What does this mathematical rebus means ?

There was a minor accident with a doctor's son but the doctor noticed no major injury. After the treatment, the father of that doctors son is sitting with the son of the doctor without the doctor being in the room.

How can this be possible?

In a competitive exam, each correct answer could win you 10 points and each wrong answer could lose you 5 points. You sat in the exam and answered all the 20 questions, which were given in the exam.
When you checked the result, you scored 125 marks on the test.

Can you calculate how many answers given by you were wrong?

How can a man go eight days without sleep?

What 8 letter word can have a letter taken away and it still makes a word. Take another letter away and it still makes a word. Keep on doing that until you have one letter left. What is the word?

What is the next shape from answers A, B, C, and D figure?

What type of tree can I carry in my hand?

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

Peter wakes up daily to pick up his cycle and crosses the border between Spain and France daily with a bag on his shoulder. He is investigated daily by the officials but they don't find anything suspicious.

If we tell you that he is smuggling something what would it be?

In one of the popular batman series movie "Batman Forever", there was a riddle that goes like "Tear me off and then scratch my head and I was red then and now I am back. Who am I?