IIM-K (BMSAT) 2025 (QA) PYQs

If $a, b, c$ are real numbers and $a^2 + b^2 + c^2 = 1$, then the set of values $ab + bc + ca$ can take is:

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

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 $x+7$?