NTA JEE Main 2025 April 4th Shift 2

Consider a n-type semiconductor in which $$n_e$$ and $$n_h$$ are number of electrons and holes, respectively.
(A) Holes are minority carriers
(B) The dopant is a pentavalent atom
(C) $$n_e n_h \neq n_i^2$$
       (where $$n_{i}$$ is number of electrons or holes in semiconductor when it is intrinsic form)
(D) $$n_e n_h \geq n_i^2$$
(E) The holes are not generated due to the donors
Choose the correct answer from the options given below :

Match List-I with List-II.

Choose the correct answer from the options given below : 

Displacement of a wave is expressed as $$x(t) = 5\cos\left(628t + \frac{\pi}{2}\right)$$ m. The wavelength of the wave when its velocity is 300 m/s is :

A finite size object is placed normal to the principal axis at a distance of 30 cm from a convex mirror of focal length 30 cm. A plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is :

In an electromagnetic system, a quantity defined as the ratio of electric dipole moment and magnetic dipole moment has dimension of $$[M^P L^Q T^R A^S]$$. The value of P and Q are :

A particle of charge 1.6 $$\mu$$C and mass 16 $$\mu$$g is present in a strong magnetic field of $$6.28 T$$. The particle is then fired perpendicular to magnetic field. The time required for the particle to return to original location for the first time is ______ s. ($$\pi = 3.14$$)

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ($$\omega_1$$) about its diameter. After some time during the rotation its starts loosing mass at a uniform rate, with no change in its shape. The angular velocity of the sphere when its radius become R/2 is $$x\omega_1$$. The value of x is ______.

If an optical medium possesses a relative permeability of $$\frac{10}{\pi}$$ and relative permittivity of $$\frac{1}{0.0885}$$, then the velocity of light is greater in vacuum than that in this medium by ______ times.
$$(\mu_{\circ}=4\pi \times 10^{-7} H/m, \in_{\circ} = 8.85 \times 10^{-12} F/m, c = 3 \times 10^{8} m/s)$$

In a Young's double slit experiment, two slits are located 1.5 mm apart. The distance of screen from slits is 2 m and the wavelength of the source is 400 nm. If the 20 maxima of the double slit pattern are contained within the centre maximum of the single slit diffraction pattern, then the width of each slit is $$x \times 10^{-3}$$ cm, where x-value is ______.

An inductor of self inductance 1 H connected in series with a resistor of $$100\pi$$ ohm and an ac supply of $$100\pi$$ volt, 50 Hz. Maximum current flowing in the circuit is ______ A.