JEE Physics Practice Questions

Easy•Alternating Current

In a series LCR circuit,

L = 0.1

H and

C = 10

μF. The resonant frequency is:

Medium•Atoms

The ratio of energies of hydrogen atom in 2nd and 4th excited states is:

Easy•Bohr Model

The energy of an electron in the nth orbit of hydrogen atom is given by Eₙ = -13.6/n² eV. The energy required to excite the electron from n = 1 to n = 2 is:

Medium•Capacitors

[JEE Mains 2026] An air-filled parallel plate capacitor of capacitance C has plate separation d. A dielectric slab (K = 2) of width d/2 is inserted between the plates. What is the new capacitance?

Easy•Capacitance

Three capacitors of

2

μF,

3

μF, and

6

μF are connected in series. The equivalent capacitance is:

Easy•Capacitors

[JEE Mains 2026] Two capacitors C and 2C are charged to potentials V and 2V respectively. They are then connected in parallel with opposite polarity. What is the common potential?

Easy•Center Of Mass

Two particles of masses

3

kg and

5

kg are placed at

(2, 3)

and

(6, 7)

respectively. The coordinates of center of mass are:

Easy•Circular Motion

A particle moves in a circle of radius

2

m with constant speed

4

m/s. Its centripetal acceleration is:

Medium•Ray Optics

[JEE Mains 2026] A convex lens of focal length 10 cm and a concave lens of focal length 20 cm are placed in contact. An object is placed 30 cm from the combination. What is the position of the final image?

Easy•Communication

An audio signal of amplitude

3

V modulates a carrier of amplitude

15

V. The modulation index is:

Easy•Current Electricity

A wire of resistance

10

Ω carries a current of

2

A. The potential difference across it is:

Medium•Current Electricity

In the circuit shown, each resistor has resistance

R

. The equivalent resistance between points A and B is: ``` A ---[R]---+---[R]---B | [R] | -------+------- ```

Medium•Waves

[JEE Mains 2026] A detector moves from point A towards a stationary source and then moves away to point B. The observed frequencies differ by 20%. If the source emits a frequency of 500 Hz, and the speed of the detector is v

_d

, what is the ratio v

_d

/v (where v is the speed of sound)?

Easy•Dual Nature

The energy of a photon of wavelength

620

nm is (Take

hc = 1240

eV·nm):

Easy•Electric Field

The electric field at a distance of 2 m from a point charge of 4 μC in vacuum is:

Easy•Electromagnetic Induction

[JEE Mains 2026] In a series R–L circuit, the voltage of the battery is 12 V. Resistance is 4 Ω and inductance is 2 H. Find the energy stored in the inductor when the current reaches half of its maximum value.

Easy•Electromagnetic Induction

A coil of

100

turns has magnetic flux changing from

0.02

Wb to

0.04

Wb in

0.1

s. The induced EMF is:

Easy•Electromagnetism

A circular loop of radius

7

cm carries a current of

2

A. Its magnetic moment is:

Hard•Electromagnetism

A series LCR circuit is connected to a

45 \sin (\omega t)

Volt source. The resonant angular frequency of the circuit is

10^{5} \mathrm{rad} \mathrm{s}^{-1}

and current amplitude at resonance is

I_{0}

. When the angular frequency of the source is

\omega=8 \times 10^{4} \mathrm{rad} \mathrm{s}^{-1}

, the current amplitude in the circuit is

0.05 I_{0}

. If

L=50 \mathrm{mH}

, match each entry in List-I with an appropriate value from List-II and choose the correct option.

\textbf{List-I}

(P)

I_{0}

in

\mathrm{mA}

(Q) The quality factor of the circuit (R) The bandwidth of the circuit in

\mathrm{rad} \mathrm{s}^{-1}

(S) The peak power dissipated at resonance in Watt

\textbf{List-II}

(1) 44.4 (2) 18 (3) 400 (4) 2250 (5) 500

Medium•Electromagnetism

A current carrying wire heats a metal rod. The wire provides a constant power

(P)

to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature

(T)

in the metal rod changes with time

(t)

as

T(t)=T_{0}\left(1+\beta t^{\frac{1}{4}}\right)

where

\beta

is a constant with appropriate dimension while

T_{0}

is a constant with dimension of temperature. The heat capacity of the metal is,

Easy•Electrostatics

Two identical point charges

q

are placed

r

apart in vacuum. If the magnitude of the electrostatic force between them is

F

, what will be the force when the distance between them is doubled?

