JAM 2026 Question Paper Physics (PH)

JAM 2026 Physics (PH)

Section A: Q.1 – Q.10 Carry ONE mark each.

Q.1 Light of wavelength 632 nm is passing through an optically active medium of
thickness 20 cm. The optical rotation exhibited by the medium is 18°.
Which of the following options correctly states the magnitude of the difference
in refractive indices corresponding to the left and the right circularly polarized
light?

(A) 1.81 × 10−5

(B) 3.16 × 10−7

(C) 3.62 × 10−5

(D) 6.32 × 10−7

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JAM 2026 Physics (PH)

Q.2 Consider an n-type silicon in which the fully ionized dopant concentration is
1017 . The intrinsic electron density is 1.5 × 1010 . Which of the
following options correctly states the equilibrium hole concentration in ?

(A) 2.25 × 103

(B) 1.55 × 103

(C) 3.01 × 103

(D) 4.52 × 103

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JAM 2026 Physics (PH)

Q.3 Consider the superposition of two electromagnetic waves with their electric
field vectors given by ⃗ ( , ) = ̂ cos( − ) and ⃗ ( , ) =
̂ sin( − + ), where and are the amplitudes, k is the
wavenumber, ω is the angular frequency, and φ is the relative phase. Which of
the following options represents a resultant elliptically polarized wave with its
semi-major axis either along ̂ or ̂?

(A) φ = 0 and ≠

(B) φ = and =

(C) φ = and ≠

(D) φ = 0 and =

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JAM 2026 Physics (PH)

Q.4 Which of the following options represents the simplified form of the Boolean
equation ! = ̅ #$ %̅ + ̅#%̅ + #$ %̅ + #%̅ ?

(A) #$

(B) ̅#%̅

(C) #$ %

(D) %̅

Q.5 A quantum particle is confined in a one-dimensional space of 0 ≤ ( ≤ 2.
Consider a normalized wavefunction of the particle as

ψ(() = +,/5/1 + 12(π(/2)4 sin(π(/2).

Which of the following options gives the correct value of ,?

(A) 2

(B) 3

(C) 4

(D) 1

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JAM 2026 Physics (PH)

Q.6 Consider the normalized superposed state 6 = 7 8+ , where 7 and

are the ground and first excited states of a simple harmonic oscillator,
respectively. 7 and are imaginary superposition coefficients. Which of the
following options is correct for the expectation value of (〈(〉 + = 〈,〉)?

(A) Imaginary

(B) Real

(C) Zero

(D) Complex with non-zero real and imaginary parts

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Q.7 The potential of a quantum harmonic oscillator is modified from ( to

( + 3?(, where and ? are constants and x is the position variable. When,

the values of ? = 2 and = 1, which of the following options gives the change
in the ground state energy?

(? and are in appropriate units)

(A) − 3

(B) − 6

(C) − 12

(D) − 18

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Q.8 Consider the following linear second order differential equation

BC D
+ F = 0,
BEC

GD
where is a positive constant. The boundary conditions are I = 1, and
GH HJ7

F( = 0) = .

Which of the following options gives the value of F( = )?
K

(A) 1

(B) 2L

(C) 0

(D) 1

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Q.9 Consider the electrostatic potential in two dimensions M((, F) = ( N F O . What is
the line integral of the corresponding electric field along the path shown in the
figure?

(A) 0

(B) 1

(C) 2

(D)

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Q.10 Consider the matrix

0 1 1
= P0 0 1Q .
1 0 0

The value of det( ) is:

(A) 4

(B) 1

(C) 1
4

(D) 0

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Section A: Q.11 – Q.30 Carry TWO marks each.

Q.11 Consider the circuit of the figure, the voltage VW , in Volts, is:

(A) 0

(B) 1.25

(C) 9.8

(D) 10

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Q.12 A particle of mass moves in a potential given by

D
M((, F, ) = − ,
(X C YD C YZ C )

where is a constant.

Which of the following statements is correct?

(A) The force corresponding to the potential is central

(B) Angular momentum of the system is not conserved

(C) Linear momentum along the F-direction is conserved

(D) Energy of the system is not conserved

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JAM 2026 Physics (PH)

Q.13 ( ⃗ , #⃗ ) are the electric and magnetic fields in a rest frame. ( ⃗ ′, #⃗ ′) represent the
corresponding quantities in a reference frame moving with a constant velocity
\⃗7 . Using the invariance of Lorentz force ]⃗ = ^ ⃗ + ^ \⃗ × #⃗ under Galilean
transformations, identify the correct relation.

