Download GATE Previous Last 10 Years 2010-2020 PH Physics 2018 Question Paper With Solution And Answer Key

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GATE 2018
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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

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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 = 2p, sin x and cos x are both decreasing functions in the interval ___________.
(A) (0, p/2) (B) (p/2, p) (C) (p, 3p/2) (D) (3p/2, 2p)

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Q.4 The area of an equilateral triangle is v3. 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

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(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)

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(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?

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(A) 72 (B) 73 (C) 74 (D) 75

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

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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

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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

Q.9 If x² + x - 1 = 0 what is the value of x⁴ + 3x³?

(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

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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.

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(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

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Firstranker's choice
GATE 2018
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Q. 1 – Q. 25 carry one mark each.

Q.1 The eigenvalues of a Hermitian matrix are all

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(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) R(r)

0

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r/a₀

(B) R(r)

r/a₀

(C) R(r)

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0
r/a₀

(D) R(r)

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0
r/a₀

Q.3 Given the following table,
Group I
P: Stern-Gerlach experiment

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Q: Zeeman effect
R: Frank-Hertz experiment
S: Davisson-Germer experiment
Group II
1: Wave nature of particles

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2: Quantization of energy of electrons in the atoms
3: Existence of electron spin
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

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(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, ?, f), the unit vector ? at (10, p/4,p/2) is
(A) k (B) (î + j) / v2 (C)(î - j) / v2 (D)(-k)

Q.5 The scale factors corresponding to the covariant metric tensor g_ij in spherical polar coordinates are
(A) 1, r², r² sin² ? (B) 1, r², sin² 0

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(C) 1, 1, 1 (D) 1, r, r sin ?

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

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(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?
? ?

? ?

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?

(A) ? and ? (B) ?, ?, and ?
(C) ? and ? (D) ?.?.?.? and ?

Q.8 Among electric field (E), magnetic field (B), angular momentum (L), and vector potential (A), which is/are odd under parity (space inversion) operation?

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(A) E only (B) E & A only (C) E & B only (D) B & L 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 ?_e and anharmonicity constant x_e is
(A) 2?_e (1 - x_e) (B)3?_e(1-3x_e) (C) 3?_e(1 – 2x_e) (D) 3?_e(1 – 4x_e)

Q.10 Match the physical effects and order of magnitude of their energy scales given below, where a = e²/4pe0hc is fine structure constant; m_e and m_p are electron and proton mass, respectively.
Group I Group II

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P: Lamb shift 1: ~0(a⁴m_ec²)
Q: Fine structure 2: ~O(a⁵m_ec²)
R: Bohr energy 3: ~0(a⁴m_ec²/m_p)
S: Hyperfine structure 4: ~0(a²m_ec²)

(A) P-3, Q-1, R-2, S-4 (B) P-2, Q-3, R-1, S-4

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(C) P-4, Q-2, R-1, S-3 (D) P-2, Q-4, R-1, S-3

Q.11 The logic expression ABC + ABC + ABC + ABC can be simplified to
(A) A XOR C (B) A AND C (C) 0 (D) 1

Q.12 At low temperatures (T), the specific heat of common metals is described by (with a and ß as constants)
(?) a ? + ß ?³ (?) ß?³ exp(-a/T) (C) a? + ß ?⁵ (D) ß?⁵ exp(-a/T)

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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
A₁ X

Which one of the following is the correct implementation of this multiplexer?

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(A) Q.14 The elementary particle is placed in the baryon decuplet, shown below, at
++
Strangeness

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 ?) 3ea₀

Q.16 The high temperature magnetic susceptibility of solids having ions with magnetic moments

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T->8
can be described by ? ? C/(T+?) with T as absolute temperature and ? as constant. The three behaviors i.e. paramagnetic, ferromagnetic and anti-ferromagnetic are described, respectively, by
(A) ? < 0, ? > 0, 0 = 0 (?) ? > 0, ? < 0, 0 = 0
(C) 0 = 0, ? < 0, ? > 0 (D) 0 = 0, 0 > 0, ? < 0

Q.17 Which one of the following is an allowed electric dipole transition?

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(A) ¹ S₀? ³ S₁ (B) ² P_3/2 ? ²D_5/2 (C) ²D_5/2 ? ²P_1/2 (D) ³ P₀?⁵ D₀

Q.18 In the decay, µ⁺ ? e⁺ + ?_e + X, what is X?
(?) ? (B) ?_e (C) ?_µ (D) ?_µ

Q.19 A spaceship is travelling with a velocity of 0.7c opposite to its own velocity. A person in the space station 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 (ideal) circuit shown below,

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= 0); Assert(dstOffset >= 0); Assert(count >= 0); } } public static class String { public static bool IsNullOrEmpty(string value) { return (value == null || value.Length == 0); } }
} namespace System
{ public class Object { } public class Type { public string AssemblyQualifiedName { get; set; } } public class Array { public int Length { get; set; } public static void Reverse(Array array) { } } public class Exception : System.SystemException { public Exception(string message) : base(message) { } public Exception(string message, Exception innerException) : base(message, innerException) { } } public class SystemException : Exception { public SystemException(string message) : base(message) { } public SystemException(string message, Exception innerException) : base(message, innerException) { } } public struct Int32 { public static bool TryParse(string s, out Int32 result) { result = 0; return false; } }
}
namespace System.IO

