Syllabus of Online Entrance Examination - 2014

1. 50 QUESTIONS of General Awareness.

2. 50 Questions subject based as per the syllabus given below.

The above pattern will not be applicable to the courses of M.Phil Statistics, Biostatistics and M.Sc.

Nuclear Medicine.

Programmes Syllabus

1. M.Phil. Statistics Probability and Distribution theory Brief review of basic distribution theory, joint, marginal , conditional pmf’s and pdf’s,

standard discrete and continuous distr ibutions, bivariate normal, bivariate exponential and

multinomial distributions, functions of random variables and transformation of random

variables.

Compound, truncated and mixture distributions, conditional expectat ion, multiple and partial

correlations, l inear and multiple regressions. Markov, Holder, Jensen, Liapunov inequalit ies.

Sampling distributions, non -central Chi-square, t and F distributions and their properties.

Distributions of quadratic forms under normality and related distribution theory.

Order stat istics, their distributions and properties, joint and marginal distr ibutions of order

statistics, distribution of median and range, extreme values.

Statistical Inference Properties of good estimators, Unbiasedness, Consistency, Efficiency, Sufficiency Minimal sufficient statistics

and Completeness. Cramer-Rao bounds, Bhattacharya bounds. Minimum variance unbiased estimators, Rao-

Blackwell Theorem. Lehman-Scheffe theorem and their applications.

Method of Estimation, Method of Maximum Likelihood, Method of Moments, Method of Chi-Square, properties

of M.L.E. Location Invariance, scale invariance. Pitmann’s estimators for location and scale parameters.

Non-randomized and randomized tests. Size, power functions. unbiasedness. NP-Lemma and its applications in

construction of MP tests for simple null hypotheses. MLR families.

UMP tests for one sided null hypotheses against one-sided composite alternative. Generalized NP lemma,

Locally best test, UMPU tests, Similar tests, Neyman structure, UMPU tests against one-sided and two-sided

alternatives, Confidence set estimation, Relation with hypothesis testing, optimum parametric confidence sets.

DESIGN OF EXPERIMENTS

Principles of design of experiments, uniformity trails, randomized experiments, completely randomized design,

randomized block design, Latin square design .

Analysis of covariance in a general Gauss-Markov model, applications to standard designs.

Fixed, mixed and random effects models; Variance components estimation - study of various methods; Tests for

variance components; Missing plot technique - general theory and applications.

General factorial experiments, factorial effects; best estimates and testing the significance of factorial effects;

study of 2 and 3 factorial experiments in randomized blocks; Complete and partial confounding. Fractional

replication for symmetric factorials. Split plot and split block experiments.

SAMPLEING TECHNIQUES

Review of SRSWR/WOR, Ratio and regression method of estimation. Unequal probability sampling:

PPSWR/WOR methods and related est imators of a f inite population mean. Hansen -Hurwitz

and Desraj estimators for general sample size and Murthy's estimator for a sample o f size 2.

Horvitz-Thompson estimator, its variance and unbiased estimator of variance, IPPS schemes

of sampling due to Midzuno-Sen, Rao-Hartley-Cochran and Samphord.

The Jackknife and Bootstrap: estimate of bias, estimate of variance. Ratio Estimati on in

reference to Jackknife and bootstraps, Relationship between the jackknife and the bootstrap.

Interpenetrating sub sampling.

Multivariate Analysis

Multivariate Analysis: Properties of multivariate distributions, characteristic functions and moments. Bivariate

normal and Multivariate normal. Wishart matrix - its distribution and properties, Distribution of sample

generalized variance, Null and non-null distribution of simple correlation coefficient. Application in testing and

interval estimation.

Null distribution of Hotelling's T2 statistic, Application in tests on mean vector for one and more multivariate

normal populations and also on equality of the components of a mean vector in a multivariate normal

population, Fisher Behren Problem.

Classification and discrimination procedures for discrimination between two multivariate normal populations-

sample discriminant function, test associated with discriminant functions, probabilities of misclassification and

their estimation, classification into more than two multivariate normal populations.

Multivariate Analysis of variance (MANOVA) for one way classified data only, Principal components, dimension

reduction, Canonical variables and canonical correlations: definition, use, estimation and computation.

Non-Parametric Inference Non-Parametric Inference : Test for Randomness, Test based on Runs & Sign for one & two samples problems,

Median test, Wilcoxon and Mann-Whitney tests. Kolmogorov-Smrinov test for one and two samples.

Operation Research Introduction: Definition and scope of operations research, Different types of models used in OR. Various phases

of OR.

Allocation Problems: Mathematical formulation of L.P.P, Graphical method to solve a L.P.P, Convex set, Convex

combination and extreme points. Simplex method to solve a L.P.P with slack, Surplus and Artificial variables.

Construction of dual of a L.P.P.

Transportation Problem: Mathematical formulation of a transportation problem, Northwest corner rule, unit

cost penalty method and method of matrix minima. Optimality test, Unbalanced transportation problem,

Degeneracy in transportation problems.

Assignment Problems: Assignment problems, formulation of these problems and their solutions, Unbalanced

Assignment problems.

2. M.Phil. Management As per the syllabus of UGC NET.

3. M.Phil. Economics As per the syllabus of UGC NET.

4. M.Tech. (Computer Science) Part I :-

Computer Organization and Architecture: Machine instructions and addressing modes, ALU and data-path, CPU

control design, Memory interface, I/O interface (Interrupt and DMA mode), Instruction pipelining, Cache and

main memory, Secondary storage.

Discrete Mathematics: Counting principles, linear recurrence, mathematical induction, equation sets, relations and

function, predicate and propositional logic. Digital Logic: Logic functions, Minimization, Design and synthesis of

combinational and sequential circuits; Number system representation and computer arithmetic.

Part II :-

Programming and Data Structures: Programming in C; Functions, Recursion, Parameter passing, Scope, Binding;

Abstract data types, Arrays, Stacks, Queues, Linked Lists, Trees, Binary search trees, Binary heaps.

Analysis and Design of Algorithms: Analysis, Asymptotic notation, Notions of space and time complexity, Worst

and average case analysis; Design: Greedy approach, Dynamic programming, Divide-and conquer; Tree and

graph traversals, Connected components, Spanning trees, Shortest paths; Hashing, Sorting, Searching. Asymptotic

analysis (best, worst, average cases) of time and space, upper and lower bounds, Basic concepts of complexity

classes P, NP, NP-hard, NP- complete.

Part III :-

Computer Networks and Operating System: Error-Detection and Error- correction techniques, Topology, Routing

and Internetworking, Channel Allocation, Congestion Control, Processes, Threads, Concurrency,

Synchronization, Deadlock, CPU scheduling, Memory management and virtual memory, File systems.

Databases: ER-model, Relational model (relational algebra, tuple calculus), database design (integrity constraints,

normal forms), File structures Transactions and concurrency control.

Information Systems and Software Engineering: information gathering, requirement and feasibility analysis, data

flow diagrams, process specifications, input/output design, process life cycle, planning and managing the project,

design, coding, testing, implementation, maintenance.

5. M.A. in Social Science [5 years integrated course]

Indian socio economic and political systems, Modern Indian History, Indian Economic Development and Planning, Globalization, Rural Development Programs and Women Economic Empowerment.

6. MA/MSc in Earth Science [5 Yrs Integrated course]

Knowledge of Life Sciences / Biology / Geology / Geography in general, Chemistry, Physics & Maths.

7. M.A. in Social Management [5 Yrs Integrated course]

Management and Society, Management and Economy, Politics and Management, Culture and Value and Management, Technology and Management, Human Rights and Management, Socio economic policies and programs.

8. Master of Social Work (MSW) Basic Concepts: Society; Community; Association; Social Groups; Culture - Social Work; Social Welfare; Social

Service; Social Reform; Social Security; Social Justice; Social Defence; Social Policy; Social Planning; Social

Development.

Social Institutions: Marriage and Family, Religion and Caste.

Social Problems: Poverty; Illiteracy; Un-employment; Beggary; Crime; Gender Discrimination; Children-in-

Conflict with Law; Children-in-Need of Care and Protection; Alcoholism; Drug Dependence; Commercial Sex

Work; Child Labour; Human Trafficking; Corruption; Communal Tensions; Indian Labour Problems.

Development: Social and Economic Indicators. National and International Organisations involved in Social

Welfare – Role of Voluntary Action in Social Development.

Issues Concerned with Children; Youth; Women and Aged – Social Legislation pertaining to Women;

Children; and Persons with Disabilities.

Fundamental Rights; Directive Principles of State Policy – Constitutional Safeguards for Scheduled Castes and

Scheduled Tribes – Welfare Programmes for Backward Classes; and Minorities – Welfare of Physically and

Mentally Challenged.

Human Behaviour; Personality; Intelligence; Learning; Motivation; Attitudes; Leadership - Stages of Human

Development – Psychological Disorders.

Demography and Family Welfare – Demographic Trends in India – National Population Policy.

Concepts of Health and Disease; Basic Health Issues; Health Services; Health Education; Occupational Health;

Health Programmes in India; National Health Policy.Rural, Urban and Tribal Development: National

Programmes – Environmental Protection Activities – Disaster Management – Effects of Air Pollution; Prevention

and Control of Air Pollution; Standards and Types of Ventilation; Effects of Noise Exposure and Control of Noise

– Housing and Health – Waste Management.

Human Rights – Status on Protection and Promotion of Human Rights – Right to Information and Right to

Education. Liberalization, Privatization and Globalization – Impact on Personal and Social Life. Issues concerned

with Human Resource Management.

General knowledge; Reasoning ability; Verbal ability; High School Standard Maths; English Language

Vocabulary

9. MCA [Corporate] Master of Computer Applications) 6 Semesters

Unit I: Mathematics: Solution of Linear and Qandratic Equation, Convergence and Divergence of Series, Function,

Limit and Continuity, Differential and Integral Calculus, Matrix Algebra.

Unit II: Computer Fundamentals: Computer Basic, Data Representations, Binary Arithmetic, I/O Units, Computer

memory, Processor, Logic Circuits, Computer Network, network Topologies.

Unit III: Programming in ‘C’: Constants, Variable and Data Types, operators and Expressions, I/O Operators, Decision

Making, Branching, Looping, Arrays, Character Strings, Functions, Unions, Pointer and File Management.

10. MA/MSc in Financial Economics

Mathematical Economics, Contemporary Issues in Indian Economy, Economics of Growth and Development,

Basic Statistics, Basic Econometrics, Economics of Insurance, International Finance, Logical Aptitude,

Mathematical Aptitude, General Studies.

11. MA/MSc in Fashion Technology & Apparel Design

Syllabus will contain graduate level knowledge of B.A./B.Sc. in area of Food Science, Home Science, Textile,

Fashion Technology.

12. MA- Psychology Graduate course of Arts, Commerce & Science with any discipline.

13. MA- Philosophy Graduate course of Arts, Commerce & Science with any discipline.

14. MA/M.Sc. Anthropology Concept of organization of society; Forms of social organization; family, lineage, clan, moiety, Phratry, Tribe.

Definition and significance; order within and between societies; Concept of authority, power, rank, leadership,

legitimacy and control.

Introduction, Nature and Scope Branches of Biological Anthropology Bio-cultural perspective in evolutionary

processes. Applied aspects of Biological Anthropology.

