CAT (QA) PYQs

The smallest integer $n$ for which $4^n > 17^{19}$ holds, is closest to

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 positive real number such that $4 \log _{10} x+4 \log _{100} x+8 \log _{1000} x=13$, t hen greatest integer not exceeding x , is