Easy•Electrostatics

Work done in moving a charge of

2

μC between two points with potential difference

10

V is:

Easy•Electrostatics

The electric field at a distance of

2

m from a point charge of

8 \times 10^{-9}

C in vacuum is (Take

k = 9 \times 10^9

N·m²/C²):

Easy•Electrostatics

A solid sphere of radius

R

has a uniform volume charge density

\rho

. The electric field at a distance

r = R/2

from the center of the sphere is:

Easy•Electrostatics

An electric dipole of moment

\vec{p}

is placed in a non-uniform electric field

\vec{E} = E_0 x\hat{i}

, where

E_0

is a constant. If the dipole is aligned along the x-axis with its center at the origin, the net force on the dipole is:

Easy•Electrostatics

A parallel plate capacitor with plate area

A

and separation

d

is charged to a potential difference

V

. A dielectric slab of dielectric constant

K

and thickness

d

is inserted between the plates while the capacitor remains connected to the battery. The ratio of the final energy stored to the initial energy stored is:

Easy•Electrostatics

A cube of side

a

is placed in a uniform electric field

\vec{E} = E_0\hat{i}

. The total electric flux through the cube is:

Easy•Gravitation

If the radius of Earth becomes half without change in mass, the acceleration due to gravity will become:

Medium•Electrostatics

Three point charges

+2\,\mu C

,

-3\,\mu C

, and

+4\,\mu C

are placed at the vertices of an equilateral triangle of side

1

m. The electric potential at the centroid of the triangle is (Take

k = 9 \times 10^9

N·m²/C²):

Medium•Electrostatics

The electric potential in a region is given by

V = 3x^2 + 4y

volts, where

x

and

y

are in meters. The magnitude of the electric field at the point

(1, 2)

is:

Medium•Electrostatics

[JEE Mains 2026] A simple pendulum with a bob of mass m and charge q is in equilibrium in the presence of a uniform horizontal electric field E. If the thread makes an angle θ with the vertical, what is the tension in the thread?

Easy•Fluid Mechanics

The pressure at the bottom of a tank of water of depth

10

m is (g =

10

m/s², atmospheric pressure =

10^5

Pa):

Hard•General

In a radioactive sample,

{ }_{19}^{40} \mathrm{~K}

nuclei either decay into stable

{ }_{20}^{40} \mathrm{Ca}

nuclei with decay constant

4.5 \times 10^{-10}

per year or into stable

{ }_{18}^{40} \mathrm{Ar}

nuclei with decay constant

0.5 \times 10^{-10}

per year. Given that in this sample all the stable

{ }_{20}^{40} \mathrm{Ca}

and

{ }_{18}^{40} \mathrm{Ar}

nuclei are produced by the

{ }_{19}^{40} \mathrm{~K}

nuclei only. In time

t \times 10^{9}

years, if the ratio of the sum of stable

{ }_{20}^{40} \mathrm{Ca}

and

{ }_{18}^{40} \mathrm{Ar}

nuclei to the radioactive

{ }_{19}^{40} \mathrm{~K}

nuclei is 99 , the value of

t

will be, [Given:

\ln 10=2.3]

Hard•General

A thin spherical insulating shell of radius

R

carries a uniformly distributed charge such that the potential at its surface is

V_{0}

. A hole with a small area

\alpha 4 \pi R^{2}(\alpha \ll 1)

is made on the shell without affecting the rest of the shell. Which one of the following statements is correct?

Medium•General

An accident in a nuclear laboratory resulted in deposition of a certain amount of radioactive material of half-life 18 days inside the laboratory. Tests revealed that the radiation was 64 times more than the permissible level required for safe operation of the laboratory. What is the minimum number of days after which the laboratory can be considered safe for use?

Medium•General

List-I shows different radioactive decay processes and List-II provides possible emitted particles. Match each entry in List-I with an appropriate entry from List-II, and choose the correct option.

