I shave every day, but my beard stays the same. What am I?

Give it food and it will live; give it water and it will die.

Detective Rockford was jogging near the beach at 4:30 am.
He hears a sound near the shack "No Michael, Please Do not shoot me".
Next instance he heard the sound of gunfire. Rockford rushes to the shack where he finds women lying dead and a gun in close proximity of three "Doctore Lawyer and a Teacher".

Rockford immediately knew that the Lawyer has committed the crime. How?

Two batsman each on 94 runs. Seven runs needed to win in last 3 balls. Both make 100*. How?

Replace each alphabet with the number (1-9) to make the below equation correct.

AB * C = DE - F = GH / I

_ _ _ IE _ _
_ _ _ IE _
_ _ IE _ _
_ _ IE _
_ _ _ _ IE

Like you see, some letters have gone missing from these words that contain the IE pair at some or the other place. The letters that will be used to fill the blanks are given below. Use them and form meaningful words. Can you do that?

A, C, D, F, H, K, L, M, N, N, O, R, R, S, S, S, T, T, Y and Y.

Can you find out the next digit in the following series ?

0, 0, 1, 3, 2, 6, 3, 9, 4, 12, 5, ?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

I have a clock(12-hour format) and both the needles of the clock overlap at 12:00.
After how much time, they will overlap again?

There are people and strange monkeys on this island, and you can not tell who is who (Edit: until you understand what they said - see below). They speak either only the truth or only lies.
Who are the following two guys?
A: B is a lying monkey. I am human.
B: A is telling the truth.