Practice Questions

Q9. The material filled between the plates of a parallel plate capacitor has resistivity 200 Ω m . The value of capacitance of the capacitor is 2 pF. If a potential difference of 40 V is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is 50 ) (1) 0.9 mA (2) 9.0 mA (3) 9.0 μA (4) 0.9 μA

Q9. An electric dipole is placed on x−axis in proximity to a line charge of linear charge density 3. 0 × 10−6 C m−1. Line charge is placed on z− axis and positive and negative charge of dipole is at a distance of 10 mm and 12 mm from the origin respectively. If total force of 4 N is exerted on the dipole, find out the amount of positive or negative charge of the dipole. (1) 815. 1 nC (2) 8. 8 μC (3) 0. 485 mC (4) 4. 44 μC

Q10.A parallel plate capacitor with plate area '𝐴' and distance of separation '𝑑' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: 𝜀𝑥= 𝜀0 + 𝑘𝑥, for 0 < 𝑥≤ 𝑑2 ≤𝑥≤𝑑 𝜀𝑥= 𝜀0 + 𝑘𝑑- 𝑥, for 𝑑2 𝑘𝑑 (1) 2 / 𝑘𝐴 𝑘𝐴 (2) 𝜀0 + 2𝑙𝑛2𝜀0 + 𝑘𝑑 2 2𝜀0 (3) 0 (4) 𝑘𝐴 ln 2𝜀0 2 2𝜀0 - 𝑘𝑑

Q10.Two electrons each are fixed at a distance 2d. A third charge proton placed at the midpoint is displaced slightly by a distance x(x ≪d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency: ( m = mass of charged particle) (1) πε0md3 12 (2) 2πε0md3 12 ( 2q2 ) ( q2 ) 2 (3) 1 1 ( 2πε0md3q2 ) 2 (4) ( πε0md32q2 )

Q10.Two Carnot engines A and B operate in series such that engine A absorbs heat at T1 and rejects heat to a sink at temperature T. Engine B absorbs half of the heat rejected by Engine A and rejects heat to the sink at T3 . When workdone in both the cases is equal, to value of T is : (1) 2 3 T1 + 23 T3 (2) 31 T1 + 32 T3 (3) 32 T1 + 31 T3 (4) 32 T1 + 31 T3

Q10.Figure shows a rod AB , which is bent in a 120° circular arc of radius R. A charge (−Q) is uniformly → distributed over rod AB. What is the electric filed E at the centre of curvature O ? (1) 3√3Q ˆi (2) 3√3Q ˆi 8π2ε0R2 8πε0R2 (3) −3√3Q ˆi (4) 3√3Q ˆi 8π2ε0R2 16π2ε0R2

Q11.Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R2 from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period: (1) 1 (2) 2π √gR 2π√Rg (3) 2πRg (4) Image is virtual, opposite side of convex mirror.

Q12.A parallel-plate capacitor with plate area A has separation d between the plates. Two dielectric slabs of dielectric constant K1 and K2 of same area A2 and thickness d2 are inserted in the space between the plates. The capacitance of the capacitor will be given by : 2( K1+K2) (1) ε0 + + d K1+K2 K1 A ( 12 K1 K2 ) (2) ε0dA ( 21 K2 ) K1 (3) ε0 + K1+K2 + d 2( K1+K2) K2 ) A ( 12 K1 K2 ) (4) ε0dA ( 21

Q12.A simple pendulum of mass ' m ', length ' l ' and charge ′+q′ suspended in the electric field produced by two conducting parallel plates as shown. The value of deflection of pendulum in equilibrium position will be JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper × × (C1+C2)(d−t) (C1+C2)(d−t) C1( V2−V1) ] (2) tan−1[ mgq C2( V2−V1) ] (1) tan−1[ mgq × × (C1+C2)(d−t) (C1+C2)(d−t) C2( V1+V2) ] (4) tan−1[ mgq C1( V1+V2) ] (3) tan−1[ mgq

Q12.A coil having N turns is wound tightly in the form of a spiral with inner and outer radii a and b respectively. Find the magnetic field at centre, when a current I passes through coil : (1) μ0I 8 [ a+ba−b ] (2) 4(a−b)μ0I [ a1 −1b ] (3) μ0I 8 ( a+ba−b ) (4) 2(μ0INb−a) loge( ab )

Q13.The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15Ω resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10 V is maintained across AC. JEE Main 2021 (17 Mar Shift 2) JEE Main Previous Year Paper (1) 2. 44μA (2) 2. 44 mA (3) 4. 87 mA (4) 4. 87μA

Q13.Two equal capacitors are first connected in series and then in parallel. The ratio of the equivalent capacities in the two cases will be: (1) 1: 2 (2) 1: 4 (3) 4: 1 (4) 2: 1

Q13.A small square loop of side a and one turn is placed inside a larger square loop of side b and one turn (b ≫a). The two loops are coplanar with their centres coinciding. If a current I is passed in the square loop of side b, then the coefficient of mutual inductance between the two loops is : (1) 4π μ0 8√2 a2b (2) 4πμ0 8√2 b2a (3) μ0 8√2 (4) μ0 8√2 4π b 4π a

Q14.A coaxial cable consists of an inner wire of radius a surrounded by an outer shell of inner and outer radii b and c respectively. The inner wire carries an electric current i0 which is distributed uniformly across cross- sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ? (1) a2 (2) b2−a2 x2 x2 (3) x2 (4) x2 b2−a2 a2

Q14.The arm PQ of a rectangular conductor is moving from x = 0 to x = 2b outwards and then inwards from x = 2b to x = 0 as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from x = 0 to x = b. Identify the graph showing the variation of different quantities with distance: (1) A —Flux, B—Power dissipated, C —EMF (2) A —Power dissipated, B—Flux, C—EMF (3) A —Flux, B—EMF , C —Power dissipated (4) A—EMF , B—Power dissipated, C —Flux

Q15.The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 108 m s−1. The focal length of the lens is ___________. (1) 0. 30 cm (2) 15 cm (3) 1. 5 cm (4) 30 cm

Q15.Car B overtakes another car A at a relative speed of 40 m s−1 . How fast will the image of car B appear to move in the mirror of focal length 10 cm fitted in car A , when the car B is 1. 9 m away from the car A ? (1) 0. 1 m s−1 (2) 0. 2 m s−1 (3) 40 m s−1 (4) 4 m s−1

Q15.An RC circuit as shown in the figure is driven by a AC source generating a square wave. The output wave pattern monitored by CRO would look close to : (1) (2) (3) (4)

Q16.The magnetic field vector of an electromagnetic wave is given by 𝐵= 𝐵0 ^i √2 represents unit vector along 𝑥 and 𝑦-axis respectively. At 𝑡= 0 s, two electric charges 𝑞1 of 4𝜋 coulomb and 𝜋 3𝜋 of 2𝜋 coulomb located at 0, 0, and 0, 0, respectively, have the same velocity of 0 . 5c ^i, (where 𝑞2 𝑘 𝑘, 𝑐 is the velocity of light ). The ratio of the force acting on charge 𝑞1 to 𝑞2 is : (1) 1 : √2 (2) 2√2 : 1 (3) √2 : 1 (4) 2 : 1

Q17.The radiation corresponding to 3 →2 transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of 5 × 10−4 T. Assume that the radius of the largest circular path followed by these electrons is 7 mm, the work function of the metal is: (Mass of electron = 9. 1 × 10−31 kg) (1) 1. 36 eV (2) 1. 88 eV (3) 0. 16 eV (4) 0. 82 eV

Q17.There are two infinitely long straight current-carrying conductors and they are held at right angles to each other so that their common ends meet at the origin as shown in the figure given below. The ratio of current in both conductors is 1: 1. The magnetic field at point 𝑃 is_________ . (1) 𝜇0I + 𝑦2 - (𝑥+ 𝑦) (2) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 - (𝑥+ 𝑦) 4πxy√𝑥2 4π (3) 𝜇0I + 𝑦2 + (𝑥+ 𝑦) (4) 𝜇0I𝑥𝑦 √𝑥2 + 𝑦2 + (𝑥+ 𝑦) 4πxy√𝑥2 4π

Q18.At time t = 0 , a material is composed of two radioactive atoms A and B , where NA(0) = 2NB(0) The decay constant of both kind of radioactive atoms is λ . However, A disintegrates to B and B disintegrates to C . Which of the following figures represents the evolution of NB(t) with respect to time t? NB(0) (1) (2) (3) (4)

Q18.The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 5 state will be (1) 4. 17 m s−1 (2) 2. 19 m s−1 (3) 4. 34 m s−1 (4) 3. 25 m s−1

Q18.An electron and proton are separated by a large distance. The electron starts approaching the proton with energy 3 eV . The proton captures the electrons and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength 4000A What is the maximum kinetic energy of the emitted photoelectron? JEE Main 2021 (27 Jul Shift 2) JEE Main Previous Year Paper (1) 7. 61 eV (2) 1. 41 eV (3) 3. 3 eV (4) No photoelectron would be emitted

Q21.A small bob tied at one end of a thin string of length 1 m is describing a vertical circle so that the maximum and minimum tension in the string is in the ratio 5 : 1. The velocity of the bob at the highest position is ______ m s−1 . (Take g = 10 m s−2 ) JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper