$A$ stone thrown upwards has its equation of motion $s = 490t - 4.9t^2$. Then the maximum height reached by it is:

If the petrol burnt in driving a motor boat varies as the cube of the velocity,then the speed (in $km/h$) of the boat relative to the water,going against a water flow of $C \ km/h$,so that the quantity of petrol burnt is minimum,is:

Given $P(x) = x^4 + ax^3 + bx^2 + cx + d$ such that $x=0$ is the only real root of $P'(x) = 0$. If $P(-1) < P(1)$,then in the interval $[-1, 1]$:

$20$ is divided into two parts such that the product of the cube of one part and the square of the other part is maximum. The parts are:

$20 \ m$ of wire is available to fence a flower bed in the form of a circular sector. If the flower bed should have the greatest possible surface area,then the radius of the circle is (in $m$)

Find two positive numbers $x$ and $y$ such that $x+y=60$ and $x y^{3}$ is maximum.