Final answer:
Osmosis and diffusion are passive transport processes that do not require ATP, whereas movement of sperm flagella, exocytosis of neurotransmitters, and active transport of glucose do require ATP.
Step-by-step explanation:
The question pertains to which processes require adenosine triphosphate (ATP) as a source of energy. Specifically, the process that does not rely on ATP for energy is being queried.
Osmosis and diffusion are processes that do not require ATP as they are examples of passive transport, moving substances across the membrane without the expenditure of cellular energy.
On the other hand, the movement of flagella in sperm cells, exocytosis of transmitter substances from nerve terminals, and the active transport of glucose from the small intestine to the blood are all processes that do require ATP.
Therefore, the correct answer to the question 'All the following rely on ATP as a source of energy except:' is c. osmosis and diffusion.