Is this a good question?
No it isn't. The reason is that due to the broken way self-reference is worked into it, it has no answer.
Here is why.
Firstly, the answer to the question is a value from the domain { "Yes", "No" }, not one from the domain { A, B, C, D }. Those letters are just labels for the answer. That's how multiple choice testing works. The label is not the answer, the labeled answer is the answer.
Because both C and D are labels for "No", those two choices are equivalent: they constitute the same answer. It cannot be the case that C is a correct answer, but D isn't.
Because C is a label for "No", the question "is option C a correct answer?", means exactly the same thing as "is 'No' a correct answer?"
Thus, let us entertain the possibility that "No" is the correct answer, i.e. C is not correct. If "No" is the correct answer, that is equally represented either by C or D; it means that C is a valid choice, just like D. But that cannot be because "No" means "C is not a valid choice".
Thus, "Yes" must be the correct answer. But then, only the choices A and B are tied to that answer. That "Yes" answer, however, means that C is correct (and also D), and not A or B.
So the situation is not well-formed; though it may not be the intent, the question reduces to the Liar Paradox.
It may have been the intent that D must be the answer; but that can only be the case if we consider C and D to be distinct from each other, even though they both map to the same "No" answer, which is not a valid concept.
It cannot be that the "D flavored 'No'" is correct but the "C flavored 'No'" isn't; 'No' is just 'No'. The specific alphabetic labels do not contribute anything to the semantics of the "Yes" or "No".
The multiple choice test is just a format for easier grading: the correct answer is given away along with several distractors, and for the sake of simplicity, these items are all given symbolic labels, which otherwise don't mean anything.
A well-formed multiple choice question has a correct answer even if we take away the choices and ask for the answer to be stated.
In this regard, our question runs aground already: it contains a reference to one of the labels, which makes it impossible to remove the choices such that the question still makes sense.