Which three-digit number, made of consecutive digits, like 567, is 2 less than a cube and 2 more than a square?

Alex is stranded on an island covered in forest.
One day, when the wind is blowing from the west, lightning strikes the west end of the island and sets fire to the forest. The fire is very violent, burning everything in its path, and without intervention the fire will burn the whole island, killing the man in the process.

There are cliffs around the island, so he cannot jump off.

How can the Alex survive the fire? (There are no buckets or any other means to put out the fire)

A mile-long train is moving at sixty miles an hour when it reaches a mile-long tunnel. How long does it take the entire train to pass through the tunnel?

No one wants to have it, but if one got it, he does not want to lose it. What is It?

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

Imagine a box with two cogwheels, one big with 24 teeth and one small with 8 teeth. The big one is firmly attached to the center of the box which means it does not turn or move while the small one rotates around the big one.

How many times do you think that the smaller wheel will turn compared to the box when it turns once around the big one?

Why do you find that most of the buildings are deprived of the 13th floor?

A Man gave one of his sons 10 cents and another son was given 15 cents. What time is it?
Hint: Figure out the relation between time and number, is not so easy..:)

I am a word of 12 alphabets.

* Alphabets 12, 4, 7, 2, 5 : Eastern beast of burden
* Alphabets 1, 8, 10, 9 are street made famous by Sinclair Lewis.
* Alphabets 11, 3, 6 are past.

On whole it means a person suffering from delusions of greatness.

What Is it ?

What is the largest number you can write with just 3 digits?