CAT (QA) PYQs

If $\left(x^2+\frac{1}{x^2}\right)=25$ and $x>0$, then the value of $\left(x^7+\frac{1}{x^7}\right)$ is

If $p^{2}+q^{2}-29=2 p q-20=52-2 p q$, then the difference between the maximum and minimum possible value of $\left(p^{3}-q^{3}\right)$ is

The product of two positive numbers is $616$. If the ratio of the difference of their cubes to the cube of their difference is $157: 3$, then the sum of the two numbers is