What is both possible and impossible at the same time?

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 am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?

If we change the South-East direction into North and North-East into West and all others similarly.
Can you find out which direction will be in the place of South-West direction?

You have four chains. Each chain has three links in it. Although it is difficult to cut the links, you wish to make a single loop with all 12 links. What is the fewest number of cuts you must make to accomplish this task?

A maths symbol is hidden in the below Bar Graph. Can you decipher it?

Which is the correct shadow of the bird?

You knock a Table over in the library, and suddenly 20 eyes are looking at you.

You have two rectangular wires.

Both of them have property that when you light the fire from one end , it will take 60 minutes to get completely burn.

However, they do not burn at consistent speed (i.e it might be possible 1st 20% burn in 50 minutes and 80% can burn in 10 minutes).

So how could you measure 45 minutes ?

There's one "sport" in which neither the spectators nor the participants know the score or the leader until the contest ends.

What is it?