Riddles of what can clap but has no hand

I start with M, end with X, and have a never ending amount of letters.
What am I?

Answer

Mailbox.

You have a bag with 'N' strings in it. You randomly grab two ends and tie them together until there are no more loose ends.
In the end, what is the expected number of loops (strings tied to their own end)?

Answer

1 + 1/3 + 1/5 ... + 1/(2N-1).

Each time you tie two together the number of string ends available decreases by 2. The chance of grabbing a string and its end is 1/(2N-1).

In a four-competitor track and field race, it is known that: C has come immediately behind B, and D has come in between A and C.
Could you calculate the order of arrival?

Answer

1. B
2. C
3. D
4. A

As a stone inside a tree, I'll help your words outlive thee. But if you push me as I stand, the more I move the less I am.
What am I?

Answer

Pencil.

My first letter comes before my second, with a conjunction in-between. I'm flat or even digital and I may serve the queen!

Answer

M&S

Why doesn't a mountain covered with snow catch cold?

Answer

Because it has a snowcap :)

The artery was cut, but not a drop of blood was drawn. How?

Answer

Artery also means a way of transportation, so the road was cut, or being constructed on. No blood was drawn!

Frank was born in 1933 and died in 1946 at the age of 75.
How is possible?

Answer

He was born in room 1933 of Hospital.

Move only one digit to fix the following equation:

98 - 102 = 96

Answer

98¹ - 2 = 96

A man goes into a bathroom, shoots himself and walks out. How is he still alive?

Answer

He shot his reflection in the mirror.

What has no beginning and no end?

Answer

A circle

If I have it, I don't share it. If I share it, I don't have it.
What is it?

Answer

Secret.