TIFR GS 2026 Question Paper Physics IPhD

FOR TIFR GS EXAM PREPARATION

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

TIFR GS 2026 Question Paper Physics IPhD

Notes · Sample Papers · Previous Year Papers · Mock Tests

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m .co em
GS 2026 Entrance exam, Physics, Int-PhD: Section A
s
se l a
ag
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

e m
las
ag

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
s em l a
g la ag
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

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

m .
.co s e m
s em l a
g la ag
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
( ̂ − ̂)

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 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

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

m .
.co s e m
s em l a
g la ag
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
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(a)
m .co Semiconductors
s e m
s e l a
g l a ag
a
(b) Metals

(c) Superconductors

(d) Gas of atoms

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 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
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 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

m .
.co s e m
s em l 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
s em l a
g la ag
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
g la ag
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
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 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, Int-PhD: Section B

B1
Consider a uniform rod with length and
mass with one end on the wall and 1
the other end on the ground. Initially it
is at rest at an angle 1 with the wall and 2
starts slipping. What is the speed of
when the ladder’s angle with the wall is
2 ? Ignore friction.

(FYI: The moment of inertia of a uniform
1 2
rod about its centre is = .)
12

(a) sin 2 √3 (cos 1 − cos 2 )

(b) √3 (cos 1 − cos 2 )

(c) √12 (cos 1 − cos 2 )

(d) sin 2 √6 (cos 1 − cos 2 )

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a
B2
A metallic ring of radius is pushed into
a region of uniform magnetic field ̂
(shaded region) with a constant speed
as shown. The magnetic field is 0
outside. The electrical resistance of the
m
m .co
.co
loop is . What is the external force one
needs to apply on the loop to maintain
e m
em
its speed, when the distance of the
l as
as
region’s edge to the centre is (>0)?
l ag
ag
(a) 4 2 2 2
(1 − 2
)̂

(b) 2 2 2

om
(1 + )̂
c
2

m .
s e
g la 2 2

a
(c)
(1 + )̂

(d) 2 2
(1 − )̂

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 27 of 40

B3
1
Two trains of proper length each
move on neighbouring tracks. An
observer at rest with the tracks, ,
notes the speed of train 1 to be ̂
and train 2 to be − ̂. also
notes that at = 0 the front ends
2
of the two trains have the same
position, = 0. According to a ̂
train engineer sitting at the front ̂
of train 1, what is the time interval
between the passing by of the
front and the back of train 2?

(a) (1 − 2
/ 2)
2

(b)
√1 − 2/ 2
2

(c) 2/ 2
1−
√ 2/ 2
2 1+

(d)
2

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B4
a
A mass is placed on a wedge of mass ̂
and angle as shown, which in turn is ̂
placed on the horizontal ground. Initially,
and are at rest with respect to the
ground and are released from this position.
What is the acceleration of ? Assume
m
.co
that all surfaces are frictionless.
m
m .co s e m
s e l a
g l a ag
a
(a) =
cos sin
+ sin2

(b) cos
=
+

o msin
(c)
=. c
e m +

l as
ag
(d) =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
a For more Question Papers, Sample Papers, Notes & Syllabus visit Page 29 of 40

B5 Scientists have discovered a new type of particle, which can occupy a quantum state
with 0, 1 or 2 particles. If a quantum state has energy , the average occupation of
this state in a system at temperature and chemical potential is given by

( − )
(a) 2+
( − ) 2( − )
1+ +

(b) 2
( − ) 2( − )
1+ +

(c) ( − )
1+2
( − ) 2( − )
1+ +

(d) 1
( − ) 2( − )
1+ +

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a
B6 A cycle for an ideal gas consists of the following three reversible processes:

i. Isothermal expansion at from 1 to 2.

ii. Isochoric (constant volume) cooling from to .

, 1).
m
iii. Adiabatic compression from and 2 back to the initial state (

m .co
.co m
If is the constant volume heat capacity of the gas, the efficiency of this cycle
is:
m s e
s e l a
g l a ag
a(a) = 1 −
( − )
log( 2 / 1 )

(b)
= 1 −

o m
(c)
. c ( − )

em
= 1 −

las
ag
(d)
= 1 −
log( 2 / 1 )

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

B7
Consider the function:

4 − 11 3
( )= 2
( + 1)2

In the domain ∈ [1,4]. What is the difference between the maximum value of the
function and its minimum value? (Select the closest answer.)

(a) 1.45

(b) 3.2

(c) 3.96

(d) 0.82

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B8
a
An earth imaging satellite is in a near
earth circular orbit (see figure) with an
orbital period of 100 minutes and
observes earth with a light of wavelength Earth
550 nm. If it can resolve the ground with
0.5 m, the minimum diameter of the
m
.co
mirror on the satellite should be closest
m
.co m
to:

s e
s em l a
g la the system is diffraction limited. ag
aThe mass and radius of Earth are 5.97 ×
(Assume

1024 kg and 6.4 × 103 km, respectively.)

m
.co
(Figure not to scale)

e m
las
(a)
ag 1m

(b) 5m

(c) 0.5 m

m
m .co
.co
10 m
m
(d)

m s e
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

B9 In the experimental arrangement below, a plane polarised light of intensity and
wavelength 500 nm is propagating along the -axis. It is polarised along the -axis and
is incident on the first polarizer which has the transmission axis at an angle of /4 wrt
the -axis, as shown.

Subsequently, the beam passes through a flat birefringent crystal of thickness 950
and optical axis along the -axis. The crystal is kept normal to the -axis. If the
refractive indices of the crystal are = 1.514 and = 1.519, the beam intensity
measured after the second polarizer whose transmission axis is parallel to that of the
first one would be:

(a) 0

(b) /4

(c) /2

(d)

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B10
a
2 3− 3
The curve that solves = 2 and passes through the point (1,0) is given by:
3

3 3 2
(a) + − =0
m
m .co
m .co s e m
(b)
s e 2 3− 3
+ =0
l a
g l a ag
a(c) 3
+ 3
− 2
− 2
=0

(d) 2 3− 3
+ + =0

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 35 of 40

B11
The vector field, = (2 2 + 3 , 2 2 , 3 2 ) V/m, gives the electric field in a
region where ( , , ) are the cartesian coordinates, given in metres. The difference
in electric potential between the two points with coordinates ( , , ) = (1, 1, 1)
and ( , , ) = (1, 2, 3), is given by:

(a) −29 V

(b) −16 V

(c) 0V

(d) An electric potential cannot be defined for this electric field configuration

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m
m .co

m .co s e m
se g l a
B12
a
Reactions in a closed container convert one molecule of to one molecule of at a
rate Γ1 and one molecule to one molecule of at a rate Γ2 . At time = 0, there are
0 number of molecules and no or molecules in the container. At what time is
the number of molecules in the container the maximum?

m
.co
(a) log(Γ2 /Γ1 )
m
.co m
Γ2 − Γ1

m s e
s e l a
(b)l a ag
ag
log(Γ1 /Γ2 )
Γ2 − Γ1

(c) log(Γ2 ) log(Γ1 )
+
Γ2 Γ1

m
log(Γ2 ) log(Γ1 )
.co
(d)
−
Γ2 Γ1
e m
las
ag

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 37 of 40

B13
Consider a quantum particle of mass in one-dimension with a Hamiltonian:

̂2
̂= + ̂8
2

with > 0. The ground state energy of the particle scales with as:

1/5
(a) ∝

1/4
(b) ∝

1/3
(c) ∝

1/6
(d) ∝

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m
m .co

m .co s em
se g l a
B14
a
A one-dimensional quantum mechanical wave function is given by:

( )= −| − |/
,

where ∈ (−∞, ∞) and is a normalization factor. What is the expectation value
of the kinetic energy in this state?

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

(c) ℏ2 ℏ2
2
+ 2
2 2

m
c. 2ℏo 2

m
(d)

s e 2

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 39 of 40

B15

The figure below shows a circuit. The
input waveform ( ) is shown. =
5 and = 0.25 V.s/A.

1

( ) ( )

2

An ideal oscilloscope is connected be-
tween points 1 and 2, and shows a sig-
nal ( ). What is the closest repre-
sentation of ( )?

(a)

(b)

(c)

(d)

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