Practice Questions

Q26.The de Broglie wavelength of an electron in the 4th Bohr orbit is: (1) 2πa0 (2) 4πa0 (3) 6πa0 (4) 8πa0

Q28.The true statement amongst the following is: (1) Both ΔS and S are functions of temperature. (2) Both S and ΔS are not functions of temperature (3) S is not a function of temperature but ΔS is a function of temperature (4) S is a function of temperature but ΔS is not a function of temperature

Q30.Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is : (1) Cv(T2 −T1) (2) −RT(V2 −V1) (3) −RT ln V2/V1 (4) Zero

Q30.A mixture of one mole each of H2 , He and O2 each are enclosed in a cylinder of volume V at temperature T. If the partial pressure of H2 is 2 atm, the total pressure of the gases in the cylinder is: (1) 6 atm (2) 38 atm (3) 14 atm (4) 22 atm Q31. 100 mL of 0. 1 M HCl is taken in a beaker and to it 100 mL 0. 1 M NaOH of is added in steps of 2 mL and the pH is continuously measured. Which of the following graphs correctly depicts the change in pH ? (1) (2) (3) (4)

Q1. In the formula X = 5YZ2 , X and Z have dimensions of capacitance and magnetic field, respectively. What are the dimensions of Y in SI units? (1) M-1 L-2 T4 A2 (2) M-2 L0 T-4 A-2 (3) M-2 L-2 T6 A3 (4) M-3 L-2 T8 A4

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 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 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. 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. 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

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. 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. 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. 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. The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm , respectively. What will be the value of its volume in appropriate significant figures? (1) 4264 ± 81cm3 (2) 4264.4 ± 81.0 cm3 (3) 4260 ± 80 cm3 (4) 4300 ± 80 cm3 → → → →

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. Let →A1 = 3, →A2 = 5 and →A1 + →A2 = 5 . The value of 2→A1 + 3→A2 ∙3→A1 - 2→A2 is: (1) -112.5 (2) -118.5 (3) -106.5 (4) -99.5

Q1. In the cube of side 'a' shown in the figure, the vector from the central point of the face ABOD to the central point of the face BEFO will be: (1) 1 a (2) 1 2 (ˆk −ˆi) 2 a(ˆi −ˆk) (3) 1 (4) 1 2 a(ˆj −ˆi) 2 a(ˆj −ˆk)

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

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. If speed (V), acceleration (A) and force (F) are considered as fundamental units, the dimension of Young's modulus will be : (1) V−2 A2 F−2 (2) V−2 A2 F2 (3) V−4 A−2 F (4) V−4 A2 F

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. In a simple pendulum experiment for determination of acceleration due to gravity ( g ) , time taken for 20 oscillations is measures by using a watch of 1 second least count. The mean value of time taken comes out to be 30 s. The length of the pendulum is measured by using a meter scale of least count 1 mm and the value obtained is 55.0 cm. The percentage error in the determination of g is close to (1) 0.2% (2) 6.8% (3) 3.5% (4) 0.7%

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