Identify the reagent

$CHCl_3 +$ alcoholic $KOH$ generates dichlorocarbene and is used in the carbylamine test.

The carbylamine test is given by primary amines only: $RNH_2 + CHCl_3 + 3KOH \rightarrow RNC + 3KCl + 3H_2O$ So we must find which biomolecules contain a free primary amino group that can respond.

Check each compound

• Adenine: It is a purine base containing an exocyclic $-NH_2$ group at the 6-position. This behaves as a primary amino group, so adenine gives the test.
• Thymine: It is a pyrimidine base with no amino group; it has carbonyl groups instead. So does not react.
• Proline: It is an amino acid, but its amino group is secondary because it is part of a pyrrolidine ring (imino acid). Secondary amines do not give carbylamine test.
• Lysine: It has two amino groups, including a free side-chain $-NH_2$ primary amino group. Hence reacts.

Evaluate options

• A: Adenine and thymine
  Thymine does not react. So this is incorrect.

• B: Thymine and proline
  Thymine does not react, and proline is secondary amine. So incorrect.

• C: Adenine and lysine
  Both contain primary amino groups. So correct.

• D: Adenine and proline
  Proline does not give carbylamine test. So incorrect.

Final answer

The compounds that react with $CHCl_3 +$ alc. $KOH$ are: $\boxed{\text{Adenine and lysine}}$ Hence, Option C is correct.

Comparison with stored correct answer

Stored correct answer = C
Derived answer = C
Therefore, they agree.