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

Let $f(x) = a^2x^2 + 2bx + c$ where, $a \neq 0$, $b, c$ are real numbers and $x$ is a real variable then

The number of real solutions of the equation $(x^2 - 15x + 55)^{x^2-5x+6} = 1$ is: