Practice Questions

Q33.A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sphere be t1 and t2 , respectively, then (1) t1 > t2 (2) t1 = t2 (3) t1 < t2 (4) t1 = 2t2

Q34.Consider a long straight wire of a circular cross-section (radius a) carrying a steady current I. The current is uniformly distributed across this cross-section. The distances from the centre of the wire's cross-section at which the magnetic field [inside the wire, outside the wire] is half of the maximum possible magnetic field, any where due to the wire, will be (1) [a/4, 3a/2] (2) [a/4, 2a] (3) [a/2, 2a] (4) [a/2, 3a]

Q34.A sub-atomic particle of mass 10−30 kg is moving with a velocity 2.21 × 106 m/s. Under the matter wave consideration, the particle will behave closely like (h = 6.63 × 10−34 J. s) (1) Visible radiation (2) Gamma rays (3) Infra-red radiation (4) X-rays

Q34.A Carnot engine (E) is working between two temperatures 473 K and 273 K . In a new system two engines - engine E1 works between 473 K to 373 K and engine E2 works between 373 K to 273 K . If η12, η1 and η2 are the efficiencies of the engines E, E1 and E2 , respectively, then (1) η12 = η1η2 (2) η12 ≥η1 + η2 (3) η12 = η1 + η2 (4) η12 < η1 + η2

Q34. Sliding contact of a potentiometer is in the middle of the potentiometer wire having resistance Rp = 1Ω as shown in the figure. An external resistance of Re = 2Ω is connected via the sliding contact. The electric current in the circuit is : (1) 0.9 A (2) 1.35 A (3) 0.3 A (4) 1.0 A 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q35.At the interface between two materials having refractive indices n1 and n2 , the critical angle for reflection of an em wave is θ1C . The n2 material is replaced by another material having refractive index n3 such that the critical angle at the interface between n1 and n3 materials is θ2C . If n3 > n2 > n1; n2 = 25 and n3 sin θ2C −sin θ1C = 12 , then θ1C is (1) sin−1 ( 16 ) (2) sin−1 ( 13 ) (3) sin−1 ( −56 ) (4) sin−1 ( 23 )

Q35.Consider a moving coil galvanomenter (MCG): A. The torsional constant in moving coil galvanometer has dimentions [ML2 T−2] B. Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C. If we increase number of turns (N) to its double (2 N), then the voltage sensitivity doubles. D. MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E. Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below: 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) A, D Only (2) A, B, E Only (3) B, D, E Only (4) A, B Only

Q35. N equally spaced charges each of value q , are placed on a circle of radius R . The circle rotates about its axis with an angular velocity ω as shown in the figure. A bigger Amperian loop B encloses the whole circle where as a smaller Amperian loop A encloses a small segment. The difference between enclosed currents, IA −IB , for the given Amperian loops is (1) 2π N qω (2) N22π qω (3) N π qω (4) 2πN qω

Q36.A convex lens made of glass (refractive index = 1.5 ) has focal length 24 cm in air. When it is totally immersed in water (refractive index = 1.33 ), its focal length changes to (1) 24 cm (2) 96 cm (3) 48 cm (4) 72 cm

Q36.A ball of mass 100 g is projected with velocity 20 m/s at 60∘ with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is (1) 5 J (2) 15 J (3) 20 J (4) zero

Q36.A uniform rod of mass 250 g having length 100 cm is balanced on a sharp edge at 40 cm mark. A mass of 400 g is suspended at 10 cm mark. To maintain the balance of the rod, the mass to be suspended at 90 cm mark, is (1) 190 g (2) 200 g (3) 300 g (4) 290 g

Q36.A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then D is d (1) 16 (2) 10 5 (3) 15 (4) 25 4

Q36.A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities ρ1 and ρ2′ , respectively. The frequency of 9th harmonic of closed tube is identical with 4th harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is ρ1 : ρ2 = 1 : 16, then the length of the open tube is : (1) 15 7 cm (2) 207 cm (3) 15 9 cm (4) 209 cm

Q36.The width of one of the two slits in Young's double slit experiment is d while that of the other slit is x d. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is 9 : 4 then what is the value of x ? (Assume that the field strength varies according to the slit width.) (1) 4 (2) 5 (3) 3 (4) 2

