In which of following carbocation rearragement take place with change carbon skeleton :

Options

A. `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-overset(o+)CH_(2)`
B. `CH_(3)-CH_(2)-overset(o+)CH_(2)`
C. `CH_(3)-underset(CH_(3))underset(|)CH-CH_(2)-overset(o+)CH_(2)`
D. `CH_(3)-underset(CH_(3))underset(|)overset(CH_(3))overset(|)C-CH_(2)-CH_(2)-overset(o+)CH_(2)`

Explanation

To determine in which of the given carbocations rearrangement takes place with a change in the carbon skeleton, we will analyze each option step by step.

### Step 1: Identify the type of carbocation in each option.

1. **Option A:** The carbocation is a primary carbocation (R-CH2^+).
2. **Option B:** The carbocation is also a primary carbocation (R-CH(CH3)-CH2^+).
3. **Option C:** The carbocation is a primary carbocation (R-CH(CH2)-CH2^+).
4. **Option D:** The carbocation is a primary carbocation (R-CH(CH3)-CH2^+).

### Step 2: Analyze potential rearrangements for each carbocation.

1. **Option A:**
- The primary carbocation can undergo rearrangement by the migration of a methyl group from an adjacent carbon.
- This will lead to the formation of a tertiary carbocation.
- **Change in Carbon Skeleton:** Yes, the number of carbon atoms in the parent chain increases from 3 to 4.

2. **Option B:**
- This primary carbocation can undergo rearrangement by the migration of a hydride ion (H-) to form a secondary carbocation.
- **Change in Carbon Skeleton:** No, the number of carbon atoms remains the same (3).

3. **Option C:**
- This primary carbocation can also undergo rearrangement by migrating a hydride ion to form a secondary carbocation, and then a further rearrangement can lead to a tertiary carbocation.
- **Change in Carbon Skeleton:** No, the number of carbon atoms remains the same (4).

4. **Option D:**
- This primary carbocation can undergo rearrangement by the migration of a methyl group to form a tertiary carbocation.
- **Change in Carbon Skeleton:** Yes, the number of carbon atoms in the parent chain increases from 4 to 5.

### Step 3: Conclusion

Based on the analysis, the carbocations that undergo rearrangement with a change in the carbon skeleton are:
- **Option A**
- **Option D**

### Final Answer:
The carbocations in which rearrangement takes place with a change in carbon skeleton are **Option A and Option D**.

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