Step 1: Analyzing the tab tests.
- Hinsberg test (I) is used to distinguish between primary, secondary, and tertiary amines. Lysine, which contains a primary amine group, gives a positive Hinsberg test.
- Neutral \( \text{FeCl}_3 \) (II) is used for testing phenolic compounds. Tyrosine, which contains a phenolic group, gives a positive result with neutral \( \text{FeCl}_3 \).
- Cerric ammonium nitrate (III) is used to test alcohols, and Serine, which contains a hydroxyl group, will give a positive test with Cerric ammonium nitrate.
- Hoffmann Bromamide (IV) is used to test for amides, and Glutamine, being an amide, will give a positive result.
Step 2: Conclusion.
The correct matching is:
- Glutamine (\( \text{A} \)) gives a positive Hoffmann Bromamide test (IV),
- Lysine (\( \text{B} \)) gives a positive Hinsberg test (I),
- Tyrosine (\( \text{C} \)) gives a positive result with neutral \( \text{FeCl}_3 \) (II),
- Serine (\( \text{D} \)) gives a positive result with Cerric ammonium nitrate (III).
Thus, the correct answer is:
\[
\text{(B) A \(\rightarrow\) IV, B \(\rightarrow\) I, C \(\rightarrow\) II, D \(\rightarrow\) III}
\]
Final Answer: (B) A \(\rightarrow\) IV, B \(\rightarrow\) I, C \(\rightarrow\) II, D \(\rightarrow\) III.