Why Wine Glass Stem is so long?

Can you find a pattern and the missing number in the series given below?

100, 155, 258,? , 584, 819.

The day before yesterday I was 25 and the next year I will be 28. This is true only one day in a year. What day is my birthday?

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

What is a word made up of 4 letters, yet is also made up of 3. Sometimes is written with 9 letters, and then with 4. Rarely consists of 6, and never is written with 5.

A farmer and his neighbour once went to Emperor Akbar"s court with a complaint. "Your Majesty, I bought a well from him," said the farmer pointing to his neighbour, "and now he wants me to pay for the water."
"That"s right, your Majesty," said the neighbour. "I sold him the well but not the water!"?
The Emperor asked Birbal to settle the dispute. How did Birbal solve the dispute?

What Time Should the last watch show in the below figure?

You are in a land where thirty men and two women were dressed in classic black and white dresses.
They begin to fight as soon as any of them move.

Where are you?

As a whole I am both
safe and secure.

Behead me and I become
a place of meeting.

Behead me again and I am
the partner of ready.

Restore me, and I become
the domain of beasts.

What am I?

Two trains start at the same time, one from Bangalore to Mysore and the other from Mysore to Bangalore. if they arrive at their destinations one hour and four hours respectively after passing one another, how much faster is one train running than the other?