Practice Questions

Q1. The area of a square is 5.29 cm2. The area of 7 such squares taking into account the significant figures is: (1) 37.03 cm2 (2) 37.030 cm2 (3) 37.0 cm2 (4) 37 cm2

Q1. A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60o with ground level, but he finds the aeroplane right vertically above his position. If v is the speed of sound, speed of the plane is: (1) 2v (2) v √3 (3) v (4) √3 v 2 2

Q1. The force of interaction between two atoms is given by F = αβ exp (−x2αkT ); where Boltzmann constant and T is temperature and α and β are two constants. The dimensions of β is: (1) M0 L2 T−4 (2) M2LT−4 (3) MLT−2 (4) M2 L2 T−2

Q1. A particle is moving with a velocity →𝑣= 𝐾𝑦^𝑖+ 𝑥^𝑗, where 𝐾 is a constant. The general equation for its path is: (1) 𝑦2 = 𝑥+ constant (2) 𝑥𝑦= constant (3) 𝑦= 𝑥2 + constant (4) 𝑦2 = 𝑥2 + constant

Q1. In the density measurement of a cube, the mass and edge length are measured as (10.00 ± 0.10) kg and (0.10 ± 0.01) m, respectively. The error in the measurement of density is: (1) 0.31 (2) 0.10 (3) 0.07 (4) 0.01

Q1. Ship A is sailing towards north-east with velocity) →𝑣= 30 ^i + 50 ^j km h-1 where ^i points east and ^j, north. The ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards the west at 10 km h-1 . A will be at the minimum distance from B in: (1) 4.2 h (2) 3.2 h (3) 2.6 h (4) 2.2 h

Q1. The position co-ordinates of a particle moving in a 3D coordinate system is given by x = a cos ωt y = a sin ωt and z = aωt The speed of the particle is: (1) √2 aω (2) aω (3) 2aω (4) √3 aω

Q1. A particle is moving with speed v = b√x along positive x− axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0 ) (1) b2τ (2) b2τ √2 (3) b2τ (4) b2τ 2 4

Q1. A particle moves from the point (2.0^i + 4.0^j)m, at t = 0 , with an initial velocity (5.0^i + 4.0^j)ms−1. It is acted upon by a constant force which produces a constant acceleration (4.0^i + 4.0^j)ms−2. What is the distance of the particle from the origin at time 2 s? (1) 15 m (2) 20√2 m (3) 5 m (4) 10√2 m

Q1. A particle of mass m is moving along a trajectory given by x = x0 + a cosω1t y = y0 + b sinω2t The torque, acting on the particle about the origin, at t = 0 is: (1) +my0aω21ˆk (2) −m(x0bω22 −y0aω21)ˆk (3) Zero (4) m(−x0b + y0a)ω21ˆk

Q1. Let L, R, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of L in SI units will be: RCV (1) [LTA] (2) [A−1] (3) [LT 2] (4) [LA−2]

Q1. Which of the following combinations has the dimension of electrical resistance ( ϵ0 is the permittivity of vacuum and μ0 is the permeability of vacuum)? ϵ0 ϵ0 (1) (2) μ0 √ μ0 μ0 μ0 (3) (4) ϵ0 √ ϵ0

Q2. Expression for time in terms of G (universal gravitational constant), h (Planck constant) and c (speed of light) is proportional to: (1) √Ghc3 (2) √hc5G (3) √Ghc5 (4) √c3Gh

Q2. Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, h1 and h2. Which of the following is correct? (1) R2 = h1h2 (2) R2 = 4 h1h2 (3) R2 = 2 h1h2 (4) R2 = 16 h1h2

Q2. Two vectors A and B have equal magnitudes. The magnitude of A + is ' n ' times the magnitude of ( B) → → → → A − . The angle between A and B is: ( B) n+1 ] (1) cos−1[ n2−1n2+1 ] (2) sin−1[ n−1 (3) cos−1[ n−1n+1 ] (4) sin−1[ n2−1n2+1 ]

Q2. A copper wire is stretched to make it 0.5% longer. The percentage change in its electrical resistance if its volume remains unchanged is: (1) 2.5% (2) 1.0% (3) 2.0% (4) 0.5%

Q2. Two particles A, B are moving on two concentric circles of radii R1 and R2 with equal angular speed ω. At t = 0, their positions and direction of motion are shown in the figure: −−→ → The relative velocity VA −VB at t = 2ωπ is given by: (1) ω (R1 + R2)^i (2) −ω (R1 + R2)^i (3) ω (R2 −R1)^i (4) ω (R1 −R2)^i

Q2. In SI units, the dimensions of ϵ0 is: √ μ0 (1) AT2M-1L-1 (2) A2T3M-1L-2 (3) A-1TML3 (4) AT-3ML3 / 2

Q2. A bullet of mass 20 g has an initial speed of 1 m s-1, just before it starts penetrating a mud wall of thickness 20 cm. If the wall offers a mean resistance of 2.5 × 10-2 N, the speed of the bullet after emerging from the other side of the wall is close to: (1) 0.7 m s-1 (2) 0.3 m s-1 (3) 0.1 m s-1 (4) 0.4 m s-1

Q2. A particle is moving along a circular path with a constant speed of 10 ms−1 . What is the magnitude of the change in velocity of the particle, when it moves through an angle of 60∘ around the centre of the circle? (1) 10√3 m/s (2) zero (3) 10√2 m/s (4) 10 m/s

Q2. The density of a material in SI units is 128 kg m−3. In certain units in which the unit of length is 25 cm and the unit of mass is 50g, the numerical value of density of the material is: (1) 410 (2) 16 (3) 40 (4) 640

Q2. A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is: (1) 1 (2) 1 g √γg ln(1 + √γg V0) √γg tan−1(√γ V0) (3) 1 (4) 1 g g √γg sin−1(√γ V0) √2γg tan−1(√2γ V0)

Q2. The trajectory of a projectile near the surface of the earth is given as 𝑦= 2𝑥- 9𝑥2 . If it were launched at an angle θ0 with speed 𝑣0 then g = 10 m s-2: 1 5 2 3 (1) θ0 = cos-1⁡ √5 and 𝑣0 = 3 ms-1 (2) θ0 = cos-1⁡√5 and 𝑣0 = 5 ms-1 1 5 2 3 (3) θ0 = sin-1⁡ √5 and 𝑣0 = 3 ms-1 (4) θ0 = sin-1⁡√5 and 𝑣0 = 5 ms-1

Q2. The position of a particle as a function of time t, is given by x(t) = at + bt2 −ct3 where a, b and c are constants. When the particles zero acceleration, then its velocity will be: b2 (1) a + 3cb2 (2) a + 2c (3) a + b2c (4) a + 4cb2

Q2. A passenger train of length 60 m travels at a speed of 80 km / hr. Another freight train of length 120 m travels at a speed of 30 km / hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is: (1) 5 (2) 3 2 2 (3) 11 (4) 25 5 11