PUNJAB PHYSICS LECTURER PREVIOUS YEAR QUESTION PAPER 2021 WITH ANSWER KEY

Punjab Physics Lecturer Exam 2021: Complete Paper Analysis & Topic-wise Breakdown

The Punjab Physics Lecturer recruitment exam conducted in 2021 (Booklet Series D) was a comprehensive test of a candidate's grasp on postgraduate-level Physics. Comprising 150 multiple-choice questions, the paper spanned across all major domains of the M.Sc. Physics syllabus.

For aspirants preparing for upcoming lecturer or master cadre exams, analyzing this paper is crucial for understanding the examiner's mindset, the weightage of different subjects, and the overall difficulty level. Here is a detailed, topic-wise analysis of the 2021 question paper.

1. Overall Difficulty Level

The overall difficulty level of the paper can be classified as Moderate to Tough.

• Direct & Conceptual Questions: Around 60-70 questions were straightforward, formula-based, or tested fundamental definitions (e.g., identifying logic gates, Bragg's Law, properties of Fourier transforms).
• Numerical & Application-Based: About 40-50 questions required calculations or deeper application of concepts (e.g., finding the radius of a curved path in a magnetic field, collision velocities, Laplace transformations).
• Advanced Theoretical Questions: The remaining questions tested deep theoretical knowledge, especially in Quantum Mechanics, Particle Physics, and Group Theory.

2. Topic-Wise Weightage Analysis

A striking feature of this paper was its balanced approach. Almost every core subject from the master's syllabus was touched upon. Here is an approximate breakdown of the question distribution:

Subject / Topic Domain	Approx. Number of Questions	Difficulty Level
Mathematical Physics (Matrices, Fourier, Laplace, Group Theory)	18 - 20	Moderate
Quantum Mechanics (Wave functions, Potentials, Operators)	15 - 18	Moderate to Tough
Classical Mechanics & Relativity (Lagrangian, Hamiltonian, Poisson brackets)	15 - 18	Moderate
Solid State Physics (Lattices, Superconductivity, Specific Heat)	16 - 19	Moderate
Nuclear & Particle Physics (Decay, Shell Model, Quarks, Conservation Laws)	15 - 18	Easy to Moderate
Electronics & Devices (Op-Amps, Logic Gates, Diodes, Transistors)	15 - 18	Moderate
Atomic & Molecular Physics (Zeeman Effect, Raman Spectra, Lasers)	14 - 16	Tough
Electromagnetic Theory (Waveguides, Maxwell's Eq., Dipole Radiation)	12 - 14	Moderate to Tough
Statistical Mechanics & Thermodynamics	8 - 10	Moderate

3. Key Subject Highlights

• Mathematical Physics: A surprisingly high emphasis was placed on Group Theory, Fourier Transforms, and Laplace Transforms. Candidates with a strong grip on these mathematical tools had a clear advantage.
• Classical Mechanics: Heavy focus on Hamiltonian and Lagrangian dynamics, Canonical transformations, and Poisson brackets rather than basic Newtonian mechanics. Special Theory of Relativity also had a few direct numericals.
• Atomic & Molecular Physics: This section leaned towards the difficult side, with specific questions on term symbols (L-S coupling), Lande g-factors, and fine/hyperfine splitting. Laser physics (He-Ne lasers, population inversion) was also prominently featured.
• Electronics: Very scoring for well-prepared candidates. Topics included Op-Amps (integrators, ideal characteristics), basic logic gates, Zener diodes, and MOSFETs.
• Nuclear & Particle Physics: Tested elementary particle properties (quarks, isospin, baryons) and nuclear models (liquid drop, shell model). Most questions here were theoretical and memory-based.

4. Preparation Strategy for Future Aspirants

1. Do Not Skip Mathematical Physics: It forms the backbone of the exam. Ensure you are comfortable with differential equations, matrices, and transform techniques.
2. Memorize Standard Results: Many questions on Waveguides, Solid State Physics (packing fractions, lattice parameters), and Statistical Mechanics can be solved in seconds if you have standard formulas memorized.
3. Focus on Post-Graduation Topics: Unlike general science exams, this paper strictly adhered to the B.Sc./M.Sc. core syllabus. Deep dive into topics like Canonical Transformations, Quantum Perturbation, and Particle Physics.
4. Practice Time Management: With 150 questions to solve, getting stuck on a long numerical can be costly. Identify and attempt the theoretical "read-and-tick" questions first (like those in Nuclear Physics and Electronics).

Conclusion: The 2021 Punjab Physics Lecturer paper was a standard, well-set examination that rewarded conceptual clarity and wide syllabus coverage over rote memorization of basic formulas. Consistent revision of advanced topics is the key to cracking this exam.

1. The L,S and J quantum numbers corresponding to the ground state electronic configuration of boron (Z=5) are
(a) L=1, S=1/2, J=5/2
(b) L=1, S=1/2, J=1/2
(c) L=1, S=3/2, J=1/2
(d) None of these
Answer: (b)

2. The Lande g-factor for the ³P₁ level of an atom is
(a) 1/2
(b) 3/2
(c) 5/2
(d) 7/2
Answer: (b)

3. The hyperfine splitting of the spectral lines of an atom is due to
(a) The effect of external electromagnetic field
(b) The coupling between the spins of the electrons
(c) The coupling between the electron spin and the nuclear spin
(d) None of these
Answer: (c)

4. The perturbation due to the magnetic field is given by
(a) -μ . B
(b) μ . E
(c) -μ . E
(d) None of these
Answer: (a)

5. Sommerfield theory of free electron is a
(a) Classical theory
(b) Electrodynamic theory
(c) Relativity theory
(d) Quantum theory
Answer: (d)

6. Which is the Bragg's law condition in the reciprocal lattice
(a) 2K.G + G² = 0
(b) 2K.G + K² = 0
(c) 2K.G + G = 0
(d) None of these
Answer: (a)

7. The temperature below which certain materials are ferromagnetic and above which they are paramagnetic is called
(a) Weiss temperature
(b) Curie temperature
(c) Neel temperature
(d) None of these
Answer: (b)

8. If eccentricity of the equation of conic is 1, conic is
(a) Parabola
(b) Hyperbola
(c) Ellipse
(d) Circle
Answer: (a)

9. Number of coordinates required for specification of single particle in phase space are;
(a) 3
(b) 6
(c) 5
(d) 9
Answer: (b)

10. In Rutherford's scattering experiment, 10⁵ particles are scattered at an angle of 2°. The number of α-particles scattered at an angle of 20° are;
(a) 100
(b) 10000
(c) 10
(d) 1000
Answer: (c)

11. The eccentricity of the earth's orbit is 0.0167. Ratio of maximum to minimum speed of earth in its orbit is;
(a) 1.03
(b) 2.02
(c) 1.53
(d) 1.95
Answer: (a)

12. If the proper length of rod is 100cm, the length of rod travelling with velocity 0.8c is
(a) 90cm
(b) 120 cm
(c) 70 cm
(d) 60 cm
Answer: (d)

13. If m_o, p and V are rest mass, momentum and potential energy respectively of the particle and c is velocity of light, then Hamiltonian in relativistic mechanics may be expressed as;
(a) (p²c⁴ + m_o²c⁴)^1/2 + V
(b) (p⁴c² + m_o²c⁴)^1/2 + V
(c) (p²c² + m_o²c⁴)^1/2 + V
(d) (p²c² + m_o²c⁴)^1/2 + V^1/2
Answer: (c)

14. Hamiltonian for a conservative system where coordinate transformation is independent of time repersents
(a) Sum of kinetic and potential energy
(b) Kinetic energy
(c) Difference of kinetic and potential energy
(d) Potential energy
Answer: (a)

15. What is the electric flux through a closed surface surrounding an electric dipole
(a) Twice the charge enclosed
(b) Half the charge enclosed
(c) Double the charge
(d) Zero
Answer: (d)

16. The displacement current arises due to
(a) Positive charges only
(b) Negative charges only
(c) Both positive and negative charges
(d) Time varying electric field
Answer: (d)

17. Which one of the following cannot be explained by considering a harmonic approximation for the lattice vibrations in solids?
(a) Debye T³ law
(b) Einstein theory of specific heat
(c) Optical branches in lattices
(d) Thermal expansion
Answer: (d)

18. The packing fraction of hexagonal closed pack structure is
(a) 72%
(b) 74%
(c) 40%
(d) 100%
Answer: (b)

19. Bravais lattice consists of _____ space lattices.
(a) 11
(b) 12
(c) 13
(d) 14
Answer: (d)

20. The correct order of the packing efficiency in different types of unit cells is
(a) fcc < bcc < simple cubic
(b) fcc > bcc > simple cubic
(c) bcc < fcc < simple cubic
(d) None of these
Answer: (b)

