List of top Mathematics Questions asked in JEE Advanced

The integral $ \int\limits^{1/2}_{-1/2} \bigg ([x] + \log \bigg ( \frac{1+ x}{1 - x} \bigg ) \bigg ) \, dx $ equals

If $\overrightarrow{a}, \overrightarrow{b}$ and $ \overrightarrow{c}$ are unit vectors, then $|\overrightarrow{a}-\overrightarrow{b} |^2+| \overrightarrow{b}-\overrightarrow{c}|^2+| \overrightarrow{c}-\overrightarrow{a}|^2$ does not exceed

If $f (x) = xe^{x(1-x)}$ , then f (x) is

The value of $\int^{\pi}_{-\pi} \frac{ \cos^2 \, x }{ 1 + a^x } \, dx , a> 0 $ is

The complex numbers $z_1, z_2$ and $z_3$ satisfying $\frac{z_1-z_3}{z_2-z_3}=\frac{1-i \sqrt 3}{2}$ are the vertices of a triangle which is

The triangle formed by the tangent to the curve $f(x)=x^2+bx-b$ a t the point (1,1) and the coordinate axes, lies in the first quadrant. If its area is 2 sq units, then the value of b is

Let PQ and RS be tangents at the extremities of the diameter PR of a circle of radius r. If PS and RQ intersect at a point X on the circumference of the circle, then 2r equals

Let $z_1$ and $z_2$ be nth roots of unity which subtend a right angled at the origin, then n must be of the form (where, k is an integer)

If the positive numbers a,b,c,d are in AP. Then, $abc, abd, acd, bcd $ are

In the binomial expansion of $(a - b)^n , n \ge 5 $ the sum of the 5th and 6th terms is zero. Then, a /b equals

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

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

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

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 $

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.