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. `(iii)gt(ii)gt(i)`
B. `(ii)gt(i)gt(iii)`
C. `(ii)gt(iii)gt(i)`
D. `(i)gt(ii)gt(iii)`

Explanation

To determine the order of stability of the given tautomeric compounds, we will analyze each compound based on the factors that influence stability: the number of carbonyl groups (C=O), the presence of α-hydrogens, and resonance.

### Step-by-Step Solution:

1. **Identify the Compounds:**
- (i) `CH2=OH(CH)-CH2=O(C)-CH3`
- (ii) `CH3=O(C)-CH2=O(C)-CH3`
- (iii) `CH3=OH(C)=CH-O(C)-CH3`

2. **Count the C=O Groups:**
- Compound (i) has **1 C=O group**.
- Compound (ii) has **2 C=O groups**.
- Compound (iii) has **1 C=O group**.

**Observation:** Compound (ii) has the highest number of C=O groups, which generally increases stability.

3. **Count the α-Hydrogens:**
- For compound (i), the α-carbon has **2 α-hydrogens**.
- For compound (ii), the α-carbon has **2 α-hydrogens**.
- For compound (iii), the α-carbon has **1 α-hydrogen**.

**Observation:** Compounds (i) and (ii) have more α-hydrogens compared to compound (iii).

4. **Evaluate Resonance:**
- Compound (i) does not exhibit significant resonance.
- Compound (ii) can exhibit resonance due to the presence of two carbonyl groups, allowing electron delocalization.
- Compound (iii) has a structure that allows for resonance with the double bond and the adjacent carbonyl.

**Observation:** Compound (ii) has the most resonance stabilization due to two carbonyls, while compound (iii) also has resonance but is less stable than (ii).

5. **Order of Stability:**
- Based on the analysis:
- Compound (ii) is the most stable due to the highest number of C=O groups and resonance.
- Compound (iii) is next due to resonance, despite having fewer C=O groups.
- Compound (i) is the least stable due to the absence of resonance and fewer C=O groups.

### Final Order of Stability:
1. **(ii)** > 2. **(iii)** > 3. **(i)**