In a metal casting process, molten copper alloy is poured into a sand mould. The level of molten metal in the pouring basin is at a height of $$300$$ $$mm$$ from the runner having diameter of $$10$$ $$mm.$$ If the density and melting temperature of molten copper alloy are $$9000$$ $$kg/{m^3}$$ and $${1000^ \circ }C.$$ respectively then the rate of flow of molten metal into the mould neglecting friction and other losses, in $$c{m^3}/s,$$ is ______________.

In numerical integration using Simpson's rule, the approximating function in the interval is a

The value of $$\mathop {\lim }\limits_{\left( {x,y} \right) \to \left( {0,0} \right)} {{{x^2} - xy} \over {\sqrt x - \sqrt y }}$$ is

The curve $$\,\,y = {x^4}\,\,$$