Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

The host of a game show, offers the guest a choice of three doors. Behind one is a expensive car, but behind the other two are goats.
After you have chosen one door, he reveals one of the other two doors behind which is a goat (he wouldn't reveal a car).

Now he gives you the chance to switch to the other unrevealed door or stay at your initial choice. You will then get what is behind that door.

You cannot hear the goats from behind the doors, or in any way know which door has the prize.

Should you stay, or switch, or doesn't it matter?

In the Chess Board picture below white army is arranged. You need to add a black army on the board such that no piece is under any threat.
Note: Army comprised of 1 king, 1 queen, 2 rooks, 2 bishops, 2 knights, and 8 pawns.

At Delhi Cricket Clubhouse, there were four kids(Kohli, Yuvraj, Pant, and Dhoni) ages 1,2,3 and 4 and have 1,2,3 and 4 cricket balls in different orders.

We know the following facts:

Kohli has more cricket balls than his age.
Dhoni is older than Yuvraj.
One child has the same number of cricket balls as his age.
Pant has fewer cricket balls than Dhoni.
A child aged 3 has two cricket-balls.

Pant is the youngest.

Can you determine the age of the children and the number of cricket balls they have?

What kind of band never plays music?

What does does this rebus picture means ?

I went to the bookshop and spent one-half of the money that was in my purse.

When I came out, I found that I had as many cents as I had dollars and half as many dollars as I had cents when I went in. Find the money in my purse when I entered the store.

What goes up but never comes down?

I have nine bottles of wine and one of the nine bottles is poisoned.
I need to find the poisoned bottle with two facts
(1) Poison is deadly, only a sip will cost death
(2) I have two mice to do so.

How should I do it?

A man is lying dead in a field where no one is around. His head is split open and his legs are disfigured. Near to him, there is an unopened package. No living organism can be found anywhere at the crime scene.

How did he die?