After 12 years’ schooling a 3 or 4 year Bachelor’s degree plus a 2 years post-graduate education leading to M.Sc. degree in any branch of Biological Sciences/M.Tech (Biological sciences)/M.B.B.S./M.V.Sc. with a minimum of 55% marks or an equivalent grade. Candidates should have a total education of at least 17 years including 12 years of school. Candidates who have undergone integrated Master’s degree will be eligible provided they have at least 5 years of college/university education leading to a Master’s degree after completing 12 years of school. Degrees should be from an institution recognized by the Government of the respective SAARC countries.

**Admission Procedure**: Through an Entrance Test and an Interview.

**Format of the Entrance Test Question Paper and Course:**

The question paper will have two parts: Part A and Part B. All questions will be multiple-choice type with four choices of answer. Each question will carry one mark. Calculators and Log Tables may be used. There will not be negative marking.

**Part A** – This part will consist of 20 questions carrying one mark each. The paper will be of B.Sc. level. This Part will have questions from all branches of Biology. Candidates will be expected to attempt all questions from Part-A.

**Part B** – This part will consist of total 100 questions out of which the candidates will have to answer any 50 questions. Part-B will have M.Sc. level questions from the subjects of Biochemistry, Cell Biology, Molecular Biology, Immunology, Plant and animal Sciences, Genetics, Microbiology, Biophysics, Biostatistics and Bioinformatics.

See the M.Phil./Ph.D (Biotechnology) Test paper for the year 2013

**Interview:** Candidates up to five times the number of seats will be short-listed for interview on the basis of their performance in the entrance test subject to a minimum cut off. The candidate will also arrange to send two recommendation letters from teachers who have taught and assessed the candidate during graduate/postgraduate studies. Recommendation letters should testify to the intellectual acumen, knowledge of the subject and ability of the candidate to articulate ideas. Interview will carry a weightage of 30 marks. A minimum of 50% marks will have to be secured in both written test and interview in order to be eligible for the admission. Candidates invited for interview will be given a travel subsidy (upper limit INR 5000) towards actual travel cost by the shortest route as per instructions to be communicated to the selected candidates later. If candidates from outside India are unable to travel to New Delhi for the interview, they can seek permission for an interview through Skype.

A final merit list will be drawn by adding marks of the entrance test and the interview. Separate merit lists will be prepared for (a) candidates from all SAARC countries other than India, and (b) candidates from India. Equal number of candidates will be offered admission from these two lists, provided they secure overall qualifying marks of 50%. Up to 30% of the seats may be filled by candidates who have already secured JRF funding through a National competitive test in any of the SAARC countries.

After 12 years of regular schooling, a 3/4 years Bachelor's degree and a Master’s degree leading to M.A./M.Sc./M.Tech. degree in Mathematics / Computer Science with at least 55% marks or an equivalent grade.

Or

After 12 years' of regular schooling, an integrated Bachelor's and Master's degrees in Mathematics / Computer Science provided that the total duration of education is of at least 5 years.

Degrees should be from an institution recognized by the Government of the respective SAARC countries.

**Admission Procedure:** Through an Entrance Test and an Interview.

**Format of the Entrance Test Question Paper and Course:**

The duration of the test will be three hours. The test will consist of 70 multiple choice questions of one mark each. Each question will have four options with only one correct option.There will be no negative marking.Calculators are not allowed. However Log Tables may be used.The test will be divided into the following two parts:

- PART A : Undergraduate level knowledge of Mathematics – 30 Questions

- PART B : Masters level knowledge of Mathematics – 40 Questions

**Part A:**

**Real Analysis:** Elementary set theory, real number system as a complete ordered field, Archimedean property, supremum, infimum, sequence and series, monotone sequences, convergence, limit superior, limit inferior, Bolzano Weierstrass theorem, Continuity, uniform continuity, differentiability, mean value theorems; partial derivatives and Leibnitz theorem, Sequences and series of functions, uniform convergence, power series, Riemann sums, Riemann integration, improper integrals, functions of several variables, multiple integrals, line, surface and volume integrals, theorems of Green, Stokes and Gauss, Fourier series.

**Abstract Algebra:** Groups and their elementary properties, order of group, subgroups, cyclic groups, cyclic subgroups, permutation groups, Lagrange's theorem, normal subgroups and quotient groups, homomorphism of groups, isomorphism and correspondence theorems; Rings, integral domains and fields, ring homomorphism and ideals; Vector space, vector subspace, linear independence of vectors, basis and dimension of a vector space.

