Take away the whole and some still remain. What is it?

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.

There are two dice with empty faces in front of you and a marker. You can mark any number on each of the faces of the two dice, but you have to display all 31 days of the month using the two of them.

Which numbers will you mark on which dice so that you can easily depict all the dates of the month?

You have a thousand Re. 1 coins with you. You have ten bags with you and you can put any number of coins in each of the bags. The condition is that if someone asks you for any amount between 1 and 1000, you must be able to give that amount by just giving the bag (you are not allowed to open the bag and give coins).

How will you do it?

Today, I celebrated my 32nd birthday but I was born in 1972.
How is this possible?

Solve the equation in the image by looking at the pattern closely.

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?

John went to meet his friend Jacob, but when he was about to reach the main gate, John notices that Jacob had a mighty dog who was fastened to the tree. The chain is long enough that it allows the dog to reach the main gate.

How can the John reach the main gate?

Which is Odd One Out and why?

4377

3954

9862

8454

9831

What time is it when an elephant sits on a fence?