Syllabus for written examination for PGT (Biology)

           

Diversity of living world

 

 

Taxonomic aids, keys, specimen management ; Systematic and binomial system of nomenclature; Classification of living organisms( five kingdom classification, major groups and principles of classification within each group) ; General description of monera, protozoa, fungi, algae, bryophytes, pteridophyes, gymnosperms, angiosperms ( major groups of angiosperms upto sub class) ; Botanical gardens ,herbaria, zoological parks and museums .Salient features of animal      ( nonchordates up to phylum level and chordates up to class level).

                       

Structural  organisation  in  plants and  animals

 

Morphology, Anatomy and histology of angiosperms: Root , stem , leaf, flower , inflorescence, fruits and seeds, Tissues : Meristamatic and permanent ( epidermal, ground, vascular). Cambial activity, secondary growth,  type of wood. Animal tissues ; Morphology, Anatomy and histology of annelids , insects , amphibians. 

 

Structural and functional organization of cell

 

Cell cycle , detailed study of  Cell division (mitosis , meiosis) ; Cell death ; Structure  and function( metabolism) of carbohydrates, proteins, lipids and nucleic acids ; Enzymology : Classification and nomenclature of enzymes ; Structure ; Mechanism of action, single substrate and bisubstrate enzyme ;  Activators and inhibitors of enzymes ;  Factors affecting the activity of enzymes.

           

Plant physiology

 

Water relations: Properties of water, water in tissues and cells, Transport of water and solutes( food, nutrients, gases)  : Transport across cell membrane ; soil-plant-atmosphere continuum ; Minerals required by plant, their absorbable form, functions, deficiency symptoms, essentiality of mineral, N2  metabolism, biological fixation ; Cellular Metabolism: Gluconeogenesis, Glycogenesis and glycogenolysis, hormonal regulation ; Oxidation of food, respiratory efficiency of various food components ; transport and detoxification of ammonia , Lipid Metabolism ; Photosynthesis: Basic principles of light absorption, excitation energy transfer, electron transports, cycles ( C2 , C3, C4, CAM ), plant productivity, measurement of photosynthetic parameters ; Physiological responses to abiotic stresses ; Sensory photobiology ; Plant growth regulators : Growth ,differentiation / de-differentiation and re-differentiation, development ; Physiological affects and mechanism of action of plant growth hormones, Flowering : Photoperiodism and its significance, endogenous clock and its regulation, floral induction and development, vernalisation ; Plant movements.

 

Human  biology

 

Morphology, Anatomy, Histology, Physiology, Control and Disorders of Digestion,  Respiration, Body fluids and Circulation, Excretion, Skeleton system & muscle, Nervous; Physiology of high altitude. Chemical  Coordination And  Integration.

 

Sexual Reproduction

 

Plants: Structural  details of angiospermic flower, development of gametophytes, pollination and its types, agencies of pollination, pollen- pistil interaction, fertilization, Artificial hybridization (emasculation and bagging) development of seed and fruit ; Apomixis and Polyembryony ; Self incompatibility: Structural and biochemical aspects; methods to overcome incompatibility; Experimental Embryology; Human Reproduction: Morphology, Anatomy, Histology and Physiology of reproduction ;  Neuro-endocrine control ; Sexual behavior in infancy, pre-adolescence, adolescence and of adult ; Implantation, Pregnancy and Parturition ; Mammary gland and Lactation ; Infantile mammary gland, pubertal changes in mammary gland; Structure of adult mammary gland, galactopoiesis, milk let down ; Menopause. Senescence – Impact of age on reproduction.Foetal and Embryonic Gonads and Genital ducts ;Hormonal basis of sex differentiation ; Disorders of sexual differentiation development ;Reproductive Health: Problems and strategies, Population explosion –causes and effects, birth control measures- natural methods, physical / barrier, bio-chemical, hormonal, immunological, surgical methods, IUD’s , amniocentesis, female feticide, MMR, IMR, MTP, STD’s, infertility Disorders of female and female reproductive systems – Sexual dysfunction; Infertility – Causes and curative measures ; Reproductive toxicology of environmental and industrial chemicals, drug and alcohol ;Medically assisted human reproductive technologies, GIFT, IUT, ZIFT, TET ; Embryo culture.

Genetics

 

