If $\alpha = {^m}{C_2}$,then ${^\alpha}{C_2}$ is equal to

The number of words which can be formed from the letters of the word $MAXIMUM$,if two consonants cannot occur together,is

$A$ customer forgets a $4$-digit code for an Automatic Teller Machine ($A$.$T$.$M$.) in a bank. However,he remembers that this code consists of digits $3, 5, 6$ and $9$. Find the largest possible number of trials necessary to obtain the correct code.

$A$ set contains $(2n + 1)$ elements. The number of subsets of the set which contain at most $n$ elements is:

$n$ gentlemen can be made to sit on a round table in how many ways?

The principal wants to arrange $5$ students on the platform such that the boy $SUNIL$ occupies the second position and such that the girl $GITA$ is always adjacent to the girl $NITA$. How many such arrangements are possible?