The reaction proceeds in two stages:
Step 1: Oxidation with Tollens' Reagent
- Tollens' reagent \([Ag(NH_3)_2]^+ \, \text{and} \, OH^-\) selectively oxidizes aldehydes to carboxylic acids.
- In this case, the aldehyde group (\(-CHO\)) of the compound undergoes oxidation to form a carboxylic acid group (\(-COOH\)).
- The resulting product \( A \) after oxidation is:
\[
\text{A} = \text{Compound with the aldehyde oxidized to a carboxylic acid: } \text{HCOOH}.
\]
Step 2: Reduction with Sodium Borohydride
- Sodium borohydride (\( NaBH_4 \)) is a selective reducing agent that reduces aldehydes and ketones to their corresponding alcohols.
- In the given compound, the ketone group (\(-C=O\)) is reduced to a secondary alcohol (\(-CH(OH)-\)).
- The product \( B \) after reduction is:
\[
\text{B} = \text{Compound with the ketone reduced to an alcohol: } \text{HCOOH}.
\]
Final Answer:
The products \( A \) and \( B \) correspond to:
\[
\boxed{\text{Option C}}
\]