21. What causes the depletion region,
(a) Barrier potential
(b) Diffusion
(c) Doping
(d) Ions
Answer: (b)

22. Silicon atoms combine into an orderly pattern called a
(a) Valence orbit
(b) Covalent bond
(c) Semiconductor
(d) Crystal
Answer: (d)

25. Nuclear megneton is smaller than the Bohr magneton by a factor of about
(a) 10
(b) 20
(c) 200
(d) 2000
Answer: (d)

26. As the energy of nucleon in a nucleus increases, the depth of the net nuclear potential V₀
(a) Rapidly increases
(b) Rapidly decreases
(c) Slowly decreases
(d) Increases exponentially
Answer: (c)

27. In shell model it is assumed that the constituent parts of a nucleus move
(a) Independently
(b) Collectively
(c) Opposite to each other
(d) None of these
Answer: (a)

28. Pairing energy term appearing in the semi-imperials mass formula for the liquid drop model depends only on
(a) Atomic mass of nucleus M
(b) Only on mass number A
(c) Only on atomic number Z
(d) None of these
Answer: (b)

29. What are the conditions called, which are required for a signal to fulfil to be represented as Fourier series
(a) Dirichlet's conditions
(b) Gibbs phenomenon
(c) Fourier conditions
(d) Fourier phenomenon
Answer: (a)

30. What are the two types of Fourier series
(a) Trigonometric and exponential
(b) Trigonometric and logarithmic
(c) Exponential and logarithmic
(d) Trigonometric only
Answer: (a)

31. Find the Fourier transform of e^jω₀t
(a) δ(ω + ω₀)
(b) 2πδ(ω + ω₀)
(c) δ(ω - ω₀)
(d) 2πδ(ω - ω₀)
Answer: (d)

32. Find the inverse Fourier transform of δ(ω)
(a) 1/(2π)
(b) 2π
(c) 1/π
(d) π
Answer: (a)

33. Laplace of function f(t) is given by?
(a) F(s) = ∫_-∞^∞ f(t)e^-stdt
(b) F(t) = ∫_-∞^∞ f(t)e^-tdt
(c) f(s) = ∫_-∞^∞ f(t)e^-stdt
(d) f(t) = ∫_-∞^∞ f(t)e^-tdt
Answer: (a)

34. Find the Laplace transform of e^tsin(at)
(a) a / (a² + (s+1)²)
(b) a / (a² + (s-1)²)
(c) (s+1) / (a² + (s+1)²)
(d) (s+1) / (a² + (s+1)²)
Answer: (b)

35. Value of ∫_-∞^∞ e^tSin(t)Cos(t)dt=
(a) 0.5
(b) 0.75
(c) 0.2
(d) 0.71
Answer: (c)

36. Time domain function of s/(a² + s²) is given by
(a) Cos(at)
(b) Sin(at)
(c) Cos(at) Sin(at)
(d) Sin(t)
Answer: (a)

37. The composition of any two element of the group produce another element of same group. This property is known as
(a) Associative
(b) Closure
(c) Existence of identity
(d) Existence of inverse
Answer: (b)

38. Which of the below is left cancellation law
(a) A.B = C.A
(b) B.A = C.A
(c) A.B = A.C
(d) B.A = A.C
Answer: (c)

39. All subgroups other than trivial groups are called
(a) Proper group
(b) Improper group
(c) Proper subgroup
(d) Improper subgroup
Answer: (c)

40. An infinite group may be
(a) Continuous
(b) Discrete
(c) Continuous and discrete
(d) Continuous or discrete
Answer: (d)

41. A cyclic group is always
(a) Abelion
(b) Monoid
(c) Semi group
(d) Subgroup
Answer: (a)

42. {1, -1, i, -i} is
(a) Subgroup
(b) Semigroup
(c) Cyclic group
(d) Abelion group
Answer: (c)

43. Which statement is true
(a) set of all matrices multiplication forms a group
(b) set of all rational negative numbers form group under multiplication
(c) set of all singular matrices forms a group under multiplication
(d) both (b) and (c)
Answer: (*) Note: One mark was awarded to all candidates for this question in the official key.

44. Which of the following technologies does not inherently rely on quantum physics principles
(a) Lasers
(b) LEDs
(c) Transistors
(d) Reflecting telescopes
Answer: (d)

45. What does the energy of a photon depends upon
(a) Its wavelength
(b) Its speed
(c) Its intensity
(d) All the above
Answer: (a)

46. What property of quantum mechanics, dubbed as "spooky action at a distance" by Einstein, has been demonstrated with pairs of photons separated by hundreds of kilometres
(a) Superposition
(b) Wave particle duality
(c) Entanglement
(d) The uncertainty principal
Answer: (c)

47. The wave function of the quantum particle in a box of length L lies in which region
(a) 0 < X < L
(b) x < 0
(c) 0 < X < L
(d) x > L
Answer: (c)

48. Calculate the Zero-point energy for a particle in an infinite potential well for an electron confined to 1 nm atom
(a) 3.9 × 10^-29 J
(b) 4.9 × 10^-29 J
(c) 5.9 × 10^-29 J
(d) 6.9 × 10^-29 J
Answer: (b)

49. The de Broglie wave equation showed that wavelength of any moving object is equal to
(a) m/hv
(b) h/mv
(c) v/mh
(d) hm/v
Answer: (b)

50. The wave function of a particle in a box is given by
(a) √(2/L) sin(nx/L)
(b) √(2/L) sin(nπx/L)
(c) √(2/L) sin(x/L)
(d) √(2/L) sin(πx/L)
Answer: (b)

51. What are the four basic forces of the universe
(a) Strong, weak, electromagnetic, and gravitational
(b) Momentum, velocity, gravity, and friction
(c) Gravitational, strong, quantum, and Newtonian
(d) Weak, strong, medium, and variable
Answer: (a)

52. According to the Dirac equation, a given particle has
(a) negative charge
(b) an antiparticle
(c) a size limit
(d) some velocity
Answer: (b)

53. If a coordinate is cyclic then
(a) Generalized momentum conjugate to the cyclic coordinate is conserved.
(b) It is not absent in Lagrangian.
(c) It is present in Hamiltonian
(d) Corresponding angular momentum is conserved
Answer: (a)

54. In case, Lagrangian does not contain time explicitly then
(a) Ratio of Kinetic to Potential energy of the conservative system is conserved
(b) Jacobi integral becomes invariant
(c) Difference of Kinetic and Potential energy of the conservative system is conserved
(d) Total energy of the conservative system is conserved
Answer: (d)

55. If q_k and p_k are old set of generalized and momentum coordinates and Q_k and P_k are new set of generalized and momentum coordinates and the generating function is F=Σ q_kQ_k, In this case, which of the following are correct transformations
(a) p_k=Q_k, P_k=-q_k
(b) p_k=Q_k, P_k=q_k
(c) q_k=Q_k, P_k=-q_k
(d) p_k=2Q_k, P_k=-q_k
Answer: (a)

56. Electric energy in eV that can theoretically be obtained by annihilation of 1 gm of matter is
(a) 10.1 × 10³⁰
(b) 5.6 × 10³²
(c) 14.6 × 10²⁶
(d) 11.9 × 10⁴⁰
Answer: (b)

57. If (q, p) are set of canonical variables and δ_j,k is Kronecker delta then in terms of Poisson's bracket
(a) [q_j, p_k]_q,p = 2 δ_j,k
(b) [q_j, p_k]_q,p = (δ_j,k)²
(c) [q_j, p_k]_q,p = δ_j,k
(d) [q_j, p_k]_q,p = 3δ_j,k
Answer: (c)

58. The generalized co-ordinates each of them executing oscillations of one single frequency are called
(a) Abnormal coordinates
(b) General coordinates
(c) Stationary coordinates
(d) Normal coordinates
Answer: (d)

59. Moment of inertia tensor is
(a) Fourth rank tensor
(b) Third rank tensor
(c) Ninth rank tensor
(d) Second rank tensor
Answer: (d)

60. A gas molecule moving with velocity 300 m/s collides with another gas molecule of same mass which is initially at rest. After collision, first gas molecule moves along a direction making an angle 30° to its initial direction. Find the velocity of each gas molecule after collision. Assume collision to be elastic and v1 and v2 are velocities of first and second gas molecules after collision
(a) v1 ~ 260 m/s, v2 ~ 150 m/s
(b) v1 ~ 260 m/s, v2 ~ 190 m/s
(c) v1 ~ 160 m/s, v2 ~ 150 m/s
(d) v1 ~ 300 m/s, v2 ~ 150 m/s
Answer: (a)

