A boat 10 m high floating at a uniform speed of 13 meters per minute(m/min) away from a lamp post 15 m high. Then the rate at which the length of shadow of the boat increases is:

The demand function for a monopolist is given by $x = 100 - 4p$, then the marginal revenue, when $x=6$ is (where $x$ is the number of units and $p$ is the price per unit)

At x = 1, the function $f(x)=x^4-48x^2+\alpha x+120$ attains its maximum value in the interval [0, 2], then the value of $\alpha$ is:

The largest interval, in which the function $f(x) = x^3 + 2x^2 - 1$ is increasing, is:

The slope of the tangent to the curve $x = at^2$, $y = 2at$ at 't' is :

Interval in which the function $f$ given by $f(x) = \tan x - 4x$, $x \in (0, \frac{\pi}{2})$ is strictly decreasing is

Let $f(x) = (x-a)^2+(x-b)^2+(x-c)^2$ then $f(x)$ has a minimum value at $x =$