Can you solve the tricky chess rebus puzzle below by ciphering the hidden meaning?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

What's the best place to go shopping in the ocean?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

Find the next number in the sequence

5 12 24 36 ?

You need to arrange three 7 and mathematical symbols to form number 1?

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.

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

The day after tomorrow will be three days before Tuesday. Can you find out what is today?