Which word does the below Plexor means ?

How many people must be gathered together in a room, before you can be certain that there is a greater than 50/50 chance that at least two of them have the same birthday?

A four-digit number (not beginning with 0) can be represented by ABCD. There is one number such that ABCD=A^B*C^D, where A^B means A raised to the B power. Can you find it?

A wooden log balances equally on the scales when weighed with three-quarters of a pound and three-quarters of a wooden log.

Can you calculate the weight of the entire wooden log?

John, Jack and Jill are in a desert. John doesn't like Jill and hence decides to murder him. He poisons the water supply of Jill. Since it is a desert area, Jill must drink or he will die of thirst.

Jack does not know of the actions of John and also decides to murder Jill. To succeed in his ill motives, he removes the water supply of Jill so he dies of thirst.

Jill dies due to thirst. Who murdered Jill?

A charming young lady was approached by a kind looking old woman in a restaurant. The old woman said to her, 'You look exactly like my younger daughter. Sadly she passed away a couple of months back. Could you do me a favor and say 'Goodbye, mother' with a kind smile on your face when I leave?

The young lady agreed for the same and said, 'Goodbye, mother' when the old woman left. Soon after, she got the most disengaging shock of her life.

Can you guess what the shock was?

A seven-year-old kid challenged his classmates that he can make the number one disappear by adding something to it.

How can he do that?

A shepherd had 18 sheep, out of which, all but ten died.

Can you tell us how many sheep was he left with?

Two old friends, Jack and Bill, meet after a long time.

Three kids
Jack: Hey, how are you, man?
Bill: Not bad, got married and I have three kids now.
Jack: That's awesome. How old are they?
Bill: The product of their ages is 72 and the sum of their ages is the same as your birth date.
Jack: Cool..But I still don't know.
Bill: My eldest kid just started taking piano lessons.
Jack: Oh, now I get it.

How old are Bill's kids?

Considering the below equation:

V + II - VI = 10
IV - X + VIII = 20
IV - VII + VI = 30

Then, I + II + III = ?