QPT01

PHYSICS – JEE MAINS QFT‑1 2025

Marking Scheme: +4 for Correct Answer, –1 for Incorrect Answer

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Single Correct Type (Max Marks: 80)

Only ONE option is correct for each question.

Q1. 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 the surfaces \(x = 0,\, x = l,\, y = 0,\, y = l,\, z = 0,\, z = l\) is:

A. \( 2\varepsilon_0 E_0 l^2 \)
B. \( \varepsilon_0 E_0 l^2 \)
C. \( 6\varepsilon_0 E_0 l^2 \)
D. zero

Q2. 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

Q3. 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 a diametrically opposite point:

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

Q4. Diameter of a steel ball is measured using a Vernier calliper (main scale division = 0.1 cm, 10 Vernier divisions = 9 main scale divisions). Three readings:

S.No.	Main Scale (cm)	VS divisions
1	0.5	8
2	0.5	4
3	0.5	6

Zero error = –0.03 cm. The mean corrected diameter is:

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

Q5. A solid iron ball and an aluminium ball of the same diameter are released together in a lake. Neglect viscosity and \( \rho_{Al} < \rho_{Fe} \). Which reaches bottom first?

A. Aluminium Ball
B. Iron Ball
C. Both same time
D. Data insufficient

Q6. The combination of NAND gates shown is equivalent to: [Insert NAND Gates Image Here]

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

Q7. A double star system has stars \(A\) and \(B\) with periods \(T_A, T_B\), radii \(R_A, R_B\), masses \(M_A, M_B\):

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. \(T_A = T_B\)

Q8. A student is 16 m from a bus when it starts with acceleration \(9 \,\text{m/s}^2\). Minimum running speed to catch it is \( \alpha\sqrt{2} \,\text{m/s} \). \( \alpha = \) ?

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

Q9. An ideal gas goes from A to C on a PV diagram via isothermal AOC or via ABC (non‑isothermal). [Insert PV Diagram Image Here]

A. AOC requires more heat than ABC
B. ABC requires more heat than AOC
C. Both require same heat
D. Data insufficient

Q10. A battery of \(r = 2\,\Omega\) is in series with variable \(R\) initially \(4\,\Omega\). If \(R\) is increased:

A. Power in \(R\) decreases
B. Power increases
C. May increase or decrease
D. Increases then decreases

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Numerical Type (Max Marks: 20)

Write numerical answer, no choices given.

Q21. An open organ pipe is twice the length of a closed pipe. If \(f_{\text{open}}\) = 100 Hz, find the frequency of the 3rd harmonic of the closed pipe.

Q22. A proton approaches a nucleus with \(Q = 120e\) and closest approach \(= 10\,\text{fm}\). Find de Broglie wavelength at start.
Given: \(m_p = \frac{5}{3} \times 10^{-27}\,\text{kg},\ h = 4.2\times 10^{-15},\ \frac{1}{4\pi\varepsilon_0} = 9\times 10^9,\ 1\,\text{fm} = 10^{-15}\,\text{m}\).

Q23. In zero‑gravity, a bead (\(q = 1\mu \text{C}, m = 3\,\text{mg}\)) is on a rough rod (\(\mu = 0.3\)) in \(B = 0.2\,\text{T}\) ⊥ rod. Projected at 4 m/s. Find stopping distance (m).

Q24. A coil (area = 0.01 m², turns = 40) rotates at \(50\,\text{rad/s}\) in \(B = 0.05\,\text{T}\). Average Joule loss = 25 mW. Find coil resistance.

Q25. A block (m = 0.3 kg) is attached to a spring (k unknown), compressed by \(x\) and released. After moving \(x/2\), it collides and sticks with an identical block, moving at \(2\,\text{m/s}\). If total initial energy is \(E\), find \(10E\).