List of top Questions asked in JEE Main- 2022

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).

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 \(JK^{–1}\) \(mol^{–1}\)]

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.

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 :

Let a, b be two non-zero real numbers. If p and r are the roots of the equation x² – 8ax + 2a = 0 and q and s are the roots of the equation x² + 12bx + 6b = 0, such that \(\frac{1}{p}\),\(\frac{1}{q}\),\(\frac{1}{r}\),\(\frac{1}{s}\) are in A.P., then a^–1 – b^–1 is equal to _________.

If \(x=∑_{n=0}^∞a^n,y=∑_{n=0}^∞b^n,z=∑_{n=0}^∞c^n\), where a, b, c are in A.P. and |a| < 1, |b| < 1, |c| < 1, abc≠ 0, then :

Let a be an integer such that  \(lim _{x→7} \frac{18−[1−x]}{[x−3a]}\) exists, where [t] is greatest integer \(≤ t\). Then \(a\) is equal to :

A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is \(1.8 \times 10^{–5} Nsm^{–2}\) and its density is negligible as compared to that of water \((10^6 gm^{–3})\). Terminal velocity of the water drop is

Let f(x)=\(\left\{\begin{matrix}  |4x^2-8x+5|, & if\,8x^2-6x+1\geq0 \\   |4x^2-8x+5|, & if\,8x^2-6x+1<0 \end{matrix}\right.\) where [α] denotes the greatest integer less than or equal to α.Then the number of points in R where f is not differentiable is

The number of distinct real roots of \(x^4 – 4x + 1 = 0\) is :

The lengths of the sides of a triangle are 10 + x2, 10 + x2 and 20 – 2x2. If for x = k, the area of the triangle is maximum, then 3k2 is equal to :