What is both possible and impossible at the same time?

The peacock is a bird that does not lay eggs. How do they get baby peacocks?

The following alphametic has only one solution. Can you find it?
ENLIST + SILENT + LISTEN = ANAGRAM

PS: You may start the number from 0.

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

which number am I?

Chef Andrea has to light the kitchen stoves to open her restaurant for the day. There are three stoves in the kitchen: A glass stove, a brick stove, and a wood stove. She only has one match. Which does she light up first?

Can you solve the below tricky visual equation?

Two old friends, Jack and Jill, meet after a long time, and discussing as:

Jack: Hey, how are you, man?

Bill: Not bad, got married and I have three kids now.

Jack: That's awesome. How old are they?

Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.

Jack: Cool..But I still don't know.

Bill: My eldest kid just started taking piano lessons.

Jack: Oh, now I get it.

How old are Bill's kids?

A man is shown a portrait painting. He looks closely, then tells, “Brothers and sisters have I none, but that man’s father is my father’s son!” Who is the man in the portrait?

It is deaf, Dumb and Blind!!!

Still, always tells the truth. What is it?

A detective visits his friend John just to discover that John's neighbour Dr Jacob was murdered. Dr Jacob, who is a mathematician wrote the murderer's name in a code word "Hcqtfz". There were five suspects
1. Ajit
2. Pankaj
3. Ganpat
4. Deenu
5. Hariya

The Detective was instantly able to find the murderer.
Can you?