EMNA Q.28
- Option : D
- Explanation : Number of students who answered 1 or more questions wrongly = 2N-1.
Number of students who answered 2 or more questions wrongly = 2N-2
Hence number of students who answered 1 question wrongly = 2N-1- 2N-2 = 2N-2
Similarly it can be shown that number of students who answered 2 questions wrongly = 2N-2 - 2N-3 = 2N-3
Similarly we can find number of students who answered K questions wrongly where K ≥ 3
Hence total number of questions attempted wrongly
s = 2N-2+2(2N-3)+3(2N-4 )+...+(N-1)(20) + N(1) ........(1)
∴ s/2 = 2N-3+ 2(2n-4) +.......+ (N-2)(20) + (N-1)/2 + N/2.......... (2)
Substracting equations (1) from (2)
s/2 = 2N-2 + 2N-3 +...+20+1/2
=> s = 2N + 2N-2+2N-3+...+1 = 2N -1
= 8191
=> N = 13
