Take away the whole and some still remain. What is it?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

I am white when I am dirty, and black when I am clean. What am I?

In the attached figure, you can see a chessboard and two rooks placed on the chess board. What you have to find is the number of squares that do not contain the rooks. How many are there?

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

What has hands, but can’t clap?

2, 3, 5, 9, 17, _ What is the next number in the sequence?

You are given 2 eggs.
You have access to a 100-storey building.
Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100th floor, Both eggs are identical.
You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

What is the largest amount of money that you can possess in change and still if someone asks you for a dollar, you won't be able to give?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?