Which of the following pairs is correctly matched?

Options

A. `CH_(3)-CH=C=CH_(2)` , optically active
B.
C.
D. Optically inactive

Explanation

To determine which of the given pairs is correctly matched in terms of optical activity, we will analyze each compound step by step.

### Step 1: Analyze Compound A
- **Structure**: The first compound is an allene with the structure CH3-CH2.
- **Symmetry**: In this structure, both terminal ends contain two similar hydrogen atoms (H and H).
- **Conclusion**: A plane of symmetry can be drawn through the molecule, indicating that it is optically inactive.
- **Match**: The option states that this compound is optically active, which is incorrect.

### Step 2: Analyze Compound B
- **Structure**: The second compound is a cyclohexene derivative with two methyl groups.
- **Symmetry**: This compound also possesses a plane of symmetry that bisects the molecule through the two methyl groups and the center of the ring.
- **Conclusion**: Since there is a plane of symmetry, this compound is also optically inactive.
- **Match**: The option states that this compound is optically active, which is incorrect.

### Step 3: Analyze Compound C
- **Structure**: The third compound is another allene with the structure H2N-C=C-CH3 and Cl.
- **Symmetry**: Here, the terminal carbons do not have any similar groups, meaning there is no plane of symmetry.
- **Conclusion**: This compound is optically active.
- **Match**: The option states that this compound is optically active, which is correct.

### Step 4: Analyze Compound D
- **Structure**: The fourth compound is a biphenyl system with bulky substituents (NO2 and COOH).
- **Symmetry**: The bulky groups cause the two phenyl rings to adopt a three-dimensional arrangement, preventing a plane of symmetry.
- **Conclusion**: This compound is optically active.
- **Match**: The option states that this compound is optically inactive, which is incorrect.

### Final Conclusion
After analyzing all four compounds, we find that:
- Compound A: Incorrectly matched (optically inactive)
- Compound B: Incorrectly matched (optically inactive)
- Compound C: Correctly matched (optically active)
- Compound D: Incorrectly matched (optically active)

Thus, the only correct match is **Option C**.

---