The probability distribution of a random variable $X$ is given below:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

Then the variance of $X$ is

If $a, b, c, d$ are positive real numbers such that $\frac{a}{3} = \frac{a+b}{4} = \frac{a+b+c}{5} = \frac{a+b+c+d}{6}$,then the value of $\frac{a}{b+2c+3d}$ is

If $x_n = \cos \frac{\pi}{2^n} + i \sin \frac{\pi}{2^n}$,then $\prod_{n=1}^{\infty} x_n$ is equal to

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

An inductance of $\frac{200}{\pi} \ mH$,a capacitance of $\frac{10^{-3}}{\pi} \ F$ and a resistance of $10 \ \Omega$ are connected in series with an $AC$ source of $220 \ V, 50 \ Hz$. The phase angle of the circuit is:

The period of $f(x)=\cos \left(\frac{x}{3}\right)+\sin \left(\frac{x}{2}\right)$ is (in $\pi$)