(A) ⃗ ` = ⃗ and #⃗ ` = #⃗

(B) ⃗ ` = ⃗ + \⃗7 × #⃗ and #⃗ ` = #⃗

(C) ⃗ ` = ⃗ and \⃗ × #⃗ ` = (\⃗ + \⃗7 ) × #⃗

(D) ⃗ ` = \⃗7 × #⃗ and \⃗ × #⃗ ` = ⃗ + \⃗ × #⃗

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JAM 2026 Physics (PH)

Which ONE of the following figures correctly represents the probability
density, a((), of a particle undergoing simple harmonic oscillation as a function
Q.14

of position (?
The dashed line is for the classical case. The solid line is for the quantum case,
where the system is in its ground state. The dotted vertical lines on the ( axis
denote the classical turning points.

(A)

(B)

(C)

(D)

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Q.15 An observer b$( ̅, (̅ ) moves with a constant velocity in the positive (-direction
relative to an observer b( , () at rest. In the frame of reference of b$( ̅, (̅ ), a
light-ray emitted at a point P at some time reaches the (̅ -axis at the point Q.
Then, on reflection it arrives at point R, as shown in the figure.

Which of the following options represents these events as observed by b( , ()?

(A)

(B)

(C)

(D)

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Q.16 Consider a multilayered structure composed of thin films of refractive indices
no, n1, and n2 as shown in the figure. A ray traveling in the first layer hits the
interface at an angle of 20° with the horizontal. Which of the following options
is correct?

(A) The ray emerges at an angle of 20° with the horizontal in the 4th layer

(B) The ray emerges at an angle of 56° with the horizontal in the 4th layer

(C) The ray would not enter the 3rd layer

(D) The ray emerges at an angle of 44° with the horizontal in the 4th layer

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Q.17 Consider a BCC lattice with one atom per lattice point.

The maximum packing fraction is close to:

(A) 53 %

(B) 68 %

(C) 74 %

(D) 81 %

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Q.18 The output voltage V0 for the circuit shown in the figure is:

(A) (V1−V2)

(B) (V1−2V2)

(C) (V2−V1)

(D) 2(V1−V2)

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Q.19 A quantum particle of mass 10 7
kg is confined within a length of 1 d in
one-dimension. The minimum uncertainty in the measurement of velocity of the
particle, in units of e /2, rounded off to the nearest integer is:

ℏ
[Assume the minimum uncertainty product Δ(ΔpX ≈ , use Planck’s

constant h = 6.64 × 10 j
J s]

(A) 2

(B) 5

(C) 10

(D) 1

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JAM 2026 Physics (PH)

Q.20 A thin ring of mass m and radius R has a total charge Q distributed uniformly.
The ring is rotating with a constant angular velocity about an axis passing
through its center and perpendicular to its plane.

Which of the following options is correct?

(A) kKl C
The magnetic moment of the ring is
j

(B) The ratio of the magnetic moment to angular momentum is k
m

(C) kKl C
The magnetic moment of the ring is
n

(D) The ratio of the magnetic moment to angular momentum is k
m

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JAM 2026 Physics (PH)

Q.21 A mass attached to the bottom end of a vertical massless spring stretches the
spring by Δ(. The system executes oscillation with a time period o = 0.2 2. The
value of Δ(, in cm, rounded off to the nearest integer is:

[Assume the acceleration due to gravity p = 9.8 /2 ]

(A) 2

(B) 3

(C) 4

(D) 1

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Q.22 A particle is rotating along a circular path with uniform speed \, as shown in
the figure. While moving from the point a to r subtending an angle s, the
magnitude of the change in its velocity is:

(A) Zero

(B) \ cos s

s
2\ sin
(C)
2

s
\ cos
(D)
2

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JAM 2026 Physics (PH)

Q.23 A series LCR circuit contains v = 175 x, % = 62.5 e], and y = 40 z
and is connected to a source of voltage amplitude 7 = 50 M and angular
frequency = 400 {?|/2.

Which of the following statements is correct?

(A) The magnitude of the maximum voltage across the inductor is less than 50 V

(B) The magnitude of the maximum voltage across the capacitor is more than 60 V

(C) The magnitude of the maximum voltage across the resistor is 50 V

(D) The magnitude of the maximum voltage across the capacitor equals the
maximum voltage across the resistor

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JAM 2026 Physics (PH)

Q.24 A piecewise regular function }(() is shown in the figure. It is expanded in
Fourier series given by

~•
}(() = + ∑„
•J ?• cos(d () + ∑•J bƒ sin(d() ,
„

where ?7 , ?• , …• ’s are the Fourier coefficients.

