IPMAT Indore 2024 (MCQ) PYQs

Consider the following statements:
(i) When $(0 < x < 1)$, then $(\frac{1}{1+x} < 1 - x + x^2)$
(ii) When $(0 < x < 1)$, then $(\frac{1}{1+x} > 1 - x + x^2)$
(iii) When $(-1 < x < 0)$, then $(\frac{1}{1+x} < 1 - x + x^2)$
(iv) When $(-1 < x < 0)$, then $(\frac{1}{1+x} > 1 - x + x^2)$
Then the correct statements are:

The set of all real values of x satisfying the inequality $\dfrac{x^2(x+1)}{(x-1)(2x+1)^3} > 0$ is

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