Practice Questions

Q12.The magnetic field in a region is given by B = B0( a )ˆk the x and y axes. The loop is moved with a constant velocity →v= v0ˆi. The emf induced in the loop is : JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper (1) B0v20 d (2) B0v0d 2a 2a (3) B0v0d2 (4) B0v0d2 a 2a

Q13.Consider the combination of two capacitors C1 and C2 , with C2 > C1 , when connected in parallel, the equivalent capacitance is 10 times the equivalent capacitance of the same connected in series. Calculate the ratio of capacitors, C2 . C1 (1) 4 + √15 (2) 2 + √15 (3) 9 (4) 154

Q13.A deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let rd and rα be their respective radii of circular path. The value of rdrα is equal to: (1) 1 (2) √2 √2 (3) 1 (4) 2

Q13.Two resistors 𝑅1 = ( 4 ± 0 . 8 ) Ω and 𝑅2 = ( 4 ± 0 . 4 ) Ω are connected in parallel. The equivalent resistance of their parallel combination will be : (1) ( 4 ± 0 . 4 ) Ω (2) ( 2 ± 0 . 4 ) Ω (3) ( 4 ± 0 . 3 ) Ω (4) ( 2 ± 0 . 3 ) Ω

Q13.An L. C. R. circuit contains resistance of 110 Ω and a supply of 220 V at 300 rad s−1 angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by 45°. If on the other hand, the only the inductor is removed the current leads by 45° with the applied voltage. The R. M. S. current flowing in the circuit will be: (1) 2. 5 A (2) 2 A (3) 1 A (4) 1. 5 A

Q13.A proton and an α-particle, having kinetic energies Kp and Kα , respectively, enter into a magnetic field at right angles. The ratio of the radii of the trajectory of proton to that of α -particle is 2 : 1. The ratio of Kp : Kα is: (1) 1 : 8 (2) 8 : 1 (3) 1 : 4 (4) 4 : 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

Q13.A plane electromagnetic wave of frequency 100 MHz is traveling in a vacuum along the x−direction. At a → → particular point in space and time, B = 2. 0 × 10−8 ˆkT⋅ (where, ˆk is unit vector along z−direction) What is E at this point? (1) 0. 6ˆj V m−1 (2) 6. 0ˆk V m−1 (3) 6. 0ˆj V m−1 (4) 0. 6ˆk V m−1

Q13.The equivalent resistance of the given circuit between the terminals 𝐴 and 𝐵 is : 9 (1) 0 Ω (2) Ω 2 (3) 3 Ω (4) 1 Ω

Q13.The current (i) at time t = 0 and t = ∞ respectively for the given circuit is : (1) 5E 18 , 18E55 (2) 5E18 , 10E33 (3) 10E 33 , 5E18 (4) 18E55 , 5E18

Q13. A capacitor of capacitance C = 1 μF is suddenly connected to a battery of 100 V through a resistance R = 100 Ω. The time taken for the capacitor to be charged to get 50 V is: JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper (Take ln 2 = 0. 69 ) (1) 1. 44 × 10−4 s (2) 3. 33 × 10−4 s (3) 0. 69 × 10−4 s (4) 0. 30 × 10−4 s

Q13.In a circuit consisting of a capacitance and a generator with alternating emf, Eg = Egosinωt, VC and IC are the voltage and current. Correct phasor diagram for such circuit is JEE Main 2021 (22 Jul Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q13.A solenoid of 1000 turns per metre has a core with relative permeability 500. Insulated windings of the solenoid carry an electric current of 5 A. The magnetic flux density produced by the solenoid is: (Permeability of free space = 4π × 10−7 H m−1 ) (1) (π) T (2) (2 × 10−3π) T (3) ( π5 ) T (4) (10−4π) T

Q13.A bar magnet of length 14 cm is placed in the magnetic meridian with its north pole pointing towards the geographic north pole. A neutral point is obtained at a distance of 18 cm from the center of the magnet. If BH = 0. 4 G, the magnetic moment of the magnet is (1 G = 10−4 T) (1) 2. 880 × 103 J T−1 (2) 2. 880 × 102 J T−1 (3) 2. 880 J T−1 (4) 28. 80 J T−1

Q13.An electric bulb of 500 W at 100 V is used in a circuit having a 200 V supply. Calculate the resistance R to be connected in series with the bulb so that the power delivered by the bulb is 500 W. (1) 30 Ω (2) 5 Ω (3) 20 Ω (4) 10 Ω

Q13.Given below are two statements Statement I : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere. Statement II : If R is the radius of a solid metallic sphere and Q be the total charge on it. The electric field at any point on the spherical surface of radius r(< R) is zero but the electric flux passing through this closed spherical surface of radius r is not In the light of the above statements, choose the correct answer from the options given below: (1) Both Statement I and Statement II are true (2) Statement I is false but Statement II is true (3) Statement I is true but Statement II is false (4) Both Statement I and Statement II are false

Q13.Two ions of masses 4 amu and 16 amu have charges +2 e and +3 e respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then: (1) lighter ion will be deflected less than heavier ion (2) lighter ion will be deflected more than heavier ion (3) both ions will be deflected equally (4) no ion will be deflected

Q13.A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance XL = 250π Ω and an unknown capacitor. The value of capacitance to maximise the average power should be: (take π2 = 10) (1) 400 μF (2) 4 μF (3) 40 μF (4) 25 μF

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 ray of laser of a wavelength 630 nm is incident at an angle of 30° at the diamond-air interface. It is going from diamond to air. The refractive index of diamond is 2 . 42 and that of air is 1. Choose the correct option. (1) Angle of refraction is 24 . 41°. (2) Angle of refraction is 30°. (3) Refraction is not possible. (4) Angle of refraction is 53 . 4°.

Q13.An X-ray tube is operated at 1. 24 million volt. The shortest wavelength of the produced photon will be: (1) 10−3 nm (2) 10−2 nm (3) 10−4 nm (4) 10−1 nm

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.In the given potentiometer circuit arrangement, the balancing length AC is measured to be 250 cm. When the galvanometer connection is shifted from point (1) to point (2) in the given diagram, the balancing length becomes 400 cm. The ratio of the emf of two cells ε1 is: ε2 (1) 5 (2) 8 3 5 (3) 4 (4) 3 3 2 JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

Q13.What will be the magnitude of the electric field at point O as shown in the figure? Each side of the figure is l and perpendicular to the other? (1) 1 q (2) 1 q 4πε0 l2 4πε0 (2l2) (2√2 −1) (3) q (4) 1 2q 4πε0(2l)2 4πε0 2l2 (√2)

Q13.A particle is making simple harmonic motion along the X -axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 , respectively. The time period of its oscillation is given as: (1) 2+x21 (2) 2+x21 T = T = 2π√x2v21−v22 2π√x2v21+v22 (3) 2−x21 (4) 2−x21 T = T = 2π√x2v21+v22 2π√x2v21−v22