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 ten letters word
The first four letters have the power to rule,
Next, four-letter can be eaten.
The next three-letter represents a lady.
I can fly as well

what am I looking for?

Complete the following series. It.s very logical:

1, 4, 5, 6, 7, 9, 11, __?

Manish has to secure 40% marks to pass his B.tech final exams.
He got just 40 marks and failed by 40-marks.

What is the maximum marks?

Arrange the numbers 1, 2, 3, 4, 5, 6, 7, 8 and 9 above and below the division line in a manner that the thus formed fractions equal to 1/3.

(You can use one number only once)

If a zookeeper had 100 pairs of animals in her zoo, and two pairs of babies are born for each one of the original animals, then (sadly) 23 animals don’t survive, how many animals do you have left in total?

Suppose you are sitting in an interview and the interviewee asks you an aptitude question.

You have three buckets with a capacity of 4 litres, 8 litres and 10 litres and you have a large tank of water. Now you have to measure 3 litres of water precisely using those buckets. How will you do it?

Astrology starts with the alphabet A, Biology starts with B, Psychology with P and Limnology with L.

Can you find an "ology" that begins with a P?

What do the following words have in common?

Assess
Banana
Dresser
Grammar
Potato
Revive
Uneven
Voodoo

Can you find the company name in the pictogram below?