IIM-B (BBA-DBE) 2024 #2 (QA) PYQs

If $x ∈ (a, b)$ satisfies the inequality $\dfrac{x - 3}{x^2 + 3x + 2} \geq 1$, then the largest possible value of $b - a$ is

If $n \leq 4$ and $2 \leq m \leq n \leq 5,$ then what is the greatest possible value of $(n - m)(n + m)?$

Find the sum of the smallest value and the greatest value of $x$ that satisfy the inequality $|5x + 5| - 8 \leq 17$.