# Joint Entrance Screening Test (JEST) Past Year Question Papers 2018 Part 1

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## PART a: ONE-MARK QUESTIONS

Q1. When a collection of two-level systems is in equilibrium at temperature , the ratio of the population in the lower and upper levels is 2: 1. When the temperature is changed to *T*, the ratio is 8: 1. Then

(a)

(b)

(c)

(d)

Q2. A ball of mass *m* starting front rest, fails a vertical distance *h* before striking a vertical spring, which it compresses by a length . What is the spring constant of the spring?

(Hint: Measure all the vertical distances from the point where the ball first touches the uncompressed spring, i.e.. , set this point as the origin of the vertical axis.)

(a)

(b)

(c)

(d)

Q3. A collection of *N* interacting magnetic moments, each of magnitude , is subjected to a magnetic field H along the z direction. Each magnetic moment has a doubly degenerate level of energy zero and two non-degenerate levels of energies and respectively. The collection is in thermal equilibrium at temperature *T*. The total energy of the collection is

(a)

(b)

(c)

(d)

Q4. For which of the following conditions does the integral vanish for , where and are the Legendre polynomials of order *m* and *n* respectively?

(a) all

(b) *m*-*n* is an odd integer

(c) *m*-*n* is a nonzero even integer

(d)

Q5. If (*q*, *p*) is a canonically conjugate pair, which of the following is not a canonically conjugate pair?

(a)

(b)

(c)

(d) Where is the derivative of with respect to *p*.

Q6. A Germanium diode is operated at a temperature of 27 degree *C*. The diode terminal voltage is 0.3 *V* when the forward current is 10 *mA*. What is the forward current (in mA) if the terminal voltage is 0.4 *V?*

(a) 477.3

(b) 577.3

(c) 47.73

(d) 57.73

Q7. If is an infinitely differentiable function, then , where the operator , is

(a)

(b)

(c)

(d)

Q8. Consider a particle of mass *m* moving under the effect of an attractive central potential given as where . For a given angular momentum L, 3*km*/ *L* corresponds to the radius of the possible circular orbit and the corresponding energy is . The particle is released from with an inward velocity, energy, and angular momentum *L*. How long will be particle take to reach

(a) Zero

(b)

(c)

(d) Infinite

Q9. What is the difference between the maximum and the minimum eigenvalues of a system of two electrons whose Hamiltonian is , where and are the corresponding spin angular momentum operators of the two electrons?

(a)

(b)

(c)

(d) *J*

Q10. Two dielectric spheres of radius *R* are separated by a distance a such that *a ≫ R*. One of the spheres (sphere1) has a charge *q* and the other is neutral. If the linear dimensions of the systems are scaled up by a factor two, by what factor should be change on the sphere 1 be changed so that the force between the two spheres remain unchanged?

(a) 2

(b)

(c) 4

(d)

Q11. An electric charge distribution produces an electric field

where and are constants. The net charge within a sphere of radius centered at the origin is

(a)

(b)

(c)

(d)

Q12. The Laplace transform of is

(a)

(b)

(c)

(d)

Q13. Two of the eigenvalues of the matrix

are 1 and -1. What is the third eigenvalue?

(a) 2

(b) 5

(c) -2

(d) -5