NTA JEE Main 2025 April 02 Shift 2

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions $$T_1$$ and $$T_2$$, respectively, are (in N) :

A bi-convex lens has radius of curvature of both the surfaces same as 1/6 cm. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $$(R_1 \neq R_2)$$, without any change in lens power then possible combination of $$R_1$$ and $$R_2$$ is :

If $$\mu_0$$ and $$\varepsilon_0$$ are the permeability and permittivity of free space, respectively, then the dimension of $$\left(\frac{1}{\mu_0 \varepsilon_0}\right)$$ is :

Match List-I with List-II.

List-I
(A) Heat capacity of body
(B) Specific heat capacity of body
(C) Latent heat
(D) Thermal conductivity

List-II
(I) J kg$$^{-1}$$
(II) J K$$^{-1}$$
(III) J kg$$^{-1}$$ K$$^{-1}$$
(IV) J m$$^{-1}$$ K$$^{-1}$$ s$$^{-1}$$

Choose the correct answer from the options given below :

Consider a circular loop that is uniformly charged and has a radius $$a\sqrt{2}$$. Find the position along the positive z-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in xy-plane at the origin :

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in the figure below. The established torque produces an angular acceleration of 2 rad/s$$^2$$. Moment of inertia of the wheel is _________ kg m$$^2$$.
(Acceleration due to gravity = 10 m/s$$^2$$)

The internal energy of air in a $$4\,\text{m} \times 4\,\text{m} \times 3\,\text{m}$$ sized room at 1 atmospheric pressure will be _________ $$\times 10^6$$ J.
(Consider air as diatomic molecule)

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to 60°. The refractive index of the prism material is $$\sqrt{2}$$. The angle of incidence (in degrees) is _________.

The length of a light string is 1.4 m when the tension on it is 5 N. If the tension increases to 7 N, the length of the string is 1.56 m. The original length of the string is _________ m.

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is _________ $$\times 10^{10}$$ J.
(Mass of earth = $$6 \times 10^{24}$$ kg, Radius of earth = $$6.4 \times 10^6$$ m, Gravitational constant = $$6.67 \times 10^{-11}$$ Nm$$^2$$ kg$$^{-2}$$)