Note: In the following questions a statement of assertion followed by a statement of reason is given. Choose the correct answer out of the following choices.
Assertion : `(CH_3)_3 C^(+)` is more stable than `(CH_3)_2 CH^(+)` ion.
Reason : `(CH_3)_3 C^(+)` has trigonal planar structure.

Answer

To solve the question regarding the stability of the carbocations `(CH_3)_3 C^(+)` and `(CH_3)_2 CH^(+)`, we will analyze the assertion and the reason provided.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- The first carbocation is `(CH_3)_3 C^(+)`, which is a tertiary carbocation.
- The second carbocation is `(CH_3)_2 CH^(+)`, which is a secondary carbocation.

2. **Determine Stability of Carbocations**:
- The stability of carbocations generally increases with the number of alkyl groups attached to the positively charged carbon. This is due to hyperconjugation and the inductive effect of alkyl groups.
- Tertiary carbocations are more stable than secondary carbocations because they have more alkyl groups donating electron density to stabilize the positive charge.

3. **Count the Number of Alpha-Hydrogens**:
- For `(CH_3)_3 C^(+)`: There are 9 alpha-hydrogens (from the three methyl groups).
- For `(CH_3)_2 CH^(+)`: There are 6 alpha-hydrogens (from the two methyl groups and one hydrogen on the secondary carbon).
- More alpha-hydrogens contribute to greater stability.

4. **Conclusion on Assertion**:
- Since `(CH_3)_3 C^(+)` has more alkyl groups and alpha-hydrogens than `(CH_3)_2 CH^(+)`, the assertion that `(CH_3)_3 C^(+)` is more stable than `(CH_3)_2 CH^(+)` is **true**.

5. **Analyze the Reason**:
- The reason states that `(CH_3)_3 C^(+)` has a trigonal planar structure.
- While it is true that carbocations are typically trigonal planar due to sp² hybridization, the stability of the carbocation is not solely due to its shape. The stability is primarily influenced by the number of alkyl groups and hyperconjugation.

6. **Conclusion on Reason**:
- The reason provided is not a correct explanation for the assertion because it does not address the primary factor affecting stability (the number of alkyl groups). Therefore, the reason is **false**.

### Final Answer:
- The assertion is true, and the reason is false. The correct option is **B** (Assertion is true, Reason is false).