IPMAT Indore 2025 (MCQ) 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 the harmonic mean of the roots of the equation $(5 + \sqrt{2}) x ^ 2 - bx + 8 + 2\sqrt{5} = 0$ is $4$ then the value of $b$ 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