GATE Physics 2018
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GATE 2018 General Aptitude (GA) Set-4
Q. 1 – Q. 5 carry one mark each.
Q.1 “When she fell down the _______, she received many _______ but little help.”
The words that best fill the blanks in the above sentence are
(A) stairs, stares (B) stairs, stairs
(C) stares, stairs (D) stares, stares
Q.2 “In spite of being warned repeatedly, he failed to correct his _________ behaviour.”
The word that best fills the blank in the above sentence is
(A) rational (B) reasonable (C) errant (D) good
Q.3 For 0 ≤ x ≤ 2π, sin x and cos x are both decreasing functions in the interval ________.
π π 3π 3π
(A) (0, 2 ) (B) ( 2 , π) (C) (π, 2 ) (D) ( 2 , 2π)
Q.4 The area of an equilateral triangle is √3. What is the perimeter of the triangle?
(A) 2 (B) 4 (C) 6 (D) 8
Q.5 Arrange the following three-dimensional objects in the descending order of their volumes:
(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm
(ii) A cube of side 8 cm
(iii) A cylinder with base radius 7 cm and height 7 cm
(iv) A sphere of radius 7 cm
(A) (i), (ii), (iii), (iv)
(B) (ii), (i), (iv), (iii)
(C) (iii), (ii), (i), (iv)
(D) (iv), (iii), (ii), (i)
Q. 6 – Q. 10 carry two marks each.
Q.6 An automobile travels from city A to city B and returns to city A by the same route. The
speed of the vehicle during the onward and return journeys were constant at 60 km/h and
90 km/h, respectively. What is the average speed in km/h for the entire journey?
(A) 72 (B) 73 (C) 74 (D) 75
GA 1/2
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GATE 2018 General Aptitude (GA) Set-4
Q.7 A set of 4 parallel lines intersect with another set of 5 parallel lines. How many
parallelograms are formed?
(A) 20 (B) 48 (C) 60 (D) 72
Q.8 To pass a test, a candidate needs to answer at least 2 out of 3 questions correctly. A total of
6,30,000 candidates appeared for the test. Question A was correctly answered by 3,30,000
candidates. Question B was answered correctly by 2,50,000 candidates. Question C was
answered correctly by 2,60,000 candidates. Both questions A and B were answered
correctly by 1,00,000 candidates. Both questions B and C were answered correctly by
90,000 candidates. Both questions A and C were answered correctly by 80,000 candidates.
If the number of students answering all questions correctly is the same as the number
answering none, how many candidates failed to clear the test?
(A) 30,000 (B) 2,70,000 (C) 3,90,000 (D) 4,20,000
1
Q.9 If x 2 + x − 1 = 0 what is the value of x 4 + ?
x4
(A) 1 (B) 5 (C) 7 (D) 9
Q.10 In a detailed study of annual crow births in India, it was found that there was relatively no
growth during the period 2002 to 2004 and a sudden spike from 2004 to 2005. In another
unrelated study, it was found that the revenue from cracker sales in India which remained
fairly flat from 2002 to 2004, saw a sudden spike in 2005 before declining again in 2006.
The solid line in the graph below refers to annual sale of crackers and the dashed line refers
to the annual crow births in India. Choose the most appropriate inference from the above
data.
(A) There is a strong correlation between crow birth and cracker sales.
(B) Cracker usage increases crow birth rate.
(C) If cracker sale declines, crow birth will decline.
(D) Increased birth rate of crows will cause an increase in the sale of crackers.
END OF THE QUESTION PAPER
GA 2/2
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GATE 2018 Physics
Q. 1 – Q. 25 carry one mark each.
Q.1 The eigenvalues of a Hermitian matrix are all
(A) real
(B) imaginary
(C) of modulus one
(D) real and positive
Q.2 Which one of the following represents the 3p radial wave function of hydrogen atom? (a0 is
the Bohr radius)
(A) (B)
(C) (D)
Q.3 Given the following table,
Group I Group II
P: Stern-Gerlach experiment 1: Wave nature of particles
Q: Zeeman effect 2: Quantization of energy of electrons in the atoms
R: Frank-Hertz experiment 3: Existence of electron spin
S: Davisson-Germer experiment 4: Space quantization of angular momentum
which one of the following correctly matches the experiments from Group I to their
inferences in Group II?
(A) P-2, Q-3, R-4, S-1 (B) P-1, Q-3, R-2, S-4
(C) P-3, Q-4, R-2, S-1 (D) P-2, Q-1, R-4, S-3
Q.4 In spherical polar coordinates (r, θ, φ), the unit vector θ̂ at (10, π/4, π/2) is
(A) k̂ (B)
1
(ĵ + k̂ ) (C)
1
(−ĵ + k̂) (D)
1
(ĵ − k̂)
√2 √2 √2
PH 1/12
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GATE 2018 Physics
Q.5 The scale factors corresponding to the covariant metric tensor gij in spherical polar
coordinates are
(A) 1, r 2 , r 2 sin2 θ (B) 1, r 2 , sin2 θ (C) 1, 1, 1 (D) 1, r, r sin θ
Q.6 In the context of small oscillations, which one of the following does NOT apply to the
normal coordinates?
(A) Each normal coordinate has an eigen-frequency associated with it
(B) The normal coordinates are orthogonal to one another
(C) The normal coordinates are all independent
(D) The potential energy of the system is a sum of squares of the normal coordinates with
constant coefficients
Q.7 For the given unit cells of a two dimensional square lattice, which option lists all the
primitive cells?
(A) and (B) , and
(C) ,, and (D) ,,, and
Q.8 Among electric field (E⃗ ), magnetic field (B
⃗ ), angular momentum (L
⃗ ), and vector potential
(A), which is/are odd under parity (space inversion) operation?
(A) E⃗ only (B) E⃗ & A only (C) E⃗ & B
⃗ only ⃗ &L
(D) B ⃗ only
Q.9 The expression for the second overtone frequency in the vibrational absorption spectra of a
diatomic molecule in terms of the harmonic frequency ωe and anharmonicity constant xe is
(A) 2ωe (1 − xe ) (B) 2ωe (1 − 3xe ) (C) 3ωe (1 − 2xe ) (D) 3ωe (1 − 4xe )
Q.10 Match the physical effects and order of magnitude of their energy scales given below,
e2
where α = is fine structure constant; me and mp are electron and proton mass,
4πε0 ℏc
respectively.
Group I Group II
2 2
P: Lamb shift 1: ~O(α me c )
Q: Fine structure 2: ~O(α 4 me c 2 )
R: Bohr energy 3: ~O(α 4 me2 c 2 /mp )
S: Hyperfine structure 4: ~O(α 5 me c 2 )
(A) P-3, Q-1, R-2, S-4 (B) P-2, Q-3, R-1, S-4
(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-1, S-3
PH 2/12
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GATE 2018 Physics
Q.11 The logic expression A̅BC + A̅B̅ C + ABC̅ + AB̅ C̅ can be simplified to
(A) A XOR C (B) A AND C̅ (C) 0 (D) 1
Q.12 At low temperatures (T), the specific heat of common metals is described by (with α and β
as constants)
(A) α T + β T 3 (B) β T 3 (C) exp(−α/T) (D) α T + β T 5
Q.13 In a 2-to-1 multiplexer as shown below, the output X = A0 if C = 0, and X = A1 if C = 1.
C
A0
X
A1
Which one of the following is the correct implementation of this multiplexer?
(A) (B)
A0 A0
C X C X
A1 A1
(C) (D)
A0 A0
C X C X
A1 A1
Q.14 The elementary particle Ξ0 is placed in the baryon decuplet, shown below, at
(A) P (B) Q (C) R (D) S
PH 3/12
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GATE 2018 Physics
Q.15 The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is
(a0 is the Bohr radius)
(A) −3ea0 (B) zero (C) ea0 (D) 3ea0
Q.16 The high temperature magnetic susceptibility of solids having ions with magnetic moments
1
can be described by χ ∝ T+θ with T as absolute temperature and θ as constant. The three
behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described,
respectively, by
(A) θ < 0, θ > 0, θ = 0 (B) θ > 0, θ < 0, θ = 0
(C) θ = 0, θ < 0, θ > 0 (D) θ = 0, θ > 0, θ < 0
Q.17 Which one of the following is an allowed electric dipole transition?
(A) 1 S0 → 3 S1 (B) 2 P3/2 → 2 D5/2 (C) 2 D5/2 → 2 P1/2 (D) 3 P0 → 5 D0
Q.18 In the decay, μ + → e + + νe + X, what is X?
(A) γ (B) ν̅e (C) νμ (D) ν̅μ
Q.19 A spaceship is travelling with a velocity of 0.7c away from a space station. The spaceship
ejects a probe with a velocity 0.59c opposite to its own velocity. A person in the space station
would see the probe moving at a speed Xc, where the value of X is ________ (up to three
decimal places).
