What has one letter and starts with an E?

Seven Robbers robbed a bank and hide the coins in a lonely place.
They decide to divide the money equally the next morning. Two greedy robbers decided to cheat the others and reach the place at night. They equally divided the coins between them, one coin left. So they called another robber and then they decided to divide equally among the three. Sadly again one coin left. The same thing happened to the 4th 5th and the 6th robber.
However, when the 7th robber reached in the morning, they can divide the coins equally.

How many coins were there in total?

I possess a head

I flaunt a tail

But I don't have mouth or legs

Can you find out who I am?

When my father was 31 I was 8. Now he is twice as old as me. How old am I?

In four steps you need to move the word 'cold' From 'warm' by replacing one alphabet at a time such that every word formed at each step is acceptable in English Dictionary.

If,

A = 1

B = 2

C = 3

...

...

Z = 26.

Based on above rule, you need to find an eleven letter word whose letter sum is equal to 52.

What is more useful when it is broken?

I get hot but I never sweat,
I cook food but I am not a chef,
I have a door but you can't enter me,
I have a light but I am not a lamp.
Who am I?

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?

Twenty frogs are sitting on a log floating on the surface of a river. Two of them decide to jump off into the water.

How many frogs are there on the log at this moment?