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

Who is generally closer to the kids, mom or dad?

(it's a funny riddle)

Three friends named Mr. Black, Mr. Yellow and Mr. Green enter a pub on a weekend night. They are wearing either a Black, Yellow or Green shirt.

Mr. Yellow says to them, 'Did you notice that we all are wearing different color shirts than our names?'

To this, the man who was wearing the Green shirt said. 'Wow, thats right.'

Can you identify who is wearing which colour shirt ?

John and Jill are madly in love with each other. To remind Jill of his pure love, John wants to send her a ring by post but in their country where burglary is quite prominent, any package that is not locked comes under the risk of being stolen for the contents.

John and Jill possess many padlocks but neither one of them has the other key.

Can you find a way John can send the ring to Jill safely?

I am the black child of a white father, a wingless bird, flying even to the clouds of heaven. I give birth to tears of mourning in pupils that meet me, even though there is no cause for grief, and at once on my birth, I am dissolved into air. What am I?

A boy collects white seashells from the sea and brings them home every night. When he has enough of them, he decides to sell them to a trader.

The trader is ready to buy the shells and he asks the boy about the quantity. At this, the boy starts calculating. He has a giant box that contains 3 mini boxes. Two of them have another mini box inside. If the giant box can hold 50 shells, how many brown shells can he sell to the trader?

I make two people out of one. What am I?

What is more useful when it is broken?

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

A Detective reviewed the information they had on the case so far.

A lady named 'Caterina' was found shot and they already had a list of suspects - Ankit, Tarun, Harish, Manoj and Manish.
The killer is a fan of challenges him by leaving notes ad various places.
* The first was found in a toilet room.
* The second was found in an art room.
* The third was in a restroom.
* the fourth in an underwater room.
* The fifth at the no-smoking room.

All of the notes read the same thing, 'The clues are where you find the notes.' Yet, nothing was found at any place the notes were.
Detective the genius, immediately solved the case.
Who was the killer?