What always comes into a house through the keyhole?

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

What has a bottom at the top?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Can you decipher the following common phrase?

T M C
A U O
H S M
W T E

By what process could you make a 'Tea-Table' into food?

Make a sentence consisting of three words that have the whole alphabet.

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?

Your job is to measure 45 minutes if you have only two cords and matches to light the cords.

1. The two cords are twisted from various materials, so their different segments can burn at different rates.
2. Each cord burns from end to end in exactly one hour.

Describe your way of measuring the 45 minutes.

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?