TOUGHEST MATHEMATICS QUESTION IN IIT JEE

IIT JEE 2008:

The toughest question of IITJEE came in 2008 Maths Paper 1. This paper was set by IIT Roorkee. That year, a student named Shitikanth Kashyap topped the JEE Exam with a record breaking marks 433 out of 476, approximately 90.96%. Shitikanth was from Bansal Classes, Kota. When JEE exam happend, all coaching institutes of India gave wrong answer to this question. After some days of the exam, Shitikanth reached to Bansal Classes to meet V.K. Bansal. He told Bansal Sir that the answer of that question you gave was incorrect. Then, He solved that problem in front of Bansal Sir and the answer given by coaching institute is really incorrect.
The problem is:

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