Practice Questions

Q1. Given below are two statements : Statement I : Astronomical unit (Au), Parsec (Pc) and Light year (ly) are units for measuring astronomical distances. Statement II : Au < Parsec (Pc) < ly In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both Statements I and Statements II are incorrect (2) Statements I is correct but Statements II is incorrect (3) Both Statements I and Statements II are correct (4) Statements I is incorrect but Statements II is correct

Q1. If the velocity of light c, universal gravitational constant G and planck's constant h are chosen as fundamental quantities. The dimensions of mass in the new system is: 2 c 2 G1] (2) h1c1G−1 (1) [h 1 1 2 c 2 G 2 ] (4) [h 2 c 2 G−12 ] (3) [h−1 1 1 1 1

Q1. hello dummy text (1) A - III, B - I, C - II, D - IV (2) A - III, B - IV, C - I, D - II (3) A - II, B - IV, C - III, D - I (4) A - I, B - III, C - IV, D - II

Q1. A particle starts with an initial velocity of 10. 0 ms−1 along x-direction and accelerates uniformly at the rate of 2. 0 m s−2 . The time taken by the particle to reach the velocity of 60. 0 m s−1 is _____. (1) 25 s (2) 3 s (3) 6 s (4) 30 s

Q1. A person travels 𝑥 distance with velocity 𝑣1 and then 𝑥 distance with velocity 𝑣2 in the same direction. The average velocity of the person is 𝑣, then the relation between 𝑣, 𝑣1 and 𝑣2 will be 𝑣1 + 𝑣2 1 1 1 (1) 𝑣= (2) 𝑣= 𝑣1 + 𝑣2 2 2 1 1 (3) 𝑣= 𝑣1 + 𝑣2 (4) 𝑣= 𝑣1 + 𝑣2

Q1. Match List I with List II List I List II A. Torque I. M L−2 T−2 B. Stress II. M L2 T−2 C. Pressure gradient III. M L−1 T−1 Coefficient of D. IV. M L−1 T−2 viscosity Choose the correct answer from the options given below : (1) A-II, B-I, C-IV, D-III (2) A-IV, B-II, C-III, D-I (3) A-II, B-IV, C-I, D-III (4) A-III, B-IV, C-I, D-II

Q1. When vector A = 2ˆi + 3ˆj + 2ˆk is subtracted from vector B, it gives a vector equal to 2ˆj. Then the magnitude of → vector B will be: (1) √5 (2) 3 (3) √6 (4) √33

Q1. If 𝑅, 𝑋𝐿 and 𝑋𝐶 represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 𝑅 (1) 𝑅 𝑋𝐿 𝑋𝐶 (2) √𝑋𝐿𝑋𝑐 𝑅 𝑋𝐿 (3) (4) 𝑅 𝑋𝐿𝑋𝑐 𝑋𝑐

Q1. A vector in x −y plane makes an angle of 30o with y -axis. The magnitude of y -component of vector is 2√3. The magnitude of x-component of the vector will be : (1) 1 (2) 6 √3 (3) 2 (4) √3

Q1. Two trains A and B of length l and 4l are travelling into a tunnel of length L in parallel tracks from opposite directions with velocities 108 km h−1 and 72 km h−1, respectively. If train A take 35 s less time than train B to cross the tunnel then, length L of tunnel is: (Given L = 60 l) (1) 1200 m (2) 900 m (3) 1800 m (4) 2700 m

Q2. Match List I with List II List-I List-II A Spring constant I [T –1] B Angular speed II [MT –2] C Angular momentum III [ML2] D Moment of Inertia IV [ML2T –1] Choose the correct answer from the options given below: (1) A-I, B-III, C-II, D-IV (2) A-IV, B-I, C-III, D-II (3) A-II, B-I, C-IV, D-III (4) A-II, B-III, C-I, D-IV

Q2. For a train engine moving with speed of 20 ms–1 , the driver must apply brakes at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed √x ms−1 . The value of x is ______. (Assuming same retardation is produced by brakes)

Q2. The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is (1) 192 m (2) 136 m (3) 272 m (4) 68 m

