WBJEE · Maths · Permutation Combination
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 \(=1,2, \ldots \ldots \mathrm{n}\). If the total number of wrong answers given is 2047 , then \(\mathrm{n}\) is equal to
- A 10
- B 11
- C 12
- D 13
Answer & Solution
Correct Answer
(B) 11
Step-by-step Solution
Detailed explanation
Hint: Total students was gave wrong answer to exactly i - questions \(=2^{n-i}-2^{n-(i+1)}\) Total wrong answer given \(\sum_{i=0}^{n-1} i \times \left(2^{n-i}-2^{n-(i+1)}\right)+n \times 1\) \(\Rightarrow 2^{n-1}+\ldots \ldots 1=2047\) \(\Rightarrow 2^{n}=2048\)…
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