# Joint Entrance Screening Test (JEST) Past Year Question Papers 2017 Part 4

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Q 10. If be the position operator at a time t in the Heisenberg picture for a particle described by the Hamiltonian, what is in units of where is the ground state?

## Part C: 3-Mark Questions

Q 1. Consider a grounded conducting plane which is infinitely extended perpendicular to the y -axis at y = 0. If an infinite line of charge per unit length runs parallel to x -axis at y = d, then surface charge density on the conducting plane is

(a)

(b)

(c)

(d)

Q 2. A system of particles on N lattice sites is in equilibrium at temperature T and chemical potential . Multiple occupancy of the sites is forbidden. The binding energy of a particle at each site is . The probability of no site being occupied is

(a)

(b)

(c)

(d)

Q 3. The integral is

(a)

(b)

(c)

(d)

Q 4. For an electric field where k is a non-zero constant, total charge enclosed by the cube as shown below is

(a) 0

(b)

(c)

(d)

Q 5. Consider a point particle A of mass colliding elastically with another point particle B of mass at rest, where . After collision, the ratio of the kinetic energy of particle B to the initial kinetic energy of particle A is given by

(a)

(b)

(c)

(d)

Q 6. Two classical particles are distributed among sites on a ring. Each site can accommodate only one particle. If two particles occupy two nearest neighbour sites, then the energy of the system is increased by . The average energy of the system at temperature T is

(a)

(b)

(c)

(d)

Q 7. Consider a 741 operational amplifier circuit as shown below, where and . If , what is the value of with respect to the ground?

(a)

(b)

(c)

(d)

Q 8. The Fourier transform of the function up to proportionality constant is

(a)

(b)

(c)

(d)

Q 9. If , where s are the Pauli matrices and I is the identity matrix, then the trace of is

(a)

(b)

(c) 1

(d)

Q 10. A cylinder at temperature is separated into two compartments A and B by a free sliding piston. Compartments A and B are filled by Fermi gases made of spin and particles respectively. If particles in both the compartments have same mass, the ratio of equilibrium density of the gas in compartment A to that of gas in compartment B is

(a) 1

(b)

(c)

(d)