NTA JEE Main 2025 April 7th Shift 2

Match List-I with List-II.

Choose the correct answer from the options given below :

A helicopter flying horizontally with a speed of 360 km/h at an altitude of 2 km, drops an object at an instant. The object hits the ground at  a point O, 20 s after it is dropped. Displacement of 'O' from the position of helicopter where the object was released is :
(use acceleration due to gravity $$g = 10$$ m/s$$^2$$and neglect air resistance)

An object with mass 500 g moves along x-axis with speed $$v = 4\sqrt{x}$$ m/s. The force acting on the object is :

A transparent block A having refractive index $$\mu = 1.25$$ is surrounded by another medium of refractive index $$\mu = 1.0$$. A light ray is incident on the flat face of the block with incident angle $$\theta$$. What is the maximum value of $$\theta$$ for which light suffers total internal reflection at the top surface of the block?

A parallel plate capacitor has charge $$5 \times 10^{-6}$$ C. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $$4 \times 10^{-6}$$ C then the dielectric constant of the slab is _____.

An inductor of reactance 100 $$\Omega$$, a capacitor of reactance 50 $$\Omega$$, and a resistor of resistance 50 $$\Omega$$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is _____ W.

Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities are: $$\frac{L_A}{L_B} = \frac{1}{2}$$, $$\frac{r_A}{r_B} = 2$$ and $$\frac{K_A}{K_B} = \frac{1}{2}$$. The free ends of rods A and B are maintained at 400 K, 200 K respectively. The temperature of rods interface is _____ K,when equilibrium is established.

The electric field in a region is given by $$\vec{E} = (2\hat{i} + 4\hat{j} + 6\hat{k}) \times 10^3$$ N/C. The flux of the field through a rectangular surface parallel to x-z plane is 6.0 Nm$$^2$$C$$^{-1}$$. The area of the surface is _____ cm$$^2$$.

M and R be the mass and radius of a disc. A small disc of radius R/3 is removed from the bigger disc. The moment of inertia of remaining part about an axis AB passing through the centre O and perpendicular to the plane of the disc is $$\frac{4}{x}MR^2$$. The value of x is _____.

A photo-emissive substance is illuminated with a radiation of wavelength $$\lambda_i$$ so that it releases electrons with de-Broglie wavelength $$\lambda_e$$. The longest wavelength of radiation that can emit photoelectron is $$\lambda_0$$. Expression for de-Broglie wavelength is given by : (m : mass of the electron, h : Planck's constant and c : speed of light)