# How to Study?

This is a very interesting question in Maths ”How to study?” Is it? of course yes. To study any subject first of all this question arises in student’s mind.And the answer from our elders and experts is ”Learn and Practice”.And especially for mathematics do more concentration on ”Practice and Practice”.

कविवर वृंद के रचे दोहे की एक पंक्ति वास्तव में निरंतर परिश्रम का महत्व बताने वाली है। साथ ही निरंतर परिश्रम करने वाला व्यक्ति के लिए अनिवार्य सफलता प्रदान करने वाली है दोहे की यह पंक्ति। पूरा दोहा इस प्रकार है :-

”करत-करत अभ्यास के जड़मति होत सुजान । रसरी आवत-जात के, सिल पर परत निशान ।।”

I think everyone knows the meaning of above.If not for those persons this is sufficient to understand.

”Practice Makes us Perfect”

Ok, let’s come on our topic.For this, first of all, we should know our exam pattern to get excellent marks in our exam.

# JAM Maths Exam Pattern

Last year in 2016, IIT-JAM exam was made completely objective.The IIT-JAM paper consists of 60 questions which are divided among 3 sections.

For the Section A, it contains 30 questions. First 10 questions carry 1 mark each, and next 20 questions carry 2 marks each. In this part, each question has only one correct option among the given four options. An incorrect answer leads to NEGATIVE marking. For the 1 mark questions, an incorrect choice would lead to NEGATIVE 1/3 marks, and For the 2 marks questions, an incorrect choice would lead to NEGATIVE 2/3 marks. These are referred as Multiple Choice Questions (MCQ). This section contributes 50 marks.

For the Section B, it contains 10 questions, each question carrying 2 marks. In this part, each question has one or more correct option(s) among the given four options. These are referred as Multiple Select Questions (MSQ). There will be No negative marking in this part. This section contributes 20 marks.

For the Section C, it contains “Fill in the blank” type questions, 20 in number. You have to fill the blank with a numerical value using the virtual keypad on the monitor. First 10 questions carry 1 mark each, and next 10 questions carry 2 marks each. That is why these are Numerical Answer Type Questions(NAT). There will be No negative marking in this part. This section contributes 30 marks.

# Preparing for JAM IIT

Now on analyzing your exam pattern and some last year papers you will realize in JAM IIT, the questions are usually from graduation. If you have prepared well for your graduation, then you stand at an advantage while taking JAM IIT. Nevertheless, it is a good idea to set aside 3 to 4 hours of study for JAM at least for a year. Here are some points that will enable you to prepare for JAM IIT.

# Getting admitted into JAM coaching institutes

There are several coaching institutes that offer JAM coaching. You can opt for one if you desire. That will give you a structured way of learning. Having said that, there are people who clear JAM without the help of any coaching institute.

# Getting acquainted with syllabus

Depending on the course that you are opting for, get acquainted with the syllabus. The syllabus is announced by the organizing institute or respective institutes well in advance. Be sure to prepare each and every topic that has been mentioned in the syllabus.

# SYLLABUS FOR JAM MATHEMATICS

## Sequences and Series of Real Numbers:

Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibniz test for convergence of alternating series.

## Functions of One Real Variable:

Limit, continuity, intermediate value property, differentiation, Rolle’s Theorem, mean value theorem, L’Hospital rule, Taylor’s theorem, maxima and minima.

## Functions of Two or Three Real Variables:

Limit, continuity, partial derivatives, differentiability, maxima and minima. Integral Calculus: Integration as the inverse process of differentiation, definite integrals, and their properties, fundamental theorem of calculus. Double and triple integrals, change of order of integration, calculating surface areas and volumes using double integrals, calculating volumes using triple integrals.

## Differential Equations:

Ordinary differential equations of the first order of the form y’=f(x,y), Bernoulli’s equation, exact differential equations, integrating factor, orthogonal trajectories, homogeneous differential equations, variable separable equations, linear differential equations of second order with constant coefficients, method of variation of parameters, Cauchy-Euler equation.

## Vector Calculus:

Scalar and vector fields, gradient, divergence, curl, line integrals, surface integrals, Green, Stokes and Gauss theorems.

## Group Theory:

Groups, subgroups, Abelian groups, non-Abelian groups, cyclic groups, permutation groups, normal subgroups, Lagrange’s Theorem for finite groups, group homomorphisms and basic concepts of quotient groups.

## Linear Algebra:

Finite dimensional vector spaces, linear independence of vectors, basis, dimension, linear transformations, matrix representation, range space, null space, rank-nullity theorem. Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions, eigenvalues and eigenvectors for matrices, Cayley-Hamilton theorem.

## Real Analysis:

Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of a real variable), Taylor’s series, radius and interval of convergence, term-wise differentiation and integration of power series.

# Refer to past question papers

The more you solve past question papers, the better you are going to get. Solving past years question papers will not only give you an insight into what to expect but will also make you confident on the day of the exam. Past years question papers will also allow you to have an idea of the occurrence of the questions from various topics. The past year’s questions are either available online or can be bought.

# Take mock exams

There are mock exams available online which you can attempt. Taking mock tests will enable you to have a strategy in place – in terms of time management and prioritizing the topics to be tackled first.

# Refer to IIT JAM books

There are different IIT JAM books by various authors. Referring to them while you are preparing will help you extensively. Last but not the least, have the confidence and a positive attitude that you will be able to crack the exam. Best of luck.