If what is inside the inverted commas is itself a question then the question mark should also be inside them. e.g:
The Editor looked up from his screen and asked "Which nutter posted that?"
Occasionally though what is inside the inverted commas isn't itself a question but simply something which is being asked about. So the question mark then goes outside. e.g:
Who wrote "Day of the Triffids"?
Since John, Paul, George and Ringo were collectively known as 'The Beatles' (rather than just 'Beatles'), as shown in this image,
https://pbs.twimg.com/media/ChnFr2qWkAAXxQE.jpg
the definite article forms part of the group's name and should therefore be given a capital letter.
A similar problem (as to whether 'the' needs a capital) arises with the names of pubs. So some people might write
"We went to the Plough for lunch",
whereas others would use
"We went to The Plough for lunch".
I can't see that it really matters much either way but, as the definite article usually forms part of the pub's name (as displayed outside it)
http://tinyurl.com/zrjhx39
I'd prefer the use of the latter.