GATE question papers: Physics, 2010 (PH)
Some Useful Physical constants Speed of light c = 3 ´ 108 ms-1 Plank's constant h = 6.63 ´ 10-34 J s Boltzmann constant kB = 1.38 ´ 10-23 J K-1 Charge of electron e = 1.6 ´ 10-19 C
Q. No. 1 – 25 Carry One Mark Each
1. Consider an anti-symmetric tensor Pij with the indices i and j running 1 to 5. The number of independent components of the tensor is (A) 3 (B) 10 (C) 9 (D) 6
2. The value of the integral |z - 2| = 1, is (A) 2pi (B) 4pi (C) pi (D) 0
3. The eigenvalues of the matrix (A) 5, 2, -2 (B) -5, -1, -1 (C) 5, 1, -1 (D) -5, 1, 1
4. If f(x) = (A) s-2 e3x (B) s2 e-3x (C) s-2 (D) s-2 e-3x
5. The valence electrons do not directly determine the following property of a metal. (A) Electrical conductivity (B) Thermal conductivity (C) Shear modulus (D) Metallic lustre
6. Consider X-ray diffraction from a crystal with a face-centered-cubic (fcc) lattic. The lattice plane for which there is NO diffraction peak is (A) (2, 1, 2) (B) (1, 1, 1) (C) (2, 0, 0) (D) (3, 1, 1)
7. The hall coefficient, RH, of sodium depends on (A) The effective charge carrier mass and carrier density (B) The charge carrier density and relaxation time (C) The charge carrier density only (D) The effective charge carrier mass
8. The Bloch theorem states that within a
crystal, the wavefunction, Y ( (A) Y( (B) Y( (C) Y( (D) Y(
9. In an experiment involving ferromagnetic medium, the following observations were made. Which one of the plots does NOT correctly represent the property of the medium? (TC) is the Curie temperature)
10. The thermal conductivity of a given material reduces when it undergoes a transition from its normal state to the superconducting state. The reason is: (A) The cooper pairs cannot transfer energy to the lattice (B) Upon the formation of Copper pairs, the lattice becomes less efficient in heat transfer (C) The electrons in the normal state lose their ability to transfer heat because of their coupling to the cooper pairs (D) The heat capacity increases on transition to the superconducting state leading to a reduction in thermal conductivity
11. The basic process underlying the neutron b - decay is (A) d ®
(C) s
® u + e-
12. In the nuclear shell model the spin parity of 15N is given by (A)
13. Match the reactions on the left with the associated interactions on the right. (1) p+ ® m+ + vm (i) Strong (2) p0 ® g + g (ii) Electromagnetic (3) p0 + n ® p- + p (iii) Weak (A) (1, iii), (2, ii), (3, i) (B) (1, i), (2, ii), (3, iii) (C) (1, ii), (2, i), (3, iii) (D) (1, iii), (2, i), (3, isi)
14. To detect trace amounts of a gaseous species in a mixture of gases, the preferred probing tool is (A) Ionization spectroscopy with X-rays (B) NMR spectroscopy (C) ESR spectroscopy (D) Laser spectroscopy
15. The collection of N atoms is exposed to a strong resonant electromagnetic radiation with Ng atoms in the ground state and Ne atoms in the excited state, such that Ng + Ne = N. This collection of two-level atoms will have the following population distribution: (A) Ng << Ne (B) Ng
>> Ne (C) Ng » Ne = 16. Two states of an atom have definite parties. An electric dipole transition between these states is (A) Allowed if both the states have even parity (B) Allowed if both the states have odd parity (C) Allowed if the two states have opposite parities (D) Not allowed unless a static electric field is applied 17. The spectrum of radiation emitted by a black body at a temperature 1000 K peaks in the (A) Visible range of frequencies (B) Infrared range of frequencies (C) Ultraviolet range of frequencies (D) microwave range of frequencies
18. An insulating sphere of radius a carries a charge density (A) d-1 (B) d-2 (C) d-3 (D) d-4
19. The voltage resolution of a 12 - bit digital to analog converter (DAC), whose output varies from - 10 V to + 10 V is ,approximately (A) 1 mV (B) 5 mV (C) 20 mV (D) 100 mV
20. In one of the following circuits, negative feedback does not operate for a negative input. Which one is it? The opamps are running from ± 15 V supplies.
