The correct statements among the following is/are

Options

A. Stability of triphenyl methyl carbocation can be explained only by resonance effect
B. Cyclopropyl cation is more stable than tropylium cation
C. `p`-methoxy benzyl carbocation is more stable than `p`- nitrobenzyl carbocation
D. `1^(@)` Allyl carbocation is more stable than isopropyl cation.

Explanation

To solve the question regarding the stability of various carbocations, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement A: Stability of the triphenyl methyl carbocation can be explained only by a resonance effect.**
- **Analysis**: The triphenyl methyl carbocation has a structure where the positive charge is delocalized over three phenyl rings. This delocalization occurs through resonance, where the positive charge can be shared among the phenyl rings, thus stabilizing the carbocation.
- **Conclusion**: This statement is **correct** because the stability is indeed due to resonance.

2. **Statement B: Cyclopropyl cation is more stable than tropolium cation.**
- **Analysis**: The cyclopropyl cation is known to be unstable due to the angle strain and lack of resonance stabilization. In contrast, the tropolium cation is resonance-stabilized and follows Huckel's rule, making it aromatic and highly stable.
- **Conclusion**: This statement is **incorrect** because the cyclopropyl cation is less stable than the tropolium cation.

3. **Statement C: Paramethoxybenzyl carbocation is more stabilized than paranitrobenzyl carbocation.**
- **Analysis**: The paramethoxybenzyl carbocation benefits from the +M (mesomeric) effect of the methoxy group, which stabilizes the positive charge. Conversely, the para-nitro group exerts a -M effect, which destabilizes the carbocation by increasing electron density at the positively charged carbon.
- **Conclusion**: This statement is **correct** as the paramethoxybenzyl carbocation is indeed more stable than the paranitrobenzyl carbocation.

4. **Statement D: 1-degree allyl carbocation is more stable than isopropyl carbocation.**
- **Analysis**: The 1-degree allyl carbocation is resonance-stabilized, allowing the positive charge to be delocalized. The isopropyl carbocation is stabilized by hyperconjugation, which is generally less effective than resonance stabilization.
- **Conclusion**: This statement is **correct** because the resonance stabilization in the allyl carbocation makes it more stable than the isopropyl carbocation.

### Final Conclusion:
The correct statements are **A, C, and D**.