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

If $\alpha$ and $\beta$ are absolute maximum and absolute minimum values of a function $f(x)=\dfrac{x}{2}+\dfrac{2}{x}$ on the interval $[1,2]$, then the value of $\alpha+\beta$ is:

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 :-

If $y = ax^2 + bx$ has minima at $x = 2$ and the minimum value is -12, then which of the following are correct?

(A) $a = 3$

(B) $a = -3$

(C) $b = 12$

(D) $b = -12$

Choose the correct answer from the options given below:

If the function $f(x) = x^4 - 62x^2 + ax + 9$ has a critical point at $x = 1$, then $a$ is equal to:

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

If $f(x) = x^2 - 4x + 13, x \in \mathbb{R}$, then which of the following are correct?

(A) $x = 2$ is a stationary point of $f(x)$.

(B) $f(x)$ is increasing function on $(2, \infty)$

(C) $f(x)$ have maxima at $x = 2$

(D) $f(2) = 9$

Choose the correct answer from the options given below: