Questions and answers for exam Preparation

MCQs

Total Questions : 47 | Page 2 of 5 pages

Question 11. For a scalar function Ï† satisfying the Laplace equation, âˆ‡Ï† has

zero curl and non-zero divergence
non-zero curl and zero divergence
zero curl and zero divergence
non-zero curl and non-zero divergence

Discuss Question

Answer: Option C. -> zero curl and zero divergence

-NA-

Question 12. Consider the wave function Aeikr (r0/r) where ô€œ£ is the normalization constant. For r = 2r0, the
magnitude of probability current density up to two decimal places, in units of (A2Ñ›k/m), is

0.20
0.25
0.30
0.35

Discuss Question

Answer: Option B. -> 0.25

-NA-

Question 13. A spin-half particle is in a linear superposition 0.8|â†‘âŒª + 0.6|â†“âŒª of its spin-up and spin-down states. If |â†‘âŒª and |â†“âŒª are the eigenstates of Ïƒz then what is the expectation value, up to one decimal place, of the operator 10Ïƒz + 5Ïƒx ? Here, symbols have their usual meanings. ____________

Discuss Question

Answer: Option D. -> 7.6

-NA-

Question 14. Consider the decay of a pion into a muon and an anti-neutrino Ï€- â†’ Î¼- + v-Î¼ in the pion rest frame. mÏ€ = 139.6 MeV/c2, mÎ¼ = 105.7 MeV/c2, mv â‰ˆ 0 The energy (in MeV) of the emitted neutrino, to the nearest integer is ____________

Discuss Question

Answer: Option B. -> 30

-NA-

Question 15. A circularly polarized monochromatic plane wave is incident on a dielectric interface at Brewster
angle. Which one of the following statements is CORRECT ?

The reflected light is plane polarized in the plane of incidence and the transmitted light is circularly polarized.
The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is plane polarized in the plane of incidence.
The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is elliptically polarized.
There will be no reflected light and the transmitted light is circularly polarized.

Discuss Question

Answer: Option C. -> The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is elliptically polarized.

-NA-

Question 16. Which one of the following commutation relations is NOT CORRECT ? Here, symbols have their
usual meanings.

[L2, Lz] = 0
[Lx, Ly] = iÑ›Lz
[Lz, L+] = Ñ›L+
[Lz, L-] = Ñ›L-

Discuss Question

Answer: Option D. -> [Lz, L-] = Ñ›L-

-NA-

Question 17. What should be the clock frequency of a 6-bit A/D converter so that its maximum conversion time
is 32 Î¼s?

1 MHz
2 MHz
0.5 MHz
4 MHz

Discuss Question

Answer: Option B. -> 2 MHz

-NA-

Question 18. A phosphorous doped silicon semiconductor ( doping density: 1017/cm3) is heated from 100oC to
200oC. Which one of the following statements is CORRECT ?

Position of Fermi level moves towards conduction band
Position of dopant level moves towards conduction band
Position of Fermi level moves towards middle of energy gap
Position of dopant level moves towards middle of energy gap

Discuss Question

Answer: Option C. -> Position of Fermi level moves towards middle of energy gap

-NA-

Question 19. Considering the BCS theory of superconductors, which one of the following statements is NOT
CORRECT? (h is the Planck's constant and e is the electronic charge)

Presence of energy gap at temperatures below the critical temperature
Different critical temperatures for isotopes
Quantization of magnetic flux in superconducting ring in the unit of (h/e)
Presence of Meissner effect

Discuss Question

Answer: Option C. -> Quantization of magnetic flux in superconducting ring in the unit of (h/e)

-NA-

Question 20. Group I contains elementary excitations in solids. Group II gives the associated fields with these
excitations. MATCH the excitations with their associated field and select your answer as per codes
given below.Group I Group II(P) phonon (i) photon + lattice vibration(Q) plasmon (ii) electron + elastic deformation(R) polaron (iii) collective electron oscillations(S) polariton (iv) elastic wave