IPMAT Indore 2024 (MCQ) PYQs

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 $a_1, a_2, ..., a_8$ are the roots of the equation $x^8 + x^7 + ... + x + 1 = 0$, then the value of $a_1^{2025} + a_2^{2025} + ... + a_8^{2025}$ 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