Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

It walks on 4 when its young, walks on 2 when it's older, and walks on 3 when its very old?

500 women soldiers are arranged in an array of ten rows and fifty columns in accordance with their respective heights. Now, the tallest woman from each row is asked to move out in the front. From them, the shortest one is labelled as Alpha. They are then asked to resume their original position.

Now, the shortest woman in each column is asked to come out in front. The tallest among them is labelled as Beta.

Can you find out if Alpha will be taller or Beta?

A mother bought three dress for her triplets daughters(one for each) and put the dresses in the dark. One by one the girls come and pick a dress.
What is the probability that no girl will choose her own dress?

Can you fill the blank with the correct number?

6 30 870 756030 _____

There is a box in which distinct numbered balls have been kept. You have to pick two balls randomly from the lot.

If someone is offering you a 2 to 1 odds that the numbers will be relatively prime, for example
If the balls you picked had the numbers 6 and 13, you lose $1.
If the balls you picked had the numbers 5 and 25, you win $2.

Will you accept that bet?

They do not possess flesh or feathers or scales or bone
But still, they are blessed with fingers and thumbs of their own.

Which number should replace the question mark?

What can run but never walks, has a mouth but never talks, has a head but never weeps, has a bed but never sleeps?

What jumps when it walks and sits when it stands?