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)eik·r where u(r) is arbitrary
(b) ψ(r) = u(r)eiG·r
(c) ψ(r) = u(r)eiG·r where u(r)=u(r+Λ)
(d) ψ(r) = u(r)eik·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
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.
