I have branches, but no fruit, trunk or leaves. 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?

If "P" means "-", "Q" means "/", "R" means "+", and "S" means "*" then find the value of the following:

21 Q 7 R 9 S 10 P 13

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

In a box, there is a jumble of 7 red balls, 6 blue balls, 5 green balls, and 4 yellow balls. What is the minimum number of balls, will you have to pick up so that you have at least 4 balls of the same colour?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

How can you drop a raw egg from a height onto a concrete floor without cracking it?