# Joint Entrance Screening Test (JEST) Past Year Question Papers 2020 Part 2

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Q14. Consider a system of two particles at temperature . Each of them can occupy three different quantum energy levels having energies 0, and , and both of them cannot occupy the same energy level. What is the average energy of the system?

(a)

(b)

(c)

(d)

Q15. If *x* and *y* have the joint probability distribution and otherwise. What is the probability that *y* assumes a value greater than , given that *x* is equal to

(a)

(b)

(c)

(d)

Q16. The wave function of an electron in one dimension is given by

The ratio between the expected position and the most probable position is

(a) 0.856

(b) 1.563

(c) 2.784

(d) 3.567

Q17. A particle is to slide along the horizontal circular path on the inner surface of the funnel as shown in the figure. The surface of the funnel is frictionless. What must be the speed of the particle (in terms of *r* and ) if it is to execute this motion?

(a)

(b)

(c)

(d)

Q18. Two rails of a railroad track are insulated from each other and from the ground, and are connected by a millivolt meter. What is the reading of the millivolt meter when a train travels at the speed 90km/hr down the track? Assume that the vertical component of the earth՚s magnetic field is 0.2 gauss and that the tracks are separated by two meters. Use

1 gauss sec/

(a) 10

(b) 1

(c) 0.2

(d) 180

Q19. A particle of mass *m* moves in a one-dimensional potential , where is a positive constant. Given the initial conditions, and , which one of the following statements is correct?

(a) The particle undergoes simple harmonic motion about the origin with frequency

(b) The angular frequency of oscillations of the particle is

(c) The particle begins from rest and is accelerated along the positive *x* -axis such that

(d) The angular frequency of oscillations of the particle is independent of its mass

Q20. A carbon rod of resistance and a metal rod of resistance are connected in series. Let their linear temperature coefficients of resistivity have magnitudes and , respectively. The condition that the net resistance would be independent of temperature is

(a)

(b)

(c)

(d)

Q21. The 2՚s compliment of 1111 1111 is

(a) 00000001

(b) 00000000

(c) 1111 1111

(d) 1000 0000

Q22. Two tuning forks *A* and *B* are struck instantaneously to obtain Lissajous figures. The figures go through a complete cycle in 20 *s*. Fork *A* is located with wax, so that the cycle period changes to 10 *s*. If the frequency of fork *B* is 256.10 *Hz*, what is the frequency of fork *A* after loading?

(a) 256.00 *Hz*

(b) 256.05 *Hz*

(c) 256.15 *Hz*

(d) 256.20 *Hz*

Q23. Consider a classical harmonic oscillator in thermal equilibrium at a temperature *T*. If the spring constant is changed to twice its value isothermally, then the amount of work done on the system is

(a) ln 2*kT*

(b) ln 2*k T*

(c) 2 ln 2

(d) ln 2 − *k T*

Q24. The solution of the differential equation is given as .

The values of the coefficients , , and *C* are:

(a) , , and are arbitrary

(b) , , are arbitrary and

(c) , , are arbitrary and

(d) , , are arbitrary and