# Joint Entrance Screening Test (JEST) Past Year Question Papers 2020 Part 3

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Q25. A free particle of energy E, characterized by a plane wave of wavelength enters a region of constant potential -V (where ) . Within the region of the potential, the wavelength of the particle is . The ratio is:

(a)

(b) -3

(c) 3

(d)

## PART B: 3-Mark Questions

Q1. Consider a quantum particle of mass m moving in a potential

what is the degeneracy of the energy state , where measures the strength of the potential?

(a) 4

(b) 2

(c) 10

(d) 5

Q2. Consider a particle with total energy E is oscillating in a potential with and in one dimension. Which one of the following gives the relation between the time-period of oscillation T and the total energy E:

(a)

(b)

(c)

(d)

Q3. A classical gas of N particles is kept at a temperature T and is confined to move on a two-dimensional surface (xy -plane) . If an external linear force field is applied along the x -axis, then the partition function of the system will be proportional to

(a)

(b)

(c)

(d)

Q4. An electromagnetic field is given by

where

The corresponding charge density and current density are given by

(a)

(b)

(c)

(d)

Q5. A particle of mass m is placed in a potential well , where c is a positive constant and n is an even positive integer. If the particle is in equilibrium at constant temperature, which one of the following relations between average kinetic energy and average potential energy is correct.

(a)

(b)

(c)

(d)

Q6. What is the charge stored on each capacitor and in the circuit shown in the given figure?

(a)

(b)

(c)

(d)

Q7. A particle moving in two dimensions satisfies the equations of motion

with . What is the ratio of ?

(a)

(b)

(c)

(d)

Q8. Analyse the common emitter transistor circuit given in the figure. If the current gain increases by , the relative change in collector current is approximately

(a)

(b)

(c)

(d)

Q9. What is the value of the following contour integral I taken counterclockwise around the circle ?

(a)

(b)

(c)

(d)