Practice Questions

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.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.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.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.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. 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 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.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

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.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 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 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.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.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.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.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.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 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

Q14.Match List-I with List-II. List - I List - II (a) ωL > ωC1 (i) Current is in phase with emf (b) ωL = ωC1 (ii) Current lags behind the applied emf (c) ωL < ωC1 (iii) Maximum current occurs (d) Resonant frequency (iv) Current leads the emf Choose the correct answer from the options given below. (1) (a) - (ii) ; (b) - (i) ; (c) - (iv) ; (d) - (iii) (2) (a) - (ii) ; (b) - (i) ; (c) - (iii) ; (d) - (iv) (3) (a) - (iii) ; (b) - (i) ; (c) - (iv); (d) - (ii) (4) (a) - (iv) ; (b) - (iii) ; (c) - (ii); (d) - (i)

Q14.In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given the area of the plate = A ) (1) 15 Kε0 A (2) 15 Kε0 A 34 d 6 d (3) 25 Kε0 A (4) 9 Kε0 A 6 d 6 d

Q14.With what speed should a galaxy move outward with respect to earth so that the sodium- D line at wavelength ∘ ∘ 5890 A is observed at 5896 A? (1) 306 km sec−1 (2) 322 km sec−1 (3) 296 km sec−1 (4) 336 km sec−1

Q14.A bar magnet is passing through a conducting loop of radius R with velocity v. The radius of the bar magnet is such that it just passes through the loop. The induced e.m.f. in the loop can be represented by the approximate curve: (1) (2) (3) (4)

Q14.A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point P which lies on the centre of the semicircle ? (1) μ0I + 4πr (2 −π) (2) μ0I4πr (2 π) (3) μ0I + 2πr (2 π) (4) μ0I2πr (2 −π)

Q14.An aeroplane, with its wings spread 10 m, is flying at a speed of 180 km h−1 in a horizontal direction. The total intensity of earth's field at that part is 2. 5 × 10−4 Wb m−2 and the angle of dip is 60°. The emf induced JEE Main 2021 (26 Feb Shift 2) JEE Main Previous Year Paper between the tips of the plane wings will be (1) 108. 25 mV (2) 54. 125 mV (3) 88. 37 mV (4) 62. 50 mV