Q.20 For an operational amplifier (ideal) circuit shown below,
4 kΩ
2 kΩ +10 V
V1 -
V0
V2 + RL
5 kΩ
-10 V
if V1 = 1 V and V2 = 2 V, the value of V0 is ________V (up to one decimal place).
Q.21 An infinitely long straight wire is carrying a steady current I. The ratio of magnetic energy
density at distance r1 to that at r2 (= 2 r1 ) from the wire is ________.
PH 4/12
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GATE 2018 Physics
Q.22 A light beam of intensity I0 is falling normally on a surface. The surface absorbs 20% of the
intensity and the rest is reflected. The radiation pressure on the surface is given by X I0 ⁄c ,
where X is ________ (up to one decimal place). Here c is the speed of light.
Q.23 The number of independent components of a general electromagnetic field tensor is
________.
Q.24 If X is the dimensionality of a free electron gas, the energy (E) dependence of density of
1
states is given by E 2X−Y , where Y is ________.
Q.25 For nucleus 164Er, a Jπ = 2+ state is at 90 keV. Assuming 164Er to be a rigid rotor, the
energy of its 4+ state is ________ keV (up to one decimal place).
PH 5/12
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GATE 2018 Physics
Q. 26 – Q. 55 carry two marks each.
Q.26 Given V ⃗ 2 = −2î + 3ĵ + 2k̂, which one of the following V
⃗ 1 = î − ĵ and V ⃗ 3 makes
⃗ 1, V
(V ⃗ 2, V
⃗ 3) a complete set for a three dimensional real linear vector space ?
⃗ 3 = î + ĵ + 4k̂
(A) V ⃗ 3 = 2î − ĵ + 2k̂
(B) V
⃗ 3 = î + 2ĵ + 6k̂
(C) V ⃗ 3 = 2î + ĵ + 4k̂
(D) V
Q.27 An interstellar object has speed v at the point of its shortest distance R from a star of much
larger mass M. Given v 2 = 2 GM/R, the trajectory of the object is
(A) circle (B) ellipse (C) parabola (D) hyperbola
Q.28 A particle moves in one dimension under a potential V(x) = α|x| with some non-zero total
energy. Which one of the following best describes the particle trajectory in the phase
space?
(A) (B) (C) (D)
Q.29 Consider an infinitely long solenoid with N turns per unit length, radius R and carrying a
current I(t) = α cos ωt, where α is a constant and ω is the angular frequency. The
magnitude of electric field at the surface of the solenoid is
1 1
(A) 2 μ0 NRωα sin ωt (B) 2 μ0 ωNR cos ωt
(C) μ0 NRωα sin ωt (D) μ0 ωNR cos ωt
Q.30 A constant and uniform magnetic field B ⃗ = B0 k̂ pervades all space. Which one of the
following is the correct choice for the vector potential in Coulomb gauge?
(A) −B0 (x + y)î (B) B0 (x + y)ĵ (C) B0 xĵ 1
(D) − 2 B0 (xî − yĵ)
Q.31 If H is the Hamiltonian for a free particle with mass m, the commutator [x, [x, H]] is
(A) ℏ2 /m (B) −ℏ2 /m (C) −ℏ2 /(2m) (D) ℏ2 /(2m)
PH 6/12
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GATE 2018 Physics
Q.32 A long straight wire, having radius a and resistance per unit length r, carries a current I. The
magnitude and direction of the Poynting vector on the surface of the wire is
2
(A) I r⁄2πa , perpendicular to axis of the wire and pointing inwards
2
(B) I r⁄2πa , perpendicular to axis of the wire and pointing outwards
2
(C) I r⁄πa , perpendicular to axis of the wire and pointing inwards
2
(D) I r⁄πa , perpendicular to axis of the wire and pointing outwards
Q.33 Three particles are to be distributed in four non-degenerate energy levels. The possible
number of ways of distribution: (i) for distinguishable particles, and (ii) for identical Bosons,
respectively, is
(A) (i) 24, (ii) 4 (B) (i) 24, (ii) 20 (C) (i) 64, (ii) 20 (D) (i) 64, (ii) 16
Q.34 The term symbol for the electronic ground state of oxygen atom is
(A) 1S0 (B) 1D2 (C) 3P0 (D) 3P2
Q.35 The energy dispersion for electrons in one dimensional lattice with lattice parameter a is
1
given by E(k) = E0 − 2 W cos ka, where W and E0 are constants. The effective mass of
the electron near the bottom of the band is
2ℏ2 ℏ2 ℏ2 ℏ2
(A) (B) (C) (D)
Wa2 Wa2 2Wa2 4Wa2
Q.36 Amongst electrical resistivity (ρ), thermal conductivity (κ), specific heat (C), Young’s
modulus (Y), and magnetic susceptibility (χ), which quantities show a sharp change at the
superconducting transition temperature?
