Practice Questions

Q1. If P = 3ˆi + √3ˆj + 2ˆk and Q = 4ˆi + √3ˆj + 2. 5ˆk then, the unit vector in the direction of P × Q is x is x 1 (√3ˆi +ˆj −2√3ˆk). The value of

Q2. A particle is moving with constant speed in a circular path. When the particle turns by an angle 90°, the ratio of instantaneous velocity to its average velocity is 𝜋: 𝑥√2 . The value of 𝑥 will be (1) 2 (2) 5 (3) 1 (4) 7

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 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. 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 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. Form the 𝑣 - 𝑡 graph shown, the ratio of distance to displacement in 25 s of motion is: 1 (1) 1 (2) 2 (3) 5 (4) 3 3 5

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 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. 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. 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. 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 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

Q3. As shown in figure, a 70 kg garden roller is pushed with a force of →𝐹= 200 N at an angle of 30° with horizontal. The normal reaction on the roller is (Given 𝑔= 10 m s-2) (1) 800√2 N (2) 600 N (3) 800 N (4) 200√3 N Q4. 100 balls each of mass 𝑚 moving with speed 𝑣 simultaneously strike a wall normally and reflected back with same speed, in time 𝑡 s. The total force exerted by the balls on the wall is 100𝑚𝑣 200𝑚𝑣 (1) (2) 𝑡 𝑡 (3) 200 𝑚𝑣𝑡 (4) 𝑚𝑣 100𝑡

Q3. An object is allowed to fall from a height R above the earth, where R is the radius of earth. Its velocity when it strikes the earth’s surface, ignoring air resistance, will be : (1) 2√gR (2) √gR (3) √gR2 (4) √2gR

Q3. A projectile is projected at 30° from horizontal with initial velocity 40 m s−1 . The velocity of the projectile at t = 2 s from the start will be: (1) 40√3 m s−1 (2) Zero (3) 20 m s−1 (4) 20√3 m s−1

Q3. The ratio of powers of two motors is 3√x , that are capable of raising 300 kg water in 5 minutes and 50 kg √x+1 water in 2 minutes respectively from a well of 100 m deep. The value of x will be (1) 16 (2) 2 (3) 2. 4 (4) 4

Q3. An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at x = +2 m, its velocity is −4ˆj m s−1 . The object’s velocity (v) and acceleration (a) at x = –2 m will be (1) v = 4ˆi m s−1, a = 8ˆj m s−2 (2) v = 4ˆj m s−1, a = 8ˆi m s−2 (3) v = −4ˆj m s−1, a = 8ˆi m s−2 (4) v = −4ˆi m s−1, a = −8ˆj m s−2

Q3. The velocity-time graph of a body moving in a straight line is shown in figure. The ratio of displacement and distance travelled by the body in time 0 to 10 s is (1) 1 : 1 (2) 1 : 2 (3) 1 : 3 (4) 1 : 4

Q3. The figure represents the momentum time ( 𝑝- 𝑡) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively ? If 𝑡3 - 𝑡2 < 𝑡1 JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper (1) c and a (2) b and c (3) c and b (4) a and b

Q3. A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the centre. If the angular velocity of the table is halved, it will just slip when placed at a distance of _____ from the centre: (1) 8 cm (2) 4 cm (3) 1 cm (4) 2 cm

Q3. As per given figure, a weightless pulley 𝑃 is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if 𝑔= 10 m s-2) (1) 4√3 + 1 N (2) 4√3 + 1 N (3) 4√3 - 1 N (4) 4√3 - 1 N

Q3. As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle 30° , with horizontal. For μs = 0. 25 , the block will just start to move for the value of F : [Given g = 10 m ⋅s–2 ] (1) 33. 3 N (2) 25. 2 N (3) 20 N (4) 35. 7 N

Q3. The trajectory of projectile, projected from the ground is given by y = x −x220 . Where meter. The maximum height attained by the projectile will be. (1) 200 m (2) 10 m (3) 5 m (4) 10√2 m