GATE Physics 2024
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Physics (PH)
General Aptitude (GA)
Q.1 – Q.5 Carry ONE mark Each
Q.1 If ‘→’ denotes increasing order of intensity, then the meaning of the words
[smile → giggle → laugh] is analogous to [disapprove → ________ → chide].
Which one of the given options is appropriate to fill the blank?
(A) reprove
(B) praise
(C) reprise
(D) grieve
Q.2 Find the odd one out in the set: {19, 37, 21, 17, 23, 29, 31, 11}
(A) 21
(B) 29
(C) 37
(D) 23
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Physics (PH)
Q.3 In the following series, identify the number that needs to be changed to form the
Fibonacci series.
1, 1, 2, 3, 6, 8, 13, 21,…
(A) 8
(B) 21
(C) 6
(D) 13
Q.4 The real variables x, y, z, and the real constants p, q, r satisfy
x y z
2
= 2
=
pq − r qr − p rp − q 2
Given that the denominators are non-zero, the value of px + qy + rz is
(A) 0
(B) 1
(C) pqr
(D) p2 + q 2 + r 2
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Physics (PH)
Q.5 Take two long dice (rectangular parallelepiped), each having four rectangular faces
labelled as 2, 3, 5, and 7. If thrown, the long dice cannot land on the square faces
and has 1/4 probability of landing on any of the four rectangular faces. The label on
the top face of the dice is the score of the throw.
If thrown together, what is the probability of getting the sum of the two long dice
scores greater than 11?
(A) 3/8
(B) 1/8
(C) 1/16
(D) 3/16
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Physics (PH)
Q.6 – Q.10 Carry TWO marks Each
Q.6 In the given text, the blanks are numbered (i)−(iv). Select the best match for all the
blanks.
(i) (ii)
Prof. P merely a man who narrated funny stories. in his blackest
moments he was capable of self-deprecating humor.
(iii) (iv)
Prof. Q a man who hardly narrated funny stories. in his blackest
moments was he able to find humor.
(A) (i) was (ii) Only (iii) wasn’t (iv) Even
(B) (i) wasn’t (ii) Even (iii) was (iv) Only
(C) (i) was (ii) Even (iii) wasn’t (iv) Only
(D) (i) wasn’t (ii) Only (iii) was (iv) Even
Q.7 How many combinations of non-null sets A, B, C are possible from the subsets of
{2, 3, 5} satisfying the conditions: (i) A is a subset of B, and (ii) B is a subset of C?
(A) 28
(B) 27
(C) 18
(D) 19
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Physics (PH)
Q.8 The bar chart gives the batting averages of VK and RS for 11 calendar years from
2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of
the following options is true?
140
120
Batting Average
100 VK RS
80
60
40
20
0
2012 2013 2014 2015 2016 2017 2018 2019 2020 2021 2022
Calendar Year
(A) RS has a higher yearly batting average than that of VK in every world cup year.
(B) VK has a higher yearly batting average than that of RS in every world cup year.
(C) VK’s yearly batting average is consistently higher than that of RS between the two
world cup years.
(D) RS’s yearly batting average is consistently higher than that of VK in the last three
years.
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Physics (PH)
Q.9 A planar rectangular paper has two V-shaped pieces attached as shown below.
This piece of paper is folded to make the following closed three-dimensional object.
The number of folds required to form the above object is
(A) 9
(B) 7
(C) 11
(D) 8
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Physics (PH)
Q.10 Four equilateral triangles are used to form a regular closed three-dimensional object
by joining along the edges. The angle between any two faces is
(A) 30°
(B) 60°
(C) 45°
(D) 90°
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Physics (PH)
Q.11 – Q.35 Carry ONE mark Each
Q.11 If F1 (Q, q) = Qq is the generating function of a canonical transformation from
(p, q) to (P, Q), then which one of the following relations is correct?
p Q
(A) =
P q
P Q
(B) =
p q
p Q
(C) =−
P q
P Q
(D) =−
p q
Q.12 An unpolarized plane electromagnetic wave in a dielectric medium 1 is incident on
a plane interface that separates medium 1 from another dielectric medium 2.
Medium 1 and medium 2 have refractive indices n1 and n2 , respectively, with
n
n2 > n1 . If the angle of incidence is tan−1 (n2 ), which one of the following
1
statements is true?
