List of top Mathematics Questions

A bag contains $6$ red, $5$ blue and $7$ white balls. If three balls are drawn one by one (without replacement), then what is the probability that all three balls are blue?

A bag contains $n$ balls. It is given that the probability that among these n balls exactly $r$ balls are white is proportional to $r^2 (0 \le r \le n)$. A ball is drawn at random and is found to be white. Then the probability that all the balls in the bag are white, will be:

A bag contains $12$ white pearls and $18$ black pearls. Two pearls are drawn in succession without replacement. Find the probability that the first pearl is white and the second is black.

A bag contains $20$ tickets, numbered $1$ to $20$. A ticket is drawn and then another ticket is drawn without replacement. Find the probability that both tickets will show even numbers.

Let $ABCD$ be a parallelogram such that $\overrightarrow{AB} = \vec{q}, \overrightarrow{AD} = \vec{p}$ and $?BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex $B$ to the side $AD$, then $\vec{r}$ is given by :

$A= (1, -2, 3), B = (2, 1, 3), C = (4, 2, 1)$ and $G = (-1, 3, 5)$ is the centroid of the tetrahedron ABCD. If $p= D_y$ and $q = D_z$ then $ 13p-1.1q =$

$\left(^{8}C_{1} - ^{8}C_{2} + ^{8}C_{3} -^{8}C_{4} + ^{8}C_{5} - ^{8}C_{6} +^{8}C_{7} - ^{8}C_{8}\right) $ equals:

6 coins are tossed together 64 times. If throwing a head is considered as a success then the expected frequency of at least 3 successes is

$5\,\cos^{-1}\left(\frac{1-x^2}{1+x^2}\right) +7\,\sin^{-1}\left(\frac{2x}{1+x^2}\right)-4\,\tan^{-1}\left(\frac{2x}{1+x^2}\right)-\tan^{-1}x=5\pi$ , then x is equal to

$4\,tan^{-1} \frac{1}{5} -tan^{-1} \frac{1}{70} + tan^{-1} \frac{1}{99}$ is equal to

$3\,\tan^{-1}a$ is equal to

$\sqrt{-3}\sqrt{-6}$ is equal to

$|2x - 3| < |x + 5|$, then $x$ belongs to

$\sqrt{2i}$ is equal to

$20$ persons are invited for a party In how many different ways can they and the host be seated at circular table, if the two particular persons are to be seated on either side of the host?

What is the value of $\tan^{-1} \left(\frac{m}{n}\right) - \tan^{-1} \left(\frac{m-n}{m+n}\right) ? $

The number of positive integral solutions of the equation $\tan^{-1} x + \cot^{-1} y = \tan^{-1} 3 , $ is

The value of $\cos \left(\frac{1}{2} \cos^{-1} \frac{1}{8}\right) $ is equal to

In a $\Delta ABC$, if $A = tan^{-1}\, 2$ and $B = tan^{ -1}\, 3$ , then $C =$

$sin^{-1}\left(\frac{1}{\sqrt{e}}\right)> tan^{-1}\left(\frac{1}{\sqrt{\pi}}\right) $ $sin^{-1}\,x>tan^{-1}\,y$ for $x>y, \forall \,x, y \,\in\left(0, 1\right)$

The value of $cot^{-1}\left\{\frac{\sqrt{1-sin\,x}+\sqrt{1+sin\,x}}{\sqrt{1-sin\,x}-\sqrt{1+sin\,x}}\right\}\left(0 < x < \frac{\pi}{2}\right)$ is

$2^{\frac{1}{4}}, 4^{\frac{1}{8}}, 8^{\frac{1}{16}}, 16^{\frac{1}{32}}............ $ is equal to