What occurs twice in a week, once in a year but never in a day?

Below, you will find the mathematical proof that 10 equals 9.99999?. But is that possible or there is something wrong about it? Can you find the error?

x = 9.999999...
10x = 99.999999...
10x - x = 90
9x = 90
x = 10

John went to meet his friend Jacob, but when he was about to reach the main gate, John notices that Jacob had a mighty dog who was fastened to the tree. The chain is long enough that it allows the dog to reach the main gate.

How can the John reach the main gate?

When you say goodbye, I am what you need to tie.
I come as a couple and go wherever you run.
Who am I?

A guard is positioned at the one side of the bridge saying ‘A’. His task is to shoot all those who try to leave from ‘A’ to the other side and say ‘B’. He also need to welcome the person who comes from another side ‘B’ to his side ‘A’. The guard comes out of his post every 1 hour and looks down the bridge for any people trying to leave. You are at side ‘A’ and wish to go to another side ‘B’. you also know that it would take 1:45 hr to cross the bridge. How will you cross the bridge?

Find three numbers such that

* When we multiply three numbers, we will get the prime numbers.
* The difference between the second and the first number is equal to the third and second.

Railroad Crossing, look out for the cars. Can you spell that, without any R's ?

Name a key which is hardest to turn.

The first two letters signify a male, the first three letters signify a female, the first four letters signify a great, while the entire world signifies a great woman. What is the word?

What does this Rebus Picture means ?