GATE 2020 PRACTICE
SET - 1
GENERAL APTITUDE
Q. 1 – Q. 5 carry one
mark each.
1. Which of the
following options is closest in meaning to the word given below?
Elegant
(a)
Unrefined (b) tasteless
(c) Inelegant (d) Graceful
2. The question
below consists of a pair of related words followed by four pair of words.
Select the pair which best expresses
the relation in the original pair.
Die : Dice
(a) Data:datas (b)
Mouse:mice
(c) monkey:monkeys (d) Dates: Datum
3. Choose the appropriate word/phrase, out of the four
options given below, to complete the following sentence:
![](file:///C:/Users/hp/AppData/Local/Temp/msohtmlclip1/01/clip_image003.png)
(a) harbours
(b)
leads to
(c) supports (d)
affects
4. Five teams have to compete in a league, with every team
playing every other team exactly once, before going to the next round. How many
matches will have to be held to complete the league round of matches?
(a) 20
(b) 10
(c) 8
(d)5
5. Tanya is older than eric.
Cliff is older than Tanya.
Eric is older than Cliff.
If the first two
statements are true, then the third statement is
(a) true
(b) false
(c) uncertain (d)
Data insufficient
6. In a country of 1400 million population, 70% own mobile
phones. Among the mobile
phone owners, only 294 million access the Internet. Among
these Internet users, only half
buy goods from e-commerce portals. What is the percentage of
these buyers in the country?
(A) 10.50 (B) 14.70
(C) 15.00 (D)
50.00
7. Since the last one year, after a 125 basis point
reduction in repo rate by the Reserve Bank
of India, banking institutions have been making a demand to
reduce interest rates on small
saving schemes. Finally, the government announced yesterday
a reduction in interest rates
on small saving schemes to bring them on par with fixed
deposit interest rates.
Which one of the following statements can be inferred from
the given passage?
(A)Whenever the Reserve Bank of India reduces the repo rate,
the interest rates on small
saving schemes are also reduced
(B) Interest rates on small saving schemes are always
maintained on par with fixed deposit
interest rates
(C) The government sometimes takes into consideration the
demands of banking
institutions before reducing the interest rates on small
saving schemes
(D)A reduction in interest rates on small saving schemes
follow only after a reduction in
repo rate by the Reserve Bank of India
8. The nomenclature of Hindustani music has changed over the
centuries. Since the medieval
period dhrupad styles were identified as baanis. Terms like
gayaki and baaj were used to
refer to vocal and instrumental styles, respectively. With
the institutionalization of music
education the term gharana became acceptable. Gharana
originally referred to hereditary
musicians from a particular lineage, including disciples and
grand disciples.
Which one of the following pairings is NOT correct?
(A) dhrupad, baani
(B) gayaki, vocal
(C) baaj, institution
(D) gharana, lineage
9. Two trains started at 7AM from the same point. The first
train travelled north at a speed of
80km/h and the second train travelled south at a speed of
100 km/h. The time at which they
were 540 km apart is ______ AM.
(A) 9 (B) 10 (C) 11 (D) 11.30
10. “I read somewhere that in ancient times the prestige of
a kingdom depended upon the
number of taxes that it was able to levy on its people. It
was very much like the prestige of
a head-hunter in his own community.”
Based on the paragraph above, the prestige of a head-hunter
depended upon ___________
(A) the prestige of the kingdom
(B) the prestige of the heads
(C) the number of taxes he could levy
(D) the number of heads he could gather
GATE 2020 PRACTICE SET - 1
PHYSICS
Q. 1 – Q. 25 carry
one mark each.
Q.1
A satellite is moving in a circular orbit around the Earth. If T, V and
E are its average kinetic, average potential and total energies, respectively,
then which one of the following options is correct?
(A) V=-2T, E=-T (B)
V= -T, E=0 (C) V= -T/2, E=T/2 (D) V=
-3T/2, E= -T/2
Q.2 The Pauli matrices for three spin-½ particles are 1 s , r 2 s
, r ands 3 r , respectively. The dimension of
the Hilbert space required to define an operator 12 3 Oˆ =s ×
´ s s
r r r
is __________
Q.3 The eigenvalues of a Hermitian matrix are all
(A) real (B) imaginary (C) of modulus one (D) real and
positive
Q.4 In spherical polar coordinates (𝑟, 𝜃,),
the unit vector 𝜃̂ at (10, 𝜋/4,
𝜋/2)
is
(A) 𝑘̂
(B) 1 √2 (𝑗̂+ 𝑘̂) (C) 1 √2 (−𝑗̂+ 𝑘̂) (D) 1 √2 (𝑗̂− 𝑘̂)
Q.5 The decay m
® + g
+ + e is forbidden, because it
violates
(A) momentum and lepton number conservations
(B) baryon and lepton number conservations
(C) angular momentum
conservation
(D) lepton number conservation
Q.6 Measurement of hall emf for a sample gives information
about
(a) magnitude & sign of the charge carriers
(b) sign of charge and density of carriers
(c) only sign of charge carriers
(d) only density of charge carriers
Q.7. In order to observe Raman effect the wavelength of the
source used
(a) should be in visible region
(b) should be in IR
(c) should be in UV
(d) may be in any region
Q.8. According to the non-electronic nature of nuclear
forces
(a) only neutrons exist
(b) only deuterons exist
(c) all exist
(d) none
Q.9 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.10 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) 2𝜔(1 − 𝑥𝑒)
(B) 2𝜔𝑒(1
− 3𝑥𝑒)
(C) 3𝜔𝑒(1
− 2𝑥𝑒)
(D) 3𝜔𝑒(1
− 4𝑥𝑒)
Q.11 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.12 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
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Q.13 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.14 The number of independent components of a general
electromagnetic field tensor is ________.
