List of top Questions asked in JEE Main- 2022

Given below are two statements
Statement-I: When μ amount of an ideal gas undergoes adiabatic change from state (P₁, V₁, T₁) to state (P₂, V₂, T₂), then work done is
$W = \frac{μR(T2 - T1)}{1 - γ}$
,where
$γ = \frac{Cp}{Cv} $and R = universal gas constant.
Statement-II: In the above case, when work is done on the gas, the temperature of the gas would rise.
Choose the correct answer from the options given below.

Considering the reaction sequence given below, the correct statement(s) is(are)

Two metallic blocks M₁and M₂of the same cross-section area are connected (as shown in the figure). If the thermal conductivity of M₂ is K then the thermal conductivity of M₁ will be : [Assume steady state heat conduction]

How many alpha and beta particles are emitted when Uranium ₉₂U²³⁸ decays to lead₈₂Pb²⁰⁶

In the following circuit, the correct relation between output (Y) and inputs A and B will be:

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^–3/2s^–1).

Two satellites A and B, having masses in the ratio 4 : 3, are revolving in circular orbits of radii 3r and 4r respectively around the earth. The ratio of total mechanical energy of A to B is

The dimension of mutual inductance is :

A water drop of radius $1 \,cm$ is broken into $729$ equal droplets If surface tension of water is $75 \,dync / cm$, then the gain in surface energy upto first decimal place will be : [Given $\pi=314]$

A monkey of mass $50 \,kg$ climbs on a rope which can withstand the tension $(T)$ of $350 \,N$ If monkey initially climbs down with an acceleration of $4\, m / s ^2$ and then climbs up with an acceleration of $5 \,m / s ^2$ Choose the correct option $\left( g =10\, m / s ^2\right)$

The locus of the mid-point of the line segment joining the point (4, 3) and the points on the ellipse x² + 2y² = 4 is an ellipse with eccentricity:

Octahedral complexes of copper(II) undergo structural distortion (Jahn-Teller). Which one of the given copper(II) complexes will show the maximum structural distortion?
(en – ethylenediamine;H₂N−CH₂−CH₂−NH₂)

The oxide which contains an odd electron at the nitrogen atom is

A direct current of 4 A and an alternating current of peak value 4 A flow through resistance of 3 Ω and 2 Ω respectively. The ratio of heat produced in the two resistances in same interval of time will be :

The negation of the Boolean expression ((~ q) ∧ p) ⇒ ((~ p) ∨ q) is logically equivalent to:

For $n \in N$, let $S _{ n }=\left\{ z \in C :| z -3+2 i |=\frac{ n }{4}\right\}$ and $T_n=\left\{z \in C:|z-2+3 i|=\frac{1}{n}\right\}$ Then the number of elements in the set $\left\{ n \in N : S _{ n } \cap T _{ n }=\phi\right\}$ is :

Let $x, y > 0$. If $x^3y^2 = 2^{15}$, then the least value of $3x + 2y$ is

For $t \in(0,2 \pi)$, if $ABC$ is an equilateral triangle with vertices$A ( \sin t, -{\cos t}), B ( \cos t, \sin t )$ and $C ( a , b )$ such that its orthocentre lies on a circle with centre $\left(1, \frac{1}{3}\right)$, then $\left(a^2-b^2\right)$ is equal to :

If y = y(x) is the solution of the differential equation
$x$ $\frac{dy}{dx}$ $+ 2y =$ $xe^x , y(1) = 0$
then the local maximum value of the function
$z(x) = x²y(x) - e^x , x ∈ R$
is

The shortest distance between the lines $\frac{x−3}{2}=\frac{y−2}{3}=\frac{z−1}{−1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z−5}{3}$ is

The acute angle between the planes P₁ and P₂, when P₁ and P₂ are the planes passing through the intersection of the planes 5x + 8y + 13z – 29 = 0 and 8x – 7y + z – 20 = 0 and the points (2, 1, 3) and (0, 1, 2), respectively, is

If two distinct points Q, R lie on the line of intersection of the planes –x + 2y – z = 0 and 3x – 5y + 2z = 0 and
$PQ = PR = \sqrt{18}$
where the point P is (1, –2, 3), then the area of the triangle PQR is equal to

Let
$\frac{x-2}{3} = \frac{y+1}{-2} = \frac{z+3}{-1}$
lie on the plane px – qy + z = 5, for some p, q ∈ ℝ. The shortest distance of the plane from the origin is :

Let α and β be the roots of the equation x² + (2i – 1) = 0. Then, the value of |α² + β²| is equal to

The mean and variance of the data $4, 5, 6, 6, 7, 8, x, y$, where $x<y$, are $6$ and $\frac{9}{4}$, respectively. Then $x^4+y^2$ is equal to