List of top Mathematics Questions asked in JEE Main

Shortest distance between lines $\frac{(x-5)}{4}$=$\frac{(y-3)}{6}$=$\frac{(z-2)}{4}$ and $\frac{(x-3)}{7}=\frac{(y-2)}{5}=\frac{(z-9)}{6}$ is ?

The value of the integral $\int \limits_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \frac{x+\frac{\pi}{4}}{2-\cos 2 x} d x$is :

Let $y (x)=(1+x)\left(1+x^2\right)\left(1+x^4\right)\left(1+x^8\right)\left(1+x^{16}\right)$ Then $y^{\prime}-y^{\prime \prime}$ at $x=-1$ is equal to :

Let the six numbers $a_1, a_2, a_3, a_4, a_5, a_6$, be in AP and $a_1+a_3=10$ If the mean of these six numbers is $\frac{19}{2}$ and their variance is $\sigma^2$, then $8 \sigma^2$ is equal to :

Consider the lines $L_1$ and $L_2$ given by

$L_1: \frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2} $

$ L_2: \frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$

A line $L_3$ having direction ratios $1,-1,-2$, intersects $L_1$ and $L_2$ at the points $P$ and $Q$ respectively Then the length of line segment $P Q$ is

The absolute difference of the coefficients of $x^{10}$ and $x^7$ in the expansion of $\left(2x^2 + \frac{1}{2x}\right)^{11}$ is equal to:

If the four points, whose position vectors are $3 \hat{i}-4 j+2 \hat{k}, l+2 j-\hat{k}_4-2 \hat{k}-j+3 \hat{k}$ and $5 \hat{i}-2 \alpha \hat{j}+4 \hat{k}$ are coplanar, then a is equal to

Let $\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$ and $\vec{b}$ be a vector such that $\vec{a} \times \vec{b}=2 \hat{i}-\hat{k}$ and $\vec{a} \cdot \vec{b}=3$ Then the projection of $\vec{b}$ on the vector $\vec{a}-\vec{b}$ is :-

The number of points on the curve $y=54 x^5-135 x^4-70 x^3+180 x^2+210 x$ at which the normal lines are parallel $to x+90 y+2=0$ is

If $A(1, 1, 1), B(0, λ, 0), C(λ + 1, 0, 1), D(2, -2, 2)$ are co-planer then $\sum (\lambda_i + 2)^2$ is equal to

Let $f: R -\{2,6\} \rightarrow R$ be real valued function defined as $f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}$ Then range of $f$ is

The points of intersection of the line $a x+b y=0,(a \neq b)$ and the circle $x^2+y^2-2 x=0$ are $A (\alpha, 0)$ and $B (1, \beta)$ The image of the circle with $AB$ as a diameter in the line $x+y+2=0$ is :

Let $y = y(x), y > 0,$ be a solution curve of the differential equation $(1 +x^2)dy = y(x−y)dx.$ If $y(0) = 1$ and $y(2√2) = β$, then

Two circles having radius $r_1$ and $r_2$ touch both the coordinate axes. Line $x+y=2$ makes intercept 2 on both the circles. The value of $r_{1}^{2} + r_{2}^{2} - r_{1}r_{2}$ is:

Let $\alpha$ be a root of the equation $(a-c) x^2+(b-a) x+(c-b)=0$where $a , b , c$ are distinct real numbers such that the matrix $\begin{bmatrix}\alpha^2 & \alpha & 1 \\ 1 & 1 & 1 \\ a & b & c\end{bmatrix}$is singular Then, the value of $\frac{(a-c)^2}{(b-a)(c-b)}+\frac{(b-a)^2}{(a-c)(c-b)}+\frac{(c-b)^2}{(a-c)(b-a)}$ is

If (21)18 + 20·(21)17 + (20)2 · (21)16 + ……….. (20)18 = k (2119 – 2019) then k =

The sum of the absolute maximum and minimum values of the function $f(x)=\left|x^2-5 x+6\right|-3 x+2$in the interval $[-1,3]$ is equal to :

Let $H$ be the hyperbola, whose foci are $(1 \pm \sqrt{2}, 0)$ and eccentricity is $\sqrt{2}$. Then the length of its latus rectum is _____

If $sin^{-1}x=2\,tan^{-1}x$ , then the number of integral values of x is equal to:

If the mean deviation about median for the number $3,5,7,2 k , 12,16,21,24$ arranged in the ascending order, is 6 then the median is

Let $P(x_0, y_0)$ be the point on the hyperbola $3x^2 - 4y^2 = 36$, which is nearest to the line $3x + 2y = 1$. Then $\sqrt{2}(y_0 - x_0)$ is equal to:

Let awards in event A is 48 and awards in event B is 25 and awards in event C is 18 and also n(A ∪ B ∪ C) = 60, n(A ⋂ B ⋂ C) = 5, then how many got exactly two awards is?

If the system of equations
x + y + az = b
2x + 5y + 2z = 6
x + 2y + 3z = 3
Has infinitely many solutions, then 2a + 3b is equal to

Let the system of linear equations
$-x + 2y - 9z = 7$,
$-x + 3y + 72 = 9$,
$-2x + y + 5z = 8$,
$-3x + y + 13z = \lambda$
has a unique solution $x = \alpha, y = \beta, z = \gamma$. Then the distance of the point $(\alpha, \beta, \gamma)$ from the plane $2x - 2y + z = \lambda$ is:

Let $y = y(x)$ be a solution curve of the differential equation $$(1 - x^2 y)\,dx = y\,dx + x\,dy.$$ If the line $x = 1$ intersects the curve $y = y(x)$ at $y = 2$ and the line $x = 2$ intersects the curve $y = y(x)$ at $y = \alpha$, then a value of $\alpha$ is: