The sum of all three-digit numbers,formed using non-zero digits,where all the digits are perfect squares of a natural number,is

$A$ letter lock consists of three rings with $15$ different letters each. If $N$ denotes the number of ways in which it is possible to make unsuccessful attempts to open the lock, then:

The total number of two-digit numbers $n$ such that $3^{n} + 7^{n}$ is a multiple of $10$ is ..... .

For which value of $n \in N$,does $n!$ have $13$ trailing zeros?

The number of positive integral solutions of $abc = 30$ is

In a relay race there are five teams $A, B, C, D$ and $E$. What is the probability that $A, B$ and $C$ are the first three to finish (in any order)? (Assume that all finishing orders are equally likely.)