Practice Questions

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 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 wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is Options (1) 8/9 (2) 27/32 (3) 32/27 (4) 9/8

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 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.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.A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s. The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 m/s2 ) (1) 2+√2 (2) 2+√3 3 3 (3) 3+√3 (4) 3−√2 2 2

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.Earth has mass 8 times and radius 2 times that of a planet. If the escape velocity from the earth is 11.2 km/s, the escape velocity in km/s from the planet will be : (1) 2.8 (2) 11.2 (3) 5.6 (4) 8.4 → sin [ω (t −zc )] (S.I. Units). The

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. 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 electric field of an electromagnetic wave in free space is → E = 57 cos [7.5 × 106t −5 × 10−3(3x + 4y)](4^i −3^j)N/C . The associated magnetic field in Tesla is ⇀ 57 (1) B= cos [7.5 × 106t −5 × 10−3(3x + 4y)](^k) 3×108 → (2) 57 B = − cos [7.5 × 106t −5 × 10−3(3x + 4y)](^k) 3×108 → (3) 57 B = − cos [7.5 × 106t −5 × 10−3(3x + 4y)](5^k) 3×108 → (4) 57 B = cos [7.5 × 106t −5 × 10−3(3x + 4y)](5^k) 3×108

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

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.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. For the circuit shown above, equivalent GATE is : (1) OR gate (2) NAND gate (3) NOT gate (4) AND gate 2025 (29 Jan Shift 1) JEE Main Previous Year Paper

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 line charge of length ' a ' is kept at the center of an edge BC of a cube ABCDEFGH having edge length ' 2 a ' as shown in the figure. If the density of line charge is λ C per unit length, then the total electric flux through all the faces of the cube will be . (Take, ϵ0 as the free space permittivity) (1) λa (2) λa 2ϵ0 4ϵ0 (3) λa (4) λa 16ϵ0 8ϵ0

Q39.Arrange the following in the ascending order of wavelength (λ) : (A) Microwaves (λ1) (B) Ultraviolet rays (λ2) (C) Infrared rays (λ3) (D) X-rays (λ4) Choose the most appropriate answer from the options given below : (1) λ4 < λ3 < λ2 < λ1 (2) λ3 < λ4 < λ2 < λ1 (3) λ4 < λ3 < λ1 < λ2 (4) λ4 < λ2 < λ3 < λ1

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.A plane electromagnetic wave propagates along the +x direction in free space. The components of the electric field, →E and magnetic field, →B vectors associated with the wave in Cartesian frame are (1) Ex, By (2) Ey, Bz (3) Ez, By (4) Ey, Bx