PUNJAB PHYSICS LECTURER MOCK TEST 2026 SET 2

1. The residue of the complex function f(z) = z cos(1/z) at its essential singularity z = 0 is:
(a) 1
(b) 0
(c) -1/2
(d) 1/2
Answer: (c)

2. If A and B are two Hermitian operators, then the operator i[A, B] is always:
(a) Anti-Hermitian
(b) Hermitian
(c) Unitary
(d) Orthogonal
Answer: (b)

3. The density of states for a free electron gas in two dimensions (2D) is proportional to energy E as:
(a) E^1/2
(b) E
(c) E⁰ (Constant, independent of E)
(d) E^-1/2
Answer: (c)

4. In the anomalous Zeeman effect, the transition between the ²P_1/2 and ²S_1/2 states splits into how many components?
(a) 2
(b) 3
(c) 4
(d) 6
Answer: (c)

5. For a dynamical system, if the Hamiltonian H does not contain time 't' explicitly, then:
(a) Total momentum is conserved
(b) The Hamiltonian H is a constant of motion
(c) Only kinetic energy is conserved
(d) The generalized coordinates are cyclic
Answer: (b)

6. Liénard-Wiechert potentials are used in electrodynamics to describe the scalar and vector potentials of:
(a) A stationary charge distribution
(b) A steadily carrying current wire
(c) A moving point charge
(d) A static magnetic dipole
Answer: (c)

7. The eigenvalues of a unitary matrix are always:
(a) Real and positive
(b) Purely imaginary
(c) Of unit modulus (|λ| = 1)
(d) Zero
Answer: (c)

8. In the nuclear shell model, which of the following represents a "doubly magic" heavy nucleus?
(a) ⁵⁶Fe
(b) ²⁰⁸Pb
(c) ²³⁵U
(d) ¹⁹⁷Au
Answer: (b)

9. The phase velocity (v_p) of an electromagnetic wave propagating in a good conductor relates to its angular frequency (ω) as:
(a) v_p ∝ ω
(b) v_p ∝ √ω
(c) v_p ∝ 1/ω
(d) v_p ∝ 1/√ω
Answer: (b)

10. The fundamental logic gate corresponding to the Boolean algebraic expression Y = (A · B)' is the:
(a) NOR gate
(b) XOR gate
(c) AND gate
(d) NAND gate
Answer: (d)

11. According to the Third Law of Thermodynamics, the entropy of a perfect crystal at absolute zero temperature (0 K) is:
(a) Infinite
(b) Maximum
(c) Zero
(d) Dependent on the material's mass
Answer: (c)

12. For a quantum mechanical particle confined in a one-dimensional box of length L, if the length of the box is suddenly halved (L/2), the ground state energy E₁ becomes:
(a) E₁ / 2
(b) 2 E₁
(c) 4 E₁
(d) E₁ / 4
Answer: (c)

13. The Landé g-factor for a pure orbital atomic state (where total spin S = 0) is precisely:
(a) 0
(b) 1
(c) 2
(d) 3/2
Answer: (b)

14. In Solid State Physics, the volume of the primitive unit cell for a Body-Centered Cubic (BCC) lattice with lattice parameter 'a' is:
(a) a³
(b) a³ / 2
(c) a³ / 4
(d) a³ / 8
Answer: (b)

15. A semiconductor sample has an equal number of electrons and holes, but the mobility of electrons is significantly higher. The expected Hall coefficient will be:
(a) Zero
(b) Positive
(c) Negative
(d) Infinite
Answer: (c)

16. The divergence of the curl of any continuous, differentiable vector field F (∇ · (∇ × F)) is always equal to:
(a) ∇²F
(b) 1
(c) 0
(d) ∇(∇ · F)
Answer: (c)

17. The isospin quantum number (I) assigned to a pion (π meson) triplet is:
(a) 0
(b) 1/2
(c) 1
(d) 3/2
Answer: (c)

18. The specific heat of a superconductor precisely at its critical transition temperature (T_c) exhibits a:
(a) Smooth exponential drop
(b) Divergence to infinity
(c) Discontinuous jump
(d) Constant value
Answer: (c)

19. Which of the following parameters remains invariant under a Lorentz transformation?
(a) Length
(b) Time interval
(c) Total energy
(d) Proper time
Answer: (d)

20. The trace (sum of diagonal elements) of the Pauli spin matrix σ_x is:
(a) 1
(b) 2
(c) 0
(d) -1
Answer: (c)

21. The Miller indices (h k l) of a crystal plane that is parallel to the y and z axes, and cuts the x-axis at a distance 'a', are:
(a) (0 1 1)
(b) (1 1 1)
(c) (1 0 0)
(d) (0 0 1)
Answer: (c)

22. The group velocity (v_g) and phase velocity (v_p) for a non-relativistic free particle are mathematically related by:
(a) v_g = v_p
(b) v_g = 2v_p
(c) v_g = v_p / 2
(d) v_g × v_p = c²
Answer: (b)

23. The selection rule for a pure vibrational transition of a quantum harmonic oscillator is:
(a) Δv = 0
(b) Δv = ±1
(c) Δv = ±2
(d) Δv = 0, ±1
Answer: (b)

24. In the liquid drop model of the nucleus, the surface energy term is proportional to the mass number A as:
(a) A
(b) A^1/3
(c) A^2/3
(d) A^-1/3
Answer: (c)

25. The speed of an electromagnetic wave in a dielectric medium with permittivity ε and permeability μ is given by:
(a) 1 / √(εμ)
(b) √(ε/μ)
(c) εμ
(d) 1 / (εμ)
Answer: (a)

26. The rest mass of a photon is theoretically considered to be:
(a) 9.1 × 10^-31 kg
(b) 1.6 × 10^-27 kg
(c) Dependent on its frequency
(d) Zero
Answer: (d)

27. A coordinate 'q' is said to be cyclic if it does not appear explicitly in the Lagrangian. The corresponding conjugate momentum 'p' is then:
(a) Zero
(b) A constant of motion
(c) Exponentially decaying
(d) Equal to the kinetic energy
Answer: (b)

28. The number of independent components of a completely symmetric second-rank tensor in 3-dimensional space is:
(a) 3
(b) 6
(c) 9
(d) 12
Answer: (b)

29. The fundamental interaction responsible for the beta decay of a free neutron into a proton, an electron, and an antineutrino is the:
(a) Strong interaction
(b) Electromagnetic interaction
(c) Gravitational interaction
(d) Weak interaction
Answer: (d)

30. The first Born approximation in scattering theory gives highly accurate results specifically for:
(a) Low incident energies and strong scattering potentials
(b) High incident energies and weak scattering potentials
(c) Resonance scattering only
(d) Extremely long-range forces like gravity
Answer: (b)

31. In the context of the WKB approximation, the connection formulas are required primarily because:
(a) The potential energy approaches infinity
(b) The approximation fails at classical turning points where p(x) = 0
(c) The wave function becomes strictly zero everywhere
(d) The particle's energy exceeds the potential barrier
Answer: (b)

32. Fermi's Golden Rule for the transition rate in time-dependent perturbation theory indicates that the transition probability per unit time is proportional to:
(a) The density of final states
(b) The inverse of the density of final states
(c) The square of the density of final states
(d) Independent of the density of final states
Answer: (a)

33. For a one-dimensional quantum harmonic oscillator, the commutator [a, a^†] of the annihilation operator (a) and creation operator (a^†) is exactly:
(a) 0
(b) 1
(c) -1
(d) iℏ
Answer: (b)

34. According to the Larmor formula, the total power radiated by a non-relativistic point charge 'q' accelerating with an acceleration 'a' is proportional to:
(a) a
(b) a²
(c) 1/a
(d) a³
Answer: (b)

35. In a hollow rectangular waveguide of dimensions a × b (where a > b), the dominant transverse electric (TE) mode of propagation is:

(a) TE₀₀
(b) TE₀₁
(c) TE₁₀
(d) TE₁₁
Answer: (c)

36. The skin depth (δ) of an electromagnetic wave in a conducting medium with conductivity σ and permeability μ varies with angular frequency ω as:
(a) ω
(b) 1/ω
(c) 1/√ω
(d) √ω
Answer: (c)

37. The fundamental condition for Bose-Einstein condensation to occur in an ideal Bose gas is that the chemical potential (μ) must:
(a) Be positive and highly large
(b) Be exactly equal to the ground state energy
(c) Approach negative infinity
(d) Fluctuate randomly with temperature
Answer: (b)

38. At absolute zero temperature (T = 0 K), the Fermi-Dirac distribution function for an energy state exactly equal to the Fermi energy (E = E_F) yields a probability of:
(a) 1
(b) 0
(c) 1/2
(d) Undefined
Answer: (c)

39. In the canonical ensemble, the partition function Z is a sum over all accessible microstates. The probability P_i of finding the system in a specific microstate with energy E_i is given by:
(a) exp(-E_i/kT) / Z
(b) Z / exp(-E_i/kT)
(c) exp(E_i/kT) / Z
(d) 1 / (Z exp(-E_i/kT))
Answer: (a)

40. Bloch's theorem states that the wave function of an electron in a periodic crystal lattice potential can be written as ψ(r) = e^ik·r u_k(r), where u_k(r) is:
(a) A Gaussian envelope function
(b) A function with the same periodicity as the crystal lattice
(c) A purely exponentially decaying function
(d) A constant value everywhere in space
Answer: (b)

41. According to the Debye model of specific heat for solids, at very low temperatures, the lattice specific heat capacity (C_v) is proportional to:
(a) T
(b) T²
(c) T³
(d) e^-1/T
Answer: (c)

42. In a purely p-type semiconductor, the Hall coefficient (R_H) is mathematically expected to be:
(a) Zero
(b) Exactly equal to 1
(c) Negative
(d) Positive
Answer: (d)

43. The phenomenon where a superconductor perfectly expels all magnetic flux from its interior when cooled below its critical temperature is known as:
(a) The Josephson effect
(b) The Meissner effect
(c) The Hall effect
(d) The Peltier effect
Answer: (b)

44. In the semi-empirical mass formula (liquid drop model), the pairing energy term δ contributes positively to the binding energy for nuclei that are:
(a) Even-Z, Even-N
(b) Odd-Z, Odd-N
(c) Even-Z, Odd-N
(d) Odd-Z, Even-N
Answer: (a)

45. Which of the following fundamental conservation laws is strictly violated in weak nuclear interactions (such as beta decay)?
(a) Conservation of electric charge
(b) Conservation of baryon number
(c) Conservation of parity
(d) Conservation of total angular momentum
Answer: (c)

46. According to the quark model, a neutron is composed of which combination of constituent quarks?
(a) uud (two up, one down)
(b) udd (one up, two down)
(c) sss (three strange)
(d) ud̄ (one up, one anti-down)
Answer: (b)

47. A radioactive sample has a half-life of 10 days. The fraction of the original active nuclei remaining after 30 days will be:
(a) 1/3
(b) 1/4
(c) 1/8
(d) 1/9
Answer: (c)

48. In an ideal operational amplifier connected in an inverting amplifier configuration, if the input resistor is R₁ and the feedback resistor is R_f, the closed-loop voltage gain (A_v) is:
(a) 1 + (R_f / R₁)
(b) -(R_f / R₁)
(c) -(R₁ / R_f)
(d) 1 + (R₁ / R_f)
Answer: (b)

49. Applying Boolean algebra, the expression A + (A · B) simplifies directly to:
(a) B
(b) A · B
(c) A
(d) 1
Answer: (c)

50. A J-K flip-flop will systematically operate in its "toggle" mode (output state flips on every clock pulse) only when its inputs are:
(a) J = 0, K = 0
(b) J = 1, K = 0
(c) J = 0, K = 1
(d) J = 1, K = 1
Answer: (d)

51. The Zener breakdown mechanism in a heavily doped p-n junction diode fundamentally occurs due to:
(a) Avalanche multiplication of carriers
(b) Quantum tunneling of electrons across the narrow depletion region
(c) Thermal runaway heating the junction
(d) Recombination of electron-hole pairs
Answer: (b)

52. In Raman scattering spectroscopy, the spectral lines shifted to frequencies lower than the incident excitation frequency are historically called:

(a) Anti-Stokes lines
(b) Rayleigh lines
(c) Stokes lines
(d) Lyman lines
Answer: (c)

53. The strict electric dipole selection rule for the change in the orbital angular momentum quantum number (Δl) during an atomic transition is:
(a) Δl = 0
(b) Δl = ±1
(c) Δl = ±2
(d) Δl = 0, ±1
Answer: (b)

54. The fine structure splitting observed in the energy levels of the hydrogen atom is predominantly caused by the physical phenomenon of:
(a) Hyperfine coupling
(b) The external magnetic field (Zeeman effect)
(c) Spin-orbit coupling and relativistic corrections
(d) Finite nuclear mass effects
Answer: (c)

55. For a rigid diatomic molecule treated as a quantum rotator, the spacing in energy between adjacent pure rotational energy levels J and J+1:
(a) Remains constant for all values of J
(b) Increases linearly as J increases
(c) Decreases exponentially as J increases
(d) Is exactly zero
Answer: (b)

56. In order to achieve Light Amplification by Stimulated Emission of Radiation (LASER), which of the following non-equilibrium states must be established in the active medium?
(a) Absolute zero temperature
(b) Perfect thermal equilibrium
(c) Population inversion
(d) Maximum spontaneous emission
Answer: (c)

57. In the general theory of relativity, the covariant derivative of the metric tensor g_μν vanishes identically everywhere. This fundamental property is known as:
(a) Bianchi identity
(b) Metric compatibility
(c) Lorentz invariance
(d) Equivalence principle
Answer: (b)

58. According to the Bohr-van Leeuwen theorem, the classical calculation of thermal average magnetization for an electron gas in thermal equilibrium yields a result that is exactly:
(a) Infinite
(b) Proportional to the external field
(c) Zero
(d) Negative (diamagnetic)
Answer: (c)

59. A fundamental property of the Pauli spin matrices (σ_x, σ_y, σ_z) is that their determinant is always:
(a) 1
(b) -1
(c) 0
(d) i
Answer: (b)

60. For a system executing simple harmonic motion in one dimension, the phase space trajectory representing its dynamics maps out a mathematically perfect:
(a) Hyperbola
(b) Parabola
(c) Ellipse
(d) Straight line
Answer: (c)

61. In complex analysis, the function f(z) = ln(z) has a branch point at:
(a) z = 1
(b) z = i
(c) z = 0 and z = ∞
(d) It has no branch points
Answer: (c)

62. In quantum scattering theory, the partial wave analysis is most useful and practically applicable when the incident particle energy is:
(a) Extremely high
(b) Low, such that only the s-wave (l=0) contributes significantly
(c) Equal to the rest mass energy
(d) Infinite
Answer: (b)

63. The magnetic flux (Φ) passing through a closed superconducting ring is strictly quantized. The fundamental quantum of magnetic flux (Φ₀) is given by:

(a) h / e
(b) h / 2e
(c) 2h / e
(d) ℏ / e
Answer: (b)

64. According to the extreme single-particle nuclear shell model, the expected ground state spin and parity (J^π) of the ¹³C nucleus (Z=6, N=7) is:
(a) (1/2)^-
(b) (3/2)^-
(c) (1/2)⁺
(d) (5/2)⁺
Answer: (a)

65. The Common Mode Rejection Ratio (CMRR) of a differential amplifier is mathematically defined as the ratio of:
(a) Differential mode gain to common mode gain (A_d / A_c)
(b) Common mode gain to differential mode gain (A_c / A_d)
(c) Input impedance to output impedance
(d) Slew rate to bandwidth
Answer: (a)

66. In electromagnetism, a gauge transformation of the potentials A → A + ∇χ and V → V - ∂χ/∂t leaves which of the following invariant?
(a) Only the electric field E
(b) Only the magnetic field B
(c) Both the electric field E and the magnetic field B
(d) Neither E nor B
Answer: (c)

67. The grand partition function relates to the grand potential (Ω) through the fundamental thermodynamic equation:
(a) Ω = -kT ln(Z)
(b) Ω = kT ln(Z)
(c) Ω = -Z ln(kT)
(d) Ω = 1 / ln(Z)
Answer: (a)

68. The moment of inertia tensor of a completely rigid, spherically symmetric body (like a uniform solid sphere) is mathematically represented by a matrix that is:
(a) Anti-symmetric
(b) A scalar multiple of the identity matrix
(c) Traceless
(d) Singular (determinant is zero)
Answer: (b)

69. The parity operator P^ is a Hermitian and unitary operator. Its possible eigenvalues are:
(a) 0 and 1
(b) +1 and -1
(c) +i and -i
(d) All real numbers
Answer: (b)

70. In particle physics, Kaons (K-mesons) are notable because they possess a non-zero value of which quantum number?
(a) Baryon number
(b) Lepton number
(c) Strangeness
(d) Charm
Answer: (c)

71. In a one-dimensional diatomic crystal lattice, the optical phonon branch differs from the acoustic branch primarily because, at the Brillouin zone center (k=0), the optical branch frequency:

(a) Drops exactly to zero
(b) Approaches infinity
(c) Has a non-zero, finite maximum value
(d) Becomes purely imaginary
Answer: (c)

72. In tensor calculus, the Kronecker delta δⁱ_j is formally classified as a:
(a) Contravariant tensor of rank 2
(b) Covariant tensor of rank 2
(c) Mixed tensor of rank 2
(d) Scalar of rank 0
Answer: (c)

73. For a rectangular waveguide of dimensions 'a' (width) and 'b' (height) where a > b, the cutoff frequency (f_c) for the dominant TE₁₀ mode is given by:
(a) c / (2a)
(b) c / (2b)
(c) c / (a+b)
(d) 2c / a
Answer: (a)

74. The coherence time (τ_c) of a laser beam is physically related to its spectral linewidth (Δν) by the approximate relation:
(a) τ_c ≈ Δν
(b) τ_c ≈ 1 / Δν
(c) τ_c ≈ (Δν)²
(d) τ_c ≈ √Δν
Answer: (b)

75. An ideal Atwood machine consists of two masses connected by an inextensible massless string over a frictionless, massless pulley. The number of degrees of freedom for this system is:
(a) 1
(b) 2
(c) 3
(d) 4
Answer: (a)

