JEE Mains JEE Advance BITSAT
JEE Mains | PYQ

Year

All years 2026 2025 2024 2023 2022 2021

Two bodies are having kinetic energies in the ratio \(16:9\). If they have same linear momentum, the ratio of their masses respectively is:

An average force of \( 125 \, \text{N} \) is applied on a machine gun firing bullets each of mass \( 10 \, \text{g} \) at the speed of \( 250 \, \text{m/s} \) to keep it in position. The number of bullets fired per second by the machine gun is:

A car accelerates from rest to \( u \, \text{m /s} \). The energy spent in this process is \( E \, \text{J} \). The energy required to accelerate the car from \( u \, \text{m /s} \) to \( 2u \, \text{m /s}\) is in \( E \, \text{J} \). The value of \( n \) is __________.

A closed circular tube of average radius \( 15 \, \text{cm} \), whose inner walls are rough, is kept in vertical plane. A block of mass \( 1 \, \text{kg} \) just fit inside the tube. The speed of block is \( 22 \, \text{m/s} \), when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is ________ \( \text{J} \). (Given \( g = 10 \, \text{m/s}^2 \)).

A ball is dropped from a height of \( 20 \, \text{m} \). If the coefficient of restitution for the collision between ball and floor is \( 0.5 \), after hitting the floor, the ball rebounds to a height of ______ m.

A machine gun of mass \( 10 \, \text{kg} \) fires \( 20 \, \text{g} \) bullets at the rate of \( 180 \) bullets per minute with a speed of \( 100 \, \text{m s}^{-1} \) each. The recoil velocity of the gun is :

A force \( F = (5 + 3 y^{2}) \) acts on a particle in the \( y \)-direction, where \( F \) is in newton and \( y \) is in meter. The work done by the force during a displacement from \( y = 2 \, \text{m} \) to \( y = 5 \, \text{m} \) is _______ \( \text{J} \).

An object of mass \( 'm' \) initially at rest on a smooth horizontal plane starts moving under the action of force \( F = 2 \, N \). In the process of its linear motion, the angle \( \theta \) (as shown in figure) between the direction of force and horizontal varies as \( \theta = kx \), where \( k \) is a constant and \( x \) is the distance covered by the object from its initial position. The expression of kinetic energy of the object will be \( E = \dfrac{n}{k} \sin \theta \). The value of \( n \) is ___________.

A small particle moves to position \( 5\hat{i} - 2\hat{j} + \hat{k} \) from its initial position \( 2\hat{i} + 3\hat{j} - 4\hat{k} \) under the action of force \( 5\hat{i} + 2\hat{j} + 7\hat{k} \, \text{N} \). The value of work done will be \( \_\_\_\_\_\_\_ \) \( \text{J} \).

The ratio of powers of two motors is \( \dfrac{3\sqrt{x}}{\sqrt{x}+1} \), that are capable of raising \( 300 \, \text{kg} \) water in \( 5 \, \text{minutes} \) and \( 50 \, \text{kg} \) water in \( 2 \, \text{minutes} \) respectively from a well of \( 100 \, \text{m} \) deep. The value of \( x \) will be:

A body is dropped on ground from a height \( 'h_1' \) and after hitting the ground, it rebounds to a height \( 'h_2' \). If the ratio of velocities of the body just before and after hitting ground is \( 4 \), then percentage loss in kinetic energy of the body is \( \dfrac{x}{4} \). The value of \( x \) is __________.

A force \( \vec{F} = (2 + 3x)\hat{i} \) acts on a particle in the \( x \) direction where \( F \) is in newton and \( x \) is in meter. The work done by this force during a displacement from \( x = 0 \) to \( x = 4 \, \text{m} \), is _______ \( \text{J} \).

A body of mass \( 1 \, \text{kg} \) collides head on elastically with a stationary body of mass \( 3 \, \text{kg} \). After collision, the smaller body reverses its direction of motion and moves with a speed of \( 2 \, \text{m/s} \). The initial speed of the smaller body before collision is ________ \( \text{ms}^{-1} \).

A block of mass \( 10 \, \text{kg} \) is moving along x-axis under the action of force \( F = 5x \, \text{N} \). The work done by the force in moving the block from \( x = 2 \, \text{m} \) to \( 4 \, \text{m} \) will be __________ \( \text{J} \).

A body of mass \( 1 \, \text{kg} \) begins to move under the action of a time dependent force \( \vec{F} = (t\,\hat{i} + 3t^2\,\hat{j}) \, \text{N} \), where \( \hat{i} \) and \( \hat{j} \) are the unit vectors along \( x \) and \( y \) axis. The power developed by above force, at the time \( t = 2 \, \text{s} \), will be ________ \( \text{W} \).

A particle of mass \( m \) moving with velocity \( v \) collides with a stationary particle of mass \( 2m \). After collision, they stick together and continue to move together with velocity.

A body of mass \( 5 \, \text{kg} \) is moving with a momentum of \( 10 \, \text{kg m s}^{-1} \). Now a force of \( 2 \, \text{N} \) acts on the body in the direction of its motion for \( 5 \, \text{s} \). The increase in the Kinetic energy of the body is __________ \( \text{J} \).

← PreviousQuestion 5 of 17Next →

JEE Main 2023 31st Jan Evening Shift

A ball is dropped from a height of \( 20 \, \text{m} \). If the coefficient of restitution for the collision between ball and floor is \( 0.5 \), after hitting the floor, the ball rebounds to a height of ______ m.