(A) ρ, κ, C, Y (B) ρ, C, χ (C) ρ, κ, C, χ (D) κ, Y, χ
PH 7/12
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GATE 2018 Physics
Q.37 A quarter wave plate introduces a path difference of λ/4 between the two components of
polarization parallel and perpendicular to the optic axis. An electromagnetic wave with
E⃗ = (x̂ + ŷ) E0 e i(kz−ωt) is incident normally on a quarter wave plate which has its optic
axis making an angle 135° with the x-axis as shown.
The emergent electromagnetic wave would be
(A) elliptically polarized
(B) circularly polarized
(C) linearly polarized with polarization as that of incident wave
(D) linearly polarized but with polarization at 90° to that of the incident wave
Q.38 A p-doped semiconductor slab carries a current I = 100 mA in a magnetic field B = 0.2 T
as shown. One measures Vy = 0.25 mV and Vx = 2 mV. The mobility of holes in the
semiconductor is ________ m2V–1s–1 (up to two decimal places).
PH 8/12
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GATE 2018 Physics
Q.39 An n-channel FET having Gate-Source switch-off voltage VGS(OFF) = – 2 V is used to invert
a 0 – 5 V square-wave signal as shown. The maximum allowed value of R would be
________ k (up to two decimal places).
+5V
5 kΩ
Vin R Vout
5V 5V
0V
0V 100 Ω
1 kΩ
- 12 V
Q.40 Inside a large nucleus, a nucleon with mass 939 MeVc–2 has Fermi momentum 1.40 fm–1 at
absolute zero temperature. Its velocity is Xc, where the value of X is ________ (up to two
decimal places).
(ℏc = 197 MeV-fm)
Q.41 4 MeV γ-rays emitted by the de-excitation of 19F are attributed, assuming spherical
symmetry, to the transition of protons from 1d3/2 state to 1d5/2 state. If the contribution of
spin-orbit term to the total energy is written as C〈l ⋅ s〉, the magnitude of C is ________
MeV (up to one decimal place).
Q.42 An α particle is emitted by a 230
90Th nucleus. Assuming the potential to be purely
Coulombic beyond the point of separation, the height of the Coulomb barrier is
________ MeV (up to two decimal places).
e2
(4πε = 1.44 MeV-fm, r0 = 1.30 fm)
0
Q.43 For the transformation
Q = √2q e −1+2α cos p, P = √2q e −α−1 sin p
(where α is a constant) to be canonical, the value of α is________.
PH 9/12
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GATE 2018 Physics
Q.44 Given
d 2 f(x) df(x)
2
−2 + f(x) = 0,
dx dx
and boundary conditions f(0) = 1 and f(1) = 0, the value of f(0.5) is ________ (up to
two decimal places).
Q.45 The absolute value of the integral
5z 3 + 3z 2
∫ dz,
z2 − 4
over the circle |z − 1.5| = 1 in complex plane, is ________ (up to two decimal places).
Q.46 A uniform circular disc of mass m and radius R is rotating with angular speed ω about an
axis passing through its center and making an angle θ = 30∘ with the axis of the disc. If the
kinetic energy of the disc is αmω2 R 2, the value of α is ________ (up to 2 decimal places).
Q.47 The ground state energy of a particle of mass m in an infinite potential well is E0 . It
changes to E0 (1 + α × 10−3 ), when there is a small potential bump of height
π 2 ℏ2
V0 = and width a = L/100, as shown in the figure. The value of α is ________ (up
50mL2
to two decimal places).
PH 10/12
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GATE 2018 Physics
Q.48 An electromagnetic plane wave is propagating with an intensity I = 1.0 × 105 Wm–2 in a
medium with ε = 3ε0 and μ = μ0 . The amplitude of the electric field inside the medium is
________ × 103 Vm–1 (up to one decimal place).
(ε0 = 8.85 × 10−12 C2 N–1 m–2, μ0 = 4π × 10−7NA–2, c = 3 × 108 ms–1)
Q.49 A microcanonical ensemble consists of 12 atoms with each taking either energy 0 state, or
energy ε state. Both states are non-degenerate. If the total energy of this ensemble is 4ε, its
entropy will be ________ kB (up to one decimal place), where kB is the Boltzmann
constant.
Q.50 A two-state quantum system has energy eigenvalues ±ε corresponding to the normalized
1
states |ψ± ⟩. At time t = 0, the system is in quantum state [|ψ+ ⟩ + |ψ− ⟩]. The
√2
probability that the system will be in the same state at t = ℎ/(6ε) is ________ (up to two
decimal places).
Q.51 An air-conditioner maintains the room temperature at 27 oC while the outside temperature
is 47 oC. The heat conducted through the walls of the room from outside to inside due to
temperature difference is 7000 W. The minimum work done by the compressor of the air-
conditioner per unit time is ________ W.
Q.52 Two solid spheres A and B have same emissivity. The radius of A is four times the radius of
B, and temperature of A is twice the temperature of B. The ratio of the rate of heat radiated
from A to that from B is ________.
Q.53 The partition function of an ensemble at a temperature T is
ε N
Z = (2 cosh ) ,
kB T
ε
where kB is the Boltzmann constant. The heat capacity of this ensemble at T = k is
B
X NkB , where the value of X is ________ (up to two decimal places).
Q.54 An atom in its singlet state is subjected to a magnetic field. The Zeeman splitting of its
650 nm spectral line is 0.03 nm. The magnitude of the field is ________ Tesla (up to two
decimal places).
( e = 1.60 × 10−19 C, me = 9.11 × 10−31 kg, c = 3.0 × 108 ms–1)
PH 11/12
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GATE 2018 Physics
Q.55 The quantum effects in an ideal gas become important below a certain temperature TQ
when de Broglie wavelength corresponding to the root mean square thermal speed
becomes equal to the inter-atomic separation. For such a gas of atoms of mass 2 × 10−26
kg and number density 6.4 × 1025 m–3, TQ = __________ × 10−3 K (up to one decimal
place).
(kB = 1.38 × 10−23 J/K, ℎ = 6.6 × 10−34 J-s)
END OF THE QUESTION PAPER
PH 12/12
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Q.No. Type Section Key/Range Marks 1 MCQ GA A 1 2 MCQ GA C 1 3 MCQ GA B 1 4 MCQ GA C 1 5 MCQ GA D 1 6 MCQ GA A 2 7 MCQ GA C 2 8 MCQ GA D 2 9 MCQ GA C 2 10 MCQ GA A 2 1 MCQ PH A 1 2 MCQ PH B 1 3 MCQ PH C 1 4 MCQ PH D 1 5 MCQ PH D 1 6 MCQ PH B 1 7 MCQ PH C 1 8 MCQ PH B 1 9 MCQ PH D 1 10 MCQ PH C 1 11 MCQ PH A 1 12 MCQ PH A 1 13 MCQ PH A 1 14 MCQ PH C 1
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Q.No. Type Section Key/Range Marks 15 MCQ PH B 1 16 MCQ PH C 1 17 MCQ PH B 1 18 MCQ PH D 1 19 NAT PH 0.185 to 0.189 1 20 NAT PH ‐3.7 to ‐3.5 1 21 NAT PH 4 to 4 1 22 NAT PH 1.8 to 1.8 1 23 NAT PH 6 to 6 1 24 NAT PH 1 to 1 1 25 NAT PH 297.0 to 300.1 1 26 MCQ PH D 2 27 MCQ PH C 2 28 MCQ PH A 2 29 MCQ PH A 2 30 MCQ PH C 2 31 MCQ PH B 2 32 MCQ PH A 2 33 MCQ PH C 2 34 MCQ PH D 2 35 MCQ PH A 2 36 MCQ PH B 2 37 MCQ PH C 2 38 NAT PH 1.55 to 1.58 2
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Q.No. Type Section Key/Range Marks 39 NAT PH 0.70 to 0.73 2 40 NAT PH 0.28 to 0.31 2 41 NAT PH 1.6 to 1.6 2 42 NAT PH 24.4 to 27.6 2 43 NAT PH 2 to 2 2 44 NAT PH 0.81 to 0.84 2 45 NAT PH 81.60 to 81.80 2 46 NAT PH 0.21 to 0.23 2 47 NAT PH 0.78 to 0.82 2 48 NAT PH 6.5 to 6.7 2 49 NAT PH 6.1 to 6.3 2 50 NAT PH 0.25 to 0.25 2 51 NAT PH 466 to 467 2 52 NAT PH 256 to 256 2 53 NAT PH 0.41 to 0.43 2 54 NAT PH 1.51 to 1.53 2 55 NAT PH 78 to 90 2
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Source: GATE. Question paper published by GATE.