Practice Questions

Q1. Two resistance are given as 𝑅1 = ( 10 ± 0 . 5 ) Ω and 𝑅2 = ( 15 ± 0 . 5 ) Ω . The percentage error in the measurement of equivalent resistance when they are connected in parallel is (1) 6 . 33 (2) 2 . 33 (3) 5 . 33 (4) 4 . 33

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. 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

Q1. Three forces F1 = 10 N, F2 = 8 N, F3 = 6 N are acting on a particle of mass 5 kg. The forces F2 and F3 are applied perpendicularly so that particle remains at rest. If the force F1 is removed, then the acceleration of the particle is (1) 7 m s–2 (2) 0. 5 m s–2 (3) 4. 8 m s–2 (4) 2 m s–2

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. Match List I with List II List I List II A Torque I kg m–1 s–2 B Energy density II kg m s–1 C Pressure gradient III kg m–2 s–2 D Impulse IV kg m2 s–2 Choose the correct answer from the options given below : (1) A-IV, B-III, C-I, D-II (2) A-I, B-IV, C-III, D-II (3) A-IV, B-I, C-II, D-III (4) A-IV, B-I, C-III, D-II

Q1. Electric field in a certain region is given by →𝐸= 𝐴 ^i + 𝐵 ^j. The SI unit of 𝐴 and 𝐵 are : 𝑥2 𝑦3 (1) N m3 C-1; N m2 C-1 (2) N m2 C-1; N m3 C-1 (3) N m3 C; N m2 C (4) N m2 C; N m3 C

Q2. As shown in the figure, a particle is moving with constant speed π m s−1 . Considering its motion from A to B, the magnitude of the average velocity is: (1) √3 m s−1 (2) π m s−1 (3) 1. 5√3 m s−1 (4) 2√3 m s−1

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. The distance travelled by an object in time 𝑡 is given by 𝑠= 2 . 5𝑡2 . The instantaneous speed of the object at 𝑡= 5 s will be : (1) 25 m s – 1 (2) 5 m s – 1 (3) 62 . 5 m s – 1 (4) 12 . 5 m s – 1

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. 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. 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. 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

Q2. Two projectiles are projected at 30° and 60°with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is: (1) √3 : 1 (2) 1 : √3 (3) 2 : √3 (4) 1 : 3

Q2. Two forces having magnitude A and A2 are perpendicular to each other. The magnitude of their resultant is: (1) √5A (2) √5A 4 2 (3) 5A (4) √5A2 2 2

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. 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. 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. 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. Match Column-I with Column-II : Column-I (x-t graphs) Column-II (v-t graphs) A I B II C III D IV Choose the correct answer from the options given below: (1) A- II B-IV, C-III, D-I (2) A- I. B-II, C-III, D-IV (3) A- II B-III, C-IV, D-I (4) A- I, B-III. C-IV, D-II

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. 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. 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