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

Question

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

3 Answers

kritika · Answer 1 · 2021-12-26T19:36:47+0000

Ans: (B)
Hint : Total students was gave wrong answer to exactly $i-$ questions $=2^{n-1}-2^{n-(i+1)}$
Total wrong answer given $=\sum \mathrm{i} \times\left(2^{n-i}-2^{n-(i+1)}\right)$
$$
\begin{aligned}
&\Rightarrow 2^{n-1}+\ldots \ldots 1=2047 \\
&\Rightarrow 2^{n}=2048 \\
&\Rightarrow n=11
\end{aligned}
$$

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

Your answer

3 Answers

Your comment on this answer:

Your comment on this answer:

Your comment on this answer:

Related questions

Categories