List of top Questions asked in JEE Main- 2022

If the numbers appeared on the two throws of a fair six faced die are α and β, then the probability that x² + αx + β> 0, for all x ∈ R, is :

A flask contains argon and oxygen in the ratio of 3 : 2 in mass and the mixture is kept at 27°C. The ratio of their average kinetic energy per molecule respectively will be

The number of solutions of |cos x| = sinx, such that –4π ≤ x ≤ 4π is :

The area of the polygon, whose vertices are the non-real roots of the equation \(\bar z = iz^2\) is

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

The charge on capacitor of capacitance 15 μF in the figure given below is

Which of the following statements is a tautology?

The current flowing through an ac circuit is given by \(I = 5 \;sin\;(120πt)\;A\). How long will the current take to reach the peak value starting from zero?

Match List-I with List-II List-I List-II

Lis I		List II
a.	Ultraviolet rays	i.	Study crystal structure
b.	Microwaves	ii.	Greenhouse effect
c.	Infrared waves	iii.	Sterilizing surgical instrument
d.	X-rays	iv	Radar system

Choose the correct answer from the options given below :

A ball is spun with angular acceleration α = 6t² – 2t, where t is in second and α is in rads^–2. At t = 0, the ball has angular velocity of 10 rads^–1 and angular position of 4 rad. The most appropriate expression for the angular position of the ball is :

The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

Consider a light ray travelling in air is incident into a medium of refractive index √2n The incident angle is twice that of refracting angle. Then, the angle of incidence will be:

A block of mass 2 kg moving on a horizontal surface with speed of 4 ms^–1 enters a rough surface ranging from x = 0.5 m to x = 1.5 m. The retarding force in this range of rough surface is related to distance by F = –kx where k = 12 Nm^–1. The speed of the block as it just crosses the rough surface will be

Let A=\(\begin{pmatrix} 2 &-1 &-1 \\ 1&0 &-1 \\ 1&-1 &0 \end{pmatrix}\) and B=A–I. If ω=\(\frac{\sqrt3 i-1}{2}\), then the number of elements in the set {n∈{1,2,⋯,100}:\(A^n+(ωB)^n\)=A+B} is equal to _______.

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of: (Given, Planck’s constant = \(6.6 × 10^{–34}\) Js).

The letters of the work ‘MANKIND’ are written in all possible orders and arranged in serial order as in an English dictionary. Then the serial number of the word ‘MANKIND’ is ______.

If the maximum value of the term independent of t in the expansion of (t²x\(^{\frac{1}{5}}\)+\(\frac{(1−x)^{\frac{1}{10}}}{t}\)),x≥0 is K, then 8 K is equal to__________.

Identify the correct Logic Gate for the following output (Y) of two inputs A and B.

A \(\sqrt{34}\) m long ladder weighing 10kg leans on a frictionless wall. Its feet rest on the floor 3m away from the wall as shown in the figure. If F_f and F_w are the reaction forces of the floor and the wall, then ratio of \(\frac{F_w}{F_f}\) will be: (Use g = 10 m/s²)

A mixture of hydrogen and oxygen has volume 2000 \(cm^3\), temperature 300 K, pressure 100 kPa and mass 0.76 g. The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be:[Take gas constant R = 8.3 \(JK^{–1}\) \(mol^{–1}\)]

Water falls from a 40 m high dam at the rate of \(9 \times 10^4\) kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of 100 W lamps, that can be lit, is: (Take g=10ms^-2)

In the arrangement shown in figure a₁, a₂, a₃ and a₄ are the accelerations of masses m₁, m₂, m₃ and m₄ respectively. Which of the following relation is true for this arrangement

Arrange the four graphs in descending order of total work done; where W₁, W₂, W₃ and W₄ are the work done corresponding to figure a, b, c and d respectively.

total work done corresponding to figure a, b, c, d

Two objects of equal masses placed at certain distance from each other attracts each other with a force of F. If one-third mass of one object is transferred to the other object, then the new force will be

A parallel plate capacitor with plate area A and plate separation d = 2 m has a capacitance of 4 μF. The new capacitance of the system, if half of the space between them is filled with a dielectric material of dielectric constant K = 3 (as shown in figure), will be :