Why is a river so rich ?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

In a jungle where there are no street lights or any other artificial source of lights, I notice a black snake crossing the road.
How did I get sight of the snake?

People put me on the table and cut me but do not eat me. What am I?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

The picture shows the dice results in each couple of throws. If they are actually following a pattern, can you find out the missing one?

I am a normal creature, but I have five hands. I can even have more but even then I will be considered normal.

Who am I?

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

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?