what does this picture(rebus) riddle means ?

It's pretty hard to give up.
If you remove a part of it, you will be left with a bit.
Even if you remove another part, the bit still remains.
Remove one more and it still remains.

What is it?

A car meter reading shows 72927 miles a palindromic number.
what is the minimum number of miles you would need to travel to see another palindromic number on the car meter reading?

In a school, 280 students studied chemistry, 254 students studied physics and 280 students studied biology.

97 students studied chemistry as well as physics, 138 students studied physics as well as biology and 152 students studied chemistry as well as biology.

73 students studied all the three branches.

Can you find out the total number of students?

Can you find the largest Three-digit number whose sum is 14 and whose square is less than 5,00,000?

A woman lives in a skyscraper thirty-six floors high and is served by several elevators which stop at each floor going up and down. Each morning she leaves her apartment and goes to one of the elevators. Whichever one she takes is three times more likely to be going up than down. Why?

I make two people out of one. What am I?

Which number comes next in the number series?

2, 9, 30, 93, ?

At my favorite fruit stand,
an orange costs 18,
a pineapple costs 27,
and a grape costs 15.
Using the same logic, can you tell how much a mango costs?

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?