`Barium adipate overset(Dry distillation)(rarr)(A)overset(MeCO_(3)H)(rarr)(B)`
The compounds `(A)` and `(B)`, respectively, are:

Options

A. a.
B. b.
C. c.
D. d.

Explanation

To solve the question, we will follow these steps:

### Step 1: Identify the structure of Barium Adipate
Barium adipate is a barium salt of adipic acid, which has the formula \( \text{Ba(C}_6\text{H}_{10}\text{O}_4) \). It consists of a six-carbon chain with two carboxylic acid groups at each end.

### Step 2: Dry Distillation of Barium Adipate
When barium adipate undergoes dry distillation, it decomposes to form barium carbonate and cyclopentanone. The reaction can be summarized as follows:
\[ \text{Barium adipate} \xrightarrow{\text{Dry Distillation}} \text{Cyclopentanone} + \text{BaCO}_3 \]

### Step 3: Determine Compound A
From the dry distillation of barium adipate, we obtain cyclopentanone. Thus, compound A is:
\[ \text{Compound A} = \text{Cyclopentanone} \]

### Step 4: Reaction with Peroxy Acid
Next, we add peroxy acid (specifically, MeCO3H) to compound A (cyclopentanone). This reaction is known as Baeyer-Villiger oxidation, which converts ketones into esters or lactones.

### Step 5: Determine Compound B
The reaction of cyclopentanone with peroxy acid results in the formation of a six-membered lactone. The structure of compound B can be represented as follows:
\[ \text{Compound B} = \text{Cyclohexanone} \text{ (or a related lactone structure)} \]

### Conclusion
Thus, the compounds (A) and (B) are:
- Compound A: Cyclopentanone
- Compound B: A six-membered lactone derived from cyclopentanone.

### Final Answer
- Compound A: Cyclopentanone
- Compound B: A six-membered lactone