Practice Questions

Q1. An expression of energy density is given by u = αβ sin( αxkt ), where α, β are constants, x is displacement, k is Boltzmann constant and t is the temperature. The dimensions of β will be (1) [ML2 T−2θ−1] (2) [M0L2T−2] (3) [M0L0T0] (4) [M0L2T0]

Q1. Two projectile thrown at 30° and 45° with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is (1) 1 : √2 (2) 2 : 1 (3) √2 : 1 (4) 1 : 2

Q1. The dimension of mutual inductance is (1) ML2 T−2A−1 (2) ML2 T−2A−2 (3) ML2 T−3A−1 (4) ML2 T−3A−2

Q1. Two projectiles are thrown with same initial velocity making an angle of 45° and 30° with the horizontal respectively. The ratio of their respective ranges will be (1) 1: √2 (2) √2: 1 (3) 2: √3 (4) √3: 2

Q1. Two buses 𝑃 and 𝑄 start from a point at the same time and move in a straight line and their positions are represented by 𝑥𝑃𝑡= 𝛼𝑡+ 𝛽𝑡2 and 𝑥𝑄𝑡= 𝑓𝑡- 𝑡2. At what time, both the buses have same velocity ? (1) 𝛼- 𝑓 (2) 𝛼+ 𝑓 1 + 𝛽 2𝛽- 1 (3) 𝛼+ 𝑓 (4) 𝑓- 𝛼 21 + 𝛽 21 + 𝛽

Q1. An expression for a dimensionless quantity P is given by P = αβ loge( kTβx ) ; where distance; k is Boltzmann constant and T is the temperature. Then the dimensions of α will be (1) [M0L−1T0] (2) [ML0 T−2] (3) [MLT−2] (4) [ML2 T−2]

Q1. A person moved from 𝐴 to 𝐵 on a circular path as shown in figure. If the distance travelled by him is 60 m, then the magnitude of displacement would be : (Given cos135° = - 0 . 7) (1) 42 m (2) 47 m (3) 19 m (4) 40 m

Q1. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of 10 m in t s , the distance travelled by the toy in the next t s will be: (1) 10 m (2) 20 m (3) 30 m (4) 40 m

Q1. A torque meter is calibrated to reference standards of mass, length and time each with 5% accuracy. After calibration, the measured torque with this torque meter will have net accuracy of (1) 15% (2) 25% (3) 75% (4) 5%

Q1. Assertion A: Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity. Reason: Coefficient of viscosity = VelocityForcegradient (1) Both A and R true, and R is correct explanation of (2) Both A and R are true but R is NOT the correct A. explanation of A. (3) A is true but R is false. (4) A is false but R is true.

Q1. Two vectors A and B have equal magnitudes. If magnitude of A + B is equal to two times the magnitude of → → → → A − B, then the angle between A and B will be (1) cos−1( 35 ) (2) cos−1( 13 ) (3) sin−1( 13 ) (4) sin−1( 35 ) a + −b] = RT; P is pressure, V is volume, R is universal gas constant and 2 V

Q1. The distance of the Sun from earth is 1. 5 × 1011 m and its angular diameter is 2000′′ when observed from the earth. The diameter of the Sun will be (1) 2. 45 × 1010 m (2) 1. 45 × 1010 m (3) 1. 45 × 109 m (4) 0. 14 × 109 m

Q1. A silver wire has a mass (0. 6 ± 0. 006)g , radius (0. 5 ± 0. 005) mm and length (4 ± 0. 04) cm . The maximum percentage error in the measurement of its density will be (1) 7% (2) 3% (3) 4% (4) 6%

Q1. Given below are two statements: One is labelled as Assertion (A) and other is labelled as Reason (R) Assertion (A) : Time period of oscillation of a liquid drop depends on surface tension (S), if density of the liquid is ρ and radius of the drop is r, then T = 3 is dimensionally correct, where K is dimensionless. K√ρr3S 2 Reason (R) : Using dimensional analysis we get R.H.S. having different dimension than that of time period. In the light of above statements, choose the correct answer from the options given below. (1) Both (A) and (R) are true and (R) is the correct explanation of (A) (2) Both (A) and (R) are true but (R) is not the correct explanation of (A) (3) (A) is true but (R) is false (4) (A) is false but (R) is true

Q1. If 𝑍= 𝐴2𝐵3 , then the relative error in 𝑍 will be 𝐶4 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 𝛥𝐴 𝛥𝐵 𝛥𝐶 (1) 𝐴+ 𝐵+ 𝐶 (2) 𝐴+ 𝐵+ 𝐶 (3) 2𝛥𝐴 3𝛥𝐵 4𝛥𝐶 (4) 𝛥𝐴 𝛥𝐵 𝛥𝐶 𝐴+ 𝐵- 𝐶 𝐴+ 𝐵- 𝐶 Q2. →𝐴 is a vector quantity such that →𝐴= non-zero constant. Which of the following expression is true for →𝐴? (1) →𝐴· →𝐴= 0 (2) →𝐴× →𝐴< 0 (3) →𝐴× →𝐴= 0 (4) →𝐴× →𝐴> 0

Q1. Match List I with List II. List I List II (A) Torque (I) Nms-1 (B) Stress (II) Jkg-1 (C) Latent Heat (III) Nm (D) Power (IV) Nm-2 Choose the correct answer from the options given below: (1) A - III, B - II, C - I, D - IV (2) A - III, B - IV, C - II, D - I (3) A - IV, B - I, C - III, D - II (4) A - II, B - III, C - I, D - IV

Q1. Velocity (v) and acceleration (a) in two systems of units 1 and 2 are related as v2 = m2n v1 and a2 = mna1 respectively. Here m and n are constants. The relations for distance and time in two systems respectively are n2 n3 (1) = m T 2 m3 L1 = L2 and n2m T 1 = T2 (2) L1 = m2n4 L2 and T1 (3) L1 = n2m L2 and T1 = m2n4 T2 (4) n2m L1 = L2 and m2n4 T 1 = T2

Q2. A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height h while going up and coming down respectively. 3 (1) √2−1 (2) √3−√2 √2+1 √3+√2 (3) √3−1 (4) 1 √3+1 3

Q2. A bullet is shot vertically downwards with an initial velocity of 100 m s−1 from a certain height. Within 10 s, the bullet reaches the ground and instantaneously comes to rest due to the perfectly inelastic collision. The velocity-time curve for total time t = 20 s will be : (Take g = 10 m s−2 ) (1) (2) (3) (4)

Q2. A person can throw a ball upto a maximum range of 100 m . How high above the ground he can throw the same ball? (1) 25 m (2) 50 m (3) 100 m (4) 200 m

Q2. Motion of a particle in x −y plane is described by a set of following equations x = 4 sin( π2 −ωt) m and y = 4 sin(ωt) m. The path of the particle will be (1) circular (2) helical (3) parabolic (4) eliptical

Q2. The velocity of the bullet becomes one third after it penetrates 4 cm in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at (4 + x) cm inside the block. The value of x is (1) 2. 0 (2) 1. 0 (3) 0. 5 (4) 1. 5

Q2. In van dar Wall equation [P ][V T is temperature. The ratio of constants ab is dimensionally equal to : (1) P (2) V V P (3) PV (4) PV 3

Q2. A NCC parade is going at a uniform speed of 9 km h-1 under a mango tree on which a monkey is sitting at a height of 19 . 6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is : (Given 𝑔= 9 . 8 m s-2) (1) 5 m (2) 10 m (3) 19 . 8 m (4) 24 . 5 m

Q2. In the arrangement shown in figure a1, a2, a3 and a4 are the accelerations of masses m1, m2, m3 and m4 respectively. Which of the following relation is true for this arrangement? (1) 4a1 + 2a2 + a3 + a4 = 0 (2) a1 + 4a2 + 3a3 + a4 = 0 (3) a1 + 4a2 + 3a3 + 2a4 = 0 (4) 2a1 + 2a2 + 3a3 + a4 = 0