CAT (QA) PYQs

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 a, b and c are positive real numbers such that $a > 10 \ge b \ge c$ and $\frac{\log_8(a+b)}{\log_2 c} + \frac{\log_{27}(a - b)}{\log_3 c} = \frac{2}{3}$, then the greatest possible integer value of a is

For some positive real number $x$, if $\log_{\sqrt{3}}(x) + \frac{\log_x (25)}{\log_x (0.008)} = \frac{16}{3}$, then the value of $\log_3(3x^2)$ is