The correct decreasing order for acid strength is :

Options

A. `NO_2 CH_2COOH gt NCCH_2 COOH gt FCH_2 COOH gt ClCH_2 COOH`
B. `FCH_2 COOH gt NCCH_2 COOH gt NO_2 CH_2 COOH gt ClCH_2 COOH `
C. `NO_2 CH_2 COOH gt FCH_2 COOH gt CNCH_2 COOH gt ClCH_2 COOH `
D. `CNCH_2 COOH gt O_2 NCH_2 COOH gt FCH_2 COOH gt ClCH_2 COOH `

Explanation

To determine the correct decreasing order of acid strength among the given compounds, we need to analyze the effects of substituents on the acidity of the compounds. The substituents we will consider are -NO2 (nitro), -CN (cyano), -F (fluoro), and -Cl (chloro).

### Step-by-Step Solution:

1. **Identify the Compounds**:
We are comparing the acidity of compounds that have a common structure, likely a carboxylic acid (RCOOH) where R varies based on the substituents. The substituents we are considering are -NO2, -CN, -F, and -Cl.

2. **Understand the Effects of Substituents**:
- **-NO2 (Nitro group)**: This group has a strong -I (inductive) effect and a -M (mesomeric) effect due to resonance. It stabilizes the negative charge on the conjugate base (RCOO-) effectively, making the acid stronger.
- **-CN (Cyano group)**: The cyano group also has a -I effect and can exhibit a -M effect due to the presence of a triple bond with nitrogen. However, its effect is less pronounced than that of the nitro group.
- **-F (Fluoro group)**: Fluorine has a strong -I effect due to its high electronegativity, but it does not have a -M effect because it does not participate in resonance in this context.
- **-Cl (Chloro group)**: Chlorine has a weaker -I effect compared to fluorine and does not have a -M effect. Therefore, it is the least effective in stabilizing the negative charge on the conjugate base.

3. **Rank the Effects**:
Based on the strength of the -I and -M effects:
- **-NO2** has the strongest effect (both -I and -M).
- **-CN** comes next due to its -I and -M effects, but less than -NO2.
- **-F** follows due to its strong -I effect but no -M effect.
- **-Cl** has the weakest effect due to its lower electronegativity and lack of resonance.

4. **Conclusion**:
Therefore, the order of acidity from strongest to weakest is:
**-NO2 > -CN > -F > -Cl**

### Final Answer:
The correct decreasing order for acid strength is:
**-NO2 > -CN > -F > -Cl**