JEE Main entrance exam Question Bank Solutions

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.

Two radioactive sources A and B of half lives of 1 hour and 2 hours, respectively, initially contain the same number of radioactive atoms. At the end of two hours, their rates of disintegration are in the ratio of ______.

The region between two concentric spheres of radii a < b contain volume charge density ρ(r) = `"c"/"r"`, where c is constant and r is radial- distanct from centre no figure needed. A point charge q is placed at the origin, r = 0. Value of c is in such a way for which the electric field in the region between the spheres is constant (i.e. independent of r). Find the value of c:

Which of the following physical quantities has neither dimensions nor unit?

Boat travels upstream in a river and at t = 0 a wooden cork is thrown over the side with zero initial velocity. After 7.5 minutes the boat turns and starts moving downstream catches the cork when it has drifted 1 km downstream. Then the velocity of water current is ______.

A glass slab of thickness 4 cm contains the same number of waves as 5 cm of water. When both are traversed by the same monochromatic light. If the refractive index of water is `(4/3)`. What is that of glass?

A wave of frequency υ = 1000 Hz, propagates at a velocity v = 700 m/sec along x-axis. Phase difference at a given point x during a time interval M = 0.5 × 10^-3 sec is ______.

A glass capillary sealed at the upper end is of length 0.11 m and internal diameter 2 × 10^-5 m. This tube is immersed vertically into a liquid of surface tension 5.06 × 10^-2 N/m. When the length x × 10^-2 m of the tube is immersed in liquid then the liquid level inside and outside the capillary tube becomes the same, then the value of x is ______ m. (Assume atmospheric pressure is 1.01 × 105 `"N"/"m"^2`) 

In U²³⁸ ore containing Uranium the ratio of U²³⁴ to Pb²⁰⁶ nuclei is 3. Assuming that all the lead present in the ore is final stable product of U²³⁸. Half life of U²³⁸ to be 4.5 × 10⁹ years and the age of ore is ______ × 10⁹ years. (in 10⁹ years)

A displacement vector, at an angle of 30° with y-axis has an x-component of 10 units. Then the magnitude of the vector is ______.

The formula `S = ut - 1/3 at^2` where S is the distance travelled, u is the initial velocity, a is the acceleration and t is the time is ______.

A stone is dropped from the top of the tower and travels 24.5 m in the last second of its journey. The height of the tower is ______.

(g = 9.8 m/s²)

In finding the electric field using Gauss law the formula `|vec"E"| = "q"_"enc"/(epsilon_0|"A"|)` is applicable. In the formula ε₀ is permittivity of free space, A is the area of Gaussian surface and q_enc is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

The activity of a certain radionuclide decreases to 15 percent of its original value in 10 days. What is its half life?

[ln (0.15) = -1.9]

An engine is approaching a cliff at a constant speed. When it is at a distance of 0.9 km from cliff it sounds a whistle. The echo of the sound is heard by the driver after 5 seconds. Velocity of sound in air is equal to 330 ms^-1. The speed of the engine is ______ km/h.

A bar magnet is demagnetized by inserting it inside a solenoid of length 0.2 m, 100 turns, and carrying a current of 5.2 A. The coercivity of the bar magnet is ______.

The mean lives of a radioactive substance are 1620 and 405 years for β-emission and β-emission respectively. The time after which three fourth of a sample will decay if it is decaying both by β-emission and β-emission simultaneously will be ______ years.

(Take ln 2 = 0.693)

The displacement s of a particle depends on time t according to the following relation `s = 1/3t^3 - t^2 + t`. The velocity and displacement of the particle at the instant when its acceleration is zero, are respectively ______.

In the given figure, the face AC of the equilateral prism is immersed in a liquid of refractive index 'n'. For incident angle 60° at the side AC, the refracted light just grazes along face AC. The refractive index of the liquid n = `sqrtx/4`. The value of x is ______.

(Given refractive index of glass = 1.5)

Two perfectly identical wires kept under tension are in unison. When the tension in the wire is increased by 1% then on sounding them together 3 beats are heard in 2 seconds. What is the frequency of each wire?