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

Suppose that you are trapped on the surface of a frozen lake. The surface is so smooth and ideal that there is no friction at all. You cant make any grip on the ice and no wind is blowing to help you out. You have just a mobile phone with you which has got no reception disabling you to call for help.

How will you plan your escape before you freeze to death on the frozen lake?

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?

An exterior architect is asked by a builder to plant seven trees in a manner that there are exactly six rows of trees in a straight line and each row has three trees in particular.

How will he do it?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

A man fell off a smuggling boat into deep water. He could not swim and he was not wearing anything to keep him afloat. It took 30 minutes for the people on the boat to realize someone was missing. The missing man was rescued two hours later on the return trip. Why didn't he drown? Note:- He didn't know swimming, the sea was deep, and He wasn't holding anything

What does the following BrainBat signifies?

ABCDEFGHIJKLMNOPQRSTUVWYZ

QQQQQQQQQQQQQQQQQQQQQQQQQ.

A man was convicted of a minor offence in Akbar court. Akbar decided to give him a chance. He asked him to give a statement. If the statement is true, he will be killed by lions and if it is false, he will be killed by trampling of wild elephants.

The convicted person requested help from Birbal and since the crime was not a big one, Birbal decided to help him. Whatever Birbal suggested impressed Kabir and he let the convicted person go.

What did Birbal suggest to the person?

A girl is twice as old as her brother and half as old as her father. In 50 years, her brother will be half as old as his father. How old is the daughter now?

A man is sitting in a pub feeling rather poor. He sees that the man next to him is extremely rich. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.'
The rich man laughs.
The poor man says, 'I am willing to bet you all the money you have in your wallet that I can sing a genuine song with a lady's name of your choice in it.'
The rich man laughs again and says, 'OK, how about my daughter's name, Joanna Armstrong-Miller?'
The rich man goes home poor. The poor man goes home rich.

What song did he sing? A man is sitting in a pub feeling rather poor. He sees the man next to him pull a wad of £50 notes out of his wallet. He turns to the rich man and says to him, 'I have an amazing talent; I know almost every song that has ever existed.' The rich man laughs. The poor man says, 'I am willing to bet you all the money you have in your wallet that I can sing a genuine song with a lady's name of your choice in it.' The rich man laughs again and says, 'OK, how about my daughter's name, Joanna Armstrong-Miller?' The rich man goes home poor. The poor man goes home rich. What song did he sing?