What brings you down but never up?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

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

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

I am sure no one can have two things for dinner. what are they?

Three fair coins are tossed in the air and they land with heads up. Can you calculate the chances that when they are tossed again, two coins will again land with heads up?

The two towns are exactly 100 km apart. John leaves City A driving at 30 km/hr and Jacob leaves City B half an hour later driving at 60 km/hr. Who will be closer to City A when they meet?

What have one eye but still cannot see?

Which point will the car reach to go out?

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