List of top Questions asked in JEE Main- 2022

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 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

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

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 :

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

If the plane 2x + y – 5z = 0 is rotated about its line of intersection with the plane 3x – y + 4z – 7 = 0 by an angle of π/2, then the plane after the rotation passes through the point:

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

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 $60^{\circ}$ and the part $PR$ of the tower subtends an angle of $15^{\circ}$ at $A$, then the height of the tower is :

If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to

The coefficient of x¹⁰¹ in the expression (5 + x)⁵⁰⁰ + x(5 + x)⁴⁹⁹ + x²(5 + x)⁴⁹⁸ + ……+ x⁵⁰⁰, x > 0, is

The set of values of $k$, for which the circle $C : 4x^2 + 4y^2 – 12x + 8y + k = 0$ lies inside the fourth quadrant and the point $\bigg(1, -\frac{1}{3}\bigg)$ lies on or inside the circle $C$, is

If A =$\sum_{n=1}^{\infty}$$\frac{1}{( 3 + (-1)^n)^n}$ and B = $\sum_{n=1}^{\infty}$$\frac{(-1)^n}{( 3 + (-1)^n)^n}$ ,
then A/B is equal to :

Let P be the plane containing the straight line$\frac{ x−3}{9}$=$\frac{y+4}{-1}$=$\frac{z-7}{-5}$and perpendicular to the plane containing the straight lines $\frac{x}{2}=\frac{y}{3}=\frac{z}{5}$ and $\frac{x}{3}=\frac{y}{7}=\frac{z}{8}$.If d is the distance P from the point (2, –5, 11), then d² is equal to :

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) – f(c) = f(d) is :

Let S be the sample space of all five digit numbers. It p is the probability that a randomly selected number from S, is multiple of 7 but not divisible by 5, then 9p is equal to

The value of the integral $∫^{ \frac{π}{2}}_{ \frac{-π}{2}} \frac{dx}{(1+e^x)(sin^6x+cos^6x)}$ is equal to

Let $f(x)= \begin{cases} x^3-x^2+10 x-7, & x \leq 1 \\ -2 x+\log _2\left(b^2-4\right), & x>1\end{cases}$ Then the set of all values of $b$, for which $f(x)$ has maximum value at $x=1$, is :

Let Δε{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then ∆is equal to