Practice Questions

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

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 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 )

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

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.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.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.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

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

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.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)

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

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.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

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.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)

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

Q23.Consider a badminton racket with length scales as shown in the figure. JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper If the mass of the linear and circular portions of the badminton racket are same ( M ) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, r distance from the end A of the handle will be ______ Mr2 . 2

Q23.A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses ( Mm ) is x1 . The value of x will be

Q24.Consider an electrical circuit containing a two way switch S. Initially S is open and then T1 is connected to T2. As the current in R = 6 Ω attains a maximum value of steady-state level, T1 is disconnected from T2 and JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper immediately connected to T3. Potential drop across r = 3 Ω resistor immediately after T1 is connected to T3 is ______V. (Round off to the Nearest Integer)

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along X -axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y -axis at a speed of 10 m s−1 . The second piece starts moving at a speed of 20 m s−1 at an angle θ (degree) with respect to the X -axis. The configuration of pieces after the collision is shown in the figure. The value of θ to the nearest integer is _________.

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along the x -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y -axis with a speed of 10 m s−1. The second piece starts moving at an angle of 30° with respect to the x -axis. The velocity of the ball moving at 30° with x -axis is x m s−1. The configuration of pieces after the collision is shown in the figure below. The value of x to the nearest integer is JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper