TIFR GS 2026 Question Paper Physics PhD

FOR TIFR GS EXAM PREPARATION

TIFR GS 2026
Question Paper ·
Physics
EXAM YEAR TYPE SUBJECT DETAILS

TIFR GS 2026 Question Paper Physics PhD

Notes · Sample Papers · Previous Year Papers · Mock Tests

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m .co se
m A
GS 2026 Entrance exam, Physics, PhD: Section
se g la
a
A1
(1) Is it possible for the trajectory of a particle
in a two-dimensional plane with a continu-
ous velocity and acceleration to have the
shape shown in the figure?
(2) Is it possible for its acceleration vector at 𝑃
on the trajectory to point in the direction,
𝑃
m
.co
, as shown?
m
m .co s e m
s e (1) Yes (2) No
l a
ag
(a)

g l a
a
(b) (1) Yes (2) Yes

(c) (1) No (2) No

m
.co
(d) (1) No (2) Yes

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las
ag

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m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 1 of 40

A2
A steady, incompressible air stream 1
of density = 1.2 kg/m3 blows
horizontally at 0 = 15 m/s to-
wards a hill of height ℎ = 50 m.
Because the streamlines constrict
over the hilltop, the air speed there ℎ
increases to 1 = 19.5 m/s. The dif- 0

ference between the pressure at the
base and the hilltop is closest to:

(a) 681 N/m2

(b) 495 N/m2

(c) 588 N/m2

(d) 93 N/m2

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a
A3
A student performs an experiment to measure the acceleration due to gravity, , us-
ing a simple pendulum. The student measures = 1.00 ± 0.01 m and the time for
50 oscillations 50 = 100.0 ± 1.0 s. Based on this experiment, what is the calcu-
lated value of and its uncertainty, assuming that the errors on the length and time
m
.co
are statistically independent?
m
m .co s e m
(a)
s e 9.87 ± 0.22 m/s 2

l a
g l a ag
a(b) 9.87 ± 0.11 m/s2

(c) 9.87 ± 0.44 m/s2

(d) 9.87 ± 0.05 m/s2
m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 3 of 40

A4 Consider a 2 × 2 matrix defined as:

= [ 0+ ⃗ ⋅ ⃗][ 0 − ⃗ ⋅ ⃗]−1

where 0 is a non-zero real number, ⃗ is a three-dimensional non-zero real vector,
and ⃗ = ( , , ), where , , are the Pauli spin matrices. The matrix :

(a) Is Unitary but not Hermitian

(b) Is Hermitian but not Unitary

(c) Is Unitary and Hermitian

(d) Is neither Unitary nor Hermitian

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A5
a
The figure on the right shows a
positive point charge (+ ) placed
above an interface (horizontal line
in the figure) between two dielec- +
trics with permittivities, 1 and 2 .
The curves shown are field lines
of the electric displacement, ⃗⃗.
m
m .co
Which of the following statements

.co m
is true?

m s e
s e l a
g l a ag
a
(a) 2 > 1 and the sign of the net surface charge at the interface is negative

(b) 1 > 2 and the sign of the net surface charge at the interface is positive

m
m .co
(c) 2 >
s e
1 and the sign of the net surface charge at the interface is positive

g la
a
(d) 1 > 2 and the sign of the net surface charge at the interface is negative

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
s em l a
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 5 of 40

A6
A thin film of oil (refractive index, = 1.40) floats on a puddle of water (re-
fractive index, = 1.33) on a road. The film is illuminated at normal inci-
dence from air by white light. In the light reflected vertically, green colour (with
wavelength in air 0 = 560 nm) is enhanced. The smallest possible thickness of the
oil film is approximately:

(a) 100 nm

(b) 2000 nm

(c) 200 nm

(d) 360 nm

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A7
a
Four infinitely long electrodes of
negligible thickness are placed parallel to
the axis and pass through the points at
the edges of a square in the ( , ) plane (0, )
at (± , 0) and (0, ± ). The potential at (− , 0)
(0,0) is 0. If the electrodes at (± , 0) are
m
.co
maintained at a potential 0, while the
m ( , 0)
.co
electrodes at (0, ± ) are maintained at a
(0, − ) e m
potential − 0, the electric field in the
em l as
as
vicinity of the electrodes is given by:
l ag
ag

(a) 2 0
⃗⃗ = − ( ̂ − ̂)
2

m
.co
(b) ⃗⃗ = − 0 ( ̂ − ̂)

s em
g la 2
(c) a (sin( ) ̂ − sin(2 ) ̂)
⃗⃗ =
2
2
0

(d) ⃗⃗ = − 0
2+ 2
( ̂ − ̂)

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m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 7 of 40

A8 Three nearby laboratory rooms 1, 2, 3 have one smoke detector each labelled D1, D2,
D3 respectively, for fire safety. In case smoke is detected, the detector output goes to
a logic state True. However, to prevent false alarm, these outputs are connected to the
logic circuit below whose output activates a single alarm.

In which of the following cases will the alarm definitely ring:

(a) Smoke is detected in rooms 2 and 3

(b) Smoke is detected in rooms 1 and 2

(c) Smoke is detected in rooms 1 or 2

(d) Smoke is detected in any two of three rooms

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m .co

m .co s e m
se g l a
A9
a
Find:
+1
lim log ( )
→+∞ −1

m
(a)
m 2
.co
m .co s e m
s e l a
(b)
g l a 1
ag
a
(c) 0

(d) The limit does not exist

m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 9 of 40

A10
Scientists are conducting an underground experiment where two interactions, and
can occur. In general, interaction is twice as likely to occur compared to inter-
action . Interaction would give a signal in the detector with probability 1/8,
while interaction would give a signal with probability 1/2. If the detector regis-
ters a signal, what is the probability that the signal was due to interaction ?

1
(a) 3

1
(b) 5

1
(c) 9

2
(d) 3

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A11
a
The equation of state of a gas is given by:

( + 2) ( − ) = ,

where is the volume per mole and , , are constants. The internal energy per
mole of the gas is given by:
m
m 3
.co
.co m
( , )= −
2
e
Whichsofemthe following gives the adiabatic equation of state at fixed particle numberglas
a gas?
forlthe
g a
a
(a) ( − )2 3 = constant

(b) ( − )2 −3 = constant

o m
(c) c
( − ) . = constant
3

em
2 2

las
(d)
g
a ( − ) = constant 3
2 −2

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 11 of 40

A12
Electrons in a metal are accelerated under a constant electric field ⃗⃗ and experience
a drag − ⃗ due to the surrounding medium. If the density of electrons is and the
current is constant, what is the conductivity of the metal?

2
(a)
=

(b) 2
=

(c) 2
=

(d)
=

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a
A13 (Note: Either (a) or (b) can be correct, depending on the applications; both (a) or (b)
will be given full marks.)

A thermistor measures the temperature by measuring the change of electric resistiv-
ity of a material. Which of the following types of materials are most suited for mak-
ing thermistors to work in the temperature range −100 degree C to 300 degree C?

m
m .co
.co e m
(a) Semiconductors

em l as
l as ag
ag
(b) Metals

(c) Superconductors

(d) Gas of atoms

m
m .co
s e
g la
a

m
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m .co s e m
s e g l a
g la a
a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 13 of 40

A14
An electron beam is accelerated over a potential and strikes a crystal with lattice
constant 5Å. What is the minimum needed to resolve the crystal?

(a) 5V

(b) 30 V

(c) 300 V

(d) 0.5 V

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m .co

m .co s em
se g la
a y
A15

The figure on the right, shows
-q q
point charges arranged in the ,
plane on the centre, vertices, and q -2q q x
some edges of a square with verti-
ces at (±1, ±1, 0) in standard
m
.co
units. Given the charge distribu-
m
.co m
tion in the figure, the electric field q -q
far away from the charges ( =
m s e
s e
√ 2 + 2 + 2 denotes the dis- l a
g l a
tance from the origin) falls off as: ag
a
(a) 1
4

(b) 1
2

m
(c)
m .co1
s e 3

g la
(d)
a 1
5

m
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m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 15 of 40

A16
Which of these circuits made with resistor, capacitor and inductor will be the best to
get light out of the LED using a 9V battery, after the switch is closed?

(a)

(b)

(c)

(d)

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a
A17 For a medium, the dispersion relation for the propagation of light is shown below on
a linear scale:

m
m .co
m .co s e m
s e l a
g l a ag
a
Here, is the frequency of the green light. Which of the following statements is
correct?

(a) The phase velocity for the green light is smaller than the group velocity at that
frequency
m
m .co
(b)
s e
The refractive index of the medium for the red light is smaller than that for the
blue light
g la
a
(c) The phase velocity of the green light is larger than the group velocity at that
frequency

(d) The speed of light in this medium for green light is same as that in vacuum

m
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m .co s e m
s e g l a
g la a
a

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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 17 of 40

A18
Hydrogen atom has a decay rate from = 2 state to = 1 state as about 6 × 108
decays per second. If the energy level expression for the hydrogen atom is
13.6
= 2
eV

the uncertainty in the wavelength of this emission would be closest to

(a) 30 fm

(b) 0.1 fm

(c) 122 nm

(d) 19.4 nm

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a
A19
A quantum particle of mass in three-dimensions is governed by the Hamiltonian:
⃗̂2 1
̂= + 2( 2
+ 2 + 2) + ( 6 + 6)
2 2

with > 0. If 3 ( ⃗) is the third excited state of the system, which of the following is

m
.co
correct?
m
m .co s e m
(a)
s e | 3 ( ⃗)|
2
=| 3 (− ⃗)|
2
l a
g l a ag
a(b) 3 ( ⃗) is an eigenstate of
2

(c) 3 ( ⃗) is an eigenstate of

(d) 3 ( ⃗) is an eigenstate of
m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 19 of 40

A20
Consider the series:
∞
1
=∑ 3/2
=1

Which of the following statements is correct?

(a) is convergent and is greater than 2

(b) is convergent and is less than 2

(c) is convergent and is equal to 2

(d) is not convergent

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a
A21 A relativistic particle of mass moving under the central force of gravity with an-
gular momentum around a massive body of mass experiences the following po-
tential:
2 2
( )=− + 2
− 2 3
2
m
m
where the last term is the relativistic correction to the Newtonian formula. For suffi-
.co
.co
ciently large , the particle has:
s e m
s em g l a
l a a
ag
(a) Two circular orbits. The smaller one is unstable and the larger is stable

(b) Two circular orbits. The smaller one is stable and the larger is unstable

(c) Three circular orbits. The middle one is unstable and the others stable

m
(d)
m .co
Three circular orbits. The middle one is stable and the others unstable

s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 21 of 40

A22
Consider a quantum particle in a one-
dimensional potential of the shape
shown, with the well of width , and
( < 0) → ∞. The potential in the well
is − 0 and the potential for ∈ ( , ∞) is
0. Which plot describes the change in the
ground state energy ( ) as is changed
keeping 0 constant?

(a)

(b)

(c)

(d)

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A23
a
A non-interacting, classical gas is made up of Nitrogen molecules. The specific
heat at constant volume is . /( ) is given by:

(Ignore rotations about the axis of symmetry.)

3/2 for some very low , 5/2 for temperatures around the room temperature,
(a)
m
.co
7/2 for some high temperatures
m
.co e m
(b) s emfor some very low , 5/2 for temperatures around the room temperature,glas
7/2
g la 3/2 for some high temperatures a
a
(c) 3/2 for some very low , 2 for temperatures around the room temperature,
5/2 for some high temperatures

(d) 3/2 for some very low , 2 for temperatures around the room temperature, 3
m
.co
for some high temperatures

e m
las
ag

m
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m .co s e m
s e g l a
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a

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.co s e m
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a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 23 of 40

A24
The longitudinal disturbance generated by an earthquake, travels through the earth’s
crust and reaches 1000 km in 3 mins from the epicentre of the earthquake. Assuming
the density of the Earth’s crust is 2700 kg/m3, the Bulk’s modulus of the crust is
closest to:

(Ignore the shear modulus and local variations in the density and the Bulk modulus.)

(a) 8.3 × 1010 N m-2

(b) 2.1 × 1011 N m-2

(c) 8.3 × 108 N m-2

(d) 2.1 × 109 N m-2

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a
A25
An analytic transformation:
2
=

m
is applied on the complex plane. Con-

m .co
sider the circle in as shown on the

.co m
right. Which of the following represents

m s e
e
the image of in the plane?
s l a
g l a ag
a(a)

m
(b)
m .co
s e
g la
a

(c)

m
m .co
m .co (d)
s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 25 of 40

GS 2026, Physics, PhD: Section C

C1
Consider a quantum particle moving in one spatial dimension with the Hamiltonian

̂2
̂= + ( ̂)
2

Let | ( )⟩ be the state of the system where | (0)⟩ is a normalized eigenstate of this
⟨ ( )| ̂ 2 | ( )⟩
Hamiltonian. What is the value of ⟨ ( )| ̂ ̂ | ( )⟩? (Hint: Consider .)

(a) ℏ
2

(b) −ℏ

(c) ℏ

(d) 0

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C2
a
In the standard | 2 , ⟩ eigenbasis of a spin 1 particle, the matrix corresponding to
the operator ̂ 2 − ̂ 2 is given by:

(a) 0 0 1
ℏ2 ( 0 0 0)
m
.co
1 0 0
m
m .co s e m
(b)
s e 1 0 0
l a
g l a ℏ2 ( 0 2 0)
ag
a 0 0 1

(c) 0 1 0
2
ℏ (1 0 1)
0 1 0

(d) 1 0
m 0
o 0)
c
2
ℏ (0 0
m .
0 0 1
s e
g la
a

m
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m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 27 of 40

C3
The Hamiltonian of a quantum system in the basis states, |1⟩, |2⟩, and |3⟩ is given
by the matrix:

0 √2 0
(
0 √2 0 √2)
0 √2 0

If the system is in the state | (0)⟩ = (|1⟩ − |3⟩)/√2 at = 0, the probability of the
system to be in state |2⟩ at time is given by:

(a) 0

(b) sin2 (2 0 )

(c) sin2 ( 0 )

(d) 0
sin2 ( )
2

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a
C4 An (A=56, Z=26) nucleus starts from
infinity with an initial speed and moves
head on towards a (A=59, Z=27)
nucleus which is initially stationary. The
nuclei are uniformly charged spheres of
radii = 1.2 1/3fm, and a nuclear
m
.co
reaction can take place when they touch
m , ,

.co m
each other. What is the smallest for

m
which this reaction can occur? Neglect
s e
s e l a
a ag
the mass difference between neutrons and

g l
protons and nuclear forces, and assume
a
that the two nulceii remain spherical
throughout the motion.

(a) 2.70 × 107 /

1.91 × 107 /m
.co
(b)

m
e1.37
s
la × 10 / 7

g
(c)
a
(d) 0.95 × 107 /

m
m .co
m .co s e m
s e g l a
g la a
a

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.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 40

C5
A classical particle of mass moving in the − plane is constrained to move
along the curve 4 + 4 = 1. There are no other external forces acting on it. If
( , ) are the polar co-ordinates, which of the following is true?

(a) ̇ ̇
̈ +2 ∝ 2
sin 4

(b) ̈∝ 2
sin 4

(c) ̈∝ 4
sin2 2

(d) ̇ ̇
̈ +2 ∝ 4
sin2 2

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C6
a
A particle of rest mass moving at a relativistic speed collides with an identical
4
particle at rest and merges with it to form a composite of rest mass = . What
√3
is the ratio of the speed of to the initial speed ?

