What is more useful when it is broken?

I am five letter word that is under you.
If you remove my 1st letter, then I am over you.
If you remove my 1st and 2nd letters then I am all around you.

Who am I?

Can you find out the remainder when 3^300 is divided by 5?

In the following picture, E is going to slide the object down and as per the terrain and the physics, the round object is going to travel all the way till the end. Now, can you analyze who all people will die when it happens?

They came out at night, without being called.
They lost at day, without being stolen.
Who are they?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

In a certain bank, a man deposits a certain amount. According to the bank policies, the amount will be doubled up in a year but as the service charge, they will also deduct Rs. 65 by the end of every year.

If after the 6th year, the amount becomes 0, what do you think is the original amount he deposited in the bank?

I inserted a coin in a bottle and closed its mouth with the help of a cork. Now, I was able to take the coin out from the bottle without taking out the cork or breaking the bottle. Can you tell me how I did it?

A man says, "Brothers and sisters, have I none, but that man's father is my father's son." Who is that man?

There are two words one resembles the "state of rest" and the other is related to "writing/reading material".

Can you name these two words which also sound similar?