CUET Mathematics PYQs

Let $f(x) = \log_e(\sin x), x \in (0, \pi)$, then which of the following statements is/are TRUE?

(A) $f(x)$ is increasing on $(0, \pi/2)$

(B) $f(x)$ is decreasing on $(\pi/2, \pi)$

(C) $f(x)$ is increasing on $(0, \pi)$

(D) $f(x)$ is decreasing on $(0, \pi)$

Choose the correct answer from the options given below:

The maximum value of $f(x) = \frac{1}{4x^2 + 2x + 1}$ is

The rate of change of area of a circle with respect to its circumference when radius in 6 cm, is