Practice Questions

Q19.In a circuit for finding the resistance of a galvanometer by half deflection method, a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60 μA division−1 . In the absence of shunt resistance, the galvanometer produces a deflection of θ = 9 divisions when current flows in the circuit. The value of the shunt resistance that can cause the deflection of θ , is closest to: 2 (1) 550 Ω (2) 220 Ω (3) 55 Ω (4) 110 Ω

Q20.An ideal capacitor of capacitance 0 .2 μF is charged to a potential difference of 10 V . The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance 0. 5 mH . The current at a time when the potential difference across the capacitor is 5 V is: (1) 0. 15 A (2) 0. 17 A (3) 0. 34 A (4) 0. 25 A

Q20.A current of 1 A is flowing on the sides of an equilateral triangle of side 4.5 × 10−2 m . The magnetic field at the centre of the triangle will be: (1) 4 × 10−5 Wb/m2 (2) Zero (3) 2 × 10−5 Wb/m2 (4) 8 × 10−5 Wb/m2

Q20.An ideal capacitor of capacitance 0.2μF is charged to a potential difference of 10 V . The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance 0.5mH . The current at a time when the potential difference across the capacitor is 5 V , is: (1) 0.17 A (2) 0.15 A (3) 0.34 A (4) 0.25 A JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper .

Q20.A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with respect to normal axis then magnetic moment of the loop is: JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper (1) 3 qωr2 (2) 1 qωr2 2 2 (3) qωr2 (4) 4 qωr2 3

Q20.The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is B1 . When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is B2 . The ratio B1 is: B2 (1) 1 (2) 2 √2 (3) √3 (4) √2

Q21.A monochromatic beam of light has a frequency v = 2π3 × 1012 Hz and is propagating along the direction ˆi+ˆj√2 . It is polarized along the ˆk direction. The acceptance form the magnetic field is: (1) E0 ˆi+ˆj (ˆi+ˆj) (2) E0 (ˆi+ˆj) .→r+ (3 × C ( √2 ) √2 .→r −(3 × C ˆk √2 Cos[104 1012)t] Cos[104 1012)t] (3) E0 (ˆi−ˆj) (ˆi+ˆj) (4) E0 (ˆi+ˆj+ˆk) (ˆi+ˆj) + (3 × C √2 √2 .→r+ (3 × C √3 √2 .→r Cos[104 1012)t] Cos[104 1012)t] JEE Main 2018 (15 Apr) JEE Main Previous Year Paper

Q21.A copper rod of mass m slides under gravity on two smooth parallel rails, with separation l and set at an angle of θ with the horizontal. At the bottom, rails are joined by a resistance R. There is a uniform magnetic field B normal to the plane of the rails, as shown in the figure. The terminal speed of the copper rod is: (1) mgR cos θ (2) mgR sin θ B2l2 B2l2 (3) mgR tan θ (4) mgR cot θ B2l2 B2l2

Q21.A monochromatic beam of light has a frequency v = 2π3 × 1012 Hz and is propagating along the direction ^i+^j√2 It is polarized along the ^k direction. The acceptable form for the magnetic field is: (1) E0 (2) E0 cos cos ⋅→r −(3 × ⋅→r −(3 × C C ( ^i−^j√2 ) [104 ( ^i−^j√2 ) 1012)t] ( ^i−^j√2 ) [104 ( ^i+^j√2 ) 1012)t] (^i+^j+^k) (3) E0 (4) E0 cos + (3 × + (3 × C ^k cos C √3 [104 ( ^i+^j√2 )→r 1012)t] [104 ( ^i+^j√2 )→r 1012)t]

Q21.A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angular velocity ω, the maximum e.m.f. induced in the coil will be: (1) 3 nBAω (2) 3nBAω 2 (3) nBAω (4) 1 nBAω 2

Q21.An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii re, rp, rα respectively in a uniform magnetic field B. The relation between re, rp, rα is: (1) re < rα < rp (2) re > rP = rα (3) re < rp = rα (4) re < rp < rα

Q22.A plano-convex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in fig −A If the same lens is instead silvered on the curved surface and illuminated from another side as in fig- B, it acts as an optical system of focal length 10 cm. The refractive index of the material of the lens is: (1) 1. 55 (2) 1. 50 (3) 1. 75 (4) 1. 51

Q22.A power transmission line feeds input power at 2300 V to a step-down transformer with its primary windings having 4000 turns giving the output power at 230 V. If the current in the primary coil of the transformer is 5 A and its efficiency is 90 % , the output current would be: (1) 45 A (2) 50 A (3) 20 A (4) 25 A

Q22.A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length 10 cm. The refractive index of the material of lens is (1) 1.50 (2) 1.55 (3) 1.75 (4) 1.51

Q22.At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius r is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I. The smaller coil is set to rotate with a constant angular velocity ω about an axis along their common diameter. Calculate the emf induced in the smaller coil after a time t of its start of rotation. (1) μ0I ωt 2R ωr2 sin ωt (2) μ0I4R ωπr2 sin (3) μ0I 2R ωπr2 sin ωt (4) μ0I4R ωr2 sin ωt

Q22.For an RLC circuit driven with voltage of amplitude vm and frequency ω0 = √LC1 the current exhibits resonance. The quality factor, Q is given by (1) CR (2) ω0L ω0 R (3) ω0R (4) R L (ω0C) .

Q23.A particle is oscillating on the x-axis with an amplitude 2 cm about the point x0 = 10 cm with a frequency. A concave mirror of focal length 5 cm is placed at the origin (see figure). Identify the correct statements? (i) The image executes periodic motion. (ii) The image executes non-periodic motion. (iii) The turning points of the image are asymmetric with respect to the image of the point at X = 10 cm. (iv) The distance between the turning points of the oscillation of the image is 100 21 cm. (1) (ii, iii) (2) (i, iii, iv) (3) (i, iv) (4) (ii, iv)

Q23.A plane polarized monochromatic EM wave is travelling a vacuum along z direction such that at t = t1 it is found that the electric field is zero at a spatial point z1 . The next zero that occurs in its neighbourhood is at z2 . JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper The frequency of the electromagnetic wave is: (1) 3×108 (2) 6×108 |z2−z1| |z2−z1| (3) 1.5×108 (4) 1 |z2−z1| t1+ z2−z1 3×108

Q23.In an A.C. circuit, the instantaneous e.m.f. and current are given by, E = 100 sin 30t, I = 20 sin(30t −π4 ) In one cycle of A.C., the average power consumed by the circuit (in watt) and the watt-less current (in ampere) are, respectively: (1) 50, 0 (2) 50, 10 (3) 1000 , 10 (4) 50 , 0 √2 √2 → z in air and

Q23.A particle is oscillating on the X-axis with an amplitude 2 cm about the point x0 = 10 cm with a frequency ω. A concave mirror of focal length 5 cm is placed at the origin (see figure) Identify the correct statements: (A) The image executes periodic motion (B) The image executes non-periodic motion (C) The turning points of the image are asymmetric w.r.t the image of the point at x = 10 cm (D) The distance between the turning points of the oscillation of the image is 100 21 (1) (B), (D) (2) (B), (C) (3) (A), (C), (D) (4) (A), (D)

Q23.A plane electromagnetic wave of wavelength λ has an intensity I . It is propagating along the positive Y − direction. The allowed expressions for the electric and magnetic fields are given by: → → (1) I 2π (2) I 2π E = (y −ct)]ˆk, √2ε0c cos[ λ (y −ct)]ˆk, E = √ ε0c cos[ λ → → B = + 1c Eˆi B = + 1c Eˆi → → (3) I 2π (4) 2π E = (y −ct)]ˆi, √2ε0c cos[ λ (y + ct)]ˆk, E = √Iε0c cos[ λ → → B = + 1c Eˆi B = + 1c Eˆk

Q24.A convergent doublet of separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm. The separation between the two lenses is 2 cm . The focal lengths of the component lenses (1) 18 cm, 20 cm (2) 10 cm, 12 cm (3) 12 cm, 14 cm (4) 16 cm, 18 cm

Q24.Light of wavelength 550 nm falls normally on a slit of width 22.0 × 10−5 cm. The angular position of the second minima from the central maximum will be (in radians) (1) π (2) π 8 12 (3) π (4) π 4 6

Q24.An EM wave from air enters a medium. The electric fields are E1 = E01ˆx cos[2πv( c −t)] → E2 = E02ˆx cos[k(2z −ct)]in medium, where the wave number k and frequency v refer to their values in the air. The medium is non-magnetic. If ϵr1 and ϵr2 refer to relative permittivities of air and medium respectively, which of the following options, is correct? ϵr1 1 ϵr1 (1) ϵr2 = 2 (2) ϵr2 = 4 ϵr1 ϵr1 1 (3) = 2 (4) = 4 ϵr2 ϵr2

Q24.Light of wavelength 550 nm falls normally on a slit of width 22.0 × 10−5 cm. The angular position of the second minima from the central maximum will be (in radians): (1) π (2) π 4 8 (3) π (4) π 12 6