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

I am a prime number.
The double of myself is equal to the square of me.

which number am I?

What comes
Once in a Year
Twice in a Month
4 times in a Week
6 times in a Day

There is a barrel with no lid and some wine in it. 'This barrel of wine is more than half full,' said Curly. 'No it's not,' says Mo. 'It's less than half full.' Without any measuring implements and without removing any wine from the barrel, how can they easily determine who is correct?

John and his team plan to rob a safe. They got just one chance to break the code else the local police will be informed. Below are clues:
A) Exactly one number is perfectly placed: 9 8 1
B) Everything is incorrect: 9 2 4
C) Two numbers are part of the code of the safe but are wrongly placed: 0 9 3
D) One number is part of the code of the safe but is wrongly placed: 1 4 7
E) One number is part of the code of the safe but is wrongly placed: 7 8 3

f you were running a race, and you passed the person in 2nd place, what place would you be in now?

A time long back, there lived a king who ruled the great kingdom of Trojan House. As a part of the renovation of the kingdom to meet future security needs, he asked his chief architect to lay down a new play in a manner that all of his 10 castles are connected through five straight walls and each wall must connect four castles together. He also asked the architect that at least one of his castles should be protected with walls. The architect could not come up with any solution that served all of King's choices, but he suggested the best plan that you can see in the picture below. Can you find a better solution to serve the king's demand?

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

In the four images below, can you find the odd one out?