Which among the following characteristics is/are shared by Anabaena,…

The correct answer is Option (3) → Both (1) and (2)

Anabaena, Nostoc and Oscillatoria are cyanobacteria (blue-green algae). They are autotrophic microbes, and many of them fix atmospheric nitrogen. In paddy fields they act as biofertilisers. Being bacteria, they have prokaryotic cells, with no nucleus bounded by a membrane.

Option (1) Nitrogen-fixing microbes — Correct statement, but it is only one of the correct points, so on its own it is not the answer. All three fix atmospheric nitrogen, which is why the book names them as biofertilisers.

Option (2) Prokaryotic organisms — Correct statement, but it is only one of the correct points, so on its own it is not the answer. As cyanobacteria, all three are bacteria and so have prokaryotic cells.

Option (4) Eukaryotic organisms — Incorrect. Cyanobacteria are bacteria. Their cells have no true nucleus, so they are not eukaryotes.

NCERT Extract:
Microbes as Biofertilisers – “… Cyanobacteria are autotrophic microbes widely distributed in aquatic and terrestrial environments many of which can fix atmospheric nitrogen, e.g. Anabaena, Nostoc, Oscillatoria, etc. In paddy fields, cyanobacteria serve as an important biofertiliser. Blue green algae also add organic matter to the soil and increase its fertility.”