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

How many numbers of $6$ digits can be formed from the digits of the number $112233$?

The total number of $3$-digit numbers,whose sum of digits is $10$,is

How many words can be formed with the letters of the word $MATHEMATICS$ by rearranging them?

How many $3$-digit numbers are there with no digit repeated?

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?