IPMAT Indore 2024 (MCQ) PYQs

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

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