NTA JEE Mains 4th April Shift 2 2026

A metal string A is suspended from a rigid support and its free end is attached to a block of mass M. Second block having mass 2M is suspended at the bottom of the first block using a string B. The area of cross sections of strings A and B are same. The ratio of lengths of strings of A to B is 2 and the ratio of their Young's moduli $$(Y_A/Y_B)$$ is 0.5. The ratio of elongations in A to B is ______.

A water spray gun is attached to a hose of cross sectional area 30 cm$$^2$$. The gun comprises of 10 perforations each of cross sectional area of 15 mm$$^2$$. If the water flows in the hose with the speed of 50 cm/s, calculate the speed at which the water flows out from each perforation. (Neglect any edge effects)

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

Assertion A: If the average kinetic energy of H$$_2$$ and O$$_2$$ molecules, kept in two different sized containers are same, then their temperatures will be same.

Reason R: The r.m.s. speed of H$$_2$$ and O$$_2$$ molecules are same at same temperature.
Choose the correct answer from the options given below : 

The temperature of a metal strip having coefficient of linear expansion $$\alpha$$ is increased from $$T_1$$ to $$T_2$$ resulting in increase of its length by $$\Delta L_1$$. The temperature is further increased from $$T_2$$ to $$T_3$$ such that the increase in its length is $$\Delta L_2$$. Given $$T_3 + T_1 = 2T_2$$ and $$T_2 - T_1 = \Delta T$$, the value of $$\Delta L_2$$ is ______.

A uniform disc of radius R and mass M is free to oscillate about the axis A as shown in the figure. For small oscillations the time period is ______. ( g is acceleration due to gravity)

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $$\vec{E}_1 = E_0\hat{x}$$. If another electric field $$\vec{E}_2 = 2E_0(\hat{y} + \hat{z})$$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

From the circuit given below, the capacitance between terminals A and B shown in the circuit is ______ $$\mu$$F.
(take $$C_1 = C_2 = C_3 = 1$$ $$\mu$$F and $$C_4 = 2$$ $$\mu$$F.)

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

Assertion A: In electrostatics, a conductor does not store any net charge inside.

Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift.
Choose the correct answer from the options given below:

A solenoid has a core made of material with relative permeability 400. The magnetic field produced in the interior of solenoid is 1.0 T. The magnetic intensity in SI units is $$\alpha \times 10^5$$. The value of $$\alpha$$ is ______.

(Free space permeability $$\mu_0 = 4\pi \times 10^{-7}$$ SI units.)

A magnetic field vector in an electromagnetic wave is represented by $$\vec{B} = B_0\sin\left(2\pi\nu t - \frac{2\pi x}{\lambda}\right)\hat{j}$$. Its associated electric field vector is ______.