What does this simple rebus mean?

People put me on the table and cut me but do not eat me. What am I?

What is more useful when it is broken?

Find the last number in the series below:

voN luJ yaM raM ---

I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. What am I?

Can you find out the smallest number that can be conveyed as the sum of three squares in three unique ways?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?

Which statement is true out of the following?
One statement here is false.
Two statements here are false.
Three statements here are false.

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

I inserted a coin in a bottle and closed its mouth with the help of a cork. Now, I was able to take the coin out from the bottle without taking out the cork or breaking the bottle. Can you tell me how I did it?