61. Number of coordinates required for specification of single particle in phase space are
(a) 6
(b) 3
(c) 4
(d) 9
Answer: (a)

62. If the masses of hydrogen and chlorine atoms are 1 and 35.5 a.m.u., the reduced mass of HCl molecule in gms is
(a) 1.6 × 10^-24
(b) 4.3 × 10^-25
(c) 49.2 × 10^-30
(d) 1.5 × 10^-26
Answer: (a)

63. A particle of mass m is falling vertically under the influence of gravity when frictional forces obtainable from dissipative function kv²/2 are present. Maximum possible velocity for fall from rest is
(a) mg/k
(b) mg/k²
(c) m²g/k
(d) 3 mg/k
Answer: (a)

64. A vector A is solenoidal if it is
(a) Divergence is zero
(b) Gradient is zero
(c) Divergence is non-zero
(d) Curl is non-zero
Answer: (a)

65. An integrating amplifier can be fabricated using an op-amp by placing the following component in the feedback path
(a) Capacitor
(b) Resistor
(c) series combination of resistor and inductor
(d) inductor only
Answer: (a)

66. The wave function of a quantum mechanical system like an atom must be
(a) single valued and continuous everywhere
(b) single valued, finite but can be discontinuous for degenerate states
(c) must be finite but can be multivalued for nondegenerate states
(d) single valued, finite and continuous everywhere
Answer: (d)

67. Electrons of kinetic energy 10 eV are incident on the left hand side of one-dimensional potential energy barrier of height 12 eV and a variable barrier width, then
(a) Probability of tunneling of electrons from left to right is directly proportional to the energy difference of 2 eV
(b) Probability of tunneling of electrons from left to right is directly proportional to the width of potential energy barrier
(c) Probability of tunneling of electrons from left to right is inversely proportional to the energy difference of 2 eV
(d) Probability of tunneling of electrons from left to right is exponential decreasing function of barrier width
Answer: (d)

68. The role of helium atoms in He-Ne laser is to
(a) help in maintaining resonance in the cavity
(b) help in excitation and population inversion of neon atoms
(c) emits red light
(d) polarizes the laser light.
Answer: (b)

69. An unknown material has electrical resistance, which decreases with increase in temperature then
(a) it is definitely a metal
(b) possibly a semiconductor but not an insulator
(c) must be a superconductor if its resistance vanishes at absolute zero
(d) can be either a semiconductor or an insulator
Answer: (d)

70. An atomic bomb consisting of ²³⁵U explodes and releases energy of 2 × 10¹⁴ J. It is known that each ²³⁵U which undergoes fission releases 3 neutrons and 200 MeV of energy. The total number of neutrons released is
(a) 4.7 × 10²⁴
(b) 6.8 × 10²⁵
(c) 7.9 × 10²⁶
(d) 1.9 × 10²⁵
Answer: (d)

71. During pair production of an electron-positron pair by gamma rays the minimum energy of radiations must be
(a) 1.022 MeV
(b) 0.522 MeV
(c) 4.02 MeV
(d) 3.02 MeV
Answer: (a)

72. A second order phase transition is characterized by
(a) discontinuous change in volume
(b) discontinuous change in specific heat capacity
(c) discontinuous change in density
(d) irreversible changes during heating and cooling
Answer: (b)

73. The cut-off wavelength, λ_c for TE₂₀ mode for a standard rectangular waveguide is
(a) 2/a
(b) 2a
(c) a
(d) 2a²
Answer: (c)

74. The electromagnetic energy radiated per second by an oscillating electric dipole is proportional to the frequency by
(a) ω
(b) ω²
(c) ω³
(d) ω⁴
Answer: (d)

75. Light waves are incident normally from air onto a polished glass slab of refractive index 1.5, then the amount of light that is reflected back into air is
(a) 20%
(b) 10%
(c) 4%
(d) 15%
Answer: (c)

76. Brewster's law for polarization of light by reflection can be used to determine
(a) refractive index of medium
(b) density of medium
(c) polarizability of a medium
(d) none of the above
Answer: (a)

77. What type of interaction is responsible for spin-orbit coupling
(a) Gravitational
(b) Magnetic
(c) Strong
(d) Electrostatic
Answer: (b)

78. Liquid He does not solidify even at absolute zero at ambient pressures:
(a) due to phase transition at 2.2 K
(b) due to large zero point energy
(c) because of quantum tunneling
(d) Pauli Exclusion principle
Answer: (b)

79. Hall effect studies are not performed in metals because
(a) Hall Coefficient is very large.
(b) Hall Coefficient is very small
(c) Hall coefficient cannot be defined in metals
(d) Hall Coefficient has negative values.
Answer: (b)

80. A potential difference of 12 V is applied across the ends of the intrinsic silicon bar of length 0.6 cm and cross-sectional area of 0.4 cm². Assuming that n_i = 1.5 × 10¹⁶ electrons/m³, μ_n = 0.14 m²/Volt-s and μ_p = 0.05 m²/Volt-s. Total current in the bar
(a) 0.0789 mA
(b) 0.0765 mA
(c) 0.0320 mA
(d) 0.0365 mA
Answer: (d)

81. A stationary electron is accelerated with an electric voltage of 1500 V and enters into a uniform magnetic field of 0.2 T perpendicular to its direction of motion. Determine its radius of the curved path in magnetic field
(a) 8.1 × 10^-3 m
(b) 3.25 × 10² m
(c) 6.52 × 10^-4 m
(d) 2.15 m
Answer: (c)

82. The length of the space ship moving fast, was measured by an observer on earth and he reported a value which is half of its proper length. Find the speed of the space ship with respect to observer on earth:
(a) (1/2)c
(b) (√3 / 2)c
(c) (1/3)c
(d) (√3 / √5)c
Answer: (b)

83. Amplifier circuits fabricated using MOSFETS have an advantage over those using BJT's because
(a) they are current controlled devices
(b) their amplification factors are greater
(c) they have greater input impedance
(d) they have smaller input impedance
Answer: (c)

84. Microwaves are electromagnetic waves with wavelength of
(a) few micron
(b) few centimeter
(c) few kilometer
(d) few meter
Answer: (b)

85. Wavelength of photons of energy 20 eV is
(a) 1016 Å
(b) 1516 Å
(c) 621 Å
(d) 471 Å
Answer: (c)

86. The magnetic susceptibility of a high T_c superconductor compound La_xBa_2-xCuO₄ below its transition temperature is
(a) -1
(b) Zero
(c) Infinite
(d) 1
Answer: (a)

87. The lattice constant of a cubic lattice is 4.12 Å. Then the spacing between (200) planes are
(a) 2.67 × 10^-10 m
(b) 2.99 × 10^-10 m
(c) 2.06 × 10^-10 m
(d) 4.12 × 10^-10 m
Answer: (c)

88. In case more than one linearly independent wave function belongs to the same energy E the level is said to be
(a) Degenerate
(b) non degenerate
(c) Orthogonal
(d) Orthonormal
Answer: (a)

89. The approximate kinetic energy of thermal neutrons is
(a) 0.0254 eV
(b) 0.0254 MeV
(c) 0.0254 GeV
(d) 0.0254 keV
Answer: (a)

90. The magnetic flux through each turn of a 100 turn coil varies with time, t as -2t milli Weber, where t is in seconds. The induced emf at t=2s is:
(a) 1Mv
(b) -1V
(c) 4mV
(d) 0.4V
Answer: (d)

91. A light emitting diode(LED) emits light when
(a) electrons are excited from valence to conduction band
(b) it is reverse biased
(c) electrons collide with the lattice atoms
(d) electrons from the conduction band combine with holes in the valence band.
Answer: (d)

92. The heavily damped oscillator will return to its equilibrium position
(a) immediately within no time
(b) in time equal to its time period
(c) in infinite time
(d) within half of its time period.
Answer: (c)

93. The Lande g factor for ²S_1/2 state of Li is
(a) 1
(b) 2
(c) 3/2
(d) 4/3
Answer: (b)

94. Which one of the following semiconductor devices is used as temperature sensor
(a) Thermistor
(b) Schottky Diode
(c) Zerner diode
(d) Thermocouple
Answer: (a)

95. The ideal op-amp has the following characteristics
(a) its input impedance is infinite and therefore input current is zero
(b) its open-loop voltage gain is zero
(c) its output impedance is infinite therefore output voltage is independent of the load
(d) Its CMRR value is generally less than one
Answer: (a)

