Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

Can you find out the remainder when 3^300 is divided by 5?

Our product and our sum always give the same answer. Who are we?

I am a type of room you cannot enter or leave. Raised from the ground below, I could be poisonous or a delicious treat. What am I?

Which flower has two lips?

A convention is held where all the big logicians are summoned. The master places a band on everyone's forehead. Now all of them can see others bands but can't see his own. Then they are told that there are different colours of bands. All the logicians sit in circle and they are further explained that a bell will ring at regular intervals. The moment when a logician knew the colour of band on his forehead, he will leave at the next bell. If anyone leaves at the wrong bell, he will be disqualified.

The master assures the logicians that the puzzle will not be impossible for anyone of them. How will the logicians manage ?

Lifeless eyes on my smiling face and watch your child's sleeping place. In their dreams they hold me tight. What am I?

There was a competition where the contestants had to hold something. At the end of the event, the winner was a person who had no hands or feet. What was it that the contestants had to hold?

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

An apple seller is hosting a competition. He offers 1000 apples and 10 boxes to the people who pass by. The challenge is to put those 1000 apples in the 10 boxes in such a manner that if he asks for any amount of apples, the person can directly give him the boxes or a combination of boxes. If the person can do it, he promises to give a thousand apples for free.

If you happen to pass by the apple seller, will you be able to win a thousand apples?