I shave every day, but my beard stays the same. What am I?

Three cars are driving on a track that forms a perfect circle and is wide enough that multiple cars can pass anytime. The car that is leading in the race right now is driving at 55 MPH and the car that is trailing at the last is going at 45 MPH. The car that is in the middle is somewhere between these two speeds.
Right now, you can assume that there is a distance of x miles between the leading car and the middle car and x miles between the middle car and the last car and also, x is not equal to 0 or 1.
The cars maintain their speed till the leading car catches up with the last car and then every car stops. In this scenario, do you think of any point when the distance between any two pairs will again be x miles i.e. the pairs will be x distance apart at the same time ?

I know a country, If you remove the last alphabet of its name, it will become a part of your body. Do you name it?

I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I?

Name one eight-letter word with 'kst' in the middle, 'in' the beginning, 'and' at the end.?

Consider this: Arnold Schwarzenegger has a big one. Michael J. Fox has a small one. Prince doesn’t have one. The Pope has one but never uses it. Bill Clinton has one and uses it all the time. What is it?

An artist while painting a scenic beauty, decides to paint three layers of blue colour on the sky.

Which layer will go on the first?

Find three numbers such that When we multiply three numbers, we will get the prime numbers. The difference between the second and the first number is equal to the third and second.

The centre of the third figure is empty. What digit should fit inside?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?