96. When an 8 bit serial in / serial out register is used for 24 μs time delay the clock frequency must be
(a) 41.67 kHz
(b) 333 kHz
(c) 125 kHz
(d) 8 MHz
Answer: (b)

97. For the measurement of pressure the instruments used can be
(a) Mechanical
(b) Electro-mechanical
(c) Electronic
(d) All of these
Answer: (d)

98. The magnitude of spin magnetic dipole moment of an electron in terms of Bohr magneton is
(a) √3 μ_B
(b) √5 μ_B
(c) μ_B / 2
(d) None of these
Answer: (a)

99. Different methods used to achieve population inversion are
(a) Direct excitation
(b) Inelastic atom-atom collision
(c) Chemical reaction
(d) All of these
Answer: (d)

100. In stimulated emission, the emitted photons are
(a) Non-Coherent and monochromatic
(b) Coherent and monochromatic
(c) Both (a) and (b)
(d) None of these
Answer: (b)

101. When the applied external magnetic field is weak as compared to internal fields due to spin-orbit motion, a spectral line splits into number of components, this effect is called
(a) Paschen-Back effect
(b) Zeeman effect
(c) Stark effect
(d) None of these
Answer: (b)

102. If the Kα radiation of Mo (Z=42) has wavelength of 0.71 Å. The wavelength of corresponding radiation of Cu (Z=29) is
(a) 1.52 Å
(b) 1.04 nm
(c) 1.48 mm
(d) 1.02 cm
Answer: (a)

103. ²D levels of sodium would shift on applying weak magnetic field into
(a) 10 levels
(b) 8 levels
(c) 12 levels
(d) None of these
Answer: (a)

104. Of the following term symbols of the atomic state np² configurations, ¹S₀, ³P₀, ³P₁, ³P₂ which is the ground state
(a) ¹S₀
(b) ³P₀
(c) ³P₁
(d) ³P₂
Answer: (b)

105. The separation between the energy levels of a two-level atom is 2 eV. Suppose that 4 × 10²⁰ atoms are in the ground state and 7 × 10²⁰ atoms are pumped into the excited state just before lasing starts. How much energy will be released in a single laser pulse?
(a) 24 J
(b) 22 J
(c) 98 J
(d) 48 J
Answer: (d)

106. The infrared rotational absorption spectrum of a diatomic molecule shows equivalent lines with spacing 20 cm^-1. The position of the first stoke line in the rotational Raman spectrum of this molecule is
(a) 20 cm^-1
(b) 40 cm^-1
(c) 60 cm^-1
(d) 120 cm^-1
Answer: (c)

107. The separation between the first stokes and corresponding anti-stokes line of the rotational Raman spectrum in term of the rotational constant, B is
(a) 2B
(b) 4B
(c) 6B
(d) 12B
Answer: (d)

108. The order of magnitude of the energy gap of a typical superconductor is
(a) 1 MeV
(b) 1 KeV
(c) 1 eV
(d) 1 meV
Answer: (d)

109. For a three-dimensional crystal having N primitive unit cells with a basis of p atoms, the number of optical branches is,
(a) 3
(b) 3p
(c) 3p-3
(d) 3N
Answer: (c)

110. In AC Josephson effect, on applying the biasing voltage 'V', the frequency of the current will be
(a) ν = 2eV/h
(b) ν = eV/h
(c) ν = 2V/h
(d) None of these
Answer: (a)

111. Mixed state is found in
(a) Type-I superconductors
(b) Type-II superconductors
(c) Both (a) and (b)
(d) None of these
Answer: (b)

112. Einstein theory of specific heat is a
(a) Classical theory
(b) Semi-classical theory
(c) Quantum theory
(d) Electrodynamics theory
Answer: (c)

113. Diamond lattice can be considered as a combination of two fcc lattice displaced along the body diagonal by one quarter of its length. There are eight atoms per unit cell. The packing fraction of the diamond structure is
(a) 0.48
(b) 0.74
(c) 0.34
(d) 0.68
Answer: (c)

114. A dc voltage V is applied across a Josephson junction between two superconductors with a phase difference Φ₀. If I₀ and k are constants that depend on the properties of the junction, the current flowing through it has the form
(a) I₀ sin(2eVt/h + Φ₀)
(b) kV sin(2eVt/h + Φ₀)
(c) kV sin Φ₀
(d) I₀ sin Φ₀
Answer: (a)

115. The total internal energy of the domain structure in a ferromagnetic material includes
(a) Magnetostatic energy
(b) Anisotropy energy
(c) Domain wall energy
(d) All of above
Answer: (d)

116. The electrical conductivity of copper is approximately 95% of the electrical conductivity of silver, while the electron density in silver is approximately 70% of the electron density in copper. In Drude's model, the approximation ratio of mean collision time of copper (τ_Cu) to silver (τ_Ag) is
(a) 0.66
(b) 1.50
(c) 0.33
(d) None of these
Answer: (d)

117. Which is the correct relation for the Weidemann-Franz law, where K = thermal conductivity and σ is electrical conductivity
(a) σ/K = constant
(b) K/σ = constant
(c) Kσ = constant
(d) None of these
Answer: (a)

118. Einstein's theory assume that atom in solid vibrate with frequency which is
(a) same natural frequency
(b) different natural frequency
(c) independent frequency
(d) none of these
Answer: (a)

119. The half-life of Radium is 1600 years. The time taken for 15/16 of a sample of radium to decay is
(a) 1600 yr
(b) 3200 yr
(c) 800 yr
(d) 6400 yr
Answer: (d)

120. The multi polarity possible for a radioactive transition is limited by selection rules, based on
(a) Spin
(b) Angular momentum
(c) Pauli principle
(d) Parity
Answer: (b)

121. Find the maximum kinetic energy of the electron emitted in the beta decay of the free neutron. The neutron-proton mass difference is 1.30 MeV.
(a) 0.49 MeV
(b) 0.59 MeV
(c) 0.79 MeV
(d) 0.99 MeV
Answer: (c)

122. For lighter elements to be stable, the neutron to proton ratio must be
(a) 2:1
(b) 3:1
(c) 3:2
(d) 1:1
Answer: (d)

123. Which of the following is not a mode of radioactive decay
(a) Alpha decay
(b) Fusion
(c) Electron capture
(d) Positron emission
Answer: (b)

124. Nuclear force is
(a) short range and charge dependent
(b) long range and charge dependent
(c) short range and charge independent
(d) long range and charge independent
Answer: (c)

125. An X ray photon collides with a free electron, and the photon is scattered. During this collision there is conservation of
(a) momentum but not energy
(b) neither momentum nor energy
(c) energy but not momentum
(d) both momentum and energy
Answer: (d)

126. The electric charge of the quark is
(a) Zero
(b) greater than electron charge
(c) less than electron charge
(d) equal to electron charge
Answer: (c)

127. Within an isospin multiplet particles differ in
(a) Parity
(b) Charme
(c) charge
(d) baryon number
Answer: (c)

128. Shell model of the nucleus is based upon
(a) Bohr correspondence principle
(b) Ellipsoidal symmetric potential
(c) Spherically symmetric potential
(d) None of these
Answer: (c)

129. Path followed by a particle in sliding from one point to another in the absence of friction in the shortest time is a
(a) Cycloid
(b) Circle
(c) Straight line
(d) Parabola
Answer: (a)

130. Variational principle gives the necessary conditions about the quantity appearing as an integral has
(a) Stationary value
(b) Square of its value
(c) Cube of its value
(d) Exponent of its value
Answer: (a)

131. If m_o, v and V are rest mass, velocity and potential energy respectively of the particle and c is velocity of light, forces are conservative then Lagrangian in relativistic mechanics can be defined by following equation.
(a) m_oc²[1-(v²/c²)]^1/2 - V
(b) -m_oc²[1-(v²/c²)]^1/2 - V^1/2
(c) -m_oc²[1-(v²/c²)]^1/2 - V
(d) -m_o²c²[1-(v²/c²)]^1/2 - V
Answer: (c)

132. When the positively charged particles approach the heavy nucleus, the trajectory of the particles is
(a) Hyperbola
(b) Elliptical
(c) Circle
(d) Parabola
Answer: (a)

133. Poisson bracket of two constants of the motion is itself
(a) Energy
(b) A constant of motion
(c) Velocity
(d) Unity
Answer: (b)

134. If p and P are old and new momenta respectively then F(p,P,t) represents which generating function
(a) F1
(b) F3
(c) F2
(d) F4
Answer: (d)

