I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

1. What does:
TIM JOB
represent?

2. What does:
MO_ _
represent?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say "Every prisoner has been in the special room at least once". If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?

Can you move 2 matchsticks to form four equal sized squares.

A man calls his dog from the opposite side of a river. The dog crosses the river without a bridge or a boat and manages to not get wet. How is this possible?

I am a type of word that is spelt incorrectly or used differently, on purpose for humour. What am I?
Hint 1: You can find me in a joke.
Hint 2: I am a play on words.

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

There are 2 people near the river and both of them want to get on the other side. The boat can only take one of them. But they got across.
How?