Explanation:

Red Algae, Green Algae, Brown Algae, and Blue-Green Algae are all types of algae that belong to different taxonomic groups. Each of these algae exhibits different characteristics and life cycles. In the given options, we need to identify which algae do not have motile stages in their life cycle.

Definition of motile stages:
Motile stages in the life cycle of algae refer to the reproductive stages where the algae have the ability to move actively. This movement is usually facilitated by the presence of flagella or cilia.

Identifying the correct option:
Let's analyze each option to determine whether they have motile stages in their life cycle or not.

a) Red Algae and Green Algae:
Both red algae and green algae have motile stages in their life cycle. In red algae, the motile stage is present in the male gamete or sperm, which is flagellated and actively moves towards the female gamete. Similarly, in green algae, the motile stage is present in the male gamete, which is also flagellated and exhibits active movement.

b) Red Algae and Brown Algae:
Both red algae and brown algae have motile stages in their life cycle. In red algae, the motile stage is present in the male gamete, whereas in brown algae, the motile stage is present in both the male and female gametes. The motile stages in brown algae are flagellated and enable the gametes to move towards each other for fertilization.

c) Red Algae and Blue-Green Algae:
In this option, red algae and blue-green algae are mentioned. Blue-green algae, also known as cyanobacteria, do not have motile stages in their life cycle. Cyanobacteria are prokaryotes and do not possess flagella or cilia for movement. Therefore, the correct answer is option 'C'.

d) Green Algae and Brown Algae:
Both green algae and brown algae have motile stages in their life cycle. As mentioned earlier, in green algae, the motile stage is present in the male gamete, while in brown algae, both male and female gametes are flagellated and exhibit active movement.

To summarize, the correct answer is option 'C' - Red Algae and Blue-Green Algae. Blue-green algae, also known as cyanobacteria, do not have motile stages in their life cycle.