Five Students

The correct answers are b, a, True, False and False. Also, the scores are Jigyasa (0), Ani (1), Chinu (2), Viru (3) and Mayank (4).

As no two students got the same number of correct answers, the total number of correct answers must be either 15 (1+2+3+4+5) or 10 (0+1+2+3+4).

Let’s find out the maximum number of correct answers possible from the answers given by them.
For Question I = 2 (b or c)
For Question II = 2 (b or c)
For Question III = 4 (True)
For Question IV = 4 (True)
For Question V = 3 (True)

Thus, the maximum number of correct answers possible are 15 (2+2+4+4+3) which means that Ani would have given all correct answers as only he answered True for questions III, IV and V. But then Chinu and Jigyasa would have exactly 3 correct answers. And also, Mayank and Viru would have 2 correct answers. So no one got all five correct. One can also arrive at this conclusion by trial-and-error, but that would be bit lengthy.

Now, it is clear that total number of correct answers are 10 (0+1+2+3+4). Questions III and IV both can not be False. If so, total number of correct answers would not be 10. So the student who got all wrong can not be Chinu, Ani and Mayank.

If Viru got all wrong, then Chinu, Jigyasa and Mayank each would have at least 2 correct answers. It means that Ani would have to be the student with only one correct answer and the correct answers for questions I and II would be a and a respectively. But then the total number of correct answers would be 1 (a) + 1 (a) + 1 (False) + 4 (True) + 2 (False) = 9.

Thus, Jigyasa is the student with all wrong answers. The correct answers are b, a, True, False and False. Also, the scores are Jigyasa (0), Ani (1), Chinu (2), Viru (3) and Mayank (4).