NTA JEE Mains 8th April Shift 2 2026

Two identical bodies, projected with the same speed at two different angles cover the same horizontal range $$R$$. If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of $$R$$ is __________ m. (Take $$g = 10$$ m/s$$^2$$)

A solid cylinder having radius $$R$$ and length $$L$$ is slipping on a rough horizontal plane. At time $$t = 0$$ the cylinder has a translational velocity $$v_0 = 49$$ m/s, perpendicular to its axis and a rotational velocity $$v_0/4R$$ about the centre. The time taken by the cylinder to start rolling is __________ seconds. (coefficient of kinetic friction $$\mu_K = 0.25$$ and $$g = 9.8$$ m/s$$^2$$)

A liquid of density 600 kg/m$$^3$$ flowing steadily in a tube of varying cross-section. The cross-section at a point $$A$$ is 1.0 cm$$^2$$ and that at $$B$$ is 20 mm$$^2$$. Both the points $$A$$ and $$B$$ are in same horizontal plane, the speed of the liquid at $$A$$ is 10 cm/s. The difference in pressures at $$A$$ and $$B$$ points is __________ Pa.

A spherical liquid drop of radius $$R$$ acquires the terminal velocity $$v_1$$ when falls through a gas of viscosity $$\eta$$. Now the drop is broken into 64 identical droplets and each droplet acquires terminal velocity $$v_2$$ falling through the same gas. The ratio of terminal velocities $$v_1/v_2$$ is __________.

One mole of diatomic gas having rotational modes only is kept in a cylinder with a piston system. The cross-section area of the cylinder is 4 cm$$^2$$. The gas is heated slowly to raise the temperature by 1.2 $$^\circ$$C during which the piston moves by 25 mm. The amount of heat supplied to the gas is __________ J. (Atmospheric pressure = 100 kPa, $$R = 8.3$$ J/mol. K) (Neglect mass of the piston)

Initial pressure and volume of a monoatomic ideal gas are $$P$$ and $$V$$. The change in internal energy of this gas in adiabatic expansion to volume $$V_{final} = 27V$$ is __________ J.

The frequency of oscillation of a mass $$m$$ suspended by a spring is $$v_1$$. If the length of the spring is cut to half, the same mass oscillates with frequency $$v_2$$. The value of $$\frac{v_2}{v_1}$$ is __________.

A monochromatic source of light operating at 15 kW emits $$2.5 \times 10^{22}$$ photons/s. The region of an electromagnetic spectrum to which the emitted electromagnetic radiation belongs to __________. (Take $$h = 6.6 \times 10^{-34}$$ J.s and $$c = 3 \times 10^8$$ m/s).

A current carrying circular loop of radius 2 cm with unit normal $$\hat{n} = \frac{\hat{k} + \hat{i}}{\sqrt{2}}$$ is placed in a magnetic field, $$\vec{B} = B_0(3\hat{i} + 2\hat{k})$$. If $$B_0 = 4 \times 10^{-3}$$ T and current $$I = 100\sqrt{2}$$ A, the torque experienced by the loop is __________ Wb.A. ($$\pi = 3.14$$)

A 30 cm long solenoid has 10 turns per cm and area of 5 cm$$^2$$. The current through the solenoid coil varies from 2 A to 4 A in 3.14 s. The e.m.f. induced in the coil is $$\alpha \times 10^{-5}$$ V. The value of $$\alpha$$ is __________.