I have branches, but no fruit, trunk or leaves. What am I?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

The average age of 10 members of a committee is the same as it was 4 years ago, because an old member has been replaced by a young member.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

What does this rebus means ?

PROG WORKRESS

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

I make two people out of one. What am I?

I got a bee but no honey.
got an eye but am still blind.
got a sea but no water.
got a tea but no coffee.
got a why but no answer.

What Am I?

A seven-year-old kid challenged his classmates that he can make the number one disappear by adding something to it.

How can he do that?

What happened when the wheel was invented?