If 21x = 79x, what is the value of x?

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

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

In an office's desk, you find a unique method that shows the current day of the month. Two numbered cubes are used to depict the current date.

Can you find out the numbers on both the cubes so that each date can be mentioned using them?

Please note that you have to use both the cubes to display any date. Thus the 1st day must be represented by 01 and so on.

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

It has horns but can’t beep. It is like to bleat but It is not a sheep. What is it?

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 ?

Manish and Manoj play 5 games of chess.
Both Manish and Manoj win the exact same number of games. There is no tie at all.

How?

Get total of 120 by using five zeros 0,0,0,0,0 and any one mathematical operator.
Do you ?

You need to complete the maze by entering from the entrance marked below in the figure near the yellow circle, bottom left and leaving from the exit point near the green circle, bottom middle.

Rule of Game: You can move only by exchanging green and yellow circles.