**Differential Equations:** Ordinary differential. equations: First order and of higher degree, linear equations with constant coefficients, method of variation of parameters, equations reducible to linear equations with constant coefficients; Partial differential equations: Linear and quasi-linear first order partial differential equations, Lagrange and Charpits methods for solving first order partial differential equations, general solution of higher order linear partial differential equations with constant coefficients.

**Numerical Analysis:** Bisection, secant and Newton-Raphson methods for algebraic and transcendental equations, fixed point iteration, rate of convergence; Systems of linear equations: Gauss elimination and LU decomposition, Gauss Jacobe and Gauss Siedal methods, condition number; Numerical integration: trapezoidal and Simpsons rules, errors and their bounds and finite difference operators.

**3Dimensional Geometry and Vector Calculus:** Direction cosines and direction ratios, vector equation of a line, coplanar and skew lines, shortest distance between two lines, vector equation of a plane, angle between two planes, angle between a line and a plane, distance of a point from a plane; vector triple products, directional derivative, curl, divergence, gradient, Gauss- divergence theorem, Stoke's theorem and their applications.

**Mechanics:** Force vectors, equilibrium of a particle, force system resultants, equilibrium of a rigidbody, friction, kinematics of a particle, kinetics of a particle; Force and acceleration, work and energy, impulse and momentum, planar kinematics of a rigid body, planar kinetics of a rigid body: force and acceleration, work and energy, impulse and momentum; Common catenary, virtual work.

**Linear Programming:** Linear programming problem and its formulation, graphical method ofsolution, convex sets, feasible and infeasible solutions, optimal feasible solutions, simplex method, big-M and two phase methods, dual problem.

**Probability and Statistics:** Sample space, discrete and continuous random variables, cumulative distribution, mean and variance of random variable, expectation, moments generating functions, distribution: uniform, binomial, poisson, geometric, normal and exponential expectation of functions of two variables and conditional expectation.

**Part B:**

**Linear Algebra:** Algebra of matrices, rankof a matrices, systems of linear equations,eigen values and eigen vectors, minimal polynomial, Cayley-Hamilton Theroem, diagonalisation, Hermitian, Skew-Hermitian and unitary matrices; Matrix representation of linear transformations, change of basis, canonical forms, diagonal forms, triangular forms, Jordan forms; Finite dimensional inner product spaces, orthonormal basis, Gram-Schmidt orthonormalization process, self-adjoint operators; Quadratic forms, reduction and classification of quadratic forms.

**Complex Analysis:** Analytic functions, Cauchy-Riemann equations, conformal mappings, bilineartransformations; complex integration, Cauchy's theorem, Liouville's theorem, maximum modulus principle, Taylor and Laurent's series, singularities, calculus of residues, Stereographic projection.

**Analysis: ** Metric spaces, normed linear spaces, inner product spaces, Banach and Hilbert spaces,compactness, connectedness, completeness, Weierstrass approximation theorem; Functions of bounded variation, Lebesgue measure, measurable functions; Lebesgue integral, Fatou's lemma, monotone convergence theorem, dominated convergence theorem.

**Abstract Algebra: ** Conjugacyclasses, finite abelian groups, solvable groups, subgroups and normal subgroups, Cauchy Theorem and p-groups, the Structure of Groups, Sylow's theorems and their applications; ideals, prime and maximal ideals, quotient rings, Euclidean domains, Principleideal domains and unique factorization domains; Polynomial rings and irreducibility criteria; finite fields, extensions of field.

**Ordinary Differential Equations:** First order ordinary differential equation (ODE), existence anduniqueness theorems and solutions of first order initial value problems, singular solution of first order ODEs, systems of linear first order ODEs; method of solution of dx/P=dy/Q=dz/R, orthogonal trajectories, solution of Pfaffian differential equations in three variables, linear second order ODEs with variable coefficients; Sturm-Liouville boundary value problems, theory of Green's function and solution of boundary value problems using Green's function, method of Laplace transforms for solving ODEs; Series solutions, Legendre and Bessel functions and their orthogonality.

**Partial Differential Equations:** Cauchy problem for first order PDEs, method of characteristics;second order linear equations in two variables and their classification; Method of separation of variables for Laplace, Heat and Wave equations; Cauchy, Dirichlet and Neumann problems; solutions of Laplace, wave and diffusion equations in two variables; Fourier series and Fourier transform and Laplace transform methods of solutions for the above equations; theory of Green's function and solution of above equations using Green's function.

**Numerical Analysis:** Numerical solution of algebraic and transcendental equations: methods forsystem of nonlinear equations, condition for convergence, rate of convergence, methods for complex roots; Iterative methods for the solution of systems of linear equations: Jacobi, Gauss-Seidel and SOR methods; eigen values of iteration matrix, determination of optimal relaxation parameter, matrix eigenvalue problems: Jacobi method, power method; interpolation: error of polynomial interpolation, Lagrange, Hermite, Newton and spline interpolations; numerical differentiation; numerical integration: quadrature formula, method based on undetermined parameters, Gauss-Legendre quadrature, composite integration, double integration; least square polynomial approximation, rational approximation; numerical solution of ordinary differential equations: initial value problems: Taylor series methods, Euler's forward and backward methods, Runge-Kutta methods.

**Mechanics and Calculus of Variation:** Virtual work, Generalized coordinates, Lagrange's equationsfor holonomic systems, Hamilton's canonical equations, canonical transformation, Hamilton's principle and principle of least action, two-dimensional motion of rigid bodies, Euler's dynamical equations for the motion of a rigid body about an axis; Variation of a functional, variation problems with fixed boundaries, Euler-Lagrange equation, necessary and sufficient conditions for extremum, variational methods for boundary value problems in ordinary and partial differential equations.

See the M.Phil./Ph.D (Applied Mathematics) Entrance Test paper for the year 2013

**Interview:** Candidates up to five times the number of seats will be short-listed for interview on the basis of their performance in the entrance test subject to a minimum cut off. Interview will carry a weightage30 marks. A minimum of 50% marks will have to be secured in both written test and interview in order to be eligible for the admission.

Candidates invited for interview will be given a travel subsidy (upper limit Indian Rs. 5000) towards actual travel cost by the shortest route as per instructions to be communicated to the selected candidates later. If candidates from outside India are unable to travel to New Delhi for the interview, they can seek permission for an interview through Skype.

A final merit list will be drawn by adding marks of the entrance test and the interview. Separate merit lists will be made for (a) candidates from all SAARC countries other than India, and (b) candidates from India. Equal number of candidates will be offered admission from these two lists, provided they secure overall qualifying marks of 50%. Up to 30% of the seats may be filled by candidates who have already secured JRF funding through a National competitive test in any of the SAARC countries.

MA Sociology is a two year (four semesters) academic programme.

After twelve years of schooling, a 3 year Bachelor’s degree from a recognized University in any discipline with minimum 50% marks or equivalent grade. Candidates who have a 2 year Bachelor’s degree and have done first year of Master’s programme are also eligible.

**Format of the Entrance Test Paper:**

Eligible candidates need to appear for the entrance test conducted by the university. The entrance test paper would be worth 100 marks and is three hours in duration. The question paper for the admission test has three parts in the following format:

Part I would be for 25 marks consisting of 25 multiple choice questions (one mark each). All questions in this section are compulsory. The questions would measure the general awareness of the applicant about the world in general and South Asia in particular. These questions would be of 10+2 (12th Class) standard.

Part II would have 25 multiple choice questions worth one mark each. All questions are compulsory. Total marks for this part is 25. The questions would measure the applicant’s knowledge on Sociology and Social Anthropology at a general level.

Part III would have six essay type questions out of which two questions must be answered by candidates in not more than 600 words each. Each question carries 25 marks. The total marks for this section is 50.

See the MA (Sociology) Entrance Test for the year 2013.
###

### Syllabus:

Part I will test the general awareness about the world around us.

Part II will test the candidate’s general awareness of Sociology and Social Anthropology taught at undergraduate level.

Part III will test a student on: (i) her/his ability to comprehend the subject knowledge analytically and critically. (ii) her/his ability to structure an essay logically; (iii) her/his ability to write grammatically correct English.

LLM would be a two-year (four semesters) academic programme.

A minimum of 17 years’ education (12 years’ schooling + 5 years integrated BA/LLB degree with 50% marks) is the minimum prescribed eligibility. Candidates who have done 12 years’ schooling + 3 year Bachelor’s degree + 3 years’ LLB degree or 12 years' schooling and 4 years’ LLB degree with 50% marks are also eligible.

The Question Paper will consist of two Parts: Part A and Part B. Part A will have 20 objective type/multiple choice questions of 10+2 (12th Class) level, of one mark each. Part B will have 80 objective type/multiple choice questions of the LLB level carrying one mark each.

M.A. International Relations would be a two year (four semesters) academic programme.

After twelve years’ schooling, a 3-year Bachelor’s degree from a recognized university with minimum 50% marks or equivalent grade. Candidates who have a 2- year Bachelor’s degree and have done first year of Master’s programme are also eligible.

**Format of the Entrance Test question paper and course:**

Eligible candidates have to appear for an admission test conducted by the university. The admission test paper would be of 100 marks and of 3 hours duration. The question paper for the admission test would have three parts:

Part I would be of 20 marks with 20 multiple choice type questions (of 1 mark each). All questions will be compulsory in this section.

Part II would be of 50 marks with 5 short note questions of 10 marks each. There will be a choice of 5 from 10 questions. Total marks for this part will be 50.

Part III would be of 30 marks with one long descriptive/essay type question of (approximately 600 words, but not more than 1000 words) to be selected from 2 questions.

See MA International Relations Entrance Test question paper of the year 2013
###

### Syllabus:

Part I will test the general awareness about South Asia.

Part II will test information that the student has about social sciences in general and Political Science/International Relations in particular taught at the undergraduate level.

Part III will test a student on: (i) her/his ability to comprehend the subject knowledge analytically and critically. (ii) her/his ability to structure an essay logically; (iii) her/his ability to write grammatically correct English.

After 12 years’ schooling, a 3/ 4 year Bachelor’s degree in Computer Science or a relevant area* from a recognized university/ institution with at least 55% marks in aggregate or an equivalent grade, with mathematics as a subject of study at the Bachelor’s level, or at 10+2 (12th class) level.

*Relevant Areas:

- Computer Engineering
- Computer Technology
- Computer Applications
- Information Science
- Information Technology
- Software Systems
- Software Engg.
- Software Technology
- Electronics Engg.
- Electronics Engg.
- Electrical & Electronics Engg.
- Applied Physics
- Applied Statistics
- Applied Mathematics
- Instrumentation Engg.

The duration of the test will be three hours. The test will consist of 100 multiple choice questions of one mark each. Each question will have four options and out of these four options, one option will be correct.

Candidates can expect

- i. Twenty (20) questions from Part A

- ii. Thirty (30) questions from Part B

- iii. Fifty (50) questions from Part C

There will be no subjective question and no negative marking. The test will be divided into the following three parts:

**PART A: Analytical and Logical Abilities, English Language Proficiency**

Data Sufficiency, Problem Solving, Integrated Reasoning, English Grammar, Sentence Completion, Verbal Analogies, Word Groups

**PART B: Mathematical Science**

**Set Theory and Algebra:** Sets, Relations, Functions, Groups, Partial Orders, Lattice, Boolean Algebra

**Matrices and Determinants:** Determinants, Matrices, systems of Linear Equations

**Combinatorics:** Permutations, Combinations, Counting, Summation

**Probability and Statistics:** Mean, median, mode and standard deviation; Conditional probability, independent events, total probability, Baye's theorem

**Calculus:** Limit, Continuity and Differentiability, Mean value Theorems, Theorems of Integral Calculus, Evaluation of Definite and Improper Integrals, partial Derivatives, Total Derivatives, Maxima and Minima.

**Ordinary Differential Equations:** First Order First Degree Equations, Variable Separable Method, Homogeneous Equations, Exact Equations, Integrating Factors, Linear Equations.

**Vector Analysis:** Addition, Subtraction, Dot Product and Cross Products of Vectors.

**PART C: Undergraduate level Computer Science**

**Discrete Mathematics:** Sets, Relations, Functions, Boolean Algebra, Propositional logic, First order Predicate Logic

**Programming in C:** Elements of C, Identifiers, Data Types, Control Structures, Iteration, Structured Data Types: Array, Structure, Union, Strings, Pointers, Functions, Parameter Passing to Functions, Recursion.

**Algorithms: ** Elementary Space and Time Complexity Analysis, Sorting: Bubble Sort, Insertion Sort, Selection Sort, Searching: Linear and Binary Search.

**Digital Logic Design and Computer Architecture:** Number System, Data Representation, and Computer Arithmetic, Logic Gates, Combinational and Sequential Circuits, Computer Organization, Instruction Formats and Addressing, Memory Organization and I/O Interfaces.

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