Why does limewater turn milky when carbon dioxide gas is passed through it?

The correct option is A Due to the formation of calcium carbonate.
Limewater is calcium hydroxide solution (${\text{Ca(OH)}}_2$) and it is a base. Carbon dioxide (${\text{CO}}_2$) being a non-metallic oxide (acidic in nature), reacts with the calcium hydroxide to form a calcium carbonate (${\text{CaCO}}_3$). The reaction involved is given below:

${\text{Ca(OH)}}_2\text{(aq)}+{\text{CO}}_2\text{(g)}\to {\text{CaCO}}_3\text{(s)}+{\text{H}}_2\text{O}\text{(l)}$

Calcium carbonate obtained is white and insoluble in water, hence it makes limewater appear milky.