Which of the following functions are increasing on $x \in \left(0, \frac{\pi}{2}\right)$? (A) $f(x) = \sin x$ (B) $f(x) = \cos x$ (C) $f(x) = \tan x$ (D) $f(x) = \cos 3x$ Choose the correct answer from the options given below:

The difference of absoulte maximum (largest) and absoulte minimum (smallest) values of the function $f(x) = 12x^{4/3} - 6x^{1/3}, x \in [-1, 1]$ is

The equation of tangent line to $y = 2x^2 + 7$, which is parallel to the line $4x - y + 3 = 0$ is

The interval in which the function $f(x)=x^3-12x^2+36x+20$ is increasing, is

The rate of change of the area of a circular disc with respect to its circumference when radius is 3 is :

At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

For the function $f(x)=ax^3-9ax^2+9x+3, x\in R$, then which of the following statements are True?

(A) $f'(x)=3[ax^2-6ax+3]$

(B) It is increasing for $a\in\left[0,\dfrac{1}{3}\right]\ \forall x\in R$

(C) It is increasing for $a\in(-\infty,0)\ \forall x\in R$

(D) It is increasing for $\forall a\in R$

Choose the correct answer from the options given below: