Can you find out the remainder when 3^300 is divided by 5?

A river should be crossed by a father, a mother and their two sons and two daughters.
There are some rules that should be followed while crossing the river. There can be only two people in the raft while crossing. The daughters cannot be with their father unless there is the presence of the mother. The sons cannot be with their mothers unless the father is present. Unless the guard is on the board, the criminals cannot be with any of the family members. Only the adults like the father, the guard, and the mother knows to use the raft.

How will they cross the river?

One night, a man runs away from home. He turns left and keeps running. After some time he turns left again and keeps running. Later, he turns left one more time and runs back home—but when he gets home, he finds a man in a mask. Who was the man in the mask?

I am quite hot but become too cold if you remove the first two letters. What am I?

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?

My friends called me Iron59 because my parents are a chemist and a mathematician. What is my real name?

I got a bee but no honey.
got an eye but am still blind.
got a sea but no water.
got a tea but no coffee.
got a why but no answer.

What Am I?

If two fifty-foot ropes are suspended from a forty-foot ceiling that is twenty feet apart, how much rope will you be able to steal if you have a knife?

Different lights make me strange by changing me into different sizes. What am I?

What number comes next in this sequence:
7 8 5 5 3 4 4 _