List of top Mathematics Questions asked in JEE Main

Let $A$ and $B$ be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6}, P\left(\overline{A \cap B}\right)=\frac{1}{4}$ and $P\left(\bar{A}\right)=\frac{1}{4}$ where $\overline{A}$ stands for the complement of the event $A$. Then , the events $A$ and $B$ are

A number $x$ is chosen at random from the set $\{1, 2, 3, 4, ....., 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{\left(x-10\right)\left(x-50\right)}{\left(x-30\right)}\ge0$ Then $P(A)$ is :

Given an $A.P$. whose terms are all positive integers. The sum of its first nine terms is greater than $200$ and less than $220$. If the second term in it is $12$, then its $4^{th}$ term is :

Let $a ,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c = 0$ and $5bx + 2by+ d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then

The integral $\int^{^{\frac{1}{2}}}_{_0} \frac{ln \left(1+2x\right)}{1+4x^{2}}dx,$ equals :

The minimum area of a triangle formed by any tangent to the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{81}=1$ and the co-ordinate axes is :

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

The image of the line $\frac{x-2}{3}=\frac{y+1}{4} = \frac{z-2}{12}$ in the plane $2x - y + z + 3 = 0$ is the line

The variance of first $50$ even natural numbers is

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x - y + z+ 3 = 0$ is the line.

The angle between the lines whose direction cosines satisfy the equations $l + m + n = 0 $ and $ l^2= m^2 + n^2 $is

The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :

Two tangents are drawn from a point $(- 2, -1)$ to the curve, $y^{2}=4x.$ If $\alpha$ is the angle between them, then $|\tan \alpha|$ is equal to :

On the sides $AB, BC, CA$ of a $\Delta ABC, 3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices a re :

If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

A light ray emerging from the point source placed at $P( 1,3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R (6, 7)$, then the abscissa of $Q$ is:

The term independent of $x$ in expansion of $\bigg(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\bigg)^{10}$ is

If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8\, cm^2/s$, then the rate of change of its volume is :

The real number $k$ for which the equation $2x^3 + 3x + k = 0$ has two distinct real roots in $[0, 1]$

The integral $\int \frac{xdx}{2-x^{2}+\sqrt{2-x^{2}}}$ equals

Distance between two parallel planes $2x+ y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is

The expression$\frac{tan\, A}{1-cot\, A}+\frac{cot\, A}{1-tan \, A}$ can be written as

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n =10$ then the value of $n$ is