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

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

A man dies of old age on his 25 birthday. How is this possible?

A girl was sitting in her hotel room when she heard a knock on the door. She opened the door and found that a man was standing outside.
The man said, "Oh! I am really sorry, I thought this was my room."
He then walked through the corridor to the elevator. The girl did not know the man. She closed her door and called security asking them to apprehend the man.
What made her suspicious of that man? He might have been genuinely mistaken.

Replace the question mark with the correct number.

Replace all '*' with digits 1, 2, 3, 4, 5 and 6 to make below statement true.

* *
x *
=====
* * *

Name the three-letter word that can complete the below words?

A) L O _ _ _ E
B) E D U _ _ _ E
C) _ _ _ E R
D) _ _ _ T L E

A pack of cards has 40 cards. You are blindfolded. Out of 40, 25 cards are facing down while 15 are facing up. You have been asked to divide this pack of cards into two decks - so that each deck contains an equal number of face-up cards. Remember, you are blindfolded.

How will you do it?

What 5-letter word typed in all capital letters can be read the same upside down?

Most people think of me as money. But when they find me in the water, they won’t get any money out of me. What am I?