It seems you've uploaded a set of math questions. Here’s an analysis of one of them:

Example:

1. Question: A number when divided by 25 leaves a remainder of 13. What will be the remainder when the square of this number is divided by 25?

Solution: Let the number be $x$, and from the question, we know that: $x \equiv 13 \pmod{25}$ We need to find the remainder when $x^2$ is divided by 25: $x^2 \equiv 13^2 \equiv 169 \pmod{25}$ Now, divide 169 by 25: $169 \div 25 = 6 \text{ remainder } 19$ Thus, the remainder is 19.

Answer: The remainder when the square of the number is divided by 25 is 19, but it looks like 19 is not an option, so this may be a trick question.

Would you like further details or help on any specific question?

Here are 5 related questions for practice:

1. If a number divided by 30 leaves a remainder of 17, what will the remainder be when its square is divided by 30?
2. Find the smallest number that when divided by 45 leaves a remainder of 9.
3. What is the remainder when $15^2$ is divided by 20?
4. If a number gives a remainder of 4 when divided by 9, what will the remainder be when its cube is divided by 9?
5. What is the remainder when $99^2$ is divided by 25?

Tip: When dealing with remainders and modular arithmetic, try squaring, cubing, etc., the remainders directly to simplify calculations!