Physics - 2019 Past Year Paper - IIT JAM MCQ

Which one of the following crystallographic planes represent (101) Miller indices of a cubic unit cell?

The Fermi-Dirac distribution function [n(ε)] is (k_B is the Boltzmann constant, T is the temperature and ε_F is the Fermi energy)

If Ø (x,y,z) is a scalar function which satisfies the Laplace equation, then the gradient off is

In a heat engine based on the Carnot cycle, heat is added to the working substance at constant 

Isothermal compressibility is given by

For using a transistor as an amplifier, choose the correct option regarding the resistances of base-emitter (R_BE) and base-collector (R_BC) junctions

A unit vector perpendicular to the plane containing  and  is 

A thin lens of refractive index 3/2 is kept inside a liquid of refractive index 4/3. If the focal length of the lens in air is 10 cm, then its focal length inside the liquid is

The eigenvalues ofare

A quantum particle confined inside a cubic box of side L, the ground state energy is given by E₀.  The energy of the first excited state is

A small spherical ball having charge q and mass m, is tied to a thin massless nonconducting string of length l.  The other end of the string is fixed to an infinitely extended thin non-conducting sheet with uniform surface charge density σ . Under equilibrium, the string makes an angle 45° with the sheet as shown in the figure. Then σ is given by (g is the acceleration due to gravity and ε₀ is the permittivity of free space)

Consider the normal incidence of a plane electromagnetic wave with electric field given by ω over an interface at z = 0 separating two media [wave velocities v₁ and v₂ (v₂ > v₁) and wave vectors k₁ and k₂, respectively] as shown in figure. The magnetic field vector of the reflected wave is (ω is the angular frequency)

The output of following logic circuit can be simplified to

A red star having radius r_R at a temperature T_R and a white star having radius r_W at a temperature T_W , radiate the same total power.  If these stars radiate as perfect black bodies, then

The mass per unit length of a rod (length 2 m) varies as ρ = 3x kg/m. The moment of inertia (in kg m²) of the rod about a perpendicular-axis passing through the tip of the rod (at x = 0) is

For a forward biased p-n junction diode, which one of the following energy-band diagrams is correct?
(ε_F is the Fermi energy)

The amount of work done to increase the speed of an electron from c/3 to 2c/3 is (c = 3×10⁸ m/s and rest mass of electron is 0.511 MeV)

The location of Cs⁺ and Cl^– ions inside the unit cell of CsCl crystal is shown in the figure. The Bravais lattice of CsCl is

A γ-ray photon emitted from a ¹³⁷Cs source collides with an electron at rest. If the Compton shift of the photon is 3.25 × 10^–13 m, then the scattering angle is closest to (Planck’s constant h = 6.626 × 10^–34 J s, electron mass me = 9.109 × 10^–31 kg and velocity of light in free space c = 3×10⁸ m/s)

During free expansion of an ideal gas under adiabatic condition, the internal energy of the gas

In the given phase diagram for a pure substance, regions I, II, III, IV, respectively represent

Light of wavelength λ (in free space) propagates through a dispersive medium with refractive index n(λ)=1.5 + 0.6λ. The group velocity of a wave travelling inside this medium in units of 10⁸ m/s is

The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be

During the charging of a capacitor C in a series RC circuit, the typical variations in the magnitude of the charge q(t) deposited on one of the capacitor plates, and the current i(t) in the circuit, respectively are best represented by

Which one of the following is an impossible magnetic field  ?

If the motion of a particle is described by x = 5 cos(8πt), y = 5 sin(8πt) and z = 5t, then the trajectory of the particle is

A ball of mass m is falling freely under gravity through a viscous medium in which the drag force is proportional to the instantaneous velocity v of the ball. Neglecting the buoyancy force of the medium, which one of the following figures best describes the variation of v as a function of time t?