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 always enjoys poor health?

You can take four of the five letters out of this word, but the pronunciation never changes. What is the word?

Tell me the Hindi name of a Vegetable which if we remove 1st word will become a precious Stone and by removing the last word it will become a sweet eatable.

Can you identify the hidden rebus in the image below?

John, Jack and Jill are in a desert. John doesn't like Jill and hence decides to murder him. He poisons the water supply of Jill. Since it is a desert area, Jill must drink or he will die of thirst.

Jack does not know of the actions of John and also decides to murder Jill. To succeed in his ill motives, he removes the water supply of Jill so he dies of thirst.

Jill dies due to thirst. Who murdered Jill?

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

What is 3/7 chicken, 2/3 cat and 2/4 goat?

What number comes next in the series?

5 15 5 18 5 24 14 20 _

If I put in one bird per cage, I have one bird too many. If I put in two bird per cage, I have one cage too many. How many cages and birds do I have?