Why 1729 is a magic number? Answer Logically.

I am a five-letter word under you,
Remove the first letter and I am above you,
Remove the second as well and I am around you.

Who am I?

Can you name any English verb that becomes its past tense by simply rearranging the alphabets ?

We have shown you a regular water barrel as below. Without using any measuring device can you check if the barrel is more than half-filled or less than half-filled?

What kind of tree can you carry in your hand?

Whats the next number in the below number sequence pattern.

A and B have a certain number of chocolates with them. If B gives one chocolate to A, they will have an equal number of chocolates. But if A gives one chocolate to B, then A will be left with half the number of chocolates that B has.

Can you find out the number of chocolates they have right now?

John was so frustrated to be the suspect of being a sleeper terrorist that he shoot himself right between the eyes with a revolver in his toilet. The revolver and the bullets were accurate. Minutes later John walks out of the toilet unharmed.
How can this be possible?

We have four gears with below features=> Both Gear A and D has 60 teeth=> Gear B has 40 teeth=> Gear C has 20 teeth=> Every two minutes, Gear B makes 25 full turns.What is the relative speed of Gear A and Gear B?

As shown in the picture below, we can see a boy hanging on the tree branch to save his life. There are various ways in which he can die like1. A snake hanging toward the right waiting to bite the boy.2. A roaring Lion near the tree.3. Two crocodiles are ready to attack if the boy reaches near water. The tree is chopped to some extent, so can fall as if he moves a lot. Can you give this boy an escape plan?