Question

In a certain test there are n questions. In this test 2^k students gave wrong answers to at least n-k question. k = 0,1,2... n. If the no.of wrong answers is 4095 then value of n is _______

(a) 11 

(b) 12 

(c) 13 

(d) 15

Answer 1

Correct option: (b) 12

Explanation:

Number of at least r wrong answers = 2^n-r 

number of students gave wrong answers of r questions = 2^n-r - 2^{n -(r+1)} 

number of students who gave all wrong answers = 2° = 1

Number of total wrong answers.