135. If the equation of trajectory of the particle in plane polar coordinates is given by r=2a cos θ, where 2a is the diameter of the circle. In this case, force is proportional to distance from origin as;
(a) 1/r⁵
(b) 1/r⁷
(c) 1/r⁹
(d) 1/r¹¹
Answer: (a)

136. Shortest distance between two points in a plane is a
(a) Cycloid
(b) Parabola
(c) Circle
(d) Straight line
Answer: (d)

137. Residue of f(z) at a simple pole a is
(a) lim_z→a z f(z)
(b) lim_z→a (z-a) f(z)
(c) lim_z→a f(z)/(z-a)
(d) lim_z→a (z-a)/f(z)
Answer: (b)

138. The average value of the function, f(x)=4x³ in the interval 1 to 3 is
(a) 15
(b) 20
(c) 40
(d) 80
Answer: (c)

139. The cathode of a Zener diode used in a voltage regulator circuit is
(a) More positive than anode
(b) More negative than the anode
(c) At +0.7V
(d) Grounded
Answer: (a)

140. For a pair of electrons the wave function, Ψ(r₁,r₂) will be
(a) symmetric under the exchange of positions of two electrons
(b) antisymmetric under the exchange of positions of two electrons
(c) such that it cannot be normalized
(d) always a Gaussian function
Answer: (b)

141. For a two dimensional quantum mechanical harmonic oscillator the minimum total energy is
(a) Zero
(b) 3hω
(c) hω
(d) 2hω
Answer: (c)

142. Consider a one dimensional, infinite square well existing from 0 ≤ x ≤ a, if nine electrons are inside the well, then the ground state energy of the system is:
(a) 85h²/8ma²
(b) 72h²/8ma²
(c) 102h²/8ma²
(d) 96h²/8ma²
Answer: (a)

143. If ψ(x,y,z) = ψ(-x,-y,-z) then it represents
(a) Even parity
(b) Odd parity
(c) Both (a) and (b)
(d) None of these
Answer: (a)

144. Scattering cross section for Coulomb potential using Born approximation is directly proportional to
(a) sin⁴θ
(b) cos⁴θ
(c) Cosec⁴θ
(d) Cosec⁴(θ/2)
Answer: (d)

145. A particle of mass m, moves in a potential V(x) = (1/2)mω²x² + (1/2)mμv² where x is the position coordinate, v is the speed, ω and μ are constants. The canonical conjugate momentum of the particle is
(a) p = m(1+μ)v
(b) p = mv
(c) p = mμv
(d) p = m(1-μ)v
Answer: (d)

146. Which of the following statement is true
(a) AND and NOT gates are necessary and sufficient for the realization of any logical function
(b) OR and NOT gates are necessary and sufficient for the realization of any logical function
(c) NOR gates are sufficient to realize any logical function
(d) NAND gates are not sufficient to realize any logical function
Answer: (c)

147. For an atom in ³P₂ state, value of magnetic moment in Bohr magneton would be
(a) 3√(3/2) μ_B
(b) √(3/2) μ_B
(c) 3√(1/2) μ_B
(d) √3 μ_B
Answer: (a)

148. The Zeeman pattern of line contains nine equidistant components. If the upper state is known to be ³P₂ then the lower state would be
(a) ³S₂
(b) ³S₁
(c) ¹P₁
(d) None of these
Answer: (b)

149. Zeeman effect could not be proved by
(a) Quantum Mechanics
(b) Bohr Model
(c) Hamiltonian Operator
(d) L-S Coupling
Answer: (b)

150. The binding energy of the hydrogen atom (electron bound to proton) is -13.6 eV. The magnitude of binding energy of positronium (electron bound to positron) is
(a) 13.6/2 eV
(b) 13.6/1810 eV
(c) 13.6 × 1810 eV
(d) none of these
Answer: (a)

PUNJAB PHYSICS LECTURER PREVIOUS YEAR QUESTION PAPER 2021 SOLVED WITH ANSWER KEY

1.

Identify the CORRECT statement for the following vectors a = 3i + 2j and b = i + 2j.

(a) The vectors a and b are linearly independent.

(b) The vectors a and b are linearly dependent.

(c) The vectors a and b are orthogonal.

(d) The vectors a and b are normalized.

2.

The number of independent components of the symmetric tensor Aij with indices i, j = 1, 2, 3 is

(a) 1

(b) 3

(c) 6

(d) 9

3.

f(x) is a symmetric periodic function of x i.e. f(x) = f(-x). Then, in general, the Fourier series of the function f(x) will be of the form

(a) f(x) = Σ(an cos(nkx) + bn sin(nkx))

(b) f(x) = a0 + Σ(an cos(nkx))

(c) f(x) = Σ(bn sin(nkx))

(d) f(x) = a0 + Σ(bn sin(nkx))

4.

Two matrices A and B are said to be similar if B = P⁻¹AP for some invertible matrix P. Which one of the following statements is NOT TRUE ?

(a) Det A = Det B

(b) Trace of A = Trace of B

(c) A and B have same eigen vectors.

(d) A and B have same eigen values.

5.

The value of the integral ∮ (e^z sin z / z²) dz, where the contour C is the unit circle: |z - 2| = 1, is

(a) 2πi

(b) 4πi

(c) πi

(d) 0

6.

If f(x) = 0 for x < 3 and f(x) = x − 3 for x ≥ 3, then the Laplace transform of f(x) is

(a) s⁻² e^(3s)

(b) s² e^(−3s)

(c) s⁻²

(d) s⁻² e^(−3s)

7.

If F = xi + yj + zk, then its divergence is

(a) i + j + k

(b) 3

(c) x + y + z

(d) None of these

8.

If ∫ from −1 to +1 Pn(x) dx = 2, then n is

(a) 1

(b) 0

(c) −1

(d) None of these

9.

The Newton Raphson method is used to find the root of the equation x² − 2 = 0. If the iterations are started from −1, the iterations will

(a) Converge to −1

(b) Converge to √2

(c) Converge to −√2

(d) Not converge

10.

The minimum number of cards to be dealt from an arbitrarily shuffled deck of 52 cards to guarantee that three cards are from the same suit is

(a) 3

(b) 8

(c) 9

(d) 12

21.

A cylinder of mass M and radius R is rolling down without slipping on an inclined plane of angle of inclination θ. The number of generalized co-ordinates required to describe the motion of this system is

(a) 1

(b) 2

(c) 4

(d) 6

22.

Hamilton's canonical equations of motion are

(a) q̇i = ∂H/∂pi and ṗi = ∂H/∂qi

(b) q̇i = ∂H/∂pi and ṗi = −∂H/∂qi

(c) qi = ∂H/∂pi and pi = ∂H/∂qi

(d) qi = ∂H/∂pi and pi = −∂H/∂qi

23.

If a co-ordinate is cyclic, Hamiltonian would reduce the number of variables in new formulation by

(a) One

(b) Two

(c) Three

(d) Four

24.

According to the special theory of relativity, the speed v of a free particle of mass m and total energy E is

(a) v = c √(1 − mc²/E)

(b) v = √[2E/m (1 + mc²/E)]

(c) v = c √(1 − (mc²/E)²)

(d) v = c (1 + mc²/E)

25.

Let x and p denote, respectively, the co-ordinate and momentum operators satisfying the canonical commutation relation [x, p] = i in natural units (ħ = 1). Then the commutator [x, p e^(−p)] is

(a) i(1 − p)e^(−p)

(b) i(1 − p²)e^(−p)

(c) i(1 − e^(−p))

(d) i p e^(−p)

26.

The Poisson bracket of two integrals of motion is

(a) zero

(b) unity

(c) infinite

(d) integral of motion

27.

The Hamiltonian is defined as

(a) H = Σ pk q̇k + L

(b) H = Σ pk q̇k − L

(c) H = Σ qk ṗk + L

(d) H = Σ qk ṗk − L

28.

Which one of the following transformation is canonical ?

(a) P = q, Q = p

(b) P = Q, Q = −P

(c) Q = −p, P = −q

(d) Q = p, P = −q

29.

The Lagrangian of a free particle in spherical polar co-ordinates is given by L = (1/2)m[ ṙ² + r²θ̇² + r²φ̇² sin²θ ]. The quantity that conserved is

(a) ∂L/∂ṙ

(b) ∂L/∂θ̇

(c) ∂L/∂φ̇

(d) ∂L/∂φ̇ + ṙθ̇

30.

For a particle moving in a central field

(a) the kinetic energy is a constant of motion.

(b) the potential energy is velocity dependent.

(c) the motion is confined in a plane.

