What is the word or phrase?

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?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?

Make eight squares by moving only two matchsticks.
Note- Square can be of different sizes.

The person who makes it has no need for it. He who purchases it does not use it. The person who does use it does not know they are. What is it?

A lion and its tamer are standing inside a cage that measures 1 unit in radius. Both of them can effortlessly run at the speed of 1 unit maximum.

1) Suppose the lion is hungry, will he be able to eat up the tamer?
2) If yes, how long can the tamer survive?

During a secret mission, an agent gave the following code to the higher authorities
AIM DUE OAT TIE MOD

However, the information is in one word only and the rest are fake. To assist the authorities in understanding better, he also sent them a clue, If I tell you any one character of the code, you can easily find out the number of vowels in the codeword.

Can you find out the code word?

Prove that the below maths equation is true.

8 + 8 = 91

To tease, King Akbar told his most clever advisor Birbal to give his daughter one thing that she can eat when hungry, drink if she feels thirsty and can burn if she feels cold. King Akbar was shocked when Birbal gave Akbar's daughter one such thing that satisfies all of the above.

What did Birbal give to Akbar's daughter?

Christina has four daughters, and each of her daughters has a brother. How many children does Christina have?