List of top Mathematics Questions asked in JEE Advanced

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

If in the expansion of $(1 + x)^m (1 - x)^n$, the coefficients of $x$ and $x^2$ are 3 and - 6 respectively, then m is euqal to

Let $a_1,a_2,...,a_{10}$ be in AP and $h_1, h_2$ equal to .....,$h_{10}$ be in HP. If $a_1 = h_1 = 2$ and $ a_{10} = h_{10} = 3,$ then $a_4 h_7$ is

$ lim_{ n \to \infty} \frac{1}{n} \displaystyle \sum_{r = 1}^ {2n} \frac{r}{ \sqrt{ n^2 + r^2}} $ equals

Let $ S_1, S_2,...$ be squares such that for each $ n \ge 1 $ the length of a side of $ S_n $ equals the length of a diagonal of $ S_{n+1}$. If the length of a side of $ S_1 $ is 10 cm, then for which of the following values of n is the area of $S_n$ less than 1 sq cm?

If two distinct chords, drawn from the point (p, q) on the circle $x^2 + y^2 = px + qy$ (where, $ pq \ne 0$) are bisected by the X-axis, then

$\displaystyle\int_{\pi/4}^{3\pi/4}\frac{dx}{1+\cos\,x}$ is equal to

An n-digit number is a positive number with exactly n digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2,5 and 7. The smallest value of n for which this is possible, is