Find the number of different signals that can be generated by arranging at least $2$ flags in order (one below the other) on a vertical staff,if five different flags are available.

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 sum of all the $4$-digit numbers formed by taking all the digits from ${2, 3, 5, 7}$ without repetition is:

The number of times the digit $3$ will be written when listing the integers from $1$ to $1000$ is

An eight-digit number divisible by $9$ is to be formed using digits from $0$ to $9$ without repeating the digits. The number of ways in which this can be done is

There are three sections in a question paper,each containing $4$ questions. If a candidate has to answer only $5$ questions from this paper without leaving any section,then the number of ways the candidate can make the choice of questions is: