What does this mathematical rebus means ?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

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

? : 3839 :: 11 : 1209

What are the next two letters in the following series and why?
W A T N T L I T F S _ _

*Hint: Check Puzzle Title

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

Move three sticks of the spiral below to form a square.

In the figure, you can see nine stars. What you have to do is connect all of them by using just four line and without lifting your hand i.e. in a continuous flow.

13 decks of cards have been mixed. What is the minimum number of cards that must be taken out from the above-mixed cards to guarantee at least one 'four of a kind?

In a basket of apples,
when counted in twos, there was one extra
when counted in threes, there were two extra when counted in fours, there were three extra
when counted in fives, there were four extra
when counted in sixes, there was five extra.

However, if the apples were counted in sevens, no extra apple was left. Can you calculate the minimum number of apples that were present in the basket?

A new clothing store has a unique method of pricing items. A vest costs $20, a tie costs $15, a blouse costs $30, and underwear costs $45. How much would pants cost?