JEE Advanced 2022 Paper 2 Online

In a radioactive decay chain reaction, ${ }_{90}^{230} \mathrm{Th}$ nucleus decays into ${ }_{84}^{214} \mathrm{Po}$ nucleus. The ratio of the number of $\alpha$ to number of $\beta^{-}$particles emitted in this process is ________.

Two resistances $R_{1}=X \Omega$ and $R_{2}=1 \Omega$ are connected to a wire $A B$ of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from $0.2 \mathrm{~mm}$ at $A$ to $1 \mathrm{~mm}$ at ...

In Circuit-1 and Circuit- 2 shown in the figures, $R_{1}=1 \,\Omega, R_{2}=2 \,\Omega$ and $R_{3}=3 \,\Omega$.

$P_{1}$ and $P_{2}$ are the power dissipations in Circuit-1 and Circuit-2 when the switches $\mathrm{S}_{1}$ and $\mathrm{S}_{2}...

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is $6.0 \mathrm{~V}$. This potential drops to $0.6 \mathrm{~V}$ if another source with wavelength four times...

A charge $q$ is surrounded by a closed surface consisting of an inverted cone of height $h$ and base radius $R$, and a hemisphere of radius $R$ as shown in the figure. The electric flux through the conical surface is $\frac{n q}{6 \epsilon_...

In the figure, the inner (shaded) region $A$ represents a sphere of radius $r_{A}=1$, within which the electrostatic charge density varies with the radial distance $r$ from the center as $\rho_{A}=k r$, where $k$ is positive. In the spheric...

A disk of radius $\mathrm{R}$ with uniform positive charge density $\sigma$ is placed on the $x y$ plane with its center at the origin. The Coulomb potential along the $z$-axis is

$$
V(z)=\frac{\sigma}{2 \epsilon_{0}}\left(\sqrt{R^{2}+z^{2...

Consider a configuration of $n$ identical units, each consisting of three layers. The first layer is a column of air of height $h=\frac{1}{3} \mathrm{~cm}$, and the second and third layers are of equal thickness $d=$ $\frac{\sqrt{3}-1}{2} \...

An object and a concave mirror of focal length $f=10 \mathrm{~cm}$ both move along the principal axis of the mirror with constant speeds. The object moves with speed $V_{0}=15 \mathrm{~cm} \mathrm{~s}^{-1}$ towards the mirror with respect t...

In the given $P-V$ diagram, a monoatomic gas $\left(\gamma=\frac{5}{3}\right)$ is first compressed adiabatically from state $A$ to state $B$. Then it expands isothermally from state $B$ to state $C$. [Given: $\left(\frac{1}{3}\right)^{0.6} ...

Which one of the following options represents the magnetic field $\vec{B}$ at $\mathrm{O}$ due to the current flowing in the given wire segments lying on the $x y$ plane?

A bubble has surface tension $S$. The ideal gas inside the bubble has ratio of specific heats $\gamma=$ $\frac{5}{3}$. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is $P_{a...

A flat surface of a thin uniform disk $A$ of radius $R$ is glued to a horizontal table. Another thin uniform disk $B$ of mass $M$ and with the same radius $R$ rolls without slipping on the circumference of $A$, as shown in the figure. A fla...

A particle of mass $1 \mathrm{~kg}$ is subjected to a force which depends on the position as $\vec{F}=$ $-k(x \hat{\imath}+y \hat{\jmath}) \mathrm{kg}\, \mathrm{m} \mathrm{s}^{-2}$ with $k=1 \mathrm{~kg} \mathrm{~s}^{-2}$. At time $t=0$, th...

On a frictionless horizontal plane, a bob of mass $m=0.1 \mathrm{~kg}$ is attached to a spring with natural length $l_{0}=0.1 \mathrm{~m}$. The spring constant is $k_{1}=0.009 \,\mathrm{Nm}^{-1}$ when the length of the spring $l>l_{0}$ and ...

In a particular system of units, a physical quantity can be expressed in terms of the electric charge $e$, electron mass $m_{e}$, Planck's constant $h$, and Coulomb's constant $k=\frac{1}{4 \pi \epsilon_{0}}$, where $\epsilon_{0}$ is the pe...

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is $0.5 \mathrm{~mm}$. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divi...

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_{2}$. The other slit is at the interface of this medium with another medium 1 of refractive index $n_{1}\left(\neq n_{2}\right)$. The line jo...