(A) The reflected wave is unpolarized
(B) The reflected wave is polarized parallel to the plane of incidence
(C) The reflected wave is polarized perpendicular to the plane of incidence
(D) There is no transmitted wave
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Physics (PH)
Q.13 The wavefunction of a particle in an infinite one-dimensional potential well at time
t is
2 1 iπ⁄6 −iE t⁄ℏ 1 iπ⁄4 −iE t⁄ℏ
Ψ(x, t) = √ e −iE1 t⁄ℏ ψ1 (x) + e e 2 ψ2 (x) + e e 3 ψ3 (x)
3 √6 √6
where ψ1 , ψ2 and ψ3 are the normalized ground state, the normalized first excited
state and the normalized second excited state, respectively. E1 , E2 and E3 are the
eigen-energies corresponding to ψ1 , ψ2 and ψ3 , respectively. The expectation value
of energy of the particle in state Ψ(x, t) is
(A) 17
E
6 1
(B) 2
E
3 1
(C) 3
E
2 1
(D) 14 E1
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Physics (PH)
Q.14 If a thermodynamical system is adiabatically isolated and experiences a change in
volume under an externally applied constant pressure, then the thermodynamical
potential minimized at equilibrium is the
(A) enthalpy
(B) Helmholtz free energy
(C) Gibbs free energy
(D) grand potential
Q.15 The mean distance between the two atoms of HD molecule is r, where H and D
denote hydrogen and deuterium, respectively. The mass of the hydrogen atom is
mH . The energy difference between two lowest lying rotational states of HD in
multiples of ℏ2 /(mH r 2 ) is
3
(A)
2
2
(B)
3
(C) 6
4
(D)
3
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Physics (PH)
Q.16 Crystal structures of two metals A and B are two-dimensional square lattices with
same lattice constant a. Electrons in metals behave as free electrons. The Fermi
surfaces corresponding to A and B are shown by solid circles in figures.
The electron concentrations in A and B are nA and nB , respectively. The value of
n
( B ) is
nA
(A) 3
(B) 2
(C) 3√3
(D) √2
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Physics (PH)
Q.17 Consider the induced nuclear fission reaction
235 93 141
92U + n → 37Rb + 55Cs + 2n
where neutron momenta in both initial and final states are negligible. The ratio of
the kinetic energies (KE) of the daughter nuclei,
93
KE( 37Rb)
KE( 141
55Cs)
is ___________
(A) 93
141
(B) 141
93
(C) 1
(D) 0
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Physics (PH)
Q.18 The symbols C, D, Vin and V0 shown in the figure denote capacitor, ideal diode,
input voltage and output voltage, respectively.
Which one of the following output waveforms (V0) is correct for the given input
waveform (Vin )?
(A)
(B)
(C)
(D)
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Physics (PH)
Q.19 Let Ne and Te , respectively, denote number and kinetic energy of electrons produced
in a nuclear beta decay. Which one of the following distributions is correct?
(A)
(B)
(C)
(D)
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Physics (PH)
Q.20 An infinitely long cylinder of radius R carries a frozen-in magnetization
⃗⃗ = ke −s ẑ , where k is a constant and s is the distance from the axis of cylinder.
M
The magnetic permeability of free space is μ0 . There is no free current present
anywhere. The magnetic flux density (B ⃗ ) inside the cylinder is
(A) 0
(B) μ0 ke −R ẑ
(C) μ0 ke −s ẑ
(D) R
μ0 ke −s ( ) ẑ
s
Q.21 Atomic numbers of V, Cr, Fe and Zn are 23, 24, 26 and 30, respectively. Which one
of the following materials does NOT show an electron spin resonance (ESR)
spectra?
(A) V
(B) Cr
(C) Fe
(D) Zn
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Physics (PH)
Q.22 A particle is subjected to a potential
∞, x≤0
V(x) = {V0 , a ≤ x ≤ b
0, elsewhere
Here, a > 0 and b > a. If the energy of the particle E < V0, which one of the
following schematics is a valid quantum mechanical wavefunction (Ψ) for the
system?
(A)
(B)
(C)
(D)
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Physics (PH)
Q.23 Let ρ(p, q , t) be the phase space density of an ensemble of a system.
