I have no doors but I have keys, I have no rooms but I have space, you can enter but you can’t leave! What am I?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

I shave every day, but my beard stays the same. What am I?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

Solve the following series:
AZ, GT, MN, __, YB

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?

There was an aeroplane crash, every single person died, but two people survived. How is this possible?

What can jump higher than a building?

Which part of London exists in France as well ?

A donkey is behind another donkey
I'm behind that second donkey
But there is a whole nation behind me

It is a murder you can describe in a word.