Why 1729 is a magic number? Answer Logically.

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?

There are two insects on a tile. Insect X is sitting on one side of the tile (point A) and Insect Y is sitting opposite on the other side of the tile (point B). Now both of them decide to change their position and thus X starts crawling to point B and Y starts crawling to point A. When they meet and pass each other in between, X takes 20 seconds to reach B and Y takes just 5 seconds to reach A.

Can you calculate the total time each of the insects took to change their positions?

I am written with two letters.
I said with the one.
I usually am seen with the two.

Who am I?

I have an eye but still cannot see.

Who am I?

In a science lab, a petri dish hosts a healthy colony of yeast for an experiment. Now every minute, all the yeast cells divide into two. At noon, there was just a single cell of yeast and at 1:22, the Petri dish was half full. Can you calculate when the dish will be full of yeast?

Below rebus represent famous DiCaprio movie. Can you name it?

You are playing a game with your friend Jack. There are digits from 1 to 9. You both will take turn erasing one digit and adding it to your score. The first one to score 15 points will win the game.

Would you want to play first or second?

PS: The sum should be exactly 15.

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

Only one color, but not one size,
Stuck at the bottom, yet easily flies.
Present in sun, but not in rain,
Doing no harm, and feeling no pain.
What is it?