What country can make you shiver?

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

A couple went on a climbing trip. But only the husband returned from the vacation and said that his wife slipped off while climbing and died. On investigating, the local sheriff arrested him saying, 'Your travel agent called. You murdered your wife.'

The man did not inform anyone about the trip. Then how was the agent so sure that it was a murder?

A quarter is one-fourth of a dollar but Mr. John has changed the equation as below :

DOLLAR * 4 = QUARTER

Can you replace each letter with a digit to make the above solution correct?

Look at the below sequence of letters and tell us what the next letter should be:

O T T F F S S ?

What has a ring but no finger?

You need to move three matchsticks to form three squares. Can you do it?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

My location can be determined by the below rebus.
So where am i ?

A man is walking down a road with a basket of eggs. As he
is walking he meets someone who buys one-half of his eggs
plus one-half of an egg.
He walks a little further and meets another person who buys
one-half of his eggs plus one-half of an egg.
After proceeding further he meets another person who buys
one-half of his eggs plus one half an egg. At this point, he
has sold all of his eggs, and he never broke an egg.
How many eggs did the man have to start with?