List of top Mathematics Questions asked in JEE Advanced

If M and N are any two events, then the probability that exactly one of them occurs is

The expression $3\Bigg[sin^4\Bigg(\frac{3\pi}{2}-\alpha\Bigg)+sin^4(3\pi+\alpha)\Bigg]-2\Bigg[sin^6\Bigg(\frac{\pi}{2}+\alpha\Bigg)+sin^6(5\pi-\alpha)\Bigg]$ is equal to

If x+ | y |= 2y , then y as a function of x is

$ \displaystyle \lim_{n \to\infty} \left\{ \frac{1}{1-n^{2}} + \frac{2}{1-n^{2}} + .... + \frac{n}{1-n^{2}}\right\}$ is equal to

Three identical dice are rolled. The probability that the same number will appear on each of them, is

If x + | y | = 2y, th e n y as a function of x is

$\Bigg(1+cos\frac{\pi}{8}\Bigg)\Bigg(1+cos\frac{3\pi}{8}\Bigg)\Bigg(1+cos\frac{5\pi}{8}\Bigg)\Bigg(1+cos\frac{7\pi}{8}\Bigg)$ is equal to

If $G(x) = - \sqrt{25 - x^2}$ then $\displaystyle \lim_{x \to 1} \frac{G(x) - G(1)}{x - 1}$ has the value

The value of the integral $ \int^{ \pi / 2 }_ 0 \frac {\sqrt { \cot \, x }}{ \sqrt { \cot \, x } + \sqrt { \tan \, x }} \, dx \, is $

The value of tan $\bigg[cos^{-1}\bigg(\frac{4}{5}\bigg)+tan^{-1}\bigg(\frac{2}{3}\bigg)\bigg]$ is

The equation of the circle passing through (1, 1) and the points of intersection of $x^2 + y^2 + 13x - 3y =0$ and $2x^2 + 2y^2 + 4 x - 7y -2 5 = 0$ is

Fifteen coupons are numbered 1, 2....... 15, respectively. Seven coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is 9, is

The volume of the parallelopiped whose sides are given by $\overrightarrow{OA}=2\widehat{i}-3\widehat{j},\overrightarrow{OB}=\widehat{i}+\widehat{j}-\widehat{k},\overrightarrow{OC}=3\widehat{i}-\widehat{k}$ is

The domain of definition of the function $y = \frac{1}{\log{10} ( 1 -x)} + \sqrt{x + 2}$ is

Which of the following functions is periodic?

The centre of the circle passing through the point (0, 1)and touching the curve $y = x^2 at (2,4)$ is

AB is a diameter of a circle and C is any point on the circumference of the circle. Then,

The largest interval for which $ x^{12} - x^9 + x^4 - x + 1 > 0 $ is

There exist a function f (x), satisfying $f (0) = 1, f'(0) = -1, f (x) > 0$ for all x, and

The area bounded by the curves y = f (x), the X-axis and the ordinates x = 1 and x = b is (b - 1 ) sin (3b + 4). Then, f (x) is equal to

If A and B are two independent events such that $P(A) > 0,$ and $P(B)\ne 1$, then $P(\overline{A}/ \overline{B})$ is equal to

The scalar $\overrightarrow{A}.[(\overrightarrow{B}+\overrightarrow{C})\times(\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C})]$ eqy=ual

Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 and then the men select the chairs from amongst the remaining. The number of possible arrangements is

The value of the definite integral $\int _0^1 (1+e^{-x^2}) dx \, is$

The equation $\frac{x^2}{1-r}-\frac{y^2}{1+r}=1,|r|<1$ represents