Which of the following compounds gives `SN^(1), SN^(2)` and `SN^(2)` mechanisms?

Options

A.
B.
C.
D.

Explanation

To determine which of the given compounds can undergo both SN1 and SN2 mechanisms, we need to analyze the nature of each compound based on their structure and the stability of the carbocation that can be formed.

### Step-by-Step Solution:

1. **Understanding SN1 and SN2 Mechanisms**:
- **SN1 Mechanism**: This is a two-step process where the first step involves the formation of a carbocation. The stability of this carbocation is crucial; more stable carbocations (tertiary > secondary > primary) favor SN1 reactions.
- **SN2 Mechanism**: This is a one-step process where the nucleophile attacks the substrate from the opposite side of the leaving group. This mechanism is favored by less steric hindrance, typically seen in primary or methyl halides.

2. **Identifying the Compounds**:
- We need to look at the provided compounds and identify their structures to determine if they are allylic halides, benzylic halides, primary halides, or vinylic halides.

3. **Analyzing Each Compound**:
- **Compound A (Allylic Halide)**: The halogen is attached to a carbon adjacent to a double-bonded carbon (sp2 hybridized). Allylic halides can undergo both SN1 and SN2 mechanisms due to the stability of the allylic carbocation and low steric hindrance.
- **Compound B (Primary Halide)**: This compound can only undergo SN2 reactions because the primary carbocation formed in an SN1 reaction would be unstable.
- **Compound C (Benzylic Halide)**: Similar to allylic halides, benzylic halides can undergo both SN1 and SN2 mechanisms. The benzylic carbocation is stable due to resonance with the benzene ring, and it is also a primary halide.
- **Compound D (Vinylic Halide)**: Vinylic halides are not suitable for either mechanism. They form unstable carbocations and have partial double bond character in the carbon-halogen bond, making SN2 reactions unfavorable.

4. **Conclusion**:
- The compounds that can undergo both SN1 and SN2 mechanisms are **Compound A (Allylic Halide)** and **Compound C (Benzylic Halide)**.

### Final Answer:
The compounds that give SN1 and SN2 mechanisms are **Compound A (Allylic Halide)** and **Compound C (Benzylic Halide)**.

---