CAT (QA) PYQs

If y is a negative number such that $2^{y^2log_3 5} = 5^{\log_2 3}$, then y equals

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