A cat had three kittens: Snophy, Topsy and Jorden. What was the mother's name?

I look flat, but I am deep. Hidden realms I shelter. Lives I take, but the food I offer. At times I am beautiful. I can be calm, angry, and turbulent. I have no heart but offer pleasure as well as death. No man can own me, yet I encompass what all men must have. What am I?

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?

You have a square. What you have to do is cut and reassemble the square such that you create a Red Cross sign that has the same volume as that of the square.

You are given 16 witch hats. The hats are divided in four different colours – red, blue, green and yellow. Every colour has been assigned to four hats. Now each of the hat will be glued with a label of an arithmetic sign – ‘+’, ‘-‘, ‘x’ or ‘/’. But you can label one sign only once on one colour. In such an arrangement, the hats can be uniquely defined by its colour and symbol.

Can you arrange all the 16 hats in a 4x4 grid in a fashion that no two rows and columns have a repetition of colour or sign?
We have arranged four hats in the below picture to assist you.

An express train takes 3 seconds to enter the tunnel which is 1 km long.
If it is travelling at 120 km an hour, how long will it take to pass completely through the tunnel?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

Can you spot the hidden girl in the picture below?

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?

Jack have ten pairs of black socks, eight pairs of white socks and seven pairs of green socks. Everything is mixed in a draw. As there is no light he were not able to identify the colour of the socks. How many of the socks did he want to take to match one pair