In a certain examination paper, there are n questions. For j=1,2,.......n there are 2^n-1 will answered j or more questions wrongly. If the total number of wrong answers are 4095, then the value of n is

a.12
b.11
c.10
d.9

• Ans is 12.
  2^n - 1 = 2^12 - 1
  => 4095
  therefore, n =12
• 7 years agoHelpfull: Yes(8) No(1)
• (2^n)-1=4095
  =>2^n=4096
  =>2^n=2^12
  =>n=12
• 7 years agoHelpfull: Yes(2) No(0)
• Let us say there are only 3 questions. Thus there are 23–1 = 4 students who have done 1 or more questions wrongly, 23–2 = 2 students who have done 2 or more questions wrongly and 23–3 = 1 student who must have done all 3 wrongly.
  
  Thus total number of wrong answers = 4 + 2 + 1 = 7 = 23 – 1 = 2n – 1.
  In our question, the total number of wrong answers
  = 4095 = 212 – 1.
  
  Thus n = 12
• 7 years agoHelpfull: Yes(0) No(0)
• 2^n-1=4095
  =>2^n=4094=2^12
  =>n=12.
• 7 years agoHelpfull: Yes(0) No(1)