Replace the question mark with the correct number, given the pair of numbers exhibits a similar relationship?

? : 3839 :: 11 : 1209

During an experiment, a guy throws a bouncy ball from a 100 feet tall building. The ball has a specific characteristic. Every time it hits the ground, it bounces up halfway.

How many bounces do you think the ball will make before it comes to a stop ?

Doctor Alex and a bus driver John are both in love with the same woman named Olivia. The bus driver need to go for a long trip of 10 days, Before he left he gave Olivia 10 apples.

It is an eleven letter word.
The first, second, third and fourth letters form a banquet's name.
The fifth, sixth and seventh letters form a car's name.
The eighth, ninth, tenth and eleventh letters form a mode of transport.

Can you identify what word it is?

I am a three digit number.
My tens digit is five more than my ones digit.
My hundreds digit is eight less than my tens digit.
What number am I?

There were three women in all the swimming costumes!
One was happy and the other two were sad!
The happy one was crying and the sad ones were smiling.
Why was this?

There were five men at church, and it started raining while they were outside. The four that ran still got wet, but the one that was still stayed completely dry. Why did he stay dry?

You see a mathematical expression in the picture. Can you think of a movie that this expression refers to?

It belongs to you, but other people use it more than you do. What is it?

Replace the question mark with the correct number in below Picture: