The number of ways of forming a queue of $4$ boys and $3$ girls such that all the girls are not together, is:

There are $m$ books in black cover and $n$ books in blue cover,and all books are different. The number of ways these $(m+n)$ books can be arranged on a shelf so that all the books in black cover are put side by side is

The number of different permutations that can be formed by taking $4$ letters at a time from the letters of the word '$REPETITION$' is

In how many ways can $5$ prizes be distributed among $4$ boys,if each boy can receive any number of prizes?

If all the words with or without meaning made using all the letters of the word $KANPUR$ are arranged as in a dictionary, then the word at $440^{th}$ position in this arrangement is:

$A$ number lock consists of three rings. If the $1^{st}$ ring is marked with digits $0$ to $9$,the $2^{nd}$ ring is marked with prime numbers greater than $2$ but less than $30$,and the $3^{rd}$ ring is marked with all vowels,find the total number of unsuccessful attempts.