Limitless vs Unlimited

[duc]

I have just taken an English tests.Here is one of its question.Put the correct form of the suggested word:

We should use solar energy because it's cheap,clean and .....(limit)
I put ''unlimited'' but my friend choose ''limitless''

As I looked up in the dictionary,they have the same meaning.Please explain their difference for me.
_________________
Don't see your shade think you are great

[Mister Micawber]

.
Frankly, I see no difference in their use here. 'Limitless', I think, would be the choice for 'infinite'.
.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mister Micawber

[duc]

Thank you!However I'm very worried about my result
_________________
Don't see your shade think you are great

[Mister Micawber]

.
And you look worried!
.
_________________
Canadian-American native speaker
who teaches English for a living at Mister Micawber's
ESL cafe: Interview with Mister Micawber