I have branches, but no fruit, trunk or leaves. What am I?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

It's a 7-letter word.
If we remove 1 letter from it, it remains the same.
If we remove 2 letters from it, it remains the same.
If we remove 3 letters from it, it remains the same.
If we remove all the letters from it, still it remains the same.
What is it?

I had an infinite supply of water and 5 litres and 3 litres jars.

How would you measure exactly 4 litres in the least number of steps?

The doctor prescribed you to take one pill from the bottle every half an hour. The bottle is now left with only three pills.

How long do you think you have before you run out of pills?

You have a three-gallon and a five-gallon measuring device. You wish to measure out four gallons.

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."?

You have 1023 apples and 10 bags. You have to distribute these apples in these 10 bags in any way you choose. But when I ask for a certain number of apples you have to give them in terms of bags without transferring the apples from other bags. How do you distribute the apples?

I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I?