List of top Mathematics Questions asked in JEE Advanced

Let $f : R \rightarrow R$ be a function such that $f (x + y) = f (x) + f (y), \forall x, y \in R$. If $f (x )$ is differentiable at $x = 0$, then

Let P(6,3) be a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ If the norm al at the point P intersects the X -axis at (9, 0), then the eccentricity of the hyperbola is

The number of $3 \times 3$ matrices $A$ whose entries are either $0$ or $1$ and for which the system A $\begin {bmatrix} x \\ y \\ z \end {bmatrix}-\begin {bmatrix} 1 \\ 0 \\ 0 \end {bmatrix}$ has exactly two distinct solutions, is

The value(s ) of $ \int^1_0 \frac { x^4 ( 1 - x )^4 }{ ( 1 + x^2 ) } \, dx $ is are

Let $\omega$ be a complex cube root of unity with $\omega \, \ne$ 1. A fair die is thrown three times. If r$_1$, r$_2$ and r$_3$ are the numbers obtained on the die, then the probability that $\omega ^{r_1} +\omega ^{r_2} +\omega ^{r_3}=0 , $ is

Equation of the plane containing the straight line $\frac{x}{2}=\frac{y}{3}= \frac{z}{4}$ and perpendicular to the plane containing the staight lines $\frac{x}{2}=\frac{y}{4}= \frac{z}{2}$ and $\frac{x}{4}=\frac{y}{2}= \frac{z}{3}$ is

If the distance of the point $P (1, - 2,1)$ from the plane $x + 2y - 2z = a$, where $a > 0$, is $5$, then the foot of the perpendicular form $ P$ to the plane is

If the angles $A, B$ and $C$ of a triangle are in an arithmetic progression and if $a, b$ and $c$ denote the lengths of the sides opposite to $A, B$ and $C$ respectively, then the value of the expression $ \frac{a}{c} sin \, 2 C + \frac{c}{a} sin \, 2 A $ is

If $\frac{sin^4 x}{2}+\frac{cos^4 x}{3}=\frac{1}{5}$ then

For $0 < \theta < \frac{\pi}{2}$, the solution(s) of $\displaystyle\sum _{m=1}^{6} cosec \Bigg(\theta+\frac{(m-1)\pi}{4}\Bigg)cosec\Bigg(\theta+\frac{m\pi}{4}\Bigg)=4\sqrt{2}$ is/are

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $x^2 + 9y^2 = 9$ meets its auxiliary circle a t the point M. Then, the area (insqunits) of the triangle with vertices at A, M and the origin O is

Let $z = \cos \theta + i \sin \theta$. Then, the value of $\displaystyle \sum _{m=0}^{15} Im (z^{2m-1})$ at $\theta = 2^\circ$ is

The number of seven-digit integers, with sum of the digits equal to $10$ and formed by using the digits $1, 2$ and $3$ only, is

The locus of the orthocentre of the triangle formed by the lines $(1 + p )x -p y + p (1 + p) = 0 (1+ q)x-qy + < 7(1+ q) = 0$ and $y = 0$, where $p\ne q$ is

An ellipse intersects the hyperbola $2x^2-2y^2=1$ orthogonally. The eccentricity of the ellipse is reciprocal to th a t of the hyperbola. If the axes of the ellipse are along the coordinate axes, then

Let $f$ be a non-negative function defined on the interval [0,1].if $\int_0^x \sqrt{1-(f'(t))^2}dt = \int_0^x f(t) dt , 0 \le x \le 1$ and $f (0) = 0$, then

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then

A line with positive direction cosines passes through the point $P (2, -1, 2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x + y+ z = 9$ at point $Q$. The length of the line segment $PQ$ equals

In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then

The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vector $\widehat{a},\widehat{b},\widehat{c}$ such that $\widehat{a}.\widehat{b}=\widehat{b}.\widehat{c}=\widehat{c}.\widehat{a}=\frac{1}{2}.$Then, the volume of the parallelopiped is

Let $S_n= \displaystyle \sum_{k=0}^n \frac{n}{n^2+kn+k^2} \, and \, T_n= \displaystyle \sum_{k=0}^{n-1} \frac{1}{n^2+kn+k^2} , \, for \, $ $n = 1 ,2 ,3 $,... Then,

If $0 < x < 1$, then $\sqrt{1+x^2}[\{x cos(cot^{-1}x)$ $+sin(cot^{-1}x)\}^2-1]^{1/2}$ is equal to

Let $g(x) = \frac{(x -1)^n}{\log \cos^m (x -1)} ; 0 < x < 2 , m $ and $n$ are integers, m $\neq$ 0, n > 0 , and let $p$ be the left hand derivative of $|x - 1|$ at $x = 1$. If $\displaystyle \lim_{x \to 1^{+}} \, g(x) = p $ , then

An experiment has $10$ equally likely outcomes. Let $A$ and $B$ be two non-empty events of the experiment. If $A$ consists of $4$ outcomes, then the number of outcomes that $B$ must have, so that $A$ and $B$ are independent, is