$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

$A$ dictionary is printed consisting of $7$-lettered words only that can be made using the letters of the word $CRICKET$. If the words are arranged in alphabetical order,as in an ordinary dictionary,then the number of words before the word $CRICKET$ is:

Six identical coins are arranged in a row. The number of ways in which the number of tails is equal to the number of heads is

The number of natural numbers less than $1000$,in which no two digits are repeated,is:

In how many ways can $5$ girls and $3$ boys be seated in a row so that no two boys are together?

How many words can be formed using the letters of the word $MAXIMUM$ such that no two vowels are together?