CAT (QA) PYQs

If $\left(\sqrt{\frac{7}{5}}\right)^{3 x-y}=\frac{875}{2401}$ and $\left(\frac{4 a}{b}\right)^{6 x-y}=\left(\frac{2 a}{b}\right)^{y-6 x}$

for all non-zero real values of $a$ and $b$, then the value of $x + y$ is

If $12^{12x}\times4^{24x+12}\times5^{2y}=8^{4z}\times20^{12x}\times243^{3x-6}$, where $x$, $y$ and $z$ are natural numbers, then $x+y+z$ equals

The sum of all real values of $k$ for which $\small \left( \dfrac{1}{8} \right)^k \times \left( \dfrac{1}{32768} \right)^{\frac{1}{3}} = \left( \dfrac{1}{8} \right) \times \left( \dfrac{1}{32768} \right)^{\frac{1}{k}}$ is