Practice Questions

Q41.A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration ' 3a′ will be (Take ' g ' as acceleration due to gravity) (1) 2Ma (2) 3Ma 3a+g 2a−g (3) 3Ma (4) 2Ma 2a+g 3a−g

Q41.If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. (1) 27 days (2) 1 day (3) 81 days (4) 3 days

Q41.The temperature of a body in air falls from 40∘C to 24∘C in 4 minutes. The temperature of the air is 16∘C. The temperature of the body in the next 4 minutes will be: (1) 14 3 ∘C (2) 423 ∘C (3) 28 3 ∘C (4) 563 ∘C

Q42.The pair of physical quantities not having same dimensions is : (1) Pressure and Young's modulus (2) Surface tension and impulse (3) Torque and energy (4) Angular momentum and Planck's constant

Q42.In the diagram given below, there are three lenses formed. Considering negligible thickness of each of them as compared to |R1| and |R2|, i.e., the radii of curvature for upper and lower surfaces of the glass lens, the power of the combination is (1) 1 − + |R2| |R2| 6 ( |R1|1 1 ) (2) −16 ( |R1|1 1 ) (3) 1 + − |R2| |R2| 6 ( |R1|1 1 ) (4) −16 ( |R1|1 1 )

Q42.A light source of wavelength λ illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength λ , then the maximum 2 kinetic energy of ejected electrons will be (The work function of metal is 1 eV ) (1) 3 eV (2) 2 eV (3) 6 eV (4) 5 eV

Q42.The center of mass of a thin rectangular plate (fig - x ) with sides of length a and b, whose mass per unit area (σ) varies as σ = σ0xab (where σ0 is a constant), would be (1) ( 23 a, 2b ) (2) ( a2 , 2b ) (3) ( 13 a, 2b ) (4) ( 23 a, 23 b)

Q42.A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is : (1) 3 (2) 4 4 3 (3) 5 (4) 2 2 5

Q42.A parallel plate capacitor was made with two rectangular plates, each with a length of l = 3 cm and breath of b = 1 cm . The distance between the plates is 3μ m . Out of the following, which are the ways to increase the capacitance by a factor of 10 ? A. l = 30 cm, b = 1 cm, d = 1μ m B. l = 3 cm, b = 1 cm, d = 30μ m C. l = 6 cm, b = 5 cm, d = 3μ m D. l = 1 cm, b = 1 cm, d = 10μ m E. l = 5 cm, b = 2 cm, d = 1μ m Choose the correct answer from the options given below: 2025 (24 Jan Shift 1) JEE Main Previous Year Paper (1) A only (2) C only (3) B and D only (4) C and E only

Q42. A poly-atomic molecule ( CV = 3R, CP = 4R, where R is gas constant) goes from phase space point A (PA = 105 Pa, VA = 4 × 10−6 m3) to point B (PB = 5 × 104 Pa, VB = 6 × 10−6 m3) to point 2025 (29 Jan Shift 2) JEE Main Previous Year Paper C (PC = 104 Pa, VC = 8 × 10−6 m3). A to B is an adiabatic path and B to C is an isothermal path. The net heat absorbed per unit mole by the system is : (1) 500R(ln 3 + ln 4) (2) 450R(ln 4 −ln 3) (3) 500R ln 2 (4) 400R ln 4

Q42.Regarding self-inductance: A. The self-inductance of the coil depends on its geometry. B. Self-inductance does not depend on the permeability of the medium. C. Self-induced e.m.f. opposes any change in the current in a circuit. D. Self-inductance is electromagnetic analogue of mass in mechanics. E. Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below: (1) A, B, C, E only (2) B, C, D, E only (3) A, C, D, E only (4) A, B, C, D only

Q42.A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that θ(t) = 5t2 −8t, where θ(t) is the angular position of the rotating disc as a function of time t. How much power is delivered by the applied torque, when t = 2 s ? (1) 72MR2 (2) 8MR2 (3) 108MR2 (4) 60MR2

Q43.A parallel plate capacitor of capacitance 1μ F is charged to a potential difference of 20 V . The distance between plates is 1μ m . The energy density between plates of capacitor is. (1) 2 × 10−4 J/m3 (2) 1.8 × 105 J/m3 (3) 1.8 × 103 J/m3 (4) 2 × 102 J/m3

Q43.The maximum percentage error in the measurment of density of a wire is [Given, mass of wire = (0.60 ± 0.003)g radius of wire = (0.50 ± 0.01)cm length of wire = (10.00 ± 0.05)cm] (1) 8 (2) 5 (3) 4 (4) 7 for another diatomic molecules, but for rigid molecules and γ2 =

Q43.Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and ε0 is the permittivity of free space between the plates, then potential energy stored in the capacitor is (1) ε0E2Ad (2) 12 ε0E2Ad (3) 1 4 ε0E2Ad (4) 34 ε0E2Ad

Q43.The energy of a system is given as E(t) = α3e−βt , where t is the time and β = 0.3 s−1 . The errors in the measurement of α and t are 1.2% and 1.6% , respectively. At t = 5 s, maximum percentage error in the energy is : (1) 6% (2) 8.4% (3) 11.6% (4) 4%

Q43.In a Young's double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of P1 and P2 are orthogonal to each other. The polarizer P3 covers both the slits with its transmission axis at 45∘ to those of P1 and P2 . An unpolarized light of wavelength λ and intensity I0 is incident on P1 and P2 . The 2025 (24 Jan Shift 2) JEE Main Previous Year Paper intensity at a point after P3 where the path difference between the light waves from s1 and s2 is λ3 , is (1) I0 (2) I0 2 4 (3) I0 (4) I0 3

Q43.Consider I1 and I2 are the currents flowing simultaneously in two nearby coils 1 & 2, respectively. If L1 = self inductance of coil 1, M12 = mutual inductance of coil 1 with respect to coil 2, then the value of induced emf in coil 1 will be Options (1) ε1 = −L1 dI2dt −M12 dI1dt (2) ε1 = −L1 dI1dt −M12 dI2dt (3) ε1 = −L1 dI1dt −M12 dI1dt (4) ε1 = −L1 dI1dt + M12 dI2dt

Q43.The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km . (1) 12 (2) 3 (3) 6 (4) 9

Q43.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion-(A) : If Young's double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer. Reason-(R) : The speed of light reduces in an optically denser medium than air while its frequency does not change. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true but (R) is not the (2) Both (A) and (R) are true and (R) is the correct correct explanation of (A) explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true

Q43.Match List - I with List - II. List - I List - II (A) Magnetic induction (I) Ampere meter 2 (B) Magnetic intensity (II) Weber (C) Magnetic flux (III) Gauss (D) Magnetic moment (IV) Ampere/meter (1) (A)-(I), (B)-(II), (C)-(III), (D)-(IV) (2) (A)-(III), (B)-(IV), (C)-(I), (D)-(II) (3) (A)-(III), (B)-(II), (C)-(I), (D)-(IV) (4) (A)-(III), (B)-(IV), (C)-(II), (D)-(I)

Q43.Which of the following circuits has the same outpur as that of the given circuit? (1) (2) (3) (4)

Q44.Match List - I with List - II. List - I List - II (A) Permeability of free space (I) [M L2 T−2] (B) Magnetic field (II) [M T−2 A−1] (C) Magnetic moment (III) [M L T−2 A−2] (D) Torsional constant (IV) [L2 A] Choose the correct answer from the options given below : (1) (A)-(IV), (B)-(III), (C)-(I), (D)-(II) (2) (A)-(III), (B)-(II), (C)-(IV), (D)-(I) (3) (A)-(I), (B)-(IV), (C)-(II), (D)-(III) (4) (A)-(II), (B)-(I), (C)-(III), (D)-(IV)

Q44.Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor R. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below: (1) A, C Only (2) A, B, D Only (3) C, D Only (4) B, C, D Only

Q44.An object of mass ' m ' is projected from origin in a vertical xy plane at an angle 45∘ with the x axis with an initial velocity v0 . The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [ g is acceleration due to gravity] (1) mv3 o along negative z -axis (2) mv3 o along positive z -axis 2√2g 4√2g (3) mv3o along negative z -axis (4) mv3o along positive z -axis 4√2g 2√2g