Principles of Inheritance and Variation: Mendelian genetics, Inheritance of one gene, two genes, post mendelian inheritance; Recombination frequency, chromosomal theory of inheritance ; Drosophila genetics, linkage and recombinations ; Mutation :General properties of mutations ; Adaptation versus mutation ; molecular basis of gene mutation : DNA repair mechanisms ; Pedigree analysis ; Human karyotype-banding ; genetic and environmental basis of sex determination, Y- and X-linked genes; Numerical and Structural abnormalities of human chromosomes and related syndromes ; Human metabolic disorders.;Molecular Basis of Inheritance: Chemical nature of DNA and RNA, Biological functions of nucleic acids ; Search for genetic material, RNA world ; Replication ; Transcription and processing of RNA, Genetic code ; Translation, post-translational modifications ; Ribosomes and Proteins ; Regulation of Gene expression ; DNA Fingerprinting ; Gene mapping ; Chromosome banding; Restriction enzyme, nucleotide sequence comparisons and homologies ; Molecular clocks ; Genetics in modern agriculture ,animal breeding, medicine, human behaviour ; Misuse of genetics ; Genetic Counseling ; Gene therapy ; HGP ; Gene Activity in prokaryotes and eukaryotes ; Signals for gene control – Hormones and growth factors ; Totipotency & Pleuripotency ; Stem cell and Gene therapy ; Bacterial transformation, transduction and conjugation, Bacterial chromosome ; Bacteriophages : Types, structure and morphology ;Evolutionary biology: Cosmic evolution – Physical basis of life ; Theories of origin of life ; Origin of life through biochemical evolution ; Experimental evidences for origin of life ; The origin of natural selection ; Extraterrestrial life ; Evolution of the eukaryotic cell : Evolution of the Metazoa ; Evolution of chordata and the evolution of the major vertebrate classes; Origin and evolution of man : Population Genetics; Genetic variations ; Polymorphism ; Gene frequency; Hardy Weinberg equilibrium ; Genetic drift, founder effect ; adaptive radiations, ecological significance of molecular variations.

 

Biology in Human welfare

 

Health and disease ; types of diseases, common diseases in humans ; Immunology – Innate and Acquired immunity ;  Passive and active immunization ; Organization and structure of lymphoid organ ; Cells of the immune system and their differentiation ; Lymphocyte traffic ; Nature of immune response ; Structure and Functions of antibodies : Antigen-Antibody interactions ; Humoral immune response ; Cell mediated immunity ; Immunological memory ; Auto-immunity ; Allergies; HLA system in human :MHC haplotypes ; Transplantation types and problems ; Immunodeficiency disorders ;etiology of HIV ; types, genetics and biochemistry of cancer ; Drugs and alcohol abuse, Addiction , drug dependence, ill effects, prevention, its abuse in adolescents and its management;Strategies for food production and enhancement: Animal husbandry, management of farm animals, breeding strategies ( natural and artificial) and their types, economic importance of each ; Plant breeding, method of release of new variety, HYV of common cereals and pulses, bio-fortification, SCP ; Tissue culturing, somatic hybridization;Microbes in Human Welfare: Technology associated and use of Microbes in household, industries, medicine, bio-active molecules, sewage treatment and STP, Ganga and Yamuna action plan, biogas production, biocontrol agents, biofertilizers.

           

Principles of Biotechnology

 

Genetic engineering tools and technique, technique of separation and isolation of DNA, cloning vectors ,electrophoresis, bio reactors, processing  of its products. Tissue engineering ; Cryopreservation ; Fusion methods, detection and applications of monoclonal antibodies, DNA vaccines, Edible vaccines.;Application in agriculture : GMO for pest resistance, RNAi and dsRNA technology,Application in Medicine, genetically engineered products, gene therapy.

Molecular diagnosis : serum and urine analysis, PCR, ELISA ; Transgenic animals : their physiology, biological products and their use for testing the safety  of vaccine and chemicals ; Bioethics issues ; biopyracy.

 

Ecology

 

Organism and its environment, distribution of biomes, major physical factors and the physiological responses shown by organisms ; Physical adaptation of plants and animals, rules governing adaptations ; Population attributes and growth, logistic curves, Darwinian fitness ; Population interactions and their theories ; Ecosystem structure and functions, ecosystem productivity and standing crop, decomposition in nature, energy flow in GFC / DFC, ecological pyramids, succession of community ; Nutrient cycle ; ecosystem services ; Biodiversity types and its patterns, importance of diversity, its loss and their causes, conservation strategies ; Environmental issues : Types of  pollution, their indicators, causes, effects, prevention and treatment ; Deforestation, recommended forestation, reforestation, case studies of people’s participation in conservation.  

 

 

 

 

Syllabus for written examination for PGT(CHEMISTRY)

 

S.No.

Topic  (Details of the syllabus)

1.

Some Basic concepts of Chemistry: Scope of chemistry-

Historical approach to nature of matter - states of matter, properties of matter and its measurement, S. I system of units, Uncertainty in measurements, dimensional analysis, Laws of chemical combination, atomic and molecular masses, Mole concept and molar masses, percentage composition, empirical and molecular masses, equivalent weight, concept of limiting reagent

2

States of Matter: Gases, liquids and solids, three states of matter, types of intermolecular forces.

 The laws governing ideal gas behaviour, Dalton’s law of partial pressure, Kinetic molecular theory of ideal gases, Maxwell Boltzmann distribution law on molecular motion, real gases – deviation from ideal behaviour, vander Waals equation.

 Liquid and their properties.

Solids: Classification of solids, fundamental types of lattices, two and  three dimensional lattice types, Simple crystal structures, Transformation of crystal structure on varying temperature, Bragg’s law, density in solids, Calculation of Density of unit cell, packing in solids, packing efficiency energy band, band gaps, semiconductors, magnetic and dielectric properties, stoichiometric and non- stoichiometric defects in solids.

