Practice Questions

Q23.A circuit connected to an ac source of emf e = e0sin⁡100𝑡 with t in seconds, gives a phase difference of 𝜋 4 between the emf 𝑒 and current i . Which of the following circuits will exhibit this? (1) RC circuit with R = 1 kΩ and C = 1 μF (2) RL circuit with R = 1 kΩ and L = 1 mH (3) RL circuit with R = 1 kΩ and L = 10 mH (4) RC circuit with R = 1 kΩ and C = 10 μF

Q23.Sunlight of intensity 50 W m−2 is incident normally on the surface of a solar panel. Some part of incident energy ( 25%) is reflected from the surface and the rest is absorbed. The force exerted on 1 m2 surface area will be close to (c = 3 × 108 m s−1) (1) 15 × 10−8 N (2) 20 × 10−8 N (3) 10 × 10−8 N (4) 35 × 10−8 N

Q23.A transparent cube of side d, made of a material of refractive index μ2 , is immersed in a liquid of refractive index μ1 ( μ1 < μ2). A ray is incident on the face AB at an angle θ (shown in the figure). Total internal reflection takes place at the point E on the face BC. Then, θ must satisfy (1) (2) θ > sin−1 μ2 θ < sin−1 2 −1 √μ2μ21 μ1 (3) θ < sin−1 μ1 (4) 2 μ2 θ > sin−1 −1 √μ2μ21

Q23.A plano - convex lens (focal length f2 , refractive index μ2, radius of curvature R) fits exactly into a plano - concave lens (focal length f1, refractive index μ1, radius of curvature R). Their plane surfaces are parallel to each other. Then, the focal length of the combination will be: R (1) (2) f1 −f2 μ2 − μ1 (3) f1 + f2 (4) f1+f22f1f2

Q24.A plano-convex lens of refractive index μ1 and focal length f1 is kept in contact with another plano-concave lens of refractive index μ2 and focal length f2. If the radius of curvature of their spherical faces is R each and f1 = 2f2, the μ1 and μ2 are related as: (1) 2μ2 −μ1 = 1 (2) 3μ2 −2μ1 = 1 (3) μ1 + μ2 = 3 (4) 2μ1 −μ2 = 1

Q24.The electric field of a plane polarized electromagnetic wave in free space at time t = 0 is given by the → → expression E(x, y) = 10ˆjcos(6x + 8z). The magnetic field B(x, z, t) is given by ( c is the velocity of light.) (1) 1 + cos(6x + 8z −10 ct) c (6ˆk −8ˆi) cos(6x + 8z + 10 ct) (2) 1c (6ˆk 8ˆi) (3) 1 + + 8z −10 ct) c (6ˆk 8ˆi) cos(6x −8z + 10 ct) (4) 1c (6ˆk −8ˆi)cos(6x

Q24.The variation of refractive index of a crown glass thin prism with wavelength of the incident light is shown. Which of the following graphs is the correct one, if Dm is the angle of minimum deviation? JEE Main 2019 (11 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)

Q24.A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances x1 and x2(x1 > x2) from the lens. The ratio of x1 and x2 is: (1) 2 : 1 (2) 5 : 3 (3) 4 : 3 (4) 3 : 1

Q24.The magnetic field of an electromagnetic wave is given by: →B = 1.6 × 10-6cos⁡ 2 × 107𝑧+ 6 × 1015𝑡 2^𝑖+ ^𝑗 Wb m2 The associated electric field will be: (1) →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 -2 ^𝑗+ ^𝑖 V(2) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 ^𝑖- 2 ^𝑗 V m m (3) →E = 4.8 × 102 cos 2 × 107𝑧+ 6 × 1015𝑡 -^𝑖+ 2^𝑗V →E = 4.8 × 102 cos 2 × 107𝑧- 6 × 1015𝑡 2^𝑖+ ^𝑗V m(4) m

Q24.A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is: (1) 2√3 a + 2b (2) 2a + 2b (3) 2a + 2b (4) 2a + 2b3 √3

Q24.The graph shows how the magnification 𝑚 produced by a thin lens varies with image distance 𝑣. The focal length of the lens used is (1) 𝑏 (2) 𝑎 𝑐 𝑐 (3) 𝑏2𝑐 (4) 𝑏2 𝑎 𝑎𝑐

Q24.Formation of real image using a biconvex lens is shown below: If the whole set up is immersed in water without disturbing the object and the screen positions, what will one observe on the screen? (1) Image disappears (2) Magnified image (3) Erect real image (4) No change JEE Main 2019 (12 Jan Shift 2) JEE Main Previous Year Paper

Q24.Two plane mirrors are inclined to each other such that a ray of light incident on the first mirror (M1) and parallel to the second mirror (M2) is finally reflected from the second mirror (M2) and parallel to the first mirror (M1). The angle between the two mirrors will be: (1) 60o (2) 45o (3) 90o (4) 75o

Q24.A system of three polarizers P1, P2, P3 is set up such that the pass axis of P3 is crossed with respect to that of P1 . The pass axis of P2 is inclined at 60o to the pass axis of P3. When a beam of unpolarized light of intensity Io is incident on P1, the intensity of light transmitted by the three polarizers is I . The ratio (Io/I) equals (nearly): (1) 5.33 (2) 16.00 (3) 1.80 (4) 10.67

Q24.A conducting circular loop made of a thin wire has area 3.5 × 10-2 m2 and resistance 10 Ω It is placed perpendicular to a time-dependent magnetic field 𝐵𝑡= 0.4 Tsin50𝜋𝑡 The field is uniform in space. Then the net charge flowing through the loop during 𝑡= 0 s and 𝑡= 10 ms is close to (1) 1.4 𝑚𝐶 (2) 7 𝑚𝐶 (3) 21 𝑚𝐶 (4) 6 𝑚𝐶

Q25.In a Young's double slit experiment, the path difference, at a certain point on the screen, betwen two interfering waves is 1 th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is 8 close to: (1) 0.74 (2) 0.85 (3) 0.94 (4) 0.8

Q25.A particle A of mass m and charge q is accelerated by a potential difference of 50 V. Another particle B of mass 4m and charge q is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths λA is close to: λB (1) 0.07 (2) 10.00 (3) 4.47 (4) 14.14

Q25.A concave mirror for face viewing has a focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is (1) 1.60 m (2) 0.16 m (3) 0.32 m (4) 0.24 m

Q25.When a certain photosensitive surface is illuminated with a monochromatic light of frequency ν, the stopping potential of the photo current is −V02 . When the surface is illuminated by monochromatic light of frequency ν 2 , the stopping potential is −V0. The threshold frequency for photoelectric emission is (1) 5v (2) 3v 3 2 (3) 4 v (4) 2v 3

Q25.In a Young's double slit experiment slit separation 0.1 mm, one observes a bright fringe at angle 401 rad by using light of wavelength λ1. When the light of wavelength λ2 is used a bright fringe is seen at the same angle in the same set up. Given that λ1 and λ2 are in visible range (380 nm to 740 nm), their values are: (1) 400 nm, 500 nm (2) 380 nm, 525 nm (3) 625 nm, 500 nm (4) 380 nm, 500 nm

Q25.One plano-convex and one plano-concave lens of the same radius of curvature R but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is μ1 and that of 2 is μ2 , JEE Main 2019 (10 Apr Shift 1) JEE Main Previous Year Paper then the focal length of the combination is: (1) R (2) R 2−(μ1−μ2) 2(μ1−μ2) (3) 2R (4) R μ1−μ2 μ1−μ2

Q25.In a young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength λ = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular range −30o ≤θ ≤30o is: (1) 321 (2) 641 (3) 320 (4) 640

Q25.In a Young's double-slit experiment, the ratio of the slit's width is 4 : 1 . The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be (1) 25 : 9 (2) 9 : 1 4 (3) √3 + 1 : 16 (4) 4 : 1

Q25.Consider an electron in a hydrogen atom, revolving in its second excited state (having radius 4.65 Å ). The de- Broglie wavelength of this electron is: (1) 12.9 Å (2) 6.6 Å (3) 9.7 Å (4) 3.5 Å JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper

Q26.The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths λ1 of the photons emitted in this λ2 process is: (1) 7 (2) 20 5 7 (3) 9 (4) 27 7 5