IPMAT Indore 2025 (MCQ) PYQs

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

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

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