(a) 5
m
m 8
.co
m .co s e m
s e l a
a ag
1
l
(b)

ag 2

(c) 3
5

(d) 2
3 m
m .co
s e
g la
a

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 31 of 40

C7 For a static observer, an infinite wire of
negligible thickness with no net charge
density placed along direction carries ̂
a current . Another observer is moving
along the current with a relativistic
speed . The magnitude of the linear
charge density on the wire seen by the
moving observer is:

(a)
√ 2− 2

(b)
√ 2− 2

(c) √ 2− 2

(d) 0

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C8
a
A plane electromagnetic wave
with an electric field
̂
⃗⃗ ( , ⃗) = ̂ cos( − )

is incident on a hemispherical mir- ̂

m
.co
ror of radius with a perfectly re-
m
.co
flecting outer surface, placed as
shown.
e m
e m l as
l as
What is the electromagnetic force
ag
ag
acting on the mirror averaged over
one time-period of the wave?

2 2
(a) 0
2

m
c. o3
2 2
(b) 2 0

e m
las
ag 2 2
(c) 0

2 2
(d) 4 0
3

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 33 of 40

C9
The inner product of two complex functions ( ), ( ), over the interval ∈ [0,1]
is defined as:
1
⟨ | ⟩=∫ (1 − ) ∗ ( ) ( )
0

The adjoint, ̂ ϯ , of a linear operator ̂ is defined by the equation:

⟨ | ̂ ⟩ = ⟨ ̂ϯ | ⟩

What is the adjoint of the operator ̂ = ? Assume that both ( ) and ( ) are
differentiable.

(a) 2 −1
−
(1− )

(b) −

(c) 1
(1− )

(d) −1
(1− )

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se g l a
C10
a
What is the value of the following integral:

∞
sin 1
∫ 2+ 2
0

m
.co
> 0.)
m
(Assume

m .co s e m
s e l a
(a)
g l a 2 2
(1 − −
)
ag
a
(b) (1 + −
)
2 2

(c) sinh
2 2
m
.co
m sin
s e
la
(d)

ag 2 2

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 35 of 40

C11
Consider a single particle in a potential well with an energy spectrum = , for
= 0, 1, 2, 3, .., with > 0. The th
energy level has a degeneracy ( ) = 2 +
1. This system is at temperature . What is the value of ⟨ ̂ ⟩?

( is the Boltzmann constant.)

(a) 3 +1
2
( − 1)

(b) 1
( − 1)

(c) 3 +1
2
( − 1)

(d) 1
2
( − 1)

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C12
a
A system of classical non-interacting particles of mass is confined to a cubic
box of volume . Inside the box is a region of volume 0 (< ), where a constant
potential is present.

If 𝑃 is the pressure of the system, is its temperature, then:
m
m .co
m .co s e m
(a)
s e 𝑃 1
l a
ag
=

g l a − 0 (1 − − / )

a
(b) 𝑃 1
= − /
− 0

(c) 𝑃 1
= − /

m
0

.co
s em𝑃 = 1
la
(d)

ag − 0

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
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C13
A Bosonic excitation has a density of states given by:
2
( )= 0 [1 − ( − 1) ]
0

for 0 ≤ ≤ 2 0 , and 0 otherwise. If the two-dimensional system is in a tempera-
ture range ≫ 0 , the variation of the specific heat with temperature is given by:

0
(a) ∝

3
(b) ∝

2
(c) ∝

(d) ∝

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m
m .co

m .co s e m
se g l a
a
C14

Op-Amps normally cannot output
very high currents, which is
typically limited to tens of mA. To
overcome this, a transistor is used to
m
m
boost the current output onto a load
.co
.co
resistor. The circuit below uses a Si
m s e m
e
transistor with common-emitter
s l a
a
mode current gain = 120. What is
g l ag
a
approximately the current being
drawn from the output of the Op-
Amp here?

(a) 0.88 mA

m
.co
(b) 0.76 mA

s em
(c)
g la 1.23 mA
a
(d) 2.11 mA

m
m .co
m .co s e m
s e g l a
g la a
a

m .
.co s e m
s em l a
g la ag
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 39 of 40

C15
Consider a one-dimensional lattice
where each site has mass and
the lattice constant is . Nearest
neighbours are connected by
springs of constant . Which of
the following best represents the
dispersion of longitudinal oscilla-
tions in the lattice?

(a)

(b)

(c)

(d)

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