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{ public class IOException : Exception { public IOException(string message) : base(message) { } public IOException(string message, Exception innerException) : base(message, innerException) { } } public class MemoryStream : Stream { public MemoryStream() { } public MemoryStream(byte[] buffer) { } public override void Write(byte[] buffer, int offset, int count) { } public override int Read(byte[] buffer, int offset, int count) { return 0; } public byte[] ToArray() { return null; } public override bool CanRead { get { return false; } } public override bool CanSeek { get { return false; } } public override bool CanWrite { get { return false; } } public override long Length { get { return 0; } } public override long Position { get; set; } public override void Flush() { } public override long Seek(long offset, SeekOrigin origin) { return 0; } public override void SetLength(long value) { } } public class Stream { public virtual bool CanRead { get { return false; } } public virtual bool CanSeek { get { return false; } } public virtual bool CanWrite { get { return false; } } public virtual long Length { get { return 0; } } public virtual long Position { get; set; } public virtual void Flush() { } public virtual int Read(byte[] buffer, int offset, int count) { return 0; } public virtual long Seek(long offset, SeekOrigin origin) { return 0; } public virtual void SetLength(long value) { } public virtual void Write(byte[] buffer, int offset, int count) { } } public enum SeekOrigin { Begin = 0, Current = 1, End = 2, } } namespace System.Collections.Generic
{ public interface IEnumerable { IEnumerator GetEnumerator(); } public interface IEnumerator { T Current { get; } bool MoveNext(); } public class List : IEnumerable { public List() { } public List(int capacity) { } public void Add(T item) { } public T this[int index] { get { return default(T); } set { } } public int Count { get; set; } public IEnumerator GetEnumerator() { return null; } } public class Dictionary { public void Add(TKey key, TValue value) { } public bool TryGetValue(TKey key, out TValue value) { value = default(TValue); return false; } public TValue this[TKey key] { get { return default(TValue); } set { } } public ICollection Keys { get { return null; } } public ICollection Values { get { return null; } } } public interface ICollection { void Add(T item); bool Contains(T item); void Clear(); int Count { get; } } public interface ICollection { }
} namespace System.Text
{ public class StringBuilder { public StringBuilder() { } public StringBuilder(string value) { } public StringBuilder Append(string value) { return null; } public StringBuilder Append(char value) { return null; } public override string ToString() { return null; } } public class Encoding { public static Encoding UTF8 { get { return null; } } public virtual byte[] GetBytes(string s) { return null; } public virtual string GetString(byte[] bytes) { return null; } }
} namespace firstranker.componentModel

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{ public class DefaultValueAttribute : Attribute { public DefaultValueAttribute(object value) { } }
}
#pragma warning restore 1591
#pragma warning restore 1573
#pragma warning restore 1584

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#pragma warning restore 1587
#pragma warning restore 0618
#pragma warning restore 0612
#pragma warning restore 618
#pragma warning restore 612

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#pragma warning restore 169
#pragma warning restore 649
#pragma warning restore 414 #pragma clang diagnostic pop
#pragma GCC diagnostic pop 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 _________.

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.

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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 states is given by E^x-Y, where Y is _________.

Q.25 For nucleus ¹⁶⁴Er, a J^p = 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. 26 – Q. 55 carry two marks each.

Q.26 Given V1 = î – î and V2 = -2î + 3j + 2k, which one of the following V3 makes (V1, V2, V3) a complete set for a three dimensional real linear vector space ?

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(A) V3 = î + j + 4k (B) V3 = 2î – j + 2k
(C) V3 = î + 2j + 6k (D) V3 = 2î + î + 4k

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 v² = 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) = a|x| with some non-zero total energy. Which one of the following best describes the particle trajectory in the phase space?

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(A) P

X

(B) P

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X

(C) P

X

(D) P

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X

Q.29 Consider an infinitely long solenoid with N turns per unit length, radius R and carrying a current I(t) = a cos ?t, where a is a constant and ? is the angular frequency. The magnitude of electric field at the surface of the solenoid is

(A) µ?NR?a sin ?t (B) NR cos ?t
(C) µ?NR?a sin ?t (D) µ?NR cos ?t

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Q.30 A constant and uniform magnetic field B = B0k 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)j (C) B0xj (D) -B0(xî – yj)

Q.31 If H is the Hamiltonian for a free particle with mass m, the commutator [x, [x, H]] is
(A) h²/m (B) -h²/m (C) -h²/(2m) (D) h²/(2m)

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

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(A) I²/2pa , perpendicular to axis of the wire and pointing inwards
(B) I²/2pa, perpendicular to axis of the wire and pointing outwards
(C) I²r/pa, perpendicular to axis of the wire and pointing inwards
(D) I²r/pa, 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

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(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 given by E(k) = E0 - W cos ka, where W and E0 are constants. The effective mass of the electron near the bottom of the band

(A) (B) (C) (D)

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Q.36 Amongst electrical resistivity (?), thermal conductivity (?), specific heat (C), Young's modulus (Y), and magnetic susceptibility (?), which quantities show a sharp change at the superconducting transition temperature?
(?) ?, ?, C, ? (?) ?, C, ? (C) ?, ?, C, ? (D) ?, ?, ?

Q.37 A quarter wave plate introduces a path difference of ?/4 between the two components of polarization parallel and perpendicular to the optic axis. An electromagnetic wave with
E = (x + yy) E0 e^i(kz-?t) is incident normally on a quarter wave plate which has its optic axis making an angle 135° with the x-axis as shown.
Optic axis

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-
?
135°
?X

The emergent electromagnetic wave would be

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(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 V_y = 0.25 mV and V_x = 2 mV. The mobility of holes in the semiconductor is _________ m²V^-1s^-1 (up to two decimal places).

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END OF THE QUESTION PAPER