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

? : 3839 :: 11 : 1209

You see me once in June, twice in November, and not at all in May. What am I?

Client Dempsey living in one of the East Coast states of the U.S. was talking to Landon Donovan, who was living in the West Coast state of the U.S.

Dempsey: What time is it?
Donovan: Wow, It is the same time here.

How is this possible?

An office is divided into 8 cubicles. How many of the cubicles are painted if only 1/8 of the cubicles are painted?

What has lots of eyes, but can’t see?

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

Queen Elizabeth organised a royal party.

To Avoid uninvited guest royal family set a password.
Jack (an uninvited person) plan to enter the party. He stand nearby the door.

First guest comes, the security person said 'twelve' and guest replied with six.
Second guest comes , the security person said 'six' and guest replied with 'three'.

Jack thought is enough and he walked to the entry point. The security person said 'eight' , Jack replied smilingly 'four'.
He was immediately thrown out of the party. why ?

I can be cracked, made, told, and played. What am I?

I make two people out of one. What am I?

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?