List of top Mathematics Questions

The volume V and depth x of water in a vessl are connected by the relation $V = 5x - \frac{x^2}{6}$ and the volume of water is increasing , at the rate of $5 \, cm^3/sec$, when x = 2 cm. The rate at which the depth of water is increasing, is
The volume of the tetrahedron whose coterminous edges are $ \hat{j}+\hat{k}$, $ \hat{i}+\hat{k}$, $\hat{i}+\hat{j}$ is
The variance of first 25 natural numbers is
The variance of first n natural numbers is :
The variance of the numbers $2, 3, 11 $ and $x$ is $\frac{49}{4}$. Find the value of $x$.
The variance of random variable $X$ i.e. $\sigma^{2}_{x}$ or var$(X)$ is equal to
The values of the determinant $ \begin{vmatrix} x+1& x+2 &x+4 \\[0.3em] x+3 & x+5 & x+8 & \\[0.3em] x+7 & x+10 & x+14 \end{vmatrix}$
The values of x satisfying $| x - 4 | + | x - 9 | = 5$, is :
The value of $|z|^2 + |z - 3|^2 + |z - i|^2$ is minimum when $z$ equals.
The value of x, so that the matrix $=\begin{bmatrix} x+a &b& c \\[0.3em] a& x+b & c \\[0.3em] a & b & x+c \end{bmatrix}$ has rank 3 , is
The value of x where $\begin{bmatrix}6&x-2\\ 3&x\end{bmatrix}$, has no inverse is :
The value of the sum $(\,^nC_1)^2+(\,^nC_2)^2+(\,^nC_3)^2+...+(\,^nC_n)^2$ is
The value of the term independent of x in the expansion of $\left(1+\frac{x}{2}-\frac{2}{x}\right)^{4}, x \ne 0$ is equal to
The value of the expression $\frac{1}{2} ( \sqrt{3} \sin 75^{\circ} - \cos \, 75^{\circ} )$ is :
The value of the expression tan 1$^\circ$ tan 2$^\circ$ tan 3$^\circ$ tan 4$^\circ$ ______tan 87$^\circ$ tan 88$\circ$ tan 89$^\circ$ is equal to
The value of the determinant of $\begin{bmatrix}x+1&x+2&x+4\\ x+3 &x+5&x+8\\ x+7 &x+10&x+14\end{bmatrix}$ is :
The value of the definite integral $\int\limits_{0}^{1}\frac{x\,dx}{x^3+16}$ lies in the interval [a, h], The smallest such interval is
The value of $tan3A - tan2A - tanA$ is equal to
The value of $\frac{\tan \, x}{\tan \, 3x}$ wherever defined never lies between
The value of tan $(\frac {\pi} {4} + \theta)$ tan $(\frac {3\pi} {4} + \theta)$
The value of $\tan \, 20^{\circ} + 2 \, \tan \, 50^{\circ} - \tan \, 70^{\circ} $ is :
The value of $\tan \, 3A- \tan \, 2A- \tan \, A$ is:
The value of $\tan 81^{\circ} -\tan 63^{\circ} -\tan 27^{\circ} + \tan 9^{\circ}$ is equal to
The value of $\tan^{-1}\frac{1}{3}+\tan^{-1}\frac{1}{5}+\tan^{-1}\frac{1}{7}+\tan^{-1}\frac{1}{8}$ is
The value of $tan^{-1}\left(\frac{3}{4}\right)+ tan^{-1}\left(\frac{1}{7}\right)$ is