Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

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?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

Always in you, Sometimes on you;

If I surround you, I can kill you.

What am I?

How many times in a given day, minutes and hour clock comes in a straight line ?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?

It is always ahead of me yet I can never see it. What is it?

What can you catch but never throw?