GATE 2027 Sample Paper (Physics - PH)

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

GATE 2027 (Physics - PH)
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME

65 100 180 Min

GENERAL INSTRUCTIONS

1. This paper contains 65 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 or 2 marks (varies by question); for a multiple-choice question, one-third (1-mark
question) or two-thirds (2-mark question) of the allotted marks is deducted for a wrong answer; numerical-answer-type
questions carry no negative marking.

4. Total time allowed is 180 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

GATE 2027 (Physics - PH)
SAMPLE QUESTION PAPER

Questions 65 Max Marks 100 Time 180 Min

Attempt all questions. Choose the one correct option for each.

GENERAL APTITUDE

1. One percent of the people of country X are taller than 2. The product of three integers X, Y and Z is 192. Z is
6 ft. Two percent of the people of country Y are taller equal to 4 and P is equal to the average of X and Y. What
than 6 ft. There are thrice as many people in country X as is the minimum possible value of P?
in country Y. Taking both countries together, what is the
(A) 6
percentage of people taller than 6 ft?
(B) 7
(A) 3.0
(C) 8
(B) 2.5
(D) 9.5
(C) 1.5

(D) 1.25

3. When he did not come home, she _________ him lying 4. Fiscal deficit was 4% of the GDP in 2015 and that
dead on the roadside somewhere. increased to 5% in 2016. If the GDP increased by from
2015 to 2016, the percentage increase in the actual fiscal
(A) concluded
deficit is
(B) looked
(A) 37.50
(C) notice
(B) 35.70
(D) pictured
(C) 25.00

(D) 10.00

5. Two cars Start at the same time from the same 6. ________ I permitted him to leave,I wouldn't have had
location and go in the same direction. The speed Of the any problem with him being absent, _______ I?
first car is 50 km/h and the speed Of the second car is 60
(A) Had, wouldn't
km/h. The number Of hours it takes for the distance
(B) Have, would
between the two cars to be 20 km is _____ .
(C) Had, would
(A) 1
(D) Have, wouldn't
(B) 2

(C) 3

(D) 6

7. The Fishermen, ___________ the flood victims owed their
lives, were rewarded by the government.

(A) whom

(B) to which

(C) to whom

(D) that

8. Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total Of USD 3000
for the consultants. P stopped working when the hour hand moved by 210 degrees on the clock. Q stopped working

when the hour hand moved by 240 degrees. P took two tea breaks Of 15 minutes each during her shift, but took no
lunch break. Q took only one lunch break for 20 minutes, but no tea breaks. The market rate for consultants are USD
200 per hour and breaks are not paid. After paying the consultants, the client shall have USD _______ remaining in the
budget.

(A) 000.00

(B) 166.67

(C) 300.00

(D) 433.33

9. 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.

10. A final examination is the __________ of a series of
evaluations that a student has to go through.

(A) culmination

(B) consultation

(C) desperation

(D) insinuation

PHYSICS

11. The Poisson bracket x, xP + yP is equal to 12. In the nuclear reaction 13 C +v arrow13 N +X , the
y x 6 e 7
particle X is
(A) - x

(B) y (A) an electron

(C) 2p (B) an anti-electron
x
(D) P (C) a muon
y
(D) a pion

13. The internal energy U of a system is given by U (S,V) 14. In the context of small oscillations, which one of the
= λ V-2 / 3 S2 where λ is a constant of appropriate following does NOT apply to the normal coordinates?
dimensions; V and S denote the volume and entropy,
(A) Each normal coordinate has an eigen-frequency
respectively. Which one of the following gives the correct
associated with it
equation of state of the system?
(B) The normal coordinates are orthogonal to one another
(A) P V1 / 3T2 = constant
(C) The normal coordinates are all independent
(B) P VT1 / 3 = constant
(D) The potential energy of the system is a sum of squares
(C) PV1 / 3 T = constant of the normal coordinates with constant coefficients.
(D) P V2 / 3T2 = constant

15. Let a and a + , respectively denote the lowering and
raising operators of a one- dimensional simple harmonic
oscillator. Let |In> be the energy eigenstate of the simple
harmonic oscillator. Given that |In> is also an eigenstate
of , a* a a a the corresponding eigenvalue is
16.
(A) n(n-1)

(B) n(n+1)

(C) (n+1)2

(D) (n)2

(A)

(B)

(C)

(D)