\textbf{List-I}

(P)

{ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}

(Q)

{ }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb}

(R)

{ }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb}

(S)

{ }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra}

\textbf{List-II}

(1) one

\alpha

particle and one

\beta^{+}

particle (2) three

\beta^{-}

particles and one

\alpha

particle (3) two

\beta^{-}

particles and one

\alpha

particle (4) one

\alpha

particle and one

\beta^{-}

particle (5) one

\alpha

particle and two

\beta^{+}

particles

Medium•General

A heavy nucleus

Q

of half-life 20 minutes undergoes alpha-decay with probability of

60 \%

and beta-decay with probability of

40 \%

. Initially, the number of

Q

nuclei is 1000. The number of alpha-decays of

Q

in the first one hour is

Medium•General

Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is

0.5 \mathrm{~mm}

. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.

Measurement condition	Main scale reading	Circular scale reading
Two arms of gauge touching each other without wire	0 division	4 divisions
Attempt-1: With wire	4 divisions	20 divisions
Attempt-2: With wire	4 divisions	16 divisions

What are the diameter and cross-sectional area of the wire measured using the screw gauge?

Easy•Gravitation

The ratio of escape velocity to orbital velocity for a satellite orbiting close to Earth's surface is:

Medium•Gravitation

[JEE Mains 2026] A satellite is orbiting Earth at a height equal to the radius of Earth (R). What is the ratio of its orbital velocity to the escape velocity from Earth's surface?

Medium•Thermodynamics

[JEE Mains 2026] For an ideal gas, the volume is made 8 times and temperature is decreased to 1/4 of its initial value during an adiabatic process (q = 0). What is the value of γ (ratio of specific heats) for this gas?

Easy•Kinematics

A body starting from rest accelerates uniformly at

2

m/s². The distance covered in the 5th second is:

Easy•Kinematics

A projectile is thrown with velocity

20

m/s at an angle of

30°

with the horizontal. The horizontal range of the projectile is (Take

g = 10

m/s²):

Easy•Kinetic Theory

The ratio of rms speeds of

O_2

and

H_2

at the same temperature is:

Easy•Laws Of Motion

A force acts on a body of mass

5

kg for

2

s. If the velocity changes from

3

m/s to

7

m/s, the force applied is:

Easy•Magnetic Effects

A wire of length

0.5

m carrying current

2

A is placed perpendicular to a magnetic field of

0.4

T. The force on the wire is:

Easy•Magnetic Force

An electron moving with velocity 2 × 10⁶ m/s enters a uniform magnetic field of 0.5 T perpendicular to its direction of motion. The magnitude of the force experienced by the electron is: (e = 1.6 × 10⁻¹⁹ C)

Easy•Magnetism

A long straight wire carries a current of

10

A. The magnetic field at a perpendicular distance of

5

cm from the wire is (Take

\mu_0 = 4\pi \times 10^{-7}

T·m/A):

Easy•Mechanical Properties

A wire of length

2

m and cross-sectional area

10^{-6}

m² stretches by

0.1

mm under a load of

1

kg. The Young's modulus is (g =

10

m/s²):

Hard•Mechanics

A uniform wooden stick of mass

1.6 \mathrm{~kg}

and length

l

rests in an inclined manner on a smooth, vertical wall of height

h(<l)

such that a small portion of the stick extends beyond the wall. The reaction force of the wall on the stick is perpendicular to the stick. The stick makes an angle of

30^{\circ}

with the wall and the bottom of the stick is on a rough floor. The reaction of the wall on the stick is equal in magnitude to the reaction of the floor on the stick. The ratio

h / l

and the frictional force

f

at the bottom of the stick are

\left(g=10 \mathrm{~ms} \mathrm{~s}^{2}\right)

Hard•Mechanics

A bar of mass

M=1.00 \mathrm{~kg}

and length

L=0.20 \mathrm{~m}

is lying on a horizontal frictionless surface. One end of the bar is pivoted at a point about which it is free to rotate. A small mass

m=0.10 \mathrm{~kg}

is moving on the same horizontal surface with

5.00 \mathrm{~m} \mathrm{~s}^{-1}

speed on a path perpendicular to the bar. It hits the bar at a distance

L / 2

from the pivoted end and returns back on the same path with speed

\mathrm{v}

. After this elastic collision, the bar rotates with an angular velocity

\omega

. Which of the following statement is correct?

