If all possible numbers are formed by using the digits $1, 2, 3, 5, 7$ without repetition and they are arranged in descending order,then the rank of the number $327$ is

There are $9$ chairs in a room on which $6$ persons are to be seated. Out of these,one person is a guest who must occupy one specific chair. In how many ways can they sit?

The teacher wants to arrange $5$ students on the platform such that the boy $B_1$ occupies the second position and the girls $G_1$ and $G_2$ are always adjacent to each other. Then,the number of such arrangements is

The number of natural numbers less than $1000$ in which no digit is repeated is

$A$ 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:

$A$ three-digit number $n$ is such that the last two digits are equal and differ from the first digit. The number of such $n$'s is: