Practice Questions

Q2. Train A and train B are running on parallel tracks in the opposite directions with speed of 36 km hour−1 and 72 km hour−1 , respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1. 8 km hour−1 . Speed (in m s−1) of this person as observed from train B will be close to: (take the distance between the tracks as negligible) (1) 29. 5 m s−1 (2) 28. 5 m s−1 (3) 31. 5 m s−1 (4) 30. 5 m s−1

Q2. A particle of mass m is fixed to one end of a light spring having force constant k and unstretched length l. The other end is fixed. The system is given an angular speed ω about the fixed end of the spring such that it rotates in a circle in gravity free space. Then the stretch in the spring is: (1) mlω2 (2) mlω2 k−ωm k−mω2 (3) mlω2 (4) mlω2 k+mω2 k+mω

Q3. Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to: (1) 1 : 2 (2) 10 : 7 (3) 2 : 1 (4) 5 : 7

Q3. Starting from the origin at time t = 0, with initial velocity 5 ⌢j ms−1 , a particle moves in the x - y plane with a constant acceleration of + 4⌢j . At time t, its coordinates are (20 m, y0 m). The values of t and y0 (10⌢i )ms−2 are, respectively: (1) 2 s and 18 m (2) 4 s and 52 m (3) 2 s and 24 m (4) 5 s and 25 m

Q6. A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is : (1) 1 : 6 (2) 1 : 3 (3) 1 : 2 (4) 3 : 4

Q6. A fluid is flowing through a horizontal pipe of varying cross-section, with v ms−1 at a point where the pressure is P Pascal. At another point where pressure P2 Pascal its speed is V ms−1 . If the density of the fluid is ρ kg −m−3 and the flow is streamline, then V is equal to + υ2 (1) √Pρ + υ (2) √2Pρ (3) √P2ρ + υ2 (4) √Pρ + υ2

Q6. An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4cm and 4.8cm , respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is: (1) 9 (2) √3 16 2 (3) 3 (4) 81 4 256

Q7. Planet A has mass M and radius R. Planet B has half the mass and half the radius of Planet A. If the escape velocities from the Planets A and B are vA and vB, respectively, then vA = n4 . The value of n is: vB (1) 4 (2) 1 (3) 2 (4) 3

Q7. The specific heat of water = 4200 J kg–1 K–1 and the latent heat of ice = 3.4 × 105 J k g–1 . 100 grams of ice at 0 oC is placed in 200 g of water at 25 oC. The amount of ice that will melt as the temperature of water reaches 0 oC is close to (in grams) (1) 61.7 (2) 63. 8 (3) 69. 3 (4) 64. 6

Q7. A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper (1) 1 (2) 2 √2 (3) 1 (4) √2

Q10.Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+q) each, while 2, 4, 6, 8, 10 have charge (–q) each. The potential V and the electric field E at the centre of the circle are respectively : (Take V = 0 at infinity) (1) V = 10q ; E = 0 (2) V = 0, E = 10q 4πϵ0R 4πϵ0R2 (3) V = 0; E = 0 (4) V = 10q ; E = 10q 4πϵ0R 4πϵ0R2

Q10.A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T . Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT ) of the mixutre is : (1) 15 (2) 13 (3) 20 (4) 11

Q10.Match the thermodynamics processes taking place in a system with the correct conditions. In the table : ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Process Condition (I) Adiabatic (A) ΔW = 0 (II) Isothermal (B) ΔQ = 0 (III) Isochoric (C) ΔU ≠0, ΔW ≠0, ΔQ ≠0 (IV) Isobaric (D) ΔU = 0 (1) (I) - (A), (II) - (B), (III) - (D), (IV) - (D) (2) (I) - (B), (II) - (A), (III) - (D), (IV) - (C) (3) (I) - (A), (II) - (A), (III) - (B), (IV) - (C) (4) (I) - (B), (II) - (D), (III) - (A), (IV) - (C)

Q11.A potentiometer wire PQ of 1m length is connected to a standard cell E1 . Another cell E2 of emf 1. 02 V is connected with a resistance ' r' and switch S (as shown in figure). With switch S open, the null position is obtained at a distance of 49 cm from Q. The potential gradient in the potentiometer wire is : (1) 0. 02 V/ cm (2) 0. 01 V/ cm (3) 0. 03 V/ cm (4) 0. 04 V/ cm JEE Main 2020 (02 Sep Shift 2) JEE Main Previous Year Paper

Q12.In the figure, potential difference between A and B is: (1) 10 V (2) 5 V (3) 15 V (4) 0 V

Q12.Consider four conducing materials copper, tungsten, mercury and aluminum with resistivity ρC, ρT, ρM and ρA respectively. Then : (1) ρC > ρA > ρT (2) ρM > ρA > ρC (3) ρA > ρT > ρC (4) ρA > ρM > ρC JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper

Q13.A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6mA it produces a deflection of 2° , its figure of merit is close to : (1) 333° A/div (2) 6 × 10−3A/ div (3) 666° A/div. (4) 3 × 10−3A/ div JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper

Q13. The figure gives experimentally measured B vs. H variation in a ferromagnetic material. The retentivity, coercivity and saturation, respectively, of the material are: JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper (1) 1.5T, 50A/m and 1.0T (2) 1.5T, 50A/m and 1.0T (3) 150A/m, 1.0T and 1.5T (4) 1.0T, 50A/m and 1.5T → ˆi+ˆj

Q14.An AC circuit has R = 100Ω, C = 2μF and L = 80 mH, connected in series. The quality factor of the circuit is : (1) 2 (2) 0.5 (3) 20 (4) 400

Q14.A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass ? (Curves are drawn schematically and are not to scale) (1) (2) (3) (4)

Q15.An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately : (1) 72% (2) 91% (3) 85% (4) 96%

Q16.In a Young's double slit experiment, light of 500 nm is used to produce and interference pattern. When the distance between the slits is 0. 05 mm, the angular width (in degree) of the fringes formed on the distance screen is close to : (1) 0. 17° (2) 0. 57° (3) 1. 7° (4) 0. 07°

Q16.Choose the correct option relating wavelengths of different parts of electromagnetic wave spectrum: (1) λvisible < λmicro waves < λradio waves < λx-rays (2) λradio waves > λmicro waves > λvisible > λx-rays (3) λx-rays < λmicro waves < λradio waves < λvisible (4) λvisible > λx-rays > λradio waves > λmicro waves

Q17.A vessel of depth 2h is half filled with a liquid of refractive index 2√2 and the upper half with another liquid of refractive index √2 . The liquids are immiscible. The apparent depth of the inner surface of the bottom of the vessel will be JEE Main 2020 (09 Jan Shift 1) JEE Main Previous Year Paper (1) h (2) h √2 2(√2+1) (3) h (4) 3√2h 3√2 4

Q17.The correct match between the entries in column I and column II are : I II Radiation Wavelength a Microwave i 100 m b Gamma rays ii 10−15m c A.M. radio iii 10−10m JEE Main 2020 (05 Sep Shift 2) JEE Main Previous Year Paper d X–rays iv 10−3m (1) (a)–(ii), (b) – (i), (c) – (iv), (d) – (iii) (2) (a)–(i), (b) – (iii), (c) – (iv), (d) – (ii) (3) (a)–(iii), (b) – (ii), (c) – (i), (d) – (iv) (4) (a)–(iv), (b) – (ii), (c) – (i), (d) – (iii)