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Dear Shashank,
The no of students answering exactly p(1≤p≤n-1) questions wrongly is 2n-p - 2n-p-1
The no of students answering all n questions wrongly is 20. Thus, the total no of wrong answers is:
= 1(2n-1 – 2n-2) + 2(2n-2 – 2n-3) + ……..+(n-1)(21 – 20) + n(20)
=> 2n-1 + 2n-2 + 2n-3 + …..+20=2n – 1
=> 2n – 1=2047
=> 2n = 2048
=> n=11
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