Practice Questions

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.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) .

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.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

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

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. 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 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 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

Q24.A ray of light is incident at an angle of 60∘ on one face of a prism of angle 30∘ . The emergent ray of light makes an angle of 30∘ with incident ray. The angle made by the emergent ray with second face of prism will be: (1) 0° (2) 90° (3) 30° (4) 45°

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

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.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

Q25.Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I . If a third the polarizer C is placed between A and B the intensity of emergent light is 2 reduced to I . The angle between the polarizers A and C is θ , then 3 (1) 2 41 (2) 1 41 cos θ = ( 3 ) cos θ = ( 3 ) (3) 1 21 (4) 2 21 cos θ = ( 3 ) cos θ = ( 3 )

Q25.Unpolarized light of intensity I passes through an ideal polariser A . Another identical polariser B is placed behind A . The intensity of light beyond B is found to be I . Now another identical polariser C is placed 2 between A and B. The intensity beyond B is now found to be I . The angle between polariser A and C is 8 (1) 60° (2) 0° (3) 30° (4) 45°

Q25.Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are λ1 and λ2 , their de Broglie wavelength in the frame of reference attached to their centre of mass is: (1) λCM = λ1 = λ2 (2) 1 = 1 + 1 λ1 λ1 λ2 2λ1λ2 λ1+λ2 (3) λCM = (4) λCM = 2 ( ) 1+λ22 √λ2

Q25.Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de brogile wavelengths are λ1 and λ2 , their de brogile wavelength in the frame of reference attached to their centre of mass is: 2λ1λ2 (1) 1 = 1 + 1 (2) λCM = λCM λ1 λ2 √λ12+λ22 (3) λCM = λ1 = λ2 (4) λCM = λ1+λ22

Q25.A plane polarized light is incident on a polariser with its pass axis making angle θ with x -axis, as shown in the figure. At four different values of θ, θ = 8∘, 38∘, 188∘ and 218∘ , the observed intensities are same. What is the angle between the direction of polarization and x -axis (1) 203∘ (2) 45∘ (3) 98∘ (4) 128∘

Q26.The angular width of the central maximum in a single slit diffraction pattern is 60° . The width of the slit is 1 μm . The slit is illuminated by monochromatic plane waves. If another slit of the same width is made near it, JEE Main 2018 (08 Apr) JEE Main Previous Year Paper Young's fringes can be observed on a screen placed at a distance 50 cm from the slits. If the observed fringe width is 1 cm , what is slit separation distance? (i.e., the distance between the centres of each slit.) (1) 100 μm (2) 25 μm (3) 50 μm (4) 75 μm

Q26.The energy required to remove the electron from a singly ionized Helium atom is 2. 2 times the energy required to remove an electron from helium atom. The total energy required to ionize the Helium atom completely is close to JEE Main 2018 (15 Apr) JEE Main Previous Year Paper (1) 34 eV (2) 20 eV (3) 79 eV (4) 109 eV

Q26.The de-Broglie wavelength (λB) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λG) by: (1) λB = 3λG (2) λB = 2λG (3) λB = λ G (4) λB = λ G 3 2

Q26.If the de Broglie wavelengths associated with a proton and an α-particle are equal, then the ratio of velocities of the proton and the α-particle will be: (1) 1 : 4 (2) 1 : 2 (3) 4 : 1 (4) 2 : 1

Q26.The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is: (1) 20eV (2) 79eV (3) 109eV (4) 34eV JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper