In a university, a professor gave a set of three problems to the three brilliant most students of his class. See the image for the questions.

We know that everybody has got two questions right and one wrong.

Now if the first student got the first question wrong, then the second one must have that question as wrong two since both answers are the same.

Now if that is true, then we are having two different correct answers for the second and third question.

Thus, the first and second student must be correct with the first question.

Keep on applying the same logic and you will reach to the conclusion that the correct answers are:

Two for the first question

Three for the second question and

Two for the third question.