What seven-letter word has hundreds of letters in it?

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?

You have 10 balls with you. A friend of yours out of nowhere asks you to place those ten balls in five lines such that each of the lines has exactly 4 balls on them. He needs to check your intelligence. Prove him by doing the task.

You can see three almost identical images below. Can you spot the odd one out from them?

You stand in front of two doors. A guard stands next to each door. You know the following things: one path leads to paradise, the other leads to death. You cannot distinguish between the two doors. You also know that one of the two guards always tells the truth and the other always lies. You have permission to ask one guard one question to discover which door leads to paradise. What one question would you ask to guarantee you enter the door to paradise?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

Two fathers and two sons decided to go to a shop and buy some sweets upon reaching. Each of them bought 1 kg of sweet. All of them returned home after some time and found out that they had 3kg of sweets with them.

They did not eat the sweets in the way, nor threw or lose anything. Then, how can this be possible?

Replace the 'X' with any mathematical symbol to make the expression equal to 111.

18 X 12 X 2 X 3 = 111

Can you spot the man between the coffee bean in the picture below ?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?