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

Find the missing number in the sequence below:

I am a word that begins with the letter “i.” If you add the letter “a” to me, I become a new word with a different meaning, but that sounds exactly the same. What word am I?

Can you solve the below geography rebus by decoding the below rebus ?

As easy as you can get into me, it is as hard to get out of me.

Do you know what I am?

You have two buckets of 11 liters and 6 litres.
How can you measure exactly 8 litres?

A cat, a dog and a monkey were stolen. 3 suspects got caught: Harish, Manoj and Tarun. All we know is each person stole one animal, but we do not know who stole which. Here are the investigation statements. Harish said: Tarun stole the cat. Manoj said: Tarun stole the dog. Tarun said: They both were lying. I did not steal the cat or the dog. Later on, the police found out the man who stole the monkey told a lie. The man who stole the cat told the truth. Can you find out who stole which?

Can you solve the below algebraic mathematical equation?

(J+O+I+N+T)3 = JOINT

If your uncle’s sister is not your aunt, what relation is she to you?

I am a mother. However, I never give birth.

I am a father. However, I never nurse my children.

Wandering is not possible for me, but standing still happens occurs rarely.

Who am I?