IIM-K (BMSAT) 2025 (QA) PYQs

Let $P(x)$ be a quadratic polynomial such that

$\left|\begin{array}{ll} P(0) & P(1) \\ P(0) & P(2) \end{array}\right|=0$

Let $P(0)=2$ and $P(1)+P(2)+P(3)=14$. Then $P(4)$ equals

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

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