List of top Mathematics Questions asked in JEE Main

A committee of 4 persons is to be formed from 2 ladies, 2 old men and 4 young men such that it includes at least 1 lady, at least 1 old man and at most 2 young men. Then the total number of ways in which this committee can be formed is :

The ratio of the coefficient of \(x^{15}\) to the term independent of \(x\) in the expansion of \(\left(x^2+\frac{2}{x}\right)^{15}\) is :

The sum of the series: \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots\ldots\) upto 10 terms, is :

A value of \(x\) for which \(\sin\left(\cot^{-1}(1+x)\right)=\cos\left(\tan^{-1}x\right)\), is :

If \(Z_1\ne 0\) and \(Z_2\) be two complex numbers such that \(\frac{Z_2}{Z_1}\) is a purely imaginary number, then \(\left|\frac{2Z_1+3Z_2}{2Z_1-3Z_2}\right|\) is equal to :

The values of '\(a\)' for which one root of the equation \(x^2-(a+1)x+a^2+a-8=0\) exceeds 2 and the other is lesser than 2, are given by :

A tangent to the hyperbola $\frac{x^{4}}{4}-\frac{y^{2}}{2}=1$ meets x-axis at $P$ and y-axis at $Q$. Lines $PR$ and $QR$ are drawn such that $OPRQ$ is a rectangle (where $O$ is the origin). Then $R$ lies on :

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at (0, 3) is

The ellipse $E_1 : \frac{x^2}{9} + \frac{y^2}{4}$ = 1 is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse $E_2$ passing through the point (0, 4) circumscribes the rectangle R. The eccentricity of the ellipse $E_2$ is

If the image of point $P(2, 3)$ in a line $L$ is $Q(4,5)$, then the image of point $R(0,0)$ in the same line is:

If two vertices of an equilateral triangle are $A (- a, 0)$ and $B (a, 0), a > 0$, and the third vertex $C$ lies above x-axis then the equation of the circumcircle of $\Delta ABC$ is :

Let the equations of two ellipses be $E_{1} : \frac{x^{2}}{3}+\frac{y^{2}}{2}=1 and E_{2} : \frac{x^{2}}{16}+\frac{y^{2}}{b^{2}}=1$, If the product of their eccentricities is $\frac{1}{2}$, then the length of the minor axis of ellipse $E_2$ is:

Statement 1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x+y=5 \, is\, x^{2}+y^{2}-6x+2y=0.$ Statement 2 : $2x + y = 5$ is a normal to the circle $x^{2}+y^{2}-6x+2y=0.$

If $ X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right] $ and $ X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right] $ , then X is equal to

If the equations $x^2+2x+3=0$ and $ax^2+bx+c=0, a, b, c \in R$ have a common root, then $a : b : c$ is

A common tangent to the conics $x^{2}=6y$ and $2x^{2}-4y^{2}=9$ is:

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

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

If $z$ is a complex number of unit modulus and argument $\theta ,$ then $ \, arg \left(\frac{1 + z}{1 + \bar{z}}\right)$ is equal to

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777,....,$ 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

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

$ABCD$ is a trapezium such that $AB$ and $CD$ are parallel and $BC$ $\perp$ $CD$, if $\angle $ $ADB = \theta, BC = p$ and $CD = q$, then $AB$ is equal to

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:

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?