People put me on the table and cut me but do not eat me. What am I?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

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?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

Which of the following words don't belong in the group and why?
CORSET, COSTER, SECTOR, ESCORT, COURTS

It belongs to you, but other people use it more than you do. What is it?

What number does the below three word/phrase identify and why?
1. Deck
2. Year
3. Singing in the Rain

Akbar called Birbal and asked him to draw a line on the floor. He asked Birbal to make that line smaller without erasing it. Birbal smiled and did it before Akbar could blink his eyes.

How did he managed to do it?

By removing one matchstick and adding one matchstick, can you convert the word "ZOO" to an animal name?

I look at you, you look at me, I raise my right, you raise your left. What am I?