Our product and our sum always give the same answer. Who are we?

A boy and a girl are sitting on the porch.
"I'm a boy," says the child with black hair.
"I'm a girl," says the child with red hair.
If at least one of them is lying, who is which?

I am under you when I am whole.
I shift above you if you remove the first letter.
I come all around you if you remove the second as well.

Can you tell me who I am?

There are 3 apples in the basket and you take away 2. How many apples do you have now?

A family is trapped in a jungle. There is a bridge which can lead them to safety. But at one time, the bridge can only allow two people to pass through. Also, all of them are afraid of the dark and thus, they can't go alone.

Father takes 1 minute to cross, the mother takes 2 minutes, the son takes 4 and the daughter takes 5 minutes. While crossing the time taken will be according to the slower one. How can they all reach the other side in the minimum possible time?

There are a number of books on a shelf. If one book is the 4th from the left and 6th from the right, how many books are on the shelf?

Solve below rebus puzzle?

A mathematician couple was having a Frappuccino in Starbucks sitting opposite to each other. Suddenly the guy noticed the text written on the paper in front of them and exclaimed that it was wrong. The girl denied it and said it is appropriate. Both are correct. What is written on the paper?

There are 2 cops parked along a one-way street looking for traffic violations. They spot a taxi driver going in the wrong direction, yet they do nothing.

Why?

There is something which you can be arrested for attempting but not for successfully completing.