The dirtier I get, the whiter I look. Who am I?

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

A man started to town with a fox, a goose, and a sack of corn. He came to a stream which he had to cross in a tiny boat. He could only take one across at a time. He could not leave the fox alone with the goose or the goose alone with the corn. How did he get them all safely over the stream?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

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

I have an eye but still cannot see.

Who am I?

What has one letter and starts with an E?

What can run but never walk, have a mouth that never speaks, have a head that never weeps, and have a bed but never sleeps?

If an electric train is travelling south, then which way is the smoke going?

I am a white box having no key or lid.
Yet there is a golden treasure inside it.

What Am I?