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

A coin is tossed thrice. Let $$X$$ be the event that head occurs in each of the first two tosses. Let $$Y$$ be the event that a tail occurs on the third toss. Let $$Z$$ be the event that two tails occur in three tosses. Based on the above information, which one of the following statements is TRUE?

The solution to $$\,\,{x^2}{y^{11}} + x{y^1} - y = 0\,\,$$ is