Practice Questions

Q20.A square wave of the modulating signal is shown in the figure. The carrier wave is given by C(t) = 5 sin(8πt) Volt. The modulation index is (1) 0. 2 (2) 0. 1 (3) 0. 3 (4) 0. 4

Q21.For 𝑧= 𝑎2𝑥3𝑦 12, where '𝑎' is a constant. If percentage error in measurement of '𝑥' and '𝑦' are 4%and 12%, respectively, then the percentage error for '𝑧' will be _____ % .

Q21.A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0 . 5, the maximum length of the chain hanging from the table is _____ m.

Q21.A ball of mass 0. 5 kg is dropped from the height of 10 m . The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is _____ m. [Use g = 10 m s−2 ]

Q21.In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0. 5 s is measured from time of 100 oscillation with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy. The accuracy in the determination of g is found to be x%. The value of x is

Q21.A ball of mass m is thrown vertically upward. Another ball of mass 2 m is thrown an angle θ with the vertical. Both the balls stay in air for the same period of time. The ratio of the heights attained by the two balls respectively is 1 . The value of x is _____ . x

Q21.The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I1 . The x same rod is bent into a ring and its moment of inertia about a diameter is I2 . If I2I1 is xπ23 , then the value of will be ______.

Q21.A particle is moving in a straight line such that its velocity is increasing at 5 m s−1 per meter. The acceleration of the particle is _____ m s−2 at a point where its velocity is 20 m s−1 .

Q21.From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1. 5 s. A third JEE Main 2022 (24 Jun Shift 1) JEE Main Previous Year Paper ball released, from the rest from the same location, will reach the ground in _____ s.

Q21.A ball is projected vertically upward with an initial velocity of 50 m s−1 at t = 0 s. At t = 2 s, another ball is projected vertically upward with same velocity. At t =____ s, second ball will meet the first ball (g = 10 m s−2) .

Q21.A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity 𝑥√𝐹 rad s-1. If 𝐹 be the force exerted by the liquid at the other end then the value of 𝑥 will be _____ .

Q21.A body is projected from the ground at an angle of 45° with the horizontal. Its velocity after 2 s is 20 m s−1 . The maximum height reached by the body during its motion is _____ m . (use g = 10 m s−2 )

Q21.A hanging mass M is connected to a four times bigger mass by using a string pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is x 5 Mg for x =_____. Neglect mass of the string and friction of the block (bigger mass) with ice slab. (Given g = acceleration due to gravity)

Q21.A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is α = tan−1(x × 10−1). The value of x is _____ . (Given, g = 10 m s−2 ) JEE Main 2022 (27 Jun Shift 2) JEE Main Previous Year Paper

Q21.A car covers AB distance with first one-third at velocity v1 m s−1 , second one-third at v2 m s−1 and last one- third at v3 m s−1 . If v3 = 3v1, v2 = 2v1 and v1 = 11 m s−1 , then the average velocity of the car is _____ m s−1 .

Q21.Two inclined planes are placed as shown in figure. A block is projected from the Point A of inclined plane AB along its surface with a velocity just sufficient to carry it to the top Point B at a height 10 m. After reaching the Point B the block slides down on inclined plane + BC . Time it takes to reach to the point C from point A is t(√2 1)s. The value of t is _____ (use g = 10 m s−2 )

Q21.As per the given figure, two plates A and B of thermal conductivity K and 2K are joined together to form a compound plate. The thickness of plates are 4. 0 cm and 2. 5 cm respectively and the area of cross-section is 120 cm2 for each plate. The equivalent thermal conductivity of the compound plate is (1 + α5 )K , then the value of α will be _____ . Q22. 300 calories of heat is given to a heat engine, and it rejects 225 calories of heat. If source temperature is 227°C, then the temperature of sink will be _____ ∘C.

Q21.An object is projected in the air with initial velocity u at an angle θ. The projectile motion is such that the horizontal range R, is maximum. Another object is projected in the air with a horizontal range half of the range of first object. The initial velocity remains same in both the case. The value of the angle of projection, at which the second object is projected, will be _____ degree.

Q21.A pendulum of length 2 m consists of a wooden bob of mass 50 g . A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed v and the bob just completes the 3 vertical circle. The value of v is _____ m s−1 (if g = 10 m s−2 ). JEE Main 2022 (27 Jun Shift 1) JEE Main Previous Year Paper

Q21.If the projection of 2 ^𝑖+ 4 ^𝑗- 2 ^𝑘 on ^𝑖+ 2 ^𝑗+ 𝛼 ^𝑘 is zero. Then, the value of 𝛼 will be

Q21.A car is moving with speed of 150 km h-1 and after applying the brake it will move 27 m before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling _____ m distance.

Q21.If →𝐴= 2 ^i + 3 ^j - ^k m and →𝐵= ^i + 2 ^j + 2 ^k m. The magnitude of component of vector →𝐴 along vector →𝐵 will be _____ m.

Q22.A uniform disc with mass M = 4 kg and radius R = 10 cm is mounted on a fixed horizontal axle as shown in figure. A block with mass m = 2 kg hangs from a massless cord that is wrapped around the rim of the disc. During the fall of the block, the cord does not slip and there is no friction at the axle. The tension in the cord is _____ N . (Take g = 10 ms−2 ) JEE Main 2022 (28 Jun Shift 2) JEE Main Previous Year Paper

Q22.A small spherical ball of radius 0. 1 mm and density 104 kg m−3 falls freely under gravity through a distance h before entering a tank of water. If, after entering the water the velocity of ball does not change and it JEE Main 2022 (29 Jun Shift 2) JEE Main Previous Year Paper continue to fall with same constant velocity inside water, then the value of h will be ____ m. (Given g = 10 m s−2 , viscosity of water = 1. 0 × 10−5 N‐s m−2 ).

Q22.A pulley of radius 1. 5 m is rotated about its axis by a force F = (12t −3t2) N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about its axis of rotation is 4. 5 kg m2 , the number of rotations made by the pulley before its direction of motion is reversed, will be K . The value of K is _____ . π