Identify the nature of acetylene

Acetylene is ethyne, $HC\equiv CH$.

It has two important types of reactivity:

• It is an unsaturated hydrocarbon, so it can undergo addition reactions.
• It is a terminal alkyne, so the hydrogen attached to the $sp$-hybridized carbon is slightly acidic.

Check each option

Option A: $NaOH$

$NaOH$ is a strong base in water, but it is not strong enough to remove the acidic proton from acetylene to any significant extent.

Terminal alkynes react with very strong bases like $NaNH_2$, but not with ordinary $NaOH$.

Therefore, acetylene does not react with $NaOH$.

Option B: ammonical $AgNO_3$

Terminal alkynes react with ammoniacal silver nitrate to form silver acetylide.

$HC\equiv CH + 2AgNO_3 + 2NH_4OH \rightarrow AgC\equiv CAg\downarrow + 2NH_4NO_3 + 2H_2O$

So acetylene does react with ammoniacal $AgNO_3$.

Option C: $Na$

Sodium metal reacts with the acidic hydrogen of acetylene to form sodium acetylide with evolution of hydrogen gas.

$HC\equiv CH + 2Na \rightarrow NaC\equiv CNa + H_2$

So acetylene does react with $Na$.

Option D: $HCl$

Acetylene undergoes addition reaction with $HCl$ across the triple bond.

$HC\equiv CH + HCl \rightarrow CH_2=CHCl$

Thus acetylene does react with $HCl$.

Conclusion

The only reagent that will not react with acetylene is:

$\boxed{A\;:\; NaOH}$

Comparison with stored correct answer

Stored correct answer: $A$

My derived answer is also $A$, so they agree.