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In a certain examination paper, there are n questions. For $j=1, 2, \dots,n,$ there are $2^{n-i}$ students who answered $j$ or more questions wrongly. If the total number of wrong answer is $4095,$ then the value of $n$ is

  1. $12$
  2. $11$
  3. $10$
  4. $9$
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