Q37.In an experiment with photoelectric effect, the stopping potential, (1) increases with increase in the intensity of the (2) decreases with increase in the intensity of the incident light incident light (3) increases with increase in the wavelength of the (4) is ( 1e ) times the maximum kinetic energy of the incident light emitted photoelectrons

Q37.A photograph of a landscape is captured by a drone camera at a height of 18 km . The size of the camera film is 2 cm × 2 cm and the area of the landscape photographed is 400 km2 . The focal length of the lens in the drone camera is : (1) 1.8 cm (2) 0.9 cm (3) 2.8 cm (4) 2.5 cm 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q37.In the experiment for measurement of viscosity ' η ' of given liquid with a ball having radius R, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. This experiment can be utilized to assess the density of a given liquid. E. If 2025 (28 Jan Shift 1) JEE Main Previous Year Paper balls are dropped with some initial speed, the value of η will change. Choose the correct answer from the options given below: (1) A, B and E Only (2) B, D and E Only (3) A, C and D Only (4) C, D and E Only

Q37. Using the given P −V diagram, the work done by an ideal gas along the path ABCD is : (1) 3P0 V0 (2) −4P0 V0 (3) −3P0 V0 (4) 4P0 V0

Q37. List - I List - II Electric field inside (distance r > 0 from center) (A) of a uniformly charged spherical shell with (I) σ/ϵ0 surface charge density σ, and radius R. Electric field at distance r>0 from a uniformly (B) charged infinite plane sheet with surface (II) σ/2ϵ0 Match List - I with List - II. charge density σ. Choose Electric field outside (distance r>0 from center) (C) of a uniformly charged spherical shell with (III) 0 surface charge density σ, and radius R. Electric field between 2 oppositely charged σR2 (D) infinite plane parallel sheets with uniform (IV) ϵ0r2 surface charge density σ. the correct answer from the options given below : (1) (A)-(III), (B)-(II), (C)-(IV), (D)-(I) (2) (A)-(IV), (B)-(II), (C)-(III), (D)-(I) (3) (A)-(II), (B)-(I), (C)-(IV), (D)-(III) (4) (A)-(IV), (B)-(I), (C)-(III), (D)-(II)

Q37.The amount of work done to break a big water drop of radius ' R ' into 27 small drops of equal radius is 10 J . The work done required to break the same big drop into 64 small drops of equal radius will be (1) 15 J (2) 5 J (3) 20 J (4) 10 J

Q38.Due to presence of an em-wave whose electric component is given by E = 100 sin(ωt −kx)NC−1 , a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as (1) 400 sin(ωt −kx)NC−1 (2) 200 sin(ωt −kx)NC−1 (3) 50 sin(ωt −kx)NC−1 (4) 25 sin(ωt −kx)NC−1

Q38.A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of f1 in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of f2 when it is immersed in a liquid of refractive index 1.2 . If both the lenses are made of same glass of refractive index 1.5 , the ratio of f1 and f2 will be (1) 1 : 2 (2) 1 : 3 (3) 3 : 5 (4) 2 : 3

Q38. (1) Kq2 0 (3 −√2) a 0 (4 −2√2) (2) Kq2a (3) Kq2 0 (3√2 −2) a 0 (4√2 −2) (4) Kq2a

Q38.The magnetic field of an E.M. wave is given by B = ( √32 ^i + 12 ^j)30 corresponding electric field in S.I. units is : → → (1) 1 (2) 3 1 E = cos [ω (t −zc )] ( 2^i −√32 ^j)30c sin [ω (t −zc )] E = ( 4^i + 4 ^j)30c → → √3 (3) (4) E = + E = sin [ω (t + zc )] sin [ω (t + zc )] ( 12^i 2 ^j)30c ( √32 ^i −12 ^j)30c

Q39.What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ' h ' in terms of the angle of incidence ' i ' and angle of refraction ' r ', if the glass slab is placed in air medium? (1) h tan(i−r) (2) h sin(i−r) tan r cos r (3) h (4) h cos(i−r) sin r