A free living anaerobic nitrogen fixer is
Rhodospirillum
The correct option is : B.
Explanation of the correct option:
Explanation of the incorrect options:
Option A:
Beijerinkia are the free living, aerobic, nitrogen fixer, which utilizes a range of multi carbon compounds.
Option C:
Rhizobium is a symbiotic nitrogen fixing bacterium, which shows symbiosis with leguminous plants and are gram negative, aerobic bacteria.
Option D:
Azotobacter is a free living aerobic, diazotrophic nitrogen fixer which requires oxygen to grow.
Final answer: A free living anaerobic bacterium capable of fixing nitrogen is Rhodospirillum.