The order of stability of the following tautomeric compounds is
(i). `CH_(2)=overset(OH)overset(|)(CH)-CH_(2)-overset(O)overset(||)(C)-CH_(3)hArr`
(ii). `CH_(3)-overset(O)overset(||)(C)-CH_(2)-overset(O)overset(||)(C)-CH_(3)hArr`
(iii). `CH_(3)-overset(OH)overset(|)(C)=CH-overset(O)overset(||)(C)-CH_(3)`

Options

A. `I gt II gt III`
B. `III gt II gt I`
C. `II gt I gt III`
D. `II gt III gt I`

Explanation

To determine the order of stability of the given tautomeric compounds, we will analyze each compound step by step.

### Step 1: Identify the Structures
1. **Compound (i)**: `CH2=CHO-CH2-C(=O)-CH3`
- This is an enol form with a hydroxyl group (-OH) and a double bond.

2. **Compound (ii)**: `CH3-C(=O)-CH2-C(=O)-CH3`
- This is a keto form with two carbonyl groups (C=O).

3. **Compound (iii)**: `CH3-CHO=CH-C(=O)-CH3`
- This compound has a hydroxyl group and a double bond, with a carbonyl group that is conjugated with the double bond.

### Step 2: Analyze Stability
- **Keto vs Enol Forms**: Generally, keto forms are more stable than enol forms due to the greater strength of the C=O double bond compared to the C=C double bond and the presence of hydrogen bonding in the keto form.

- **Compound (i)**: The presence of the enol form makes it less stable compared to the keto form.

- **Compound (ii)**: This compound is entirely in the keto form, which is typically the most stable configuration due to the presence of two carbonyl groups.

- **Compound (iii)**: This compound has conjugation between the carbonyl group and the double bond, which allows for electron delocalization, increasing its stability compared to simple enol forms.

### Step 3: Compare Stability
1. **Compound (iii)**: Most stable due to conjugation and delocalization of electrons.
2. **Compound (ii)**: Stable due to being in the keto form with two carbonyl groups.
3. **Compound (i)**: Least stable as it is in the enol form.

### Conclusion
The order of stability of the given tautomeric compounds is:
**(iii) > (ii) > (i)**