## General Information

**About JAM**

**Joint Admission Test for M.Sc. (JAM)** is being conducted from 2004 to provide admissions to M.Sc. (Four Semesters), Joint M.Sc.-Ph.D., M.Sc.-Ph.D. Dual Degree, M.Sc.-M.Tech., etc. Programmes at the IITs and Integrated Ph.D. Degree Programmes at IISc for consolidating Science as a career option for bright students. These postgraduate programmes at IITs and IISc offer high quality education in their respective disciplines, comparable to the best in the world. The curricula for these programmes are designed to provide opportunities to the students to develop academic talent leading to challenging and rewarding professional life. JAM is open to all nationals (Indian/Foreign).

**Application procedure**

Candidates seeking admission to the academic programmers covered under JAM Applications will be accepted ONLINE only JAM website.

**Important Dates**

Events | Date(s) |

Registration and Application | September 2nd Week |

Admit Card | January 2nd Week |

Mock Tests | January 4th Week |

Date of Examination | February 2nd Week |

Result Announcement | March 4th Week |

Application for Admission | April 1st Week |

Declaration of First Admission List | May 3rd week, |

Declaration of Second Admission List | June2nd week, |

Declaration of Final Admission List | June 4th week, |

Closure of Admissions through JAM | July 1st week, |

**Admission Procedure**

Only the candidates who **qualify** in JAM (whose names appear in the Merit List) will be eligible to apply for admission to any of the corresponding academic programmers available at IITs

Candidates are advised, in their own interest, to refer to the brief profiles of the Admitting Institutes and Departments at their respective websites Applicants should note that they have to apply for admission by filling an online Application Form for Admission (henceforth called Admission Form) available only at JAM website. Based on the test paper(s) qualified, an applicant can apply to one or more academic programmers covered under that test paper(s), subject to fulfillment of the Minimum Educational Qualifications (MEQs) and the Eligibility Requirements (ERs) of the Admitting Institute(s).

Academic Programmed (s) | Institute(s) | Essential subjects in Bachelor’s Degreealong with minimum duration | Essential subjects at (10+2) level |

M.Sc. in Economics | IITR | Mathematics as one of the core subjects | No Restrictions |

M.Sc. Mathematics | IITB, IITD, IITGN, IITI,IITK, IITM,IITP, IITR,IITRPR | Mathematics for at least two years/four semesters | No Restrictions |

M.Sc. Mathematics/Mathematics and Computing | IITH | Mathematics for at least two years/four semesters | No Restrictions |

M.Sc. Mathematics and Computing | IITG | Mathematics for at least two years/four semesters | No Restrictions |

Joint M.Sc.- Ph.D. in Mathematics | IITBBS,IITKGP | Mathematics/ Statistics as a subject for at least two years/four semesters. | No Restrictions |

M.Sc.- Ph.D. Dual Degree in Operations Research | IITB | Mathematics/ Statistics as a subject for at least two years/four semesters. | No Restrictions |

M.Sc.- Ph.D. Dual Degree in Environmental Science and Engineering | IITB | Any one of Biology, Biotechnology, Chemistry, Mathematics and Physics for two years/four semesters, and any one of the other four subjects for at least one year/two semesters. | Mathematics |

Joint M.Sc.- Ph.D. in Atmosphere and Ocean Sciences | IITBBS | Mathematics and Physics and any one of these subjects among Chemistry, Computer Science, Computer Application, Geology and Statistics | No Restrictions |

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**Rank List:**

For each test paper in JAM, an All India Rank (AIR) will be assigned to all the appeared candidates based on the performance of the candidates in the test paper. Tie-Breaking: The tie-breaking criterion for awarding the ranks to candidates scoring the same aggregate marks in a test paper will be as follows:

The candidate with a higher ratio of positive marks to negative marks will be given a higher rank. If this criterion fails to break ties, the candidates concerned will be awarded the same rank.

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**Merit List:**

The results (merit lists) will be declared on March 4^{th} week. The results will be available on the website: For each test paper, an All India Merit list will be prepared based on AIR. The number of candidates included in the All India Merit List will depend on the total number of seats available in each category (OBC-NCL, SC, ST, and PwD) in a given subject. These candidates (henceforth called Qualified Candidates) are eligible to apply for admission to any of the corresponding academic programmers available (see Appendix-I) at IITs and IISc. Please note that the number of category-wise (OBC-NCL, SC, ST, and PwD) candidates included in the All India Merit List will be based on the category declared by the candidates in their application.

The Score Card (indicating the All India Rank(s) and the mark(s) obtained by the candidate) will be available for download in the JAM website from April to July to qualified candidates.

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**Minimum Educational Qualifications (MEQ)**

JAM examination will be conducted in Mathematics (MA), Mathematical Statistics (MS). Candidates are advised to become familiar with the code(s) of the test paper(s) that they wish to appear as this information is required at the time of application form submission, at the time of examination, and later at the time of admission process.