(d) the total energy is not conserved.

31.

A plane electromagnetic wave travelling in free space is incident normally on a glass plate of refractive index 1.5. If there is no absorption by the glass, its reflectivity is

(a) 4%

(b) 16%

(c) 20%

(d) 50%

32.

The electric and magnetic fields E(z,t) and B(z,t), respectively corresponding to the scalar potential φ(z,t) = 0 and vector potential A(z,t) = î tz are

(a) E = î z and B = −ĵ t

(b) E = î z and B = ĵ t

(c) E = −î z and B = −ĵ t

(d) E = −î z and B = ĵ t

33.

The space-time dependence of the electric field of a linearly polarized light in free space is given by xE₀ cos(ωt − kz). The time averaged energy density associated with the electric field is

(a) (1/4) ε₀E₀²

(b) (1/2) ε₀E₀²

(c) ε₀E₀²

(d) 2ε₀E₀²

34.

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

(a) The reflected light is plane polarized in the plane of incidence and the transmitted light is circularly polarized.

(b) The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is plane polarized in the plane of incidence.

(c) The reflected light is plane polarized perpendicular to the plane of incidence and the transmitted light is elliptically polarized.

(d) There will be no reflected light and the transmitted light is circularly polarized.

35.

An insulating sphere of radius a carries a charge density ρ(r) = ρ₀(a² − r²) cosθ; r < a. The leading order term for the electric field at a distance d, far away from the charge distribution, is proportional to

(a) d⁻¹

(b) d⁻²

(c) d⁻³

(d) d⁻⁴

36.

A magnetic dipole moment m is placed in a non-uniform magnetic field B. If the position vector of the dipole is r, the torque acting on the dipole about the origin is

(a) r × (m × B)

(b) r × ∇(m · B)

(c) m × B

(d) m × B + r × ∇(m · B)

37.

In a non-conducting medium ε = ε₀, μ = μ₀ and σ = 0, the electric field E = 20 sin(10⁸t − kz) ĵ. The magnetic field H is given by

(a) 20k cos(10⁸t − kz) î

(b) (20k / 10⁸μ₀) sin(10⁸t − kz) ĵ

(c) (20k / 10⁸μ₀) sin(10⁸t − kz) î

(d) −20k cos(10⁸t − kz) ĵ

38.

An oscillating current I(t) = I₀ e^(−iωt) flows in the direction of y-axis through a thin metal sheet of area 1.0 cm² kept in xy-plane. The rate of total energy radiated per unit area from the surfaces of the metal sheet at a distance of 100 m is

(a) (I₀ω / 12π ε₀ c³)

(b) (I₀²ω² / 12π ε₀ c³)

(c) (I₀²ω / 12π ε₀ c³)

(d) (I₀ω² / 24π ε₀ c³)

39.

A point charge q of mass m is kept at a distance d below a grounded infinite conducting sheet which lies in xy-plane. For what value of d will the charge remain stationary ?

(a) q / (4√(mgπ ε₀))

(b) q / √(mgπ ε₀)

(c) There is no finite value of d.

(d) √(mgπ ε₀) / q

40.

When a charged particle emits electromagnetic radiation, the electric field E and the Poynting vector S vary as 1/rⁿ and 1/rᵐ respectively. Which of the following choices for n and m are correct ?

(a) n = 1 and m = 1

(b) n = 2 and m = 2

(c) n = 1 and m = 2

(d) n = 2 and m = 4

41.

In a wave guide, the propagation of electromagnetic waves is characterized by cut-off frequency. For TE₁₀ mode in a rectangular waveguide of dimensions a × b (a > b), the cut-off frequency is

(a) c / 2a

(b) c / 2b

(c) c / a

(d) c / b

42.

The magnetic vector potential A for a uniform magnetic field B is given by

(a) A = B × r

(b) A = (1/2)(B × r)

(c) A = (r × B)

(d) A = (1/2)(r × B)

43.

The energy stored in a capacitor of capacitance C charged to potential V is

(a) CV²

(b) (1/2)CV²

(c) (1/2)C²V

(d) C²V²

44.

The displacement current arises due to

(a) Time varying electric field

(b) Static electric field

(c) Magnetic field

(d) Electric potential

45.

The force between two current carrying conductors is due to

(a) Electric field

(b) Magnetic field

(c) Gravitational force

(d) None

46.

Gauss law in differential form is

(a) ∇·E = ρ/ε₀

(b) ∇×E = 0

(c) ∇·B = 0

(d) ∇×B = μ₀J

47.

The Poynting vector represents

(a) Energy density

(b) Energy flow per unit area

(c) Power

(d) Electric field

48.

The continuity equation is

(a) ∇·J + ∂ρ/∂t = 0

(b) ∇×J = 0

(c) ∇·E = 0

(d) ∇×B = 0

49.

In electrostatics, the curl of electric field is

(a) zero

(b) unity

(c) infinite

(d) variable

50.

The capacitance of a parallel plate capacitor increases with

(a) Increase in distance

(b) Decrease in area

(c) Increase in dielectric constant

(d) None

51.

The electric potential due to a point charge varies as

(a) 1/r

(b) 1/r²

(c) r

(d) r²

52.

The magnetic field inside a solenoid is

(a) uniform

(b) zero

(c) infinite

(d) variable

53.

The Lorentz force is given by

(a) qE

(b) qvB

(c) q(E + v × B)

(d) mv²/r

54.

The energy density of electric field is

(a) (1/2)ε₀E²

(b) ε₀E²

(c) (1/2)E²

(d) none

55.

The magnetic flux is defined as

(a) ∫B·dA

(b) ∫E·dA

(c) ∫J·dA

(d) ∫A·dB

56.

The impedance of free space is

(a) 377 Ω

(b) 100 Ω

(c) 50 Ω

(d) 1 Ω

57.

The wavelength of EM wave is given by

(a) λ = c/f

(b) λ = f/c

(c) λ = cf

(d) λ = c²/f

58.

The refractive index is defined as

(a) c/v

(b) v/c

(c) c²/v

(d) v²/c

59.

The electric field inside a conductor is

(a) zero

(b) maximum

(c) minimum

(d) variable

60.

The magnetic field lines are

(a) closed loops

(b) open lines

(c) straight

(d) none

61.

The probability of an event is always

(a) less than 0

(b) between 0 and 1

(c) greater than 1

(d) equal to 2

62.

The standard deviation is a measure of

(a) central tendency

(b) dispersion

(c) skewness

(d) kurtosis

63.

The mean of a normal distribution is

(a) median

(b) mode

(c) both median and mode

(d) none

64.

The variance is the square of

(a) mean

(b) median

(c) standard deviation

(d) mode

65.

The binomial distribution is used for

(a) continuous variables

(b) discrete variables

(c) both

(d) none

66.

The Poisson distribution is a limiting case of

(a) binomial distribution

(b) normal distribution

(c) uniform distribution

(d) exponential distribution

67.

The correlation coefficient measures

(a) strength of relation

(b) direction only

(c) magnitude only

(d) none

68.

The regression line represents

(a) exact relation

(b) average relation

(c) no relation

(d) random relation

69.

The probability density function integrates to

(a) 0

(b) 1

(c) infinity

(d) −1

70.

The expected value of a random variable is

(a) mean

(b) variance

(c) standard deviation

(d) mode

71.

The Maxwell distribution describes

(a) velocities of gas molecules

(b) energies of photons

(c) charge distribution

(d) pressure

72.

The Boltzmann constant relates

(a) energy and temperature

(b) pressure and volume

(c) force and mass

(d) charge and voltage

73.

The entropy of an isolated system

(a) increases

(b) decreases

(c) remains constant

(d) zero

74.

The first law of thermodynamics is based on

(a) energy conservation

(b) entropy

(c) pressure

(d) temperature

75.

The efficiency of Carnot engine depends on

(a) temperatures

(b) pressure

(c) volume

(d) heat

76.

The second law of thermodynamics deals with

(a) energy

(b) entropy

(c) work

(d) heat

77.

The internal energy of an ideal gas depends on

(a) temperature

(b) pressure

(c) volume

(d) density

78.

The work done in isothermal process is

(a) zero

(b) maximum

(c) minimum

(d) constant

79.

The adiabatic process has

(a) no heat transfer

(b) constant temperature

(c) constant pressure

(d) constant volume

80.

