Find the number of squares in the below picture

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.

What is the next number in this series?

4,12,84,3612....

When I asked a girl's name she told me her name is the date '07/09/2001'.

I thought for a few seconds and then I got her name. Do you?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

Which is Odd One Out and why?

4377

3954

9862

8454

9831

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?