Q2. A vehicle travels 4 km with speed of 3 km h−1 and another 4 km with speed of 5 km h−1 , then its average speed is : (1) 4. 25 km h−1 (2) 3. 50 km h−1 (3) 4. 00 km h−1 (4) 3. 75 km h−1

Q2. The equation of a circle is given by x2 + y2 = a2 , where a is the radius. If the equation is modified to change the origin other than (0, 0), then find out the correct dimensions of A and B in a new equation : (x −At)2 + (y − Bt ) 2 = a2 The dimensions of t is given as [T−1] (1) A = [L–1T], B = [LT–1] (2) A = [LT], B = [L–1T –1] (3) A = [L–1T –1 ], B = [LT–1] (4) A = [L–1T –1], B = [LT]

Q2. An object moves with speed 𝑣1, 𝑣2 and 𝑣3 along a line segment 𝐴𝐵, 𝐵𝐶 and 𝐶𝐷 respectively as shown in figure. Where 𝐴𝐵 = 𝐵𝐶 and 𝐴𝐷 = 3 𝐴𝐵, then average speed of the object will be : (1) 𝑣1 + 𝑣2 + 𝑣3 (2) 𝑣1𝑣2𝑣3 3 3𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3 𝑣1 + 𝑣2 + 𝑣3 (3) (4) 𝑣1𝑣2 + 𝑣2𝑣3 + 𝑣3𝑣1 3𝑣1𝑣2𝑣3

Q2. The distance travelled by a particle is related to time t as x = 4t2 . The velocity of the particle at t = 5 s is (1) 40 m s–1 (2) 25 m s–1 (3) 20 m s–1 (4) 8 m s–1

Q2. If force (F), velocity (V ) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be : (1) F V 4 T −6 (2) F V −4 T −2 (3) F 2 V −2 T 6 (4) F V −2 T 2

Q2. The frequency (ν) of an oscillating liquid drop may depend upon radius (r) of the drop, density (ρ) of liquid and the surface tension (s) of the liquid as: ν = raρbsc . The values of a, b and c respectively are (1) (−32 , −12 , 12 ) (2) (−32 , 12 , 12 ) (3) ( 23 , 12 , −12 ) (4) ( 32 , −12 , 12 )

Q2. The speed of a wave produced in water is given by ν = λagbρc . Where λ, g and ρ are wavelength of wave, acceleration due to gravity and density of water respectively. The values of a, b and c respectively, are (1) 1, −1, 0 (2) 12 , 0, 12 (3) 1, 1, 0 (4) 21 , 12 , 0

Q2. A tennis ball is dropped on to the floor from a height of 9. 8 m. It rebounds to a height 5. 0 m. Ball comes in contact with the floor for 0. 2 s . The average acceleration during contact is ______ m s−2 . [Given g = 10 m s−2 ]

Q2. Match List I with List II List - I List - II A Surface tension I. kg m−1 s−1 B Pressure II. kg m s−1 C Viscosity III. kg m−1 s−2 D Impulse IV. kg s−2 Choose the correct answer from the options given below: (1) A-IV, B-III, C-II, D-I (2) A-IV, B-III, C-I, D-II (3) A-III, B-IV, C-I, D-II (4) A-II, B-I, C-III, D-IV

Q2. Match List I with List II List I List II A Angular momentum I [ML2 T−2] B Torque II [ML−2 T−2] C Stress III [ML2 T−1] D Pressure gradient IV [ML−1 T−2] Choose the correct answer from the options given below : (1) A-I, B-IV, C-III, D-II (2) A-III, B-I, C-IV, D-II (3) A-II, B-III, C-IV, D-I (4) A-IV, B-II, C-I, D-III

Q2. A disc is rolling without slipping on a surface. The radius of the disc is R. At t = 0, the top most point on the disc is A as shown in figure. When the disc completes half of its rotation, the displacement of point A from its initial position is (1) 2R (2) R√(π2 + 4) (3) R√(π2 + 1) (4) 2R√(1 + 4π2)

Q2. The initial speed of a projectile fired from ground is 𝑢. At the highest point during its motion, the speed of √3 projectile is 𝑢. The time of flight of the projectile is: 2 (1) 𝑢 (2) 𝑢 2𝑔 𝑔 2𝑢 √3𝑢 (3) (4) 𝑔 𝑔