IIM-K (BMSAT) 2025 (QA) PYQs

The difference between the maximum real root and the minimum real root of the equation $(x^2 - 5)^4 + (x^2 - 7)^4 = 16$ is

If one of the roots of the equation $x^2 + ax + 3a = 0$ is $1$, then its other root is

If $8x^2 - 2kx + k = 0$ is a quadratic equation in $x$, such that one of its roots is $p$ times the other, and $p, k$ are positive real numbers, then $k$ equals