Bio-cultural Evolution of Humans Multiregional Vs. out of Africa theories of Modern Human origins Phenotypic

and Genotypic variation, Distribution of Human Variation, Historical overview of concept of Race, Criteria of

Racial Classification, Genetic aspects of race mixture. Racism, UNESCO Statement of Race.

Archaeology, Relation of Archaeology with Sciences, Social Sciences and Anthropology Major Branches,

Prehistory, Proto-history and Ethno-Archaeology.

Field work tradition in Anthropology, Ethnography as a holistic documentation of culture.

Introduction to major concepts in Indian Anthropology.

15. MA- Public Health Personal Hygiene, Organ Hygiene and health care, immunization, epidemiology, communicable diseases / non communicable diseases, sanitation and hospital waste management, water and water borne diseases, nutrition and health, dietary deficiency diseases, health statistics, word organization related with health care, health programmes in India, occupational health, demography and family planning, environment and health and neonatal health.

16. MA-Public administration General Knowledge – 50% Indian Political System and Administration – 50%

17. MA- Community Development Community Development concept, Definition, meaning, need, history, principles, objectives and scope. Rural development concept, definition, meaning, need, objects and scope. Rural Development in India – Origin and background – early experiments like Srinekethan, Sevagram, Marthandam, Gurugen experiment, Baroda experiment, Firka development in Madras. Nilokheri experiment, Etowah pilot project etc. Approaches to rural development – Gandhian contractive program – contribution of Vinobaji. Agrarian relations and movements in India with special reference to Bhoodan and Gramdhan. Role of NGOs, Industries in rural development. Slums in India: Theories, causes and conditions, poverty in urban areas, culture of poverty in slums, poverty alleviation programmes. Concept of Region. Types of Regions – functional and formal region. Techniques of regions delimitation. Regionalisation in India. Physiographic, Economic, Linguistic. Classification and Hierarchy of regions. The Concept of Rural – Urban Continuum. Definition, Scope and Methods of Regional Planning, Town and Country Planning. Water Shed Planning. Agro-Climatic Regional Planning, District – Level Planning, Micro-level planning. Relevance of micro-level planning in local self government.

18. MA- Disaster Management Concepts, Approaches and theories of disasters, Relief, rehabilitation and reconstruction, Role of national and international agencies in disaster management, Natural and human induced disasters, Finance and insurance in Disaster Management.

19. MA-Gender Studies Women and Society, Women and Politics, Women and Culture, Women and Technology, Women and Rights and Women and Policies and programs.

20. MA-Hindi

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21. MA-Development Studies Syllabus will cover subject areas of social science, Indian history particularly modern Indian history and freedom

struggle, Indian Polity, Indian Economy, Basic concept on society and its structure.

Indian Geography (Demography, Census, Environment etc.)

22. MA-Education Syllabus is divided into two parts-

1. General Knowledge and Current affairs. All the disciplines upto class 10th.

2. General awareness relating to teaching aptitude, reasoning, numerical ability, language proficiency and

awareness relating to educational planning, policy, provisions, schemes, committees & commissions.

23. BPEd (4 Year Integrated Physical Education Course)/ 8 Sem.

10+2 level knowledge from any stream (Arts/ Science/Commerce).

Master of Science (M.Sc.) Programmes (4 Semester)

25 MSc - Basic Science [5 Yrs Integrated course] (On the pattern of IISER)

GENERAL :

There is no specific syllabus for the General section. This section aims to test the candidate’s general ability to

comprehend qualitative and quantitative aspects of a given scientific passage and interpretation of graphs of

simple systems. This will be done by giving a passage on some scientific topic and questions based on the

concepts elaborated in the passage will be asked. Questions are designed to test the candidate’s familiarity

with (and not a detailed understanding of) major historical milestones in mathematics, physics, chemistry,

biology, astronomy, computer science and environment. There will be some questions designed to test the

grasp of mathematics up to 10th

standard and application capabilities of the same to simple problems.

BIOLOGY :

Cell Biology-

Cell theory and cells as unit of life. Tools and techniques of cell studies - use of microscope and calibration

(microscopy), elements of microscope. Biomembranes – transport mechanism, cellular respiration. Cell

organelles - structure and functions. Discovery and structure of DNA, processes of replication, transcription,

genetic code and translation. Principles of the basic techniques in molecular biology.

Anatomy and Physiology-

Digestive System - Modes of nutrition. Structure of alimentary canal and associated glands, digestive enzymes

and gastrointestinal hormones. Absorption of products of digestion, peristalsis, balanced diet. Respiratory

System - Gaseous exchange in animals. Structure of respiratory organs, mechanism of breathing, gaseous

transport, tissue respiration. Circulatory System - Open and closed systems. Functions of blood and 1ymph.

Microscopic structure of blood and blood vessels. Structures and working of heart. Distribution of arteries and

veins. Circulation of blood coagulation. Blood groups. Excretory System - Elimination of nitrogenous waste.

Osmoconformers and osmoregulators. Structure and function of kidney tubules. Arrangement of excretory

organs. Nervous System - General account of brain, spinal cord and nerves. Reflex actions (simple and

conditioned). Sense organs (eye and ear).

Reproductive System --- Sexual and asexual reproduction. General arrangement and functions of reproductive

organs. Developmental Biology --- Basic features of development in animals. Types of eggs, fertilization,

cleavage, blastula. Stem cells- definition, types, uses, advantages and

disadvantages,induced pluripotent stem cells. Diversity of Animal Life ---Principles of classification, binomial

nomenclature. General classification of animal phyla up to classes (invertebrates) and upto sub-classes/ order

(vertebrates), General characters of fishes, amphibians, reptiles, birds and mammals. Genetics and Evolution --

- Fundamentals of genetics and evolution. Human genetics - human chromosomes, sex-determination, sex-

linked inheritance. Evidences and theories of organic evolution. Organization of the heredity material in

chromosomes. Equational division. Reduction division. Mitosis and meiosis compared and contrasted.