The Hamiltonian of the system is H(p, q ). If {A, B} denotes the Poisson bracket of
A and B, then
dρ
=0
dt
implies
(A) ∂ρ
=0
∂t
(B) ∂ρ
∝ {ρ, H}
∂t
(C) ∂ρ p∙q
∝ {ρ, }
∂t 2
(D) ∂ρ q∙q
∝ {ρ, }
∂t 2
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Physics (PH)
Q.24 Consider the following circuit:
Suppose the input signal P is
and the input signal Q is
Which one of the following output signals is correct?
(A)
(B)
(C)
(D)
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Physics (PH)
Q.25 An inertial observer sees two spacecrafts S and T flying away from each other along
x-axis with individual speed 0.5c, where c is the speed of light. The speed of T with
respect to S is
(A) 4
c
5
(B) 4
c
3
(C) c
(D) 2
c
3
Q.26 Let P, Q and R be three different nuclei. Which one of the following nuclear
processes is possible?
(A) νe + AzP → z+1AQ + e −
(B) νe + AzP → z−1AR + e +
(C) νe + AzP → AzP + e + + e −
(D) νe + AzP → AzP + γ
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Physics (PH)
Q.27 The temperature dependence of the electrical conductivity (σ) of three intrinsic
semiconductors A, B and C is shown in figure.
Let EA , EB and EC be the bandgaps of A, B and C, respectively. Which one of the
following relations is correct?
(A) EC > EA > EB
(B) EB > EC > EA
(C) EA > EB > EC
(D) EA > EC > EB
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Physics (PH)
Q.28 Following trial wavefunctions
′
φ1 = e −Z (r1 +r2)
and
′
φ2 = e −Z (r1 +r2) (1 + g|r1 − r2 |)
are used to get a variational estimate of the ground state energy of the helium atom.
Z ′ and g are the variational parameters, r1and r2 are the position vectors of the
electrons. Let E0 be the exact ground state energy of the helium atom. E1 and E2 are
the variational estimates of the ground state energy of the helium atom
corresponding to φ1 and φ2 , respectively. Which one of the following options is
true?
(A) E1 ≤ E0 , E2 ≤ E0 , E1 ≥ E2
(B) E1 ≥ E0 , E2 ≤ E0 , E1 ≥ E2
(C) E1 ≤ E0 , E2 ≥ E0 , E1 ≤ E2
(D) E1 ≥ E0 , E2 ≥ E0 , E1 ≥ E2
Q.29 The wavefunction for a particle is given by the form e −(iαx+β) , where α and β are
real constants. In which one of the following potentials V(x), the particle is moving?
(A) V(x) ∝ α 2 x 2
(B) V(x) ∝ e −αx
(C) V(x) = 0
(D) V(x) ∝ sin(αx)
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Physics (PH)
Q.30 Consider a volume integral
1
I = ∫ ∇2 ( ) dV
V r
over a volume V, where r = √x 2 + y 2 + z 2 . Which of the following statement
is/are correct?
(A) I = −4π, if r = 0 is inside the volume V
(B) Integrand vanishes for r ≠ 0
(C) I = 0, if r = 0 is not inside the volume V
(D) Integrand diverges as r → ∞
Q.31 The complex function
2
−(z−1)
e
has __________
(A) a simple pole at z = 1
(B) an essential singularity at z = 1
(C) a residue equal to −2 at z = 1
(D) a branch point at z = 1
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Physics (PH)
Q.32 The minimum number of basic logic gates required to realize the Boolean
expression B ∙ (A + B) + A ∙ (B̅ + A) is _____ (in integer).
Q.33 3754
The vapor pressure (P) of solid ammonia is given by ln(P) = 23.03 − , while
T
3063
that of liquid ammonia is given by ln(P) = 19.49 − , where T is the
T
temperature in K.
The temperature of the triple point of ammonia is _____ K (rounded off to two
decimal places).
Q.34 The electric field in a region depends only on x and y coordinates as
(x x̂ + y ŷ )
E⃗ = k
x2 + y2
where k is a constant. The flux of E⃗ through the surface of a sphere of radius R with
its center at the origin is nπkR, where the value of n is _____ (in integer).
