Assertion : In `CO_(2)` molecule C atoms undergoes `sp^(2)` hybridisation
Reason : `CO_(2)` molecule has net dipole moment.

Explanation

To analyze the given question, we need to evaluate both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that in the carbon dioxide (CO₂) molecule, the carbon atom undergoes sp² hybridization.

- **Hybridization Calculation**:
- The hybridization of an atom can be determined using the formula:
\[ \text{Hybridization} = \frac{1}{2} \left( V + M - C \right) \]
where:
- \( V \) = Valency of the central atom (for carbon, \( V = 4 \))
- \( M \) = Number of monovalent atoms (in CO₂, there are no monovalent atoms, so \( M = 0 \))
- \( C \) = Charge on the molecule (CO₂ is neutral, so \( C = 0 \))

Plugging in the values:
\[ \text{Hybridization} = \frac{1}{2} \left( 4 + 0 - 0 \right) = \frac{4}{2} = 2 \]
This indicates that the carbon atom undergoes sp hybridization, not sp².

- **Conclusion for Assertion**: The assertion is **false**.

### Step 2: Analyze the Reason
The reason states that the carbon dioxide molecule has a net dipole moment.

- **Dipole Moment Analysis**:
- CO₂ has a linear structure due to sp hybridization, with the carbon atom in the center and two oxygen atoms on either side.
- Oxygen is more electronegative than carbon, which creates a dipole moment directed from carbon to each oxygen atom.
- However, because the molecule is linear, the dipole moments from the two C=O bonds are equal in magnitude but opposite in direction. Therefore, they cancel each other out.

- **Conclusion for Reason**: The reason is also **false**.

### Final Conclusion
Since both the assertion and the reason are false, the correct answer is option 4: Both assertion and reason are false.

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