I am quite hot but become too cold if you remove the first two letters. What am I?

Move three sticks of the spiral below to form a square.

Can you find out the remainder when 3^300 is divided by 5?

Which is the smallest number that you can write using all the vowels exactly once?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

In the figure, you can see nine stars. What you have to do is connect all of them by using just four line and without lifting your hand i.e. in a continuous flow.

I am beautiful, up in the sky. I am magical, yet I cannot fly. To people I bring luck, and to some people, riches. The boy at my end does whatever he wishes. What am I?

They are the five precious gems of an everyday sort and all can be found on a Tennis Court. Who are they?

A sea diver is a real show-off. He showed everyone that he can hold his breath underwater for 15 minutes.

I went to the diver and told him that I can be underwater for double the time i.e 30 minutes.
He responded that he will give me 100$ if I would be able to do it. I won 100$.

What did I do?