IIM-K (BMSAT) 2025 (QA) PYQs

If $x^{2}+\frac{1}{x^{2}}=83$ and $x>1$, then the value of $x^{3}-\frac{1}{x^{3}}$ is

If $x = \sqrt[3]{28}$ and $y = \sqrt[3]{27}$, find the value of $x + y - \frac{1}{x^2+xy+y^2}$.

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 $x+7$?