$A$ stone is thrown vertically upwards from the top of a tower $64 \ m$ high according to the law $s=48t-16t^{2}$. The greatest height attained by the stone above the ground is (in $m$)

$A$ wire of length $20$ units is divided into two parts such that the product of one part and the cube of the other part is maximum. Then,the product of these parts is:

If $\frac{dy}{dx} = (x - 1)^3 (x - 2)^4$,then $y$ has:

Let $f(x)$ be a polynomial of degree $3$ such that $f(-1)=10$,$f(1)=-6$,$f(x)$ has a critical point at $x=-1$,and $f^{\prime}(x)$ has a critical point at $x=1$. Then $f(x)$ has a local minima at $x=$

$A$ box open from the top is made from a rectangular sheet of dimensions $a \times b$ by cutting squares of side $x$ from each of the four corners and folding up the flaps. If the volume of the box is maximum,then $x$ is equal to:

The cost function at American Gadget is $C(x) = x^3 - 6x^2 + 15x$ (where $x$ is in thousands of units and $x > 0$). The production level at which the average cost is minimum is: