Replace the question mark with the number below given a simple math problem.

There is a square of a particular number which when doubled, becomes 7 more than its quarter.

Can you find the number?

What has six faces, but does not wear makeup, has twenty-one eyes, but cannot see?

The barber of Town shaves all men living in the town. No man living in the town is allowed to shave himself. The barber lives in that town. Who then shaves the barber of the town?

You have two strings whose only known property is that when you light one end of either string it takes exactly one hour to burn. The rate at which the strings will burn is completely random and each string is different. How do you measure 45 minutes?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

A tree doubled in height each year until it reached its maximum height over the course of ten years. How many years did it take for the tree to reach half its maximum height?

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

What is in seasons, seconds, centuries and minutes but not in decades, years or days?