Which of the following options is correct?

(A) ?7 = 3L

(B) All ?• are zero

(C) All …• are zero

3L
?7 =
(D)
2

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JAM 2026 Physics (PH)

Q.25 Using Taylor series, expand }(() = ( − around (7 = 1 up to second order
N

in (. The coefficient of ( is:

(A) −2

(B) 3

(C) 2

(D) −3

Q.26 Consider a 2 × 2 matrix . The determinant of is −1 and the trace( ) = 1.
Which of the following options gives the eigenvalues of ?

(A) 1, 0

Y√‡ √‡
,
(B)

Y√‡ √‡
,
(C)
j j

√‡ √‡
, 1−
(D)

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JAM 2026 Physics (PH)

Q.27 Consider the following vector M⃗ = ( F ˆ.

Which of the following statements is correct for the resultant vector ∇⃗ × ∇⃗ × M⃗ ?

(A) It lies in (F – plane

(B) It lies in F – plane

(C) It lies in ( - plane

(D) It is along the x direction

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JAM 2026 Physics (PH)

Q.28 Two coherent plane waves having wavelength Š and wavevectors

⃗ = ( ̂−
√
̂) and ⃗ = (− ̂−
√
̂), are incident on a screen
‹ ‹
placed on the ( - plane. The overlap of the waves on the plane of the screen
produces interference fringes.

The fringe width (center-to-center spacing of bright fringes) will be:

(A) Š
2

(B) 2Š

(C) √3Š
2

(D) Š

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JAM 2026 Physics (PH)

Q.29 Consider a Carnot cycle as shown in the figure. The ideal gas expanded from
volume M1 to M2 along the path AB. During this process, the temperature o1 is
constant and the entropy changes from Œ1 to Œ2 . o2 is the temperature of the
cold bath.

Which of the following statements is correct?

(A) Work done along the path AB is • # = −Ž yo1 ln M2
M 1

(B) Work done along the path BC is •#% = 0

(C) Work done along the path CD is •%• = −Ž yo1 ln M2
M 1

(D) Work done along the path DA is •• = 0

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JAM 2026 Physics (PH)

Q.30 The speed of an object of mass 20 kg increases from 2 m/s to 6 m/s in 10 s.

The power required, in Watts, is:

(A) 64

(B) 54

(C) 32

(D) 72

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Section B: Q.31 – Q.40 Carry TWO marks each.

Q.31 The displacement of a vibrating string of finite length stretched along the
( −axis is given by

F((, ) = 2 cos( () sin( )

where, is the amplitude, = 2L/Š is the wavenumber and is the angular
frequency.

Which of the following statements is/are correct for the standing wave?

(A) The nodes are at ( = d ‹, where n is an integer

(B) The antinodes are at ( = ‘d + ’ ‹, where n is an integer

(C) The nodes are at ( = ‘d + ’ ‹, where n is an integer

(D) The antinodes are at ( = d ‹, where n is an integer

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JAM 2026 Physics (PH)

Q.32 In the circuit shown in the figure, the Zener voltage Vz is 20 V and the
maximum Zener current IZM is 60 mA.

For what value(s) of the input voltage Vi , the Zener diode is in ON state?

(A) 20 V

(B) 25 V

(C) 35 V

(D) 40 V

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Q.33 Consider a particle of mass in a rotating frame. The force acting on the
particle is expressed as ]⃗ = (] + ] ) “̂” + (] + ]j ) “̂• , where “̂” and “̂• are
the radial and angular unit vectors, respectively, and ] = {– , ] =
− {s— , ] = {s–, ]j = 2 {— s— .

Which of the following statements is/are correct?

(A) “̂” and “̂• are not constant unit vectors

(B) ] and ] are fictitious forces

(C) ] and ]j are fictitious forces

(D) ] and ] are zero in uniform circular motion

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Q.34 The events are represented by coordinates ( , (, F, ) in some frame of
reference. Which of the following statements is/are correct?

/ is the speed of light4

(A) Events (1,0, −10,1) and (−1,1, −9,1) are space-like separated

(B) Events (−1,0, −9,1) and (1,1, −10,1) are space-like separated

(C) Events (−10,0,1, −1) and (−9,1, −1, −1) are light-like separated

(D) Events (9, −1,1, −1) and (−10,1,0, −1) are time-like separated

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Q.35 A ball of mass climbs the potential ˜(() = − ( , as shown in the figure.

Assuming that the total energy of the system = \ + ˜(() is conserved,

which of the following correctly describe(s) the plot of velocity (v) as a function
of position (x) of the system for < 0?

(A)

(B)

(C)

(D)

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JAM 2026 Physics (PH)

Q.36 An LC oscillator circuit contains a capacitor of 4.0 µF. The maximum potential
difference across the capacitor is 2 V and the maximum current through the
inductor is 80 mA.

Which of the following statements is/are correct?

(A) The value of inductance is 2.5 mH

(B) The frequency of oscillator is 3.2 kHz

(C) The time for the charge in the capacitor to rise from zero to the maximum is
nearly 0.157 ms

(D) The maximum potential difference across the inductor is 2.0 V

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Q.37 Consider an ideal gas of entropy Œ, molar specific heat %™ , pressure a and
volume M.

Which of the following options is/are true?

(A) Internal energy of the gas depends only on the temperature

(B) Œ ∝ ln M , assuming %™ is constant

(C) Π= 0

(D) Internal energy of the gas depends both on temperature and pressure

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Q.38 Two small circular copper loops P and Q of radii R1 and R2, respectively, are
coaxially placed along the x-axis as shown in the figure. The loops are at a
distance s apart, where s >> R1, R2. The loop Q carrying a steady current I is
moving away along x-axis with a speed \.

Which of the following statements is/are correct?

(A) The magnetic field at the center of P is ∝
›C

(B) The magnetic flux through the loop P is ∝
›C

(C) The emf induced in the loop P is ∝
›œ

(D) The emf induced in the loop P is ∝ \

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JAM 2026 Physics (PH)

Q.39 A charge r is distributed uniformly on the surface of a sphere of radius R.
It is placed inside a concentric conducting hollow sphere of radius 2R. The
outer sphere is earthed.

Which of the following statements is/are correct?

(A) The charge on the inner surface of the outer sphere is r

(B) The flux through a closed surface through the material of the outer sphere is k
••

(C) The charge on the outer surface of the outer sphere is zero

(D) The potential at a radial distance r between the two spheres, y < { < 2y, is
k
j •• ”

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JAM 2026 Physics (PH)

Q.40 Which of the following statements is/are true for a first order phase transition?

[%Ÿ is the molar heat capacity, o is the critical temperature and S is the entropy]

(A) At the transition point %Ÿ → ∞

(B) The derivative of the Gibbs function with respect to pressure changes
continuously across the phase transition

(C) The two thermodynamic states between which the transition takes place are
distinct

(D) Entropy changes discontinuously with temperature at o

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JAM 2026 Physics (PH)

Section C: Q.41 – Q.50 Carry ONE mark each.

Q.41 Considering the diameter of the pupil of a human eye to be 2 mm, the angular
resolution of the eye at a wavelength of 500 nm, in minute of arc, is___ .

(Rounded off to two decimal places)

Q.42 Consider a 10 mW laser beam focused using a biconvex lens to a circular spot of
area 10 7
. The magnitude of the electric field in the focal plane of the lens,
in M/ , is ___. (Rounded off to one decimal place)

[Use permittivity of free space £8 = 8.854 × 10 % /(Ž ), and speed of
light = 3 × 10N /2]

Q.43 An OP-AMP has differential gain of G = 4000, two input voltages M¤ = 120
µV and M¤ = 80 µV, and CMRR = 100. The output voltage, in mV, is _______.
(Answer in integer)

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JAM 2026 Physics (PH)

Q.44 A particle of mass 10 7
kg is moving along a circular orbit of radius 1 nm. The
speed of the particle corresponds to the average thermal energy at temperature
10 nK. Assuming the Bohr’s angular momentum quantization condition, the
quantum number of the circular path of the particle is ___.

(Answer in integer)

[Use ℎ = 6.64 × 10 j
J s and ¦ =1.38 × 10 J/K]

Q.45 One mole of an ideal gas undergoes a reversible isothermal expansion from
M¤ = 1.5 × 10 ‡ to M§ = 1.6 × 10 ‡ at a temperature 273 ¨. The
amount of heat transfer during the process is ©y, where y is the gas constant.
The value of © is ___ .

(Rounded off to one decimal place)

Q.46 The value of ª1 − = √3« is ___.

(Answer in integer)

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Q.47 Two thermodynamic systems separated by diathermic wall have the equations
‡
of state ˜ = y Ž o and ˜ = y Ž o , where y is the gas constant.

Ž , Ž and o , o are the mole numbers and the temperature of the two systems,
respectively. The composite system in equilibrium has the total energy
1.5 × 10 Joule. If Ž = 3 and Ž = 2, then the internal energy ˜ of the
system one is _______.

(Answer in integer)

Q.48 Light of wavelength 500 nm is incident on the surface of Na metal for
photoelectric emission. The corresponding threshold wavelength is 600 nm. The
maximum kinetic energy of the emitted electron, in eV, is ___ .

(Rounded off to two decimal places)

[Use Planck’s constant h = 6.625 ×10-34 J s, speed of light c = 3 × 10N m/s,
charge of electron “ = 1.6 × 10 O
C]

Q.49 The first order Bragg peak for (100) plane of a material with simple cubic
structure is measured using an X-ray of wavelength 1Å. If the lattice constant is
5 Å then the Bragg peak is observed at an angle, in degrees, _____.

(Rounded off to two decimal places)

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JAM 2026 Physics (PH)

Q.50 Consider an ensemble of hydrogen gas. The temperature, in ¨, at which the rms
speed of the hydrogen molecule is twice the rms speed of the molecule at 300 ¨
is ________.

(Answer in integer)

Section C: Q.51 – Q.60 Carry TWO marks each.

Q.51 A particle of mass undergoes periodic motion in one-dimension with its total
GX
energy given as = (— + j ( j , where is a positive constant and (— = GH .

Assuming that is conserved, the time period o has the relation o ∝ /•
.
The value of d is ______.

(Answer in integer)

Q.52 A spacecraft is placed 200 above Earth in a circular orbit. The minimum
change in the speed required to place the spacecraft in a parabolic orbit, in
/2, is _____.

(Rounded off to one decimal place)

[Use ¬ = 6.67 × 10 Ž / p , mass of Earth = 6 × 10 j p, radius of
Earth = 6400 ]

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JAM 2026 Physics (PH)

Q.53 Consider a light source having a spectral linewidth of 1010 Hz, used in a
Michelson interferometer. The mirrors M1 and M2 are equidistant from the
beam-splitter of negligible thickness as shown in the figure. The minimum
distance d2 that the mirror M1 is to be moved for the interference pattern to
completely disappear, in , is ___.

(Rounded off to one decimal place)

[Use speed of light to be 3 × 10N /2]

Q.54 Muons are unstable relativistic particles created at high altitudes above the
Earth, having a lifetime of 2.2 × 10 n 2 in their rest frame. As measured by an
observer on the ground, the minimum velocity the muon requires to travel a
distance of 6000 is \. The value of \/ is ______.

(Rounded off to three decimal places)

[Speed of light = 3 × 10N /2]

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Q.55 On the surface of a thin water film of refractive index 1.33, two light beams of
wavelength Š = 0.64 e and Š = 0.40 e are incident at an angle of 30°.
The light of wavelength Š exhibits maximum reflection, but that of wavelength
Š is not reflected at all. The minimum thickness of the water film, in e , is
_____ .

(Rounded off to two decimal places)
[Assume refractive index is independent of wavelength]

Q.56 An electron is confined in a one-dimensional box of width v = 10 Å. The
electron in the first excited state de-excites to the ground state. The wavelength
of the emitted radiation, in µm, is ___.

(Rounded off to one decimal place)

[Use the mass of the electron ¯ = 9.1 × 10 kg, Planck’s constant
ℎ = 6.625 ×10-34 J s, = 3 × 10N /2 ]

Q.57 An electron is accelerated through a potential of 200 V and then it passes
through a slit of width 1.0 d held normal to the path of the electron. Assuming
the uncertainty relation Δ(ΔpX ≈ ℏ/2 , maximum scattering angle of the
electron after the slit is © × 10 radian.

The value of © is _____.

(Rounded off to nearest integer)

Given ℏ = 1.054 ×10-34 J s

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Q.58 A uniform electric field of 70 V/m makes an angle of 60° with the positive x-
axis, as shown in the figure. The potential difference between the points P and
Q which are 2 m and √3 m away from the origin, in Volts, is _____.

(Rounded off to one decimal place)

Q.59 Consider a simple pendulum of length ° and time period o. In a laboratory
experiment, the time for 100 oscillations is measured to be 80 2 using a stop-
watch with least count 1 2. The gravitational constant is known with a
percentage error of 2.5%.

The percentage error in the measured length of the pendulum, in %, is _____ .

(Answer in integer)

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Q.60 A particle of mass m in a potential M(() = ( is described by normalized
(•Y )
wavefunction ∑„
•J7ª√2« • ((), where ² • ³ are the eigenstates of the

´ ¶
particle. The energy corresponding to the wavefunction, in units of µ , is
m

_____.

(Rounded off to two decimal places)

~
[Given: ∑„
•J7(?)
•
= , ? > 14
~

END OF THE QUESTION PAPER

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