Which of the following is false about Spirogyra?

The correct answer is each chloroplast contains a single pyrenoid.

Let us understand why this statement is false by examining the biology of Spirogyra:
Spirogyra is a genus of filamentous charophyte green algae of the order Zygnematales, named for the helical or spiral arrangement of the chloroplasts that is diagnostic of the genus.

1. Chloroplasts and Pyrenoids in Spirogyra:
In Spirogyra cells, the chloroplasts are ribbon-shaped, spirally arranged bands. Within these ribbon-like chloroplasts, there are multiple, conspicuous bead-like bodies called pyrenoids embedded at intervals. Pyrenoids are centers of carbon fixation and starch synthesis. Because each chloroplast in Spirogyra contains multiple pyrenoids rather than a single one, the statement that "each chloroplast contains a single pyrenoid" is false.

2. Verification of the other features:
- Complex nucleolus: The nucleolus of Spirogyra is indeed complex and shows organized regions such as the nucleolar organizing region (NOR) and specific ribonucleoprotein structures.
- Polycentric chromosomes: Spirogyra chromosomes are known to have diffuse centromeres (holocentric or polycentric), meaning they do not have a single localized centromere during cell division.
- Heterothallism: Some species of Spirogyra exhibit heterothallism, where conjugation occurs between filaments of two different mating types (male and female strains).

Therefore, the false statement among the options is that each chloroplast contains a single pyrenoid.