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

Spelt forwards I’m what you do every day, spelled backwards I’m something you hate. What am I?

Replace the question mark with the correct number.

2 + 2= 4
3 + 3= 18
4 + 4= 48
5 + 5= ?

There are five people. One of them shot and killed one of the other five.
We know following clues:
1. Dan ran in the NY City Marathon yesterday with one of the innocent men.
2. Mike consider being a farmer before he moved to the city.
3. Jeff is a top notch computer consultant and wants to install Ben new computer next week.
4. The murderer had his leg amputated last month.
5. Ben met Jack for the first time six months ago.
6. Jack has been in seclusion since the crime.
7. Dan used to drink heavily.
8. Ben and Jeff built their last computers together.
9. The murderer is Jack's brother. They grew up together in Seattle.

Consider yourself to be a famous detective "Sherlock Homles", Can you find the killer?

If you remove one from eleven, it becomes ten. If you remove one from nine, it becomes ten.

How is this possible?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

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?

A word I know,
Six letters contain,
Subtract just one,
And twelve is what remains.

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

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?