21. A system of N non-interacting classical point particles is constrained to move on the two-dimensional surface of a sphere. The internal energy of the system is (A)
22. Which of the following atoms cannot exhibit Bose-Einstein condensation. even in principle? (A) tH1 (B) 4Hez (C) 21Na11 (D) 40K19
23. For the set of all Lorentz transformations with velocities along the x-axis, consider the two statements given below: P: If L is a Lorentz transformation then, L-1 is also a Lorentz transformation. Q: If L1 and L2 are Lorentz transformations then, L1L2 is necessarily a Lorentz transformation. Choose the correct option. (A) P is true and Q is false. (B) Both P and Q are true (C) Both P and Q are false. (D) P is false and Q is true
24. Which of the following is an allowed wavefunction for a particle in a bound state? N is a constant and a, b > 0. (A) y
= N (C) y
= Ne-ax
25. A particle is confined within a spherical region of radius one femtometer (10-15m). Its momentum can be expected to be about (A) Q.26 - Q.55 carry two marks each. 26. For the complex function, f(z) = (A) z = 0 is a branch point (B) z = 0 is a pole of order one (C) z = 0 is a removable singularity (D) z = 0 is a essential singularity 27. The solution of the differential equation for
y(t) : (A) (C) t cosh)t) (D) t sinh (t)
28. Given the recurrence relation for the Legendre polynomials (2n + 1) x Pn(x) = (n+1) Pn+1(x) + n Pn-1(x) which of the following integrals has a non-zero value? (A) (C)
29. For a two-dimensional free electron gas, the electronic density n, and the Fermi energy EF , are related by (A) n =
30. Far away from any of the resonance frequencies of a medium, the real part of the dielectric permittivity is (A) Always independent of frequency (B) Monotonically decreasing with frequency (C) Monotonically increasing with frequency (D) A non-monotonic function of frequency
31. The ground state wavefunction of deuteron is in a superposition of s and d states. Which of the following is NOT true as consequence? (A) It has a non-zero quadruple moment (B) The neutron-proton potential is non-central (C) The orbital wavefunction is not spherically symmetric (D) The hamiltonian does not conserve the total angular momentum
32. The first three energy levels of 228Th90 are shown below 4+ ----------------- 187 keV 2+ ------------------ 57.5 keV 0+ --------------------- 0 keV The expected spin-parity and energy of the next level are given by (A) (6* ; 400 keV) (B) (6* ; 300 keV) (C) (2* ; 400 keV) (D) (4* ; 300 keV)
33. The quark content of å+, K-, p- and p is indicated: |å+ñ = |uusñ;
| K-ñ = |s In the pricess, p- + p ® K- + å+ , considering strong interactions only, which of the following statements is true? (A) The process is allowed because DS = 0 (B) The process is allowed because Dl3 = 0 (C) The process is not allowed because DS ¹ 0 and Dl3 ¹ 0 (D) The process is not allowed because the baryon number is violated
34. The three principal moments of inertia of a methanol (CH3 OH) molecule have the property Ix = Iy = I and Iz ¹ I. The rotational energy eigenvalues are (A) (C)
35. A particle of mass m is confined in the potential
V (x) =
Let the wavefunction of the particle be given by where y0 and y1 are the eigenfunctions of the ground state and the first excited state respectively. The expectation value of the energy is (A)
36. Match the typical spectra of stable molecules with the corresponding wave-number range 1. Electronic spectra i. 106 cm-1 and above 2. Rotational spectra ii. 105 - 106 cm-1 3. Molecular dissociation iii. 100 - 102 cm-1 (A) 1 - ii, 2 - i, 3 - iii (B) 1 - ii, 2 - iii, 3 - i (C) 1 - iii, 2 - ii, 3 - i (D) 1 - i, 2 - ii, 3 - iii
37. Consider the operations P : (A) (C)
38. Two magnetic dipoles of magnitude m each are placed in a plane as shoen.
The energy of interaction given by (A) Zero (B) (C)
39. Consider a conducting loop of radius a and loop resistance R placed in a region with a magnetic field B thereby enclosing a flux f0. The loop is connected to an electronic circuit as shown, the capacitor being initially uncharged.
If the loop is pulled out of the region of the magnetic field at a constant speed u, the final output voltage Vout is independent of (A) f0 (B) u (C) R (D) C
40. The figure shows a constant current source charging a capacitor that is initially uncharged.
If the switch is closed at t = 0, which of the following plots depicts correctly the output voltage of the circuit as a function of time?
