What two things can you never eat for breakfast?

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?

If 5 cats catch 5 mice in 5 minutes, how long will it take one cat to catch a mouse?

What has to be broken before you can use it?

If you had a pizza with crust thickness 'a' and radius 'z', what's the volume of the pizza?

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

There is so small cabin inside a deep forest.
All the forest burned out to worst possible but the inside of the cabin is still the same.
However all the person inside the cabin die.

How come ?

A man is approaching a broad and barren land. He has a package with him. If somehow, he is unable to open the package before reaching the land, he will die.

Can you guess what is present in the package?

Katniss and Peeta are liars. They both lie on some specific days.

Katniss lies on Fridays, Saturdays and Sundays. She speaks the truth on all other days.

Peeta lies on Tuesdays, Wednesdays and Thursdays. He speaks the truth on all other days.

Can you tell that one day of the week when both of them will say "Tomorrow, I will lie."?

What is the centre of gravity?