Explanation:

- In the examination, each paper has a maximum of 100 marks, and the total for the four papers is 400.

- To achieve 99%, a student must score 396 marks out of 400.

- The problem becomes how to distribute these 4 marks lost over four subjects.

- The student can lose 1 to 4 marks in any subject(s), without exceeding a total of 4 marks lost.

- The task is to find the number of integer solutions for:

- \( x_1 + x_2 + x_3 + x_4 = 4 \)

- Where each \( x_i \) is a non-negative integer.

- Using the formula for non-negative integer solutions \(( \binom{n+k-1}{k-1} )\), where \( n \) is 4 (marks lost) and \( k \) is 4 (papers):

- \(\binom{4+4-1}{4-1} = \binom{7}{3} = 35\).

- The correct answer is Option 4: 35