Practice Questions

Q2. A man in a car at location Q on a straight highway is moving with speed v . He decides to reach a point P in a field at a distance d from highway (point M ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance RM, so that the time taken to reach P is minimum? (1) d (2) d √3 2 (3) d (4) d √2

Q4. A particle is moving in a circular path of radius a under the action of an attractive potential U = −k . Its total 2r2 energy is: (1) −32 a2k (2) – 4a2k (3) k (4) Zero 2a2

Q6. A proton of mass m collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of 90∘ with respect to each other. The mass of unknown particle is: (1) m (2) m √3 2 (3) 2 m (4) m

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R . And the other mass, in a circular 2 orbit of radius 3R 2 . The difference between the final and the initial total energies is (1) + Gm6R (2) −Gm2R (3) −Gm6R (4) Gm2R

Q7. A body of mass m is moving in a circular orbit of radius R about a planet of mass M . At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius R , and the other mass, in a circular 2 orbit of radius 3R . The difference between the final and initial total energies is: 2 (1) −GMm2R (2) + GMm6R (3) −GMm6R (4) GMm2R

Q8. Take the mean distance of the moon and the sun from the earth to be 0.4 × 106 km and 150 × 106 km respectively. Their masses are 8 × 1022 kg and 2× 1030 kg respectively. The radius of the earth is 6400 km. Let ΔF1 be the difference in the forces exerted by the moon at the nearest and farthest points on the earth and ΔF2 be the difference in the force exerted by the sun at the nearest and farthest points on the earth. Then, the number closest to ΔF1 is: ΔF2 (1) 2 (2) 6 (3) 10−2 (4) 0.6

Q8. Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point P is: (1) 181 MR2 (2) 19 MR2 2 2 (3) 55 MR2 (4) 73 MR2 2 2

Q8. A thin uniform bar of length L and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m moving in the same horizontal plane from opposite sides of the bar with speeds 2v and v respectively. The masses stick to the bar after collision at a distance L and L respectively from the centre of the bar. If the bar 3 6 starts rotating about its center of mass as a result of collision, the angular speed of the bar will be: (1) v (2) 6v 6 L 5 L (3) 3v (4) v 5 L 5 L

Q9. A thin uniform tube is bent into a circle of radius r in the virtical plane. Equal volumes of two immiscible liquids, whose densities are ρ1 and ρ2 (ρ1 > ρ2) fill half the circle. The angle θ between the radius vector passing through the common interface and the vertical is π (1) θ = tan−1 2 (2) θ = tan−1 π2 [ ( ρ1−ρ2ρ1+ρ2 )] ( ρ1+ρ2ρ1−ρ2 ) (3) θ = tan−1 π ρ2 ρ1 (4) θ = tan−1 π2 ρ2ρ1 ( ) ( )

Q11.An oscillator of mass M is at rest in its equilibrium position in a potential, V = 12 k(x –X)2 . A particle of mass m comes from the right with speed u and collides completely inelastic with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is: (M = 10, m = 5, u = 1, k = 1) (1) 2 (2) 1 3 √3 2 (3) √35 (4) 1

Q11.Two Carnot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature T. Engine B receives heat rejected by engine A and in turn rejects it to JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper a reservoir at 100 K. If the efficiencies of the two engines A and B are represented by ηA and ηB respectively, then what is the value of ηA ηB (1) 12 (2) 12 7 5 (3) 5 (4) 7 12 12

Q17.A parallel plate capacitor with area 200 cm2 and separation between the plates 1.5 cm, is connected across a battery of emf V. If the force of attraction between the plates is 25 × 10−6 N , the value of V is approximately: C2 2 = 8.85 × 10−12 (ε0 N.m ) ) (1) 150 V (2) 100 V (3) 250 V (4) 300 V

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 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

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.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.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

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 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)

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

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

Q27.Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths λN, λA respectively. The ratio λN is closest to: λA (1) 10−1 (2) 10−6 (3) 10 (4) 10−10 JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper

Q27.An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let λn, λg be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let ∧n be the wavelength of the emitted photon in the transition from the nth state to the ground state. For large n, (A, B are constants) (1) ∧2n ≈λ (2) ∧n ≈A + λ2nB (3) ∧n ≈A + Bλn (4) ∧2n ≈A + Bλ2n

Q27.A solution containing active cobalt 6027Co having activity of 0.8μCi and decay constant λ is injected in an animal's body. If 1 cm3 of blood is drawn from the animal's body after 10hrs of injection, the activity found was 300 decays per minute. What is the volume of blood that is flowing in the body? (1Ci = 3.7 × 1010 decay per second and at t = 10hrs−λt = 0.84) (1) 6 litres (2) 7 litres (3) 4 litres (4) 5 litres