"Any question" places a strict limit on the number of questions allowable to exactly one. For example, there was exactly one question as to who wore the pants. However, where the number of questions has not been determined, or is unrestricted, then the plural should be used.
Is there any question that I am correct? I don' think so. (The only question might be "are you correct".) However, any questions you have should be added to the comments below. (Questions might be "are you serious?", "what authority do you cite?", "why is your speellling so bad?" and so forth.)
Close-minded was first, but closed-minded is dominant:
Here's the earliest close-minded reference I can find from a Narrative of a Journey in the Interior of China, by Clarke Abel, 1818:
I found closed minded back to 1913 in The Century Magazine:
Edit:
After considering @FumbleFingers' comments here and his subsequent answer, I have to agree that most of the earlier close-minded references found through Google Books (including the one above) are using close |kloʊs| in this sense (from NOAD):
• not willing to give away money or information; secretive : you're very close about your work, aren't you?
This is also proven by this definition of uncommunicative from John Craig's A New Universal Etymological Technological, and Pronouncing Dictionary of the English Language, 1859:
It seems the phrase was once a common description for someone who "kept their own counsel"—usually used as a derogative, but sometimes as a compliment.
However, I did find this earlier use of close-minded specifically to mean the opposite of open-minded from an 1898 issue of The Outlook:
I also found evidence of a shift towards this sense of close-minded in other writings by the early 1900s. So, to conclude, I think the only thing new about the confusion evident by the 1960s was the frequency of the two terms in print.
I realize this may not ultimately answer the question, which is correct, but the timeline seems significant to me.
Best Answer
There is nothing wrong with "no-brainer question".
A compound noun is a noun that is composed of two or more nouns. When there are two nouns like "no-brainer question", the first noun functions as a noun modifier.
Another broadly used idiom is "rocket science" which means:
[Dictionary.com]
If you say "This isn't a rocket science question", it means it is no-brainer.