An extended state of considerably slowed down body functions is known as
a. hibernation
b. insomnia
c. stupor
d. torpor

The answer is a. hibernation. 

Hibernation is an extended state of decreased body function, primarily body temperature and metabolism rate. It occurs during the winter when food availability is reduced. Also, hibernation helps animals to preserve energy that would be used to maintain body temperature during long cold winters. It should be distinguished from torpor which is a short-term reduction of body functions. 
Stupor is the lack of consciousness and mental function, while insomnia is a sleep disorder.