NTA JEE Main 2025 April 3rd Shift 1

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 $$\mu(M+m)g$$.

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

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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.

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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.

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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