Easy•Work Energy Power

A body of mass

2

kg has momentum

10

kg·m/s. Its kinetic energy is:

Hard•Mechanics

A rocket is launched normal to the surface of the Earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is

3 \times 10^{5}

times heavier than the Earth and is at a distance

2.5 \times 10^{4}

times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is

v_{e}=11.2 \mathrm{~km} \mathrm{~s}^{-1}

. The minimum initial velocity

\left(v_{S}\right)

required for the rocket to be able to leave the Sun-Earth system is closest to (Ignore the rotation and revolution of the Earth and the presence of any other planet)

[\mathrm{A}] \quad v_{S}=22 \mathrm{~km} \mathrm{~s}^{-1}

[\mathrm{B}] v_{S}=42 \mathrm{~km} \mathrm{~s}^{-1}

[\mathrm{C}] \quad v_{S}=62 \mathrm{~km} \mathrm{~s}^{-1}

D.

v_{S}=72 \mathrm{~km} \mathrm{~s}^{-1}

Medium•Mechanics

Consider an expanding sphere of instantaneous radius

R

whose total mass remains constant. The expansion is such that the instantaneous density

\rho

remains uniform throughout the volume. The rate of fractional change in density

\left(\frac{1}{\rho} \frac{d \rho}{d t}\right)

is constant. The velocity

v

of any point on the surface of the expanding sphere is proportional to

Medium•Mechanics

Consider a spherical gaseous cloud of mass density

\rho(r)

in free space where

r

is the radial distance from its center. The gaseous cloud is made of particles of equal mass

m

moving in circular orbits about the common center with the same kinetic energy

K

. The force acting on the particles is their mutual gravitational force. If

\rho(r)

is constant in time, the particle number density

n(r)=\rho(r) / m

is [

G

is universal gravitational constant]

Medium•Mechanics

Two satellites

\mathrm{P}

and

\mathrm{Q}

are moving in different circular orbits around the Earth (radius

R

). The heights of

\mathrm{P}

and

\mathrm{Q}

from the Earth surface are

h_{\mathrm{P}}

and

h_{\mathrm{Q}}

, respectively, where

h_{\mathrm{P}}=R / 3

. The accelerations of

\mathrm{P}

and

\mathrm{Q}

due to Earth's gravity are

g_{\mathrm{P}}

and

g_{\mathrm{Q}}

, respectively. If

g_{\mathrm{P}} / g_{\mathrm{Q}}=36 / 25

, what is the value of

h_{\mathrm{Q}}

?

Medium•Mechanics

A particle of mass

m

is moving in the

x y

-plane such that its velocity at a point

(x, y)

is given as

\overrightarrow{\mathrm{v}}=\alpha(y \hat{x}+2 x \hat{y})

, where

\alpha

is a non-zero constant. What is the force

\vec{F}

acting on the particle?

Medium•Mechanics

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is

\delta T=0.01

seconds and he measures the depth of the well to be

L=20

meters. Take the acceleration due to gravity

g=10 \mathrm{~ms}^{-2}

and the velocity of sound is

300 \mathrm{~ms}^{-1}

. Then the fractional error in the measurement,

\delta L / L

, is closest to

Easy•Modern Physics

The work function of a metal is

4.2

eV. The maximum wavelength of light that can eject photoelectrons from this metal is (Take

hc = 1240

eV·nm):

Hard•Modern Physics

The electrostatic energy of

Z

protons uniformly distributed throughout a spherical nucleus of radius

R

is given by

E=\frac{3}{5} \frac{Z(Z-1) e^{2}}{4 \pi \varepsilon_{0} R}

The measured masses of the neutron,

{ }_{1}^{1} \mathrm{H},{ }_{7}^{15} \mathrm{~N}

and

{ }_{8}^{15} \mathrm{O}

are

1.008665 \mathrm{u}, 1.007825 \mathrm{u}

,

15.000109 \mathrm{u}

and

15.003065 \mathrm{u}

, respectively. Given that the radii of both the

{ }_{7}^{15} \mathrm{~N}

and

{ }_{8}^{15} \mathrm{O}

nuclei are same,

1 \mathrm{u}=931.5 \mathrm{MeV} / c^{2}

(

c

is the speed of light) and

e^{2} /\left(4 \pi \varepsilon_{0}\right)=1.44 \mathrm{MeV} \mathrm{fm}

. Assuming that the difference between the binding energies of

{ }_{7}^{15} \mathrm{~N}

and

{ }_{8}^{15} \mathrm{O}

is purely due to the electrostatic energy, the radius of either of the nuclei is

\left(1 \mathrm{fm}=10^{-15} \mathrm{~m}\right)

