Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

ENEMY = 2 * LINK
LINK + 2 = HELL

Then what will be TAXI + HELL? Select from the options below:
a) ROTTEN
b) DANGER
c) HEAVEN
4) MORTAL

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?

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

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

Given that

(78)^9 = 6
And (69)^4 = 11

Can you find out

(99)^2 =?

(Note: This is Logical, not Mathematical)

The captain of a ship was telling this interesting story: "We travelled the sea far and wide. At one time, two of my sailors were standing on opposite sides of the ship. One was looking west and the other one east. And at the same time, they could see each other clearly." How can that be possible?

15 caves are arranged in a circle at the temple of doom. One of these caves has the treasure of gems and wealth. Each day the treasure keepers can move the treasure to an adjacent cave or can keep it in the same cave. Every day two treasure seekers visit the place and have enough time to enter any two caves of their choice.

How do the treasure seekers ensure that they find the treasure in the minimum number of possible days?

There is an ancient kingdom where every married woman keeps information regarding the fidelity of other men. However, what they don't know is the fidelity of their own husbands. Also, there is an ancient belief that they don't tell each other about the fidelity of their husbands.

On a certain day, the queen of the kingdom declares that she has identified at least one unfaithful man in the kingdom. She allows the wives to identify and gives them authority to kill their husbands if they are unfaithful at midnight.

How will the wives manage it?

The host of a game show offers the guest a choice of three doors. Behind one is an 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?

Which is the smallest number that you can write using all the vowels exactly once?