$A$ polygon has $35$ diagonals; then the number of its sides is:

Let $A$ be a set containing $10$ distinct elements. Then the total number of distinct functions from $A$ to $A$ is:

How many three-digit numbers can be formed from the digits $2, 3, 5, 6, 7,$ and $9$ which are divisible by $5$,given that no digit is repeated?

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

Let $n$ be the number of different $5$-digit numbers,divisible by $4$,formed with the digits $1, 2, 3, 4, 5,$ and $6$,such that no digit is repeated in the numbers. What is the value of $n$?

In how many different ways can the letters of the word '$DETAIL$' be arranged in such a way that the vowels occupy only the odd positions?