If a manufacturer's total cost 'C' is given by $C = \dfrac{x^2}{25} + 3x$, then the marginal cost when 7 units are produced will be:-

The curve $x = y^2$ and $xy = k$ cut orthogonally, then $k^2$ is equal to:

The function $f(x) = 2\log_e(x-2) - x^2 + 4x + 1, (x > 2)$ is increasing on the interval:

A square board of side 36cm is made into a box without top by cutting a square from each corner and folding up the flaps to form a box then maximum volume of the box is

The point on the curve $y^2 = 8x$ for which the abscissa and ordinate change at the same rate, is

For the function $f(x) = \frac{1}{x^2+2x+2}$

which of the following statements are TRUE?

A. $f(x)$ is increasing on $(-\infty, -1)$

B. $f(x)$ is decreasing on $(-\infty, -1)$

C. $f(x)$ is decreasing on $(-1, \infty)$

D. maximum value of $f(x)$ is 1

Choose the correct answer from the options given below:

The demand function (in Rs.) for a product is given by $P = 20 - 0.25x$, where P is the price per unit and x is the number of units sold, then the price of one unit, when the revenue is maximized, is: