Find the Next Number in the Sequence

2 9 3 1 8 4 3 6 5 7 ?

An ape is trying to climb on a pole that is 60 feet high. Due to the slippery surface, the ape climbs 3 feet in a minute only to slip back 2 feet.

How much time do you think the monkey will take to reach the top of the pole?

During which month do people sleep the least?

Analyze and find the missing item in the sequence:
16, 06, 68, 88, __, 98

The below mentioned letters have been placed in a order using a logic.

DEAD, BALL, FEAR, SHOP

Can you find the logic?

A woman lives in a skyscraper thirty-six floors high and is served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

Can you arrange four 9's and use at most 2 math symbols, to make the total 100?

It comprises roots which nobody sees,
Much taller than those trees,
Up and up it goes,
Still it never grows?

Mr Black, Mr Gray, and Mr White are fighting in a truel. They each get a gun and take turns shooting at each other until only one person is left. Mr Black, who hits his shot 1/3 of the time, gets to shoot first. Mr Gray, who hits his shot 2/3 of the time, gets to shoot next, assuming he is still alive. Mr White, who hits his shot all the time, shoots next, assuming he is also alive. The cycle repeats. If you are Mr Black, where should you shoot first for the highest chance of survival?

The more of this there is, the less you see. What is it?