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

• 2^n-1+2^n-2+.....+2^n-n=4095
  2^n(1/2+1/2^2+......+1/2^n)=4095
  2^n(1-1/2^n)=4095
  2^n-1=4095
  2^n=4096
  n=12.
• 3 years agoHelpfull: Yes(2) No(0)
• 2^n-1
  = 2¹²-1 = 4095
  
  Ans n= 12
• 3 years agoHelpfull: Yes(0) No(0)
• be put j=1
  so 2^n-j=4095
  2^n-1=4095
  2^n=4096
  n=12
• 2 years agoHelpfull: Yes(0) No(0)
• Let us say there are only 3 questions.
  Thus there are
  2
  3
  −
  1
  =
  4
  students who have answered 1 or more questions wrongly,
  2
  3
  −
  2
  =
  2
  students who have answered 2 or more questions wrongly and
  2
  3
  −
  3
  =
  1
  student who must have answered all 3 wrongly.
  Thus total number of wrong answers
  =
  4
  +
  2
  +
  1
  =
  7
  =
  2
  3
  −
  1
  =
  2
  n
  −
  1
  .
  In our question, the total number of wrong answers
  =
  4095
  =
  2
  12
  −
  1.
  Thus n = 12.
• 6 Months agoHelpfull: Yes(0) No(0)