JEE Main entrance exam Question Bank Solutions

The abscissae of two points A and B are the roots of the equation x² + 2ax – b² = 0, and their ordinates are the roots of the equation x² + 2px – q² = 0. The radius of the circle with AB as diameter is ______.

Length of intercept made by line x + y = 2 on the circle x² + y² – 4x – 6y – 3 = 0 is ______.

If the angle between the tangent t The circle x² + 4² + 2x + 4y – 11 = 0 from p(3, 3) is  `tan^-1(a/b)` where a and b are relatively prime then the value of a – 3b is ______.

The equation of a circle passing through (3, –6) and touching both the axes is ______.

The value of p so that the straight line xcosα + ysinα – p = 0 may touch the circle x² + y² – 2ax cosα – 2by sinα – a²sin²α = 0 is ______.

If two circles `x^2 + y^2 + 2n_1x + 2y + 1/2` = 0 and `x^2 + y^2 + n_2x + n_2y + n_1 = 1/2`, intersect each other orthogonally where n₁, n₂ ∈ I, then number of possible of ordered pairs (n₁, n₂) is ______.

A cylinder of fixed capacity of 44.8 litres contains helium gas at standard temperature and pressure. The amount of heat needed to raise the temperature of gas in the cylinder by 20.0°C will be : (Given: gas constant R = 8.3JK^-1 moI^-1)

Assertion A: The photoelectric effect does not takes place, if the energy of the incident radiation is less than the work function of a metal.

Reason R: Kinetic energy of the photoelectrons is zero, if the energy of the incident radiation is equal to the work function of a metal.

A particle of mass 500 gm is moving in a straight line with velocity v = bx^5/2. The work done by the net force during its displacement from x = 0 to x = 4 m is : (Take b = 0.25 m^-3/2 s^-1).

In Van der Waals equation `["P" + "a"/"V"^2]` [V - b] = RT ; P is pressure, V volume, R is universal gas constant and T is temperature.

The ratio of constants `"a"/"b"` is dimensionally equal to:

The electric field at a point associated with a light wave is given by

E = 200[sin(6 × 10¹⁵)t + sin(9 × 10¹⁵)t]Vm^-1

Given: h = 4.14 × 10^-15 eVs.

If this light falls on a metal surface having a work function of 2.50eV, the maximum kinetic energy of the photoelectrons will be ______.

The escape velocity of a body on a planet 'A' is 12 kms^–1. The escape velocity of the body on another planet 'B', whose density is four times and radius is half of the planet 'A', is ______.

A longitudinal wave is represented by x = 10 sin 2π `("nt" - x/lambda)` cm. The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to ______.

The time period of a satellite revolving around the earth in a given orbit is 7 hours. If the radius of the orbit is increased to three times its previous value, then the approximate new time period of the satellite will be ______.

The motion of a simple pendulum executing S.H.M. is represented by the following equation.

y = Asin(πt + Φ), where time is measured in seconds. The length of the pendulum is ______.

In the given figure, the block of mass m is dropped from point 'A'. The expression for the kinetic energy of the block when it reaches point 'B' is ______.

300 cal. of heat is given to a heat engine and it rejects 225 cal. of heat. If source temperature is 227°C, then the temperature of sink will be ______ °C.

`sqrt"d"_1` and `sqrt"d"_2` are the impact parameters corresponding to scattering angles 60° and 90° respectively, when an α particle is approaching a gold nucleus. For d₁ = xd₂, the value of x will be ______.

A transistor is used in an amplifier circuit in common emitter mode. If the base current changes by 100µA, it brings a change of 10 mA in collector current. If the load resistance is 2kΩ and input resistance is 1kΩ, the value of power gain is x × 104 . The value of x is ______.

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 × 10⁵ ms^-1. The speed with which the electron enters the p side will be `x/3 xx 10^5 "ms"^-1`, and the value of x is ______.

(Given the mass of electron = 9 × 10^-31 kg, the charge on electron = 1.6 × 10^-19 C.)