Practice Questions

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.Following plots show Magnetization ( 𝑀) vs Magnetising field ( 𝐻) and Magnetic susceptibility ( χ ) vs Temperature ( 𝑇) graph : Which of the following combination will be represented by a diamagnetic material? (1) ( b ) , ( c ) (2) ( b ) , ( d ) (3) ( a ) , ( d ) (4) ( a ) , ( c )

Q14.An AC current is given by I = I1sinωt + I2cosωt. A hot wire ammeter will give a reading: 2 2 −I 2 +I 1 1 2 2 (1) √I 2 (2) √I 2 2 (3) I1+I2 (4) I1+I2 √2 2√2

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.A coaxial cable consists of an inner wire of radius a surrounded by an outer shell of inner and outer radii b and c respectively. The inner wire carries an electric current i0 which is distributed uniformly across cross- sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ? (1) a2 (2) b2−a2 x2 x2 (3) x2 (4) x2 b2−a2 a2

Q14.If you are provided a set of resistances, 2 Ω, 4 Ω, 6 Ω and 8 Ω. Connect these resistances to obtain an equivalent resistance of 46 3 Ω. (1) 2 Ω and 6 Ω are in parallel with 4 Ω and 8 Ω in series (2) 4 Ω and 6 Ω are in parallel with 2 Ω and 8 Ω in series (3) 2 Ω and 4 Ω are in parallel with 6 Ω and 8 Ω in series (4) 6 Ω and 8 Ω are in parallel with 2 Ω and 4 Ω in series

Q14.In a series LCR circuit, the inductive reactance (XL) is 10 Ω and the capacitive reactance (XC) is 4 Ω. The resistance (R) in the circuit is 6 Ω. The power factor of the circuit is : (1) 21 (2) 2√21 (3) 1 (4) √3 √2 2 JEE Main 2021 (18 Mar Shift 2) JEE Main Previous Year Paper

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

Q14.Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter 0. 1 μm. If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that (1) its size increases, and intensity increases (2) its size decreases, and intensity decreases (3) its size decreases, but intensity increases (4) its size increases, but intensity decreases

Q14.Five equal resistances are connected in a network as shown in figure. The net resistance between the points A and B is : JEE Main 2021 (26 Feb Shift 1) JEE Main Previous Year Paper (1) R (2) R2 (3) 3R2 (4) 2R

Q14.In the Young's double slit experiment, the distance between the slits varies in time as 𝑑𝑡= 𝑑0 + 𝑎0 sin𝜔𝑡; where 𝑑0, 𝜔 and 𝑎0 are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as: (1) 2𝜆𝐷𝑑02 2 (2) 2𝜆𝐷𝑎02 2 𝑑0 - 𝑎0 𝑑0 - 𝑎0 𝜆𝐷 (3) 𝜆𝐷 2𝑎0 (4) 𝑑0 + 𝑎0 𝑑0

Q15.In Young's double slit arrangement, slits are separated by a gap of 0. 5 mm , and the screen is placed at a distance of 0. 5 m from them. The distance between the first and the third bright fringe formed when the slits o are illuminated by a monochromatic light of 5890 A is :- (1) 1178 × 10–9 m (2) 1178 × 10–6 m (3) 1178 × 10–12 m (4) 5890 × 10–7 m

Q15.In the given circuit the AC source has ω = 100 rad s−1 . Considering the inductor and capacitor to be ideal, what will be the current I flowing through the circuit? (1) 5. 9 A (2) 6 A (3) 0. 94 A (4) 3. 16 A

Q15.Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio Imax−Imin Imax+Imin will be (1) 2√2x (2) √2x x+1 2x+1 (3) 2√2x (4) √2x 2x+1 x+1 JEE Main 2021 (25 Feb Shift 1) JEE Main Previous Year Paper

Q15.An alternating current is given by the equation i = i1 sin ωt + i2 cos ωt. The rms current will be: (1) 1 (i1 + i2)2 (2) 1 (i1 + i2) √2 √2 2 (3) 1 1 1 2 (i21 + i22) 2 (4) √21 (i21 + i22)

Q15.The thickness at the centre of a plano convex lens is 3 mm and the diameter is 6 cm. If the speed of light in the material of the lens is 2 × 108 m s−1. The focal length of the lens is ___________. (1) 0. 30 cm (2) 15 cm (3) 1. 5 cm (4) 30 cm

Q15.The time taken for the magnetic energy to reach 25% of its maximum value, when a solenoid of resistance R, inductance L is connected to a battery, is : (1) L ln5 (2) infinite R (3) R L ln2 (4) RL ln10

Q15.A cell 𝐸1 of emf 6 V and internal resistance 2Ω is connected with another cell 𝐸2 of emf 4 V and internal resistance 8 Ω (as shown in the figure). The potential difference across points 𝑋 and 𝑌 is: (1) 10 . 0 V (2) 5 . 6 V (3) 2 . 0 V (4) 3 . 6 V

Q15.Two capacitors of capacities 2C and C are joined in parallel and charged up to potential V . The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be: (1) V (2) V K+2 K (3) 3V (4) 3V K+2 K

Q15.What should be the order of arrangement of de-Broglie wavelength of electron 𝜆e, an 𝛼-particle 𝜆α and proton 𝜆p given that all have the same kinetic energy ? (1) 𝜆𝑒= 𝜆𝑝= 𝜆𝛼 (2) 𝜆e < 𝜆p < 𝜆α (3) 𝜆e > 𝜆p > 𝜆α (4) 𝜆e = 𝜆p > 𝜆α

Q15.Intensity of sunlight is observed as 0. 092 Wm−2 at a point in free space. What will be the peak value of magnetic field at that point ? (ε0 = 8. 85 × 10−12 C2 N−1 m−2) (1) 2. 77 × 10−8 T (2) 1. 96 × 10−8 T (3) 8. 31 T (4) 5. 88 T

Q15.At an angle of 30° to the magnetic meridian, the apparent dip is 45°. Find the true dip: (1) tan−1 √3 (2) tan−1 1 √3 (3) tan−1 2 (4) tan−1 √32 √3

Q15.A coil is placed in a magnetic field →𝐵 as shown below : → A current is induced in the coil because 𝐵 is : (1) parallel to the plane of coil and increasing with (2) outward and increasing with time time (3) outward and decreasing with time (4) parallel to the plane of coil and decreasing with time + ^j cos𝑘𝑧- 𝜔𝑡 where ^i, ^j

Q15.For the given circuit the current 𝑖 through the battery when the key in closed and the steady state has been reached is (1) 10 A (2) 6 A (3) 25 A (4) 0 A

Q15.Find the peak current and resonant frequency of the following circuit (as shown in figure). (1) 2 A and 50 Hz (2) 0. 2 A and 100 Hz (3) 2 A and 100 Hz (4) 0. 2 A and 50 Hz