Significance of meiosis. Mendel's laws of inheritance. Discovery of linkage, sex-linked inheritance. Crossing-

over, stage 10 at which crossing-over occurs. Neurospora genetics. Mutation - discovery, types of Mutation

and Mutations in diploids. Role of mutations in evolution. Elaboration of Mendel's laws of inheritance.

Monohybrid or Dihybrid crosses.

Immunology- Basics of immune mechanisms and diseases- active and passive immunity, T and

B cell responses, antigen presentation, principles of vaccination, monoclonal antibodies and their uses,

immunology of AIDS. Enzymes- catalysis, kinetics, activation energy, competitive and non-competitive

inhibition.

Ecology- Physical and biological factors influencing organisms. Food chains, pyramids of numbers and biomass.

Biological equilibrium. Interspecific associations.

Botany -

Anatomy and Physiology of Plants - Meristems. Plant growth and development. Internal and external

regulators of growth and development in plant. Internal structure of root, stem, secondary growth and leaves.

Xylem and Phloem - their cell elements and functions. Internal structure of dicot and monocot leaves.

Photosynthesis - history, importance, factors and mechanism, stomatal mechanism, transpiration and

respiration. Comparative study of dicot and monocot anatomy. Absorption and cell-water relations, transport

of water and minerals, tropic and turgor movements. Significance of life-cycles with special reference to

alternation of generations as exemplified in Funaria, Selaginella and Pinus (no structural details). Systematics

- Principles of classical and new systematics. Binomial nomenclature. Familiarity with taxa.

Humans and Environment-

Soil, rainfall and temperature with reference to natural resources. Our natural resources - their uses and abuses.

Environmental pollution and preventive measures.

CHEMISTRY:

Physical Chemistry- Measurements in chemistry - SI units for fundamental quantities, significant figures, significant figures in

calculations General topics - Concept of atoms and molecules. Dalton’s atomic theory. Mole concept.

Chemical formulae. Balanced chemical equations. Calculations (based on mole concept) involving common

oxidation-reduction, neutralisation and displacement reactions. Concentration in terms of mole fraction,

molarity, molality and normality. Gaseous and liquid states - Absolute scale of temperature. ideal gas

equation. Deviation from ideality, van der Waals equation. Kinetic theory of gases, average, root mean square

and most probable velocities and their relation with temperature. Law of partial pressures. Vapour pressure.

Diffusion of gases.

Atomic structure and chemical bonding - Bohr model, spectrum of hydrogen atom, quantum numbers. Wave-

particle duality, de Broglie hypothesis. Uncertainty principle. Qualitative quantum mechanical picture of

hydrogen atom, shapes of s, p and d orbitals. Electronic configurations of elements (up to atomic number 36).

Aufbau principle. Pauli’s exclusion principle and Hund’s rule. Orbital overlap and covalent bond.

Hybridisation involving s, p and d orbitals only. Orbital energy diagrams for homonuclear diatomic species.

Hydrogen bond. Polarity in molecules, dipole moment (qualitative aspects only). VSEPR model and shapes of

molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal,

tetrahedral and octahedral).

Energetics - First law of thermodynamics. Internal energy, work and heat, pressure-volume work. Enthalpy,

Hess’s law. Heat of reaction, fusion and vapourization. Second law of thermodynamics. Entropy. Free energy.

Criterion of spontaneity.

Chemical equilibrium - Law of mass action. Equilibrium constant. Le Chatelier's principle (effect of

concentration, temperature and pressure). Significance of ΔG and ΔGº in chemical equilibrium. Solubility

product, common ion effect, pH and buffer solutions. Acids and bases (Bronsted and Lewis concepts).

Hydrolysis of salts.

Electrochemistry - Electrochemical cells and cell reactions. Standard electrode potentials. Nernst equation and

its relation to ΔG. Electrochemical series, emf of galvanic cells. Faraday's laws of electrolysis. Electrolytic

conductance, specific, equivalent and molar conductivity, Kohlrausch's law. Concentration cells.

Chemical kinetics - Rates of chemical reactions. Order of reactions. Rate constant. First order reactions.

Temperature dependence of rate constant (Arrhenius equation).

Solid state - Classification of solids. Crystalline state, seven crystal systems (cell parameters a, b, c, alpha,

beta, gamma), close packed structure of solids (cubic), packing in fcc, bcc and hcp lattices. Nearest

neighbours, ionic radii. Simple ionic compounds, point defects. Solutions - Raoult's law. Molecular weight

determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point.

Nuclear chemistry - Radioactivity. Isotopes and isobars. Properties of alpha, beta and gamma rays. Kinetics of

radioactive decay (decay series excluded), carbon dating. Stability of nuclei with respect to proton-neutron

ratio. Brief discussion on fission and fusion reactions.

Inorganic Chemistry-

Study of different groups in periodic table –

Group 1A (Preparation, properties and reactions of alkali metals, with emphasis on chemistry of Na and K and

their compounds - oxides, peroxides,hydroxides, carbon

ates, bicarbonates, chlorides and sulphates)

Group 2A (preparation, properties and reactions alkaline earth metals with emphasis on Mg and Ca and their

compounds such as oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates)

Group 3A (chemistry of Boron and its compounds – diborane)

Group 8A (preparation, properties and reactions inert gases with emphasis on

chemistry of Xenon)

Group 7A (halogen chemistry with special emphasis on chemistry of chlorine)

Study of nonmetals - C, S, N, P (especially oxides and oxyacids compounds of these elements, in addition

phosphines for P, ammonia for N) and O (peroxide and ozone), Si (silicones and silicates). (Allotropes of C, S,

N should be covered.)

Transition elements (3d series) - Definition, general characteristics, variable oxidation states and their

stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic

moment. Coordination compounds - nomenclature of mononuclear coordination compounds. cis-trans and

ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear,

tetrahedral, square planar and octahedral).

Metals and metallurgy - General methods involving chemical principles. General operation stages involved in

metallurgical operation. Metallurgy of p-block element (emphasis on Al). Metallurgy of Fe-triad (Fe, Co, And

Ni with more emphasis on

Fe metallurgy). Metallurgy of coinage metals (Cu, Ag with more emphasis on Cu)

Organic Chemistry-

Concepts - Hybridisation of carbon. Sigma and pi-bonds. Shapes of simple organic molecules. Structural and

geometrical isomerism. Optical isomerism of compounds containing up to two asymmetric centres, (R, S and

E, Z nomenclature excluded). IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono-

functional and bi-functional compounds).

Conformations of ethane and butane (Newman projections). Resonance and

hyperconjugation. Keto-enol tautomerism. Determination of empirical and molecular

formulae of simple compounds (only combustionmethod). Hydrogen bonds-definition and their effects on

physical properties of alcohols and carboxylic acids. Inductive and resonance effects on acidity and basicity of

organic acids and bases. Polarity and inductive effects in

alkyl halides. Reactive intermediates produced during homolytic and heterolytic bond cleavage. Formation,

structure and stability of carbocations, carbanions and free radicals. Preparation, properties and reactions of

alkanes - Homologous series, physical properties of alkanes (melting points, boiling points and density).

Combustion and halogenation of alkanes.

Preparation of alkanes by Wurtz reaction and decarboxylation reactions. Preparation, properties and reactions

of alkenes and alkynes - physical properties of alkenes and alkynes (boiling points, density and dipole

moments). Acidity of alkynes. Acid catalysed hydration of alkenes and

alkynes (excluding the stereochemistry of addition and elimination). Reactions of alkenes with

KMnO 4 and ozone. Reduction of alkenes and alkynes. Preparation of alkenes and alkynes by elimination

reactions. Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O

(X=halogen). Addition reactions of alkynes; Metal acetylides Reactions of benzene - Structure and

aromaticity. Electrophilic substitution reactions - halogenation, nitration, sulphonation, Friedel-Crafts

alkylation and acylation. Effect of o-, m- and p- directing groups in monosubstituted benzenes.

Phenols - Acidity, electrophilic substitution reactions (halogenation, nitration and

sulphonation). Reimer-Tieman reaction, Kolbe reaction.

Characteristic reactions of the following (including those mentioned above)

Alkyl halides - rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution

reactions Alcohols - esterification, dehydration and oxidation, reaction with sodium, phosphorus halides,

ZnCl2/ concentrated HCl, conversion of alcohols into aldehydes and ketones. Ethers - Preparation by

Williamson's Synthesis. Aldehydes and Ketones - oxidation, reduction, oxime and hydrazone formation. aldol

condensation, Perkin reaction.

Cannizzaro reaction. Haloform reaction and nu cleophilic addition reactions (Grignard addition). Carboxylic

acids - formation of esters, acid chlorides and amides, ester hydrolysis.

Amines - basicity of substituted anilines and aliphatic amines, preparation from nitro

compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines,

Sandmeyer and related reactions of diazonium salts. carbylamine reaction. Haloarenes - nucleophilic aromatic

substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).

Carbohydrate - Classification. mono- and di- saccharides (glucose and sucrose). Oxidation, reduction,

glycoside formation and hydrolysis of sucrose.

Amino acids and peptides - General structure (only primary structure for peptides) and physical properties.

Some examples for separation of amino acid mixture using physical properties.

MATHEMATICS :

Algebra-

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of

modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations. Quadratic

equations with real coefficients, relations between roots and coefficients, formation of quadratic equations

with given roots, symmetric functions of roots.

Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite

arithmetic and geometric progressions, infinite geometric series, sums of squares and cubes of the first n

natural numbers.

Logarithms and their properties.

Permutations and combinations, Binomial theorem for positive integral index, properties of binomial

coefficients. Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a

scalar and product of matrices, transpose of a matrix, determinant of a square matrix of order up to three,

inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and

skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three

variables.

Addition and multiplication rules of probability, conditional probability, Bayes Theorem, independence of

events, computation of probability of events using permutations and combinations.

Trigonometry-

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving

multiple and sub-multiple angles, general solution of trigonometric equations.

Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a

triangle, inverse trigonometric functions (principal value only).

Analytical geometry-

Two dimensions - Cartesian coordinates, distance between two points, section formulae, shift of origin.

Equation of a straight line in various forms, angle between two lines, distance of a point from a line. Lines

through the point of intersection of two given lines, equation of the bisector of the angle between two lines,

concurre

ncy of lines. Centroid, orthocentre, incentre and circumcentre of a triangle.

Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle,

intersection of a circle with a straight line or a circle, equation of a circle through the points of intersection of

two circles and those of a circle and a straight line.

Equations of a parabola, ellipse and hyperbola in standard form, their foci, directories and eccentricity,

parametric equations, equations of tangent and normal. Locus Problems.

Three dimensions - Direction cosines and direction ratios, equation of a straight line in space, equation of a

plane, distance of a point from a plane.

Differential calculus-

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and

quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric,

exponential and logarithmic functions.

Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two

functions, L’Hospital rule for evaluation of limits of functions.

Even and odd functions, inverse of a function, continuity of composite functions, intermediate value property

of continuous functions. Derivative of a function, derivative of the sum, difference, product and quotient of

two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric,

exponential and logarithmic functions.

Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative,

tangents and normals, increasing and decreasing functions, maximum and minimum values of a function,

Rolle’s Theorem and Lagrange’s Mean Value Theorem.

Integral calculus-

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals

and their properties, Fundamental Theorem of Integral Calculus. Integration by parts, integration by the

methods of substitution and partial fractions, application of definite integrals to the determination of areas

involving simple curves.

Formation of ordinary differential equations, solution of homogeneous differential equations, separation of

variables method, linear first order differential equations

Vectors-

Addition of vectors, scalar multiplication, dot and cross products, scalar triple products and their geometrical

interpretations.

PHYSICS:

General- Units and dimensions, dimensional analysis. least count, significant figures. Methods of measurement (Direct,

Indirect, Null) and measurement of length, time, mass, temperature, potential difference, current and

resistance. Design of some simple experiments. Identification of independent, dependent and control variables.

Identification of sample size, range and interval. Identification of appropriate measurement techniques and

instruments. Graphical representation, interpretation and analysis of data. Errors in the measurements and

error analysis.

Mechanics-

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles. Uniform circular motion.

Relative velocity. Newton’s lawsof motion. Inertial and uniformly accelerated frames of reference. Static and

dynamic friction. Kinetic and potential energy. Work and power. Conservation of linear momentum and

mechanical energy. Systems of particles. Centre of mass and its motion. Impulse. Elastic and inelastic

collisions.

Law of gravitation. Gravitational potential and field. Acceleration due to gravity. Motion of planets and

satellites in circular orbits. Escape velocity.

Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies

with simple geometrical shapes. Angular momentum, Torque. Conservation of angular momentum. Dynamics

of rigid bodies with fixed axis of rotation. Rolling without slipping of rings, cylinders and spheres.

Equilibrium of rigid bodies. Collision of point masses with rigid bodies.

Linear and angular simple harmonic motions. Hooke’s law, Young’s modulus.

Pressure in a fluid. Pascal’s law. Buoyancy. Surface energy and surface tension, capillary rise. Viscosity -

Stoke’s and Poiseuille’s law, Terminal velocity. Streamline flow, equation of continuity. Bernoulli’s theorem.

Plane wave motion, longitudinal and transverse waves, superposition of waves. Progressive and stationary

waves. Vibration of strings and air columns. Resonance. Beats. Speed of sound in gases. Doppler effect (in

sound).

Thermal physics-

Thermal expansion of solids, liquids and gases. Calorimetry, latent heat. Heat conduction in one dimension.

Elementary concepts of convection and radiation. Newton’s law of cooling. Ideal gas laws. Specific heats (CV

and CP for monoatomic and diatomic gases). Isothermal and adiabatic processes, bulk modulus of gases.

Equivalence of heat and work. First and second law of thermodynamics and its applications (only for ideal

gases). Entropy. Blackbody radiation - absorptive and emissive powers. Kirchhoff’s law. Wien’s displacement

law, Stefan’s law.

Electricity and magnetism-

Coulomb’s law. Electric field and potential. Electrical potential energy of a system of point charges and of

electrical dipoles in a uniform electrostatic field; Electric field lines. Flux of electric field. Gauss’s law and its

application in simple cases, such as to find field due to infinitely long straight wire. uniformly charged infinite

plane sheet and uniformly charged thin spherical shell. Capacitance - Calculation of capacitance with and

without dielectrics. Capacitors in series and parallel. Energy stored in a capacitor.

Electric current. Ohm’s law. Series and parallel arrangements of resistances and cells. Kirchhoff’s laws and

simple applications; Heating effect of current.

Biot-Savart’s law and Ampere’s law. Magnetic field near a current carrying straight wire, along the axis of a

circular coil and inside a long straight solenoid. Force on a moving charge and on a current carrying wire in a

uniform magnetic field.

Magnetic moment of a current loop. Effect of a uniform magnetic field on a current loop. Moving coil

galvanometer, voltmeter,ammeter and their conversions.

Electromagnetic induction - Faraday’s law, Lenz’s law. Self and mutual inductance. RC, LR and LC circuits

with and A.C. Sources.

Optics-

Rectilinear propagation of light. Reflection and refraction at plane and spherical surfaces, Deviation and

dispersion of light by a prism. Thin lenses. Combination of mirrors and thin lenses. Magnification. Wave

nature of light - Huygen’s principle,

interference limited to Young’s double slit experiment. Elementary idea of diffraction – Rayleigh criterion.

Elementary idea of polarization – Brewster’s law and the law of Malus.

Modern physics-

Atomic nucleus. Alpha, beta and gamma radiations. Law of radioactive decay. Decay constant. Half-life and

mean life. Binding energy and its calculation. Fission and fusion processes. Energy calculation in these

processes.

Photoelectric effect. Bohr’s theory of hydrogenlike atoms. Characteristic and continuous X-rays, Moseley’s

law. de Broglie wavelength of matter waves. Heisenberg’s uncertainty principle.

26 M.Sc. Biostatistics Descriptive Statistics

Statistical Data, Types of Data: attributes and variables, discrete & continuous data, Primary data,

Secondary data, Different types of scales- nominal, ordinal, ratio and interval. Presentation of data:

Construction of tables with one or more factors of classification. Diagrammatic and graphical

representation of grouped data. Frequency distributions, cumulative frequency distribution and their

representation, histogram, frequency polygon and ogives. Stem and leaf chart. Box Plot, Univariate data-

Concepts of central tendency, dispersion and relative dispersion, moments, measures of skewness and

kurtosis. Bivariate Data: Scatter diagram. Correlation coefficient and its properties, Correlation ratio. Rank

– Spearman’s and Kendall’s measures of correlation. Principle of least squares, linear regression, fitting of

curves reducible to polynomials by transformation. Multiple regression, Multiple and partial correlation

coefficients. Sampling distribution for discrete data. Analyses of contingency tables; hypothesis of

homogeneity and independence.

Probability Theory and Distributions

Random experiment, trial, sample point and sample space, events, operations of events, concepts of

equally likely, mutually exclusive and exhaustive events. Definition of probability: Classical, relative

frequency and axiomatic approaches. Discrete probability space, properties of probability under set

theoretic approach Independence of events, Conditional probability, total and compound probability

theorems, Bayes theorem and its applications.

Random variables – discrete and continuous, probability mass function (pmf) and probability density

function (pdf), Cumulative distribution function (cdf) and their properties. Joint pmf / pdf of several

random variables. Marginal and conditional distributions of functions of discrete and continuous random

variables,. Independence of random variables, Expectation of a random variable and its properties,

Moment Generating Function (m.g.f) and Characteristic Function.

Review of Standard univariate and bivariate- discrete and continuous distributions: degenerate, discrete

uniform, binomial, Poisson, geometric and negative binomial, hyper-geometric, continuous uniform,

normal distributions, exponential distributions , reproductive property of standard distributions.

Chebyshev’s inequality. Weak law of large numbers and Central Limit Theorem for a sequence of

independently and identically distributed random variables and their applications. Law of large numbers

and central theorem. Review of Sampling Distributions, .2 , t and F distributions.

Elements of Demography

Introduction to Demography: Source of Demography Data: Census, vital events, registration, survey, extent

of under registration, Chandrasekhar Deming Index Mortality, Measurements: Crude and specific rates,

direct and indirect methods of standardization, Determinants of mortality

Fertility: Crude and specific rates, gross reproduction rates, net reproduction rates, parity progression

ratio, child-women ratio. Determinants of fertility, fertility differentials.

Life table- construction and uses, Abridged Life table-construction and uses, Concept of model life table.

Sampling Theory

Concepts of population and sample, advantages of sampling, census and sample surveys, Basic concepts in

sampling and designing of a large scale surveys. Types of sample – the convenience sample, Judgment

sample and the probability sample; simple random sampling with and without replacement.

Systematic sampling, Stratified sampling, Estimation of mean, Proportion and standard error using the

above probability sampling, probability proportional to size sampling, Estimation of sample size for

clinical experiments, sources of error in surveys.

Inference

Parametric models, parameters, problem of inference, Estimation: properties of point estimations,

Minimum variance unbiased estimator, best linear unbiased estimator, interval estimation: Confidence

interval for mean, variance of normal distribution, proportions, Correlation and regression coefficients.

Confidence interval of mean and variable for small samples.

Testing Hypothesis: Critical region and level o significance, test of a simple hypothesis against simple

alternative, composite hypothesis, Neyman-Pearson test of hypothesis, UMP test, UMP unbiased test,

Likelihood ratio test, Test on the mean of normal population, difference between the mean of two normal

population, Test on the variance of normal populations, .2 -test, .2 - goodness of fit test and test of

independence in contingency tables. Test of proportion, test of correlation and regression coefficient, Test

based on .2 , t and F.

Designs of Experiment

Need for designing of experiments, Fundamental principles of design of experiments. Basic deigns-CRD,

RBD and LSD. Their layout and analyses. Orthogonality of classification in two-way lay-outs, advantages of

orthogonality relation, simple illustrations.

Fixed, mixed and random effect models; Variance components estimation – study of various methods;

Analysis of co-variance, missing plot techniques -general theory and application, Cross-over design.

Factorial experiments: 2n, 32 factorial experiments, illustrations, main effects and interactions,

confounding and illustrations.

27 MSc-Life Science Knowledge of Life Science / Zoology / Botany / Biotechnology / Agriculture Biotechnology in general.

28 M.Sc. Climate Change and Biodiversity Conservation

Requires knowledge of Life science, Biology in general with special emphasis on Zoology.

29 M.Sc. Post Harvest Technology and Management

Candidate should have Graduation level knowledge in area of Agriculture Science, Biology, and Forestry.

30 M.Sc. Human Genomics and Proteomics

Graduate level (10+2+3) knowledge of Biochemistry, Biotechnology, Genetics, B.Sc. Biotechnology and B.Sc.

Biology.

31 M.Sc. Regenerative Biology and Tissue Engineering

Graduate level (10+2+3) knowledge of Life Science, Biotechnology, Biochemistry.

32 M.Sc. System Biology and Bioinformatics

Graduate level (10+2+3) knowledge of Biophysics, Bioinformatics, Biotechnology, Biochemistry or B.Sc. with

Biology.

33 M.Sc. Nano-science and Nano-technology

Graduate level knowledge of Chemistry, Physics, Zoology Botany, Basic Biochemistry and Molecular Biology,

Basic Concepts of Drugs, Antibiotic, Basic Agriculture with emphasis on fertilizers, Soil Science/Agricultural

Chemistry, Basic Microbiology& Instrumentation.

34 M.Sc. Information Security Digital signature & data Representation, Computer Organization & Architecture, Programming in C and C++,

Operating system, Data Structure, Database Management Systems, Computer Networks, Information System and

Software Engineering.

35 M.Sc. Nuclear Medicine General scientific awareness and scientific aptitude (50 questions) Atom, nucleus, atomic model, valency, periodic table, states of matter, boiling point, evaporation, freezing,

materials, ores, alloy, chemical reactions, acid, base.

Biodiversity, evolution of life on earth, food chains, vitamins, water cycle, human body, hormones.

Dimension and units, Newton’s laws of motion, gravitation, current scientific and technological events and of

such matters of everyday observation and experience, light and related events.

Reasoning on number system, mean, mode, median, relationship concepts, fundamental arithmetical operations,

percentage, ratio and proportion, averages, interest, profit and loss, graphs, time and distance.

Origin of the earth, universe and our galaxy, constitution of atmosphere, planet, satellite, Indian satellite program,

ocean, solar energy, environmental problems of India and world, pollution and its kind.

Knowledge about various scientific organizations and funding agencies.

Physics (10 questions) Radioactivity, Isotopes and nuclides, binding forces between nuclear particles, alpha and beta particles, gamma

radiation, mechanisms of radioactive decay, fission and fusion, half life, interaction of electrons, X-rays and -

rays with matter, radiation detectors, electric field, Gauss and Coulomb’s law, Magentic field, Amperes’s law,

Biot-Savert law, Faradey law, Lenz’s law, electromagnetic wave and its properties, electromagnetic spectrum,

semiconductor – p-type and n-type materials, pn junction, diodes, transistors, FET, biasing of diode and

transistor, wave particle duality, de-Broglie wave length, Heisenberg’s uncertainty principle.

Chemistry (10 questions) Inorganic Chemistry: Atomic and molecular structure, periodic properties, chemical bonding, oxidation and

reduction, acid and bases (HSAB principle), chemistry of transition elements, lanthanides, actinides, symmetry

and symmetry elements, bio-inorganic chemistry, electronic spectra.

Organic Chemistry: Structure and bonding, reaction mechanism, stereochemistry, UV, IR, mass, NMR

spectroscopy, synthetic reagents, study of alkenes, alkynes, dienes, arenes and various functional groups,

synthetic polymers, dyes, carbohydrates and proteins.

Physical Chemistry: Quantum mechanics, thermodynamics, chemical equilibrium, chemical kinetics and

catalysis, electrochemistry, rotational, vibrational and electronic spectrum, gaseous, liquid, solid and colloidal

state.

Mathematics (10 questions) Calculus: Differentiation, Integration, Maxima- Minima, Tangents and Normal, Area and Volumes of finite

curve, System of linear system equation, Binomial Theorem, Permutation & Combination, Elements of

Probability, Binomial, Poisson and Normal Distribution, Sequence and series and their convergence, Matrix and

Linear algebra: Elementry matrix operations, eigen values and eigen vectors , trace of matrices and related

properties of matrices,Vector space, subspace, span, rank- nullity theorem.

Biology (10 questions) Cell biology: Prokaryotic and eukaryotic cell-structure and organelle functions. Functions of sub-organells of

cell i.e., Nucleus, Endoplasmic reticulum, Golgi apparatus, Peroxisomes and mitochondria. Structure of Cell

membrane types and regulation of transport.

Metabolism: Carbohydrate, Lipids, amino acids and nucleotides turn over and its regulation, Metabolic

disorders. Glycolysis, TCA cycle, Urea cycle, Gluconeogenesis, Glyoxalate cycle and pentose phosphate

pathway. ATP synthesis-oxidative and photo-phosphorylation.

Molecular Biology: Prokaryotic and eukaryotic Replication, Transcription Translation, mechanism and their

regulation. DNA Repair systems. Recombination. Concept of Recombinant DNA Technology : Cloning vectors:

Plasmids, Bacteriophages, Cosmids, phagemids, YACs, Restriction enzymes, Ligases, PCR.

Bio-Techniques: Principles, types and applications of Chromatography, Centrifugation, Electrophoresis,

Spectrophotometry and Blotting techniques.

Animal & Plant physiology: Physiology and development of circulatory, nervous system. Endocrine and

exocrine system: hormone diversity and action. Transport across plant cell, Transpiration, Photosystems,

Flowering, plant hormones. Plant tissue culture and production of transgenic plants, Enzymes

Computer Science (10 questions) History of Computers, Functioning of Computer Systems, Components of Computer System, I/O Storage

Devices, CPU, Computer Arithmetic and Boolean algebra.

Introduction to Data Communication & Network-LAN, MAN, WAN, Topologies, Internet, Introduction to

Operating System-DOS/WINDOWS, Computer Software, Elements of Computer Software, System Software.

Flowcharts & Algorithms, Programming Languages: C and C++, Assembly & High Level Languages, General

Overview of IT and Its Applications.

36 M.Sc. Medical Biotechnology Basic knowledge of the following subject at graduation level: Chemistry, Botany, Zoology along with allied

subjects like Biotechnology, Biochemistry, Microbiology with special emphasis in Molecular Biology,

recombinant DNA technology, Immunology and Biophysical techniques. The knowledge in Physics and

Computers at 10+2 level.

Master of Visual Arts (M.V.A.) Programmes (4 semesters)

37 Applied Arts

Candidates having B.V.A./B.F.A. four years degree courses with 50% marks (45% for SC/ST/PH) of the recognized University / Institute.

38 Painting, Sculpture and Classical Arts

Master of Performing Arts (M.P.A.) Programmes (4 semesters)

39 Classical Dance and Kathak The applicant must have a Graduate degree with 50% marks (45% marks for SC/ST/PH) in B.A. / B.A. (Honours) with music or B. Dance / B.P.A. or Graduation from a recognized university with one of the following; a) ‘Sangeet Praveen’ from Prayag sangit samiti, Allahabad; b) ‘Parangat’’ from Bhatkhande Music Institute, Deemed University, Lucknow ; c) ‘Sangeet Nipun’ from Bhatkande Sangeet Vidhya Peeth, Lucknow; d) Kovid from Indira Kala Sangeet University.

40 Instrumental Music

41 Vocal Music