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. `IIIgtIIgtI`
B. `IIgtIgtIII`
C. `IIgtIIIgtI`
D. `IgtIIgtIII`

Explanation

To determine the order of stability of the given tautomeric compounds, we will analyze each compound based on their structural features and stability factors such as resonance, keto-enol tautomerism, and steric effects.

### Step 1: Analyze Compound (i)
The first compound is `CH₂=OH(CH)-CH₂=O(C)-CH₃`.
- This compound has a hydroxyl group (OH) and a carbonyl group (C=O) present.
- The presence of the hydroxyl group suggests it can exist in an enol form, which is generally less stable compared to the keto form due to the lack of resonance stabilization.

### Step 2: Analyze Compound (ii)
The second compound is `CH₃=O(C)-CH₂=O(C)-CH₃`.
- This compound features two carbonyl groups (C=O) and is in a keto form.
- Keto forms are generally more stable than enol forms due to the presence of a double bond between carbon and oxygen, which provides resonance stabilization.

### Step 3: Analyze Compound (iii)
The third compound is `CH₃=OH(C)=CH-O(C)-CH₃`.
- This compound contains both a hydroxyl group and a carbonyl group, and it is in a form that allows for resonance stabilization.
- The presence of a double bond adjacent to the hydroxyl group allows for resonance, making this compound more stable than the first compound.

### Step 4: Compare Stability
- **Compound (iii)** is the most stable due to resonance stabilization.
- **Compound (ii)** is next, as it is in a keto form which is more stable than enol forms.
- **Compound (i)** is the least stable due to the presence of an enol form and lack of significant resonance stabilization.

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