution of N<sub>B</sub>(t) / N... | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734266774/exam_images/ribrlolghscvdsvlv4lm.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2021 (Online) 26th August Evening Shift Physics - Atoms and Nuclei Quest... | ["C"] | null | A $$\to$$ B, B $$\to$$ C<br><br>$${{d{N_B}} \over {dt}} = \lambda {N_A} - \lambda {N_B}$$<br><br>$${{d{N_B}} \over {dt}} = 2\lambda {N_{{B_0}}}{e^{ - \lambda t}} - \lambda {N_B}$$<br><br>$${e^{ - \lambda t}}\left( {{{d{N_B}} \over {dt}} + \lambda {N_B}} \right) = 2\lambda {N_{{B_0}}}{e^{ - \lambda t}} \times {e^{\lambd... | mcq | jee-main-2021-online-26th-august-evening-shift | 9,211 |
1ktdycxoc | physics | atoms-and-nuclei | nucleus-and-radioactivity | There are 10<sup>10</sup> radioactive nuclei in a given radioactive element, its half-life time is 1 minute. How many nuclei will remain after 30 seconds? $$\left( {\sqrt 2 = 1.414} \right)$$ | [{"identifier": "A", "content": "2 $$\\times$$ 10<sup>10</sup>"}, {"identifier": "B", "content": "7 $$\\times$$ 10<sup>9</sup>"}, {"identifier": "C", "content": "10<sup>5</sup>"}, {"identifier": "D", "content": "4 $$\\times$$ 10<sup>10</sup>"}] | ["B"] | null | $${N \over {{N_0}}} = {\left( {{1 \over 2}} \right)^{{t \over {{t^{1/2}}}}}}$$<br><br>$${N \over {{{10}^{10}}}} = {\left( {{1 \over 2}} \right)^{{{30} \over {60}}}}$$<br><br>$$ \Rightarrow N = {10^{10}} \times {\left( {{1 \over 2}} \right)^{{1 \over 2}}} = {{{{10}^{10}}} \over {\sqrt 2 }} \approx 7 \times {10^9}$$ | mcq | jee-main-2021-online-27th-august-morning-shift | 9,212 |
1kth2lm1p | physics | atoms-and-nuclei | nucleus-and-radioactivity | A sample of a radioactive nucleus A disintegrates to another radioactive nucleus B, which in turn disintegrates to some other stable nucleus C. Plot of a graph showing the variation of number of atoms of nucleus B versus time is :<br/><br/>(Assume that at t = 0, there are no B atoms in the sample) | [{"identifier": "A", "content": "<img src=\"https://res.cloudinary.com/dckxllbjy/image/upload/v1734263309/exam_images/t2l3ewau81hn7k4puhm7.webp\" style=\"max-width: 100%;height: auto;display: block;margin: 0 auto;\" loading=\"lazy\" alt=\"JEE Main 2021 (Online) 31st August Morning Shift Physics - Atoms and Nuclei Quest... | ["D"] | null | A $$\to$$ B $$\to$$ C (stable)<br><br>Initially no. of atoms of B = 0 at t = 0, no. of atoms of B will starts increasing & reaches maximum value when rate of decay of B = rate of formation of B.<br><br>After that maximum value, no. of atoms will starts decreasing as growth & decay both are exponential functions... | mcq | jee-main-2021-online-31st-august-morning-shift | 9,213 |
1ktmofoon | physics | atoms-and-nuclei | nucleus-and-radioactivity | The half life period of radioactive element x is same as the mean life time of another radioactive element y. Initially they have the same number of atoms. Then : | [{"identifier": "A", "content": "x-will decay faster than y."}, {"identifier": "B", "content": "y-will decay faster than x."}, {"identifier": "C", "content": "x and y have same decay rate initially and later on different decay rate."}, {"identifier": "D", "content": "x and y decay at the same rate always."}] | ["B"] | null | Given, ($$\tau$$<sub>1/2</sub>)<sub>x</sub> = ($$\tau$$)<sub>y</sub><br/><br/>Here, $$\tau$$<sub>1/2</sub> = half-life period of radioactive element and $$\tau$$ = mean life period of radioactive element.<br/><br/>As we know the expression,<br/><br/>Half-life of the radioactive element x,<br/><br/>$${\tau _{1/2}} = {{\... | mcq | jee-main-2021-online-1st-september-evening-shift | 9,214 |
1l546vpll | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The activity of a radioactive material is 2.56 $$\times$$ 10<sup>$$-$$3</sup> Ci. If the half life of the material is 5 days, after how many days the activity will become 2 $$\times$$ 10<sup>$$-$$5</sup> Ci ?</p> | [{"identifier": "A", "content": "30 days"}, {"identifier": "B", "content": "35 days"}, {"identifier": "C", "content": "40 days"}, {"identifier": "D", "content": "25 days"}] | ["B"] | null | By Radioactive Decay law,
<br/><br/>$$
\begin{aligned}
& \mathrm{R}=\mathrm{R}_{\mathrm{o}} e^{-\lambda t} \\\\
& \Rightarrow 2 \times 10^{-5}=2.56 \times 10^{-3} e^{-\lambda t}
\end{aligned}
$$
<br/><br/>[Where, $\mathrm{R} =$ Activity at time $t$
<br/><br/>$\lambda =$ Activity constant of Radioactive sample
<br/><br/... | mcq | jee-main-2022-online-29th-june-morning-shift | 9,215 |
1l54urzkk | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>In the following nuclear reaction,</p>
<p>$$D\buildrel \alpha \over
\longrightarrow {D_1}\buildrel {{\beta ^ - }} \over
\longrightarrow {D_2}\buildrel \alpha \over
\longrightarrow {D_3}\buildrel \gamma \over
\longrightarrow {D_4}$$</p>
<p>Mass number of D is 182 and atomic number is 74. Mass number and atomic... | [{"identifier": "A", "content": "174 and 71"}, {"identifier": "B", "content": "174 and 69"}, {"identifier": "C", "content": "172 and 69"}, {"identifier": "D", "content": "172 and 71"}] | ["A"] | null | <p>Equivalent reaction can be written as</p>
<p>$$D\buildrel {} \over
\longrightarrow {D_4} + 2\alpha + {\beta ^ - } + \gamma $$</p>
<p>$$\Rightarrow$$ Mass number of D<sub>4</sub> = Mass number of D $$-$$ 2 $$\times$$ 4</p>
<p>= 182 $$-$$ 8 = 174</p>
<p>$$\Rightarrow$$ Atomic number of D<sub>4</sub></p>
<p>= Atomic ... | mcq | jee-main-2022-online-29th-june-evening-shift | 9,216 |
1l54wybh2 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6.25% of its initial value. The value of x is ____________.</p> | [] | null | 20 | <p>$$N = {N_0}{e^{ - \lambda t}}$$</p>
<p>$$ \Rightarrow {{6.25} \over {100}} = {e^{ - \lambda t}}$$</p>
<p>$$ \Rightarrow {e^{ - \lambda t}} = {1 \over {16}} = {\left( {{1 \over 2}} \right)^4}$$</p>
<p>$$ \Rightarrow t = 4{t_{1/2}}$$</p>
<p>$$ \Rightarrow t = 20$$ years</p> | integer | jee-main-2022-online-29th-june-evening-shift | 9,217 |
1l55lkgaa | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Following statements related to radioactivity are given below :</p>
<p>(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.</p>
<p>(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.</p>
<p>(C) Slope of the graph of log<... | [{"identifier": "A", "content": "(A) and (B) only"}, {"identifier": "B", "content": "(B) and (D) only"}, {"identifier": "C", "content": "(B) and (C) only"}, {"identifier": "D", "content": "(C) and (D) only"}] | ["C"] | null | <p>Radioactive decay is a random and spontaneous process it depends on unbalancing of nucleus.</p>
<p>$$N = {N_0}{e^{ - \lambda t}}$$ ..... (B)</p>
<p>$$\ln N = - \lambda t + \ln {N_0}$$</p>
<p>So, slope $$ = - \lambda $$ ..... (C)</p>
<p>$${t_{1/2}} = {{\ln 2} \over \lambda }$$</p>
<p>So $${t_{1/2}} \times \lambda ... | mcq | jee-main-2022-online-28th-june-evening-shift | 9,218 |
1l58c8yho | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>How many alpha and beta particles are emitted when Uranium <sub>92</sub>U<sup>238</sup> decays to lead <sub>82</sub>Pb<sup>206</sup> ?</p> | [{"identifier": "A", "content": "3 alpha particles and 5 beta particles"}, {"identifier": "B", "content": "6 alpha particles and 4 beta particles"}, {"identifier": "C", "content": "4 alpha particles and 5 beta particles"}, {"identifier": "D", "content": "8 alpha particles and 6 beta particles"}] | ["D"] | null | <p>$${}_{92}{U^{238}}\buildrel {} \over
\longrightarrow {}_{82}P{b^{206}} + x\left( {{}_2H{e^4}} \right) + {}_y\left( {{}_{ - 1}{\beta ^0}} \right)$$</p>
<p>$$238 = 206 + 4x + 0$$</p>
<p>$$ \Rightarrow 4x = 32 \Rightarrow x = 8$$</p>
<p>also, $$92 = 82 + 2x - y$$</p>
<p>$$y = 82 + 16 - 92 = 6$$</p> | mcq | jee-main-2022-online-26th-june-morning-shift | 9,219 |
1l59pi0p5 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Which of the following figure represents the variation of $${l_n}\left( {{R \over {{R_0}}}} \right)$$ with $${l_n}A$$ (if R = radius of a nucleus and A = its mass number)</p> | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l5bqhail/7bc3d5e9-f980-4c2e-9912-aaaceec9b29d/e03ba2d0-fe56-11ec-b169-b5046c590266/file-1l5bqhaim.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l5bqhail/7bc3d5e9-f980-4c2e-9912-aaaceec9b29d/e03... | ["B"] | null | <p>We know that</p>
<p>$$R = {R_0}{A^{1/3}}$$</p>
<p>$$ \Rightarrow \underbrace {\ln \left( {{R \over {{R_0}}}} \right)}_y=\underbrace {{1 \over 3}}_m\underbrace {\ln (A)}_x$$</p>
<p>$$\Rightarrow$$ Straight line</p> | mcq | jee-main-2022-online-25th-june-evening-shift | 9,221 |
1l5bck1ix | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A sample contains 10<sup>$$-$$2</sup> kg each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of their atomic weights is 1 : 2. The ratio of the amounts of A and B after 16 s is $${x \over {100}}$$. The value of x is ___________.</p> | [] | null | 25 | <p>$${N_1} = {{\left( {{{{{10}^{ - 2}}} \over 1}} \right)} \over {{2^4}}}$$</p>
<p>$${N_2} = {{\left( {{{{{10}^{ - 2}}} \over 2}} \right)} \over {{2^2}}}$$</p>
<p>$$ \Rightarrow {{{N_1}} \over {{N_2}}} = {1 \over 2}$$</p>
<p>$$\therefore$$ Mass ratio of A and B,</p>
<p>$${{{m_1}} \over {{m_2}}} = {{{N_1}} \over {{N_2}}... | integer | jee-main-2022-online-24th-june-evening-shift | 9,222 |
1l6gjzb1w | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :</p>
<p>$$\left(\right.$$Take $$\left.\log _{10} 1.88=0.274\right)$$</p> | [{"identifier": "A", "content": "$$0.02 \\min ^{-1}$$"}, {"identifier": "B", "content": "$$2.7 \\min ^{-1}$$"}, {"identifier": "C", "content": "$$0.063 \\min ^{-1}$$"}, {"identifier": "D", "content": "$$6.3 \\min ^{-1}$$"}] | ["C"] | null | <p>$${A_0} = 4250$$</p>
<p>$$A = 2250 = {A_0}{e^{ - \lambda t}}$$</p>
<p>$$ \Rightarrow {{2250} \over {4250}} = {e^{ - \lambda t}}$$</p>
<p>$$ \Rightarrow \lambda (10) = \ln \left( {{{4250} \over {2250}}} \right)$$</p>
<p>$$\lambda (10) = 0.636$$</p>
<p>$$\lambda = 0.063$$</p> | mcq | jee-main-2022-online-26th-july-morning-shift | 9,223 |
1l6i1poyw | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Mass numbers of two nuclei are in the ratio of $$4: 3$$. Their nuclear densities will be in the ratio of</p> | [{"identifier": "A", "content": "4 : 3"}, {"identifier": "B", "content": "$$\\left(\\frac{3}{4}\\right)^{\\frac{1}{3}}$$"}, {"identifier": "C", "content": "1 : 1"}, {"identifier": "D", "content": "$$\\left(\\frac{4}{3}\\right)^{\\frac{1}{3}}$$"}] | ["C"] | null | <p>$$\therefore$$ $$R = {R_0}{A^{{1 \over 3}}}$$</p>
<p>$$ \Rightarrow {{{R_1}} \over {{R_2}}} = {\left( {{{{A_1}} \over {{A_2}}}} \right)^{{1 \over 3}}} = {\left( {{4 \over 3}} \right)^{{1 \over 3}}}$$</p>
<p>$$\therefore$$ Density ratio, $${{{\rho _1}} \over {{\rho _2}}} = {{{A_1}/{V_1}} \over {{A_2}/{V_2}}}$$</p>
<p... | mcq | jee-main-2022-online-26th-july-evening-shift | 9,224 |
1l6jikx3u | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>What is the half-life period of a radioactive material if its activity drops to $$1 / 16^{\text {th }}$$ of its initial value in 30 years?</p> | [{"identifier": "A", "content": "9.5 years"}, {"identifier": "B", "content": "8.5 years"}, {"identifier": "C", "content": "7.5 years"}, {"identifier": "D", "content": "10.5 years"}] | ["C"] | null | <p>$$\because$$ $$A = {{{A_0}} \over {{2^{{t \over {{T_{1/2}}}}}}}}$$</p>
<p>$$ \Rightarrow {2^{{t \over {{T_{1/2}}}}}} = {{{A_0}} \over A} = 16$$</p>
<p>$$ \Rightarrow {t \over {{T_{1/2}}}} = 4$$</p>
<p>$$ \Rightarrow {{30} \over {{T_{1/2}}}} = 4$$</p>
<p>$$ \Rightarrow {T_{1/2}} = {{30} \over 4}$$</p>
<p>$$ = 7.5$$ y... | mcq | jee-main-2022-online-27th-july-morning-shift | 9,225 |
1l6mayrhu | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The half life period of a radioactive substance is 60 days. The time taken for $$\frac{7}{8}$$th of its original mass to disintegrate will be :</p> | [{"identifier": "A", "content": "120 days"}, {"identifier": "B", "content": "130 days"}, {"identifier": "C", "content": "180 days"}, {"identifier": "D", "content": "20 days"}] | ["C"] | null | <p>$$\because$$ $$N = {{{N_0}} \over {{2^{{t \over {{T_{1/2}}}}}}}}$$</p>
<p>$$ \Rightarrow {2^{{t \over {{T_{1/2}}}}}} = {{{N_0}} \over N} = {{{N_0}} \over {\left( {{{{N_0}} \over 8}} \right)}}$$</p>
<p>$$ \Rightarrow {2^{{t \over {{T_{1/2}}}}}} = 8 = {2^3}$$</p>
<p>$$ \Rightarrow t = 3 \times {T_{1/2}} = 3 \times 60$... | mcq | jee-main-2022-online-28th-july-morning-shift | 9,227 |
1l6mb5k47 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be _________ hours.</p> | [] | null | 15 | <p>$${T_{1/2}} = 150$$ minutes</p>
<p>$${A_0} = 64x$$, where x is safe limit</p>
<p>$$x = 64x \times {2^{ - {n \over {{T_{1/2}}}}}}$$</p>
<p>$$ \Rightarrow {1 \over {64}} = {2^{ - {n \over {{T_{1/2}}}}}}$$</p>
<p>or $${n \over {{T_{1/2}}}} = 6$$</p>
<p>$$ \Rightarrow n = 6 \times 150$$ minutes</p>
<p>= 15 hours</p> | integer | jee-main-2022-online-28th-july-morning-shift | 9,228 |
1l6nszg99 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A radioactive sample decays $$\frac{7}{8}$$ times its original quantity in 15 minutes. The half-life of the sample is</p> | [{"identifier": "A", "content": "5 min"}, {"identifier": "B", "content": "7.5 min"}, {"identifier": "C", "content": "15 min"}, {"identifier": "D", "content": "30 min"}] | ["A"] | null | <p>$$N = {{{N_0}} \over {{2^{{t \over {{T_{1/2}}}}}}}}$$</p>
<p>$$ \Rightarrow {2^{{t \over {{T_{1/2}}}}}} = {{{N_0}} \over N} = {{{N_0}} \over {\left( {{{{N_0}} \over 8}} \right)}} = 8$$</p>
<p>$$ \Rightarrow {t \over {{T_{1/2}}}} = 3$$</p>
<p>$$ \Rightarrow {T_{1/2}} = {{15} \over 3} = 5$$ min</p> | mcq | jee-main-2022-online-28th-july-evening-shift | 9,229 |
1l6rizkvj | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Two radioactive materials A and B have decay constants $$25 \lambda$$ and $$16 \lambda$$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $$\frac{1}{a \lambda}$$. The value of a is _________.</p> | [] | null | 9 | $N_{A}=N_{0} e^{-25 \lambda t}$
<br/><br/>$N_{B}=N_{0} e^{-16 \lambda t}$
<br/><br/>$\frac{N_{B}}{N_{A}}=e=e^{9 \lambda t}$
<br/><br/>$t=\frac{1}{9 \lambda}$ | integer | jee-main-2022-online-29th-july-evening-shift | 9,231 |
ldqwb5wx | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11} \mathrm{~s}$. The value of $\alpha$ is __________.</p> | [] | null | 300 | <p>$$ \Rightarrow {\lambda _{eff}} = {\lambda _1} + {\lambda _2}$$</p>
<p>$$ \Rightarrow {{\ln 2} \over {{t_{1/2}}}} = {{\ln 2} \over {{{({t_{1/2}})}_1}}} + {{\ln 2} \over {{{({t_{1/2}})}_2}}}$$</p>
<p>$$ \Rightarrow {t_{1/2}} = {{{{({t_{1/2}})}_1} \times {{({t_{1/2}})}_2}} \over {{{({t_{1/2}})}_1} + {{({t_{1/2}})}_2}}... | integer | jee-main-2023-online-30th-january-evening-shift | 9,234 |
1ldsoitcb | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>If a radioactive element having half-life of $$30 \mathrm{~min}$$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $$90 \mathrm{~min}$$. will be</p> | [{"identifier": "A", "content": "$$\\frac{1}{16}$$"}, {"identifier": "B", "content": "$$\\frac{1}{4}$$"}, {"identifier": "C", "content": "$$\\frac{1}{8}$$"}, {"identifier": "D", "content": "$$\\frac{1}{2}$$"}] | ["C"] | null | $t_{\text {half }}=30 \mathrm{~min}$.
