JEE Main 2025 Physics Paper: 29 Jan, Shift 2

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A. If the rate of change of potential difference between the plates is $7\times 10^{8}\text{ V/s}$ then the integer value of the distance between the parallel plates is $($ Take, $\epsilon_0=9\times 10^{-12}\frac{\text{F}}{\text{m}},\ \pi=\frac{22}{7})$ ____________ $\mu\text{m}$.

A capacitor, $C_1 = 6\ \mu\text{F}$ is charged to a potential difference of $V_0 = 5\text{ V}$ using a 5V battery. The battery is removed and another capacitor, $C_2 = 12\ \mu\text{F}$ is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the charges ($q_1$ and $q_2$) on the capacitors $C_1$ and $C_2$ when equilibrium condition is reached.

In an experiment with photoelectric effect, the stopping potential,

A plane electromagnetic wave propagates along the + x direction in free space. The components of the electric field, $\vec{E}$ and magnetic field, $\vec{B}$ vectors associated with the wave in Cartesian frame are

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density $\sigma_0$. Choose the correct option from the following.

A point charge causes an electric flux of $-2 \times 10^{4}\text{ N m}^2\text{C}^{-1}$ to pass through a spherical Gaussian surface of 8.0 cm radius, centred on the charge. The value of the point charge is: (Given $\epsilon_0 = 8.85 \times 10^{-12}\text{ C}^2\text{N}^{-1}\text{m}^{-2}$)

Two planets, $A$ and $B$ are orbiting a common star in circular orbits of radii $R_A$ and $R_B$, respectively, with $R_B =$ $2R_A$. The planet $B$ is $4\sqrt{2}$ times more massive than planet $A$. The ratio $\left(\frac{L_B}{L_A}\right)$ of angular momentum $(L_B)$ of planet $B$ to that of planet $A\,(L_A)$ is closest to integer ________.

The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have

A cup of coffee cools from 90°C to 80°C in t minutes when the room temperature is 20°C. The time taken by the similar cup of coffee to cool from 80°C to 60°C at the same room temperature is:

Match List - I with List - II.

Choose the correct answer from the options given below:

Two cars P and Q are moving on a road in the same direction. Acceleration of car P increases linearly with time whereas car Q moves with a constant acceleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

The magnetic field inside a 200 turns solenoid of radius 10 cm is $2.9 \times 10^{-4}\text{ Tesla}$. If the solenoid carries a current of 0.29 A, then the length of the solenoid is _______ $\pi\text{cm}$.

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is

Two identical symmetric double convex lenses of focal length f are cut into two equal parts L1, L2 by AB plane and L3, L4 by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L1 and L3 is

A convex lens made of glass (refractive index = 1.5) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33), its focal length changes to

Two concave refracting surfaces of equal radii of curvature and refractive index 1.5 face each other in air as shown in figure. A point object O is placed midway, between P and B. The separation between the images of O, formed by each refracting surface is:

The truth table for the circuit given below is:

A poly-atomic molecule $(C_V = 3R, C_P = 4R$, where $R$ is gas constant) goes from phase space point $A\left(P_A = 10^{5}\text{ Pa},\ V_A = 4 \times 10^{-6}\text{ m}^3\right)$ to point $B\left(P_B = 5 \times 10^{4}\text{ Pa},\ V_B = 6 \times 10^{-6}\text{ m}^3\right)$ to point $C\ (P_C = 10^{4}\text{ Pa}, V_C = 8 \times 10^{-6}\text{ m}^3$ ). A to $B$ is an adiabatic path and $B$ to $C$ is an isothermal path. The net heat absorbed per unit mole by the system is:

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A): With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process.

Reason (R): In isothermal process, PV = constant, while in adiabatic process $PV^{\gamma}$ = constant. Here $\gamma$ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below:

A physical quantity $Q$ is related to four observables $a, b, c, d$ as follows:

$Q = \frac{ab^{4}}{cd}$

where, $a = (60 \pm 3)\text{ Pa};\ b = (20 \pm 0.1)\text{ m};\ c = (40 \pm 0.2)\text{ Nsm}^{-2}$ and $d = (50 \pm 0.1)\text{ m}$, then the percentage error in Q is $\frac{x}{1000}$, where $x =$ _________.

Match List - I with List - II.

Choose the correct answer from the options given below:

A sand dropper drops sand of mass m(t) on a conveyer belt at a rate proportional to the square root of speed (v) of the belt, i.e., $\frac{dm}{dt} \propto \sqrt{v}$. If P is the power delivered to run the belt at constant speed then which of the following relationship is true?