List of top Mathematics Questions asked in JEE Advanced

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

The area (in sq units) bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is

The set of all real numbers x for which $x^2-|x+2|+x>0$ is

Let f(x) =$\int_1^x \sqrt{2-t^2}dt $ Then, the real roots of the equation $x^2-f'(x)=0$ are

If $a_1,a_2,...,a_n$ are positive real numbers whose product is a fixed number c, then the minimum value of $ a_1 + a_2 +...+ a_{n-1}+2a_n$ is

Let $\omega=-\frac{1}{2}+i\frac{\sqrt 3}{2},$ then value of the determinant $\begin {vmatrix} 1 & 1& 1 \\ 1 & -1-\omega^2 & \omega^2 \\ 1 & \omega^2 & \omega \\ \end {vmatrix} is $

If $0 < \alpha

The number of arrangements of the letters of the word BANANA in which the two N's do not appear adjacently, is

Let $a, b, c$ be in an AP and $a^2,b^2,c^2$ be in GP, if $a < b < c$ and $a+b+c= \frac{3}{2}$, then the value of a is

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)

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

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

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