Find the next number in the series below

21 32 54 87 131 ?

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 have a mouth but I don't eat.
I have a bank but have no money.
I have a bed but i dont sleep.
I wave but have no hands.

Who Am I ?

After teaching his class all about Roman numerals (X = 10, IX=9 and so on) the teacher asked his class to draw a single continuous line and turn IX into 6. The teacher's only stipulation was that the pen could not be lifted from the paper until the line was complete.

I have a five and a three-gallon jar. Assuming there is an infinite supply of water, how can I measure one-gallon water?

What begins with T, ends with T, and has T in it?

Which city is three-fifths chick two third cat and 50% goat?

What am I?

The captain of a ship is telling you an interesting story and then poses a question. He says, “I have travelled the oceans far and wide. One time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly. Can you tell me how that was possible?”

You are on a Boat in the mid of a river. You have two cigarettes with you. One of these two you have to light, how will you light the cigarette?