List of top Questions asked in JEE Main- 2022

What is the half-life period of a radioactive material if its activity drops to 1/16 th of its initial value in 30 years?

A parallel plate capacitor filled with a medium of dielectric constant 10, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant 15. Then the energy of capacitor will

An EM wave propagating in x-direction has a wavelength of 8 mm. The electric field vibrating y-direction has maximum magnitude of 60 Vm^–1. Choose the correct equations for electric and magnetic field if the EM wave is propagating in vacuum:

A parallel beam of light of wavelength 900 nm and intensity 100 Wm^–2 is incident on a surface perpendicular to the beam. The number of photons crossing 1 cm^–2 area perpendicular to the beam in one second is

If \(t = \sqrt{x} + 4\), then \(\left.\frac{dx}{dt}\right|_{t=4}\) is

Given below are two statements:
Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.
Statement II: In a material medium, the EM wave travels with speed
\(V=\frac{1}{\sqrt{µ0ε0}}\) In the light of the above statements, choose the correct answer from the options given below.

A metallic conductor of length 1 m rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity 5 rad s^–1. If the horizontal component of earth’s magnetic field is 0.2 × 10^–4 T, then emf induced between the two ends of the conductor is:

Given below are two statements.
Statement-I: The law of gravitation holds good for any pair of bodies in the universe.
Statement-II: The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct answer from the options given below

Let K₁and K₂be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ₁and λ₂, respectively are incident on a metallic surface. If λ₁= 3λ₂then:

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

A long cylindrical volume contains a uniformly distributed charge of density ρ. The radius of cylindrical volume is R. A charge particle (q) revolves around the cylinder in a circular path. The kinetic energy of the particle is:

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A :n-p-n transistor permits more current than a p-n-p transistor.
Reason R: Electrons have greater mobility as a charge carrier.

Choose the correct answer from the options given below:

An aluminium wire is stretched to make its length, 0.4% larger. The percentage change in resistance is

Let \(x(t)=2\sqrt2costsin\sqrt2t \) and \(y(t)=2\sqrt2sintsin\sqrt2t\) ,\(t ∈(0,\frac{π}{2})\)

Then \(\frac{1+(\frac{dy}{dx})^2}{\frac{d^2y}{dx^2}}\) at \(t=\frac{π}{4}\) is equal to

The major product of the following reaction contains ______ bromine atom(s).

0.01 M KMnO₄ solution was added to 20.0 mL of 0.05 M Mohr’s salt solution through a burette. The initial reading of 50 mL burette is zero. The volume of KMnO₄ solution left in burette after the end point is _____ml. [nearest integer]

Let y = y(x) be the solution of the differential equation \(\frac{dy}{dx}+\frac{√2y}{2cos^4x−cos2x}=xe^{tan−1}(√2cot2x),0<x<\frac{π}{2}\) with \(y(\frac{π}{4})=\frac{π^2}{32}\) If \(y(\frac{π}{3})=\frac{π^2}{18}e^{−tan−1}(α)\) then the value of \(3α^2\) is equal to ______

Let R₁ = {(a, b) ∈ N × N : |a – b| ≤ 13} and R₂ = {(a, b) ∈ N × N : |a – b| ≠ 13}. Then on N:

Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

Let d be the distance between the foot of perpendiculars of the point P(1, 2, –1) and Q(2, –1, 3) on the plane –x + y + z = 1. Then d²is equal to ____.

The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives atleast 4 and atmost 7 candies, C₃ receives atleast 2 and atmost 6 candies, is equal to:

The term independent of x in the expansion of
\((1−x^2+3x^3)(\frac{5}{2}x^3−\frac{1}{5x^2})11,x≠0 \)
is:

If n arithmetic means are inserted between a and 100 such that the ratio of the first mean to the last mean is 1 : 7 and a + n = 33, then the value of n is:

The number of elements in the set \(S = \{ \theta \in [-4\pi, 4\pi] : 3 \cos^2(2\theta) + 6 \cos^2(\theta) - 10\cos(2\theta) + 5 = 0 \}\) is______.

The number of solutions of the equation \(2\theta - \cos^2(\theta) + \sqrt{2} = 0\) in R is equal to ___________.