Practice Questions

Q16.Experimentally it is found that 12. 8 eV energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is 9 × 10−10 m. x The value of the x is: _____. ( 1 eV = 1. 6 × 10−19 J, 1 = 9 × 109 Nm2C2 and electronic charge = 1. 6 × 10−19 C) 4πε0

Q16.A thin infinite sheet charge and an infinite line charge of respective charge densities +σ and +λ are placed parallel at 5 m distance from each other. Points P and Q are at π3 m and π4 m perpendicular distances from line charge towards sheet charge, respectively. Ep and Eq are the magnitudes of resultant electric field intensities at point P and Q respectively. If EP = a4 for 2|σ| = |λ|, then the value of a is _____. EQ

Q16.For a charged spherical ball, electrostatic potential inside the ball varies with r as V = 2ar2 + b. Here, a and b are constant and r is the distance from the center. The volume charge density inside the ball is −λaε. The value of λ is ______. ε = permittivity of medium.

Q16.As shown in figure, a cuboid lies in a region with electric field E = 2x2ˆi −4yˆj + 6ˆk N C−1 . The magnitude of charge within the cuboid is nε0 C. The value of n is ______ (if dimension of cuboid is 1 × 2 × 3 m3 )

Q17.In the given circuit. C1 = 2μF, C2 = 0. 2μF, C3 = 2μF, C4 = 4μF, C5 = 2μF, C6 = 2μF. The charge stored on capacitor C4 is ______ μC. JEE Main 2023 (11 Apr Shift 2) JEE Main Previous Year Paper

Q17.A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of 𝜆. An alpha particle having certain kinetic energy has the same de-Brogle wavelength 𝜆. The ratio of kinetic energy of proton and that of alpha particle is : (1) 2 : 1 (2) 4 : 1 (3) 1 : 2 (4) 1 : 4 JEE Main 2023 (01 Feb Shift 1) JEE Main Previous Year Paper

Q18.Equivalent resistance between the adjacent corners of a regular n -sided polygon of uniform wire of resistance R would be : (1) (n−1)R (2) (n−1)R n2 (2n−1) (3) n2R (4) (n−1)R n−1 n

Q18.A single current carrying loop of wire carrying current I flowing in anticlockwise direction seen from +ve z direction and lying in xy plane is shown in figure. The plot of ˆj component of magnetic field (By) at a distance a (less than radius of the coil) and on yz plane vs z coordinate looks like JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q19.Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetising field. In the light of given statements, choose the correct answer from the options given below (1) Both Statement I and Statement II are False (2) Statement I is incorrect but Statement II is true (3) Statement I is correct but Statement II is false (4) Both Statement I and Statement II are true

Q20.As shown in the figure the voltmeter reads 2 V across 5 Ω resistor. The resistance of the voltmeter is _____ Ω

Q20.Find the mutual inductance in the arrangement, when a small circular loop of wire of radius R is placed inside a large square loop of wire of side L(L ≫R) . The loops are coplanar and their centres coincide : JEE Main 2023 (29 Jan Shift 1) JEE Main Previous Year Paper (1) M = √2μ0R2L (2) M = 2√2μ0RL2 (3) M = 2√2μ0R2L (4) M = √2μ0RL2

Q21.A conducting circular loop is placed in a uniform magnetic field of 0. 4 T with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of 1 mm s−1 . The magnitude of induced emf in the loop at an instant when the radius of the loop is 2 cm will be _______ μV .

Q22.Two long parallel wires carrying currents 8 A and 15 A in opposite directions are placed at a distance of 7 cm from each other. A point P is at equidistant from both the wires such that the lines joining the point P to the wires are perpendicular to each other. The magnitude of magnetic field at P is ______ ×10−6 T. (Given: √2 = 1. 4 )

Q25.Two equal positive point charges are separated by a distance 2𝑎. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge becomes maximum is 𝑎 The value of 𝑥 is ______. 𝑞0 √𝑥. JEE Main 2023 (01 Feb Shift 1) JEE Main Previous Year Paper

Q25.An electron revolves around an infinite cylindrical wire having uniform linear charge density 2 × 10-8 C m-1 in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ______________ × 106 m s-1. Given mass of electron = 9 × 10-31 kg

Q26.As shown in the figure, a configuration of two equal point charges 𝑞0 = + 2𝜇C is placed on an inclined plane. Mass of each point charge is 20 g. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height ℎ= 𝑥× 10-3 m. The value of 𝑥 is 1 Take = 9 × 109 N m2 C-2, 𝑔= 10 m s-2 4𝜋𝜀0 𝑥

Q27.For a nucleus AZX having mass number A and atomic number Z = –a1A 3 . A. The surface energy per nucleon (bs) 2 B. The Coulomb contribution to the binding energy bc = −a2 Z(Z−1)4 . A 3 JEE Main 2023 (08 Apr Shift 1) JEE Main Previous Year Paper C. The volume energy bv = a3A D. Decrease in the binding energy is proportional to surface area. E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( a1, a2 and a3 are constants) Choose the most appropriate answer from the options given below: (1) B, C, E only (2) C, D only (3) A, B, C, D only (4) B, C only

Q28.A square loop of side 2 . 0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2 . 5 A and angular frequency 700 rad s-1. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is 𝑥× 10-4 V. The value of 𝑥 is ___________ ( Take, 𝜋= 22 7

Q29.A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2 . 15 m within water when sunlight is incident at an angle of 30° with the surface of water. If swimming pool is filled to a height of ) ________ . 1 . 5 m, then the height of the pole above the water surface in centimeters is (𝑛𝑤= 43 ∘

Q29.As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is 30 cm and refraction index of the material for both the lenses is 1 . 75. Both the lenses are placed at distance of 40 cm from each other. Due to the combination, the image of the object is formed at distance x = ______ cm, from concave lens.

Q29.A point object 𝑂 is placed in front of two thin symmetrical coaxial convex lenses 𝐿1 and 𝐿2 with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens 𝐿1 as shown in the figure. The distance between the object and the image formed by the system of two lenses is _____________ cm

Q3. A body of mass 10 kg is projected at an angle of 45° with the horizontal. The trajectory of the body is observed to pass through a point (20, 10). If T is the time of flight, then its momentum vector, at time t = T , is _____ . √2 [Take g = 10 m s−2 ] N s (1) 100ˆi + (100√2 −200)ˆj N s (2) 100√2ˆi + (100 −200√2)ˆj N s (3) 100ˆi + (100 −200√2)ˆj N s (4) 100√2ˆi + (100√2 −200)ˆj

Q3. A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration ac is varying with time t as ac = k2rt2 , where k is a constant. The power delivered to the particle by the force acting on it is - (1) Zero (2) 2mk2r2t (3) mk2r2t (4) 2mk2rt

Q5. A √34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If Ff and Fw are the reaction forces of the floor and the wall, then ratio of Fw will Ff be : (Use g = 10 m s−2 .) (1) 6 (2) 3 √110 √113 (3) 3 (4) 2 √109 √109

Q7. An ice cube of dimensions 60 cm × 50 cm × 20 cm is placed in an insulation box of wall thickness 1 cm. The box keeping the ice cube at 0°C of temperature is brought to a room of temperature 40°C. The rate of melting of ice is approximately: (Latent heat of fusion of ice is 3 . 4 × 105 J kg-1 and thermal conducting of insulation wall is 0 . 05 W m-1 °C-1) JEE Main 2022 (26 Jul Shift 2) JEE Main Previous Year Paper (1) 61 × 10-1 kg s-1 (2) 61 × 10-5 kg s-1 (3) 208 kg s-1 (4) 30 × 10-5 kg s-1