18. The intrinsic/permanent electric dipole moment in
the ground state of hydrogen atom is ( ��0 is the Bohr
radius)

(A) −3����0

(B) zero
17.
(C) ����0

(D) 3����0
(A) 1.4 to 1.9

(B) 1.5 to 1.8

(C) 1.4 to 1.6

(D) 1.4 to 1.7

19. Using Hund's rule. the total angular momentum 20. As shown in the figure, an ideal gas is confined to
quantum number J for the electronic ground state of the chamber A of an insulated container, with vacuum in
nitrogen atom is chamber B. When the plug in the wall separating the
chambers A and B is removed, the gas fills both the
(A) 1/2
chambers. Which one of the following statements is true?
(B) 3/2
(A) The temperature of the gas remains unchanged
(C) 0
(B) Internal energy of the gas decreases
(D) 1
(C) Temperature of the gas decreases as it expands to fill
the space in chamber B

(D) Internal energy of the gas increases as its atoms have
more space to move around

21. The scale factors corresponding to the covariant 22. An unpolarized light wave is incident from air on a
metric tensor ������ in spherical polar coordinates are: glass surface at the Brewster angle. The angle between
the reflected and the refracted wave is
(A) 1, ��2, ��2 sin2 ��

(B) 1, ��2, sin2 �� (A) 0°

(C) 1, 1, 1 (B) 45°

(D) 1, ��, �� sin �� (C) 90°

(D) 120°

23.  Which one of the following is a solution of d2 u(x)d x2 24. The value of the magnetic field required to maintain
=k2 u(x) for k real? non-relativistic protons of energy 1 MeV in a circular
orbit of radius 100 mm is ______________ Tesla. (Given: m
(A) e-kx p
= 1.67 * 10-27 kg, e = 1.6 * 10-19 C)
(B) sink x
(A) 1.41 to 1.47
(C) cosk x
(B) 1.48 to 1.49
(D) sinh x
(C) 1.51 to 1.60

(D) 1.41 to 1.43

25. The wavefunction of which orbital is spherically 26. Which one of the following is a universal logic gate?
symmetric:
(A) AND
(A) P (B) NOT
x
(B) P (C) OR
y
(C) s (D) NAND
(D) d
xy

27. The pole of the function ��(��) = cot �� at �� = 0 is 28. Low energy collision (s-wave scattering) of pion π+
with deuteron (d) results in the production of two
(A) a removable singularity
protons π+ + �� → �� + ��). The relative orbital angular
(B) an essential singularity
momentum (in units of ℏ) of the resulting two-proton
(C) a simple pole system for this reaction is
(D) a second order pole
(A) 0

(B) 1

(C) 2

(D) 3

29. For a gas under isothermal conditions, its pressure P 30. A large number �� of ideal bosons, each of mass m, are
varies with volume V as P ∝ V −5/3. The bulk modulus B is trapped in a three-dimensional potential V(r)=m ω2 r22 ,
proportional to The bosonic system is kept at temperature �� which is
much lower than the Bose-Einstein condensation
(A) V −1/2
temperature ����. The chemical potential (��) satisfies
(B) V −2/3
(A) μ ≤ (3)/(2) ℏ ω
(C) V −3/5
(B) 2 h ω>μ>(3)/(2) h ω
(D) V −5/3
(C) 3 ℏ ω>μ>2 ℏ ω

(D) μ=3 ℏ ω

31. Which one of the following operators is Hermitian? 32. A one dimensional simple harmonic oscillator with
Hamiltonian H =p22 m+(1)/(2) k x2 subjected to a small
(A) i (p x2-x2 p )2 0
x x
perturbation,H = α x+β x3+γ x4 . The order connection
1
(B) i (p x2+x2 p )2
x x to the ground state energy is dependent on
(C) ei p a
x
(A) only β
(D) e-i p a
x
(B) α and γ

(C) α and β

(D) only γ

33. Consider a one-dimensional non-magnetic crystal 34. A particle X is produced in the process π++p arrow K
with one atom per unit cell. Assume that the valence ++X via the strong interaction. If the quark content of

electrons (i) do not interact with each other and (ii) the K+ is u s , the quark content of X is
interact weakly with the ions. If n is the number of
(A) c s
valence electrons per unit cell, then at 0 K,
(B) u u d
(A) the crystal is metallic for any value of n
(C) u u s
(B) the crystal is non-metallic for any value of n
(D) u d
(C) the crystal is metallic for even values of n

(D) the crystal is metallic for odd values of n

36. The expression for the second overtone frequency in
the vibrational absorption spectra of a diatomic molecule
35. in terms of the harmonic frequency ���� and anharmonicity
constant ���� is

(A) 2����(1 − ����)

(A) (B) 2����(1 − 3����)

(C) 3����(1 − 2����)

(D) 3����(1 − 4����)

(B)

(C)

(D)

37. In order to measure a maximum of 1V with a 38. If the half-life of an elementary particle moving with
resolution of 1mV using a n-bit A/D converter, working speed 0.9c in the laboratory frame is 5 × 10−8 s, then the
under the principle of ladder network, the minimum value proper half-life is __________ × 10−8 s. (cc = 3 × 108
of n is _____________ . mm/ss)

(A) 9.99 to 10.01 (A) 2.1 to 2.3

(B) 10.01 to 10.02 (B) 2.2 to 2.3

(C) 9.99 to 10.0 (C) 2.0 to 2.1

(D) 9.98 to 9.99 (D) 2.3 to 2.4

39. Consider the motion of a particle along the x-axis in a 40. The minimum number of flip-flops required to
potential ��(��) = ��|��|. Its ground state energy ��૦ is estimated
construct a mod-75 counter is _______.
using the uncertainty principle. Then ��0 is proportional to
(A) 6.99 to 7.00
(A) F(1)/(3) (B) 6.99 to 7.01
(B) F(1)/(2) (C) 7.01 to 7.03
(C) F(2)/(5) (D) 6.99 to 7.03
(D) F(2)/(3)

41. A 3-bit analog-to-digital converter is designed to 42. Consider a one-dimensional lattice with a weak
digitize analog signals ranging from 0 V to 10 V. For this periodic potential U(x)=U ((2 π x)/(a)) . The gap at the
0
converter, the binary output corresponding to an input of edge of the Brillouin zone (k=(π)/(a)) is:
6 V is
(A) U
0
(A) 011 (B) U 2
0
(B) 101 (C) 2U
0
(C) 100 (D) U 4
0
(D) 010

43. The donor concentration in a sample of n-type silicon 44. The vector potential inside a long solenoid, with n
is increased by a factor of 100. The shift in the position of turns per unit length and carrying current ��, written in
the Fermi level at 300 K, assuming the sample to be non cylindrical coordinates is A (��, ��, ��) =��₀���� . If the
n I2
term μ
0
degenerate is __________ meV. (k T = 25 me V at 300 K) s(α φ φ+β φ s) , where �� ≠ 0 , �� ≠ 0, is added to A (��, ��, ��), the
B
magnetic field remains the same if
(A) 117 to 120

(B) 115 to 117 (A) �� = ��

(C) 114 to 117 (B) �� = −��

(D) 118 to 121 (C) �� = 2��

(D) �� =��/2

45. If the Lagrangian L =(1)/(2) m((d q)/(d t))2-(1)/(2) m
0
ω2 q2 which one of the following is TRUE? 46.

(A) Both the canonical momentum and equation of motion
(A) 34.9 to 35.1
do not change
(B) 34.9 to 35.0
(B) Canonical momentum changes, equation of motion does
(C) 35.0 to 35.1
not change
(D) 35.1 to 35.2
(C) Canonical momentum does not change, equation of
motion changes

(D) Both the canonical momentum and equation of motion
change

47. Neutrons moving with speed 103 m/s are used for the 48. At a given temperature, T, the average energy per
determination of crystal structure. If the Bragg angle for particle of a non-interacting gas of two-dimensional
the first order diffraction is 30°, the interplanar spacing classical harmonic oscillators is ________________ k T (k is
B B
of the crystal is _________ Å. (Given: mn = 1.675 × 10-27 the Boltzmann constant).
kg, ℎ=6.626 × 10-34J.s)
(A) 1.99 to 2.01
(A) 3.92 to 3.94 (B) 1.99 to 2.00
(B) 3.91 to 5.15 (C) 2.02 to 2.05
(C) 3.91 to 4.15 (D) 2.04 to 2.06
(D) 3.91 to 4.12

49. The number of normal Zeeman splitting components 50. Match the physical effects and order of magnitude of
of 1P → 1D transition is their energy scales given below, where �� = e²/4πε0hc is
fine structure constant; ���� and ���� are electron and proton
(A) 3
mass, respectively.
(B) 4
(A) P-3, Q-1, R-2, S-4
(C) 8
(B) P-2, Q-3, R-1, S-4
(D) 9
(C) P-4, Q-2, R-1, S-3

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

51. The elementary particle Ξ0 is placed in the baryon 52.  Identical charges q are placed at five vertices of a
decuplet, shown below, at regular hexagon of side a . The magnitude of the electric
field and the electrostatic potential at the centre of the
(A) P
hexagon are respectively
(B) Q
(A) 0,0
(C) R
(B) q4 π ε a2, q4 π ε a
(D) S 0 0
2
(C) q4 π ε a , 5 q4 π ε a
0 0
(D) √(5) q4 π ε a2, √(5) q4 π ε a
0 0

53. Which one of the following is a fermion?

(A) α particle

(B) Be7 nucleus 54.
4
(C) Hydrogen atom
(A) orthogonal
(D) Deuteron
(B) symmetric

(C) anti-symmetric

(D) unitary

55. Consider the Lagrangian L=a((d x)/(d t))2+b((d y)/(d 56. A particle is moving in a central force field given by
t))2+c x y where a, b and c are constants. If p and p are F=-kr3 r , where is the r unit vector pointing away from
x y
the momenta conjugate to the coordinates x and y the center of the field. The potential energy of the
respectively, then the Hamiltonian is particle is given by

(A) p 24 a+p 24 b-c x y (A) kr2
x y
(B) p 2 a+p 22 b-c x y
2 (B) k2r2
x y
(C) p 22 a+p 22 b+c x y (C) - kr2
x y
(D) p 2 a+p 2 b+c x y (D) - k2r2
x y

57. For the following circuit, the correct logic values for 58. Consider a one-dimensional gas of �� non-interacting
the entries X₂ and Y₂ in the truth table are particles of mass �� with the Hamiltonian for a single
particle given by, H=p22 m+(1)/(2) m ω2(x2+2 x) The
(A) 1 and 0
high temperature specific heat in units of �� = ������ (���� is the
(B) 0 and 0
Boltzmann constant) is
(C) 0 and 1
(A) 1
(D) 1 and 1
(B) 1.5

(C) 2

(D) 2.5

59. Which one of the following three-quark states (qqq), 60. The spin-orbit interaction term of an electron moving
denoted by X, CANNOT be a possible baryon? The in a central field is written as f(r) l · s , where r is the
corresponding electric charge is indicated in the radial distance of the electron from the origin. If an
superscript. electron moves inside a uniformly charged sphere, then

(A) X+ + (A) ��(��) = constant

(B) X+ (B) ��(��) ∝ ��−¹

(C) X- (C) ��(��) ∝ ��−²

(D) X- - (D) ��(��) ∝ ��−³

62.  The eigenvalues of a Hermitian matrix are all

(A) real

(B) imaginary

(C) of modulus one

61. (D) real and positive

(A) 2.2 to 2.4

(B) 2.3 to 2.4

(C) 2.1 to 2.3

(D) 2.5 to 2.7

63. The value of the integral ∫ ∞ (k x)x2+a2 d x , where 64. Choose the correct statement related to the Fermi
-∞
k >0 and a>0, is energy (E ) and the chemical potential ( �� ) of a metal.
F

(A) (π)/(a) e-k a (A) �� = Eonly at 0 K
F
(B) (2π)/(a) e-k a (B) �� = Eat finite temperature
F
(C) (π)/(2a) e-k a (C) �� Eat 0 K
F
(D) (3π)/(a) e-k a (D) �� > Eat finite temperature
F

65. For the differential equation d2 yd x2-n(n+1) yx2=0
where �� is a constant, the product of its two independent
solutions is

(A) 1/x

(B) x

(C) xn

(D) 1xm+1

ANSWER KEY

1. (D) 2. (B) 3. (D) 4. (A) 5. (B) 6. (C) 7. (C)

8. (B) 9. (C) 10. (A) 11. (B) 12. (A) 13. (A) 14. (B)

15. (A) 16. (A) 17. (D) 18. (B) 19. (B) 20. (A) 21. (D)

22. (C) 23. (A) 24. (A) 25. (C) 26. (D) 27. (C) 28. (B)

29. (D) 30. (A) 31. (A) 32. (D) 33. (D) 34. (C) 35. (A)

36. (D) 37. (A) 38. (A) 39. (D) 40. (B) 41. (C) 42. (A)

43. (C) 44. (D) 45. (B) 46. (A) 47. (C) 48. (A) 49. (A)

50. (C) 51. (C) 52. (C) 53. (B) 54. (D) 55. (A) 56. (D)

57. (A) 58. (A) 59. (D) 60. (A) 61. (B) 62. (A) 63. (A)

64. (A) 65. (B)