List of top Questions asked in JEE Main- 2022

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

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

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

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

Let
$f(x)=\frac{x−1}{x+1},x∈R− \left\{0,−1,1\right\}$
If ƒⁿ⁺¹(x) = ƒ(ƒⁿ(x)) for all n∈N, then ƒ⁶(6) + ƒ⁷(7) is equal to :

Let A be a matrix of order 3×3 and det (A) = 2. Then det (det (A) adj (5 adj (A³))) is equal to ______.

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is

The value of $ tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )$ is equal to:

Let R be the point (3, 7) and let P and Q be two points on the line x + y = 5 such that PQR is an equilateral triangle, Then the area of ΔPQR is

Let the system of linear equations \[ x + 2y + z = 2, \quad \alpha x + 3y - z = \alpha, \quad -\alpha x + y + 2z = -\alpha \] be inconsistent. Then $\alpha$ is equal to:

The integral $\int_0^{\frac{\pi}{2}} \frac{1}{3 + 2\sin x + \cos x} \, dx$ is equal to

If $\lim_{{x \to 0}} \frac{\alpha e^x + \beta e^{-x} + \gamma \sin x}{x \sin^2 x} = \frac{2}{3}$, where $\alpha, \beta, \gamma \in \mathbb{R}$ then which of the following is NOT correct?

In an isosceles triangle ABC, the vertex A is $(6, 1)$ and the equation of the base BC is $2x + y = 4$. Let the point B lie on the line $x + 3y = 7$. If $(α, β)$ is the centroid of ΔABC, then $15(α + β)$ is equal to :

If the tangents drawn at the points $P$ and $Q$ on the parabola $y^2=2 x-3$ intersect at the point $R (0,1)$, then the orthocentre of the triangle $PQR$ is :

Let Q be the mirror image of the point P(1, 2, 1) with respect to the plane x + 2y + 2z = 16. Let T be a plane passing through the point Q and contains the line
$\vec{r}=−\hat{k}+λ(\hat{i}+\hat{j}+2\hat{k}), λ ∈ R.$
Then, which of the following points lies on T?

If α, β, γ, δ are the roots of the equation x⁴ + x³ + x² + x + 1 = 0, then α²⁰²¹ + β²⁰²¹ + γ²⁰²¹ + δ²⁰²¹ is equal to

If $\alpha, \beta, \gamma, \delta$ are the roots of the equation $x ^4+ x ^3+ x ^2+ x +1=0$, then $\alpha^{2021}+\beta^{2021}+\gamma^{2021}+\delta^{2021}$ is equal to

The statement $(\sim( p \Leftrightarrow \sim q )) \wedge q$ is :

If the system of equations αx + y + z = 5, x + 2y + 3z = 4, x + 3y +5z = β has infinitely many solutions, then the ordered pair (α, β) is equal to:

If $∫\frac{1}{x}$ $√{\frac{1-x}{1+x}}$ dx = $g(x) + c,g(1) = 0$ , then g $(\frac{1}{2})$
is equal to