Find the next number in the sequence

1, 2, 6, 21, 88, __?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

How many sides does a circle have?

A King wants to send the diamond ring to his girlfriend securely. He got multiple locks and their corresponding keys. His girlfriend does not have any keys to these locks and if he sends the key without a lock, the key can be copied in the way. How can King send the ring to his girlfriend securely?

I am Huge on Sunday and Saturday.
I am small from Tuesday to Thursday.
I do not exist on Monday and Friday.
Who am I?

Assume there are approximately 5,000,000,000 (5 billion) people on Earth. What would you estimate to be the result, if you multiply together the number of fingers on every person's left hand? (For the purposes of this exercise, thumbs count as fingers, for five fingers per hand.) If you cannot estimate the number then try to guess how long the number would be.

P is the father of Q and S is the son of R. T is the brother of P and has a daughter U. If R is the sister of P, then what is the relation between U, Q and S?

John gave half of the apples he had plus one more to Jacob. He gave half of the remaining ones plus one more to James. Now, John was left with just one apple.

Can you find out how many did he have in the beginning?

Where do you go to learn how to make ice cream?