GATE PHYSICS PRACTICE SET 1

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

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

3. Choose the appropriate word/phrase, out of the four options given below, to complete the following sentence:

Apparent lifelessness dormant life.

(a) harbours (b) leads to

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

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

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

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

(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

(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

(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

(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

(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

(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

(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).

Q.17 Coth z is singular points at .

Q.18 Homogeneity of time leads to conservation of .

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

(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

(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

(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) 𝑃³ 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

(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

(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.

(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

(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

(a) (a+bx )lnx (b) (a+bx)e^x (c) (a+bx²) e^-x2 (d) (a+bx²) e^x

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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Milan Tomic

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GATE PHYSICS PRACTICE SET 1

GATE PHYSICS PRACTICE SET 1

Milan Tomic

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GATE PHYSICS PRACTICE SET 1

GATE PHYSICS PRACTICE SET 1

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