List of top Mathematics Questions

$f(x)=x^3 - 3x + 5 $ then $ f \left( \sin \frac{3 \pi }{ 2} \right) + f \left( \cos \frac{3 \pi}{2} \right) = $

$f(x)=\frac{\sqrt{1+px}\,-\,\sqrt{1-px}}{x}, -1\leq x\leq 0=\frac{2x+1}{x-2}, 0 \leq x \leq 1$ is continuous in the interval [-1, 1], thenp equals.

Express $50^{\circ}\, 37'\, 30''$ in radian.

Express $i^{-35}$ in the form of $a + ib$.

Express $\left(\frac{1}{3}+3i\right)^{3}$ in the form of $a +ib$.

Express $\frac{5+\sqrt{2}i}{1-\sqrt{2}i}$ in the form of $a + ib$ .

Expand $(1 - x + x^2)^4$.

Evaluate : $\int\frac{sin x}{sin 4x} dx$

Evaluate : $\int\frac{x^{3}+x}{x^{4}-9}dx$

Evaluate of the following limits. $=\displaystyle \lim_{x \to 2}$$\left\{\frac{\left(x^{2}-4\right)}{\sqrt{3x-2}-\sqrt{x+2}} \right\}=$

Evaluate: $\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} cos\,2x \,dx $

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 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

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

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