If x is real, then minimum value of $x^2 - 8x + 17$ is :

Let $f(x) = x^2 + \frac{250}{x}$ be any function defined on $\mathbb{R} - \{0\}$, where $\mathbb{R}$ is the set of real numbers. Then which of the following are TRUE?

(A) $f'(x) = 2x + \frac{250}{x^2}$

(B) $x = 5$ in the only critical point of $f(x)$

(C) minimum value of $f(x)$ is 75

(D) maximum value of $f(x)$ is 50.

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The interval in which the function $f(x) = -x^2 - 2x + 18$ is decreasing is :

The absolute maximum value of the function $f(x) = 2x^3 - 15x^2 + 36x + 7$ on the interval [1,5] is

A cylindrical drum of radius 7 cm and height 2 m is being kept in a vertical position filled with milk. If the milk is leaking at 14 cm³/sec from its lower base, then the rate of decrease in the level of milk is:

[Take $\pi = \frac{22}{7}$]

The minimum value of $f(x) = |2x - 1|$ is

Match List-I with List-II

$\begin{array}{|l|l|} \hline \rule{0pt}{2.8ex}\text{List-I} & \text{List-II} \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(A) The minimum value of } f(x) = (2x - 1)^2 + 3 & \text{(I) } 4 \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(B) The maximum value of } f(x) = -|x + 1| + 4 & \text{(II) } 10 \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(C) The minimum value of } f(x) = \sin(2x) + 6 & \text{(III) } 3 \\[1.2ex] \hline \rule{0pt}{2.8ex}\text{(D) The maximum value of } f(x) = -(x - 1)^2 + 10 & \text{(IV) } 5 \\[1.2ex] \hline \end{array}$

Choose the correct answer from the options given below: