JEE Main entrance exam Question Bank Solutions for Physics (JEE Main)

A circular disc reaches from top to bottom of an inclined plane of length 'L'. When it slips down the plane, it takes time ' t₁'. when it rolls down the plane, it takes time t₂. The value of `t_2/t_1` is `sqrt(3/x)`. The value of x will be ______.

There is a uniform spherically symmetric surface charge density at a distance R_o from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V (R(t)) of the distribution as a function of its instantaneous radius R(t) is:

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of the magnetic dipole moment of circular loop will be:

Two strings A and B, made of same material, are stretched by same tension. The radius of string A is double of the radius of B. A transverse wave travels on A with speed `v_A` and on B with speed `v_B`. The ratio `v_A/v_B` is ______.

Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity 'u' at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of 'u' in ms^-1. [use g = 10 ms ^-2]:

A small toy starts moving from the position of rest under constant acceleration. If it travels a distance of 10 minutes, the distance travelled by the toy in the next will be ______.

Two vectors `vec"A"` and `vec"B"` have equal magnitudes. If magnitude of `vec"A"` + `vec"B"` is equal to two times the magnitude of `vec"A"` - `vec"B"`, then the angle between  `vec"A"` and `vec"B"` will be :

A person can throw a ball up to a maximum range of 100 m. How high above the ground he can throw the same ball?

A radioactive material decays by simultaneous emissions of two particles with half-lives of 1400 years and 700 years respectively. What will be the time after which one-third of the material remains? (Take In3 = 1.1)

The amplitude of wave disturbance propagating in the positive x-direction given is by `1/(1 + x)^2` at time t = 0 and `1/(1 + (x - 2)^2)` at t = 1 s, where x and y are in 2 metres. The shape of wave does not change during the propagation. The velocity of the wave will be ______ m/s.

A series LCR circuit driven by 300 V at a frequency of 50 Hz contains a resistance R = 3 kΩ, an inductor of inductive reactance X_L = 250 πΩ, and an unknown capacitor. The value of capacitance to maximize the average power should be ______.

If E, L, M, and G denote the quantities as energy, angular momentum, mass, and constant of gravitation respectively, then the dimensions of P in the formula P = EL²M^-5G^-2 are ______.

Consider four conducting materials copper, tungsten, mercury and aluminium with resistivity ρ_C, ρ_T, ρ_M and ρ_A respectively. Then:

The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of 20 ms^-2. The gases come out at a relative speed of 500 ms^-1 with respect to the rocket.

The position of a particle is x - y plane is described by the variables x = at³ and y = 2at. Then the acceleration of the particle ______.

In SI units, the dimensions of `sqrt((ε_0)/(mu_0))` is ______.

A series LCR circuit containing a resistance of 120 Ω has angular resonance frequency 4 × 10⁵ rad s^-1. At resonance the voltage across resistance and inductance are 60 V and 40 V respectively. At what frequency the current in the circuit lags the voltage by 45°. Give answer in ______ × 10⁵ rad s^-1.

In the figure, the optical fibre is l = 2 m long and has a diameter of d = 20 µm. If a ray of light is incident on one end of the fibre at angle θ₁ = 40°, the number of reflections it makes before emerging from the other end is close to:

(Refractive index of fibre is 1.31 and sin 40° = 0.64)

The count rate of activity of a radioactive sample of a very large population decreased from 1024 to 128 in 3 minutes. Then the rate of disintegration at the end of 5 minutes is ______.

A particle of mass 10^-2 kg is moving along the positive x-axis under the influence of a force F(x) = `-"K"/(2x)^2` where K = 10^-2 Nm².  At time t = 0 it is at x = 1.0 m and its velocity is v = 0. The velocity of particle will be ______ m/s, when it reaches x = 0.50 m.