Statement I:- Hydrogen gas is not evolved when zinc reacts with cold water.

Statement II:- Sodium reacts vigorously with cold water to produce sodium hydroxide and hydrogen gas.

The correct option is C Both statements are true.

Zinc does not react with cold water to produce hydrogen gas. It produces hydrogen gas on reacting with steam. The reaction involved is:

$\text{Zinc}+\text{Water}\to \text{Zinc hydroxide}+\text{Hydrogen gas}$

Sodium reacts with vigorously with cold water to produce sodium hydroxide and hydrogen gas. The reaction involved is:

$\text{Sodium}+\text{Water}\to \text{Sodium hydroxide}+\text{Hydrogen gas}$