You can see it everyday, But cannot touch it at will. What is it?

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?

When it is alive we sing, when it is dead we clap our hands. What is it?

Teacher ask the student

'Why are you standing on that chair in music class ?'.

what did student replied ?

A man in a car saw a Golden Door, Silver Door and a Bronze Door. What door did he open first?

A large container is kept in open under the rain. Every passing hour, the water collected inside the container becomes double what it was.

In ten hours, the container is filled completely. Can you calculate how long would it have taken to be filled in half?

If,

6 / 7 = 2
3 / 9 = 7
8 / 2 = 6

Then

4 / 5 = ?

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

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?