1
JEE Advanced 2024 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

A particle of mass $m$ is moving in a circular orbit under the influence of the central force $F(r)=-k r$, corresponding to the potential energy $V(r)=k r^2 / 2$, where $k$ is a positive force constant and $r$ is the radial distance from the origin. According to the Bohr's quantization rule, the angular momentum of the particle is given by $L=n \hbar$, where $\hbar=h /(2 \pi), h$ is the Planck's constant, and $n$ a positive integer. If $v$ and $E$ are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

A
$r^2=n \hbar \sqrt{\frac{1}{m k}}$
B
$v^2=n \hbar \sqrt{\frac{k}{m^3}}$
C
$\frac{L}{m r^2}=\sqrt{\frac{k}{m}}$
D
$E=\frac{n \hbar}{2} \sqrt{\frac{k}{m}}$
2
JEE Advanced 2022 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2

The binding energy of nucleons in a nucleus can be affected by the pairwise Coulomb repulsion. Assume that all nucleons are uniformly distributed inside the nucleus. Let the binding energy of a proton be $E_{b}^{p}$ and the binding energy of a neutron be $E_{b}^{n}$ in the nucleus.

Which of the following statement(s) is(are) correct?

A
$E_{b}^{p}-E_{b}^{n}$ is proportional to $Z(Z-1)$ where $Z$ is the atomic number of the nucleus.
B
$E_{b}^{p}-E_{b}^{n}$ is proportional to $A^{-\frac{1}{3}}$ where $A$ is the mass number of the nucleus.
C
$E_{b}^{p}-E_{b}^{n}$ is positive.
D
$E_{b}^{p}$ increases if the nucleus undergoes a beta decay emitting a positron.
3
JEE Advanced 2021 Paper 2 Online
MCQ (More than One Correct Answer)
+4
-2
A heavy nucleus N, at rest, undergoes fission N $$\to$$ P + Q, where P and Q are two lighter nuclei. Let $$\delta$$ = MN $$-$$ MP $$-$$ MQ, where MP, MQ and MN are the masses of P, Q and N, respectively. EP and EQ are the kinetic energies of P and Q, respectively. The speeds of P and Q are vP and vQ, respectively. If c is the speed of light, which of the following statement(s) is(are) correct?
A
$${E_P} + {E_Q} = {c^2}\delta$$
B
$${E_P} = \left( {{{{M_P}} \over {{M_P} + {M_Q}}}} \right){c^2}\delta$$
C
$${{{v_P}} \over {{v_Q}}} = {{{M_Q}} \over {{M_P}}}$$
D
The magnitude of momentum for P as well Q is $$c\sqrt {2\mu \delta }$$, where $$\mu = {{{M_P}{M_Q}} \over {({M_P} + {M_Q})}}$$
4
JEE Advanced 2021 Paper 1 Online
MCQ (More than One Correct Answer)
+4
-2
Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?
A
The ratio of the longest wavelength to the shortest wavelength in Balmer series is 9/5
B
There is an overlap between the wavelength ranges of Balmer and Paschen series
C
The wavelengths of Lyman series are given by $$\left( {1 + {1 \over {{m^2}}}} \right){\lambda _0}$$, where $${\lambda _0}$$ is the shortest wavelength of Lyman series and m is an integer
D
The wavelength ranges of Lyman and Balmer series do not overlap
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