<br/><br/>
In 90 min. there will be 3 half lives
<br/><br/>
$$
\begin{aligned}
\text { Number of remaining } & =\left(\frac{N_{0}}{2^{3}}\right) \\\\
& =\frac{N_{0}}{8}
\end{aligned}
$$
<br/><br/>
$\therefore \quad$ Fraction will be $\frac{1}{8}$ | mcq | jee-main-2023-online-29th-january-morning-shift | 9,236 |
1ldsqfj3d | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A radioactive element $$_{92}^{242}$$X emits two $$\alpha$$-particles, one electron and two positrons. The product nucleus is represented by $$_{\mathrm{P}}^{234}$$Y. The value of P is __________.</p> | [] | null | 87 | ${ }_{92}^{242} \mathrm{X} \stackrel{{ }^{2 \alpha}}{\longrightarrow}{ }_{88}^{234} \mathrm{~A} \stackrel{\mathrm{e}^{-}}{\longrightarrow}{ }_{89}^{234} \mathrm{~B} \stackrel{2 \mathrm{e}^{+}}{\longrightarrow}{ }_{87}^{234} \mathrm{Y}$<br/><br/>So, $P=87$ | integer | jee-main-2023-online-29th-january-morning-shift | 9,237 |
1ldydsmry | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Consider the following radioactive decay process</p>
<p>$$_{84}^{218}A\buildrel \alpha \over
\longrightarrow {A_1}\buildrel {{\beta ^ - }} \over
\longrightarrow {A_2}\buildrel \gamma \over
\longrightarrow {A_3}\buildrel \alpha \over
\longrightarrow {A_4}\buildrel {{\beta ^ + }} \over
\longrightarrow {A_5}\bu... | [{"identifier": "A", "content": "210 and 84"}, {"identifier": "B", "content": "210 and 80"}, {"identifier": "C", "content": "211 and 80"}, {"identifier": "D", "content": "210 and 82"}] | ["B"] | null | ${ }_{84}^{218} A \stackrel{\alpha}{\longrightarrow}{ }_{82}^{214} A_{4} \stackrel{\beta^{-}}{\longrightarrow}{ }_{83}^{214} A_{2} \stackrel{\gamma}{\longrightarrow}{ }_{83}^{214} A_{3} \stackrel{\alpha}{\longrightarrow}{ }_{81}^{210} A_{4} \stackrel{\beta^{+}}{\longrightarrow}{ }_{80}^{210} A_{5} \stackrel{\gamma}{\lo... | mcq | jee-main-2023-online-24th-january-morning-shift | 9,240 |
1ldyeovoe | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Assume that protons and neutrons have equal masses. Mass of a nucleon is $$1.6\times10^{-27}$$ kg and radius of nucleus is $$1.5\times10^{-15}~\mathrm{A^{1/3}}$$ m. The approximate ratio of the nuclear density and water density is $$n\times10^{13}$$. The value of $$n$$ is __________.</p> | [] | null | 11 | Radius $=1.5 \times 10^{-15} A^{1 / 3}$
<br/><br/>
$$
\text { Volume }=\frac{4 \pi}{3} r^{3}
$$
<br/><br/>
Mass of nucleus $=\left(1.6 \times 10^{-27}\right) \mathrm{A} \mathrm{kg}$
<br/><br/>
$$
\text { Density of nucleus }=\frac{1.6 \times 10^{-27} \times A}{\frac{4}{3} \times \pi \times\left(1.5 \times 10^{-15} A^{\... | integer | jee-main-2023-online-24th-january-morning-shift | 9,241 |
lgnygjbo | physics | atoms-and-nuclei | nucleus-and-radioactivity | The half-life of a radioactive nucleus is 5 years. The fraction of the original sample that would decay in 15 years is: | [{"identifier": "A", "content": "$\\frac{1}{8}$"}, {"identifier": "B", "content": "$\\frac{3}{4}$"}, {"identifier": "C", "content": "$\\frac{7}{8}$"}, {"identifier": "D", "content": "$\\frac{1}{4}$"}] | ["C"] | null | The decay of a radioactive nucleus is an exponential process, and the fraction of the original sample that remains after time $t$ is given by:
<br/><br/>
$N(t) = N_0 e^{-\lambda t}$
<br/><br/>
where $N_0$ is the initial number of nuclei, $N(t)$ is the number of nuclei remaining after time $t$, and $\lambda$ is the deca... | mcq | jee-main-2023-online-15th-april-morning-shift | 9,242 |
1lgoybtwf | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Given below are two statements: one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$</p>
<p>Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 .</p>
<p>Reason R : Nuclear force is shor... | [{"identifier": "A", "content": "$$\\mathrm{A}$$ is false but $$\\mathbf{R}$$ is true"}, {"identifier": "B", "content": "$$\\mathrm{A}$$ is true but $$\\mathbf{R}$$ is false"}, {"identifier": "C", "content": "Both $$\\mathbf{A}$$ and $$\\mathbf{R}$$ are true and $$\\mathbf{R}$$ is the correct explanation of $$\\mathbf{... | ["C"] | null | The statement about the binding energy per nucleon is true, and is known as the semi-empirical mass formula. According to this formula, the binding energy per nucleon for nuclei in the range of mass numbers 30 to 170 is nearly constant, with a maximum value around mass number 60.
