Physics Verified Solutions

JEE Main 2025 — 04 April 2025 (Physics) Solutions

Step-by-step Physics explanations, formulas used, alternative methods, and practice mode for 04 April 2025 (Shift 2).

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Physics Questions (25 Questions)

Practice Mode Interactive

Q1physicsKinematics & Vectors• Class 11

ModerateMCQ

A particle of mass m moves in a circular path of radius R with variable speed v = α√s, where s is the distance traversed along the circle and α is a positive constant. The magnitude of the net acceleration of the particle after covering one complete revolution is:

α² √(1 + (4π)²)

(α² / 2) √(1 + 16π²)

α² √(1/4 + 4π²)

(α² / 2) √(1 + (4πR)²)

Official Key:B• Topic: Non-Uniform Circular Motion

Q2physicsThermodynamics & Kinetic Theory (KTG)• Class 11

EasyMCQ

An ideal gas undergoes a thermodynamic cyclic process consisting of three steps: (i) Isobaric expansion at pressure P₀ from volume V₀ to 2V₀, (ii) Isochoric cooling to pressure P₀/2, and (iii) Isothermal compression back to initial state (P₀, V₀). The total work done by the gas in one complete cycle is:

P₀V₀ [ 1 - ln 2 ]

P₀V₀ [ 1 - 2 ln 2 ]

P₀V₀ [ 1/2 + ln 2 ]

P₀V₀ [ 1 - (1/2) ln 2 ]

Official Key:A• Topic: Cyclic Processes & Work Done

Q3physicsRotational Dynamics & COM• Class 11

EasyMCQ

A solid uniform sphere of mass M and radius R rolls without slipping down an inclined plane of inclination θ. The linear acceleration of the center of mass of the sphere is:

(5/7) g sin θ

(3/5) g sin θ

(2/3) g sin θ

(1/2) g sin θ

Official Key:A• Topic: Pure Rolling Motion on Incline

Q4physicsOptics (Ray & Wave Optics)• Class 12

ModerateMCQ

In a Young’s Double Slit Experiment, monochromatic light of wavelength λ = 600 nm illuminates two slits separated by distance d = 1 mm. The screen is placed at distance D = 2 m. When a thin transparent mica sheet of thickness t = 1.8 μm and refractive index μ = 1.5 is placed in front of one slit, the central bright fringe shifts by a distance of:

1.8 mm

2.4 mm

0.9 mm

3.6 mm

Official Key:A• Topic: Young’s Double Slit Experiment & Fringe Shifts

Q5physicsMagnetic Effects of Current & Magnetism• Class 12

EasyMCQ

Two long parallel straight wires carrying currents of I₁ = 10 A and I₂ = 20 A in the same direction are separated by a distance of 10 cm in air. The force per unit length between the wires is:

4 × 10⁻⁴ N/m (Attractive)

4 × 10⁻⁴ N/m (Repulsive)

2 × 10⁻⁴ N/m (Attractive)

8 × 10⁻⁴ N/m (Repulsive)

Official Key:A• Topic: Force Between Parallel Currents

Q6physicsElectromagnetic Induction & AC Circuits• Class 12

EasyMCQ

In a series LCR resonant circuit, the inductance L = 10 mH, capacitance C = 1 μF, and resistance R = 10 Ω. The Quality Factor (Q-factor) of the circuit is equal to:

100

0.1

Official Key:A• Topic: LCR Resonance & Quality Factor

Q7physicsElectrostatics & Capacitors• Class 12

ModerateMCQ

Two concentric conducting spherical shells of radii R and 2R carry charges +Q and +2Q respectively. The electric potential at a distance r = 1.5R from the common center is:

k [ Q / (1.5R) + 2Q / (2R) ] = (5/3) kQ/R

k [ 3Q / (1.5R) ] = 2 kQ/R

k [ Q / R + 2Q / (1.5R) ]

k [ Q / (1.5R) ]

Official Key:A• Topic: Concentric Spherical Shells Potential

Q8physicsLaws of Motion & Friction• Class 11

EasyMCQ

A block of mass m = 2 kg rests on a rough horizontal surface with static friction coefficient μ_s = 0.5. If a horizontal force F = 8 N is applied on the block, the frictional force acting on the block is: (Take g = 10 m/s²)

8 N (Static)

10 N (Limiting)

0 N

4 N

Official Key:A• Topic: Static vs Limiting Friction

Q9physicsOscillations (SHM) & Waves• Class 11

EasyMCQ

An open organ pipe of length L₁ and a closed organ pipe of length L₂ vibrate in their fundamental modes. If their fundamental frequencies are equal, the ratio L₁ / L₂ is:

2 : 1

1 : 2

4 : 1

1 : 1

Official Key:A• Topic: Organ Pipes & Standing Sound Waves

Q10physicsModern Physics & Semiconductors• Class 12

ModerateMCQ

In a hydrogen-like atom, an electron makes a transition from n = 3 to n = 1 level. The ratio of the de Broglie wavelength of the electron in orbit n = 3 to that in orbit n = 1 is:

3 : 1

9 : 1

1 : 3

1 : 9

Official Key:A• Topic: Bohr Model & de Broglie Wavelength

Q11physicsGravitation & Planetary Motion• Class 11

EasyMCQ

The escape velocity from the surface of Earth is v_e = 11.2 km/s. If a planet has twice the radius and 8 times the mass of Earth, the escape velocity from its surface is:

22.4 km/s

11.2 km/s

44.8 km/s

5.6 km/s

Official Key:A• Topic: Escape Velocity

Q12physicsOptics (Ray & Wave Optics)• Class 12

EasyMCQ

A convex lens of focal length f = 20 cm in air is immersed in water (refractive index μ_w = 4/3). If the refractive index of glass is μ_g = 3/2, the focal length of the lens in water is:

80 cm

40 cm

20 cm

10 cm

Official Key:A• Topic: Lens Maker’s Formula

Q13physicsWork, Energy & Power• Class 11

EasyMCQ

The work done by an external agent in slowly stretching a spring of force constant k = 200 N/m from an elongation of x₁ = 5 cm to x₂ = 15 cm is:

2.0 Joules

1.0 Joules

4.0 Joules

0.5 Joules

Official Key:A• Topic: Spring Potential Energy

Q14physicsModern Physics & Semiconductors• Class 12

EasyMCQ

In an intrinsic semiconductor at room temperature, the number of conduction electrons is n_e and holes is n_h. When doped with a trivalent impurity (acceptor):

n_h >> n_e (P-type semiconductor)

n_e >> n_h (N-type semiconductor)

n_e = n_h

n_e and n_h both become zero

Official Key:A• Topic: Semiconductors & Doping

Q15physicsElectromagnetic Induction & AC Circuits• Class 12

EasyMCQ

A metal rod of length L = 1 m rotates with uniform angular velocity ω = 20 rad/s in a plane perpendicular to a uniform magnetic field B = 0.5 T about an axis passing through one of its ends. The induced EMF across the rod is:

5.0 Volts

10.0 Volts

2.5 Volts

20.0 Volts

Official Key:A• Topic: Rotating Rod Motional EMF

Q16physicsElectrostatics & Capacitors• Class 12

EasyMCQ

A parallel plate capacitor with air between the plates has capacitance C₀ = 10 μF. When a dielectric slab of dielectric constant K = 4 is inserted to completely fill the space between the plates while the capacitor remains connected to a battery of voltage V = 12 V, the charge stored in the capacitor increases by:

360 μC

480 μC

120 μC

240 μC

Official Key:A• Topic: Dielectric Insertion with Battery Connected

Q17physicsCurrent Electricity & Circuits• Class 12

EasyMCQ

In a meter bridge experiment, the balance point is obtained at 40 cm from the left end when a resistance of 6 Ω is connected in the left gap. The unknown resistance X in the right gap is equal to:

9.0 Ω

4.0 Ω

6.0 Ω

12.0 Ω

Official Key:A• Topic: Meter Bridge Resistance Measurement

Q18physicsThermodynamics & Kinetic Theory (KTG)• Class 11

EasyMCQ

A thermodynamic engine operates between temperatures T₁ = 600 K (source) and T₂ = 300 K (sink). If the engine absorbs 1000 Joules of heat from the source in each cycle, the maximum possible mechanical work produced per cycle is:

500 Joules

600 Joules

300 Joules

1000 Joules

Official Key:A• Topic: Carnot Cycle Efficiency

Q19physicsOscillations (SHM) & Waves• Class 11

EasyMCQ

A particle executes Simple Harmonic Motion (SHM) with an amplitude A = 10 cm and time period T = 6 s. The time taken by the particle to travel from the mean position (x = 0) to half of its amplitude (x = 5 cm) is:

0.5 seconds

1.0 seconds

1.5 seconds

0.25 seconds

Official Key:A• Topic: SHM Time Period & Phase

Q20physicsKinematics & Vectors• Class 11

ModerateMCQ

A projectile is launched with speed u = 40 m/s at an angle of 30° with the horizontal. The radius of curvature of its trajectory at the highest point is: (Take g = 10 m/s²)

120 meters

160 meters

80 meters

240 meters

Official Key:A• Topic: Projectile Motion Radius of Curvature

Q21physicsModern Physics & Semiconductors• Class 12

EasyNumerical

An electron is accelerated from rest across a potential difference of V = 150 Volts. The de Broglie wavelength associated with the electron is equal to (in Angstroms, Å, rounded to two decimal places):

Official Key:1.00• Topic: Dual Nature of Matter & de Broglie Wavelength

Q22physicsWork, Energy & Power• Class 11

EasyNumerical

A body of mass m = 5 kg falls freely from rest under gravity from a height h = 20 m. The power delivered by the gravitational force on the body just before it hits the ground is (in Watts): (Take g = 10 m/s²)

Official Key:1000• Topic: Instantaneous Mechanical Power

Q23physicsMagnetic Effects of Current & Magnetism• Class 12

EasyNumerical

A circular coil of 50 turns and radius 10 cm carries a steady current of 2 A. The magnetic dipole moment of the coil is (in A·m², take π = 3.14):

Official Key:3.14• Topic: Magnetic Dipole Moment of Coils

Q24physicsOptics (Ray & Wave Optics)• Class 12

EasyNumerical

A light ray passes through an equilateral triangular glass prism of refractive index μ = √3 with minimum deviation. The angle of minimum deviation (in degrees) is:

Official Key:60• Topic: Prism Formula & Minimum Deviation

Q25physicsModern Physics & Semiconductors• Class 12

EasyNumerical

A radioactive sample has a half-life of T_half = 10 days. If the initial activity is A₀ = 800 Bq, the time required (in days) for its activity to reduce to 100 Bq is:

Official Key:30• Topic: Radioactive Decay Law