Average MCQs

If the average of x and $$\frac{1}{x}$$ (x $$ \ne $$ 0) is M, then the average of x² and $$\frac{1}{{{x^2}}}$$ is :

A man has 'n' magical eggs whose average weight is 'k' gm. Each of the 'n' eggs produces 'n' eggs next day such that the average weight of 'n' eggs produced is same as that of the parental egg for each 'n' groups individually i.e. each egg produces 'n' eggs of next generation and average weight of all the 'n' eggs of next generation is same as the weight of the mother egg. This process is continued without any change in pattern. What is the total weight of all the eggs of r^th generation, where the initial number of eggs with man are considered as the eggs of first generation.

The average of x numbers is y² and the average of y numbers is x². So the average of all the numbers taken together is: