The order of decreasing stability of the carbanions :
`(CH_(3))_(3)C^(-)(I),(CH_(3))_(2)CH^(-)(II), CH_(3)CH_(2)^(-)(III), C_(6)H_(5)CH_(2)^(-)(IV)` is

Options

A. `IgtIIgtIIIgtIV`
B. `IVgtIIIgtIIgtI`
C. `IVgtIgtIIgtIII`
D. `IgtIIgtIVgtIII.`

Explanation

To determine the order of decreasing stability of the given carbanions, we need to analyze the structure and stability of each carbanion based on the degree of substitution and the presence of resonance.

### Step-by-Step Solution:

1. **Identify the Carbanions:**
- (I) \((CH_3)_3C^-\) - Tertiary carbanion
- (II) \((CH_3)_2CH^-\) - Secondary carbanion
- (III) \(CH_3CH_2^-\) - Primary carbanion
- (IV) \(C_6H_5CH_2^-\) - Benzyl carbanion

2. **Analyze the Stability Factors:**
- **Tertiary Carbanion (I)**: This carbanion has three alkyl groups attached. Alkyl groups are electron-donating, which can help stabilize the negative charge. However, tertiary carbanions are generally less stable than secondary and primary due to steric hindrance.

- **Secondary Carbanion (II)**: This carbanion has two alkyl groups. It is more stable than a tertiary carbanion because the negative charge is better stabilized by the two electron-donating groups compared to three in the tertiary case.

- **Primary Carbanion (III)**: This carbanion has only one alkyl group. It is less stable than both secondary and tertiary carbanions because it has less electron donation to stabilize the negative charge.

- **Benzyl Carbanion (IV)**: This carbanion is stabilized by resonance. The negative charge can delocalize into the benzene ring, making it significantly more stable than the others.

3. **Order of Stability:**
- The most stable carbanion is the benzyl carbanion (IV) due to resonance stabilization.
- Next is the primary carbanion (III) because it has some stability from the single alkyl group.
- Then comes the secondary carbanion (II) which is less stable than the primary due to the electron-donating effect being less pronounced.
- Finally, the tertiary carbanion (I) is the least stable due to steric hindrance and less effective stabilization of the negative charge.

4. **Final Order:**
- The order of decreasing stability of the carbanions is:
- \(C_6H_5CH_2^- (IV) > CH_3CH_2^- (III) > (CH_3)_2CH^- (II) > (CH_3)_3C^- (I)\)

### Conclusion:
The correct order of decreasing stability of the carbanions is:
**IV > III > II > I**