What is so fragile that saying its name breaks it?

Can you find out the remainder when 3^300 is divided by 5?

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?

What can jump higher than a building?

Why do you find that most of the buildings are deprived of the 13th floor?

You are a cab driver who pools passengers. You pick 3 people from a destination and drop 1 after an hour. 2 people climb aboard at the same time and you drop 3 at the next destination. After some time, you pick 2 passengers only to drop 1 after a short distance where 3 more passengers climb up the cab. You leave the rest of the passengers one by one to their destination and then come back home.

Can you tell the eye color of the cab driver?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

Can you count the number of lines in the below picture?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

If you go to the movies and you're paying, is it cheaper to take one friend to the movies twice, or two friends to the movies at the same time?