Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

There was a kingdom in which the king had no heir to take over his thrown. Even the queen was dead and he himself was on the verge of dying. He thought about it and then summoned all of the teenagers. He gave one seed each to all of them and asked them to grow the plant. He announced that the one with the most beautiful plant will become the king/queen of the empire after the death of the king.

After a month, all of them were called. The king looked at all of the plants but announced the girl with an empty pot as the queen of the empire. Why?

A rubber ball keeps on bouncing back to 2/3 of the height from which it is dropped. Can you calculate the fraction of its original height that the ball will bounce after it is dropped and it has bounced four times without any hindrance ?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

A train leaves from point A for point B at 80 mph. After half an hour, another train leaves from point B for point A at 60 mph.

Which of the trains will be farther from point A when they meet ?

Can you guess the name of the month by looking the below rebus ?

You have a roll of cloth 1km long. You have a machine which cuts this roll into pieces of 10-meter-long cloth.

How long would it take for the machine to cut the roll if each cut took 4 secs?

If there are fifteen crows on a fence and the farmer shoots a third of them, how many crows are left?

If it took eight men ten hours to build a wall, how long would it take four men to build it?

It is a six-letter word.
The first four letters are me.
The second and last letters are the same.
The fourth second and last letter is payment.

Who is it?