To determine which combination produces H₂ gas, we need to analyze the reactivity of metals with different reagents. Hydrogen gas is typically produced when a metal reacts with an acid or base, but only if the metal is sufficiently reactive and the reaction conditions favor H₂ evolution.

Step-by-Step Analysis:

Option (a): Zn metal and NaOH

Zinc (Zn) is amphoteric and reacts with NaOH to produce hydrogen gas. The reaction is:

This is correct and produces H₂.

Option (b): Cu metal and conc. HNO₃

Copper (Cu) reacts with concentrated HNO₃ to produce NO₂ gas, not H₂:

No H₂ is produced.

Option (c): Au metal and NaCN (aq) in the presence of air

Gold (Au) dissolves in NaCN solution in the presence of air to form a complex, but it does not produce H₂:

NaOH is produced, but no H₂ gas is evolved.

Option (d): Fe metal and conc. HNO₃

Iron (Fe) becomes passive with concentrated HNO₃ due to the formation of a protective oxide layer. It does not produce H₂; instead, it may produce NO₂ if reaction occurs.

Conclusion:

Only option (a) produces H₂ gas. Zinc reacts with NaOH to liberate hydrogen, while the other options do not.

Related Topics:

Reactivity Series: Metals above hydrogen in the reactivity series can displace H₂ from acids, but amphoteric metals like Zn and Al can also produce H₂ with bases.

Passivation: Some metals like Fe and Al form protective layers with oxidizing agents, preventing further reaction.

Key Formulae:

For amphoteric metals with base: $\mathrm{Zn}+2\mathrm{NaOH}\to {\mathrm{Na}}_2\mathrm{ZnO}{O}_2+H_2$

For metals with acid: $\mathrm{Metal}+\mathrm{Acid}\to \mathrm{Salt}+H_2$ (if metal is reactive).