76. For a degenerate free electron gas in 3D, the Fermi momentum (p_F) depends on the electron number density (n) as:
(a) n
(b) n^1/2
(c) n^1/3
(d) n^2/3
Answer: (c)

77. Clebsch-Gordan coefficients arise in quantum mechanics during the mathematical process of:
(a) Solving the radial part of the hydrogen atom
(b) Adding two angular momenta
(c) Calculating time-dependent transition probabilities
(d) Normalizing wave functions in infinite wells
Answer: (b)

78. Compared to TTL (Transistor-Transistor Logic), the CMOS (Complementary Metal-Oxide-Semiconductor) logic family is best known for its:
(a) Much faster switching speeds
(b) High static power dissipation
(c) Extremely low static power consumption
(d) Inability to act as a logic gate
Answer: (c)

79. In nuclear gamma decay, a transition from an initial state of spin-parity 2⁺ to a final ground state of 0⁺ can proceed exclusively via which multipole radiation?
(a) Electric dipole (E1)
(b) Magnetic dipole (M1)
(c) Electric quadrupole (E2)
(d) Magnetic quadrupole (M2)
Answer: (c)

80. In solid-state band theory, the effective mass (m*) of an electron is inversely proportional to the:
(a) Electron's charge
(b) First derivative of energy with respect to wave vector (dE/dk)
(c) Second derivative of energy with respect to wave vector (d²E/dk²)
(d) Lattice constant of the crystal
Answer: (c)

81. A quarter-wave plate introduces a phase difference between the ordinary and extraordinary rays equal to:
(a) π / 4
(b) π / 2
(c) π
(d) 2π
Answer: (b)

82. The Paschen-Back effect occurs when an atom is placed in an external magnetic field that is:

(a) Extremely weak compared to internal spin-orbit coupling
(b) Modulating at a high radio frequency
(c) Extremely strong, disrupting the internal L-S coupling
(d) Strictly zero
Answer: (c)

83. The Bessel functions J_n(x) form an orthogonal set of functions with respect to a weight function w(x) equal to:
(a) 1
(b) x
(c) e^-x
(d) 1/x
Answer: (b)

84. In the special theory of relativity, the standard Minkowski spacetime metric tensor η_μν (using the + - - - convention) has a determinant equal to:
(a) +1
(b) 0
(c) -1
(d) -4
Answer: (c)

85. Coherent states in quantum mechanics, heavily used in quantum optics, are specifically defined as the exact eigenstates of the:
(a) Hamiltonian operator
(b) Position operator
(c) Annihilation operator
(d) Creation operator
Answer: (c)

86. In a Bipolar Junction Transistor (BJT), the Early effect (base-width modulation) causes the collector current to:
(a) Decrease as collector-base voltage increases
(b) Increase slightly as collector-base voltage increases
(c) Drop abruptly to zero
(d) Remain absolutely constant regardless of voltage
Answer: (b)

87. A key operational advantage of a Proportional Counter over a Geiger-Muller (GM) counter is its ability to:
(a) Operate at much higher applied voltages
(b) Discriminate between different types of incident radiation based on energy
(c) Detect neutrinos easily
(d) Work without a quenching gas
Answer: (b)

88. One of Maxwell's thermodynamic relations states that (∂S / ∂V)_T is exactly equal to:
(a) (∂P / ∂T)_V
(b) -(∂P / ∂T)_V
(c) (∂T / ∂P)_S
(d) (∂V / ∂T)_P
Answer: (a)

89. The Curie-Weiss law for the magnetic susceptibility (χ) of a ferromagnetic material above its Curie temperature (T_C) is given by:
(a) χ = C / T
(b) χ = C / (T - T_C)
(c) χ = C (T - T_C)
(d) χ = C / T²
Answer: (b)

90. The average power radiated by an oscillating electric dipole is proportional to the driving angular frequency ω raised to the power of:
(a) 2
(b) 3
(c) 4
(d) -2
Answer: (c)

91. In mathematical physics, the Green's function G(x, x') for a linear differential operator L mathematically represents the impulse response to a:
(a) Step function
(b) Sinusoidal source
(c) Dirac delta function point source δ(x - x')
(d) Gaussian distribution
Answer: (c)

92. The quantum mechanical operator for the z-component of orbital angular momentum, L_z, expressed in spherical polar coordinates is:
(a) -iℏ (∂/∂r)
(b) -iℏ (∂/∂θ)
(c) -iℏ (∂/∂φ)
(d) -iℏ r (∂/∂r)
Answer: (c)

93. The London penetration depth (λ_L) in a superconductor dictates how far a magnetic field penetrates into the material. It depends on the number density of superconducting electrons (n_s) as:
(a) λ_L ∝ n_s
(b) λ_L ∝ 1 / n_s
(c) λ_L ∝ 1 / √n_s
(d) λ_L ∝ √n_s
Answer: (c)

94. The Mössbauer effect refers to the phenomenon of:
(a) Recoil-free emission and absorption of gamma rays by atomic nuclei bound in a solid crystal
(b) Splitting of nuclear energy levels in a strong magnetic field
(c) Emission of electrons due to high-energy gamma ray bombardment
(d) Spontaneous fission of superheavy elements
Answer: (a)

95. In a circular waveguide of radius 'a', the dominant mode of propagation (the one with the lowest cutoff frequency) is the:
(a) TM₀₁ mode
(b) TE₀₁ mode
(c) TE₁₁ mode
(d) TM₁₁ mode
Answer: (c)

96. Maxwell's thermodynamic relations can be derived from the exact differentials of thermodynamic potentials. The relation (∂T / ∂V)_S = -(∂P / ∂S)_V is derived from the:
(a) Internal Energy (U)
(b) Helmholtz Free Energy (F)
(c) Enthalpy (H)
(d) Gibbs Free Energy (G)
Answer: (a)

97. The maximum rate of change of the output voltage of an operational amplifier in response to a step input is defined as its:
(a) Gain-bandwidth product
(b) Slew rate
(c) Common-mode rejection ratio
(d) Unity-gain frequency
Answer: (b)

98. In classical mechanics, the Euler-Lagrange equations are invariant under the addition of a specific type of term to the Lagrangian. This term must be:
(a) A constant total energy term
(b) A total time derivative of any function of coordinates and time, dF(q,t)/dt
(c) A purely velocity-dependent dissipative function
(d) A harmonic oscillator potential
Answer: (b)

99. The theoretical particle mediating the strong force between quarks is called the:
(a) Photon
(b) W Boson
(c) Gluon
(d) Pion
Answer: (c)

100. The Franck-Condon principle in molecular physics is based on the assumption that during an electronic transition:

(a) The nuclear internuclear distance and velocity remain practically unchanged
(b) The molecule must dissociate completely
(c) The vibrational quantum number must change by exactly ±1
(d) The total spin of the molecule must invert
Answer: (a)

101. The Laplace transform of the Heaviside unit step function u(t-a) is:
(a) e^-as / s
(b) e^as / s
(c) 1 / (s-a)
(d) 1 / (s+a)
Answer: (a)

102. In first-order time-independent perturbation theory, the first-order correction to the energy of the n-th state (E_n⁽¹⁾) due to a perturbation H' is calculated as:
(a) <ψ_n | H' | ψ_n>
(b) Σ_m≠n |<ψ_m | H' | ψ_n>|² / (E_n - E_m)
(c) <ψ_n | (H')² | ψ_n>
(d) 0
Answer: (a)

103. The shape of the first Brillouin zone for a two-dimensional square lattice with lattice constant 'a' is a:

(a) Hexagon
(b) Square of side 2π/a
(c) Circle of radius π/a
(d) Rectangle
Answer: (b)

104. The process of internal conversion in a nucleus involves the:
(a) Conversion of a neutron into a proton
(b) Emission of an orbital electron instead of a gamma-ray photon during de-excitation
(c) Absorption of an external photon to create an electron-positron pair
(d) Capture of a K-shell electron by the nucleus
Answer: (b)

105. Liénard-Wiechert potentials are "retarded" potentials, meaning the potential at position r and time t depends on the state of the source charge at a prior time t_r. The retardation time delay is given by:
(a) |r| / c
(b) |r - r'(t_r)| / c
(c) c / |r|
(d) 0
Answer: (b)

106. In a system exhibiting Bose-Einstein condensation, the fraction of particles in the ground state (N₀/N) varies with absolute temperature T (for T < T_c) according to:
(a) 1 - (T/T_c)^3/2
(b) 1 - (T/T_c)²
(c) (T/T_c)^3/2
(d) e^-T/T_c
Answer: (a)

107. In digital electronics, a Karnaugh map (K-map) is primarily utilized for:
(a) Designing active band-pass filters
(b) Systematically minimizing Boolean logic expressions
(c) Converting analog signals to digital signals
(d) Generating clock pulses
Answer: (b)

108. The Euler equations of motion for a rigid body simplify significantly if the coordinate axes are chosen to be the:
(a) Axes of the laboratory frame
(b) Axes passing through the center of mass parallel to the laboratory frame
(c) Principal axes of inertia of the body
(d) Axes tangential to the body's surface
Answer: (c)

109. The CP (Charge Conjugation and Parity) violation, which helps explain the matter-antimatter asymmetry in the universe, was first experimentally observed in the decay of:
(a) Protons
(b) Neutral Kaons
(c) Muons
(d) Neutrons
Answer: (b)

