CAT (QA) PYQs

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

If $x$ is a real number, then $\sqrt{\log_e \frac{4x-x^2}{3}}$ is a real number if and only if

For a real number $a$, if $\frac{\log _{15} a+\log _{32} a}{\left(\log _{15} a\right)\left(\log _{32} a\right)}=4$ then a must lie in the range.