Mathematics Tes...

If $\omega$ is a cube root of unity, then the value of $(1-\omega +{\omega }^2)(1+\omega -{\omega }^2)$ is:

If ${\sin }^{-1}x+{\sin }^{-1}y=\frac{5\pi }{6}$, then what is the value of ${\cos }^{-1}x+{\cos }^{-1}y$?

An organization awarded 48 medals in event ' A ', 25 in event ' B' and 18 in event ' C '. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events ?

Evaluate the integral ${\int }_0^1\frac{e^x}{1+e^{2x}}dx$.

If given constraints are $5x+4y\ge 2,x\le 6,y\le 7$, then the maximum value of the function $z=x+2y$ is:

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is α and the number of persons who speak only Hindi is β, then the eccentricity of the ellipse 25( β²x²+α²y² )=α²β² is :

Let $\overrightarrow{a}=2\hat{i}-7\hat{j}+5\hat{k},\overrightarrow{b}=\hat{i}+\hat{k}$ and $\overrightarrow{c}=\hat{i}+2\hat{j}-3\hat{k}$ be three given vectors. If $\overrightarrow{r}$ is a vector such that $\overrightarrow{r}\times \overrightarrow{a}=\overrightarrow{c}\times \overrightarrow{a}$ and $\overrightarrow{r}\cdot \overrightarrow{b}=0$, then $\mid \overrightarrow{r}|$ is equal to :

A unit vector which is perpendicular to the vector $2\hat{\mathrm{i}}-\hat{\mathrm{j}}+2\hat{\mathrm{k}}$ and is coplanar with the vectors $\hat{i}+\hat{j}-\hat{k}$ and $2\hat{i}+2\hat{j}-\hat{k}$ is:

Solve the linear inequality:

$\frac{x}{4}<\frac{(5x-2)}{3}-\frac{(7x-3)}{5}$