It's not clear from the question if you've literally used quotation marks and a hyphen or not. You should not use both.
Stylistically, it's more common than not to use a hyphen. But some people choose to use quotation marks instead, especially if there are many words being used adjectivally:
It was a once-in-a-lifetime moment.
It was a "once in a lifetime" moment.
Whichever style is used, the punctuation makes it clear that the group of words before the noun act together to modify the noun.
In the case of a simple two-word modifier, you sometimes don't need to do anything:
She ate an ice cream sandwich.
Although some people would write ice-cream sandwich, there is no real need because ice cream (in open form) is a common noun that's clearly understood by everyone.
Note that if, for some reason, you actually needed to talk about a cream sandwich (whatever that might be) modified by ice, hyphenation would have to be explicitly used so as to make it clear it wasn't meant in the common sense:
He owned an ice sculpture.
She ate an ice cream-sandwich.
I can't think of a scenario where an ice cream-sandwich could be an actual thing (as opposed to an everyday ice cream sandwich), or where ice would be used instead of iced, but if it were an actual thing, then the hyphen in that case would be essential.
Having said all of that, different style guides give different guidance.
The Chicago Manual of Style has a 12-page document on hyphenation, with specific examples and use cases. The most recent version of the guide is behind a paywall, but public versions of older versions can be found. Generally speaking, Chicago recommends that adjectival phrases be hyphenated—but it's document is 12-pages long because of the many specific exceptions.
Generally speaking, the Associated Press is more in favour of open adjectival phrases. But it too recommends hyphenated adjectival phrases if there's any likelihood of misinterpretation.
In your case, I doubt anybody would misunderstand what you mean if you used multiple choice questions or multiple response questions. So, unless you're following a specific rule, there's no semantic reason that would clearly indicate you should hyphenate.
However, whatever you do, be consistent. Either hyphenate both, or don't hyphenate either. (I can think of no stylistic or syntactical reason why one phrase would require different treatment from the other.)