P. G. ENTRANCE EXAMS

P. G. ENTRANCE EXAMS

JOINT ADMISSION FOR MATHEMATICS (JAM)

These are the entrance exams of POST GRADUATE COURSES (P.G.)

The Joint Admission Test for M.Sc, Integrated Ph.D Degree Programs, Joint M.Sc-Ph.D, M.Sc.-Ph.D dual degree and many more is conducted by IISc (Indian Institute of Science) and IITs (Indian Institute of Technology) every year. The purpose of this effort by IISc and IIT for JAM is to consolidate Science as a career option for bright students across the country.

JAM Examination will be conducted ONLINE only as a Computer Based Test (CBT) for all Test Papers.

All the seven Test Papers of JAM will be of fully objective type, with three different patterns of questions as follows:

  • Multiple Choice Questions (MCQ) : Each MCQ type question has four choices out of which only one choice is the correct answer.
  • Multiple Select Questions (MSQ): 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.
  • Numerical Answer Type (NAT) Questions: For each NAT type question, the answer is a signed real number which needs to be entered using the virtual keypad on the monitor. No choices will be shown for these type of questions. All candidates have to apply only ONLINE.

No hardcopies of documents (except challan) are to be sent to the Organizing Institute. The documents (if applicable) are to be uploaded to the online application website only. No hardcopy of JAM score card will be sent to the JAM qualified candidates by the Organizing Institute. It can only be downloaded from JAM website.

PATTERN

JAM examination will be conducted for the seven test papers, namely: Biological Sciences (BL), Biotechnology (BT), Chemistry (CY), Geology (GG), Mathematics (MA), Mathematical Statistics (MS) and Physics (PH). All seven test papers will be of fully objective type, with three different patterns of questions as follows:

Multiple Choice Questions (MCQ): Each MCQ type question has four choices out of which only one choice is the correct answer.

Multiple Select Questions (MSQ): 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.

Numerical Answer Type (NAT) Questions: For each NAT type question, the answer is a signed real number which needs to be entered using the virtual keypad on the monitor. No choices will be shown for these types of questions.

SYLLABUS AND ALL

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) carrying one or two marks 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 carrying one or two marks each. For these NAT type questions, the answer is a signed real number which needs to be entered using the virtual keyboard 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.

MARKING SCHEME

In all sections, questions not attempted will result in zero mark. In Section – A (MCQ), wrong answer will result in negative marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer.

For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section – B (MSQ),

There are no negative and no partial marking provisions. There is no negative marking in Section – C that is for NAT questions

ONLINE TEST RULES

An on-screen virtual scientific calculator will be available for the candidates to do the calculations. Physical calculators, charts, graph sheets, tables, cellular phone or any other electronic gadgets are NOT allowed in the examination hall.

A scribble pad will be provided for rough work and this has to be returned back at the end of the examination.

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 keypad (the keyboard of the computer will be disabled). At the end of the 3-hour window, the computer will automatically close the screen from further actions.

Syllabus

JAM: MATHEMATICS

Sequences and Series of Real Numbers: Sequences and series of real numbers, Convergent and divergent sequences, bounded and monotone sequences, Convergence criteria for sequences of real numbers, Cauchy sequences, absolute and conditional convergence; Tests of convergence for series of positive terms – comparison test, ratio test, root test; Leibnitz test for convergence of alternating series.

Functions of One Variable: limit, continuity, differentiation, Rolle's Theorem, Mean value theorem. Taylor's theorem, Maxima and minima.

Functions of Two Real Variables: limit, continuity, partial derivatives, differentiability, maxima and minima. Method of Lagrange multipliers, Homogeneous functions including Euler's theorem.

Integral Calculus: Integration as the inverse process of differentiation, definite integrals and their properties, Fundamental theorem of integral calculus. Double and triple integrals, change of order of integration. Calculating surface areas and volumes using double integrals and applications. Calculating volumes using triple integrals and applications.

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-separable solutions, Linear differential equations of second and higher order with constant coefficients, method of variation of parameters. Cauchy-Euler equation.

Vector Calculus: Scalar and vector fields, gradient, divergence, curl and Laplacian. Scalar line integrals and vector line integrals, scalar surface integrals and vector surface integrals, Green's, Stokes and Gauss theorems and their applications.

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 (only group theory).

Linear Algebra: Vector spaces, Linear dependence of vectors, basis, dimension, linear transformations, matrix representation with respect to an ordered basis, Range space and null space, rank-nullity theorem; Rank and inverse of a matrix, determinant, solutions of systems of linear equations, consistency conditions. Eigenvalues and eigenvectors. Cayley-Hamilton theorem. Symmetric, skew-symmetric, hermitian, skew-hermitian, orthogonal and unitary matrices.

Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets; completeness of R, Power series (of real variable) including Taylor's and Maclaurin's, domain of convergence, term-wise differentiation and integration of power series.

Books

  • Play with Graphs (arihant Publication). (Amit M Agarwal)
  • Calculus – Monty J. Strauss
  • Principle of Mathematical Analysis -S.L.Gupta, N.R. Gupta (Pearson Publication)
  • Introduction to Real Analysis - William F.Trench (Pearson Publication)
  • Real Analysis – Robert G Bartle (Wiley Publication)
  • Linear Algebra Schaum's Series -(Tata McGraw-Hill Publication)
  • Linear Algebra and its applications -Gilbert Strang
  • Linear Algebra -Vivek Sahai, Vikas Bist(Narosa Publication)
  • Linear Algebra and its Applications David C. Lay
  • A First Course In Abstract Algebra -John B. Fraleigh
  • Contemporary Abstract Algebra -Joseph A. Gallian
  • Modren Algebra - Surjeet Singh and Qazi Zameeruddin (Vikas Publication)
  • Differential Equations - Earl Codington (PHI Publication )
  • Differential Equations -Shepley L. Ross
  • Integral Calculus by F. Ayres (Schaum's)
  • Vector Analysis: Schaum's Outlines Series
  • Vector Analysis by Murrey Spiegel

MARKING SCHEME

In all sections, questions not attempted will result in zero mark. In Section – A (MCQ), wrong answer will result in negative marks. For all 1 mark questions, 1/3 marks will be deducted for each wrong answer.

For all 2 marks questions, 2/3 marks will be deducted for each wrong answer. In Section – B (MSQ),

There are no negative and no partial marking provisions. There is no negative marking in Section – C that is for NAT questions