The specific heat at constant pressure is always

(a) greater than Cv

(b) less than Cv

(c) equal to Cv

(d) zero

81. A common emitter transistor amplifier circuit is operated under a fixed bias. In this circuit, the operating point

(a) remains fixed with an increase in temperature

(b) moves towards cut-off region with an increase in temperature

(c) moves towards saturation region with a decrease in temperature

(d) moves towards saturation region with an increase in temperature

82. The resolution of a D/A converter is approximately 0.4% of its full scale range. It is –

(a) An 8-bit converter

(b) A 10-bit converter

(c) A 12-bit converter

(d) A 16-bit converter

83. The speed of conversion is maximum in

(a) Successive-approximation A/D converter

(b) Parallel-comparator A/D converter

(c) Counter ramp A/D converter

(d) Dual-slope A/D converter

84. Which of the following statements is true ?

(a) AND and NOT gates are necessary and sufficient for the realization of any logical function.

(b) OR and NOT gates are necessary and sufficient for the realization of any logical function.

(c) NOR gates are sufficient to realize any logical function.

(d) NAND gates are not sufficient to realize any logical function.

85. The terminal count of a modulus-13 binary counter is –

(a) 0000

(b) 1111

(c) 1101

(d) 1100

86. When an 8 bit serial in/serial out register is used for a 24 μs time delay, the clock frequency must be –

(a) 41.67 kHz

(b) 333 kHz

(c) 125 kHz

(d) 8 MHz

87. In Miller integrator a resistance is used in parallel with the capacitance in the feedback path

(a) to speed up the integration

(b) to avoid the open loop for dc

(c) to give high input impedance

(d) no differentiation occurs

88. The Schmitt trigger based circuits are better because they

(a) work faster

(b) protect from false signals such as noises

(c) have longer life

(d) require less number of components.

89. The depletion region in a p-n junction is created by –

(a) Ionization

(b) Diffusion

(c) Recombination

(d) All of these

90. The dynamic resistance of an ideal p-n junction with a forwards current of 10 mA at room temperature –

(a) 2.5 ohm

(b) 0.4 ohm

(c) 250 ohm

(d) 4.0 ohm

91. The input to a lock-in amplifier has the form

Vi(t) = Vi sin(ωt + θi)

where Vi, ω, θi are the amplitude, frequency and phase of the input signal respectively. This signal is multiplied by a reference signal of the same frequency ω, amplitude Vr and phase θr. If the multiplied signal is fed to a low pass filter of cut-off frequency ω, the final output signal is

(a) ½ ViVr cos(θi − θr)

(b) ViVr [cos(θi − θr) − cos(½ωt + θi + θr)]

(c) ViVr sin(θi − θr)

(d) ViVr [cos(θi − θr) + cos(½ωt + θi + θr)]

92. Band-pass and band-reject filters can be implemented by combining a low pass and a high pass filter in series and in parallel, respectively. If the cut-off frequencies of the low pass and high pass filters are ω₀LP and ω₀HP, respectively, the condition required to implement the band-pass and band-reject filters are, respectively –

(a) ω₀HP < ω₀LP and ω₀HP < ω₀LP

(b) ω₀HP < ω₀LP and ω₀HP > ω₀LP

(c) ω₀HP > ω₀LP and ω₀HP < ω₀LP

(d) ω₀HP > ω₀LP and ω₀HP > ω₀LP

93. Dead time of proportional counter is –

(a) about 1.5 μs

(b) about 270 μs

(c) about 0.25 μs

(d) about 100 μs

94. In a thermocouple pressure gauge, the temperature of heater element is a function of pressure for pressure range

(a) above atmosphere

(b) below 1 mm of Hg

(c) below 10⁻³ mm of Hg

(d) below 1 μm of Hg

95. Radiation pyrometers are used in the temperature range of –

(a) 0 - 500 °C

(b) 500 - 1000 °C

(c) -250 - 500 °C

(d) 1200 - 2500 °C

96. A set of readings has a wide range and therefore it has –

(a) low precision

(b) high precision

(c) low accuracy

(d) high accuracy

97. The voltage of a circuit is measured by a voltmeter having high input impedance comparable with the output impedance of the circuit thereby causing error in voltage measurement. This error may be called –

(a) gross error

(b) random error

(c) error caused by misuse of instrument

(d) error caused by loading effect.

98. The degree to which information on a map or in a digital database matches true or accepted values is referred to as :

(a) precision and accuracy

(b) precision

(c) accuracy

(d) None of the above

99. Systematic error occurred due to the poor calibration of the instrument that can be corrected by

(a) taking several readings

(b) replacing instruments

(c) taking mean of values

(d) taking median of values

100. One factor in the accuracy of reconstructed PCM signal is the

(a) signal bandwidth

(b) carrier frequency

(c) number of bits used for quantization

(d) baud rate

101. Strain gauge can be used to monitor change in

(a) Pressure

(b) Torque

(c) Displacement

(d) All of these

102. Which bridge is utilized in signal conditioning circuits for balancing purposes ?

(a) Maxwell Bridge

(b) Wheatstone Bridge

(c) Wein Bridge

(d) Kelvin Bridge

103. If the gain of closed loop inverting amplifier is 3.9, with input resistor value of 1.6 kΩ, what value of feedback resistor is needed ?

(a) 2.4 kΩ

(b) 410 Ω

(c) 6240 Ω

(d) 0.62 kΩ

104. Op-amps used as high- and low-pass filter circuits employ which configuration ?

(a) Comparator

(b) Non-inverting

(c) Open-loop

(d) Inverting

105. The value of coefficient of correlation lies between

(a) 0 to 1

(b) 1 to -10

(c) 0 to -1

(d) -1 to +1

106. The first Stokes line of a rotational Raman spectrum is observed at 12.96 cm⁻¹. Considering rigid rotor approximation, the rotational constant is given by –

(a) 6.48 cm⁻¹

(b) 3.24 cm⁻¹

(c) 2.16 cm⁻¹

(d) 1.62 cm⁻¹

107. For a multi-electron, l, L and S specify the one-electron orbital angular momentum, total orbital angular momentum and total spin angular momentum, respectively. The selection rules for electric dipole transition between the two electronic energy levels, specified by l, L and S are

(a) ΔL = 0, ±1; ΔS = 0; Δl = 0, ±1

(b) ΔL = 0, ±1; ΔS = 0; Δl = ±1

(c) ΔL = 0, ±1; ΔS = ±1; Δl = 0, ±1

(d) ΔL = 0, ±1; ΔS = ±1; Δl = ±1

108. The coherence length of laser light is –

(a) Directly proportional to the length of the active medium

(b) Directly proportional to the width of the spectral line

(c) Inversely proportional to the width of the spectral line

(d) Inversely proportional to the length of the active laser medium.

109. The Lβ line of X-rays emitted from an atom with principal quantum numbers n = 1, 2, 3 .. arises from the transition

(a) n = 4 → n = 2

(b) n = 3 → n = 2

(c) n = 5 → n = 2

(d) n = 3 → n = 1

110. The last two terms of the electronic configuration of manganese (Mn) atom is 3d⁵ 4s². The term factor of Mn⁴⁺ ion is –

(a) ⁴D₁/₂

(b) ⁴F₃/₂

(c) ³F₉/₂

(d) ³D₇/₂

111. An atomic transition ¹P → ¹S in a magnetic field 1 Tesla shows Zeeman splitting. Given that the Bohr magneton μB = 9.27 × 10⁻²⁴ J/T, and the wavelength corresponding to the transition is 250 nm, the separation in the Zeeman spectral lines is approximately –

(a) 0.01 nm

(b) 0.1 nm

(c) 1.0 nm

(d) 10 nm

112. Consider the hydrogen-deuterium molecule HD. If the mean distance between the two atoms is 0.08 nm and the mass of the hydrogen atom is 938 MeV/c², then the energy difference ΔE between the two lowest rotational states is approximately –

(a) 10⁻¹ eV

(b) 10⁻² eV

(c) 2 × 10⁻² eV

(d) 10⁻³ eV

113. For an electron in hydrogen atom the states are characterized by the usual quantum numbers n, l, ml. The electric dipole transition between any two states requires that –

(a) Δl = 0; Δml = 0, ±1

(b) Δl = ±1; Δml = ±1, ±2

(c) Δl = ±1; Δml = 0, ±1

(d) Δl = ±1; Δml = 0, ±2

114. In a Stern-Gerlach experiment the atomic beam whose angular momentum state is to be determined, must travel through –

(a) homogeneous radio frequency magnetic field

(b) homogeneous static magnetic field

(c) inhomogeneous static magnetic field

(d) inhomogeneous radio frequency magnetic field.

