# Joint Entrance Screening Test (JEST) Past Year Question Papers 2018 Part 2

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Q14. In a thermodynamic process, the volume of one mole of an ideal is varied as where is a constant. The adiabatic exponent of the gas is . What is the amount of heat received by the gas if the temperature of the gas increases by in the process?

(a)

(b)

(c)

(d)

Q15. , where is Dirac distribution, is

(a) 1

(b)

(c)

(d)

Q16. The integral is

(a)

(b)

(c)

(d) Zero

Q17. A one-dimensional harmonic oscillator (mass *m* and frequency ) is in a state such that the only possible outcomes of an energy measurement are , or , where is the energy of the *n*-th excited state. If *H* is the Hamiltonian of the oscillator,

, and , then the probability that the energy measurement yields is

(a)

(b)

(c)

(d)

Q18. The charge density as a function of the radial distance *r* is given by for *r < R* and zero otherwise. The electric flux over the surface of an ellipsoid with axes 3*R*, 4*R*, and 5*R* centered at the origin is

(a)

(b)

(c)

(d) Zero

Q19. A quantum particle of mass *m* is moving on a horizontal circular path of radius *a*. The particle is prepared in a quantum state described by the wave function , being the azimuthal angle. If a measurement of the *z* -component of orbital angular momentum of die particle is carried out, the possible outcomes and the corresponding probabilities are

(a) with

(b)

(c) with

(d) with

Q20. Consider two canonically conjugate operators and such that , where *I* is identity operator. If , where are complex numbers and the value of is

(a)

(b)

(c)

(d) z

Q21. Suppose the spin degree of freedom of two particles (nonzero rest mass and nonzero spin) is described completely by a Hilbert space of dimension twenty-one. Which of the following could be the spin of one of the particles?

(a) *2*

(b)

(c) 1

(d)

Q22. For a classical system of non-interacting particles in the presence of a spherically symmetric potential , what is the mean energy per particle? is a constant.

(a)

(b)

(c)

(d)

Q23. A particle of mass 1*kg* is undergoing small oscillation about the equilibrium point in the potential for *x >* 0 meters. The time period (in seconds) of the oscillation is -

(a)

(b)

(c) 1.0

(d)

Q24. A block of mass *M* is moving on a frictionless inclined surface of a wedge of mass *m* under the influence of gravity. The wedge is lying on a rigid frictionless horizontal surface. The configuration can be described using the radius vectors and shown in the figure. How many constraints are present and what are the types?

(a) One constraint; holonomic and scleronomous

(b) Two constraints; both are holonomic; one is scleronomous and rheonomous

(c) Two constraints; both are scleronomous; one is holonomic and other is nonholonomic.

(d) Two constraints; both are holonomic and scleronomous

Q25. An electromagnetic wave of wavelength is incident normally on a dielectric slab of thickness *t*. If *K* is the dielectric constant of the slab. The change in phase of the emergent wave compared with the case of propagation in the absence of the dielectric slab is

(a)

(b)

(c)

(d)