Can you find out which number multiplied by itself will give the output as 12345678987654321?

The more you take me, the more you leave me behind.
Who Am I?

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

In a boat, the father of a sailor's son is sitting with the son of the sailor. However, the sailor is not present on the boat.

Can this even be possible?

There is a square piece of paper with a hole that is denoted by the circle on the top right side in the given picture. You have to cut the paper in a manner that it forms two and only two separate pieces of paper and then rearrange the pieces in a manner that the holes come in the centre of the paper.

A Man gave one of his sons 10 cents and another son was given 15 cents. What time is it?
Hint: Figure out the relation between time and number, is not so easy..:)

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

Below, you can see three complete equations and one incomplete. Based on the three complete ones, can you complete the incomplete one?

5 $ 4 $ 3 $ 9 = 4215
6 $ 9 $ 2 $ 6 = 3816
4 $ 7 $ 3 $ 3 = 1122
7 $ 2 $ 7 $ 4 = ____

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?