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

? : 3839 :: 11 : 1209

John bought a new car. He has a habit of eating ice cream from a particular ice cream shop while returning home from office. Whenever, he eats strawberry ice cream, he faces no problem. But whenever, he eats chocolate ice cream, the car starts giving problem. At first, he thinks, it is just a co-incidence but when this awkward incident happens for 3-4 times, he reports this problem to the company.

The mechanic of the company checks but finds no problem at all. The next day, when he stops by to eat chocolate ice cream, the car again starts giving problem.

Can you find the possible reason?

Irene killed hundreds of people mercilessly and yet the police were not able to put her behind the bars. Why?

I know a nine-letter word having only one vowel.
Do you ?

You are presented with three boxes. One of them has a red ball inside and the other two have a black ball inside each of them. You are asked to pick up the one with red ball and you pick one. Now, one of the other boxes is opened and it is found to have a black ball.

You are presented with a chance to change your box with the one that is left closed. Will you change your box? Why or why not?

Look at this sequence from top to bottom. What is the next number in the sequence?
1
11
21
1211
111221
312211

A and B have a certain number of chocolates with them. If B gives one chocolate to A, they will have an equal number of chocolates. But if A gives one chocolate to B, then A will be left with half the number of chocolates that B has.

Can you find out the number of chocolates they have right now?

I am the beginning of everything, the end of everywhere. I'm the beginning of eternity, the end of time and space. What 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.

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?