CAT (QA) PYQs

How many distinct positive integer-valued solutions exist to the equation $\left(x^{2}-7 x+11\right)^{\left(x^{2}-13 x+42\right)}=1 ?$

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

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