Which of the following functions are strictly decreasing on $\left(0, \dfrac{\pi}{2}\right)$?

A. $\cos x$

B. $-\cot x$

C. $\cos 2x$

D. $\sin x$

Choose the correct answer from the options given below:

The minimum value of the function $f(x) = x^3 + (10-x)^3$ occurs at:

If maximum value of $f(x) = 2x^3 + 3x^2 - 6ax + 10$ occurs at $x = -3$, then the value of $\alpha$ is ____

The interval for which the function $f(x)=\frac{x}{x^2+x+1}$ is an increasing function, is:

A solid sphere of gold of radius 5 cm, is being melted in a furnace such that the radius is decreasing uniformly. When the radius is 1cm, the rate at which surface area (A) is decreasing w.r.t. time ($t$) is equal to

($\frac{dv}{dt}$ = rate at which volume is decreasing w.r.t. $t$)

The approximate volume of a cube of side a meters on increasing the side by 4% is:

$f(x)=\sin x+\frac{1}{2} \cos 2 x \text { in }\left[0, \frac{\pi}{2}\right]$

(A) $f^{\prime}(x)=\cos x-\sin 2 x$

(B) The critical points of the function are $x=\frac{\pi}{6}$ and $x=\frac{\pi}{2}$

(C) The minimum value of the function is $2$

(D) The maximum value of the function is $\frac{3}{4}$

Choose the correct answer from the options given below :