<br/><br/>
The statement about nuclear ... | mcq | jee-main-2023-online-13th-april-evening-shift | 9,243 |
1lguxq9ko | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If $$\lambda_{A}$$ and $$\lambda_{B}$$ are decay constants of A and B respectively, then choose the correct relation from the given options.<p></p></p> | [{"identifier": "A", "content": "$$\\lambda_{\\mathrm{A}}=\\lambda_{\\mathrm{B}} \\ln 2$$"}, {"identifier": "B", "content": "$$\\lambda_{\\mathrm{A}} \\ln 2=\\lambda_{\\mathrm{B}}$$"}, {"identifier": "C", "content": "$$\\lambda_{\\mathrm{A}}=2 \\lambda_{\\mathrm{B}}$$"}, {"identifier": "D", "content": "$$\\lambda_{\\ma... | ["A"] | null | <p>We are given that the half-life of A is the same as the average life of B. The relationship between half-life ($T_{1/2}$) and the decay constant ($\lambda$) is:</p>
<p>$$T_{1/2} = \frac{\ln 2}{\lambda}$$</p>
<p>For the average life ($\tau$), the relationship with the decay constant is:</p>
<p>$$\tau = \frac{1}{\lamb... | mcq | jee-main-2023-online-11th-april-morning-shift | 9,244 |
1lgvr9a97 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The half life of a radioactive substance is T. The time taken, for disintegrating $$\frac{7}{8}$$th part of its original mass will be:</p> | [{"identifier": "A", "content": "8T"}, {"identifier": "B", "content": "3T"}, {"identifier": "C", "content": "T"}, {"identifier": "D", "content": "2T"}] | ["B"] | null | <p>Let's use the formula for the remaining mass of a radioactive substance after a certain time:</p>
<p>$$N(t) = N_0(1/2)^{t/T}$$</p>
<p>where N(t) is the mass at time t, N₀ is the initial mass, T is the half-life, and t is the time elapsed.</p>
<p>We are given that $$\frac{7}{8}$$th of the original mass has disint... | mcq | jee-main-2023-online-10th-april-evening-shift | 9,245 |
1lgyfo324 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The decay constant for a radioactive nuclide is 1.5 $$\times$$ 10$$^{-5}$$ s$$^{-1}$$. Atomic weight of the substance is 60 g mole$$^{-1}$$, ($$N_A=6\times10^{23}$$). The activity of 1.0 $$\mu$$g of the substance is ___________ $$\times$$ 10$$^{10}$$ Bq.</p> | [] | null | 15 | <p>The activity of a radioactive substance is defined as the rate of decay or disintegration of the substance. It is given by the following formula:</p>
<p>$$A = \lambda N$$</p>
<p>where $A$ is the activity, $\lambda$ is the decay constant, and $N$ is the number of radioactive atoms present.</p>
<p>We can use this form... | integer | jee-main-2023-online-10th-april-morning-shift | 9,246 |
1lgyqhy15 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A radio active material is reduced to $$1 / 8$$ of its original amount in 3 days. If $$8 \times 10^{-3} \mathrm{~kg}$$ of the material is left after 5 days the initial amount of the material is</p> | [{"identifier": "A", "content": "64 g"}, {"identifier": "B", "content": "256 g"}, {"identifier": "C", "content": "32 g"}, {"identifier": "D", "content": "40 g"}] | ["B"] | null | <p>The decay of a radioactive material follows an exponential decay law, which can be expressed as:</p>
<p>$$ N = N_0 \cdot \left(\frac{1}{2}\right)^{\frac{t}{T}} $$</p>
<p>where:</p>
<ul>
<li>$$N$$ is the final amount of the material,</li>
<li>$$N_0$$ is the initial amount of the material,</li>
<li>$$t$$ is the elapse... | mcq | jee-main-2023-online-8th-april-evening-shift | 9,247 |
lsbljadf | physics | atoms-and-nuclei | nucleus-and-radioactivity | The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______. | [] | null | 27 | <p>According to the empirical formula relating the radius of a nucleus ($ R $) with its mass number ($ A $), we know that the radius of a nucleus is proportional to the cube root of its mass number. This relationship is given as:</p>
<p>$$ R = R_0 A^{1/3} $$</p>
<p>where $ R_0 $ is a constant with an approximate valu... | integer | jee-main-2024-online-1st-february-morning-shift | 9,248 |
jaoe38c1lsd5kg87 | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :</p> | [{"identifier": "A", "content": "32"}, {"identifier": "B", "content": "24"}, {"identifier": "C", "content": "20"}, {"identifier": "D", "content": "40"}] | ["B"] | null | <p>$$\begin{aligned}
& \mathrm{R}_1=\frac{\mathrm{R}_2}{2} \\
& \mathrm{R}_0\left(\mathrm{~A}_1\right)^{1 / 3}=\frac{\mathrm{R}_0}{2}\left(\mathrm{~A}_2\right)^{1 / 3} \\
& \mathrm{~A}_1=\frac{1}{8} \mathrm{~A}_2 \\
& \mathrm{~A}_1=\frac{192}{8}=24
\end{aligned}$$</p> | mcq | jee-main-2024-online-31st-january-evening-shift | 9,249 |
jaoe38c1lsd8l07l | physics | atoms-and-nuclei | nucleus-and-radioactivity | <p>A nucleus has mass number $$A_1$$ and volume $$V_1$$. Another nucleus has mass number $$A_2$$ and Volume $$V_2$$. If relation between mass number is $$A_2=4 A_1$$, then $$\frac{V_2}{V_1}=$$ __________.</p> | [] | null | 4 | <p>For a nucleus</p>
<p>Volume: $$\mathrm{V}=\frac{4}{3} \pi \mathrm{R}^3$$</p>
<p>$$\begin{aligned}
& \mathrm{R}=\mathrm{R}_0(\mathrm{A})^{1 / 3} \\
& \mathrm{~V}=\frac{4}{3} \pi \mathrm{R}_0^3 \mathrm{A} \\
& \Rightarrow \frac{\mathrm{V}_2}{\mathrm{~V}_1}=\frac{\mathrm{A}_2}{\mathrm{~A}_1}=4
\end{aligned}$$</p> | integer | jee-main-2024-online-31st-january-evening-shift | 9,250 |
zbKkZZBt4GGS5jMqp1Cir | physics | capacitor | capacitance | The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure :
<br/><br/><img src="data:image/png;base64,UklGRsgNAABXRUJQVlA4ILwNAAAwmgCdASoAA4wBP4G+1mY2LywnINCpWsAwCWlu+F+sA9smvIj18cf5XuC/2+RF8+Z3eyXbN3isAXdWTd/spjCPIf+/m+JP1kUQMoytiUUQ4s75RS9xZ3yil7izvlFL2vLPzQW6b+ojJIBmR+qYj4JZ+aMm5gyX... | [{"identifier": "A", "content": "zero"}, {"identifier": "B", "content": "1.5 $$\\mu $$A"}, {"identifier": "C", "content": "2 $$\\mu $$A"}, {"identifier": "D", "content": "3 $$\\mu $$A"}] | ["A"] | null | <p>As we know, Current, $$I = {{dq} \over {dt}}$$</p>
<p>= Slope of q versus t graph</p>
<p>= Zero at t = 4s; (as graph is a line parallel to time axis at t = 4s)</p> | mcq | jee-main-2019-online-12th-january-evening-slot | 9,252 |
3RjkvkyLxiJH3UeKaI7k9k2k5hh7cpw | physics | capacitor | capacitance | A capacitor is made of two square plates each
of side 'a' making a very small angle $$\alpha $$ between
them, as shown in figure. The capacitance will
be close to :
<img src="data:image/png;base64,UklGRngLAABXRUJQVlA4IGwLAAAwRwCdASpVAckAPm02mUikIyKhI9RJOIANiWlu4XMuABnZ13/pL/QPAV+Zf0j8Xf3c9d/xL5j+pfkB+7nq3dID4geqr6m/bP5... | [{"identifier": "A", "content": "$${{{\\varepsilon _0}{a^2}} \\over d}\\left( {1 + {{\\alpha a} \\over {d}}} \\right)$$"}, {"identifier": "B", "content": "$${{{\\varepsilon _0}{a^2}} \\over d}\\left( {1 - {{\\alpha a} \\over {4d}}} \\right)$$"}, {"identifier": "C", "content": "$${{{\\varepsilon _0}{a^2}} \\over d}\\lef... | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265549/exam_images/whpnlsckjv39blojiwfm.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 8th January Evening Slot Physics - Capacitor Question 93 English Explanation">
<br>dC = $${{{\vare... | mcq | jee-main-2020-online-8th-january-evening-slot | 9,253 |
gbs27J8Hl751F28nwfjgy2xukexwq8ar | physics | capacitor | capacitance | A 10 $$\mu $$F capacitor is fully charged to a potential
difference of 50 V. After removing the source
voltage it is connected to an uncharged
capacitor in parallel. Now the potential
difference across them becomes 20 V. The
capacitance of the second capacitor is : | [{"identifier": "A", "content": "20 $$\\mu $$F"}, {"identifier": "B", "content": "15 $$\\mu $$F"}, {"identifier": "C", "content": "10 $$\\mu $$F"}, {"identifier": "D", "content": "30 $$\\mu $$F"}] | ["B"] | null | Initially,
