IPMAT Indore 2023 (MCQ) PYQs

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

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

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