Dear Shashank,

The no of students answering exactly p(1≤p≤n-1) questions wrongly is 2^n-p - 2^n-p-1

The no of students answering all n questions wrongly is 2⁰. Thus, the total no of wrong answers is:

= 1(2^n-1 – 2^n-2) + 2(2^n-2 – 2^n-3) + ……..+(n-1)(2¹ – 2⁰) + n(2⁰)

=> 2^n-1 + 2^n-2 + 2^n-3 + …..+2⁰=2ⁿ – 1

=> 2ⁿ – 1=2047

=> 2ⁿ = 2048

=> n=11

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