<br><br>Charge on capacitor 10 μF
<br><br>Q = CV = (10 μF) (50V)
<br><br>Q = 500 μC
<br><br>Final Charge on 10 μF capacitor
<br><br>Q = CV = (10 μF) (20V)
<br><br>Q = 200 μC
<br><br>From charge conservation,
<br><br>Charge on unknown capacitor
<br><br>Q = 500 μC – 200 μC = 300 μC
<br><br>$$ \Rightarrow $$ Ca... | mcq | jee-main-2020-online-2nd-september-evening-slot | 9,254 |
1l6dyg0j5 | physics | capacitor | capacitance | <p>A condenser of $$2 \,\mu \mathrm{F}$$ capacitance is charged steadily from 0 to $$5 \,\mathrm{C}$$. Which of the following graph represents correctly the variation of potential difference $$(\mathrm{V})$$ across it's plates with respect to the charge $$(Q)$$ on the condenser?</p> | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l6eovk3c/f92ecf63-0812-47b5-88d1-5fbbe689e7ec/2c072690-13c3-11ed-aaaa-fbfc70dd81e0/file-1l6eovk3d.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l6eovk3c/f92ecf63-0812-47b5-88d1-5fbbe689e7ec/2c0... | ["A"] | null | <p>Q = CV</p>
<p>As capacitance is constant so, Q $$\propto$$ V</p>
<p>So graph between V and Q will be a straight line.</p>
<p>Initially voltage, $${V_i} = {{{Q_i}} \over C} = {0 \over {2 \times {{10}^{ - 6}}}} = 0 V$$</p> </p>
<p>and $${V_f} = {{{Q_f}} \over C} = {5 \over {2 \times {{10}^{ - 6}}}} = 2.5 \times {10^6}... | mcq | jee-main-2022-online-25th-july-morning-shift | 9,256 |
1l6f4kiud | physics | capacitor | capacitance | <p>Capacitance of an isolated conducting sphere of radius R<sub>1</sub> becomes n times when it is enclosed by a concentric conducting sphere of radius R<sub>2</sub> connected to earth. The ratio of their radii $$\left( {{{{R_2}} \over {{R_1}}}} \right)$$ is :</p> | [{"identifier": "A", "content": "$${n \\over {n - 1}}$$"}, {"identifier": "B", "content": "$${{2n} \\over {2n + 1}}$$"}, {"identifier": "C", "content": "$${{n + 1} \\over n}$$"}, {"identifier": "D", "content": "$${{2n + 1} \\over n}$$"}] | ["A"] | null | <p>Initially $$ = {C_0} = 4\pi {\varepsilon _0}{R_1}$$</p>
<p>Finally $${{4\pi {\varepsilon _0}{R_1}{R_2}} \over {{R_2} - {R_1}}} = n{C_0} = 4\pi {\varepsilon _0}n{R_1}$$</p>
<p>$$ \Rightarrow $$ $${{{R_2}} \over {{R_2} - {R_1}}} = n$$</p>
<p>$$ \Rightarrow $$$$1 - {{{R_1}} \over {{R_2}}} = {1 \over n}$$</p>
<p>$$ \Rig... | mcq | jee-main-2022-online-25th-july-evening-shift | 9,257 |
1ldnwkn50 | physics | capacitor | capacitance | <p>Given below are two statements: One is labeled as Assertion A and the other is labeled as Reason R.</p>
<p><b>Assertion A :</b> Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one.</p... | [{"identifier": "A", "content": "Both $$\\mathbf{A}$$ and $$\\mathbf{R}$$ are true but $$\\mathbf{R}$$ is not the correct explanation of $$\\mathbf{A}$$"}, {"identifier": "B", "content": "Both $$\\mathbf{A}$$ and $$\\mathbf{R}$$ are true and $$\\mathbf{R}$$ is the correct explanation of $$\\mathbf{A}$$"}, {"identifier"... | ["C"] | null | The amount of charge on each sphere will be the same if they are charged to the same potential. Whether the sphere is solid or hollow doesn't affect the amount of charge stored on the sphere as long as they have the same radii and are charged to the same potential.
<br/><br/>Therefore, assertion A is false
<br/><br/>As... | mcq | jee-main-2023-online-1st-february-evening-shift | 9,258 |
lsanatnf | physics | capacitor | capacitance | In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ $\mu$ C.<br/><br/>
<img src="data:image/png;base64,UklGRuYQAABXRUJQVlA4INoQAACQAAGdASoAAzYCP4HA3GM2MjumItTp63AwCWlu+C/0/I9I+nMvn8+rBG/Ph9R/8T1cXKK9bD+0h/qPHv+Q44yDjv5291D/oqP/71+Hxq4o0VwZFrNwj4FwnFGiuDEIqILqDOuk6sjzukS5Gx+AWDIt... | [] | null | 60 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lsc14w9u/67a33826-53b1-48ab-9be9-ddb8be9d75df/85a80420-c5d9-11ee-baf2-61ef5327b65c/file-6y3zli1lsc14w9v.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lsc14w9u/67a33826-53b1-48ab-9be9-ddb8be9d75df/85a80420-c5d9-11ee-ba... | integer | jee-main-2024-online-1st-february-evening-shift | 9,259 |
luyitai0 | physics | capacitor | capacitance | <p>A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $$\frac{A}{3}$$ and the height is $$d$$, the capacitance of the arrangement is :</p>
<p><img src="data:image/png;base64,UklGRlQLAABXRUJQVlA4IEgLAABQwwCdASoAAxECP4HA3GU2MS2nI... | [{"identifier": "A", "content": "$$\\frac{11 \\epsilon_{\\mathrm{o}} \\mathrm{A}}{20 \\mathrm{~d}}$$\n"}, {"identifier": "B", "content": "$$\\frac{13 \\epsilon_{\\mathrm{o}} \\mathrm{A}}{17 \\mathrm{~d}}$$\n"}, {"identifier": "C", "content": "$$\\frac{18 \\epsilon_{\\mathrm{o}} \\mathrm{A}}{11 \\mathrm{~d}}$$\n"}, {"id... | ["D"] | null | <p>$$\begin{aligned}
& C=C_1+C_2+C_3 \\
& =\frac{A \epsilon_0}{3 d}+\frac{A}{6} \frac{\epsilon_0}{d}+\frac{A \epsilon_0}{g D} \\
& =\frac{A \epsilon_0}{d}\left(\frac{1}{3}+\frac{1}{6}+\frac{1}{9}\right) \\
& =\frac{11}{18} \frac{A \epsilon_0}{d}
\end{aligned}$$</p> | mcq | jee-main-2024-online-9th-april-morning-shift | 9,260 |
mJFG2q42WCIz3vJH | physics | capacitor | capacitor-in-circuit | In the given circuit, charges $${Q_2}$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\,\mu F$$ to $$3\mu F.$$ $${Q_2}$$ as a function of $$'C'$$ is given properly by:
<br/>$$\left( {figures\,\,are\,\,drawn\,\,schematically\,\,and\,\,are\,\,not\,\,to\,\,scale} \right)$$
<br/><br/><img src="data:image... | [{"identifier": "A", "content": "<img src=\"https://app-content.cdn.examgoal.net/fly/@width/image/1l91evknq/38effe94-7dda-42e7-8fb4-71a42d405dcf/86de1f60-47da-11ed-8284-6d7e98c66709/file-1l91evknr.png?format=png\" data-orsrc=\"https://app-content.cdn.examgoal.net/image/1l91evknq/38effe94-7dda-42e7-8fb4-71a42d405dcf/86d... | ["D"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l91eyqe7/e672db6e-ef4b-411f-9575-03dfdb825efb/deb9baf0-47da-11ed-8284-6d7e98c66709/file-1l91eyqe8.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l91eyqe7/e672db6e-ef4b-411f-9575-03dfdb825efb/deb9baf0-47da-11ed-8284-6d7e98c66709/fi... | mcq | jee-main-2015-offline | 9,261 |
QW5tIIm7zz4elrnc | physics | capacitor | capacitor-in-circuit | A combination of capacitors is set up as shown in the figure. The magnitude of the electric field, due to a point charge $$Q$$ (having a charge equal to the sum of the charges on the $$4$$ $$\mu \,F$$ and $$9$$ $$\mu \,F$$ capacitors), at a point distance $$30$$ $$m$$ from it, would equal : <br/><br/>
<img src="data:i... | [{"identifier": "A", "content": "$$420N/C$$ "}, {"identifier": "B", "content": "$$480N/C$$ "}, {"identifier": "C", "content": "$$240N/C$$ "}, {"identifier": "D", "content": "$$360N/C$$ "}] | ["A"] | null | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l7zdo6ze/5c1beedc-bce8-48f1-bbac-1d8834adb6e2/07d51ba0-32f0-11ed-8cf6-c1445513adbd/file-1l7zdo6zf.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l7zdo6ze/5c1beedc-bce8-48f1-bbac-1d8834adb6e2/07d51ba0-32f0-11ed-8cf6-c1445513adbd/fi... | mcq | jee-main-2016-offline | 9,262 |
2L4gBqTcmw5pPLaM | physics | capacitor | capacitor-in-circuit | A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large
number of 1 $$\mu $$F capacitors are available which can withstand a potential difference of not more than 300 V.
The minimum number of capacitors required to achieve this is: | [{"identifier": "A", "content": "2"}, {"identifier": "B", "content": "16"}, {"identifier": "C", "content": "32"}, {"identifier": "D", "content": "24"}] | ["C"] | null | To get a capacitance of 2 μF arrangement of capacitors of capacitance 1μF as shown in figure
8 capacitors of 1μF in parallel with four such branches in series i.e., 32 such capacitors are
required.
<picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265977/exam_ima... | mcq | jee-main-2017-offline | 9,263 |
E0MkJhyzzabrdor4Riztx | physics | capacitor | capacitor-in-circuit | A capacitor C<sub>1</sub> = 1.0 $$\mu $$F is charged up to a voltage V = 60 V by connecting it to battery B through switch (1). Now C<sub>1</sub> is disconnected from battery and connected to a circuit consisting of two uncharged capacitors $${C_2} = 3.0\mu F$$ and C<sub>3</sub> = 6.0 $$\mu $$F through switch (2), as s... | [{"identifier": "A", "content": "40 $$\\mu $$C"}, {"identifier": "B", "content": "36 $$\\mu $$C"}, {"identifier": "C", "content": "20 $$\\mu $$C"}, {"identifier": "D", "content": "54 $$\\mu $$C"}] | ["A"] | null | <p>Given : C<sub>1</sub> = 1.0 $$\mu$$F; C<sub>2</sub> = 3.0 $$\mu$$F; C<sub>3</sub> = 6.0 $$\mu$$F</p>
<p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l32mogyk/82aecc69-5618-41fb-adb1-736104bc25e8/86c161c0-d1bc-11ec-9218-efb2cf12c71b/file-1l32mogyl.png?format=png" data-orsrc="https://app-content.cd... | mcq | jee-main-2018-online-15th-april-evening-slot | 9,264 |
KkpBru2IV6wWZyfaZ54cK | physics | capacitor | capacitor-in-circuit | In the figure shown below, the charge on the left plate of the 10$$\mu $$F capacitor is –30$$\mu $$C. The charge on the right plate of the 6 $$\mu $$F capacitor is :
<br/><br/><img src="data:image/png;base64,UklGRpYRAABXRUJQVlA4IIoRAAAwaQCdASoAA7oAPm0ylkkkIqKhIZCaAIANiWlu4XGxxPkBCcC3vyX/WPxs8D/7t/X/2D9AfxX57+sfkn/bvayz... | [{"identifier": "A", "content": "+ 12 $$\\mu $$C"}, {"identifier": "B", "content": "+ 18 $$\\mu $$C"}, {"identifier": "C", "content": "$$-$$ 18 $$\\mu $$C"}, {"identifier": "D", "content": "$$-$$ 12 $$\\mu $$C"}] | ["B"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265563/exam_images/czhbewttwqucxtrh7c8j.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 11th January Morning Slot Physics - Capacitor Question 111 English Explanation">
<br>6$$\mu $$F ... | mcq | jee-main-2019-online-11th-january-morning-slot | 9,265 |
W85pbBiIRQT1tpU08viHA | physics | capacitor | capacitor-in-circuit | In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is :
<br/><br/><img src="data:image/png;base64,UklGRtoJAABXRUJQVlA4IM4JAADQiwCdASr2AsgBP4G+2WY2LzmnILE5QzAwCWlu/C45il6HZ1/frb/ku4LHTtAexWU7EAZGStm... | [{"identifier": "A", "content": "$${1 \\over 8}{{{Q^2}} \\over C}$$"}, {"identifier": "B", "content": "$${5 \\over 8}{{{Q^2}} \\over C}$$"}, {"identifier": "C", "content": "$${3 \\over 4}{{{Q^2}} \\over C}$$"}, {"identifier": "D", "content": "$${3 \\over 8}{{{Q^2}} \\over C}$$"}] | ["D"] | null | V<sub>i</sub> = $${1 \over 2}$$CE<sup>2</sup>
<br><br>V<sub>f</sub> = $${{{{\left( {CE} \right)}^2}} \over {2 \times 4c}}$$ = $${1 \over 2}{{C{E^2}} \over 4}$$
<br><br>$$\Delta $$E = $${1 \over 2}$$CE<sup>2</sup> $$ \times $$ $${3 \over 4}$$ = $${3 \over 8}$$ CE<sup>2</sup> | mcq | jee-main-2019-online-12th-january-morning-slot | 9,266 |
bCYmbtUKIwG3UW47iZ3rsa0w2w9jx6l5qeb | physics | capacitor | capacitor-in-circuit | In the given circuit, the charge on 4 $$\mu $$F capacitor will be :
<img src="data:image/png;base64,UklGRooHAABXRUJQVlA4IH4HAACQXACdASrsAhYBP4HA2mY2L60nIJJJQsAwCWlu6BMI72LZb4+X/8H3EZEOfVn/7ZZXcNZ9y6h0nRlW77/3MLwgfNfDbdLmvhtuMVIEOqWClTMZiuDshA+a+G26XNe+tHyXWDR+cdp+S6waNdaNeFE5H+4sgd2Q5DsZZBJafkusGj847T8qgrR8l1g0fnH17cNM... | [{"identifier": "A", "content": "5.4 $$\\mu $$C"}, {"identifier": "B", "content": "9.6 $$\\mu $$C"}, {"identifier": "C", "content": "13.4 $$\\mu $$C"}, {"identifier": "D", "content": "24 $$\\mu $$C"}] | ["D"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266283/exam_images/eekuwohadt53rlibakgl.webp" style="max-width: 100%; height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2019 (Online) 12th April Evening Slot Physics - Capacitor Question 97 English Explanation">
<br><br>As V = $${... | mcq | jee-main-2019-online-12th-april-evening-slot | 9,267 |
HS8c9Kl8xOPLoLKfoRjgy2xukexz4olh | physics | capacitor | capacitor-in-circuit | An ideal cell of emf 10 V is connected in circuit
shown in figure. Each resistance is 2 $$\Omega $$. The
potential difference (in V) across the capacitor
when it is fully charged is ______.
<img src="data:image/png;base64,UklGRsIYAABXRUJQVlA4ILYYAABQkwCdASquAUwBPm02lkikIyKhIhOq0IANiWlu/EsYvynx4ux8lvC38z/HvwW/wH9n/a392f... | [] | null | 8 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734263396/exam_images/hlprqzrgt1vaqx0zctwg.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2020 (Online) 2nd September Evening Slot Physics - Capacitor Question 89 English Explanation 1">
<br><br>Capacit... | integer | jee-main-2020-online-2nd-september-evening-slot | 9,268 |
E4yjF5kLSlxDZBoWYWjgy2xukf16jr4m | physics | capacitor | capacitor-in-circuit | In the circuit shown in the figure, the total charge is 750 $$\mu $$C and the voltage across capacitor C<sub>2</sub>
is
20 V. Then the charge on capacitor C<sub>2</sub>
is :
<img src="data:image/png;base64,UklGRroIAABXRUJQVlA4IK4IAAAQTgCdASqBARQBPm02mkgkIyKhJPKZSIANiWlu4W/RG/OT8Y/zz8XfAD+x/0z+p+Ar6f/Cfklk/3s/8g/pP/G+... | [{"identifier": "A", "content": "160 $$\\mu $$C"}, {"identifier": "B", "content": "450 $$\\mu $$C"}, {"identifier": "C", "content": "590 $$\\mu $$C"}, {"identifier": "D", "content": "650 $$\\mu $$C"}] | ["C"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734267199/exam_images/xqgwn2ym20hqecwpghm3.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266213/exam_images/lhnwbwuehwhsinb7jfdc.webp"><source media="(max-wid... | mcq | jee-main-2020-online-3rd-september-morning-slot | 9,269 |
NEI39yrQaGBnVKon8B1kmkc9ba4 | physics | capacitor | capacitor-in-circuit | A 2$$\mu$$F capacitor C<sub>1</sub> is first charged to a potential difference of 10V using a battery. Then the battery is removed and the capacitor is connected to an uncharged capacitor C<sub>2</sub> of 8 $$\mu$$F. The charge in C<sub>2</sub> on equilibrium condition is ____________ $$\mu$$C. (Round off to the Neares... | [] | null | 16 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266102/exam_images/qvjaxc4hgyu1y48sy5ep.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 17th March Evening Shift Physics - Capacitor Question 75 English Explanation">
<br>When battery is... | integer | jee-main-2021-online-17th-march-evening-shift | 9,271 |
1krywprsj | physics | capacitor | capacitor-in-circuit | Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be : | [{"identifier": "A", "content": "$${V \\over {K + 2}}$$"}, {"identifier": "B", "content": "$${V \\over K}$$"}, {"identifier": "C", "content": "$${{3V} \\over {K + 2}}$$"}, {"identifier": "D", "content": "$${{3V} \\over K}$$"}] | ["C"] | null | <picture><source media="(max-width: 320px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734266738/exam_images/xflr79tlppprwioi3yzr.webp"><source media="(max-width: 500px)" srcset="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265422/exam_images/s2lvcun6qhwloigbu5sy.webp"><img src="https://res.c... | mcq | jee-main-2021-online-27th-july-morning-shift | 9,272 |
