Practice Questions

Q28.The output of the circuit is low (zero) for : (A) X = 0, Y = 0 (B) X = 0, Y = 1 (C) X = 1, Y = 0 (D) X = 1, Y = 1 Choose the correct answer from the options given below : (1) (B), (C) and (D) only (2) (A), (B) and (C) only (3) (A), (C) and (D) only (4) (A), (B) and (D) only

Q28.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury 2025 (29 Jan Shift 1) JEE Main Previous Year Paper tube, the tube will be damaged. Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor + , where ω is frequency of the supply across resistor R and inductor L . If the choke (R/√R2 ω2L2) coil were not used, the voltage across the resistor would be the same as the applied voltage. In the light of the above statements, choose the most appropriate answer from the options given below : (1) (A) is true but (R) is false (2) Both (A) and (R) are true and (R) is the correct explanation of (A) (3) (A) is false but (R) is true (4) Both (A) and (R) are true but (R) is not the correct explanation of (A)

Q28.Two charges 7μc and −4μc are placed at (−7 cm, 0, 0) and (7 cm, 0, 0) respectively. Given, ϵ0 = 8.85 × 10−12C2 N−1 m−2 , the electrostatic potential energy of the charge configuration is : (1) -1.8 J (2) -2.0 J (3) -1.5 J (4) -1.2 J

Q28.The torque due to the force (2^i + ^j + 2^k) about the origin, acting on a particle whose position vector is (^i + ^j + ^k), would be (1) ^i −^k (2) ^i + ^k (3) ^j + ^k (4) ^i −^j + ^k

Q28.An alternating current is given by I = IA sin ωt + IB cos ωt. The r.m.s current will be ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ 2025 (24 Jan Shift 1) JEE Main Previous Year Paper (1) |IA+IB| (2) A+I2B √2 √I2 2 B + I2B (4) √I2A+I2 (3) √I2A 2

Q29.A car of mass ' m ' moves on a banked road having radius ' r ' and banking angle θ. To avoid slipping from banked road, the maximum permissible speed of the car is v0 . The coefficient of friction μ between the wheels of the car and the banked road is θ θ tan tan 0−rg (1) μ = v2o+rg (2) μ = v2 θ tan θ rg−v2 tan rg+v2o 0 θ θ tan v2o+rg tan 0−rg (4) μ = (3) μ = v2 θ tan θ rg+v2 tan rg−v2o 0

Q29.As shown below, bob A of a pendulum having massless string of length ' R ' is released from 60∘ to the vertical. It hits another bob B of half the mass that is at rest on a friction less table in the center. Assuming elastic collision, the magnitude of the velocity of bob A after the collision will be (take g as acceleration due to gravity.) (1) 4 3 √Rg (2) 23 √Rg (3) √Rg (4) 13 √Rg

Q29.Given a thin convex lens (refractive index μ2 ), kept in a liquid (refractive index μ1, μ1 < μ2 ) having radii of curvatures |R1| and |R2|. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place? (1) μ1|R1|⋅|R2| (2) μ1|R1|⋅|R2| μ2(|R1|+|R2|)−μ1|R2| μ2(|R1|+|R2|)−μ1|R1| (3) (μ2+μ1)|R1| (4) μ1|R1|⋅|R2| (μ2−μ1) μ2(2|R1|+|R2|)−μ1√|R1|⋅|R2|

Q29.Young's double slit inteference apparatus is immersed in a liquid of refractive index 1.44. It has slit separation of 1.5 mm . The slits are illuminated by a parallel beam of light whose wavelength in air is 690 nm . The fringe-width on a screen placed behind the plane of slits at a distance of 0.72 m , will be : (1) 0.23 mm (2) 0.33 mm (3) 0.63 mm (4) 0.46 mm

Q29.A symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4 D then the power of a part of the divided lens is (1) D (2) 8D (3) 2D (4) 4D

Q29.Two point charges −4μc and 4μc, constituting an electric dipole, are placed at (−9, 0, 0)cm and (9, 0, 0)cm in a uniform electric field of strength 104NC−1 . The work done on the dipole in rotating it from the equilibrium through 180∘ is : (1) 18.4 mJ (2) 14.4 mJ (3) 12.4 mJ (4) 16.4 mJ

Q29.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : With the increase in the pressure of an ideal gas, the volume falls off more rapidly in an isothermal process in comparison to the adiabatic process. Reason (R) : In isothermal process, PV = constant, while in adiabatic process PVγ = constant. Here γ is the ratio of specific heats, P is the pressure and V is the volume of the ideal gas. In the light of the above statements, choose the correct answer from the options given below : (1) Both (A) and (R) are true and (R) is the correct (2) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true 2025 (29 Jan Shift 2) JEE Main Previous Year Paper

Q29.A thin prism P1 with angle 4∘ made of glass having refractive index 1.54 , is combined with another thin prism P2 made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism P2 in degrees is (1) 3 (2) 16/3 (3) 4 (4) 1.5

Q29.A body of mass 4 kg is placed on a plane at a point P having coordinate (3, 4)m . Under the action of force → F = (2^i + 3^j)N , it moves to a new point Q having coordinates (6, 10)m in 4 sec . The average power and instanteous power at the end of 4 sec are in the ratio of : (1) 13 : 6 (2) 4 : 3 (3) 1 : 2 (4) 6 : 13

Q29.An amount of ice of mass 10−3 kg and temperature −10∘C is transformed to vapour of temperature 110∘C by applying heat. The total amount of work required for this conversion is, (Take, specific heat of ice = 2100Jkg−1 K−1 , specific heat of water = 4180Jkg−1 K−1 , specific heat of steam = 1920Jkg−1 K−1 , Latent heat of ice = 3.35 × 105Jkg−1 and Latent heat of steam = 2.25 × 106 Jkg−1 ) (1) 3043 J (2) 3024 J (3) 3003 J (4) 3022 J

Q30. The truth table for the circuit given below is : (1) (2) (3) (4)

Q30.An electron in the ground state of the hydrogen atom has the orbital radius of 5.3 × 10−11 m while that for the electron in third excited state is 8.48 × 10−10 m . The ratio of the de Broglie wavelengths of electron in the excited state to that in the ground state is (1) 3 (2) 16 (3) 9 (4) 4

Q30.Match List - I with List - II. (1) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (2) (A)-(I), (B)-(III), (C)-(IV), (D)-(II) (3) (A)-(III), (B)-(I), (C)-(II), (D)-(IV) (4) (A)-(III), (B)-(I), (C)-(IV), (D)-(II)

Q30.A satellite is launched into a circular orbit of radius ' R ' around the earth. A second satellite is launched into an orbit of radius 1.03 R . The time period of revolution of the second satellite is larger than the first one approximately by (1) 9% (2) 3% (3) 4.5% (4) 2.5%

Q30.For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are V0 and E0 , respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) V0 and E04 (2) zero and E016 (3) zero and E0 (4) V0 and E0 8 2 16

Q30.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum. Reason ( R): Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true and (R) is the correct (2) Both (A) and (R) are true but (R) is not the explanation of (A) correct explanation of (A) (3) (A) is false but (R) is true (4) (A) is true but ( R) is false

Q30.Refer to the circuit diagram given in the figure. which of the following observations are correct? A. Total resistance of circuit is 6Ω B. Current in Ammeter is 1 A C. Potential across AB is 4 Volts. D. Potential across 2025 (23 Jan Shift 1) JEE Main Previous Year Paper CD is 4 Volts E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below: (1) A, B and D Only (2) A, B and C Only (3) A, C and D Only (4) B, C and E Only

Q30.The magnitude of heat exchanged by a system for the given cyclic process ABCA (as shown in figure) is (in SI unit) : (1) 5π (2) 40π (3) 10π (4) zero

Q30.A particle of mass ' m ' and charge ' q ' is fastened to one end ' A ' of a massless string having equilibrium length l, whose other end is fixed at point ' O '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x -axis is (1) √qEl2 m (2) √qElm (3) √qEl4 m (4) √2qElm

Q30.A massless spring gets elongated by amount x1 under a tension of 5 N . Its elongation is x2 under the tension of 7 N . For the elongation of (5x1 −2x2), the tension in the spring will be, (1) 39 N (2) 15 N (3) 11 N (4) 20 N