Consider the sequence of numbers $(1,2,3, \ldots \ldots, 13)$. A person choose three numbers at random from the sequence. The probability that the chosen three number form an A.P. is

A mapping is selected at random from all mappings $f: A \rightarrow A$, where set $A=\{1,2,3 \ldots, n\}$. If the probability that the mapping is injective is $\frac{3}{32}$, then the value of $n$ is

If ' $a$ ' is an integer lying in $[-5,30]$, then the probability that the graph of $y=x^2+2(a+4) x-5 a+64$ lies above the $x-$ axis is

Four natural numbers selected at random are multiplied together, then the probability that the digit in the unit's place in the product be $1,3,7$ or 9 is