A free living anaerobic nitrogen fixing bacterium is :

Options

A. Rhizobium
B. Anabaena
C. Azotobacter
D. Clostridium

Explanation

To identify a free-living anaerobic nitrogen-fixing bacterium, we can follow these steps:

### Step 1: Understand the definitions
- **Free-living**: This means the bacterium does not form a symbiotic relationship with other organisms.
- **Anaerobic**: This indicates that the bacterium can survive and thrive in environments without oxygen.
- **Nitrogen-fixing**: This refers to the ability of the bacterium to convert atmospheric nitrogen (N2) into ammonia (NH3), which can be utilized by plants.

### Step 2: Analyze the options provided
1. **Rhizobium**: This bacterium is known for its symbiotic relationship with legumes, thus it is not free-living.
2. **Anabena**: This is a cyanobacterium that also forms symbiotic associations with other organisms, so it is not free-living.
3. **Azotobacter**: This bacterium is free-living but is aerobic, meaning it requires oxygen for respiration, which does not fit our criteria of being anaerobic.
4. **Clostridium**: This bacterium is free-living and anaerobic, meaning it can survive without oxygen and does not form symbiotic relationships.

### Step 3: Conclusion
Based on the analysis of the options, the correct answer is **Clostridium**, as it is a free-living anaerobic nitrogen-fixing bacterium.

### Final Answer
**Clostridium**

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