What happened when the wheel was invented?

Can you solve below mathematical equation?

2^1234 - 2^1233

Give it food and it will live; give it water and it will die.

Jack and Joseph are well-known golf rivals. One Day during a match, they were level at a score of 30. Jack hit a bad shot and Joseph added 10 to his score. Joseph then hit an awesome shot and he won the game.

How ?

Can you fill the blank with the correct number?

6 30 870 756030 _____

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

You order chicken wings at KFC in the boxes of 6, 9 and 20. What is the largest number of wings that you cannot obtain by buying in any combination of the boxes?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?

What number when divided in half becomes zero?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?