NTA JEE Main 2025 April 3rd Shift 1 - Physics

During the melting of a slab of ice at 273 K at atmospheric pressure :

Consider a completely full cylindrical water tank of height 1.6 m and cross-sectional area 0.5 m$$^2$$. It has a small hole in its side at a height 90 cm from the bottom. Assume, the cross-sectional area of the hole to be negligibly small as compared to that of the water tank. If a load 50 kg is applied at the top surface of the water in the tank then the velocity of the water coming out at the instant when the hole is opened is : $$(g = 10\,\text{m/s}^2)$$

Choose the correct logic circuit for the given truth table having inputs A and B.

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2m away from it, is :

A wire of length 25 m and cross-sectional area 5 mm$$^2$$ having resistivity of $$2 \times 10^{-6}\,\Omega$$ m is bent into a complete circle. The resistance between diametrically opposite points will be

Two blocks of masses m and M, $$(M \gt m)$$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then ($$\mu$$ = coefficient of friction between the two blocks)

(A) The time period of small oscillation of the two blocks is $$T = 2\pi\sqrt{\frac{m+M}{k}}$$
(B) The acceleration of the blocks is $$a = \frac{kx}{M+m}$$
(C) The magnitude of the frictional force on upper block is $$\frac{m\mu|x|}{M+m}$$
(D) The maximum amplitude of the upper block, if it does not slip, is $$\frac{\mu(M+m)g}{k}$$
(E) Maximum frictional force can be $$\mu(M+m)g$$.

Choose the correct answer from the options given below :

Which of the following curves possibly represent one-dimensional motion of a particle ?

Choose the correct answer from the options given below :

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $$\varepsilon_1$$ and $$\varepsilon_2$$, as shown in figures. The distance between the plates is d and area of each plate is A. If capacitance in first configuration and second configuration are $$C_1$$ and $$C_2$$ respectively, then $$\frac{C_1}{C_2}$$ is :

Match the LIST-I with LIST-II.

Choose the correct answer from the options given below :

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, then the acceleration of the center of the sphere is

A piston of mass M is hung from a massless spring whose restoring force law goes as $$F = -kx^3$$, where k is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with 'n' moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in lower part of the chamber, so that the piston goes up from a height $$L_0$$ to $$L_1$$, the total energy delivered by the filament is (Assume spring to be in its natural length before heating)

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of 800 cm$$^3$$ and temperature 27°C. The change in temperature when the gas is adiabatically compressed to 200 cm$$^3$$ is :
(Take $$\gamma = 1.5$$ : $$\gamma$$ is the ratio of specific heats at constant pressure and at constant volume)

Match the LIST-I with LIST-II.

Choose the correct answer from the options given below :

The electrostatic potential on the surface of uniformly charged spherical shell of radius R = 10 cm is 120 V. The potential at the centre of shell, at a distance r = 5 cm from centre, and at a distance r = 15 cm from the centre of the shell, respectively, are :

The work function of a metal is $$3 eV$$. The color of the visible light that is required to cause emission of photoelectrons is

A particle is released from height S above the surface of the earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively.

A person measures mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the additions of the masses of 3 particles will be.

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is

The angle of projection of a particle is measured from the vertical axis as $$\phi$$ and the maximum height reached by the particle is $$h_m$$. Here $$h_m$$ as function of $$\phi$$ can be presented as

Consider following statements for refraction of light through prism, when angle of deviation is minimum.
(A) The refracted ray inside prism becomes parallel to the base.
(B) Larger angle prisms provide smaller angle of minimum deviation.
(C) Angle of incidence and angle of emergence becomes equal.
(D) There are always two sets of angle of incidence for which deviation will be same except at minimum deviation setting.
(E) Angle of refraction becomes double of prism angle.

Choose the correct answer from the options given below.

Three identical spheres of mass m, are placed at the vertices of an equilateral triangle of length a. When released, they interact only through gravitational force and collide after a time $$T = 4$$ seconds. If the sides of the triangle are increased to length 2a and also the masses of the spheres are made 2m, then they will collide after _________ seconds.

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is _________ mN.

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is xI. The value of x is __________.

A loop ABCDA, carrying current $$I = 12$$ A, is placed in a plane, consists of two semi-circular segments of radius $$R_1 = 6\pi$$ m and $$R_2 = 4\pi$$ m. The magnitude of the resultant magnetic field at center O is $$k \times 10^{-7}$$ T. The value of k is __________.
(Given $$\mu_0 = 4\pi \times 10^{-7}$$ Tm A$$^{-1}$$)

In the figure shown below, a resistance of 150.4 $$\Omega$$ is connected in series to an ammeter A of resistance 240 $$\Omega$$. A shunt resistance of 10 $$\Omega$$ is connected in parallel with the ammeter. The reading of the ammeter is _________ mA.