List of top Mathematics Questions asked in JEE Advanced

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.

If $f(x)=\int_{x^2}^{x^2+1} e^{-t {^2}}dt$ then f(x) increases in

Two numbers are selected randomly from the set $S = \{1, 2, 3, 4, 5, 6\}$ without replacement. The probability that minimum of the two numbers is less than $4$, is

In [0, 1] Lagranges Mean Value theorem is NOT applicable to

The centre of circle inscribed in square formed by the lines $x^2 - 8x + 12 = 0$ and $y^2 - 14y + 45 = 0$, is

Let T > 0 be a fixed real number. Suppose, f is a continuous function such that for all $x \in R. f(x+T)=f(x). \, If \, I = \int_0^T f(x)dx$ then the value of $\int_3^{3+3T} f(2x)dx$

The sum $\displaystyle \sum_{i-0}^{m} \binom{10}{i} \binom{20}{m-i},$ where $ \binom{p}{q}=0 \, if \, p>q,$ is maximum when m is equal to