What is both possible and impossible at the same time?

An equation has been laid down using a few matchsticks. However, as you can see, the equation is not correct. Can you correct the equation if you are allowed to add or remove 5 matchsticks?

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

Five lovely ladies(Sophia, Isabella, Madison, Emma and Olivia) planned a picnic.

They each buy one thing each for the picnic.

Sophia, Emma and Olivia got a drink : orange-Juice, apple-juice, and mango-juice.
Olivia got the drink with the same letter as the one in her first name.
Emma loves mango-juice.
The other two bring some food : chocolates and pizza.
Also Madison is allergic to cheese.

So which ladies bought what ?

In an interview, a boy was asked an unusual question 'How two persons sitting with a table in between them can't see each other?' He was unable to reply. Can you?

81 x 9 = 801. What must you do to make the this equation true?

You may enter, but you may not come in. I have space, but no room. I have keys, but open no lock. What am I?

I have no life, but I can die. What am I?

Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Something Extraordinary happened on May 6th 19778 at 12:34am what was that?