JEE Main entrance exam Question Bank Solutions

A rod of mass 'm' hinged at one end is free to rotate in a horizontal plane. A small bullet of mass m/4 travelling with speed 'u' hits the rod and attaches to it at its centre. Find the angular speed of rotation of rod just after the bullet hits the rod 3. [take length of the rod as 'l']

If R is the radius of the earth and g is the acceleration due to gravity on the earth's surface, the mean density of the earth is ______.

A spherical surface of radius R separates two medium of refractive indices µ₁ and µ₂, as shown in figure. Where should an object be placed in the medium 1 so that a real image is formed in medium 2 at the same distance?

Consider a gravity-free hall in which an experimenter of mass 50 kg is resting on a 5 kg pillow, 8 ft above the floor of the hall. He pushes the pillow down so that it starts falling at a speed of 8 ft/s. The pillow makes a perfectly elastic collision with the floor, rebounds and reaches the experimenter's head. The time elapsed in the process is ______ s.

Four particles A, B, C, and D with masses m_A = m, m_B = 2m, m_C = 3m, and m_D = 4m are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is ______.

Radiation coming from transitions n = 2 to n = 1 of hydrogen atoms fall on He⁺ ions in n = 1 and n = 2 states. The possible transition of helium ions as they absorb energy from the radiation is ______.

A ball of mass m = 20 kg released from height h = 10m falls on the Earth's surface. The speed of the Earth when the ball reaches the Earth's surface is ______ × 10^-23 m/s.

A ball is immersed in water kept in container and released. At the same time container is accelerated in horizontal direction with acceleration, `sqrt44` m/s². Acceleration of ball w.r.t. container is ______ m/s² (specific gravity of ball = 12/17, g = 10 m/s²)

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating: It is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to:

A body starts moving from its origin at t = 0 with a velocity of `5hati` in the x-y plane under the action of force producing an acceleration of `(3hati + 2hatj)` m/s², then y-co-ordinate is ______ m of the body when x-co-ordinate is 84 m.

Which of the following is true for X-rays?

Zener breakdown occurs in a p-n junction having p and n both:

The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation index will be ______.

The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to be 3V. The modulation index is 0.6x where x is ______.

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal are ______. 

A pebble is thrown vertically upwards from the bridge with an initial velocity of 4.9 m/s. It strikes the water after 2 s. If acceleration due to gravity is 9.8 m/s². The height of the bridge and velocity with which the pebble strikes the water will respectively be ______.

A particle is moving in a straight line such that its velocity is increasing at 5 ms^-1 per meter. The acceleration of the particle is ______  ms^-2 at a point where its velocity is 20 ms^-1.

The speed versus time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be ______.

An automobile, travelling at 40 km/h, can be stopped at a distance of 40 m by applying brakes. If the same automobile is travelling at 80 km/h, the minimum stopping distance, in metres, is ______. (assume no skidding)

The relation between time t and distance x is t = ax² + bx where a and bare constants. The acceleration is ______.