Practice Questions

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 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. A B Y 0 0 1 0 1 1 1 0 0 1 1 1 To obtain the given truth table, following logic gate should be placed at G: 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) OR Gate (2) AND Gate (3) NOR Gate (4) NAND Gate

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

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 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.A galvanometer having a coil of resistance 30Ω need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be 30 X Ω, where X is Options (1) 596 (2) 149 (3) 298 (4) 447

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

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.A ball having kinetic energy KE, is projected at an angle of 60∘ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ? (1) (KE) (2) (KE) 8 2 (3) (KE) (4) (KE) 16 4

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.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.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.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.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.The position of a particle moving on x-axis is given by x(t) = A sin t + B cos2 t + Ct2 + D , where t is time. The dimension of ABC is D (1) L2T −2 (2) L2 (3) L (4) L3 T−2

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.Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2 , respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is (1) k1 (2) k2 √k1k2 (3) (4) k2 k1 √k2k1

Q28.The output of the circuit is low (zero) for : (A) X = 0, Y = 0 (B) X = 0, Y = 1 (C) X = 1, Y = 0 (D) X = 1, Y = 1 Choose the correct answer from the options given below : (1) (B), (C) and (D) only (2) (A), (B) and (C) only (3) (A), (C) and (D) only (4) (A), (B) and (D) only

Q28.The torque due to the force (2^i + ^j + 2^k) about the origin, acting on a particle whose position vector is (^i + ^j + ^k), would be (1) ^i −^k (2) ^i + ^k (3) ^j + ^k (4) ^i −^j + ^k

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 charges 7μc and −4μc are placed at (−7 cm, 0, 0) and (7 cm, 0, 0) respectively. Given, ϵ0 = 8.85 × 10−12C2 N−1 m−2 , the electrostatic potential energy of the charge configuration is : (1) -1.8 J (2) -2.0 J (3) -1.5 J (4) -1.2 J

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

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