If two different numbers are taken from the set $\left\{ {0,1,2,3, \ldots ,10} \right\}$, then the probability that their sum as well as absolute difference are both multiple of $4$, is 

There are $3$ bags $A, B$ & $C$. Bag $A$ contains $1$ Red & $2$ Green balls, bag $B$ contains $2$ Red & $1$ Green balls and bag $C$ contains only one green ball. One ball is drawn from bag $A$ & put into bag $B$ then one ball is drawn from $B$ & put into bag $C$ & finally one ball is drawn from bag $C$ & put into bag $A$. When this operation is completed, probability that bag $A$ contains $2$ Red & $1$ Green balls, is -

A bag contains $3$ red, $7$ white and $4$ black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is

Two numbers $x$ $\&$ $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, ......, 1000\}$. Then the probability that $|x^4 - y^4|$ is divisible by $5$, is -

A bag contains $6$ white, $7$ red and $5$ black balls. If $3$ balls are drawn from the bag at random, then the probability that all of them are white is