110. In atomic physics, the Lamb shift experimentally demonstrated a minute energy difference between the 2²S_1/2 and 2²P_1/2 levels of hydrogen. This shift is successfully explained by:
(a) Simple Bohr theory
(b) The Dirac equation alone
(c) Quantum Electrodynamics (QED) via vacuum polarization and electron self-energy
(d) The finite size of the proton
Answer: (c)

111. In tensor calculus, if Aⁱ is a contravariant vector and B_j is a covariant vector, their inner product AⁱB_i forms a:
(a) Tensor of rank 2
(b) Vector (tensor of rank 1)
(c) Scalar invariant (tensor of rank 0)
(d) Matrix
Answer: (c)

112. According to the WKB approximation, the transmission coefficient (T) for a particle of mass m and energy E tunneling through a wide, smooth potential barrier V(x) (where V(x) > E) is roughly proportional to:

(a) exp [ -(2/ℏ) ∫ √(2m(E - V(x))) dx ]
(b) exp [ -(2/ℏ) ∫ √(2m(V(x) - E)) dx ]
(c) exp [ (2/ℏ) ∫ √(2m(V(x) - E)) dx ]
(d) cos [ (1/ℏ) ∫ √(2m(E - V(x))) dx ]
Answer: (b)

113. In a semiconductor where both electrons and holes contribute to conduction, the net Hall coefficient R_H vanishes to zero if:
(a) n = p (intrinsic condition)
(b) nμ_e = pμ_h
(c) nμ_e² = pμ_h²
(d) μ_e = μ_h
Answer: (c)

114. The Q-value of a nuclear reaction is defined as the difference between the sum of the rest mass energies of the initial reactants and the final products. An exothermic reaction has a Q-value that is:
(a) Zero
(b) Negative
(c) Positive
(d) Imaginary
Answer: (c)

115. According to the Fresnel equations, when unpolarized light reflects off a dielectric surface at Brewster's angle, the reflected light is:
(a) Completely unpolarized
(b) Circularly polarized
(c) Linearly polarized parallel to the plane of incidence
(d) Linearly polarized perpendicular to the plane of incidence
Answer: (d)

116. The single-particle partition function Z for a classical one-dimensional harmonic oscillator of frequency ν at temperature T is given by:
(a) kT / hν
(b) hν / kT
(c) exp(-hν / kT)
(d) 1 / (1 - exp(-hν / kT))
Answer: (a)

117. An RC phase-shift oscillator generally uses three identical RC high-pass sections in its feedback network. For the circuit to oscillate, the amplifier must provide a phase shift of:
(a) 0°
(b) 90°
(c) 180°
(d) 360°
Answer: (c)

118. In the theory of small oscillations of a conservative system around a point of stable equilibrium, the eigenvalues of the secular determinant directly correspond to the system's:
(a) Normal coordinates
(b) Total mechanical energies
(c) Squares of the normal mode angular frequencies (ω²)
(d) Damping coefficients
Answer: (c)

119. In Quantum Electrodynamics (QED), Møller scattering describes the fundamental interaction between:

(a) An electron and a positron (e^- e⁺ → e^- e⁺)
(b) Two electrons (e^- e^- → e^- e^-)
(c) An electron and a photon (e^- γ → e^- γ)
(d) A photon and a photon (γ γ → γ γ)
Answer: (b)

120. In the rotational Raman spectrum of a diatomic molecule, the transition selection rules (ΔJ = ±2) lead to the formation of S-branch and O-branch lines. The spacing between adjacent S-branch lines is:
(a) 2B
(b) 4B
(c) 6B
(d) 8B
Answer: (b)

121. In complex analysis, if a function f(z) has a pole of order 'm' at z = a, then the residue at this pole can be evaluated using the formula:
(a) lim_z→a (z-a)^m f(z)
(b) lim_z→a [1/(m-1)!] (d^m-1/dz^m-1) [ (z-a)^m f(z) ]
(c) lim_z→a [1/m!] (d^m/dz^m) [ (z-a) f(z) ]
(d) lim_z→a (d/dz) [ (z-a)^m f(z) ]
Answer: (b)

122. If F(s) is the Laplace transform of f(t), then the Laplace transform of the derivative f'(t) is given by:
(a) s F(s) - f(0)
(b) F(s) / s
(c) s F(s) + f(0)
(d) dF(s)/ds
Answer: (a)

123. For a canonical transformation in classical mechanics, the fundamental Poisson brackets of the new coordinates (Q, P) must satisfy:
(a) [Q_i, Q_j] = 1, [P_i, P_j] = 1
(b) [Q_i, P_j] = 0
(c) [Q_i, P_j] = δ_ij
(d) [Q_i, P_j] = -1
Answer: (c)

124. The metric tensor g_μν for flat three-dimensional space in spherical polar coordinates (r, θ, φ) is a diagonal matrix with elements:
(a) (1, 1, 1)
(b) (1, r², r²sin²θ)
(c) (1, r, r sinθ)
(d) (1, r², sin²θ)
Answer: (b)

125. For a system of two identical fermions, the total wave function (including both spatial and spin parts) must be:
(a) Symmetric under particle exchange
(b) Antisymmetric under particle exchange
(c) Spherically symmetric
(d) Independent of particle spin
Answer: (b)

126. In the WKB approximation, the solutions near the classical turning points (where E = V(x)) diverge. To connect the oscillatory and exponentially decaying solutions across a turning point, one typically uses:

(a) Hermite polynomials
(b) Legendre polynomials
(c) Airy functions
(d) Bessel functions
Answer: (c)

127. The Clebsch-Gordan coefficients, which arise when adding two angular momenta j₁ and j₂ to form a total angular momentum J, are non-zero only if:
(a) J = j₁ + j₂ only
(b) |j₁ - j₂| ≤ J ≤ j₁ + j₂
(c) J = |j₁ - j₂| only
(d) J is an integer
Answer: (b)

128. Retarded potentials in electrodynamics imply that the electromagnetic field at a point 'r' and time 't' depends on the source charge/current distribution at:
(a) The same time 't'
(b) A future time t + (|r-r'|/c)
(c) A past time t - (|r-r'|/c)
(d) Time t = 0
Answer: (c)

129. The time-averaged Poynting vector <S> representing the angular distribution of radiation from an oscillating electric dipole is proportional to:

(a) sin(θ)
(b) cos²(θ)
(c) sin²(θ)
(d) 1 / cos(θ)
Answer: (c)

130. A TM (Transverse Magnetic) mode propagating in a hollow metallic cylindrical waveguide has the defining characteristic that:
(a) The longitudinal electric field E_z = 0
(b) The longitudinal magnetic field B_z = 0
(c) Both E_z = 0 and B_z = 0
(d) The transverse fields are zero
Answer: (b)

131. In statistical mechanics, the Fermi-Dirac distribution function f(E) becomes exactly a step function (f(E)=1 for E<E_F and f(E)=0 for E>E_F) at what temperature?

(a) T = ∞
(b) T = T_F (Fermi temperature)
(c) T = 0 K
(d) T = 300 K
Answer: (c)

132. The critical temperature T_c for Bose-Einstein condensation of an ideal, non-interacting Bose gas depends on the particle number density 'n' as:
(a) n^1/3
(b) n^2/3
(c) n
(d) Independent of n
Answer: (b)

133. The canonical partition function Z for N identical, indistinguishable classical non-interacting particles is related to the single-particle partition function Z₁ by:
(a) Z = Z₁^N
(b) Z = N * Z₁
(c) Z = Z₁^N / N!
(d) Z = N! * Z₁^N
Answer: (c)

134. In the Kronig-Penney model of a 1D crystal lattice, energy band gaps appear specifically at the boundaries of the Brillouin zones, which occur when the wave vector 'k' equals:

(a) 0
(b) ± nπ / a (where n = 1, 2, 3...)
(c) ± π / 2a
(d) ± 2nπa
Answer: (b)

135. In BCS theory, the coherence length (ξ) of a superconductor roughly represents:
(a) The depth to which a magnetic field can penetrate
(b) The spatial extent of a Cooper pair
(c) The mean free path of normal electrons
(d) The distance between adjacent lattice ions
Answer: (b)

136. The Hall coefficient R_H of a material is experimentally found to be inversely proportional to the:
(a) Applied magnetic field
(b) Applied electric field
(c) Charge carrier density
(d) Sample thickness
Answer: (c)

137. According to the liquid drop model, the plot of atomic masses of isobars (nuclei with the same A) against their atomic number Z yields a curve that is approximately a:
(a) Straight line
(b) Parabola
(c) Hyperbola
(d) Sine wave
Answer: (b)

138. The legendary "Wu experiment" involving the beta decay of Cobalt-60 atoms aligned in a magnetic field definitively proved that:
(a) Energy is not conserved in weak interactions
(b) Parity is maximally violated in weak interactions
(c) Neutrinos have mass
(d) The strong force is charge-independent
Answer: (b)

139. The Gell-Mann-Nishijima formula relates the electric charge (Q) of a hadron to its isospin component (I₃), baryon number (B), and strangeness (S). The formula is:
(a) Q = I₃ + (B + S)/2
(b) Q = I₃ + B + S
(c) Q = 2I₃ + B + S
(d) Q = I₃ + (B - S)/2
Answer: (a)

140. In Quantum Chromodynamics (QCD), the fundamental vertex represents the interaction between:
(a) An electron, a positron, and a photon
(b) A quark, an antiquark, and a gluon
(c) A proton, a neutron, and a pion
(d) A W boson and a lepton pair
Answer: (b)

141. The basic building block Feynman diagram in Quantum Electrodynamics (QED) always consists of a vertex joining:

(a) Two straight fermion lines and one wavy photon line
(b) Three wavy photon lines
(c) Two wavy photon lines and one straight fermion line
(d) Three straight fermion lines
Answer: (a)

142. The Landé g-factor for an atomic state with total angular momentum J, orbital angular momentum L, and spin S is given by g = 1 + [J(J+1) + S(S+1) - L(L+1)] / [2J(J+1)]. For a ²S_1/2 state, 'g' equals:
(a) 1
(b) 2
(c) 3/2
(d) 0
Answer: (b)

143. The first-order Stark effect (linear splitting of energy levels in an electric field) is non-zero in the hydrogen atom only for states where:
(a) The principal quantum number n = 1
(b) There is an accidental degeneracy of states with opposite parity (e.g., 2s and 2p)
(c) The electron spin is parallel to the external field
(d) The orbital angular momentum L = 0
Answer: (b)

144. In the vibration-rotation spectrum of a diatomic molecule, the spectral lines corresponding to transitions where the rotational quantum number changes by ΔJ = -1 constitute the:

(a) P-branch
(b) Q-branch
(c) R-branch
(d) S-branch
Answer: (a)

145. An operational amplifier (Op-Amp) connected as a differentiator circuit utilizes:
(a) A resistor in the input and a capacitor in the feedback path
(b) A capacitor in the input and a resistor in the feedback path
(c) Capacitors in both the input and feedback paths
(d) An inductor in the feedback path
Answer: (b)

146. In an astable multivibrator built using a 555 Timer IC with external resistors R_A, R_B, and timing capacitor C, the charging time constant is proportional to:
(a) (R_A + R_B) C
(b) R_B C
(c) R_A C
(d) (R_A + 2R_B) C
Answer: (a)

147. A Karnaugh map (K-map) is a graphical tool used primarily to simplify Boolean algebra expressions in the form of:
(a) Sum of Products (SOP) or Product of Sums (POS)
(b) Sequential state diagrams
(c) Analog voltage levels
(d) Fourier series expansions
Answer: (a)

148. The "magic numbers" in nuclear physics (2, 8, 20, 28, 50, 82, 126) represent nuclei with exceptionally high stability. These numbers are successfully explained by adding which interaction to the nuclear shell model?
(a) Coulomb repulsion
(b) Strong spin-orbit (L·S) coupling
(c) Weak interaction
(d) Tensor force
Answer: (b)

149. The Maxwell thermodynamic relation derived directly from the exact differential of Enthalpy (dH = T dS + V dP) is:
(a) (∂T / ∂P)_S = (∂V / ∂S)_P
(b) (∂S / ∂V)_T = (∂P / ∂T)_V
(c) (∂T / ∂V)_S = -(∂P / ∂S)_V
(d) (∂S / ∂P)_T = -(∂V / ∂T)_P
Answer: (a)

150. A particle of mass 'm' is moving in a 3D harmonic oscillator potential V(r) = (1/2)mω²r². The degree of degeneracy of its first excited energy state is:
(a) 1 (Non-degenerate)
(b) 3
(c) 6
(d) 9
Answer: (b)

Punjab Physics Lecturer Mock Test 2026

Physics Lecturer Mock Test - Part 1

1. The eigenvalues of a Hermitian matrix are always:
(a) Real
(b) Imaginary
(c) Zero
(d) Complex numbers with non-zero imaginary parts
Answer: (a)

2. The Laplace transform of sin(at) is given by:
(a) s / (s² + a²)
(b) a / (s² + a²)
(c) s / (s² - a²)
(d) a / (s² - a²)
Answer: (b)

3. If a complex function f(z) has a simple pole at z=a, the residue is given by:
(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)² f(z)
Answer: (b)

4. The trace of a square matrix is equal to the:
(a) Product of its eigenvalues
(b) Sum of its eigenvalues
(c) Determinant of the matrix
(d) Inverse of the matrix
Answer: (b)

5. The number of degrees of freedom for a free rigid body moving in three-dimensional space is:
(a) 3
(b) 6
(c) 9
(d) Infinite
Answer: (b)

6. The fundamental Poisson bracket [q_i, p_j] for canonical variables is equal to:
(a) 0
(b) 1
(c) δ_ij (Kronecker delta)
(d) iℏ
Answer: (c)

7. The Hamiltonian represents the total energy of a conservative system if the Lagrangian:
(a) Contains time explicitly
(b) Does not contain time explicitly
(c) Is a linear function of velocities
(d) Is zero
Answer: (b)

8. A transformation from coordinates (q, p) to (Q, P) is canonical if the Poisson bracket [Q, P] is:
(a) 0
(b) 1
(c) -1
(d) ℏ
Answer: (b)

9. In quantum mechanics, the commutator [x, p_x] is equal to:
(a) 0
(b) ℏ
(c) iℏ
(d) -iℏ
Answer: (c)

10. The zero-point energy of a one-dimensional quantum harmonic oscillator of angular frequency ω is:
(a) 0
(b) (1/2) ℏω
(c) ℏω
(d) (3/2) ℏω
Answer: (b)

11. If a total wave function is antisymmetric under the exchange of any two identical particles, the particles are:
(a) Bosons
(b) Photons
(c) Phonons
(d) Fermions
Answer: (d)

12. The expectation value of momentum <p> for a particle in a stationary state within a one-dimensional box is:
(a) Infinite
(b) Zero
(c) p² / 2m
(d) ℏk
Answer: (b)

13. Bragg's law of X-ray diffraction is mathematically expressed as:
(a) d sinθ = nλ
(b) 2d sinθ = nλ
(c) d cosθ = nλ
(d) 2d cosθ = nλ
Answer: (b)

14. At absolute zero (T = 0 K), the probability of an electron occupying the Fermi energy level is:
(a) 0
(b) 0.5
(c) 1
(d) Infinite
Answer: (b)

15. The diamond crystal structure is formed by the interpenetration of two sub-lattices which are:
(a) Simple cubic
(b) Body-centered cubic (BCC)
(c) Face-centered cubic (FCC)
(d) Hexagonal close-packed (HCP)
Answer: (c)

16. The expulsion of magnetic flux from the interior of a superconducting material is known as the:
(a) Josephson effect
(b) Meissner effect
(c) Hall effect
(d) Peltier effect
Answer: (b)

17. Which of the following is considered a "doubly magic" nucleus?
(a) ⁴He
(b) ¹²C
(c) ⁵⁶Fe
(d) ²³⁵U
Answer: (a)

18. According to the standard model, the quark composition of a neutron is:
(a) uud
(b) udd
(c) uuu
(d) ddd
Answer: (b)

19. In a beta-minus (β^-) decay, a neutron transforms into a proton while emitting:
(a) A positron and a neutrino
(b) An electron and an antineutrino
(c) An alpha particle
(d) A gamma ray
Answer: (b)

20. The relationship between the half-life (T_1/2) and the decay constant (λ) of a radioactive substance is:
(a) T_1/2 = λ / 0.693
(b) T_1/2 = 0.693 × λ
(c) T_1/2 = 0.693 / λ
(d) T_1/2 = 1 / λ
Answer: (c)

21. The Common-Mode Rejection Ratio (CMRR) of an ideal Operational Amplifier is:
(a) Zero
(b) 1
(c) Infinite
(d) Less than 1
Answer: (c)

22. Which of the following logic gates is known as a "Universal Gate"?
(a) AND
(b) OR
(c) XOR
(d) NAND
Answer: (d)

23. A Zener diode in a circuit is primarily used for:
(a) Rectification
(b) Amplification
(c) Voltage regulation
(d) Generating oscillations
Answer: (c)

24. In an n-type semiconductor, the majority charge carriers are:
(a) Holes
(b) Electrons
(c) Protons
(d) Positrons
Answer: (b)

25. The direction of propagation of an electromagnetic wave is given by the direction of:
(a) Vector E
(b) Vector B
(c) E × B
(d) B × E
Answer: (c)

26. The skin depth (depth of penetration) of an electromagnetic wave in a good conductor is proportional to:
(a) ω
(b) ω²
(c) 1 / √ω
(d) 1 / ω
Answer: (c)

27. Maxwell's equation ∇ · B = 0 signifies that:
(a) Magnetic monopoles do not exist
(b) Time-varying magnetic fields produce electric fields
(c) Magnetic fields are conservative
(d) Light is an electromagnetic wave
Answer: (a)

28. When unpolarized light is incident at Brewster's angle on a transparent dielectric, the reflected and refracted rays are:
(a) Parallel to each other
(b) At 45° to each other
(c) Perpendicular to each other
(d) Totally internally reflected
Answer: (c)

29. Particles with integer spin (like photons) follow which type of statistical distribution?
(a) Maxwell-Boltzmann
(b) Fermi-Dirac
(c) Bose-Einstein
(d) Rayleigh-Jeans
Answer: (c)

30. For a system with two non-degenerate energy levels 0 and E, the single-particle partition function at temperature T is:
(a) exp(-E/kT)
(b) 1 + exp(-E/kT)
(c) 1 - exp(-E/kT)
(d) exp(E/kT)
Answer: (b)

Physics Lecturer Mock Test - Part 2

31. The ground state energy of a hydrogen atom is -13.6 eV. The energy of its first excited state is:
(a) -3.4 eV
(b) -6.8 eV
(c) -27.2 eV
(d) 0 eV
Answer: (a)

32. In the Stern-Gerlach experiment, the magnetic field used to split the beam of silver atoms must be:
(a) Uniform
(b) Non-uniform
(c) Time-varying
(d) Zero
Answer: (b)

33. The Pauli spin matrices anti-commute with each other. The anti-commutator {σ_x, σ_y} is equal to:
(a) 0
(b) 2iσ_z
(c) 1
(d) iσ_z
Answer: (a)

34. The parity of spherical harmonics Y_lm(θ, φ) is given by:
(a) (-1)^m
(b) (-1)^l
(c) (-1)^l+m
(d) 1
Answer: (b)

35. According to the variational principle in quantum mechanics, the trial energy E_trial compared to the true ground state energy E₀ is always:
(a) ≤ E₀
(b) ≥ E₀
(c) = E₀
(d) < E₀
Answer: (b)

36. A symmetric tensor of rank 2 in 3-dimensional space has how many independent components?
(a) 9
(b) 6
(c) 3
(d) 8
Answer: (b)

37. The singularities of the complex function f(z) = 1 / (z² + 1) are located at:
(a) z = 1, -1
(b) z = i, -i
(c) z = 0
(d) It has no singularities
Answer: (b)

38. If a matrix is Unitary, the absolute value of its determinant is always:
(a) 0
(b) 1
(c) -1
(d) Infinite
Answer: (b)

39. The generating function (1 - 2xt + t²)^-1/2 is associated with which of the following polynomials?
(a) Hermite polynomials
(b) Laguerre polynomials
(c) Legendre polynomials
(d) Bessel functions
Answer: (c)

40. The value of the integral ∫_-∞^∞ δ(x-a) f(x) dx is:
(a) 0
(b) f(0)
(c) f(a)
(d) 1
Answer: (c)

41. According to the Debye model, the specific heat of a solid at very low temperatures varies with temperature T as:
(a) T
(b) T²
(c) T³
(d) Independent of T
Answer: (c)

42. The Fermi energy of a free electron gas in 3D is proportional to the electron density 'n' as:
(a) n^1/3
(b) n^2/3
(c) n
(d) n^3/2
Answer: (b)

43. In the Hall effect experiment, the developed Hall voltage is proportional to:
(a) The applied current only
(b) The applied magnetic field only
(c) Both the applied current and magnetic field
(d) Neither the current nor the magnetic field
Answer: (c)

44. In a superconductor, the superconducting energy gap is at its maximum value at:
(a) The critical temperature T_c
(b) T = 0 K
(c) Room temperature
(d) Temperatures above T_c
Answer: (b)

45. The reciprocal lattice of a Face-Centered Cubic (FCC) crystal is a:
(a) Simple cubic lattice
(b) Body-Centered Cubic (BCC) lattice
(c) Face-Centered Cubic (FCC) lattice
(d) Hexagonal close-packed lattice
Answer: (b)

46. In the semi-empirical mass formula (liquid drop model), the volume energy term is proportional to the mass number 'A' as:
(a) A^1/3
(b) A^2/3
(c) A
(d) Z²
Answer: (c)

47. Which of the following elementary particles belongs to the Lepton family?
(a) Proton
(b) Neutron
(c) Pion
(d) Muon
Answer: (d)

48. The conservation of strangeness number is violated in which fundamental interaction?
(a) Strong interactions
(b) Electromagnetic interactions
(c) Weak interactions
(d) None of the above
Answer: (c)

49. The binding energy per nucleon is maximum for which of the following nuclei?
(a) ⁴He
(b) ⁵⁶Fe
(c) ²³⁵U
(d) ¹²C
Answer: (b)

50. In a nuclear reactor, what is the primary function of the moderator?
(a) To absorb excess neutrons
(b) To slow down fast neutrons to thermal energies
(c) To cool the reactor core
(d) To accelerate neutrons for better fission
Answer: (b)

51. In a Common-Emitter (CE) transistor amplifier, the phase difference between the input and output voltage is:
(a) 0°
(b) 90°
(c) 180°
(d) 270°
Answer: (c)

52. An ideal voltmeter should have an internal resistance equal to:
(a) Zero
(b) 1 ohm
(c) 100 ohms
(d) Infinity
Answer: (d)

53. A JK flip-flop is in its "toggle" state when the inputs are:
(a) J = 0, K = 0
(b) J = 1, K = 0
(c) J = 0, K = 1
(d) J = 1, K = 1
Answer: (d)

54. The depletion region of an unbiased p-n junction diode contains:
(a) Only free electrons
(b) Only holes
(c) Mobile charge carriers
(d) Immobile ions
Answer: (d)

55. The bandwidth of an ideal operational amplifier (Op-Amp) is:
(a) Zero
(b) Infinite
(c) 1 MHz
(d) 100 Hz
Answer: (b)

56. In electromagnetic theory, the Poynting vector S represents the directional energy flux and is defined as:
(a) E × B
(b) E × H
(c) B × E
(d) H × E
Answer: (b)

57. For a plane electromagnetic wave propagating in a vacuum, the ratio of the magnitudes of the electric field to the magnetic field (E/B) is equal to:
(a) ε₀
(b) μ₀
(c) c (speed of light)
(d) c²
Answer: (c)

58. According to the first law of thermodynamics, during an isothermal process for an ideal gas:
(a) The heat exchanged is zero
(b) The work done is zero
(c) The change in internal energy is zero
(d) The pressure remains constant
Answer: (c)

59. The efficiency of a Carnot engine operating between a source at temperature T₁ and a sink at temperature T₂ is given by:
(a) 1 - (T₁ / T₂)
(b) 1 - (T₂ / T₁)
(c) T₂ / T₁
(d) (T₁ - T₂) / (T₁ + T₂)
Answer: (b)

60. In statistical mechanics, a microcanonical ensemble represents an isolated system where the following macroscopic variables are kept constant:
(a) Number of particles (N), Volume (V), and Temperature (T)
(b) Chemical potential (μ), Volume (V), and Temperature (T)
(c) Number of particles (N), Volume (V), and Energy (E)
(d) Number of particles (N), Pressure (P), and Temperature (T)
Answer: (c)

Physics Lecturer Mock Test - Part 3

61. The partition function of a canonical ensemble depends on which set of macroscopic variables?
(a) Temperature (T), Volume (V), and Number of particles (N)
(b) Energy (E), Volume (V), and Number of particles (N)
(c) Temperature (T), Pressure (P), and Number of particles (N)
(d) Temperature (T), Volume (V), and Chemical potential (μ)
Answer: (a)

62. The splitting of spectral lines under the influence of a strong electric field is known as the:
(a) Zeeman effect
(b) Paschen-Back effect
(c) Stark effect
(d) Compton effect
Answer: (c)

63. In Solid State Physics, phonons are considered as the quantized modes of:
(a) Electromagnetic radiation
(b) Lattice vibrations
(c) Electron spin
(d) Nuclear charge
Answer: (b)

64. The expectation value of the position operator <x> for the ground state of a one-dimensional quantum harmonic oscillator is:
(a) 0
(b) ℏ / mω
(c) L / 2
(d) Infinite
Answer: (a)

65. In a p-n junction diode, the width of the depletion layer:
(a) Increases with forward bias
(b) Decreases with reverse bias
(c) Increases with reverse bias
(d) Is independent of bias voltage
Answer: (c)

66. In the semi-empirical mass formula, the asymmetry energy term is proportional to:
(a) (N - Z)² / A
(b) (N + Z)² / A
(c) Z² / A^1/3
(d) A
Answer: (a)

67. The ratio of the electric field (E) to the magnetic field intensity (H) in a vacuum represents the intrinsic impedance of free space, which has the unit of:
(a) Velocity
(b) Resistance (Ohms)
(c) Capacitance (Farads)
(d) Inductance (Henries)
Answer: (b)

68. A vector field V is said to be irrotational if:
(a) ∇ · V = 0
(b) ∇ × V = 0
(c) ∇² V = 0
(d) ∇( ∇ · V ) = 0
Answer: (b)

69. In classical mechanics, the Hamilton-Jacobi equation takes the form of a:
(a) First-order linear partial differential equation
(b) First-order non-linear partial differential equation
(c) Second-order linear partial differential equation
(d) Second-order non-linear partial differential equation
Answer: (b)

70. If the Hall coefficient of a material is found to be zero, the material is most likely a/an:
(a) Good metal
(b) n-type semiconductor
(c) Insulator
(d) Intrinsic semiconductor
Answer: (d)

71. Heisenberg's uncertainty principle states that the minimum uncertainty product ΔxΔp_x for a quantum system is:
(a) ℏ
(b) ℏ / 2
(c) 0
(d) 2ℏ
Answer: (b)

72. The specific selection rule for transitions in a pure rotational Raman spectrum is:
(a) ΔJ = 0, ±1
(b) ΔJ = ±1
(c) ΔJ = 0, ±2
(d) ΔJ = ±2
Answer: (c)

73. Radioactive beta decay is fundamentally mediated by the:
(a) Strong nuclear force
(b) Electromagnetic force
(c) Weak nuclear force
(d) Gravitational force
Answer: (c)

74. The voltage gain of an ideal voltage follower (common-collector amplifier) is approximately:
(a) 0
(b) 1
(c) 100
(d) Infinite
Answer: (b)

75. For an electromagnetic wave propagating through a good conductor, the phase difference between the electric and magnetic fields is:
(a) 0°
(b) 45°
(c) 90°
(d) 180°
Answer: (b)

76. The value of the complex contour integral ∮ (1/z) dz around the unit circle |z|=1 is:
(a) 0
(b) 2πi
(c) πi
(d) 1
Answer: (b)

77. According to Kepler's second law, the areal velocity of a planet around the sun is constant. This is a direct consequence of the conservation of:
(a) Linear momentum
(b) Kinetic energy
(c) Angular momentum
(d) Total mechanical energy
Answer: (c)

78. Which of the following statistical distributions applies to indistinguishable particles with half-integral spin?
(a) Maxwell-Boltzmann
(b) Bose-Einstein
(c) Fermi-Dirac
(d) None of the above
Answer: (c)

79. The fine structure splitting of the hydrogen atom spectrum is primarily due to:
(a) Relativistic correction only
(b) Spin-orbit coupling only
(c) Both relativistic correction and spin-orbit coupling
(d) The finite size and mass of the nucleus
Answer: (c)

80. In the Kronig-Penney model of solid-state physics, the permitted energy bands are separated by:
(a) Allowed zones
(b) Forbidden gaps
(c) Brillouin zones
(d) Fermi surfaces
Answer: (b)

81. The spherical harmonics Y_l,m(θ, φ) are simultaneous eigenfunctions of which quantum mechanical operators?
(a) L_x and L_y
(b) L² and L_z
(c) L_z and Hamiltonian (H)
(d) L² and L_x
Answer: (b)

82. Which of the following detectors is primarily used for accurately measuring the energy spectrum of gamma rays?
(a) Geiger-Muller counter
(b) Scintillation counter combined with a photomultiplier tube
(c) Bubble chamber
(d) Cloud chamber
Answer: (b)

83. An astable multivibrator circuit operates as a:
(a) Free-running oscillator (square wave generator)
(b) Voltage regulator
(c) High-pass active filter
(d) Bistable flip-flop
Answer: (a)

84. The cutoff frequency for the Transverse Electromagnetic (TEM) mode in a hollow rectangular waveguide is:
(a) 0 Hz
(b) Infinite
(c) Dependent on the internal dimensions
(d) TEM mode cannot propagate in a hollow waveguide
Answer: (d)

85. In mathematical physics, a tensor of rank zero is equivalent to a:
(a) Vector
(b) Scalar
(c) Matrix
(d) Dyadic
Answer: (b)

86. The Lagrangian of a free particle of mass 'm' in cylindrical coordinates (r, θ, z) is given by:
(a) (1/2)m(ṙ² + r²θ̇² + ż²)
(b) (1/2)m(ṙ² + θ̇² + ż²)
(c) (1/2)m(ṙ² + rθ̇² + ż²)
(d) (1/2)m(ṙ² + r²θ̇ + ż²)
Answer: (a)

87. The density of states for a free electron gas in three dimensions is proportional to:
(a) E
(b) E^1/2
(c) E²
(d) E^-1/2
Answer: (b)

88. In the L-S coupling scheme, the allowed values of the total angular momentum quantum number J for a ³P state are:
(a) 0, 1, 2
(b) 1, 2, 3
(c) 1/2, 3/2
(d) 0 only
Answer: (a)

89. The effective mass of an electron in a semiconductor crystal lattice is inversely proportional to the:
(a) First derivative of the E-k curve
(b) Second derivative of the E-k curve (d²E/dk²)
(c) Width of the forbidden band gap
(d) Absolute temperature of the crystal
Answer: (b)

90. A quantum mechanical state is said to be "degenerate" if:
(a) It represents a particle with zero total energy
(b) The wave function is perfectly antisymmetric
(c) Two or more linearly independent states share the exact same energy eigenvalue
(d) The particle escapes its confining potential well
Answer: (c)

91. The residue of the complex function f(z) = e^z / z³ at the pole z = 0 is:
(a) 1
(b) 1/2
(c) 1/6
(d) 0
Answer: (b)

92. The Pauli exclusion principle is a direct mathematical consequence of the:
(a) Heisenberg uncertainty principle
(b) Spin-statistics theorem
(c) Bohr correspondence principle
(d) Equivalence principle
Answer: (b)

93. For a particle in a one-dimensional box of length L, the uncertainty in position Δx for highly excited states (n → ∞) approaches:
(a) 0
(b) L / 2
(c) L / √12
(d) L
Answer: (c)

94. The Lande g-factor for a pure spin state of an electron (L = 0, S = 1/2) is approximately:
(a) 0
(b) 1
(c) 2
(d) 3
Answer: (c)

95. In statistical mechanics, energy fluctuations within a canonical ensemble are directly proportional to the system's:
(a) Entropy
(b) Specific heat at constant volume
(c) Chemical potential
(d) Compressibility
Answer: (b)

96. The Poisson bracket of the angular momentum components {L_x, L_y} in classical mechanics is equal to:
(a) 0
(b) 1
(c) L_z
(d) -L_z
Answer: (c)

97. The rest mass energy of an electron is approximately:
(a) 0.511 MeV
(b) 1.022 MeV
(c) 938 MeV
(d) 13.6 eV
Answer: (a)

98. A particle moving with a velocity v = (√3 / 2)c has a Lorentz factor (γ) equal to:
(a) 1.5
(b) 2
(c) 2.5
(d) 4
Answer: (b)

99. The critical magnetic field (H_c) of a superconductor at its critical temperature (T = T_c) is:
(a) Maximum
(b) Zero
(c) Infinite
(d) Independent of temperature
Answer: (b)

100. Which type of magnetic material inherently exhibits a small, negative magnetic susceptibility?
(a) Paramagnetic
(b) Ferromagnetic
(c) Diamagnetic
(d) Antiferromagnetic
Answer: (c)

101. In the Debye theory of specific heat, at extremely low temperatures, the specific heat capacity (C_v) of a solid is proportional to:
(a) T
(b) T²
(c) T³
(d) T⁴
Answer: (c)

102. An alpha particle is structurally identical to the nucleus of which element?
(a) Hydrogen
(b) Deuterium
(c) Helium
(d) Lithium
Answer: (c)

103. The fundamental interaction responsible for nuclear beta decay is mediated by the exchange of:
(a) Gluons
(b) Photons
(c) W and Z bosons
(d) Gravitons
Answer: (c)

104. According to the quark model, the composition of a positive pion (π⁺) is:
(a) uud
(b) up quark and an anti-down quark (u d̄)
(c) down quark and an anti-up quark (d ū)
(d) udd
Answer: (b)

105. The logic gate that produces a HIGH (1) output strictly only when all of its inputs are HIGH (1) is the:
(a) OR gate
(b) NAND gate
(c) AND gate
(d) XOR gate
Answer: (c)

106. In a standard Bipolar Junction Transistor (BJT), the base region is manufactured to be:
(a) Heavily doped and very thick
(b) Lightly doped and very thin
(c) Moderately doped and thick
(d) Heavily doped and thin
Answer: (b)

107. The slew rate of an ideal operational amplifier is theoretically:
(a) 0 V/μs
(b) 1 V/μs
(c) Infinite
(d) Equal to its bandwidth
Answer: (c)

108. The Coulomb gauge condition in electromagnetic theory specifies that the divergence of the magnetic vector potential A (∇ · A) is:
(a) μ₀J
(b) Infinite
(c) Zero
(d) -∂V/∂t
Answer: (c)

109. When unpolarized light passes from air into a dielectric medium of refractive index 'n', the Brewster angle (θ_B) for complete polarization is given by:
(a) sin^-1(n)
(b) cos^-1(n)
(c) tan^-1(n)
(d) cot^-1(n)
Answer: (c)

110. The characteristic impedance of free space for the propagation of electromagnetic waves is approximately:
(a) 50 Ω
(b) 120 Ω
(c) 377 Ω
(d) Infinite
Answer: (c)

111. In a three-dimensional isotropic quantum harmonic oscillator, the zero-point energy is:
(a) (1/2) ℏω
(b) ℏω
(c) (3/2) ℏω
(d) 3 ℏω
Answer: (c)

112. The first Born approximation in quantum scattering theory is most valid when the scattering potential is:
(a) Extremely strong
(b) Weak and acts over a short range
(c) A purely Coulombic infinite potential
(d) Strongly attractive
Answer: (b)

113. The phase space trajectory of a one-dimensional linear harmonic oscillator forms an:
(a) Ellipse
(b) Parabola
(c) Hyperbola
(d) Straight line
Answer: (a)

114. According to the equipartition theorem, the number of degrees of freedom for a rigid diatomic molecule at normal room temperature is:
(a) 3
(b) 5
(c) 6
(d) 7
Answer: (b)

