What is harder to catch the faster you run?

I am the beginning of everything, the end of everywhere. I'm the beginning of eternity, the end of time and space. What am I?

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member. Find how much younger is the new member ?

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

Can you find the number?

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

You see me once in June, twice in November, and not at all in May. What am I?

Take away my first letter, then take away my second letter. Then take away the rest of my letters, yet I remain the same. What am I?

A number with an interesting property:

When I divide it by 2, the remainder is 1.
When I divide it by 3, the remainder is 2.
When I divide it by 4, the remainder is 3.
When I divide it by 5, the remainder is 4.
When I divide it by 6, the remainder is 5.
When I divide it by 7, the remainder is 6.
When I divide it by 8, the remainder is 7.
When I divide it by 9, the remainder is 8.
When I divide it by 10, the remainder is 9.

It's not a small number, but it's not really big, either.
When I looked for a smaller number with this property I couldn't find one.

Can you find it?

What Time Should the last watch show in the below figure?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?