What goes up but never comes down?

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?

What has one eye, but can’t see?

I have cities, but no houses. I have mountains, but no trees. I have water, but no fish. What am I?

What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

An old Woman left INR 33,333 to be divided equally among two fathers and two sons and each was to receive INR 11,111.
How was this possible?

Open a Laptop which is password protected. Hint for the password is given as below:

1 mobile 3 books 2 Boards 1 night 4 balls 2 lighters 1 ghost 1 hat 3 watches

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?

If 21x = 79x, what is the value of x?

People make me, save me, change me, raise me. What am I?