Celui ou ce?

Only celui works in this context. There's a grammatical difference between celui (a demonstrative pronoun) and ce (a demonstrative adjective). Let me demonstrate (pun intended ;)

C'est celui que j'aime. -- It is him that I love.
Cest ce mec que j'aime. -- It is that guy that I love.

Celui (celle, ceux) can stand by themselves, like "him" in the example. But ce (cette, ces) always needs a noun following.

Which exercise/quiz is this related to ? 

The answer to your question depends on what you are trying to say - although as Chris notes, a choice directly between 'celui' and 'ce' is not an option. However, there are more 'problems' with your example sentences than just choosing between celui and ce. Without context cannot be sure what will fit better. 

Best to repost the question with the linked lesson/quiz.  External questions/tests should not be posted here for responses.