42. CO2 molecule has the first few energy levels uniformly separated by approximately 2.5 me V. At a temperature of 300 K, the ratio of the number of molecules in the 4th excited to the number in the 2nd excited state is about (A) 0.5 (B) 0.6 (C) 0.8 (D) 0.9
43. Which among the following sets of Maxwell relations is correct? (U - internal energy, H - enthalpy, A - Helmholtz free energy and G - Gibbs free energy and G - Gibbs free energy) (A) T = (C) P =
44. For a spin-s particle, in the eigen basis of (A) (C)
45. A particle is placed in a region with the
potential V (x) = Then. (A) x = 0 and x = (B) x = 0 is a points of stable
equilibrium and x = (C) x = 0 and x = (D) There are no points of stable or unstable equilibrium
46. A p0 meson at rest decays into two photons, which move along the x-axis. They are both detected simultaneously after a time, t = 10 s. In an inertial frame moving with a velocity V = 0.6 c in the direction of one of the photons, the time interval between the two detections is (A) 15 s (B) 0 s (C) 10 s (D) 20 s
47. A particle of mass m is confined in an infinite potential well: V(x)
=
It is
subjected to a perturbing potential Vp(x) = V0 sin
(A) E(1) = 0; E(2) < 0 (B) E(1) > 0; E(2) = 0 (C) E(1) = 0; E(2) depends on the sign of V0 (D) E(1) < 0; E(2) < 0
48. The number of distinct spectral lines that are observed in the resultant Zeeman spectrum is (A) 2 (B) 3 (C) 4 (D) 6
49. The spectral line corresponding to the transition Is observed along the direction of the applied magnetic field. The emitted electromagnetic field is (A) Circularly polarized (B) Linearly polarized (C) Unpolarized (D) Not emitted along the magnetic field directin
Common Data for Questions 50 and 51:
The partition function for a gas of photons is given by In
Z =
50. The specific heat of the photon gas varies with temperature as (A) (B) (C) (D)
51. The pressure of the photon gas is (A) (C)
Linked Answer Questions
Statement for Linked Answer Questions 52 and 53: 52. For a plane wave of angular frequency w and propagation vector (A) (B) (C) (D)
53. If e
and m assume negative values in a
certain frequency range, then the directions of the propagation vector (A) (B) (C) (D)
Statement for Linked Answer Questions 54 and 55:
The Lagrangian for a simple pendulum is given by: L =
54. Hamilton's equations are then given by (A) Pq = -mgl sin q; q
= (B) Pq = mgl sin q; q = (C) Pq = -mq; q = (D) Pq = -
55. The poisson bracket between q and q is (A) {q,
q} = 1 (B) {q, q}
= (C) {q,
q} =
General Aptitude (GA) Questions
Q.56 - Q.60 carry one mark each.
56. Choose the most appropriate word from the options given below to complete the following sentence His rather casual remarks on politics ------------- his lack of seriousness about the subject. (A) masked (B) belied (C) betrayed (D) suppressed
57. Which of the following options is the closest in meaning to the word below: Circuitous (A) cyclic (B) indirect (C) confusing (D) crooked
58. Choose the most appropriate word from the options given below to complete the following sentence: If we manage to ------------- our natural resources, we would leave a better planet for our children. (A) uphold (B) restrain (C) conserve (D) conserve
59. 25 persons are in a room. 15 of them play hockey,17 of them play football and 10 of them play both hockey and football. Then the number of persons playing neither hockey nor football is: (A) 2 (B) 17 (C) 13 (D) 3
60. The question below consists of a pair of related words followed by four pairs of words. Select the pair that best expresses the relation in the original pair. Unemployed : Worker (A) fallow : land (B) unaware : sleeper (C) wit : jester (D) renovated : house
Q.61 - Q.65 carry two marks each.
61. If 137 + 276 = 435 how much is 731 + 672? (A) 534 (B) 1403 (C) 1623 (D) 1513
62. Hari (H); Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All were born on 1st January. The age difference between any two successive siblings (that is born one after another is less than 3 years. Given the following facts: i. Hari's age + Gita's age + Irfan's age + Saira's age. ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest. iii. There are no twins. In what order were they born (oldest first)? (A) HSIG (B) SGHI (C) IGSH (D) IHSG
63. Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tools for their cause.
Which of the following statements best sums up the meaning of the above passage: (A) Modern warfare has resulted in civil strife. (B) Chemical agents are useful in modern warfare. (C) Use of chemical agents in warfare would be undesirable. (D) People in military establishments like to use chemical agents in war.
64. 5skilled workers can build a wall kin 20 days; 8 semi-skilled workers can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the wall? (A) 20 days (B) 18 days (C) 16 days (D) 15 days
65. Given digits 2, 2, 3, 3, 4, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed?
(A) 50 (B) 51 (C) 52(D) 54
END OF TEH QUESTION PAPER |
dz,
where the contour C is the unit circle:
are
then
the Laplace transform of f(x) is
),
of an electron has the form
)
where u(
is
an arbitrary vector
where u(
is
a reciprocal lattice vector
),
is
a lattice vector and 
)
(B) d
(B) 
(C) 
(D) 
(D) Ng
cos
NkBT (B) 
NkBT (C) NkBT (D) 
NkBT 
(B) 
(D) 
(B) 
(C) 
(D) 
,
which of the following statements is correct?
cosh(t),
subject to the initial conditions y(0) = 0 and 
is
(B) 
(D) 
(B) n
= 
(C) n
= 
(D) n
= 
(B) 
(D) 
(B) 
(C) 
(D) 
(parity)
and T : t 
,
which of the following set of transformations is correct?
(B) 
(D) 
(D) 
P
= 
(B) V
= 
T
= 
V=
(D) P
= 
S
= 
,
Sz the expectation value 
|s
m
(B) 
(D) 
.
where k, 
are
points of stable equilibrium
within
the well. Let E
(B) 
(D) 
propagating
in the medium Maxwell's equations reduce to 
and
the poynting vector 
in
that frequency range are related as 
(D) {