In which of the following processes is $CO_2$ not produced?

Chemical $A$ is used for water softening to remove temporary hardness. $A$ reacts with sodium carbonate to generate caustic soda. When $CO_2$ is bubbled through a solution of $A$,it turns cloudy. What is the chemical formula of $A$?

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\frac{\pi}{3}$. Then,the perimeter of the triangle is

Seven white balls and three black balls are randomly arranged in a row. The probability that no two black balls are placed adjacently is

The instantaneous angular position of a point on a rotating wheel is given by the equation $\theta(t) = 2t^3 - 6t^2$. The torque on the wheel becomes zero at $t = $ ....... $\text{sec}$.

$A$ random variable $X$ has the probability distribution given below. Its variance is

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$k$	$2k$	$3k$	$2k$	$k$