List of top Mathematics Questions

Evaluate: $\int\frac{sin \,2x}{sin\left(x -\frac{\pi}{3}\right) sin\left(x+\frac{\pi}{3}\right)} dx $

Evaluate: $\int\limits_{0}^{\frac{\pi}{4 }} \sqrt{1-sin\, 2x} \,\,\, dx $

Evaluate : $ \int\limits_{0}^{\pi/2}\frac{ cos \,x}{\left(cos \frac{x}{2} +sin \frac{x}{2}\right)^{3}} dx$

Evaluate: $\int\left\{\left(2x-3\right)^{5}+\frac{1}{\left(7x-5\right)^{3}}+\frac{1}{\sqrt{5x-4}}+\frac{1}{2-3x}+\sqrt{3x+2}\right\}dx$

Evaluate : $\int\left(e^{x\,log\,a} + e^{a\,log\,x} + e^{a\,log\,a} \right)dx$

Evaluate:$\int\limits_{0}^{2\pi} sin\left(\frac{\pi}{4}+\frac{x}{2}\right)dx $

Evaluate : $\int\frac{1}{sin \,x +\sqrt{3} \,cos\, x} dx$

Evaluate $2\,cos\,22 \frac{1^{\circ}}{2}\cdot cos\,67 \frac{1^{\circ}}{2}$.

Evaluate $(i) 5! (ii) 7!$

Equation of $YOZ$ plane is

Equation of the vertical line passing through the point (-4,5) is

Equation of the hyperbola with eccentricity $ \frac{3}{2}$ and foci at $(?2 ,0)$ is

Equation of a line passing through $(1, 2, -3)$ and parallel to the line $\frac{x-2}{1}=\frac{y+1}{3}=\frac{z-1}{4}$ is

Eight coins are thrown simultaneously. Find the probability of getting atleast $6$ heads.

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