List of top Mathematics Questions asked in JEE Advanced

The value of $\int \limits \frac {(x^2-1)dx}{x^3 \sqrt {2x^4-2x^2+1}} $ is

A plane passes through $ (1 ,-2 ,1 )$ and is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4, $ then the distance of the plane from the point $ (1, 2, 2)$ is

For x > 0, $ lim_{ x \to 0} \Bigg [ (sin \, x)^{1/x} + \bigg( \frac{1}{x}\bigg)^{sin \, x} \Bigg ] $ is

Let, $\overrightarrow{a}=\widehat{i}+2\widehat{j}+\widehat{k}, \overrightarrow{c}=\widehat{i}+\widehat{j}+\widehat{k}.$ A vector coplanar to $\overrightarrow{a}$ and $\overrightarrow{c}$ of magnitude $\frac{1}{\sqrt{3}},$ then the vector is

If a, b,c are the sides of a triangle ABC such that $x^2 - 2(a+b+c)x+3\lambda(ab+bc+ca)=0$ has real roots, then

If $r, s, t$ are prime numbers and p , q are the positive integers such th a t LCM of p , q is $r^2 s^4 t^2$ then the number of ordered pairs (p, q) is

f(x) is cubic polynomial with f(2) = 18 and f(1) = -1. Also f(x) has local maxima at x = -1 and f '(x) has local minima at x = 0, then

If $e_1$ is the eccentricity of the ellipse $\frac {x^2}{16}+\frac{y^2}{25}=1$ and $e_2$ is the eccentricity of the hyperbola passing through the foci of the ellipse and $e_1e_2=1$ then equation of the hyperbola is

If $2A+3B =\begin{bmatrix} {2}&{-1} &{4}\\ {3}&{2}& {5} \\ \end{bmatrix} $ and $A+2B \begin{bmatrix} {5}&{0} &{3}\\ {1}&{6}& {2} \\ \end{bmatrix} $then $B =$

If $x dy = y(dx+y dy),y(1)=1$ and $y(x) > 0$. Then, $y(-3)$ is equal to

if $p=\begin {bmatrix} \sqrt 3 /2 & 1/2 \\ -1/2 & \sqrt 3/2 \end {bmatrix} , A=\begin {bmatrix} 1 & 1 \\ 0 & 1 \end {bmatrix}$ and $ Q=PAP^T,\ then$ $P^TQ^{2005}P $ is

If $\int_{sin x}^1 \, t^2 f(t) dt =1-sin x, \forall x \in (0,\pi/2), \, then \, f\bigg(\frac{1}{\sqrt 3}\bigg)$ is

A variable plane $ \frac{x}{a}+ \frac{y}{b}+ \frac{z}{c} =1$ at a unit distance from origin cuts the coordinate axes at A. Band C. Centroid (x, y, z) satisfies the equation $ \frac{1}{x^2}+ \frac{1}{y^2}+ \frac{1}{z^2} =K.$ The value of K is

In a $\triangle$ ABC, among the following which one is true?

The number of ordered pairs $(\alpha, \beta), $ where $\alpha, \beta \in(-\pi, \pi)$ satisfying cos $(\alpha-\beta)=1 and cos (\alpha+\beta)=\frac{1}{e}$ is

If $\overrightarrow{a}$ and $\overrightarrow{b_1}$ are two unit vectors such that $\overrightarrow{a}+2\overrightarrow{b}$ and $5\overrightarrow{a}-4\overrightarrow{b}$ b, are perpendicular to each other, then the angle between $\overrightarrow{a} and \overrightarrow{b}$ is

The shaded region, where $P = (-1,0), Q = (-1 + \sqrt 2,\sqrt 2 )R = (-1 + \sqrt 2,-\sqrt 2), S = (1,0)$ is represented by

The minimum value of $| a + b\omega + c \omega^2|$ , where $ a, b$ and $c$ are all not equal integers and $\omega \, (\ne 1)$ is a cube root of unity, is

The area of the equilateral triangle, in which three coins of radius 1 cm are placed, as shown in the figure, is

Let $f (x) = ax^2 + bx + c, a \ne 0$ and $\Delta =b^2 -4ac.$ If $a+ \beta,$ $a^2+ \beta^2$ and $a^3+ \beta^3$ are in GP, then

If f (x) is continuous and differentiable function and f (1/n) = 0 $\forall$ n $\ge$ 1and n $\in$ I, then

If the lines $\frac{x-1}{2}=\frac{y+3}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-k}{2}=\frac{z}{1}$ intersect, then the value of k is

The unit vector which is orthogonal to the vector $3\widehat{i} + 2\widehat{j} + 6\widehat{k}$ and is coplanar with the vectors $ 2\widehat{i} + \widehat{j} + \widehat{k}$ and $\widehat{i} + \widehat{j} + \widehat{k}$ is

If three natural numbers from $1$ to $100$ are selected randomly then probability that all are divisible by both $2$ and $3$, is

Area of triangle formed by the lines $ x + y = 3$ and angle bisectors of the pair of straight lines $x^2 - y^2 + 2y = 1$ is