Variance of first n natural numbers is ________.

Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads, then probability distribution of x is

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five is

If $0< x<1$, then $\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{\frac{1}{2}}$ is equal to