List of top Questions asked in IIT JAM

Sand falls on a conveyor belt at the rate of 1.5 kg/s. If the belt is moving with a constant speed of 7 m/s, the power needed to keep the conveyor belt running is:

A particle of mass \( m \) is placed in a three-dimensional cubic box of side \( a \). What is the degeneracy of its energy level with energy \( \frac{14 \hbar^2 \pi^2}{2m a^2} \)?

An object of mass \( m \) with non-zero angular momentum \( \ell \) is moving under the influence of gravitational force of a much larger mass (ignore drag). Which of the following statement(s) is (are) correct?

A particle of mass \( m \) fixed in space is observed from a frame rotating about its \( z \)-axis with angular speed \( \omega \). The particle is in the frame’s \( xy \)-plane at a distance \( R \) from its origin. If the Coriolis and centrifugal forces on the particle are \( F_{\text{COR}} \) and \( F_{\text{CF}} \), respectively, then (all the symbols have their standard meaning and refer to the rotating frame),

Consider a circular parallel plate capacitor of radius \( R \) with separation \( d \) between the plates (\( d \ll R \)). The plates are placed symmetrically about the origin. If a sinusoidal voltage \( V = V_0 \sin(\omega t) \) is applied between the plates, which of the following statement(s) is (are) true?

For an atomic nucleus with atomic number \( Z \) and mass number \( A \), which of the following is (are) correct?

Consider a one-dimensional harmonic oscillator of angular frequency \( \omega \). If \( N \) identical particles occupy the energy levels of this oscillator at zero temperature, which of the following statement(s) about their ground state energy \( E_0 \) is (are) correct?

For a point dipole of dipole moment \( \mathbf{p} = p \hat{z} \) located at the origin, which of the following is (are) correct?

A dielectric sphere of radius \( R \) has constant polarization \( \mathbf{P} = P_0 \hat{z} \) so that the field inside the sphere is \( \mathbf{E} = - \frac{P_0}{3 \epsilon_0} \hat{z} \). Then, which of the following is (are) correct?

A photon of frequency \( \nu \) strikes an electron of mass \( m \) initially at rest. After scattering at an angle \( \phi \), the photon loses half of its energy. If the electron recoils at an angle \( \theta \), which of the following is (are) true?

Unpolarized light is incident on a combination of a polarizer, a \( \lambda/2 \) plate and a \( \lambda/4 \) plate kept one after the other. What will be the output polarization for the following configurations?
Configuration 1: Axes of the polarizer, the \( \lambda/2 \) plate and the \( \lambda/4 \) plate are all parallel to each other.
Configuration 2: The \( \lambda/2 \) plate is rotated by 45° with respect to configuration 1.
Configuration 3: The \( \lambda/4 \) plate is rotated by 45° with respect to configuration 1.

In the radiation emitted by a black body, the ratio of the spectral densities at frequencies \( 2\nu \) and \( \nu \) will vary with \( \nu \) as:

KC1 has the NaCl type structure which is fcc with two-atom basis, one at \( (0, 0, 0) \) and the other at \( \left( \frac{1}{2}, \frac{1}{2}, \frac{1}{2} \right) \). Assume that the atomic form factors of \( K^+ \) and \( Cl^- \) are identical. In an x-ray diffraction experiment on KC1, which of the following \( (h k l) \) peaks will be observed?

Consider two identical, finite, isolated systems of constant heat capacity \( C \) at temperatures \( T_1 \) and \( T_2 \) (\( T_1>T_2 \)). An engine works between them until their temperatures become equal. Taking into account that the work performed by the engine will be maximum (\( W_{\text{max}} \)) if the process is reversible (equivalently, the entropy change of the entire system is zero), the value of \( W_{\text{max}} \) is:

A white dwarf star has volume \( V \) and contains \( N \) electrons so that the density of electrons is \( n = \frac{N}{V} \). Taking the temperature of the star to be 0 K, the average energy per electron in the star is \( \epsilon_0 = \frac{3h^2}{10m} (3n)^{2/3 \), where \( m \) is the mass of the electron. The electronic pressure in the star is:}

Consider a system of \( N \) particles obeying classical statistics, each of which can have an energy 0 or \( E \). The system is in thermal contact with a reservoir maintained at a temperature \( T \). Let \( k \) denote the Boltzmann constant. Which one of the following statements regarding the total energy \( U \) and the heat capacity \( C \) of the system is correct?

Consider Rydberg (hydrogen-like) atoms in a highly excited state with \( n \) around 300. The wavelength of radiation coming out of these atoms for transitions to the adjacent states lies in the range:

A plane in a cubic lattice makes intercepts of \( a, a/2 \) and \( 2a/3 \) with the three crystallographic axes, respectively. The Miller indices for this plane are:

Which of the following is due to inhomogeneous refractive index of earth’s atmosphere?

For the three matrices given below, which one of the choices is correct?

If the Boolean function \( Z = PQ + PQR + PQRS + PQRST + PQRSTU \), then \( Z \) is:

The dispersion relation for electromagnetic waves travelling in a plasma is given as \( \omega^2 = c^2k^2 + \omega_p^2 \), where \( c \) and \( \omega_p \) are constants. In this plasma, the group velocity is: