CAT (QA) PYQs

If $x$ and $y$ are positive real numbers such that $\log_{x}\left(x^{2}+12\right)=4$ and $3 \log _{y} x=1$, then $x+y$ equals

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

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