CUET Mathematics 2026 30th May Shift 2 PYQs

For the function $f(x) = \frac{x^4}{4} - 2x^3 + \frac{11}{2}x^2 - 6x$, which of the following statements are TRUE?

(A) Critical points of $f(x)$ are $x = 1, 2$ and $3$.

(B) $f(x)$ is increasing over $(1,2)$.

(C) $f(x)$ is decreasing over $(2,3)$.

(D) $f(x)$ is increasing over $(3,\infty)$.

Choose the correct answer from the options given below:

If the maximum value of the function $f(x) = \frac{2\log_e x}{x}$, $x > 0$ occurs at $x = e$, then $e^3 f''(e)$ is equal to

Consider a closed cylinder of radius $r$ with a fixed surface area. The volume of the cylinder is maximum when its height is