In a certain test, there are n questions. In this test 2^ n-i students gave wrong answers to at least i questions, where i =1,2, n . If the total number of wrong answers given is 2047 , then n is equal to

Step-by-step solution

Hint: Total students was gave wrong answer to exactly i - questions =2^ n-i -2^ n-(i+1) Total wrong answer given ( _ i=0 ^ n-1 i (2^ n-i -2^ n-(i+1) )+n 1 ) 2^ n-1 + 1=2047 2^ n =2048 n =11