List of top Mathematics Questions asked in JEE Main

For a triangle $A B C$, the value of $\cos 2 A+\cos 2 B+\cos 2 C$ is least If its inradius is $3$ and incentre is $M$, then which of the following is NOT correct?

Let $a, b, c>, a^3, b^3$ and $c^3$ be in AP, and $\log _a b, \log _c a$ and $\log _b c$ be in GP If the sum of first 20 terms of an AP, whose first term is $\frac{a+4 b+c}{3}$ and the common difference is $\frac{a-8 b+c}{10}$ is $-444$, then $a b c$ is equal to:

If $P$ is a $3 \times 3$ real matrix such that $P^T=a P+(a-1) I$, where $a>$, then

The number of ways of selecting two numbers $a$ and $b, a \in\{2,4,6, \ldots , 100\}$ and $b \in\{1,3,5, \ldots , 99\}$ such that 2 is the remainder when $a+b$ is divided by 23 is

For $\alpha, \beta \in R$, suppose the system of linear equations $ x-y+z=5 $ $2 x+2 y+\alpha z=8 $ $3 x-y+4 z=\beta$ has infinitely many solutions Then $\alpha$ and $\beta$ are the roots of

The solution of the differential equation $\frac{d y}{d x}=-\left(\frac{x^2+3 y^2}{3 x^2+y^2}\right), y(1)=0$ is

If a plane passes through the points $(-1, k, 0),(2, k,-1),(1,1,2)$ and is parallel to the line $\frac{x-1}{1}=\frac{2 y+1}{2}=\frac{z+1}{-1}$, then the value of $\frac{k^2+1}{(k-1)(k-2)}$ is

The complex number $z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}$ is equal to :

Among the relations
$S=\left\{(a, b): a, b \in R -\{0\}, 2+\frac{a}{b}>\right\}$
and $T=\left\{(a, b): a, b \in R , a^2-b^2 \in Z\right\}$,

Let the mean and standard deviation of marks of class A of $100$ students be respectively $40$ and $\alpha$ (> 0 ), and the mean and standard deviation of marks of class B of $n$ students be respectively $55$ and 30 $-\alpha$. If the mean and variance of the marks of the combined class of $100+ n$ students are respectively $50$ and $350$ , then the sum of variances of classes $A$ and $B$ is :

Let $f^1(x)=\frac{3 x+2}{2 x+3}, x \in R -\left\{\frac{-3}{2}\right\}$ For $n \geq 2$, define $f^{ n }(x)=f^1 o f^{ n -1}(x)$ if $f^5(x)=\frac{ a x+ b }{ b x+ a }, \operatorname{gcd}( a , b )=1$, then $a + b$ is equal to ______ .

If the equation of the plane passing through the point $(1,1,2)$ and perpendicular to the line $x-3 y+$ $2 z-1=0=4 x-y+z$ is $A t+ B y+ C z=1$, then $140( C - B + A )$ is equal to______

If for log_{cos x} (cot x) - 4log_{(sin x)} cot x = 1, x = sin^-1 $(\frac{\alpha+\sqrt{\beta}}{2})$. Find (α + β), given x ∈ $(0,\frac{\pi}{2})$

Suppose $ f: \mathbb{R} \to (0, \infty) $ be a differentiable function such that: $ 5f(x + y) = f(x) \cdot f(y), \quad \forall x, y \in \mathbb{R} $. If $ f(3) = 320 $, then the value of:$ \sum_{n=0}^{5} f(n) $ is equal to:

Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1,2 , 3 and 5 , and are divisible by 15 , is equal to _____

Let $ \lambda_1 < \lambda_2 $ be two values of $ \lambda $ such that the angle between the planes:
$ P_1 : \vec{r} \cdot (3\hat{i} - 5\hat{j} + \hat{k}) = 7 $
$ P_2 : \vec{r} \cdot (\lambda\hat{i} + \hat{j} - 3\hat{k}) = 9 $
is $ \sin^{-1}\left(\frac{2\sqrt{6}}{5}\right) $. Then, the square of the length of the perpendicular from the point $ (38\lambda, 10\lambda, 2) $ to the plane $ P_1 $ is:

Let $ A = \begin{pmatrix} m & n \\ p & q \end{pmatrix} $, $ d = |A| \neq 0 $, and $ |A - d(\text{Adj}(A))| = 0 $. Then

Let $ z = 1 + i $ and $ z_1 = \frac{1 + \bar{z}}{z(1 - z) + 1} $, where $ \bar{z} $ denotes the conjugate of $ z $. Then$\frac{12}{\pi} \arg(z_1)$ is equal to:

The $4^{\text {th }}$ term of $G P$ is $500$ and its common ratio is $\frac{1}{m}, m \in N$ Let $S_n$ denote the sum of the first $n$ terms of this GP If $S_6>S_5+1$ and $S_7< S_6+\frac{1}{2}$, then the number of possible values of $m$ is

$ \lim_{x \to 0} \frac{48 x^4}{x} \int_0^x \frac{t^3}{t^6 + 1} \, dt $ is equal to:

The line $l_1$ passes through the point $(2,6,2)$ and is perpendicular to the plane $2 x+y-2 z=10$. Then the shortest distance between the line $l_1$ and the line $\frac{x+1}{2}=\frac{y+4}{-3}=\frac{z}{2}$ is :

The value of $\frac{8}{\pi} \int\limits_0^{\frac{\pi}{2}} \frac{(\cos x)^{2023}}{(\sin x)^{2023}+(\cos x)^{2023}} d x$ is

Let a tangent to the curve $9 x^2+16 y^2=144$ intersect the coordinate axes at the points $A$ and $B$. Then, the minimum length of the line segment $AB$ is

Let $\alpha>0$ If $\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} d x=\frac{16+20 \sqrt{2}}{15}$, then $\alpha$ is equal to :

A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses If he can choose at most two language courses, then the number of ways he can choose five courses is