The demand function for a certain product is represented by the equation: $p = 20 + 5x - 3x^2$, where $x$ is the number of units demanded and $p$ is the price per unit (in Rs.), then the marginal revenue when 2 units are sold is:

Consider the function $f(x) = x^3 - 3x$. Then

Match List-I with List-II

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If the sum of the length of the hypotenues and a side of a right angled triangle is L cm then the angle between hypotenuse and other side of the triangle for which the area of the triangle is maximum, is:

If the function $f(x) = x^2-2kx+7$ is increasing on [1, 5] then $k$ belongs to

For x ∈ ℝ - {0}, the function f(x) = $\frac{3}{x}$ + 7 is decreasing when

The function $f(x) = x^2 - 4x + 6$ is

(A) Strictly decreasing on $(-\infty, 2) \cup (2, \infty)$

(B) Strictly increasing on $(2, \infty)$

(C) Strictly increasing on $(-\infty, \infty)$

(D) Strictly decreasing on $(-\infty, 2)$

Choose the correct answer from the options given below:

Let the median of a variable equilateral triangle is increasing at the rate of $2\sqrt{3}$ cm/s. Then the rate at which its each side is increasing is: