Practice Questions

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.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.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.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.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.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.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.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

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.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

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.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.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.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)

Q31.A bob of mass m is suspended at a point O by a light string of length l and left to perform vertical motion (circular) as shown in figure. Initially, by applying horizontal velocity v0 at the point ' A ', the string becomes slack when, the bob reaches at the point ' D '. The ratio of the kinetic energy of the bob at the points B and C is ______ -. (1) 1 (2) 2 (3) 4 (4) 3

Q31.The difference of temperature in a material can convert heat energy into electrical energy. To harvest the heat energy, the material should have (1) high thermal conductivity and high electrical (2) low thermal conductivity and low electrical conductivity conductivity (3) high thermal conductivity and low electrical (4) low thermal conductivity and high electrical conductivity conductivity

Q31.A uniform magnetic field of 0.4 T acts perpendicular to a circular copper disc 20 cm in radius. The disc is having a uniform angular velocity of 10πrads−1 about an axis through its centre and perpendicular to the disc. What is the potential difference developed between the axis of the disc and the rim ? (π = 3.14) (1) 0.5024 V (2) V (3) 0.2512V V (4) 0.1256V V

Q31.A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.] (1) 137.5 nm (2) 275 nm (3) 94.8 nm (4) 68.7 nm

Q31.Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α) and (45∘+ α), respectively, with the horizontal direction. The ratio of their maximum heights attained is : (1) 1−tan α (2) 1−sin 2α 1+tan α 1+sin 2α (3) 1+sin 2α (4) 1+sin α 1−sin 2α 1−sin α

Q32. An infinite wire has a circular bend of radius a, and carrying a current I as shown in figure. The magnitude of 2025 (28 Jan Shift 2) JEE Main Previous Year Paper magnetic field at the origin O of the arc is given by : μ0 (1) a 4π I [ π2 + 1] (2) 4πμ0 aI [ 3π2 + 2] μ0 (3) 2π a I [ π2 + 2] (4) 4πμ0 aI [ 3π2 + 1]

Q32.Water flows in a horizontal pipe whose one end is closed with a valve. The reading of the pressure gauge attached to the pipe is P1 . The reading of the pressure gauge falls to P2 when the valve is opened. The speed of water flowing in the pipe is proportional to (1) P1 −P2 (2) (P1 −P2)4 (3) (P1 −P2)2 (4) √P1 −P2

Q32.Given is a thin convex lens of glass (refractive index μ ) and each side having radius of curvature R. One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that 2025 (22 Jan Shift 1) JEE Main Previous Year Paper the image gets formed on the object itself ? (1) R/μ (2) R/(2μ −3) (3) μR (4) R/(2μ −1)

Q32.In photoelectric effect, the stopping potential (V0)v/s frequency (ν) curve is plotted. ( h is the Planck's constant and ϕ0 is work function of metal ) (A) V0v/sν is linear. (B) The slope of V0v/sν curve = ϕ0h (C) h constant is related to the slope of V0v/sν line. (D) The value of electric charge of electron is not required to determine h using the V0v/sν curve. (E) The work function can be estimated without knowing the value of h. Choose the correct answer from the options given below : (1) (C) and (D) only (2) (A), (C) and (E) only (3) (A), (B) and (C) only (4) (D) and (E) only