What is both possible and impossible at the same time?

What is greater than gold but cannot be bought. it can never be sold and can earn if its sought. though it can be broken, it can still be fixed. for by birth it can't start nor by death it is ended.what am i?

A professor thinks of two consecutive numbers between 1 and 10.
'A' knows the 1st number and 'B' knows the second number

A: I do not know your number.
B: Nor do I know your number.
A: Now I know.

What are the four solutions for this?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

What is the longest word in the dictionary?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

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

A sundial has the fewest moving parts of any timepiece. Which has the most?

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

Name a key which is hardest to turn.