Q.35 The Hamiltonian of a system of N particles in volume V at temperature T is
2N 2N
H = ∑ ai qi2 + ∑ bi pi2
i=1 i=1
where ai and bi are positive constants. The ensemble average of the Hamiltonian is
αNkB T, where kB is the Boltzmann constant. The value of α is ____ (in integer).
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Physics (PH)
Q.36 – Q.65 Carry TWO marks Each
Q.36 Binding energy and rest mass energy of a two-nucleon bound state are denoted by
B and mc 2 , respectively, where c is the speed of light. The minimum energy of a
photon required to dissociate the bound state is
(A) B
(B) B
B (1 + )
2mc 2
(C) B
B (1 − )
2mc 2
(D) B − mc 2
Q.37 The spin-orbit interaction in a hydrogen-like atom is given by the Hamiltonian
⃗ ∙S
H ′ = −kL
where k is a real constant. The splitting between levels 2p3/2 and 2p1/2 due to this
interaction is
(A) 1 2
kℏ
2
(B) 3 2
kℏ
2
(C) 3 2
kℏ
4
(D) 2kℏ2
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Physics (PH)
Q.38 Consider the Lagrangian L = mẋ ẏ − mω02 xy. If px and py denote the generalized
momenta conjugate to x and y, respectively, then the canonical equations of motion
are
(A) px py
ẋ = , ṗx = −mω02 x , ẏ = , ṗy = −mω02 y
m m
(B) px py
ẋ = , ṗx = mω02 x , ẏ = , ṗy = mω02 y
m m
(C) py px
ẋ = , ṗx = −mω02 y , ẏ = , ṗy = −mω02 x
m m
(D) py px
ẋ = , ṗx = mω02 y , ẏ = , ṗy = mω02 x
m m
Q.39 The X-ray diffraction pattern of a monatomic cubic crystal with rigid spherical
atoms of radius 1.56 Å shows several Bragg reflections of which the reflection
appearing at the lowest 2θ value is from (111) plane. If the wavelength of X-ray
used is 0.78 Å, the Bragg angle (in 2θ, rounded off to one decimal place)
corresponding to this reflection and the crystal structure, respectively, are
(A) 21.6 and body centered cubic
(B) 17.6 and face centered cubic
(C) 10.8 and body centered cubic
(D) 8.8 and face centered cubic
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Physics (PH)
Q.40 In a parallel plate capacitor, the plate at x = 0 is grounded and the plate at x = d is
maintained at a potential V0. The space between the two plates is filled with a linear
x
dielectric of permittivity ε = ε0 (1 + d), where ε0 is the permittivity of free space.
Neglecting the edge effects, the electric field (E⃗ ) inside the capacitor is
(A) V0
− x̂
(d + x) ln 2
(B) V0
− x̂
d
(C) V0
− x̂
(d + x)
(D) V0 d
− x̂
(d + x)x
Q.41 The equation of motion for the forced simple harmonic oscillator is
ẍ (t) + ω2 x(t) = F cos(ωt)
where x(t = 0) = 0 and ẋ (t = 0) = 0. Which one of the following options is
correct?
(A) x(t) ∝ t sin(ωt)
(B) x(t) ∝ t cos(ωt)
(C) x(t) = ∞
(D) x(t) ∝ e ωt
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Physics (PH)
Q.42 An atom is subjected to a weak uniform magnetic field B ⃗ . The number of lines in
its Zeeman spectrum for transition from n = 2, l = 1 to n = 1, l = 0 is
(A) 8
(B) 10
(C) 12
(D) 5
Q.43 1 2 1 0
Consider two matrices: P = [ ] and Q = [ ].
0 1 0 1
Which of the following statement is/are true?
(A) P and Q have same set of eigenvalues
(B) P and Q commute with each other
(C) P and Q have different sets of linearly independent eigenvectors
(D) P is diagonalizable
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Physics (PH)
Q.44 An infinite one dimensional lattice extends along x-axis. At each lattice site there
1
exists an ion with spin 2 . The spin can point either in +z or – z direction only. Let
SP, SF, and SA denote the entropies of paramagnetic, ferromagnetic and
antiferromagnetic configurations, respectively. Which of the following relation
is/are true?
(A) SP > SF
(B) SA > S F
(C) SA = 4 S F
(D) SP > SA
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Physics (PH)
Q.45 Consider a vector field F = (2xz + 3y 2 )ŷ + 4yz 2 ẑ . The closed path
(Γ: A → B → C → D → A) in z = 0 plane is shown in figure.
∮Γ F . ⃗⃗⃗
dl denotes the line integral of F along the closed path Γ. Which of the
following option is/are true?
MSQ
(A)
∮ F . ⃗⃗⃗
dl = 0
Γ
(B) F is non-conservative
(C) ⃗∇. F = 0
(D) F can be written as the gradient of a scalar field
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Physics (PH)
Q.46 Two point charges of charge +q each are placed a distance 2d apart. A grounded
solid conducting sphere of radius a is placed midway between them.
Assume a2 ≪ d2 . Which of the following statement is/are true?
(A) d
If a > 8 , the net force acting on the charges is directed towards each other
(B) The potential at the surface of the sphere is zero
(C) 2aq
Total induced charge on the sphere is (− d )
(D) The potential at the center of the sphere is non-zero
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Physics (PH)
Q.47 A particle of mass m is moving in the potential
1
V(x) = { V0 + mω02 x 2 , x > 0,
2
∞, x ≤ 0,
Figures P, Q, R and S show different combinations of the values of ω0 and V0.
(P) (Q) (R) (S)
Ej , Ej , Ej and Ej with j = 0, 1, 2, …, are the eigen-energies of the j-th level
for the potentials shown in figures P, Q, R and S, respectively. Which of the
statement is/are true?
(A) (P) (Q)
E0 = E0
(B) (Q) (S)
E0 = E0
(C) (P) (R)
E0 = E1
(D) (R) (Q)
E0 ≠ E0
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Physics (PH)
Q.48 The non-relativistic Hamiltonian for a single electron atom is
p2
H0 = − V(r)
2m
where V(r) is the Coulomb potential and m is the mass of the electron. Considering
the spin-orbit interaction term
1 1 dV
H′ = ⃗ ∙S
L
2m2 c 2 r dr
added to H0 , which of the following statement is/are true?
(A) H′ commutes with L2
(B) H′ commutes with Lz and Sz
(C) For a given value of principal quantum number n and orbital angular momentum
quantum number l, there are 2(2l + 1) degenerate eigenstates of H0
(D) H0 , L2 , S 2 , Lz and Sz have a set of simultaneous eigenstates
Q.49 Decays of mesons and baryons can be categorized as weak, strong and
electromagnetic decays depending upon the interactions involved in the processes.
Which of the following option is/are true?
(A) π 0 → γγ is a weak decay
(B) ∧0 → π 0 + p is an electromagnetic decay
(C) K0 → π+ + π− is a weak decay
(D) ∆++ → p + π + is a strong decay
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Physics (PH)
Q.50 An extrinsic semiconductor shown in figure carries a current of 2 mA along its
length parallel to +x axis.
When the majority charge carrier concentration is 12.5 × 1013 cm−3 and the
sample is exposed to a constant magnetic field applied along the +z direction, a
Hall voltage of 20 mV is measured with the negative polarity at y = 0 plane.
Take the electric charge as 1.6 × 10−19 C. The concentration of minority charge
carrier is negligible. Which of the following statement is/are true?
(A) The majority charge carrier is electron
(B) The magnitude of the applied magnetic field is 1 Tesla
(C) The electric field corresponding to the Hall voltage is in the +y direction
(D) The magnitude of Hall coefficient is 50,000 m3 C -1
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Physics (PH)
Q.51 Aα and Bβ (α, β = 1,2,3, ⋯ , n) are contravariant and covariant vectors,
respectively. By convention, any repeated indices are summed over. Which of the
following expression is/are tensors?
(A) Aα Bβ
(B) Aα Bβ
Aα Bα
(C) Aα
Bβ
(D) Aα + Bβ
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Physics (PH)
Q.52 The temperature T dependence of magnetic susceptibility χ (Column I) of certain
magnetic materials (Column II) are given below. Which of the following option
is/are correct?
Column I Column II
(1) (P) Diamagnetic
(2) (Q) Paramagnetic
(3) (R) Ferromagnetic
(4) (S) Antiferromagnetic
(A) 2 − P, 4 − Q, 3 − S
(B) 4 − P, 1 − Q, 2 − R
(C) 4 − Q, 2 − R, 1 − S
(D) 3 − P, 4 − Q, 2 − R
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Physics (PH)
Q.53 The curves P and Q schematically show the variation of X-ray intensity with
wavelength at two different accelerating voltages for a given target material. In the
figure λ1 = 0.25 Å, λ2 = 0.5 Å, λ3 = 1.0 Å, and λ4 = 2.25 Å. Take Planck’s
constant as 6.6 × 10−34 Js, speed of light as 3 × 108 ms-1 and elementary charge
as 1.6 × 10−19 C.
Which of the following statement is/are true?
(A) The accelerating potential corresponding to curve P is greater than that of curve Q
(B) The accelerating potential applied to obtain curve Q is 24750 V
(C) Peaks (II) and (IV) correspond to radiative transitions from L to K shells
(D) Peaks (I) and (III) correspond to radiative transitions from N to K shells
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Physics (PH)
Q.54 Apart from the acoustic modes, 9 optical modes are identified from the
measurements of phonon dispersions of a solid with chemical formula An Bm , where
A and B denote the atomic species, and n and m are integers. Which of the following
combination of n and m is/are possible?
(A) n = 1, m = 1
(B) n = 2, m = 2
(C) n = 3, m = 1
(D) n = 4, m = 4
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Physics (PH)
Q.55 An oscillating electric dipole of moment d (t) = d0 cos(ωt) ẑ is placed at origin as
shown in figure.
Consider a point P(r, θ, φ) at a very large distance from the dipole. Here r, θ and
φ are spherical polar coordinates. Which of the following statement is/are true for
intensity of radiation?
(A) Intensity is zero if P is on the z axis
(B) π π
Intensity is zero at P (r = R, θ = 2 , φ = 4 )
(C) π π
Intensity at P (r = R, θ = 2 , φ = 4 ) is greater than that
π π
at P (r = R, θ = 4 , φ = 4 )
(D) π π π π
Intensity at P (r = R, θ = 2 , φ = 4 ) is equal to that at P (r = R, θ = 4 , φ = 4 )
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Physics (PH)
Q.56 The Fourier transform and its inverse transform are respectively defined as
1 +∞ 1 +∞
f̃ (ω) = ∫−∞ f(x)e iωx dx and f(x) = ∫−∞ f̃ (ω)e −iωx dω. Consider two
√2π √2π
functions f and g. Another function f ∗ g is defined as
+∞
1
(f ∗ g)(x) = ∫ f(y)g(x − y)dy
√2π −∞
Which of the following relation is/are true?
Note: Tilde (~) denotes the Fourier transform.
(A) f∗g = g∗f
(B) f̃
∗ g = g̃
∗f
(C) f̃ ̃
∗ g = fg
(D) f̃
∗ g = f̃g̃
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Physics (PH)
Q.57 A material behaves as a superconductor below a critical temperature Tc and as a
normal conductor above Tc . A magnetic field B ⃗ = Bẑ is applied when T > Tc .
The material is then cooled below Tc in the presence of B ⃗ . Which of the following
figure represent the correct configuration of magnetic field lines?
(A)
(B)
(C)
(D)
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Physics (PH)
Q.58 A typical biasing of a silicon transistor is shown in figure.
The value of common-emitter current gain β for the transistor is 100. Ignore reverse
saturation current. The output voltage V0 (in V) is ____ (in integer).
Q.59 The canonical partition function of an ideal gas is
N
1 V
Q(T, V, N) = [ ]
N! (λ(T))3
where T, V, N and λ(T) denote temperature, volume, number of particles, and
thermal de Broglie wavelength, respectively. Let kB be the Boltzmann constant and
μ be the chemical potential. Take ln(N!) = N ln(N) − N.
N
If the number density ( V ) is 2.5 × 1025 m−3 at a temperature T,
e μ/(kBT)
then
(λ(T))3
× 10−25 is _______ m−3 (rounded off to one decimal place).
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Physics (PH)
Q.60 1
Lagrangian of a particle of mass m is L = 2 mẋ 2 − λx 4 , where λ is a positive
constant. If the particle oscillates with total energy E, then the time period of
oscillations is
1
E 4
( )
λ dx
a∫
0
√( 2 ) (E − λx 4 )
m
The value of a is _____ (in integer).
