The letters of the word $MODESTY$ are written in all possible orders and these words are written out as in a dictionary. Then,the rank of the word $MODESTY$ is:

Find the number of distinct arrangements of the letters of the word $CALCUTTA$.

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:

How many words can be formed using the letters of the word $COURTESY$ such that the first letter is $C$ and the last letter is $Y$?

How many $3$-digit even numbers can be formed using the digits $1, 2, 3, 4, 6, 7$,if no digit is repeated?

If $3$ books on Physics,$2$ books on Chemistry,and $4$ books on Mathematics are to be arranged on a shelf so that all the Physics books are together and all the Mathematics books are together,then the number of such arrangements is