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 $(x+6\sqrt{2})^{\frac{1}{2}} - (x-6\sqrt{2})^{\frac{1}{2}} = 2\sqrt{2}$, then x equals

The number of integers that satisfy the equality $(x^2 - 5x + 7)^{x + 1} = 1$ is