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:

Water is running into a conical vessel, 18cm deep and 6cm in radius, at the rate of 0.1 $cm^3$/sec. If the water is 4cm deep, then the water level rising at the rate

In which of the following interval the function $f(x) = x^x, x > 0$ is strictly increasing?

The function $f(x) = -x^3 + 12x^2 - 36x + 21$ is

A. Increasing on $(-\infty, 2)$

B. Decreasing on $(-\infty, 2)$

C. Increasing on $(2, 6)$

D. Decreasing on $(6, \infty)$

Choose the correct answer from the options given below:

The demand for a certain product is represented by the function

$p = 150 + 10x - x^2$ (in Rs.)

where $x$ is the number of units demanded and $p$ is the price per unit, then the value of marginal revenue, when 10 units are sold is

If it is given that at $x = 1$, the function $f(x) = x^4 - 62x^2 + 2ax + b$ attains its maximum value on the interval [0, 2], then the value of a is:

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