How can you make number one disappear by adding something to it?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

I welcome the day with a show of light, I stealthily came here in the night. I bathe the earthy stuff at dawn, But by noon, alas! I'm gone.

What number replaces the question mark

A man comes across a coin that is dated 226 B.C. Can you calculate its worth?

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?

If 1+9+8=1, what is 2+8+9?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside. The man said, "Oh! I am really sorry, I thought this was my room." He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man. What made her suspicious of that man? He might have been genuinely mistaken.

I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

Can you identify the hidden rebus in the image below?