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

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?

Why 1729 is a magic number? Answer Logically.

Today is a very icy and cold morning in Newcastle. Mr Shearer, an office bus driver arrived to pick up the employees from the last stop. Shearer suddenly remembers that he needs to pick a newly joined 4miles to the north. Mr Shearer lost his direction compass, a few minutes later Shearer is able to figure that he is moving in the correct direction i.e. north. How did Shearer know that he is moving in the correct direction?

You are in a room with no metal objects except for two iron rods. Only one of them is a magnet.
How can you identify which one is a magnet?

Can you count the number of children in the picture below

A bag contains 64 balls of eight different colours. There are eight of each colour (including red). What is the least number you would have to pick, without looking, to be sure of selecting 3 red balls?

A girl has as many brothers as sisters, but each brother has only half as many brothers as sisters. How many brothers and sisters are there in the family?

Count the number of triangles in the below picture?

A girl was standing near the window thinking something. All of a sudden she decides something and throws something out of the window. She dies very soon after throwing it. She was perfectly healthy and had no disease or allergy. No one killed her and she did not commit suicide.

Can you think of any possible explanation that is logical as well for what happened there?