If the best and the worst paper never appear together,then in how many ways can six examination papers be arranged?

If $f: R \rightarrow R$ is defined by $f(x) = x - [x]$,where $[x]$ is the greatest integer not exceeding $x$,then the set of points of discontinuity of $f$ is

$\int_0^1 x^{3/2} \sqrt{1-x} \, dx$ is equal to

In the interval $(-3, 3)$,the function $f(x) = \frac{x}{3} + \frac{3}{x}, x \neq 0$ is :

$\lim _{x \rightarrow \infty}\left(\frac{x+5}{x+2}\right)^{x+3}$ equals

What is obtained by the electrolysis of carnallite?