Q.15 If 𝑋 is the dimensionality of
a free electron gas, the energy (𝐸) dependence of density of
states is given by 𝐸 1 2 𝑋− , where 𝑌
is ________.
Q.16 For nucleus 164Er, a 𝐽 𝜋 =
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).
![](file:///C:/Users/hp/AppData/Local/Temp/msohtmlclip1/01/clip_image004.png)
![](file:///C:/Users/hp/AppData/Local/Temp/msohtmlclip1/01/clip_image005.png)
Q.19 An operator for a spin-½ particle is given by Aˆ = ls
×B r r
, where ( ), ˆ ˆ 2 B B xy =
+ r s
r denotes Pauli matrices
and l is a constant. The
eigenvalues of Aˆ are
(A) ±
l B / 2 (B) ± l B (C) 0, l B (D ) 0, -l B
Q.20 In Bose-Einstein condensates, the particles
(A) have strong interparticle attraction
(B) condense in real
space
(C) have overlapping
wavefuntions
(D) have large and
positive chemical potential
Q.21 For a black body radiation in a cavity, photons are
created and annihilated freely as a result of emission and absorption by the
walls of the cavity. This is because
(A) the chemical potential of the photons is zero
(B) photons obey
Pauli exclusion principle
(C) photons are
spin-1 particles
(D) the entropy of the photons is very large
Q.22 The energy dependence of the density of states for a
two dimensional non-relativistic electron gas is given by, g (E) = CEn , where C is constant.
The value of n is ______________
Q.23 The lattice parameters a, b, c of an orthorhombic
crystal are related by abc =
2 3 = . In units of a, the
interplanar separation between the (110) planes is __________ (upto three
decimal places)
Q.24 A point charge is placed between two semi-infinite conducting
plates which are inclined at an angle of 30o with respect to each other. The
number of image charges is ______________.
Q.25 The mean kinetic energy of a nucleon in a nucleus of
atomic weight A varies as An , where n is ______________ (upto two decimal
places)
Q. 26 – Q. 55 carry
two marks each.
Q.26 The excitation wavelength of laser in a Raman effect
experiment is 546 nm. If the Stokes’ line is observed at 552 nm, then the
wavenumber of the anti-Stokes’ line (in cm -1) is ___________
Q.27 The number of permitted transitions from 2 P3/2 ® 2 S1/2 in the presence of
a weak magnetic field is __________
Q.28 A long solenoid is embedded in a conducting medium and
is insulated from the medium. If the current through the solenoid is increased
at a constant rate, the induced current in the medium as a function of the
radial distance r from the axis of the solenoid is proportional to
(A) r
2inside the solenoid and 1/r outside (B) r inside the
solenoid and 1/r2
outside (C) r2 inside the solenoid and 1/r2
outside (D) r
inside the solenoid and 1/r
outside
Q.29 Match the phrases in Group I and Group II and identify
the correct option.
Group I
Group II
(P) Electron spin
resonance (ESR)
Q) Nuclear magnetic
resonance (NMR)
(R) Transition
between vibrational states of a molecule
(S) Electronic
transition
Group
II
(i) radio
frequency
(iii) microwave
frequency
(ii) visible range frequency
(iv) far-infrared range
Q.30 Consider the motion of the Sun with respect to the
rotation of the Earth about its axis. If Fc and FCo denote the centrifugal and
the Coriolis forces, respectively, acting on the Sun, then
(A) Fc is radially
outward and FCo = Fc
(B) Fc is radially
inward and FCo = Fc
(C) Fc is radially outward and FCo = Fc r
(D) Fc is radially outward
and FCo = Fc
Q.31 In a rigid-rotator of mass M, if the energy of the
first excited state is 1 meV, then the fourth excited state energy (in meV) is
_____________
Q.32 The average energy U of a one dimensional quantum
oscillator of frequency w
and in contact with a heat bath at temperature T is given by
Q.33 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.34 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.35 The term symbol for the electronic ground state of
oxygen atom is
(A) 𝑆 1 0 (B) 𝐷
1 2 (C) 𝑃 3 0 (D) 𝑃 3
2
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
Q.37 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.38 An 𝛼 particle is emitted by a
90Th 230 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)
Q.39 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.40 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 airconditioner per unit time is
________ W.
Q.41 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.42 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).
