What is black when you buy it, red when you use it, and gray when you throw it away?

Find the mistake in the below maths equations

A = 2
A(A-1) = 2(A-1)
A2-A = 2A-2
A2-2A = A-2
A(A-2) = A-2
A = 1

Christina, Allison and Lena are 3 daughters of John a well-known Mathematician, When I asked John the age of their daughters. He replied "The current age of her daughters is prime. Also, the difference between their ages is also prime."

How old are the daughters?

Using four sevens (7) and a one (1) create the number 100. Except for the five numerals, you can use the usual mathematical operations (+, -, x, :), root and brackets ()

Consider this: Arnold Schwarzenegger has a big one. Michael J. Fox has a small one. Prince doesn’t have one. The Pope has one but never uses it. Bill Clinton has one and uses it all the time. What is it?

During which month do people sleep the least?

Can you guess the name of the month by looking the below rebus ?

Vin Diesel is pulling a theft and has planned to run away with all the cash kept in the safe. But the only way to open the safe is the 13 character password. He has a set of five clues given to him by a trustworthy source.

Exactly two of the below statements are false.
The password is contained within this sentence.
The password is not in this hint.
The password is within only one of these statements.
At least one of the above statements is a lie.

In a family supper, a grandfather, a grandmother, two fathers, two mothers, four children, three grandchildren, one brother, two sisters, two sons, two daughters, one daughter-in-law, and one mother-in-law need to sit at a table.

There are only seven chairs available at the place. How many more chairs do they have to borrow so that everyone can sit down together for the suppers if everybody requires a separate chair?

I have eight fingers and two thumbs but I do not live. What Am I?