What number when divided in half becomes zero?

Two natural numbers have a sum of less than 100 and are greater than one.

John knows the product of the numbers and Jacob knows the sum of numbers.

The following conversation takes place between them:
John: 'I am not aware of those numbers.'
Jacob: 'I knew you wouldn't be. I am not aware myself.'
John: 'Now I know them!'
Jacob: 'Now I know them, too!'

What are the two numbers?

I speak without a mouth, and hear without ears. I have no-body, but I come alive with the wind. What am I?

Can you place six matchsticks in a manner that each of the matchsticks is in touch with the other five matchsticks?

A few friends are enjoying their sea voyage in a boat full of apples. On the way, they felt hungry and thus decided to eat the apples. Together, they ate two dozen of apples. When they have eaten the apples, will there be any change in the water level?

Can you count the number of squares in the given picture?

The centre of the third figure is empty. What digit should fit inside?

I start and end with 500 and carry a 5 in my heart. But I require the first letter and the first number to be complete. I am the name of a King.

Who am I ?

Birbal was jester, counsellor, and fool to the great Moghul emperor, Akbar.
The villagers loved to talk of Birbal's wisdom and cleverness,
and the emperor loved to try to outsmart him.
One day Akbar (emperor) drew a line across the floor.
"Birbal," he ordered, "you must make this line shorter, but you cannot erase any bit of it."
Everyone present thought the emperor had finally outsmarted Birbal.
It was clearly an impossible task.
Yet within moments the emperor and everyone else present had to agree that Birbal had made the line shorter without erasing any of it.
How could this be?

He loves to dance, twist and prance, he shakes his tail, and as a way he sails, wingless he flies into the sky. What is he?