1ktfk4b19 | physics | capacitor | capacitor-in-circuit | Three capacitors C<sub>1</sub> = 2$$\mu$$F, C<sub>2</sub> = 6$$\mu$$F and C<sub>3</sub> = 12$$\mu$$F are connected as shown in figure. Find the ratio of the charges on capacitors C<sub>1</sub>, C<sub>2</sub> and C<sub>3</sub> respectively :<br/><br/><img src="data:image/png;base64,UklGRoQHAABXRUJQVlA4IHgHAACwPQCdASo/Ae... | [{"identifier": "A", "content": "2 : 1 : 1"}, {"identifier": "B", "content": "2 : 3 : 3"}, {"identifier": "C", "content": "1 : 2 : 2"}, {"identifier": "D", "content": "3 : 4 : 4"}] | ["C"] | null | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734265527/exam_images/ifu6jmcu1hkhwwx9vj5i.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 27th August Evening Shift Physics - Capacitor Question 62 English Explanation"><br>(V<sub>D</sub> ... | mcq | jee-main-2021-online-27th-august-evening-shift | 9,273 |
1kth6gim5 | physics | capacitor | capacitor-in-circuit | A capacitor of 50 $$\mu$$F is connected in a circuit as shown in figure. The charge on the upper plate of the capacitor is ______________$$\mu$$C.<br/><br/><img src="data:image/png;base64,UklGRjoOAABXRUJQVlA4IC4OAADQZwCdASq5AWMBPm02l0kkIyUhITLJsKANiWlu4XPxG/OH8Rfyj8afCL+r/jt4kvnX7T+S3qG/AHUh/rnol8w3tP8U/p3/E/t37rfB/+E/... | [] | null | 100 | <img src="https://res.cloudinary.com/dckxllbjy/image/upload/v1734264490/exam_images/mxh1bbuzpym0ablibwhg.webp" style="max-width: 100%;height: auto;display: block;margin: 0 auto;" loading="lazy" alt="JEE Main 2021 (Online) 31st August Morning Shift Physics - Capacitor Question 61 English Explanation"><br><br>Potential D... | integer | jee-main-2021-online-31st-august-morning-shift | 9,274 |
1l58bpi8e | physics | capacitor | capacitor-in-circuit | <p>Two capacitors having capacitance C<sub>1</sub> and C<sub>2</sub> respectively are connected as shown in figure. Initially, capacitor C<sub>1</sub> is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor C<sub>1</sub> is now connected to uncharged capacitor C<s... | [{"identifier": "A", "content": "$${{{C_1}{C_2}} \\over {({C_1} + {C_2})}}V$$"}, {"identifier": "B", "content": "$${{({C_1} + {C_2})} \\over {{C_1}{C_2}}}V$$"}, {"identifier": "C", "content": "$$({C_1} + {C_2})V$$"}, {"identifier": "D", "content": "$$({C_1} - {C_2})V$$"}] | ["A"] | null | $$
V_{\text {common }}=\frac{C_1 V}{C_1+C_2}
$$
<br/><br/>$\Rightarrow$ Charge on capacitor $C_2$ | mcq | jee-main-2022-online-26th-june-morning-shift | 9,276 |
1l58hp3w0 | physics | capacitor | capacitor-in-circuit | <p>The charge on capacitor of capacitance 15$$\mu$$F in the figure given below is :</p>
<p> <img src="data:image/png;base64,UklGRrYKAABXRUJQVlA4IKoKAADwtQCdASoAA/MBP4HA3GU2MK2nIZOJYsAwCWlu/CX4wMzeTjRkp6+je1TIps/O6X+L46qC6r/c+553//9SZWEEofMhObw+pzvcPm/3guGnVLy+KGdL44W5sr+eBmAgFEdmHLba/inpbEsoVza6zpfldk5EVKuX8KKePSZnpbOT... | [{"identifier": "A", "content": "60$$\\mu$$c"}, {"identifier": "B", "content": "130$$\\mu$$c"}, {"identifier": "C", "content": "260$$\\mu$$c"}, {"identifier": "D", "content": "585$$\\mu$$c"}] | ["A"] | null | <p>$${C_{eq}} = {{120} \over {26}}\mu F$$</p>
<p>$$ \Rightarrow {Q_{flown}}$$ or $$Q = {{13 \times 120} \over {26}}\mu C = 60\mu C$$</p>
<p>$$\Rightarrow$$ Charge on 15 $$\mu$$F capacitor = 60 $$\mu$$C</p>
<p>As all the capacitors are in series.</p> | mcq | jee-main-2022-online-26th-june-evening-shift | 9,277 |
1l6f5t9f9 | physics | capacitor | capacitor-in-circuit | <p>Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential difference 18 V. The battery is then disconnected and the space between the plates of the capacitor of capacity C is completely filled with a material of dielectric constant 9. The final potential diff... | [] | null | 6 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6umubk6/bb6034f0-8796-4414-a5a4-1fb6bd4e7762/c1c29170-1c87-11ed-b633-f353ad3cb8e4/file-1l6umubk7.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6umubk6/bb6034f0-8796-4414-a5a4-1fb6bd4e7762/c1c29170-1c87-11ed-b633-f353ad3cb8e4... | integer | jee-main-2022-online-25th-july-evening-shift | 9,278 |
1l6gnpcwd | physics | capacitor | capacitor-in-circuit | <p>A composite parallel plate capacitor is made up of two different dielectric materials with different thickness $$\left(t_{1}\right.$$ and $$\left.t_{2}\right)$$ as shown in figure. The two different dielectric materials are separated by a conducting foil $$\mathrm{F}$$. The voltage of the conducting foil is V.</p>
<... | [] | null | 60 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l6v6m9cv/d8fd9171-c17a-44aa-acbf-e6e58ce89dde/182ae6f0-1cd5-11ed-843d-81ad9f680592/file-1l6v6m9cw.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1l6v6m9cv/d8fd9171-c17a-44aa-acbf-e6e58ce89dde/182ae6f0-1cd5-11ed-843d-81ad9f680592... | integer | jee-main-2022-online-26th-july-morning-shift | 9,279 |
ldo7k9mv | physics | capacitor | capacitor-in-circuit | For the given circuit, in the steady state, $\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=$
________ V.<br/><br/>
<img src="data:image/png;base64,UklGRi4TAABXRUJQVlA4ICITAAAwKAGdASrcAgADP4HA2GW2MDknIbIJWyAwCWlu/HyY3GVHZ1+fs5/uN2uz1OKdxuJpiUK/+ghI5ezH//6ifvoPjbUUqmNtRSqY21FKpjbUUqmNtRSqYBHNbNmd4Dhic0uGxf... | [] | null | 1 | In steady state, capacitor behaves as an open circuit. Circuit is :
<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lebxj12a/27a5fba1-a796-4204-b0d5-f8af05b80519/62dd0020-b0a0-11ed-a0da-1fff956b892c/file-1lebxj12b.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1lebxj12a/... | integer | jee-main-2023-online-31st-january-evening-shift | 9,281 |
lgnyz1y4 | physics | capacitor | capacitor-in-circuit | In the given figure the total charge stored in the combination of capacitors is $100~ \mu \mathrm{C}$. The value of ' $x$ ' is _________.<br/><br/>
<img src="data:image/png;base64,UklGRjINAABXRUJQVlA4ICYNAADQyQCdASoPAgADP4G812U2LqwnIREKMsAwCWlu/A/VGEAico0TG4Xj9Sf7X1cXGa/HD20A7Z5ggMPunv//1GnI7KjkchAyE+p8HI5CBkJ9SNEFWN3X... | [] | null | 5 | Charge on $\mathrm{C}_1$ is $\mathrm{Q}_1=2 \times 10=20 \mu \mathrm{C}$ .....(i)<br/><br/>
Charge on $\mathrm{C}_2$ is $\mathrm{Q}_2=\mathrm{x} \times 10=10 \mathrm{x} \mu \mathrm{C}$ .....(ii)<br/><br/>
Charge on $\mathrm{C}_3$ is $\mathrm{Q}_3=3 \times 10=30 \mu \mathrm{C}$ .....(iii)<br/><br/>
Total charge $20+10 \... | integer | jee-main-2023-online-15th-april-morning-shift | 9,282 |
