List of top Mathematics Questions

Eight coins are thrown simultaneously. What is the probability of getting atleast $3$ heads?

Each diagonal element of a skew-symmetric matrix is

$\frac{dy}{dx} = \frac{4x + 2y + 1}{ x -2y + 3}$ is a differential equation of the type

Domain of $cos^{-1}\, [x]$ is

$ \displaystyle\lim_{x \to \frac{\pi}{2}} \frac{1 - \sin \, x}{\cos \, x}$ is equal to

$\displaystyle\lim_{x\to \frac{\pi}{2}} \frac{\cos \, x}{ x - \frac{\pi}{2}}$ equals:

$\displaystyle\lim_{x \to \infty} \frac{ (2x -3)(3x -4)}{(4x - 5)(5x - 6)}$ is equal to:

$\displaystyle\lim_{x \to 0}\left[\frac{sin\left[x-3\right]}{\left[x-3\right]}\right]$, where [ . ] denotes greatest integer function is

$\displaystyle \lim_{x \to 1}$$\left[\left(\frac{4x}{x^{2}-x^{-1}}-\frac{1-3x+x^{2}}{1-x^{3}}\right)^{-1}+3\left(\frac{x^{4}-1}{x^{3}-x^{-1}}\right)\right]$ is

$\displaystyle \lim_{n \to \infty}$$\left(\frac{1}{n^{2}}+\frac{3}{n^{2}}+\frac{5}{n^{2}}+.....+\frac{2n+1}{n^{2}}\right)$ is equal to

$\displaystyle \lim_{x \to 0}$ $\frac{1-cos\,mx}{1-cos\,nx}=$

$\displaystyle \lim_{x \to 0}$ $\left(cos\,x+sin\,x\right)^{\frac{1}{x}}$ equals

$\displaystyle \lim_{h \to 0}$ $\frac{\left(a+h^{2}\right)sin\left(a+h\right)-a^{2}\,sin\,a}{h}=$

Differential coefficient of $\sqrt{sec\sqrt{x}}$ is

Differential coefficient of $tan^{-1} \frac{2x}{1-x^{2}}$ with respect to $sin^{-1} \frac{2x}{1+x^{2}}$ will be

Differential co-efficient of $\log_{10} x $ w.r.t. $log_x 10$ is

Derivative of the function $f(x) = log_5(log_7x)$, $x > 7$ is

Derivative of $\sec^{-1} \left( \frac{1}{2x^2 + 1 } \right)$ w.r.t. $\sqrt{ 1 + 3x} $ at $x = - \frac{1}{3}$ is

Derivative of the function $f(x) = 7x^{-3} $ is

$\Delta =\begin{vmatrix} sin^2x & cos^2x & 1 \\[0.3em] cos^2x &sin^2x & 1 \\[0.3em] -10 & 12& 2 \end{vmatrix}$

$\frac{d}{dx}\left\{cosec^{-1}\left(\frac{1+x^{2}}{2x}\right)\right\}$ is equal to

$\frac{d}{dx}\left(tan^{-1}\left(\frac{\sqrt{x}-\sqrt{a}}{1+\sqrt{xa}}\right)\right)$, $x$, $a > 0$, is

If $ lim_{ x \to 0 } [ 1 + x \, log \, (1 + b^2) ]^{\frac{1}{x}} = 2 b sin^2 \, \theta, b > 0 \, and \, \theta \in ( - \pi , \pi), $ then the value of $ \theta $ is