Two Problems from IIT-JEE

IIT-JEE (Joint Entrance Examination for admission to Indian Institutes of Technology) is the most prestigious examination at 10+2 level in India. The questions are supposed to be tough and require ingenuity on the part of the student. There is a booming ecosystem of books, coaching classes and correspondence classes around IIT-JEE. But I find this ecosystem to be quite detrimental in improving the abilities of the student.