Can you solve below mathematical equation?

2^1234 - 2^1233

French Police inspects a room where there are no windows, no doors, no tables and is almost empty expect there is just a puddle of water. They found a dead man who obviously hung herself from the ceiling, but they are not able to figure out how this had happened.

John and Jacob entered the crime scene and easily able to solve the case.

How did the man die?

In a mathematical quiz, you are asked the following question:

Use three 9s in a mathematical expression without dividing or multiplying to form the number one.

Can you answer the question?

Mr Red Lives in the red house.
Mr Green Lives in the greenhouse.
Mr Yellow Lives in the yellow house.

Who lives in the Whitehouse?

If you’ve got me, you want to share me; if you share me, you haven’t kept me. What am I?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

If,
9 * 8 * 7 = 65
8 * 7 * 6 = 50
7 * 6 * 5 = 37

Find
6 * 5 * 4 = ?

Can you find out the missing number?

? 4 5 3 5

9 5 7 10 3

While preparing the table for dinner, wife came up with an idea to tease his mathematician husband. She asked her husband to pick nine toothpicks and make ten without breaking any toothpick.

The husband was also smart and did it within seconds. How ?

I have no life, but I can die. What am I?