Let N denote the set of all natural numbers. Define two binary relations on N as _R = {(x, y) $$ \in $$ N $$ \times $$ N : 2x + y = 10} and R₂ = {(x, y) $$ \in $$ N $$ \times $$ N : x + 2y = 10}. Then :

Two different families A and B are blessed with equal numbe of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $${1 \over {12}},$$ then the number of children in each family is :

If an angle A of a $$\Delta $$ABC satiesfies 5 cosA + 3 = 0, then the roots of the quadratic equation, 9x² + 27x + 20 = 0 are :

The mean and the standard deviation(s.d.) of five observations are9 and 0, respectively. If one of the observations is changed such that the mean of the new set of five observations becomes 10, then their s.d. is :