Practice Questions

Q26.Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Three identical spheres of same mass undergo one dimensional motion as shown in figure with initial velocities vA = 5 m/s, vB = 2 m/s, vC = 4 m/s. If we wait sufficiently long for elastic collision to happen, then vA = 4 m/s, vB = 2 m/s, vC = 5 m/s will be the final velocities. Reason (R): In an elastic collision ∣∣ ∣ ∣ ∣ 2025 (29 Jan Shift 2) JEE Main Previous Year Paper between identical masses, two objects exchange their velocities. 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) Both (A) and (R) are true but (R) is NOT the correct explanation of (A) (3) Both (A) and (R) are true and (R) is the correct (4) (A) is true but (R) is false explanation of (A)

Q26.An electron is made to enter symmetrically between two parallel and equally but oppositely charged metal plates, each of 10 cm length. The electron emerges out of the electric field region with a horizontal component of velocity 106 m/s. If the magnitude of the electric field between the plates is 9.1 V/cm , then the vertical component of velocity of electron is (mass of electron = 9.1 × 10−31 kg and charge of electron = 1.6 × 10−19C ) (1) 0 (2) 1 × 106 m/s (3) 16 × 106 m/s (4) 16 × 104 m/s

Q26.A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are ∣∣ 2025 (23 Jan Shift 1) JEE Main Previous Year Paper made of opposite charge q separated by a distance 2a . For the charge particle at P not to experience any net force, which of the following correctly describes the situation? (1) a r ∼10 (2) ar ∼20 (3) a r ∼0.5 (4) ar ∼3

Q26.During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000Å and it becomes 6000Å when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is (1) 4000Å (2) 2000Å (3) 3000Å (4) 6000Å

Q26.An electric dipole of mass m, charge q, and length l is placed in a uniform electric field E = E0^i. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be: (1) 1 ml (2) ml 2π √ 2qE0 2π√ qE0 (3) 1 ml (4) ml 2π √2qE0 2π√ 2qE0

Q26. A bar magnet has total length 2l = 20 units and the field point P is at a distance d = 10 units from the centre of the magnet. If the relative uncertainty of length measurement is 1% , then uncertainty of the magnetic field at point P is : (1) 4% (2) 15% (3) 5% (4) 10%

Q26.Three infinitely long wires with linear charge density λ are placed along the x −axis, y-axis and z− axis respectively. Which of the following denotes an equipotential surface? (1) xyz = constant (2) xy + yz + zx = constant (3) (x2 + y2) (y2 + z2) (z2 + x2) = constant (4) (x + y)(y + z)(z + x) = constant

Q27.A spherical surface of radius of curvature R, separates air from glass (refractive index = 1.5 ). The centre of curvature is in the glass medium. A point object ' O ' placed in air on the optic axis of the surface, so that its real image is formed at ' I ' inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to (1) 5 R (2) 3 R (3) 1.5 R (4) 2 R

Q27.Consider the following statements: A. The junction area of solar cell is made very narrow compared to a photo diode. B. Solar cells are not connected with any external bias. C. LED is made of lightly doped p-n junction. D. Increase of forward current results in continuous increase of LED light intensity. E. LEDs have to be connected in forward bias for emission of light. Choose the correct answer from the options given below: (1) B, E Only (2) B, D, E Only (3) A, C Only (4) A, C, E Only

Q27.Two identical symmetric double convex lenses of focal length f are cut into two equal parts L1, L2 by AB plane and L3, L4 by XY plane as shown in figure respectively. The ratio of focal lengths of lenses L1 and L3 is (1) 1:1 (2) 1:2 (3) 1:4 (4) 2:1

Q27.The position vector of a moving body at any instant of time is given as →r = . The magnitude (5t2^i −5t^j)m and direction of velocity at t = 2 s is, (1) 5√15 m/s, making an angle of tan−1 4 with - ve (2) 5√15 m/s, making an angle of tan−1 4 with + ve Y axis X axis (3) 5√17 m/s, making an angle of tan−1 4 with + ve (4) 5√17 m/s, making an angle of tan−1 4 with - ve X axis Y axis

Q27.A coil of area A and N turns is rotating with angular velocity ω in a uniform magnetic field →B about an axis perpendicular to →B. Magnetic flux φ and induced emf ε across it, at an instant when →B is parallel to the plane of coil, are : (1) φ = AB, ε = 0 (2) φ = 0, ε = 0 (3) φ = 0, ε = NABω (4) φ = AB, ε = NABω

Q27.Given below are two statements : Statement-I : The equivalent emf of two nonideal batteries connected in parallel is smaller than either of the two emfs. Statement-II : The equivalent internal resistance of two nonideal batteries connected in parallel is smaller than the internal resistance of either of the two batteries. In the light of the above statements, choose the correct answer from the options given below. (1) Both Statement-I and Statement-II are false (2) Statement-I is false but Statement-II is true (3) Both Statement-I and Statement-II are true (4) Statement-I is true but Statement-II is false

Q27.A small rigid spherical ball of mass M is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity) (1) 2 Mg (2) Mg (3) 3 2 Mg (4) Mg2

Q27.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: A sound wave has higher speed in solids than gases. Reason R: Gases have higher value of Bulk modulus than solids. In the light of the above statements, choose the correct answer from the options given below ⎪ ⎪ 2025 (28 Jan Shift 1) JEE Main Previous Year Paper (1) Both A and R are true but R is NOT the correct (2) A is true but R is false explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A

Q27.A concave mirror produces an image of an object such that the distance between the object and image is 20 cm . If the magnification of the image is ' -3 ', then the magnitude of the radius of curvature of the mirror is : (1) 30 cm (2) 3.75 cm (3) 15 cm (4) 7.5 cm 2025 (28 Jan Shift 2) JEE Main Previous Year Paper

Q28.A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R/2 is removed from the original disc as shown in 2025 (22 Jan Shift 1) JEE Main Previous Year Paper the figure. Find the moment of inertia of the remaining part of the original disc about the axis as given above. (1) 32 7 MR2 (2) 329 MR2 (3) 17 32 MR2 (4) 1332 MR2

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

Q28.Two capacitors C1 and C2 are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are U1 and U2 , respectively. Which of the given statements is true? (1) C2 > C1, U2 < U1 (2) C1 > C2, U1 > U2 (3) C1 > C2, U1 < U2 (4) C2 > C1, U2 > U1

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)

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.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.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 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.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