Hard•Modern Physics

A photoelectric material having work-function

\phi_{0}

is illuminated with light of wavelength

\lambda\left(\lambda<\frac{h c}{\phi_{0}}\right)

. The fastest photoelectron has a de Broglie wavelength

\lambda_{d}

. A change in wavelength of the incident light by

\Delta \lambda

results in a change

\Delta \lambda_{d}

in

\lambda_{d}

. Then the ratio

\Delta \lambda_{d} / \Delta \lambda

is proportional to

[\mathrm{A}] \quad \lambda_{d} / \lambda

[\mathrm{B}] \quad \lambda_{d}^{2} / \lambda^{2}

[\mathrm{C}] \lambda_{d}^{3} / \lambda

[\mathrm{D}] \lambda_{d}^{3} / \lambda^{2}

Hard•Modern Physics

When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is

6.0 \mathrm{~V}

. This potential drops to

0.6 \mathrm{~V}

if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take

\frac{h c}{e}=1.24 \times

10^{-6} \mathrm{~J} \mathrm{mC}^{-1}

.]

Medium•Modern Physics

A human body has a surface area of approximately

1 \mathrm{~m}^{2}

. The normal body temperature is

10 \mathrm{~K}

above the surrounding room temperature

T_{0}

. Take the room temperature to be

T_{0}=300 \mathrm{~K}

. For

T_{0}=300 \mathrm{~K}

, the value of

\sigma T_{0}^{4}=460 \mathrm{Wm}^{-2}

(where

\sigma

is the StefanBoltzmann constant). Which of the following options is/are correct?

Medium•Modern Physics

In a historical experiment to determine Planck's constant, a metal surface was irradiated with light of different wavelengths. The emitted photoelectron energies were measured by applying a stopping potential. The relevant data for the wavelength

(\lambda)

of incident light and the corresponding stopping potential

\left(V_{0}\right)

are given below :

$\lambda(\mu \mathrm{m})$	$V_{0}($ Volt $)$
0.3	2.0
0.4	1.0
0.5	0.4

Given that

c=3 \times 10^{8} \mathrm{~m} \mathrm{~s}^{-1}

and

e=1.6 \times 10^{-19} \mathrm{C}

, Planck's constant (in units of

J \mathrm{~s}

) found from such an experiment is

Medium•Modern Physics

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option. [Given: Wien's constant as

2.9 \times 10^{-3} \mathrm{~m}-\mathrm{K}

and

\frac{h c}{e}=1.24 \times 10^{-6} \mathrm{~V}-\mathrm{m}

]

\textbf{List-I}

(P)

2000 \mathrm{~K}

(Q)

3000 \mathrm{~K}

(R)

5000 \mathrm{~K}

(S)

10000 \mathrm{~K}

\textbf{List-II}

(1) The radiation at peak wavelength can lead to emission of photoelectrons from a metal of work function

4 \mathrm{eV}

. (2) The radiation at peak wavelength is visible to human eye. (3) The radiation at peak emission wavelength will result in the widest central maximum of a single slit diffraction. (4) The power emitted per unit area is

1 / 16

of that emitted by a blackbody at temperature

6000 \mathrm{~K}

. (5) The radiation at peak emission wavelength can be used to image human bones.

Medium•Modern Physics

Young's modulus of elasticity

Y

is expressed in terms of three derived quantities, namely, the gravitational constant

G

, Planck's constant

h

and the speed of light

c

, as

Y=c^{\alpha} h^{\beta} G^{\gamma}

. Which of the following is the correct option?

Medium•Laws Of Motion

[JEE Mains 2026] Two masses M and 4M are placed at a distance d apart. A third mass m is placed between them. If the net gravitational force on mass m due to M and 4M is F when m is at distance d/3 from M, what is F in terms of GmM/d²?

Easy•Momentum

A force of 10 N acts on a body of mass 2 kg for 3 seconds. If the body was initially at rest, its final velocity is:

Easy•Nuclei

A radioactive sample has a half-life of

4

days. The fraction remaining after

12

days is:

Medium•Optics

A double convex lens made of glass (refractive index

1.5

) has both radii of curvature equal to

20

cm. The power of the lens is:

Easy•Oscillations

If the length of a simple pendulum is increased by

44\%

, the percentage change in time period is:

Medium•Photoelectric Effect

The work function of a metal is 2 eV. Light of wavelength 400 nm is incident on it. The maximum kinetic energy of the emitted photoelectrons is: (h = 6.6 × 10⁻³⁴ J·s, c = 3 × 10⁸ m/s, 1 eV = 1.6 × 10⁻¹⁹ J)

Easy•Power

A 10 Ω resistor carries a current of 2 A. The power dissipated in the resistor is:

Medium•Kinematics

[JEE Mains 2026] A particle is projected at an angle of 60° with the ground. When the projectile makes an angle of 30° with the horizontal, its speed is 20 m/s. What is the initial velocity of the projectile?

Easy•Ray Optics

An object is placed

20

cm from a concave mirror of focal length

10

cm. The image distance is:

Medium•Ray Optics

[JEE Mains 2026] The refractive index of a prism with angle A = 45° is √2. What should be the angle of incidence for a light ray such that the emerging ray grazes out of the other surface?

Easy•Refraction

Light travels from a medium with refractive index 1.5 to air. The critical angle for total internal reflection is:

Easy•Current Electricity

A wire of length 2 m and cross-sectional area 1 mm² has resistivity 1.7 × 10⁻⁸ Ω·m. The resistance of the wire is:

Medium•Rotational Motion

A disc rotating at

60

rpm has its radius halved with no external torque. The new angular velocity is:

Medium•Rotational Motion

The moment of inertia of a uniform circular disc of mass

M

and radius

R

about an axis tangent to the disc and lying in its plane is:

Easy•Semiconductors

In a p-n junction diode, the depletion region is formed due to:

Easy•Simple Harmonic Motion

A simple pendulum of length 1 m oscillates on Earth (g = 10 m/s²). Its time period is approximately:

Easy•Sound

Two tuning forks of frequencies

256

Hz and

260

Hz are sounded together. The beat frequency is:

Easy•Thermal Properties

A metal rod of length

1

m at

20°C

has coefficient of linear expansion

2 \times 10^{-5}

/°C. Its length at

70°C

is:

Medium•Thermal Properties

[JEE Mains 2026] Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion of the rods are 2 × 10⁻⁵ /°C and 3 × 10⁻⁵ /°C. If the temperature is increased from 20°C to 120°C, find the final length of the combination (in cm).

Easy•Thermodynamics

An ideal gas at

27°C

is heated at constant pressure to

327°C

. The ratio of final to initial volume is:

Hard•Thermodynamics

List I describes thermodynamic processes in four different systems. List II gives the magnitudes (either exactly or as a close approximation) of possible changes in the internal energy of the system due to the process. List-I (I)

10^{-3} \mathrm{~kg}

of water at

100^{\circ} \mathrm{C}

is converted to steam at the same temperature, at a pressure of

10^5 \mathrm{~Pa}

. The volume of the system changes from

10^{-6} \mathrm{~m}^3

to

10^{-3} \mathrm{~m}^3

in the process. Latent heat of water

=2250 \mathrm{~kJ} / \mathrm{kg}

. (II) 0.2 moles of a rigid diatomic ideal gas with volume

V

at temperature

500 \mathrm{~K}

undergoes an isobaric expansion to volume

3 \mathrm{~V}

. Assume

R=8.0 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}

. (III) One mole of a monatomic ideal gas is compressed adiabatically from volume

V=\frac{1}{3} m^3

and pressure

2 \mathrm{kPa}

to volume

\frac{V}{8}

. (IV) Three moles of a diatomic ideal gas whose molecules can vibrate, is given

9 \mathrm{~kJ}

of heat and undergoes isobaric expansion. List-II (P)

2 \mathrm{~kJ}

(Q)

7 \mathrm{~kJ}

(R)

4 \mathrm{~kJ}

(S)

5 \mathrm{~kJ}

(T)

3 \mathrm{~kJ}

Which one of the following options is correct?\

Easy•Work, Energy And Power

[JEE Mains 2026] The potential energy of a particle varies with position x as U(x) = 4x² - 8x + 3 (in SI units). At what position is the particle in stable equilibrium?

