I am a seven-letter word but if you remove four of my letters I will have one left. What word am I?

You find yourself in a strange place guarded by two guards.One of the guard always say truth while other always lies.You don't know the identity of the two.You can ask only one question to go out from there. What should you ask?

You have to fill the below given grid in a manner that every row and column contains the digits 1 to 6. Also, make sure that the squares that are connected with each other must contains the same digit.

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

What brings you down but never up?

Three doctors said that Bill was their brother. Bill says he has no brothers. How many brothers does Bill actually have?

We are a group of eight brothers. We consider the weak, yet we protect the king in every battle. If we move ahead, we never turn back. Who are we?

Two boys were admitted to a school. When the headmaster asks them about their parents, they tell him that they have same parents (father and mother). On further inquiry, it turns out that they both share the same date for their birthday.

"Are you twins," ask the headmaster.
"No," replies the boys.

Is it possible?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?

I want to fill my bucket using both cold and hot water.
I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and the cold water tap fills the bucket in exact 4 hours.
I turn both of them simultaneously but I forgot to turn off another tap which removes the water out of the bucket. This tap can empty the bucket in 12 hours.

How Long will it take to fill the bucket?