CUET Mathematics 2026 19th May Shift 1 PYQs

The volume of spherical balloon is increasing at the rate of $4 \text{ cm}^3/ \text{sec}$. The rate of increase of its surface area, when the radius is 3cm will be :-

The sides of an equilateral triangle are increasing at the rate of 5 cm/sec. The rate at which the area increases when the side is 20 cm, is

The function $f(x) = \log_e(\sin x), x \in (0, \pi)$ is

(A) strictly increasing on $\left(0, \frac{\pi}{2}\right)$

(B) strictly decreasing on $\left(0, \frac{\pi}{2}\right)$

(C) strictly increasing on $\left(\frac{\pi}{2}, \pi\right)$

(D) strictly decreasing on $\left(\frac{\pi}{2}, \pi\right)$

(E) strictly increasing on $(0, \pi)$

Choose the correct answer from the options given below: