JEE Main 2025 Apr 3 Shift 2 — Physics

Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	Boltzmann constant	I.	$\mathrm{ML^2T^{-1}}$
B.	Coefficient of viscosity	II.	$\mathrm{MLT^{-3}K^{-1}}$
C.	Planck's constant	III.	$\mathrm{ML^2T^{-2}K^{-1}}$
D.	Thermal conductivity	IV.	$\mathrm{ML^{-1}T^{-1}}$

Choose the correct answer from the options given below:

A particle is projected with velocity $u$ so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as $\frac{nu^2}{25g}$, where value of $n$ is: (Given, '$g$' is the acceleration due to gravity.)

A particle moves along the $x$-axis and has its displacement $x$ varying with time $t$ according to the equation:

$$x = c_0(t^2 - 2) + c(t - 2)^2$$

where $c_0$ and $c$ are constants of appropriate dimensions. Then, which of the following statements is correct?

block A (m₁ = 10 kg) moving with velocity v towards block B (m₂ = 5 kg) which has a spring of k = 3000 N/m attached, both on a horizontal surface

Consider two blocks A and B of masses $m_1 = 10$ kg and $m_2 = 5$ kg that are placed on a frictionless table. The block A moves with a constant speed $v = 3$ m/s towards the block B kept at rest. A spring with spring constant $k = 3000$ N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

Two cylindrical vessels of equal cross sectional area of $2\,\mathrm{m^2}$ contain water upto heights 10 m and 6 m, respectively. If the vessels are connected at their bottom then the work done by the force of gravity is (Density of water is $10^3\,\mathrm{kg/m^3}$ and $g = 10\,\mathrm{m/s^2}$)

A block of mass 1 kg, moving along $x$ with speed $v_i = 10$ m/s enters a rough region ranging from $x = 0.1$ m to $x = 1.9$ m. The retarding force acting on the block in this range is $F_r = -kx$ N, with $k = 10$ N/m. Then the final speed of the block as it crosses rough region is.

A solid steel ball of diameter 3.6 mm acquired terminal velocity $2.45 \times 10^{-2}$ m/s while falling under gravity through an oil of density $925\,\mathrm{kg\,m^{-3}}$. Take density of steel as $7825\,\mathrm{kg\,m^{-3}}$ and $g$ as $9.8\,\mathrm{m/s^2}$. The viscosity of the oil in SI unit is

An ideal gas exists in a state with pressure $P_0$, volume $V_0$. It is isothermally expanded to 4 times of its initial volume ($V_0$), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4% when heated by 1°C. Its initial temperature must be:

In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is:

A magnetic dipole experiences a torque of $80\sqrt{3}$ N m when placed in uniform magnetic field in such a way that dipole moment makes angle of 60° with magnetic field. The potential energy of the dipole is :

An electric bulb rated as 100W-220V is connected to an ac source of rms voltage 220V. The peak value of current through the bulb is :

Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is: (in pF)

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is 91.6%, then the loss of power in units of cal/s is

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : If Oxygen ion ($\mathrm{O^{-2}}$) and Hydrogen ion ($\mathrm{H^+}$) enter normal to the magnetic field with equal momentum, then the path of $\mathrm{O^{-2}}$ ion has a smaller curvature than that of $\mathrm{H^+}$.

Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly.

In the light of the above statements, choose the correct answer from the options given below

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

A monochromatic light of frequency $5 \times 10^{14}$ Hz travelling through air, is incident on a medium of refractive index '2'. Wavelength of the refracted light will be :

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is :

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R

Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.

Reason R : The formulation of Bohr model does not include repulsive force between electrons.

In the light of the above statements, choose the correct answer from the options given below

The truth table corresponding to the circuit given below is :

logic circuit — inputs A and B feed an OR gate; the OR gate output and input A feed an AND gate whose output is C

A physical quantity $C$ is related to four other quantities $p$, $q$, $r$ and $s$ as follows

$$C = \frac{pq^2}{r^3\sqrt{s}}.$$

The percentage errors in the measurement of $p$, $q$, $r$ and $s$ are 1%, 2%, 3% and 2%, respectively. The percentage error in the measurement of $C$ will be __________ %.

The excess pressure inside a soap bubble A in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is $n$ times the volume of the bubble B, then, the value of $n$ is __________.

Two cells of emfs 1 V and 2 V and internal resistances $2\ \Omega$ and $1\ \Omega$, respectively, are connected in series with an external resistance of $6\ \Omega$. The total current in the circuit is $I_1$. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is $I_2$. The value of $\left(\frac{I_1}{I_2}\right)$ is $\frac{x}{3}$. The value of $x$ is __________.

Light from a point source in air falls on a spherical glass surface (refractive index, $\mu = 1.5$ and radius of curvature $= 50$ cm). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is __________ m.

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy 2.86 eV. The integer value of n will be __________.