Consider the following question I came across:
Let $n$ be a large integer. Which of the following statements is TRUE?
$n^{1/\sqrt{\log_2 n}} < \sqrt{\log_2 n} < n^{1/100}$
$n^{1/100} < n^{1/\sqrt{\log_2 n}} < \sqrt{\log_2 n}$
$n^{1/\sqrt{\log_2 n}} < n^{1/100} < \sqrt{\log_2 n}$
$\sqrt{\log_2 n} < n^{1/\sqrt{\log_2 n}} < n^{1/100}$
$\sqrt{\log_2 n} < n^{1/100} < n^{1/\sqrt{\log_2 n}}$
To me the answer seems to be: $ n^{1/100} < \sqrt{\log_2 n} < n^{1/\sqrt{\log_2 n}}$
and limited empirical investigations also point in similiar direction. But this answer is not a part of the given options. Can I safely conclude that the options are invalid or am I missing something? I do not have access to solutions.