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:

For the function $f(x) = e^x + e^{-x}$

(A) $f'(x) = e^x - e^{-x}$

(B) The critical point is $x = 0$

(C) The minimum value is 1

(D) $x = 0$ is the point of local minimum.

Choose the correct answer from the options given below:

The point of local maxima of the function $f(x) = (x - 2)^5(x + 2)^2$ is

Match List-I with List-II

The function $f(x) = (x - 1)(x + 1)^2$ has

Choose the correct answer from the options given below:

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 volume of a cube is increasing at the rate of 27 cm$^3$/s. How fast is the surface area increasing when the length of the cube is 12 cm.

The equation of tangent to the curve $x = a \cos^3 t, y = a \sin^3 t$ at t is :