The Minimum Educational Qualifications (MEQs) for admissions to various Academic Programmers covered under JAM are given below, along with the names of the Test Papers with their Codes and the Institute offering the Academic Programmers. Admission to each of the Academic Programmers shall be offered on the basis of merit in the corresponding Test Paper(s) of JAM.

Test Papers and their Codes, corresponding Academic Programmers offered by the Admitting Institutes and their Minimum Educational Qualifications for Admission

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**Eligibility Requirements**

The candidates who qualify in JAM shall have to fulfill the following Eligibility Requirement (ER) for admissions in IISc and IITs. All candidates admitted through JAM should have a Bachelor’s degree. At least 55% aggregate marks, without rounding off, (taking into account all subjects, including Languages and Subsidiaries, all years combined) for General/OBC-NCL Category Candidates and at least 50% aggregate marks, without rounding off, (taking into account all subjects, including Languages and Subsidiaries, all years combined) for SC/ST and PwD Category Candidates in the qualifying degree.

For Candidates with letter grades/CGPA (instead of percentage of marks), the equivalence in percentage of marks will be decided by the Admitting Institute(s). Proof of having passed the Qualifying Degree with the Minimum Educational Qualifications (MEQ) as specified by the admitting institute should be submitted by September EOD .At the time of admission, all admitted candidates will have to submit a physical fitness certificate from a registered medical practitioner in the prescribed form. At the time of admission, the admitted candidates may also have to undergo a physical fitness test by a medical board constituted by the Admitting Institute. In case a candidate is not found physically fit to pursue his/her chosen course of study, his/her admission is liable to be cancelled.

Note:

(a) It will entirely be the responsibility of the Candidate to prove that he/she satisfies the Minimum Educational Qualifications (MEQs) and Eligibility Requirements (ERs) for Admissions.

(b) The Admitting Institute has the right to cancel, at any stage, the admission of a candidate who is found to have been admitted to a course to which he/she is not entitled, being unqualified or ineligible in accordance with the rules and regulations in force.

- Guide Lines
**Previous Year Cut off**

JAM Cut off 2017 | ||||||

Programme Code | General | OBC(NCL) | SC | ST | PwD | |

Mathematics (MA) | 19.51 | 17.56 | 9.76 | 9.76 | 9.76 | |

Mathematical Statistics (MS) | 19.04 | 17.14 | 9.52 | 9.52 | 9.52 | |

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**Exam Pattern**

The JAM examination for all the seven test papers will be carried out as **ONLINE** Computer Based Test (CBT) where the candidates will be shown the questions in a random sequence on a computer screen. For all the seven test papers, the duration of the examination will be 3 hours. The medium for all the test papers will be English only. There will be a total of 60 questions carrying 100 marks. The entire paper will be divided into three sections, A, B and C. All sections are compulsory. Questions in each section are of different types as given below:

**Section–A** contains a total of 30 Multiple Choice Questions (MCQ) involving 10 questions of one mark each and 20 questions of two mark each. Each MCQ type question has four choices out of which only one choice is the correct answer. Candidates can mark the answer by clicking the choice.

**Section–B** contains a total of 10 Multiple Select Questions (MSQ) carrying two marks each. Each MSQ type question is similar to MCQ but with a difference that there may be one or more than one choice(s) that are correct out of the four given choices. The candidate gets full credit if he/she selects all the correct answers only and no wrong answers. Candidates can mark the answer(s) by clicking the choice(s).

**Section–C** contains a total of 20 Numerical Answer Type (NAT) questions involving 10 questions of one mark each and 10 questions of two marks each. For these NAT type questions, the answer is a signed real number, which needs to be entered using the virtual numeric keypad on the monitor. No choices will be shown for these types of questions. Candidates have to enter the answer by using a virtual numeric keypad.

In all sections, questions not attempted will result in zero mark. In Section – A (MCQ), wrong answer will result in **negative** marks. For each wrong answer of 1 mark questions, 1/3 marks will be deducted and similarly for each wrong answer of 2 marks questions, 2/3 marks will be deducted. In Section – B (MSQ), there are **no negative** and **no partial** marking provisions. There is **no negative** marking in Section – C (NAT) as well.

There is provision of using **online virtual calculator** and hence, the candidates should not bring any calculator with them.

The candidates are required to select the answer for MCQ and MSQ type questions, and to enter the answer for NAT questions using only a mouse on a virtual numeric keypad (the keyboard of the computer will be disabled). At the end of the 3-hours the computer will automatically close the examination.Use of unfair means by a candidate in JAM, whether detected at the time of examination, or at any other stage, will lead to cancellation of his/her candidature as well as disqualification of the candidate from appearing in JAM in future.

- Exam Analysis

### Syllabi

:*Real Analysis*- Interior points, limit points, open sets, closed sets,
- Bounded sets, connected sets, compact sets, completeness of R.
- Power series (of real variable),Taylor’s series,
- Radius and interval of convergence, term-wise differentiation and integration of power series.

*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 of functions,
- Continuity of functions,
- Differentiation of functions,
- Intermediate value property,
- Rolle’s Theorem, mean value theorem,
- L’Hospital rule, Taylor’s theorem,
- Maxima and Minima.

:*Functions of Two or Three Real Variables*- Limit of functions,
- Continuity of functions,
- Partial derivatives of functions,
- Differentiability of functions,
- Maxima and Minima of functions

:*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 formy’=f(x,y),
- Exact differential equations,
- Integrating factor, orthogonal trajectories,
- homogeneous differential equations,
- Variable separable equations,
- Bernoulli’s equation,
- 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, Nullspace, rank-nullity theorem.
- Rank and inverse of a matrix, determinant,
- Solutions of systems of linear equations, consistency conditions,
- Eigen values and eigenvectors for matrices,
- Cayley-Hamilton theorem.

**MATHEMATICAL STATISTICS (MS)**

The Mathematical Statistics (MS) test paper comprises of Mathematics (40%weightage) and Statistics (60% weightage).

*MATHEMATICS*

** Sequences and Series**: Convergence of sequences of real numbers, Comparison, rootand ratio tests for convergence of series of real numbers.

** Differential Calculus**: Limits, continuity and differentiability of functions of one and twovariables. Rolle’s theorem, mean value theorems, Taylor’s theorem, indeterminateforms, maxima and minima of functions of one and two variables.

** Integral Calculus**: Fundamental theorems of integral calculus. Double and tripleintegrals, applications of definite integrals, arc lengths, areas and volumes.

** Matrices**: Rank, inverse of a matrix. Systems of linear equations. Linear transformations, eigenvalues and eigenvectors. Cayley-Hamilton theorem, symmetric,skew-symmetric and orthogonal matrices.

*STATISTICS*

** Probability**: Axiomatic definition of probability and properties, conditional probability,multiplication rule. Theorem of total probability. Bayes’ theorem and independence ofevents.

** Random Variables**: Probability mass function, probability density function andcumulative distribution functions, distribution of a function of a random variable.

Mathematical expectation, moments and moment generating function. Chebyshev’sinequality.

** Standard Distributions**: Binomial, negative binomial, geometric, Poisson,hypergeometric, uniform, exponential, gamma, beta and normal distributions. Poisson and normal approximations of a binomial distribution.

** Joint Distributions**: Joint, marginal and conditional distributions. Distribution offunctions of random variables. Joint moment generating function. Product moments,correlation, simple linear regression. Independence of random variables.Sampling distributions: Chi-square, t and F distributions, and their properties.

** Limit Theorems**: Weak law of large numbers. Central limit theorem (i.i.d.with finitevariance case only).

** Estimation**: Unbiasedness, consistency and efficiency of estimators, method ofmoments and method of maximum likelihood. Sufficiency, factorization theorem.Completeness, Rao-Blackwell and Lehmann-Scheffe theorems, uniformly minimumvariance unbiased estimators. Rao-Cramer inequality. Confidence intervals for theparameters of univariate normal, two independent normal, and one parameterexponential distributions.

** Testing of Hypotheses**: Basic concepts, applications of Neyman-Pearson Lemma fortesting simple and composite hypotheses. Likelihood ratio tests for parameters ofunivariate normal distribution.

### Reference Book

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### Upcoming Batches

WEEKEND/REGULAR CLASS ROOM COURES (IIT-JAM-2019)

This Batch is Regular Batch, there will be Weekly 6-days classes , 15 Lecture in each Week , every week 2 Question Discussion , 1 Performance Review Test and Performance Review Test discussion.

**Important Dates: **

IIT-JAM Regular /Weekend Batch for 2019 | |||

Batch-I | Batch-II | Batch-III | |

Registration and Application: | Open | Open | Open |

Batch Starts: | 20-Jan-18 | 15-Feb-18 | 26-May-18 |

Syllabi Complete: | 10-Nov-18 | 25-Nov-18 | 30-Dec-18 |

TEST SERIES : | 01-Dec-18 | 01-Dec-18 | 01-Jan-19 |

Exam Date: | 2^{nd} Week of Feb-19 | 2^{nd} Week of Feb-19 | 2^{nd} Week of Feb-19 |

CRASH COURSE (IIT-JAM-2019)

This is a 50 days **crash course** In This batch weekly 6-days classes. 30 hours Lecture in each Week, every week 100 Questions discussions. Every week performance review test and performance review test discussion.

**Important Dates **

Crash Course JAM-2019 | |

Registration and Application | Open |

Batch Starts: | 15-Dec-18 |

Syllabi Complete: | 30-JAN-19 |

TEST SERIES : | 10-JAN-19 |

Exam Date: | 2^{nd} Week of Feb-19 |

**Previous Year Papers**

** Question Paper Answer Key**

**JAM_MA_2017_QP JAM_MA_Key_2017**

**JAM_MA_2016_QP JAM_MA_Key_2016**

**JAM_MA_2015_QP JAM_MA_Key_2015**

**JAM_MA_2014_QP JAM_MA_Key_2014**

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**Free Practice Test:**

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