Hard•Thermodynamics

A gas is enclosed in a cylinder with a movable frictionless piston. Its initial thermodynamic state at pressure

P_{i}=10^{5} \mathrm{~Pa}

and volume

V_{i}=10^{-3} \mathrm{~m}^{3}

changes to a final state at

P_{f}=(1 / 32) \times 10^{5} \mathrm{~Pa}

and

V_{f}=8 \times 10^{-3} \mathrm{~m}^{3}

in an adiabatic quasi-static process, such that

P^{3} V^{5}=

constant. Consider another thermodynamic process that brings the system from the same initial state to the same final state in two steps: an isobaric expansion at

P_{i}

followed by an isochoric (isovolumetric) process at volume

V_{f}

. The amount of heat supplied to the system in the two-step process is approximately

Hard•Thermodynamics

One mole of an ideal gas expands adiabatically from an initial state

\left(T_{\mathrm{A}}, V_{0}\right)

to final state

\left(T_{\mathrm{f}}, 5 V_{0}\right)

. Another mole of the same gas expands isothermally from a different initial state

\left(T_{\mathrm{B}}, V_{0}\right)

to the same final state

\left(T_{\mathrm{f}}, 5 V_{0}\right)

. The ratio of the specific heats at constant pressure and constant volume of this ideal gas is

\gamma

. What is the ratio

T_{\mathrm{A}} / T_{\mathrm{B}}

?

Medium•Thermodynamics

An ideal gas expands isothermally from volume

V

to

2V

. If the same gas expands from volume

V

to

2V

adiabatically, then the work done in isothermal expansion is:

Medium•Thermodynamics

The ends

\mathrm{Q}

and

\mathrm{R}

of two thin wires,

\mathrm{PQ}

and RS, are soldered (joined) together. Initially each of the wires has a length of

1 \mathrm{~m}

at

10^{\circ} \mathrm{C}

. Now the end

P

is maintained at

10^{\circ} \mathrm{C}

, while the end

\mathrm{S}

is heated and maintained at

400^{\circ} \mathrm{C}

. The system is thermally insulated from its surroundings. If the thermal conductivity of wire

\mathrm{PQ}

is twice that of the wire

R S

and the coefficient of linear thermal expansion of

\mathrm{PQ}

is

1.2 \times 10^{-5} \mathrm{~K}^{-1}

, the change in length of the wire

P Q

is

Medium•Thermodynamics

An ideal gas is in thermodynamic equilibrium. The number of degrees of freedom of a molecule of the gas is

n

. The internal energy of one mole of the gas is

U_{n}

and the speed of sound in the gas is

\mathrm{v}_{n}

. At a fixed temperature and pressure, which of the following is the correct option?

Easy•Units And Dimensions

[JEE Mains 2026] Find the dimensions of the expression ε₀E²t, where ε₀ is permittivity, E is electric field, and t is time.

Easy•Units And Dimensions

The dimensional formula of Planck's constant is:

Easy•Wave Optics

In a Young's double slit experiment, the slit separation is 0.1 mm and the screen is placed 1 m from the slits. If light of wavelength 600 nm is used, the fringe width is:

Easy•Wave Optics

In YDSE, the slit separation is

1

mm, screen distance is

1

m, and wavelength is

600

nm. The fringe width is:

Easy•Waves

A wave has frequency

500

Hz and wavelength

0.5

m. Its velocity is:

Medium•Waves

A string of length

1

m and linear mass density

0.01

kg/m is stretched with a tension of

40

N. The frequency of the second harmonic is:

Medium•Waves

[JEE Mains 2026] In an open organ pipe, the 3rd and 6th harmonic frequencies differ by 3200 Hz. If the speed of sound is 320 m/s, find the length of the organ pipe.

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