1lgp14emp | physics | capacitor | capacitor-in-circuit | <p>In the circuit shown, the energy stored in the capacitor is $$n ~\mu \mathrm{J}$$. The value of $$n$$ is __________</p>
<p><img src="data:image/png;base64,UklGRlQLAABXRUJQVlA4IEgLAACwpgCdASoAA5YBP4G61WY2LbenIbBJYvAwCWlu4WYT+mNwvj6CtCbPrt1l9A0d3+88SbyX3gTfnvxKF2V8+fPnz58+fPnz58+fPnz58+fPnz58+fPntSC4UhG9nYEhl420+8pFuK... | [] | null | 75 | $$
\begin{aligned}
& \mathrm{I}_1=\frac{12}{3+9}=1 \mathrm{~A} \\\\
& \mathrm{I}_2=\frac{12}{4+2}=2 \mathrm{~A}
\end{aligned}
$$<br><br><img src="https://app-content.cdn.examgoal.net/fly/@width/image/1lgsno4xb/175e8e59-bf33-4635-8e37-5b57673ff282/97662f00-e16b-11ed-b529-e972ab4de0e3/file-1lgsno4xc.png?format=pn... | integer | jee-main-2023-online-13th-april-evening-shift | 9,283 |
1lgsxqsld | physics | capacitor | capacitor-in-circuit | <p>In the given circuit, $$\mathrm{C}_{1}=2 \mu \mathrm{F}, \mathrm{C}_{2}=0.2 \mu \mathrm{F}, \mathrm{C}_{3}=2 \mu \mathrm{F}, \mathrm{C}_{4}=4 \mu \mathrm{F}, \mathrm{C}_{5}=2 \mu \mathrm{F}, \mathrm{C}_{6}=2 \mu \mathrm{F}$$, The charge stored on capacitor $$\mathrm{C}_{4}$$ is ____________ $$\mu \mathrm{C}$$.</p>
<... | [] | null | 4 | <img src="https://app-content.cdn.examgoal.net/fly/@width/image/1libki1h3/0730c3f0-f336-45fd-9237-3def8f9ee9b7/4e356070-ff9e-11ed-bd74-05e0eb917e20/file-1libki1h4.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/1libki1h3/0730c3f0-f336-45fd-9237-3def8f9ee9b7/4e356070-ff9e-11ed-bd74-05e0eb917e20/fi... | integer | jee-main-2023-online-11th-april-evening-shift | 9,284 |
jaoe38c1lsc4l3bn | physics | capacitor | capacitor-in-circuit | <p>The charge accumulated on the capacitor connected in the following circuit is _______ $$\mu \mathrm{C}$$ (Given $$\mathrm{C}=150 \mu \mathrm{F})$$</p>
<p><img src="data:image/png;base64,UklGRv4LAABXRUJQVlA4IPILAACwpgCdASoAA2YBP4HA2GS2MSynIrLZqsAwCWlu4XBlYmNwur6S9Gtw1yM4K7acRbCU9VVSX/8JilkIxmI8oLs3sX5RSt5DVFK3kNUUreQ... | [] | null | 400 | <p><img src="https://app-content.cdn.examgoal.net/fly/@width/image/6y3zli1lscu3le1/3221a380-d3b9-4f64-9a81-f85f78708d33/ca2f96a0-c64a-11ee-9d8b-f1be86a1b2f3/file-6y3zli1lscu3le2.png?format=png" data-orsrc="https://app-content.cdn.examgoal.net/image/6y3zli1lscu3le1/3221a380-d3b9-4f64-9a81-f85f78708d33/ca2f96a0-c64a-11ee... | integer | jee-main-2024-online-27th-january-morning-shift | 9,285 |
yv9bwg3OJELXJL4K | physics | capacitor | capacitors-with-dielectric | A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor | [{"identifier": "A", "content": "decreases "}, {"identifier": "B", "content": "remains unchanged "}, {"identifier": "C", "content": "becomes infinite "}, {"identifier": "D", "content": "increases "}] | ["B"] | null | The capacitancce of parallel plate capacitor in which a metal plate of thickness $$t$$ is inserted is given by
<br><br>$$C = {{{\varepsilon _0}A} \over {d - t}}.\,\,\,\,\,$$
<br><br>Here $$t \to 0\,\,\,\,\,\,$$ $$\therefore$$ $$C = {{{\varepsilon _0}A} \over d}$$ | mcq | aieee-2003 | 9,286 |
Gq1uYqgcrJNWiydf | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor with air between the plates has capacitance of $$9$$ $$pF.$$ The separation between its plates is $$'d'.$$ The space between the plates has dielectric constant $${k_1}$$ $$=3$$ and thickness $${d \over 3}$$ while the other one has dielectric constant $${k_2} = 6$$ and thickness $${{2d} \over ... | [{"identifier": "A", "content": "$$1.8$$ $$pF$$ "}, {"identifier": "B", "content": "$$45$$ $$pF$$ "}, {"identifier": "C", "content": "$$40.5$$ $$pF$$ "}, {"identifier": "D", "content": "$$20.25$$ $$pF$$ "}] | ["C"] | null | <img class="question-image" src="https://imagex.cdn.examgoal.net/dCrxyqN2t9qic3vxL/3sLhZsfK0H88LZCPg6LGhLCmdtHkX/NsSodhvhgkZE8gIkM7A6dJ/image.svg" loading="lazy" alt="AIEEE 2008 Physics - Capacitor Question 133 English Explanation">
<br><br>The given capacitance is equal to two capacitances connected in series where
<b... | mcq | aieee-2008 | 9,287 |
wtYxiZj40C8pK7cQ | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor is made of two circular plates separated by a distance $$5$$ $$mm$$ and with a dielectric of dielectric constant $$2.2$$ between them. When the electric field in the dielectric is $$3 \times {10^4}\,V/m$$ the charge density of the positive plate will be close to: | [{"identifier": "A", "content": "$$6 \\times {10^{ - 7}}\\,\\,C/{m^2}$$ "}, {"identifier": "B", "content": "$$3 \\times {10^{ - 7}}\\,\\,C/{m^2}$$ "}, {"identifier": "C", "content": "$$3 \\times {10^4}\\,\\,C/{m^2}$$ "}, {"identifier": "D", "content": "$$6 \\times {10^4}\\,\\,C/{m^2}$$ "}] | ["A"] | null | Electric field in presence of dielectric between the two plates of a parallel plate capacitor is given by,
<br><br>$$E = {\sigma \over {K{\varepsilon _0}}}$$
<br><br>Then, charge density
<br><br>$$\sigma = K{\varepsilon _0}E$$
<br><br>$$ = 2.2 \times 8.85 \times {10^{ - 12}} \times 3 \times {10^4} \approx 6 \times {1... | mcq | jee-main-2014-offline | 9,288 |
Do8uNl62T269hDBsbgDlI | physics | capacitor | capacitors-with-dielectric | A combination of parallel plate capacitors is maintained at a certain potential difference.
<br/><br/><img src="data:image/png;base64,UklGRgoHAABXRUJQVlA4IP4GAACQXgCdASoAA+IAP4G+2WQ2MCymodTaCsAwCWlu4XCBG/Pn862hcbCcrc954qx+eRE4cjj0lom3aNQZiaZ8CtBGJKaYmmfAtvKDItPJNUZXmTfcGQgKOR0rb7gyAPPzFYMNgW2CStvuDEt86Q/Njdx6DvSxIcdKsE... | [{"identifier": "A", "content": "3"}, {"identifier": "B", "content": "4"}, {"identifier": "C", "content": "5"}, {"identifier": "D", "content": "6"}] | ["C"] | null | <p>Before introducing the slab between the plates of all three capacitors, we have</p>
<p>$${C_1} = {{{\varepsilon _0}A} \over 3}$$</p>
<p>After introducing the slab between the plates of all three capacitors, we have</p>
<p>$${C_1} = K{{{\varepsilon _0}A} \over 3} + {{{\varepsilon _0}A} \over {2.4}}$$</p>
<p>As the ca... | mcq | jee-main-2017-online-9th-april-morning-slot | 9,289 |
fvaGJwNGLcoazjij | physics | capacitor | capacitors-with-dielectric | A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material
of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be : | [{"identifier": "A", "content": "0.9 n C"}, {"identifier": "B", "content": "1.2 n C"}, {"identifier": "C", "content": "0.3 n C"}, {"identifier": "D", "content": "2.4 n C"}] | ["B"] | null | Charge on Capacitor initially,
<br><br>Q<sub>i</sub> = CV
<br><br>After inserting dielectric of dielectric constant = K,
<br><br>new capacitance, Q<sub>f</sub> = (KC) $$ \vee $$
<br><br>$$\therefore\,\,\,$$ Induced charges on dielectric
<br><br>= Q<sub>f</sub> $$-$$ Q<sub>i</sub>
<br><br>= KCV $$-$$ CV
<br><br>= (K $... | mcq | jee-main-2018-offline | 9,290 |
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