CAT (QA) PYQs

$\dfrac{1}{\log _{2} 100}-\dfrac{1}{\log _{4} 100}+\dfrac{1}{\log _{5} 100}-\dfrac{1}{\log _{10} 100}+\dfrac{1}{\log _{20} 100}-\dfrac{1}{\log _{25} 100}+\dfrac{1}{\log _{50} 100}= \ ?$

For all possible integers $n$ satisfying $2.25 \leq 2+2^{n+2} \leq 202$, the number of integer values of $3+3^{n+1}$ is

If $x$ is a real number such that $\log_3 5 = \log_5 (2 + x)$, then which of the following is true?