115. The ratio of specific heats (γ = C_p/C_v) for a monoatomic ideal gas is exactly:
(a) 1.33 (or 4/3)
(b) 1.40 (or 7/5)
(c) 1.67 (or 5/3)
(d) 1.00
Answer: (c)

116. In a pure, intrinsic semiconductor at absolute zero (0 K), the Fermi level lies:
(a) Inside the conduction band
(b) Inside the valence band
(c) Exactly in the middle of the forbidden energy gap
(d) Closer to the conduction band than the valence band
Answer: (c)

117. The transition of a metal to a superconducting state is considered a:
(a) First-order phase transition
(b) Second-order phase transition
(c) Third-order phase transition
(d) It is not a phase transition
Answer: (b)

118. The mean life (τ) of a radioactive substance is mathematically related to its half-life (T_1/2) by the formula:
(a) τ = T_1/2 × ln(2)
(b) τ = T_1/2 / ln(2)
(c) τ = T_1/2 / 2
(d) τ = (T_1/2)²
Answer: (b)

119. The fundamental selection rule governing an allowed electric dipole transition in an atom requires that the change in the orbital angular momentum quantum number (Δl) must be:
(a) 0
(b) ±1
(c) 0, ±1
(d) ±2
Answer: (b)

120. A step-down transformer fundamentally operates on the principle of:
(a) Self-induction
(b) Mutual induction
(c) Electrostatic induction
(d) Magnetic levitation
Answer: (b)

Physics Lecturer Mock Test - Part 5 (Final Set)

121. According to Cauchy's integral formula, if f(z) is analytic within and on a simple closed contour C, and 'a' is a point inside C, then the value of ∮ [f(z)/(z-a)] dz is:
(a) 0
(b) 2πi f(a)
(c) πi f(a)
(d) f(a) / 2πi
Answer: (b)

122. The fundamental commutator [L_y, L_z] for the components of orbital angular momentum is equal to:
(a) 0
(b) iℏ L_x
(c) -iℏ L_x
(d) ℏ L_x
Answer: (b)

123. If the volume of a primitive cell in a direct crystal lattice is V, then the volume of the corresponding primitive cell in the reciprocal lattice is:
(a) V
(b) 1 / V
(c) (2π)³ / V
(d) (2π) / V³
Answer: (c)

124. Gamow's theory successfully explained the phenomenon of alpha decay by utilizing the quantum mechanical concept of:
(a) Spin-orbit coupling
(b) Quantum tunneling
(c) Exchange interaction
(d) Parity violation
Answer: (b)

125. According to De Morgan's first theorem in Boolean algebra, the complement of a product (A · B)' is equal to:
(a) A' · B'
(b) A' + B'
(c) A + B
(d) (A + B)'
Answer: (b)

126. Maxwell's addition of the "displacement current" term to Ampere's law was necessitated by the requirement to satisfy the:
(a) Conservation of energy
(b) Conservation of linear momentum
(c) Equation of continuity (conservation of charge)
(d) Conservation of angular momentum
Answer: (c)

127. In a grand canonical ensemble, the thermodynamic system is allowed to exchange:
(a) Energy only
(b) Particles only
(c) Both energy and particles
(d) Neither energy nor particles
Answer: (c)

128. For laser action to occur in a medium, the most essential prerequisite condition is:
(a) Spontaneous emission
(b) Thermal equilibrium
(c) Population inversion
(d) Absolute zero temperature
Answer: (c)

129. The baryon number (B) assigned to a proton and a neutron, respectively, is:
(a) 0, 0
(b) +1, +1
(c) +1, 0
(d) +1, -1
Answer: (b)

130. The metric tensor g_μν used in the general theory of relativity is a:
(a) Symmetric tensor of rank 2
(b) Antisymmetric tensor of rank 2
(c) Vector (tensor of rank 1)
(d) Scalar (tensor of rank 0)
Answer: (a)

131. The proper time interval between two events in special relativity is measured by an observer who:
(a) Is moving at the speed of light
(b) Is at rest relative to the events
(c) Views the events occurring at different spatial locations
(d) Accelerates uniformly between the events
Answer: (b)

132. The first-order correction to the ground state energy of a one-dimensional quantum harmonic oscillator subjected to a linear perturbation H' = cx is:
(a) c
(b) c²
(c) 0
(d) -c
Answer: (c)

133. The isotope effect in superconductivity demonstrates that the critical temperature (T_c) is inversely proportional to the isotopic mass (M) as T_c ∝ M^-α, where α is approximately:
(a) 1
(b) 1.5
(c) 0.5
(d) 2
Answer: (c)

134. For an inverting operational amplifier circuit with input resistance R_in and feedback resistance R_f, the closed-loop voltage gain is:
(a) R_f / R_in
(b) -R_f / R_in
(c) 1 + (R_f / R_in)
(d) -R_in / R_f
Answer: (b)

135. The dominant (lowest cutoff frequency) propagation mode in a standard air-filled rectangular waveguide is typically the:
(a) TM₁₁ mode
(b) TE₀₁ mode
(c) TE₁₀ mode
(d) TEM mode
Answer: (c)

136. At absolute zero temperature (0 K), the probability of finding an electron in an energy state exactly at the Fermi energy level (E = E_F) is mathematically defined as:
(a) 1
(b) 0
(c) 0.5 (by the limit of the distribution function)
(d) Infinite
Answer: (c)

137. The Normal Zeeman effect involves the splitting of a single spectral line into how many distinct components when viewed perpendicular to the magnetic field?
(a) 2
(b) 3
(c) 5
(d) 1
Answer: (b)

138. In the quark model of particle physics, quarks are hypothesized to possess an additional internal quantum number known as:
(a) Isospin
(b) Color charge
(c) Baryon number
(d) Hypercharge
Answer: (b)

139. The value of the Legendre polynomial P_n(x) at x = 1, i.e., P_n(1), is always equal to:
(a) 0
(b) n
(c) 1
(d) (-1)ⁿ
Answer: (c)

140. If a particle is moving exclusively under the influence of a central force field, which of its physical quantities remains strictly conserved?
(a) Linear velocity
(b) Linear momentum
(c) Angular momentum
(d) Kinetic energy
Answer: (c)

141. The eigenvalues of the Pauli spin matrix σ_z are:
(a) 0, 1
(b) +1, -1
(c) +i, -i
(d) 1/2, -1/2
Answer: (b)

142. For a one-dimensional crystal lattice of lattice constant 'a', the boundaries of the first Brillouin zone are located at k equal to:
(a) ± π/a
(b) ± 2π/a
(c) ± π/2a
(d) 0
Answer: (a)

143. A semiconductor tunnel diode exhibits a unique electrical characteristic known as:
(a) Infinite resistance
(b) Negative dynamic resistance
(c) Perfect insulation
(d) Constant current output
Answer: (b)

144. To produce a circularly polarized electromagnetic wave, the phase difference between two orthogonal linearly polarized waves of equal amplitude must be:
(a) 0
(b) π / 4
(c) π / 2
(d) π
Answer: (c)

145. In statistical thermodynamics, the chemical potential (μ) of a photon gas in blackbody radiation is:
(a) Equal to its thermal energy kT
(b) Infinite
(c) Exactly zero
(d) Dependent entirely on the cavity volume
Answer: (c)

146. The rotational energy levels of a quantum rigid diatomic molecule are given by E_J = B J(J+1). The spacing between adjacent energy levels:
(a) Remains constant
(b) Decreases as J increases
(c) Increases linearly as J increases
(d) Is zero
Answer: (c)

147. The CPT theorem in particle physics asserts that all physical laws must remain invariant under the simultaneous transformation of:
(a) Charge conjugation, Parity, and Time reversal
(b) Color, Parity, and Time reversal
(c) Charge conjugation, Position, and Temperature
(d) Charge conjugation, Parity, and Translation
Answer: (a)

148. The value of the fine-structure constant (α) in atomic physics is approximately:
(a) 1 / 137
(b) 137
(c) 1 / 1836
(d) 1.022
Answer: (a)

149. The Geiger-Muller (GM) counter is generally unsuitable for accurately identifying the type of incident radiation because:
(a) It is too slow to register counts
(b) The output pulse height is independent of the initial ionization energy
(c) It can only detect alpha particles
(d) It requires a strong magnetic field to operate
Answer: (b)

150. A differential equation is called "linear" if the dependent variable and all its derivatives appear only in:
(a) The first degree (power of 1)
(b) The second degree
(c) Transcendental functions
(d) Products with each other
Answer: (a)

Punjab Board 8th Class Result 2026 ( Out Soon) Date : Check PSEB Roll Number Wise Result @ pseb.ac.in

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Punjab Board 8th Class Result 2026: Check PSEB Roll Number Wise Result @ pseb.ac.in

Published on March 17, 2026 | By PB.JOBSOFTODAY.IN Editorial Team

The wait is almost over for lakhs of students! The Punjab School Education Board (PSEB) is gearing up to announce the Punjab Board 8th Class Result 2026. Following the successful completion of the examinations held between February 17 and February 27, 2026, students and parents are eagerly anticipating the outcome. The board will publish the official PSEB Class 8 result online through its official portal at pseb.ac.in.