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

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

There is something which you can be arrested for attempting but not for successfully completing.

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.

A maths symbol is hidden in the below Bar Graph. Can you decipher it?

If you say my name, I will no longer exist. What am I?

If all the below statements are true

1. Gianni was either in Italy or France in 1997.
2. If Gianni did not kill Versace, Hilton must have killed him.
3. If Versace died of suffocation, then either Gianni killed him or Versace committed suicide.
4. If Gianni was in Italy in 1997, then Gianni did not kill Versace.
5. Versace died of suffocation, but he did not kill himself.

Who killed Versace and where was Gianni in 1997?

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

When monkey rotate the gear, which mark will be hit 1 or 2 ?

In the given picture, you can find two letters missing. When two particular letters are placed in the missing spots, you get an eight-letter word while reading in the anti-clockwise direction. Can you find out the missing letters and the missing word eventually?