Practice Questions

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.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

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.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.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. 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)

Q38.A capacitor, C1 = 6μ F is charged to a potential difference of V0 = 5 V using a 5 V battery. The battery is removed and another capacitor, C2 = 12μ F is inserted in place of the battery. When the switch 'S' is closed, the charge flows between the capacitors for some time until equilibrium condition is reached. What are the 2025 (29 Jan Shift 2) JEE Main Previous Year Paper charges (q1 and q2) on the capacitors C1 and C2 when equilibrium condition is reached. (1) q1 = 10μC, q2 = 20μC (2) q1 = 30μC, q2 = 15μC (3) q1 = 20μC, q2 = 10μC (4) q1 = 15μC, q2 = 30μC

Q38.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R): The mass 2025 (22 Jan Shift 2) JEE Main Previous Year Paper of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below : (1) (A) is false but (R) is true (2) (A) is true but (R) is false (3) Both (A) and (R) are true and (R) is the correct (4) Both (A) and (R) are true but (R) is NOT the explanation of (A) correct explanation of (A)

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

Q38.A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is grams. (Latent heat of fusion of lead = 2.5 × 104JKg−1 and specific heat capacity of lead = 125JKg−1 K−1) (1) 10 (2) 20 (3) 5 (4) 15

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

Q39.Given below are two statements : Statement I : In a vernier callipers, one vernier scale division is always smaller than one main scale division. Statement II : The vernier constant is given by one main scale division multiplied by the number of vernier scale divisions. In the light of the above statements, choose the correct answer from the options given below. (1) Statement I is true but Statement II is false (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q39.A bead of mass ' m ' slides without friction on the wall of a vertical circular hoop of radius ' R ' as shown in figure. The bead moves under the combined action of gravity and a massless spring ( k ) attached to the bottom of the hoop. The equilibrium length of the spring is ' R '. If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes ' R ', would be (spring constant is ' k ', g is accleration due to gravity) (1) √3Rg + kR2m (2) 2√gR + kR2m (3) √2Rg + kR2m (4) √2Rg + 4kR2m

Q39.An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/m3 . If the pressure inside the bubble is 2100 N/m2 greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g = 10 m/s2 ) (1) 0.1 (2) 0.05 (3) 0.02 (4) 0.25

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

Q40.Which one of the following is the correct dimensional formula for the capacitance in F ? M, L, T and C stand for unit of mass, length, time and charge, (1) [F] = [C2M−1 L−2 T2] (2) [F] = [C2M−2 L2 T2] (3) [F] = [CM−2 L−2 T−2] (4) [F] = [CM−1 L−2 T2]

Q40.A radioactive nucleus n2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n1 . If initial number of both nuclei are the same, what is the ratio of number of nuclei of n2 to the number of nuclei of n1 , after one half-life of n1 ? (1) 1/8 (2) 8 (3) 4 (4) 1/4

Q40.A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination 45∘ . If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be (1) 1 g (2) 1 g √2 3√2 (3) √2 g (4) √2g 3

Q40.A cup of coffee cools from 90∘C to 80∘C in t minutes when the room temperature is 20∘C. The time taken by the similar cup of coffee to cool from 80∘C to 60∘C at the same room temperature is : (1) 13 10 t (2) 1013 t (3) 13 5 t (4) 135 t

Q41.The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is (1) 5 (2) 4 (3) 6 (4) 8

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

Q41.A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ × 10−2 s, where the value of y is (Acceleration due to gravity, g = 10 m/s2 , density of water = 103 kg/m3 ) 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) 6 (2) 2 (3) 4 (4) 1

Q41.Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below: 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) C, D, E Only (2) A, D, E Only (3) B, C, D Only (4) A, B, C Only