IIM-K (BMSAT) 2025 (QA) PYQs

The value of $\frac{325 \times 325 \times 325+175 \times 175 \times 175}{325 \times 325-325 \times 175+175 \times 175}$ is

Say $y = 3\sqrt{2} - 4$, find $y^2 + \frac{1}{y^2}$.

Which of the following is the value of $m$ for which the polynomial $x^4 + 10x^3 + 25x^2 + 15x + m$ is exactly divisible by $x+7$?