The number of times the digit $5$ will be written when listing the integers from $1$ to $1000$ is

Let $x$ and $y$ be two $2$-digit numbers such that $y$ is obtained by reversing the digits of $x$. Suppose they also satisfy $x^2-y^2=m^2$ for some positive integer $m$. The value of $x+y+m$ is

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word $'EXAMINATION'$ is

The tens digit of the sum $1! + 4! + 7! + 10! + 12! + 13! + 16! + 17!$ is divisible by which of the following?

All the letters of the word $ANIMAL$ are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word $ANIMAL$ is $x$,then the permutation with rank $x$,among the permutations obtained by permuting the letters of the word $PERSON$ and arranging the permutations thus formed in dictionary order is

$A$ bag contains $n$ white and $n$ black balls. Pairs of balls are drawn at random without replacement successively,until the bag is empty. If the number of ways in which each pair consists of one white and one black ball is $14400$,then $n$ is equal to