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Explanation:

no two students have scored equal points in the same round.
Let Vagisha's score in the Debate and Extempore rounds be x. Thus, the table becomes as shown below.

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Possibility (I): Raghav scored 8 points in the debate round.
The total value of the blanks will be = 29 − 8 − 3 − 10 = 7. Since each of the blanks has at least 4 points, this case is not possible.
Possibility (II): Vagisha's score in the extempore round is twice of Aarav's in the same round.
Thus, x = 8 or 10
If x = 8, the total of remaining blanks = 33 - 8 - 8 - 8 = 9. The only possible values for the blanks are 4 and 5. Since, Both BP and CP already have 4 points, Vagisha cannot get 4 points. Thus, this case is not possible.
If , the total of remaining blanks = . Thus, this case is also not possible.
Possibility (III): Vagisha scored 6 points in the debate round.
If x = 6, the total of remaining blanks = 33 - 8 - 6 - 6 = 13. In this case, the remaining scores can be 6 and 7, respectively, such that it satisfies the condition in statement 2. Thus, this case is possible.
Possibility (IV): Vagisha scores more points than Aavanya in the business quiz round.
Let Vagisha scores 8 points in BQ and x = 4. Thus, Vagisha's points in the CP round = 33 - 4 - 4 - 8 - 8 = 9. Since Aavanya already scored 9 points in CP, this is not possible.
Let Vagisha scores 8 points in BQ and x = 6. Thus, Vagisha's points in the CP round = 33 - 8 - 6 - 6 - 8 = 5. This looks plausible but in this case, Raghav's possible points do not fit the conditions.
Similarly, for other cases, this possibility is found to be invalid.
Hence, the answer is option C.