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

If the number of $5$-element subsets of the set $A = \{a_1, a_2, \dots, a_{20}\}$ of $20$ distinct elements is $k$ times the number of $5$-element subsets containing $a_4$,then $k$ is

$A$ question paper had ten questions. Each question could only be answered as True $(T)$ or False $(F)$. Each candidate answered all the questions. Yet,no two candidates wrote the answer in an identical sequence. How many different sequences of answers are possible?

The number of ways in which $5$ beads of different colours form a necklace is

Find how many words can be formed out of the letters of the word '$ORIENTAL$' so that vowels always occupy the odd places.

In how many ways can $5$ sportsmen be selected from a group of $10$?