In how many ways can $15$ members of a council sit along a circular table,if the Secretary must sit on one side of the Chairman and the Deputy Secretary on the other side?

If the ratio $C(2n, 3) : C(n, 3)$ is equal to $11 : 1$,find $n$.

The number of words (with or without meaning) that can be formed from all the letters of the word "$LETTER$" in which vowels never come together is

$A$ committee of $12$ is to be formed from $9$ women and $8$ men in which at least $5$ women have to be included in a committee. Then the number of committees in which the women are in majority and men are in majority are respectively

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)

For a set of $5$ true-or-false questions,no student has written all the correct answers,and no $2$ students have given the same sequence of answers. What is the maximum number of students in the class,for this to be possible?