IPMAT Indore 2025 (MCQ) PYQs

If the polynomial $ax^2 + bx + 5$ leaves a remainder $3$ when divided by $x - 1$, and a remainder $2$ when divided by $x + 1$, then $2b - 4a$ equals

The remainder when $1! + 2! + 3! + ... + 95!$ is divided by $15$ is

The polynomial $4x ^ {10} - x ^ 9 + 3x ^ {11} - 5x ^ 7 + c x ^ 6 + 2x ^ 5 - x ^ 4 + x ^ 3 - 4x ^ 2 + 6x - 2$ when divided by $x - 1$ leaves a remainder $2.$ Then the value of $c + 6$ is