Q43. The Temperature of two identical gases is from initial
temperature to same final temperature. For gas A the process is carried out as
constant volume while for gas B it is carried at constant pressure. The change
in entropy
(a) Is greater for gas A
(b) Is greater for gas B
(c) same for A and B
(d) The entropies of
A and B do not change in these processes
Q.44 The contour integral of the function 1 z - 2 taken clockwise around
thee circle z = 5 is
(a) -
2p i (b) 4p i (c) 2- p i (d) zero
Q45. The rotational constant for HCI molecule is 1 10.5 cm- . The wave number (in 1
cm- ) of the third line in
the pure rotational spectra is
(a) 21.0 (b) 31.5 (c) 63.0 (d) 73.5
Q46. Consider two single-particle levels whose energies are e and -e . Into thee levels, we place two
electrons (no more than one electron of the same spin per level). The entropy
of system at T = 0 is
(a) 0 (b) ln 6 (c) ¥
(d) 1
Q47. Consider NaCl crystal, which is cubic with a lattice
spacing of , say, 0 1A (Angstrom). It has some free electrons captured within
the lattice. Estimate the longest wavelength of the light that such electron
can absorb:
(a) 1A (b) 2A (c)
100 A (d) 1000 A
Q48. For central potential V (r)=a/r2 where a is negative constant,
(a) Orbits are elliptical,
(b) Orbits are closed, but not elliptical
(c) There are no closed orbits
(d) The existence of
closed orbits depends on the total energy
Q49. The total number of 1’s in a 15 bit shift register is
to be counted by clocking into a counter which is preset to 0 . The counter
must have which one of the following:
(a) 4 - bits (b) 5 - bits (c) 16 - bits (d) 6 – bits
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GATE PHYSICS PRACTICE SET 1
Q50. A system of spin-half particles are placed in a uniform non-zero magnetic field. In the infinite temperature limit,
(a) all particles are in the higher energy state.
(b) one third of the
particles are in lower and two third in the higher energy state.
(c) all are in the
lower energy state.
(d) half the particles are in the lower and half in the
higher energy state.
Q51. According to the Debye theory for specific heat of
solids, the solid is an
(a) isotropic elastic medium and the motion of the atoms is
coupled
(b) anisotropic
elastic medium and the motion of the atoms l’s coupled
(c) isotropic elastic medium and the motion of the atoms is
not coupled
(d) anisotropic
elastic medium and the motion of the atoms is not coupled
Q52. The solution for the differential equation
D2y/dx2-2dy/dx+y=0
Is
(a) (a+bx )lnx (b)
(a+bx)ex (c) (a+bx2) e-x2 (d) (a+bx2) ex
Q53. For a nucleus having homogeneous spherical charge
distribution, what would be the nature of the corresponding nuclear Form
Factor?
(a) Exponential (b) Gaussian (c) Oscillating (d) Constant
Q54. Total energy of a simple pendulum E . When the
displacement is half of the amplitude, its potential energy is:
(a) E/4 (b) 3E/4 (c)
E (d) E/2
Q55. The direction of propagation of electromagnetic wave is
given by direction of:
(a) Vector E (b)
Vector H (c) Vector( E x H )(d) None of these
Q56. In the fission of 235U92 the mass
ratio of the fission fragment is 1:5 . What is the ratio of the velocities of
these fragments?
(a) 3:2 (b) 2:3 (c) 9:4 (d) 4:9
Q57. With the positive z -axis chosen to be upwards, the
Lagrangian of a particle of mass m falling under gravity is
Q58. If Hˆ and pˆ respectively denotes the Hamiltonian and the
momentum operator for a free particle, then the function sin kx and cos kx are
eigenfunctions
(a) of both Hˆ and pˆ (b) only of Hˆ but not of pˆ (c) only
of pˆ but not of Hˆ (d) of neither Hˆ nor p
Q59. Consider a 2 - dimensional electron gas with a density
of 1019 m-2 . The Fermi energy of
the system is…………………eV (up to two decimal places).
Q60. A free electron of energy 1eV is incident upon a
one-dimensional finite potential step of height 0.75eV . The probability of its
reflection from the barrier is…………. (up to two decimal places).
Q61. The imaginary part of an analytic complex function is
v(x,y)=2xy+3y . The real part of the function is zero at the origin. The value
of the real part of the function at 1+
i is ……………... (up to two decimal places)
Q62. J P
for the ground state of the 13C6 nucleus is
(a) 1+ (b) 3/ 2 -
(c) 3/ 2 +
(d) 1/ 2 -
Q63. A uniform solid cylinder is released on a horizontal
surface with speed 5 / m s without any rotation (slipping without rolling). The
cylinder eventually starts rolling without slipping. If the mass and radius of
the cylinder are 10 gm and 1cm respectively, the final linear velocity of the
cylinder is……………… m s/ . (up to two decimal places).
Q64. Using Hund’s rule the total angular momentum quantum
number J for the electronic ground state of the nitrogen atom is
(a) 1/ 2 (b) 3/ 2 (c) 0 (d) 1
Q65. Positronium is an atom made of an electron and a
positron. Given the Bohr radius for the ground state of the Hydrogen atom to be
0.53 Angstroms, the Bohr radius for the ground state of positronium
is…………Angstroms. (up to two decimal places).
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