The reactions of bromopropane with the given reagents are as follows:
1. A. Reaction with KOH (alc):
Bromopropane reacts with alcoholic KOH to undergo dehydrohalogenation, forming an alkene.
\[
\text{CH}_3-\text{CH}_2-\text{CH}_2\text{Br} + \text{KOH(alc)} \rightarrow \text{CH}_3-\text{CH}=\text{CH}_2 \, (\text{Alkene}).
\]
2. B. Reaction with KCN (alc):
Bromopropane reacts with alcoholic KCN to undergo a nucleophilic substitution reaction, forming a nitrile.
\[
\text{CH}_3-\text{CH}_2-\text{CH}_2\text{Br} + \text{KCN} \rightarrow \text{CH}_3-\text{CH}_2-\text{CH}_2\text{CN} \, (\text{Nitrile}).
\]
3. C. Reaction with AgNO\(_2\):
Bromopropane reacts with silver nitrite (AgNO\(_2\)) to form a nitroalkane via substitution.
\[
\text{CH}_3-\text{CH}_2-\text{CH}_2\text{Br} + \text{AgNO}_2 \rightarrow \text{CH}_3-\text{CH}_2-\text{CH}_2\text{NO}_2 + \text{AgBr} \, (\text{Nitroalkane}).
\]
4. D. Reaction with H\(_3\)CCOOAg:
Bromopropane reacts with silver acetate (H\(_3\)CCOOAg) to form an ester via substitution.
\[
\text{CH}_3-\text{CH}_2-\text{CH}_2\text{Br} + \text{CH}_3\text{COOAg} \rightarrow \text{CH}_3-\text{CH}_2-\text{CH}_2\text{COOCH}_3 + \text{AgBr} \, (\text{Ester}).
\]
Thus, the correct matching is:
\[
\text{A–III, B–I, C–IV, D–II}.
\]