List of top Mathematics Questions asked in JEE Advanced

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

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

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

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

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

If the line $2x+\sqrt6y=2$ touches the hyperbola $x^2-2y^2=4$, then the point of contact is

If f(x) is differentiable and $\int_0^{t^2}x f(x) dx =\frac{2}{5}t^5,$ then $f\bigg(\frac{4}{25}\bigg)$ equals

The sides of a triangle are in the ratio $ 1 : \sqrt 3 : 2 $, then the angles of the triangle are in the ratio

Given both $\theta and \phi are acute angles and sin \theta=\frac{1}{2}, cos \phi=\frac{1}{3},$ then the value of $\theta+\phi $ belongs to

If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre (2,1), then the radius of the circle is

If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is

If $^{n-1}C_r =(k^2 -3) \, ^nC_{r+1}$then k belongs to

If one root is square of the other root of the equation $x^2+px+q=0,$ then the relation between p and q is