List of top Questions asked in JEE Main- 2022

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

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

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

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

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 :

The value of $ tan^{-1}(\frac{cos\frac{15}{4}-1}{sin(\frac{π}{4})} )$ 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 $\alpha, \beta, \gamma, \delta$ 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 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 $∫\frac{1}{x}$ $√{\frac{1-x}{1+x}}$ dx = $g(x) + c,g(1) = 0$ , then g $(\frac{1}{2})$
is equal to

The value of 2 sin(12°) – sin(72°) is

Let P be the plane passing through the intersection of the planes

r→.(i+3k−k)=5 and r→ .(2i−j+k)=3,

and the point (2, 1, –2). Let the position vectors of the points X and Y be

i−2j+4k and 5i−j+2k

respectively. Then the points

Let n ≥ 5 be an integer. If 9ⁿ – 8n – 1 = 64α and 6ⁿ – 5n – 1 = 25β, then α – β is equal to

if $∫ \frac{(x^2+1)e^x}{(x+1)^2}dx = ƒ(x)e^x+C$ where $C$ is a constant, then $\frac{d^3ƒ}{dx^3}$ at $x = 1$ is equal to :

$sin^{-1}\bigg(sin\frac{2π}{3}\bigg)+cos^{-1}\bigg(cos\frac{7π}{6}\bigg)+tan^{-1}\bigg(tan\frac{3π}{4}\bigg)$ is equal to:

Let ℝ → ℝ be function defined as
f(x) = αsin($(\frac{π[x]}{2})$+[2-x],α∈R
where [t] is the greatest integer less than or equal to t.
If lim x→1 f(x) exists, then the value of$∫_0^4$ f(x)dx
is equal to

Let A and B be any two 3 × 3 symmetric and skew symmetric matrices, respectively. Then Which of the following is NOT true?

Let y = y(x) be the solution of the differential equation
$x ( 1 - x² ) \frac{dy}{dx} + ( 3x²y - y - 4x³ ) = 0, x > 1$
with y(2) = –2. Then y(3) is equal to