`MeCOOEt underset(underset((iii)^(Theta)OH)((ii)HNO_(2)))overset((i)NH_(2)NH_(2))rarr (B)underset(MeOH)rarr(C)`
Which of the following statements are correct about the given reaction?

Options

A. The compounds `(B)` and `( C)`, respectively, are `Me-N=C=O` and `MeNHCOOMe`.
B. The compounds `(B)` and `( C)`, respectively, are `Et-N=C=O` and `MeNH_2`.
C. The reaction proceeds via the formation of acyl nitrene `(MeCO ddot N: )` as the intermediate species.
D. The reaction proceeds via the formation of acyl nitrene `(EtCO ddot N: )` as the intermediate species.

Explanation

To analyze the given reaction and determine which statements are correct, let's break down the steps involved in the reaction from the starting material to the final product.

### Step-by-Step Solution:

1. **Identify the Starting Material**:
The starting material is an ester, specifically MeCOOEt (ethyl ester of acetic acid).

2. **Reaction with Hydrazine (NH2NH2)**:
- When the ester reacts with hydrazine, one of the hydrogen atoms from hydrazine replaces the ethyl group (OEt) in the ester, leading to the formation of ethanol (EtOH) and a hydrazone intermediate.
- The structure of the intermediate can be represented as MeC(=O)N2H4 (where N2H4 represents the hydrazine part).

3. **Reaction with Nitrous Acid (HNO2)**:
- The next step involves the reaction of the hydrazone with nitrous acid (HNO2). This reaction converts the NH2 group into an OH group, resulting in the formation of an acyl nitroso compound.
- The product at this stage can be represented as MeC(=O)N2OH.

4. **Lawson Rearrangement**:
- The acyl nitroso compound undergoes rearrangement known as Lawson rearrangement. In this step, hydroxide ion (OH-) removes a hydrogen from nitrogen, giving nitrogen a negative charge.
- The nitrogen then forms a bond with the carbonyl carbon, resulting in a new intermediate.

5. **Formation of Compound B**:
- After the rearrangement, the structure can be represented as MeC(=O)N(-) (where N has a negative charge).
- This intermediate is known as acyl nitrate.

6. **Final Reaction with Methanol**:
- The acyl nitrate intermediate reacts with methanol (MeOH). During this reaction, the bond between the carbon and nitrogen breaks, leading to the formation of the final product.
- The final compound can be represented as MeO-C(=O)NMe (where N is bonded to a methyl group).

7. **Identify the Final Product (Compound C)**:
- The final product C is thus MeO-C(=O)NMe, which contains a methoxy group and a methyl group attached to the nitrogen.

### Conclusion:
Based on the above steps, we can evaluate the correctness of the statements regarding the reaction:

- **Statement A**: The compound B was correctly identified as MeC(=O)N2OH. This statement is correct.
- **Statement B**: This statement claims there was ethyl in the final product, which is incorrect since the final product contains methyl groups.
- **Statement C**: The reaction proceeds via the formation of acyl nitrate, which is true.

### Correct Statements:
- The correct statements are **A and C**.