I would like to know the difference between "definite" and "certain". I think they're synonyms but is there any difference? for example in this exercise: "Although it is impossible to give a _____ age, we believe that the woman was between 25 and 30 when she died." the correct answer is "definite", why not "certain"? Thank you all for your answers.
They each have multiple meanings, with some overlap. The word "certain" even appears in some of the definitions of "definite".
certain: not having any doubt about something : convinced or sure. "I am certain that it will rain tomorrow."
definite: confident or certain about doing something or that something will happen. "It will definitely rain tomorrow."
certain: fixed or settled. "There are certain standards to pass."
definite: having distinct or certain limits. "There are definite standards to pass."
But there are other uses that have different implications. For instance:
certain: of a specific but unspecified character, quantity, or degree. "The house has a certain charm." Using "definite charm" in this case simply doesn't fit.
definite: free of all ambiguity, uncertainty, or obscurity. "We need a definite answer." Using "certain answer" in this case wouldn't mean the same thing.
To answer your specific question about "_____ age", I think that both would be grammatically correct there but can give different interpretations if you use those last two definitions I cited above. 'Certain' gives more of an implication that you don't much care what the age is. 'Definite' gives more of an implication that you want to know the specific age.
They are synonymous for the most part.
Definite can also be used to describe the limits of something.
"A definite area."
Certain can also be used to describe something which is inevitable.
"The outcome is certain."
As for OP's example sentence, I believe that definite is a better choice simply because it sounds more assertive. But really, both are viable choices.