For the function $f(x) = x^5 - 5x^4 + 5x^3 - 1$, which of the following are true?

(A) $f(x)$ has local minimum value equal to -28.

(B) $f(x)$ has point of inflection at $x=1$.

(C) $f(x)$ has point of local maxima at $x=1$.

(D) $f(x)$ has the local maximum value equal to 2.

Choose the correct answer from the options given below:

The slope of the tangent to the curve $y = 3x^2 + 2kx - 5$ at $x=1$ is $9$. The value of $k$ is :

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm, is:

If the lengths of the three sides of a trapezium other than the base are $10 \mathrm{~cm}$ each, then the maximum area of the trapezium is:

The marginal cost (MC) and marginal revenue (MR) functions of a product are $MC = 20 + \frac{x}{20}$ and $MR = 30$ respectively. If the fixed cost is 200, then the maximum value of the profit 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 :-

A closed right circular cylinder has a volume of 2156 cm³. The radius of its base so that its total surface area may be minimum, is equal to: