What is the coolest letter in the alphabet?

I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

John was visiting his friend Jacob. He found out that his friend's wife had just killed a burglar in self-defense.
John asks Jacob about what happened and he told that "His wife was watching television when suddenly the bell rang. She thought that it is her husband Jacob but she found the burglar who attacked her instantly and she got so frightened that she killed the burglar immediately with the knife.
John asked the police to arrest his friend's wife. Why?

John is asked to stand behind Jacob and Jacob is asked to stand behind John. Both of them feel confused about it and don't know what to do?

But it is quite possible, do you know how?

what does the below math rebus puzzle mean?

What is wrong in the below Picture?

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

When you stop to look, you can always see me. But if you try to touch me, you can never feel me. Although you walk towards me, I remain the same distance from you. What am I?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

What number comes next in this sequence:
7 8 5 5 3 4 4 _