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

$X=x$	$P(X=x)$
$0$	$0.4$
$1$	$0.3$
$2$	$0.1$
$3$	$0.1$
$4$	$0.1$

The variance of $X$ is:

The value of $\lim_{n \rightarrow \infty} \frac{1}{n^3} \sum_{k=1}^n (k^2 x)$ is

Observe the following reaction: $2 A + B \longrightarrow C$. The rate of formation of $C$ is $2.2 \times 10^{-3} \ mol \ L^{-1} \ min^{-1}$. What is the value of $-\frac{d[A]}{dt}$ (in $mol \ L^{-1} \ min^{-1}$)?

$A$ plate of thickness $t$ made of a material of refractive index $\mu$ is placed in front of one of the slits in a double-slit experiment. What should be the minimum thickness $t$ for which the intensity at the centre of the fringe pattern is zero?

$A$ coil of $n$ turns and resistance $R \ \Omega$ is connected in series with a resistance $R/2$. The combination is moved for time $t$ seconds through a magnetic flux change from $\phi_{1}$ to $\phi_{2}$. The induced current in the circuit is:

If the plane $3x - 2y - z - 18 = 0$ meets the coordinate axes at $A$, $B$, and $C$, then the centroid of $\triangle ABC$ is: