Can you convert the number zero(0) into a positive number using just one mathematical operator ?

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

A chess tournament is taking place on knock-out terms (the one who loses the match is out of the game).
(a) If 10 matches are played in total, how many players participated?
(b) If 20 players took part in the tournament, how many matches were played?

A man walked into a pub and went straight towards the Barman. He asked for a dirty martini from the Barman. The Barman thought something and then pulled out a pistol from his drawer and aimed it directly at the man. Why did he do that?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

I never was there, I am always to be.
You have never ever seen me, not ever you will.
Yet I am the confidence of everyone.

Who Am I?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

This is a picture puzzle. You have to guess the name of the movie that can be related to the picture.

What common phrase is represented by the below lines

Easy going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Medium going:
Weak, 'I'm going.'
Tough, 'I'm staying.'

Tough going:
Weak, 'I can't do it, I'm staying!'
Tough, 'Let's get going.'

On rolling two dices (six-sided normal dice) together, what is the probability that the first one comes up with a 2 and the second one comes up with a 5?