List of top Mathematics Questions asked in JEE Advanced

Let AB be a chord of the circle $x^2 + y^2 = r^2$ subtending a right angle at the centre. Then, the locus of the centroid of the $\Delta PAB$ as P moves on the circle, is

Let $ \alpha, \beta$ be the roots of $x^2 - x + p = 0$ and $y, \delta$ be the roots of $x^2 - 4x + q = 0$ if $ \alpha, \beta, y \delta$ are in GP, then the integer values of p and q respectively are

Let $f(x) = (1 + b^2)x^2 + 2bx + 1$ and let m(b) be the minimum value of f(x). As b varies, the range of m(b) is

Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term is 3/4 then

If $\alpha$ and $\beta$ are $(\alpha < \beta)$ the roots of the equation $x^2+bx+c=0,$ where $c < 0 < b$,the

If $ x^2 + y^2 = 1$, then

A straight line through the origin O meets the parallel lines $4x + 2y = 9 $ and $2x + y + 6 = 0$ at points P and Q respectively. Then, the point O divides the segment PQ in the ratio

Let f : R $\to$ R be any function. Define g : R $\to$ R by g(x) = |f(x)| for all x. Then g is

For the equation $3x^2+px+3=0,p>0,$ if one of the root is square of the other, then p is equal to

If $\overrightarrow{a}, \overrightarrow{b}$ and $\overrightarrow{c}$ are unit coplanar vectors, then the scalar triple product $[2\overrightarrow{a}-\overrightarrow{b}2\overrightarrow{b}-\overrightarrow{c}2\overrightarrow{c}-\overrightarrow{a}]$ is

In a $\triangle ABC, $ 2 ac sin $ \bigg [ \frac{1}{2} (A - B + C ) \bigg ] $ is equal to

The incentre of the triangle with vertices $(1, \sqrt{3}), (0,0)$ and $ (2,0) is $

Let $f(x) = \begin{cases} |x|, & \quad \text{for}\, 0 < | x | \le 2 \\ 1, & \quad \text{for} \, x = 0 \end{cases}$ then at x = 0, f has

For all $x\,\in\,(0,1)$

If $a, b, c, d$ are positive real numbers such that $a + b +c + d = 2,$ then $M =(a + b) (c+d) $ satisfies the relation.

For $2 \le \, r \, \le \, n,\binom{n}{r}+2 \binom{n}{r-1}+\binom{n+2}{r}$ is equal to

if $\ f ( x )$ $=\bigg \{ \begin {array} \ e^{\cos x}\sin \ x \\ 2 \\ \end {array} \begin {array} \ for |x|\le 2 \\ \text{otherwise} \\ \end {array}$ then $\int^{3}_{-2} f ( x ) \ dx$ is equal to

The value of the integral $ \int^{e^2}_{e^{-1}} \bigg | \frac{ \log_e \, x }{ x } \bigg | \, dx $ is

If $ i = \sqrt -1$ then $ 4 + 5 \bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{334}+3\bigg(-\frac{1}{2}+\frac{i\sqrt 3}{2}\bigg)^{365}$ is equal to

In a $\triangle PQR, \angle R = \frac{\pi}{2} , \, if \, tan \, \bigg( \frac{ P}{2}\bigg) $ and \, tan $ \bigg( \frac{ Q}{2}\bigg)$ are the roots of the equation $ ax^2 + bx + c = 0 \, (a \ne 0 )$, then

The function f (x) = $ [ x]^2 - [ x]^2 $ (where, [x] is the greatest integer less than or equal to x), is discontinuous at

Let $PQR$ be a right angled isosceles triangle, right angled at $P (2,1)$. If the equation of the line $QR$ is $2x + y = 3$, then the equation representing the pair of lines PQ and PR is

For a positive integer n, let $f_n(\theta)=\Bigg(tan\frac{\theta}{2}\Bigg)(1+sec \theta)(1+sec 2\theta)(1+ sec 2^2 \theta)... (1+sec 2^n \theta), then$

For a positive integer n let $a (n) = 1 + \frac{1}{2} + \frac{1}{3} + \frac{1}{4} + ...+ \frac{1}{(2^n)-1},$ then

The harmonic mean of the roots of the equation $ (5+\sqrt 2)\, x^2 - (4+\sqrt 5)\, x + 8 + 2\sqrt5 = 0 $ is