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

The function $$f\left( x \right) = {x^2} = x + x + x + ....x$$ times, is defined

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

A product is an assemble of $$5$$ different components. The product can be sequentially assembled in two possible ways. If the $$5$$ components are placed in a box and these are drawn at random from the box, then the probability of getting a correct sequence is