JEE Advanced 2012 Maths Question Paper-2 with Answer Keys

JEE Advanced Mathematics Paper-2 (Paper-2) is a national level test conducted every year in May/June, by the Indian Institute of Technology and the JEE Main Exam conducted in April/May. It is a test of the skill level in Mathematics at the Undergraduate level. The test is for IIT entrance examination and other National Level Entrance Exams in India. Paper-2 is a subject of JEE Main and JEE Advanced and hence there are two versions of paper-2. The syllabus is for Class XII (10+2) level in India. The time duration of the test is two hours. The minimum marks in this paper is 100. There is no negative marking. The questions are to be answered in 200 minutes. For both questions and time (200 min) an answer can have a maximum of five marks. An incorrect answer is given one mark while a correct answer is given five marks. This is one of the toughest question sets in the whole Indian engineering entrance examinations. This year there are a total of 14,400+ candidates appearing for JEE Advanced Mathematics paper-2.

JEE Advanced Math is based on the standard of CBSE. JEE Advanced will be of three sections: Paper 1, Paper 2 and Paper 3. All three papers will be given on a first-come-first-served basis on the website. Students must visit the site and download the registration form available at the home page, fill the registration form and pay the fees of JEE Advance Math 2012 as per instructions mentioned on the website. Registration forms are open from 5th to 28th April 2012. After Registration, candidates will be required to complete the JEE Advanced Math Registration form and upload the digital signature as per instructions mentioned on the website. If a candidate fails to register with the above instructions, he/she will not be allowed to appear in the exam.

JEE Advanced Math Questions for Paper 1:

All the questions of JEE Advance Math Paper 1 are multiple choice questions with negative marking. There is no penalty for wrong answers. So, candidates need to solve all questions carefully and within the given time limit. Only the candidates who solve all questions of Paper 1 within a given time will be allowed to proceed to Paper 2.

Paper 2 has three sections. All the questions of Paper 2 are based on two dimensional graphs or three dimensional figures and have four answer options. Candidates will have a time limit to solve the questions. The paper is a multiple choice question (MCQ) and a candidate has to choose the answer option from the list available on the screen.

The paper contains 100 objective type questions out of which 50 objective type questions have multiple choices, one choice question and two choice questions. There is no negative marking. For each question, 1 mark is given for each correct answer selected. Thus, each question carries 1 mark.

The question paper for the paper-2 has two sections. First section contains multiple choice questions. Second section contains objective type questions. Marks of both the sections will be considered in calculating the merit list.

Marks obtained in each of the four papers will be calculated separately and the merit of the student will be determined based on the obtained marks. The following link contains syllabus for paper-2 and paper-3 along with the exam pattern.

Note: The question paper consists of two sections, each consisting of the multiple choice questions and the objective type questions. There is no negative marking for any section.

Multiple Choice Questions

Marks for the multiple choice questions will be calculated as per the number of correct answers selected. There is no negative marking.

Objective type questions

Marks for the objective type questions will be calculated as per the marks for the part-I and part-II papers of paper-2 and the marks in the paper-2 Physics and Chemistry components as per the marks for the relevant sections of the paper-2 Chemistry or Physics. There is no negative marking.

The candidates will have to carry the exam print-out to the invigilator within 15 minutes from the start of the exam. The invigilator will count the number of question papers and the candidates who attempted the examination after 11:00 will be issued the invigilator fee. There will be no negative marking in this examination.

The syllabus for the JEE Advanced Mathematics Paper-2 is as Follows.

Fundamental Mathematics:

There are two modules in this section. The modules can be of two parts. The first part will contain topics related to arithmetic and algebra and the second part related to geometry. The details will be given below.

Module 1: Arithmetic Syllabus: 

• Arithmetic of integers

• Modulus operations

• Division

• Addition and subtraction

• Multiplication

• Prime numbers and factorisation

• Factorization of numbers: powers of two, powers of three, powers of five, powers of seven

• Fractions: reciprocal and positive

• Ratio of parts and decomposition of numbers into ratios of integers

The concept of integer is well known to an intelligent student. An integer can be written in the form a+bi. It can be proved that a+bi is an algebraic integer. The concepts of imaginary numbers are introduced in module 1.

The students may understand the topics of module 1. We will discuss them from the basics. Let us see module 2.

Module 2: Geometry

This module deals with the topics related to Euclidean Geometry. The topics in this section are straight lines, circles, parallel and perpendicular lines, segments, parallels and perpendicular segments, congruency, tangents and chords. The topics in this section may be given to the students if they have prior knowledge. If not, we will present it gradually as they progress in the course.