List of top Mathematics Questions asked in JEE Advanced

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

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

If $\omega (\ne 1)$ be a cube root of unity and $(1 + \omega^2)^n = (1 + \omega^4)^n,$ then the least positive value of n is

An infinite GP has first term x and sum 5, then x belongs to

Coefficient of $t^{24} $ in $ (1+t^2)^{12}) (1+t^{12}(1+t^{24})$ is

If I(m,n) =$\int_0^1 t^m(1+t)n dt ,$ then the expression for I(m, n) in terms of I(m + 1, n - 1) is

If a $a \in \bigg(0,\frac{\pi}{2}\bigg),$ then $\sqrt {x^2+x} +\frac{\tan^2\, a}{\sqrt {x^2+x}} $ is always greater than or equal to

If $y (t)$ is a solution of $(1+t) \frac {dy}{dt}-ty=1 $ and $ y(0)=-1, $ then y(1) is equal to

The area of the quadrilateral formed by the tangents at the end points of latusrectum to the ellipse is $\frac{x^2}{9}+\frac{y^2}{5}=1$, is

If $ lim_{x \to 0 } \frac{ \{(a - n) nx - tan \, x \} sin \, nx }{x^2} = 0, $ where n is non-zero real number, then a is equal to

If $A = \begin {bmatrix} \alpha & 0 \\ 1 & 1 \end {bmatrix}$ and $B= \begin {bmatrix} 1 & 0 \\ 5 & 1 \end {bmatrix}$ then value of $\alpha$ for which $A^2=B$ is

$ lim_{ h \to 0 } \frac{ f (2 h + 2 + h^2 ) - f \, (2)}{ f \, ( h - h^2 + 1) - f (1)} $, given thta f ' (2) = 6 and f ' (1) = 4.