Q.61 A particle of mass m in an infinite potential well of width a is subjected to a
ℎ2
perturbation, V ′ = as shown in figure, where ℎ is Planck’s constant.
40ma2
The first order energy shift of the fourth energy eigenstate due to this perturbation
is
ℎ2
( )
Nma2
The value of N is _____ (in integer).
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Physics (PH)
Q.62 Consider a three-dimensional system of non-interacting bosons with zero chemical
potential. The energy of the system ε ∝ k 2 , where k is the wavevector. The low
temperature specific heat of the system at constant volume depends on the
n
temperature as CV ∝ T 2 . The value of n is _____ (in integer).
Q.63 Consider the operational amplifier circuit shown in figure.
The output voltage V0 is _____ V (in integer).
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Physics (PH)
Q.64 An electron in the Coulomb field of a proton is in the following state of coherent
superposition of orthonormal states ψnlm
1 1 √5
Ψ = ψ100 + ψ210 − ψ
3 √3 3 320
Let E1 , E2 , and E3 represent the first three energy levels of the system. A sequence
of measurements is done on the same system at different times. Energy is measured
first at time t1 and the outcome is E2 . Then total angular momentum is measured at
time t2 > t1 and finally energy is measured again at t3 > t2 . The probability of
finding the system in a state with energy E2 after the final measurement is P/9.
The value of P is _____ (in integer).
Q.65 According to the nuclear shell model, the absolute value of the difference in
magnetic moments of 158O and 157N , in the units of nuclear magneton (μN ) is a/3.
The magnitude of a is _____ (in integer).
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Physics(PH)
Final Answer Key
Question
Q. No. Session Section Key/Range Mark
Type
1 2 MCQ GA A 1
2 2 MCQ GA A 1
3 2 MCQ GA C 1
4 2 MCQ GA A 1
5 2 MCQ GA D 1
6 2 MCQ GA B 2
7 2 MCQ GA MTA 2
8 2 MCQ GA C 2
9 2 MCQ GA A 2
10 2 MCQ GA MTA 2
11 2 MCQ PH C 1
12 2 MCQ PH C 1
13 2 MCQ PH A 1
14 2 MCQ PH A 1
15 2 MCQ PH A 1
16 2 MCQ PH B 1
17 2 MCQ PH B 1
18 2 MCQ PH A 1
19 2 MCQ PH C 1
20 2 MCQ PH C 1
21 2 MCQ PH D 1
22 2 MCQ PH B 1
23 2 MCQ PH B 1
24 2 MCQ PH A 1
25 2 MCQ PH A 1
26 2 MCQ PH A 1
27 2 MCQ PH D 1
28 2 MCQ PH D 1
29 2 MCQ PH C 1
30 2 MSQ PH A; B; C 1
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31 2 MSQ PH B; C 1
32 2 NAT PH 1 to 1 1
33 2 NAT PH 195.10 to 195.30 1
34 2 NAT PH 4 to 4 1
35 2 NAT PH 2 to 2 1
36 2 MCQ PH B 2
37 2 MCQ PH B 2
38 2 MCQ PH C 2
39 2 MCQ PH B 2
40 2 MCQ PH A 2
41 2 MCQ PH A 2
42 2 MCQ PH B 2
43 2 MSQ PH A; B; C 2
44 2 MSQ PH A; D 2
45 2 MSQ PH A; B 2
46 2 MSQ PH A; B; C 2
47 2 MSQ PH B; C; D 2
48 2 MSQ PH A; C; D 2
49 2 MSQ PH C; D 2
50 2 MSQ PH A; B 2
51 2 MSQ PH A; B 2
52 2 MSQ PH C; D 2
53 2 MSQ PH A; B; C 2
54 2 MSQ PH B; C 2
55 2 MSQ PH A; C 2
56 2 MSQ PH A; B; D 2
57 2 MSQ PH A; C 2
58 2 NAT PH 12 to 12 2
59 2 NAT PH 2.5 to 2.5 2
60 2 NAT PH 4 to 4 2
61 2 NAT PH 160 to 160 2
62 2 NAT PH 3 to 3 2
63 2 NAT PH -12 to -12 2
64 2 NAT PH 9 to 9 2
65 2 NAT PH 2 to 3 2
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Source: GATE. Question paper published by GATE.