In an examination, the maximum marks for each of the four papers namely P, Q, R and S are
- 100.Marks scored by the students are in integers. A student can score 99% in n different ways. What is the value of n ?
- A.16
- B.17
- C.23
- D.35
▶ Answer & Explanation
Correct answer: D. 35
To score 99% in an examination where each of the four papers has a maximum of 100 marks, a student needs to score a total of 396 marks out of 400. This means the student can afford to lose exactly 4 marks in total across the four papers. These 4 marks can be lost in various combinations: either by losing 1 mark in each of the four papers (1 way), or by losing 2 marks in one paper and 1 mark in two others (4 * C(3,2) = 12 ways), or by losing 3 marks in one paper and 1 mark in another (4 * 3 = 12 ways), or by losing 4 marks in one paper (4 ways), or by losing 2 marks in two papers (C(4,2) = 6 ways). Summing these up: 1 + 12 + 12 + 4 + 6 = 35 ways.
Source: UPSC csat 2023