How can you drop a raw egg from a height onto a concrete floor without cracking it?

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

which number am I?

A pet show was happening in my locality. I went down along with my kids. In that show, I noticed that all except two of the entries were cats. All except two were dogs and all except two were Monkeys.

Can you find out how many of each animals were present in that pet show?

There is one thing that goes round the house and also inside the house but never even share a brief touch. What is it?

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

I am the one who remains awake when you sleep. But I need to rest when you awake. Who Am I?

They are three errirs in this question. Can you find them?

On a certain day, John celebrated his birthday. Two days later, his older twin brother Jacob celebrated his birthday.

Is this even possible? How can it be?

Find a 9-digit number, which you will gradually round off starting with units, then tenth, hundred etc., until you get to the last numeral, which you do not round off. The rounding alternates (up, down, up ...). After rounding off 8 times, the final number is 500000000. The original number is commensurable by 6 and 7, all the numbers from 1 to 9 are used, and after rounding four times the sum of the not rounded numerals equals 24.

Complete the given grid with valid words. You can only use the letters AAEEIIMMPPTT.

Hint: The grid reads the same across as down.