115. The doublet observed in alkali spectra are due to –

(a) screening of the K-electrons

(b) spin-orbit interaction of the electrons

(c) pressure of isotopes

(d) none of the above

116. The hyperfine splitting of the spectral lines of an atom is due to

(a) the coupling between the spins of two or more electrons

(b) the coupling between the spins and the angular momentum of the electrons

(c) the coupling between the electron and the nuclear spin

(d) the effect of external electromagnetic fields

117. If 50 kV is the applied potential in an X-ray tube, then the minimum wavelength of X-rays produced is –

(a) 0.2 nm

(b) 2 nm

(c) 0.2 Å

(d) 2 Å

118. Consider the pure rotational spectrum of a diatomic rigid rotor. The separation between two consecutive lines (Δν̄) in the spectrum –

(a) is directly proportional to the moment of inertia of the rotor.

(b) is inversely proportional to the moment of inertia of the rotor.

(c) depends on the angular momentum.

(d) is directly proportional to the square of the interatomic separation.

119. For Raman spectrum, the selection rules are

(a) ΔJ = 0, ±1; Δm₁ = 0, ±1

(b) ΔJ = ±1, ±2; Δm₁ = ±1, ±2

(c) ΔJ = 0, ±2; Δm₁ = 0, ±1

(d) ΔJ = ±2; Δm₁ = ±1

120. L-S coupling often occurs in –

(a) all atoms

(b) lighter atoms

(c) heavier atoms

(d) occurs only in nuclei

121. Which one of the following CANNOT be explained by considering a harmonic approximation for the lattice vibration in solids?

(a) Debye's T³ law

(b) Dulong Petit's law

(c) Optical branches in lattices

(d) Thermal expansion

122. 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)

(a) Presence of energy gap at temperatures below the critical temperatures

(b) Different critical temperatures for isotopes

(c) Quantization of magnetic flux in superconducting ring in the unit of (h/e)

(d) Presence of Meissner effect

123. The temperature (T) dependence of magnetic susceptibility (χ) of a ferromagnetic substance with a Curie temperature Tc is given by

(a) C/(T − Tc), for T < Tc

(b) C/(T − Tc), for T > Tc

(c) C/(T + Tc), for T < Tc

(d) C/(T + Tc), for T > Tc

124. For a three dimensional crystal having N primitive unit cells with a basis of p atoms, the number of optical branches is

(a) 3

(b) 3p

(c) 3p − 3

(d) 3N − 3p

125. Consider X-ray diffraction from a crystal with a face-centered cubic (fcc) lattice. The lattice plane for which there is NO diffraction peak is

(a) (212)

(b) (111)

(c) (200)

(d) (311)

126. The Hall co-efficient, 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

127. Which one of the following axes of rotational symmetry is NOT permissible in single crystals ?

(a) Two-fold axis

(b) three-fold axis

(c) four-fold axis

(d) five-fold axis

128. The Bloch theorem states that within a crystal, the wavefunction, ψ(r), of an electron has the form –

(a) ψ(r) = u(r)e^ik·r where u(r) is arbitrary

(b) ψ(r) = u(r)e^iG·r

(c) ψ(r) = u(r)e^iG·r where u(r)=u(r+Λ)

(d) ψ(r) = u(r)e^ik·r where u(r)=u(r+Λ)

129. A low density oxygen gas at low temperature, only the translational and rotational modes are excited. The specific heat per molecule is

(a) ½ kB

(b) kB

(c) 3/2 kB

(d) 5/2 kB

130. Electron dispersion relation:

εk = 2ε₀ [ sin²(ka/2) − (1/6) sin²(ka) ]

(a) ε₀/4

(b) ε₀

(c) 2ε₀/3

(d) 5ε₀/3

131. Electronic contribution to specific heat at low temperature is

(a) exponential function of T

(b) linear function of T

(c) zero

(d) none

132. Velocity at point of inflexion in E–k diagram is

(a) minimum

(b) maximum

(c) zero

(d) not known

133. In BCS theory Tc depends on isotope mass as

(a) Tc ∝ M⁻¹

(b) Tc ∝ M

(c) Tc ∝ M⁻¹/²

(d) Tc ∝ M¹/²

134. Maximum radius of interstitial sphere in BCC is

(a) r[(2/√3) − 1]

(b) r[(√3/2) − 1]

(c) r[√3 − 1]

(d) r[√2 − 1]

135. If dielectric constant = 5.6 and refractive index = 1.5, ratio of polarizability is

(a) 0.5

(b) 0.7

(c) 0.8

(d) 0.9

136. Deuteron data suggest nuclear forces have

(a) only spin & isospin dependence

(b) no spin & no tensor

(c) spin only

(d) spin with tensor component

137. Fundamental particles are

(a) proton, electron, neutron

(b) proton, electron, proton

(c) electron, photon, neutrino

(d) quark, electron, meson

138. β decay transition 2⁺ → 3⁺ is

(a) allowed by both

(b) Fermi only

(c) Gamow-Teller only

(d) not allowed

139. Surface term in mass formula depends on A as

(a) A⁻¹/³

(b) A¹/³

(c) A²/³

(d) A

140. Neutron is detected due to

(a) ionization

(b) scintillation

(c) electron-hole pairs

(d) secondary nuclear reactions

141. Basic process in neutron β-decay is

(a) d → u + e⁻ + ν̅e

(b) d → u + e⁻

(c) s → u + e⁻ + ν̅e

(d) u → d + e⁻ + ν̅e

142. Spin parity of ¹⁵N is

(a) 1⁻/2

(b) 1⁺/2

(c) 3⁻/2

(d) 3⁺/2

143. Weak nuclear forces act on

(a) both hadrons and leptons

(b) hadrons only

(c) all particles

(d) all charged particles

144. Disintegration series giving ²⁰⁹Bi is

(a) Thorium

(b) Neptunium

(c) Uranium

(d) Actinium

145. K⁺ meson is

(a) uud

(b) c̅

(c) u s̅

(d) s u̅

146. Decreasing lifetime order

(a) π⁰, n, p, Δ⁺

(b) p, n, Δ⁺, π⁰

(c) p, n, π⁰, Δ⁺

(d) Δ⁺, n, π⁺, p

147. Binding energy comparison

(a) helium more stable

(b) deuteron more stable

(c) both less stable

(d) equal

148. β⁻ emitters lie

(a) below stability line

(b) on stability line

(c) above stability line

(d) below N=Z line

149. Reaction:

4¹H → ⁴He + 2e⁰ + 26 MeV

(a) fusion

(b) fission

(c) β-decay

(d) γ-decay

150. Baryon & lepton numbers are

(a) 0,0,1,0

(b) 1,1,0,1

(c) 1,0,0,1

(d) 0,1,1,0

Here is the HTML code for the answer key table. I have formatted it to be fully responsive, meaning it will display cleanly on your blog whether your readers are on a desktop or a mobile device. You can copy and paste this directly into the **HTML view** of your Blogger editor. ```html

Official Answer Key: Paper - II (Physics) - Booklet Series A

Q.No	Ans	Q.No	Ans	Q.No	Ans	Q.No	Ans	Q.No	Ans
1	A	31	A	61	D	91	A	121	D
2	C	32	D	62	B	92	B	122	C
3	B	33	A	63	D	93	A	123	B
4	C	34	C	64	B	94	B	124	C
5	D	35	B	65	C	95	D	125	A
6	D	36	B	66	B	96	A	126	C
7	B	37	C	67	C	97	D	127	D
8	B	38	B	68	B	98	C	128	D
9	C	39	A	69	A	99	B	129	D
10	C	40	C	70	D	100	C	130	A
11	A	41	D	71	D	101	D	131	B
12	D	42	B	72	A	102	B	132	B
13	D	43	C	73	A	103	C	133	C
14	C	44	B	74	C	104	D	134	A
15	C	45	D	75	D	105	D	135	A
16	C	46	*	76	C	106	C	136	D
17	B	47	B	77	B	107	B	137	C
18	B	48	D	78	B	108	C	138	C
19	B	49	D	79	B	109	A	139	C
20	D	50	*	80	*	110	B	140	D
21	B	51	B	81	D	111	A	141	A
22	B	52	B	82	A	112	B	142	A
23	B	53	A	83	B	113	C	143	*
24	C	54	D	84	C	114	C	144	B
25	A	55	B	85	D	115	B	145	C
26	D	56	A	86	B	116	C	146	C
27	B	57	C	87	B	117	C	147	A
28	D	58	*	88	B	118	B	148	C
29	C	59	B	89	D	119	C	149	*
30	C	60	C	90	A	120	B	150	C

Note: An asterisk ( * ) indicates that the question may have been withdrawn or marks were awarded to all candidates for that specific question.

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