QFT-1

JEE Mains QFT‑1 2025 – FULL PAPER

General Instructions:

• All questions carry equal marks.
• Marking Scheme for Single Correct Type (MCQs): +4 for correct answer, −1 for wrong answer.
• Marking Scheme for Numerical Type: +4 for correct answer, 0 for wrong answer.
• Use of calculators is not permitted.
• Use the given constants where required.

PHYSICS (Maximum Marks: 100)

Section A – Single Correct Type
(+4 for correct, −1 for wrong)

1. The electric field in a region is given by \( \vec{E} = \frac{E_0}{l} \hat{i} \). The charge contained inside a cubical volume bounded by \( x = 0, x = l, y = 0, y = l, z = 0, z = l \) is:

   • A. \( 2\epsilon_0 E_0 l^2 \)
   • B. \( \epsilon_0 E_0 l^2 \)
   • C. \( 6\epsilon_0 E_0 l^2 \)
   • D. zero

2. The molar specific heat of a gas from kinetic theory is \( \frac{5}{2}R \). If it is not specified whether it is \( C_p \) or \( C_v \), one could conclude that the molecules of the gas:

   • A. Are definitely monoatomic
   • B. Are definitely rigid diatomic
   • C. Are definitely non-rigid diatomic
   • D. Can be monoatomic or rigid diatomic

3. A particle of mass \( M \) is moving in a horizontal circle of radius \( R \) with uniform speed \( V \). When it moves from one point to the diametrically opposite point, its:

   • A. Momentum does not change
   • B. Momentum changes by \( 2MV \)
   • C. Kinetic energy changes by \( \frac{MV^2}{4} \)
   • D. Kinetic energy changes by \( MV^2 \)

4. Diameter of a steel ball is measured using a Vernier callipers … If the zero error is −0.03 cm, then the mean corrected diameter is:

   • A. 0.53 cm
   • B. 0.56 cm
   • C. 0.59 cm
   • D. 0.52 cm

5. A solid iron ball and an aluminium ball of the same diameter are released together in a lake. Which ball will reach the bottom first? (Neglect viscosity and \( \rho_{Al} < \rho_{Fe} \)):

   • A. Aluminium Ball
   • B. Iron Ball
   • C. Both will reach at the same time
   • D. Data insufficient

6. The combination of NAND gates shown is equivalent to:

   
   • A. An OR gate and an AND gate respectively
   • B. An AND gate and a NOT gate respectively
   • C. An AND gate and an OR gate respectively
   • D. An OR gate and a NOT gate respectively

7. A double star system … Choose the correct option:

   • A. If \( T_A > T_B \), then \( R_A > R_B \)
   • B. If \( T_A > T_B \), then \( M_A > M_B \)
   • C. \( \left( \frac{T_A}{T_B} \right)^2 = \left( \frac{R_A}{R_B} \right)^3 \)
   • D. \( T_A = T_B \)

8. A student is at a distance of 16 m from a bus when the bus begins to move with a constant acceleration of 9 m/s². The minimum velocity with which the student should run towards the bus to catch it is \( \alpha \sqrt{2} \) m/s. The value of \( \alpha \) is:

   • A. 10
   • B. 12
   • C. 15
   • D. 20

9. An ideal gas is taken from point A to point C on a P–V diagram through two processes AOC and ABC as shown in the figure. Process AOC is isothermal:

   • A. Process AOC requires more heat than process ABC
   • B. Process ABC requires more heat than process AOC
   • C. Both require same heat
   • D. Data insufficient for comparison

10. A battery of internal resistance 2 Ω is connected to a variable resistor (4 Ω to 10 Ω). With resistance initially 4 Ω, if the value is increased then:

    • A. Power consumed will decrease
    • B. Power consumed will increase
    • C. Power may increase or decrease
    • D. Power will first increase then decrease

11. To estimate \( g = 4\pi^2 \frac{L}{T^2} \), error in \( L \) is ± 2% and error in \( T \) is ± 3%. The error in \( g \) is:

    • A. ± 8%
    • B. ± 5%
    • C. ± 3%
    • D. ± 6%

12. A machine 70% efficient raises a 10 kg body ... On reaching the ground, KE of body is:

    • A. 0
    • B. 70 J
    • C. 50 J
    • D. 35 J

13. A ray of light is incident at 45° from air to glass slab at A. Minimum refractive index of slab for TIR at B is:

    • A. \( \sqrt{\frac{3}{2}} \)
    • B. \( \sqrt{\frac{2}{3}} \)
    • C. \( \sqrt{\frac{3}{4}} \)
    • D. None of these

14. Light beam exerts force 4.8×10⁻⁴ N on area 0.04 m², absorbs 80%, transmits rest. Speed of light = 3×10⁸ m/s. Find intensity in W/cm²:

    • A. 300
    • B. 400
    • C. 450
    • D. 500

15. Four light‑weight rods ... Conclusion:

    • A. B is paramagnetic
    • B. C is diamagnetic
    • C. D is ferromagnetic
    • D. A is non‑magnetic

16. A gas satisfies PV\(^{5/3}\) = K. Dimensional formula of K is:

    • A. \( ML^4T^{-2} \)
    • B. \( ML^2T^{-2} \)
    • C. \( ML^6T^{-2} \)
    • D. \( MLT^{-2} \)

17. In a series LR AC circuit ... Reactance of inductor is:

    • A. \( \frac{\sqrt7}{2} \)
    • B. \( \sqrt2 \)
    • C. \( 2\sqrt2 \)
    • D. \( 2\sqrt3 \)

18. Wheel with I = 2.5, ω from 40 to 60 rad/s, torque = 10 Nm. Time taken is:

    • A. 6 s
    • B. 5 s
    • C. 4.5 s
    • D. 4 s

19. Identify correct nuclear force statements:

    • A. (i) only
    • B. (ii), (iii)
    • C. (i), (ii)
    • D. (i), (ii), (iii)

20. De Broglie λ of electron moving at 1.5×10⁸ m/s equals that of a photon. Ratio KE_electron / E_photon is:

    • A. 1.5
    • B. 1
    • C. 0.5
    • D. 0.25

Section B – Numerical Type
(+4 for correct, 0 for wrong)

1. The length of an open organ pipe is twice that of another closed organ pipe. Fundamental frequency of the open pipe is 100 Hz. The frequency of the 3rd harmonic of the closed pipe is: ______ Hz
2. A proton is fired ... closest approach = 10 fm. Find de Broglie λ at start (in fm): ______
3. In gravity‑free space, a charged bead moves along a rough rod in a B‑field. Distance covered before rest: ______ m
4. A circular coil with area 0.01 m², 40 turns, rotated in a 0.05 T field at ω=50 rad/s. Average power loss due to Joule heating = 25 mW. Find coil resistance: ______ Ω
5. Block of m=0.3 kg on spring (k=?). Compressed x, released. After x/2 displacement hits identical block, moves at 2 m/s. If total initial spring energy is E, find 10E: ______