3

Structure of Atom:Structure of Atom (Classical Theory), Dalton’s atomic theory, Bohr’s model of atom, Structure of atom (modern theory), de Broglie’s relationship, Heisenberg’s uncertainty principal, Classical wave equation, Schrödinger’s wave equation, Probability distribution curve, Quantum numbers, Pauli’s exclusion principle, Aufbau principle, Hund’s rule of maximum multiplicity.

4

Equilibrium: Reversible reactions, criteria of equilibrium, Law of mass action, equilibrium constant, Kc and Kp , Le Chatelier principle, Ionic equilibrium, Ostwald’s  dilution Law, solution of  acids, bases,  ionic  equilibria in  solution, Common ion effect – its application to qualitative analysis or salt analysis acids and bases, Bronsted- Lowry theory of acids and bases, Lewis concept of acid and bases, relative strengths of acids and bases, their quantitative estimation, buffer solution and its use, determination of pH, theories of indicators, conductometric titration, Solubility product, hydrolysis.

5.

Surface Chemistry:Adsorption, absorption, sorption, Physical adsorption, Chemisorption adsorption, isotherms ( Freundlich, Langmuir),  application of adsorption, types of Catalysis, Shape catalysis, enzyme catalysis, theories of catalysis, classification of colloids, preparation of Colloidal Solution (lyophobic and lyophilic), Special characteristics of colloidal solutions , electrophoresis, Precipitation of colloids – Hardy Schulze law, multimolecular and macromolecular colloids, Emulsion and Gels.

6

Chemical Kinetics: Theories of reaction rates, rate of reaction , molecularity  and order of reaction, Fast reactions- Luminescence and energy transfer process, reaction mechanisms(Simple and complex reactions).  Methods of determining order, effect of temperature on rates of reaction, Arrhenius equation.

 

7

Redox Reaction and Electrochemistry: Oxidation and reduction, redox reaction and its application, oxidation number, Strong and weak electrolytes, activity coefficient, conductance and conductivity, Kohlrausch law, resistance and resistivity molar conductivity, equivalent conductivity, Qualitative and quantitative aspect of electrolysis, electrochemical cell and electrolytic cell, Electrode and electrode potential and standard electrode potential, Electrochemical series and its applications, Nernst equation and its application, Equilibrium constant and EMF of the cell,  Electro chemical theory of rusting

 

8

Solutions:Solution and its types, expression of concentration of solution, solubility and factors affecting the solubility of a solid in a liquid (temperature and pressure), Vapour pressure of a liquid, Raoult’s law for both volatile and non volatile solute,Ideal and non ideal solution, Colligative properties, abnormal molecular masses and Van’t Hoff factor.

 

9

Chemical bonding and Molecular Structure: Valence electrons and Lewis structures, Ionic bond, Covalent bond, Bond parameters ,Co-ordinate bond, polarity and dipole moment, Quantitative idea of – valence bond theory, molecular orbital theory (LCAO), Concept of hybridization involving  s, p, d orbitals, Hydrogen bond, Resonance, VSEPR theory.

10.

Thermodynamics:Macroscopic properties of the system, modes of transfer of energy between system and surrounding, Phase transition, phase rule and phase diagram, First Law, second law and third law, of thermodynamics. Internal energy and enthalpy of the reaction, their measurement and application, spontaneity of process, Entropy and spontaneity, Helmholtz and Gibb’s free energy, Thermodynamics of electrochemical cells.

 

11.

Classification of elements and periodicity in properties: Significance of classification, brief history of the development of periodic table, periodic laws, name of the elements with Z>100 according to IUPAC system, classification of elements into s, p, d, f –block elements and their characteristics,

Periodic trends in the properties of elements – Ionization enthalpy, Electron gain enthalpy, electronegativity, atomic radii, ionic radii, periodicity of valency or oxidation state.

 

12.

Hydrogen:Position of Hydrogen in periodic table, occurrence, isotopes, Preparation of hydrogen, on small and commercial scale, hydrides, water, hard and soft water, heavy water, hydrogen peroxide, hydrogen economy, hydrogen as a fuel.

 

13.

General principles and processes of isolation of elements and s – block elements: Principles and methods of extraction, oxidation and reduction as applied to the extraction procedures of Al, Cu, Zn and Fe.

s – block elements, general introduction – Electronic configuration, occurrence,

Anomalous properties of the first element of each group, diagonal relationship,

Trends in variation of the properties, reaction of alkali and alkaline earth metals.

Preparation and properties and uses of some important compounds: - sodium carbonate, sodium bicarbonate, sodium chloride, sodium hydroxide, calcium hydroxide and calcium carbonate, industrial uses of lime and lime stone, biological importance of sodium, potassium, magnesium and calcium, Refining methods

 

14.

p – Block Elements: Electronic configuration, variation in physical and chemical properties of groups 13 to 18, physical and chemical properties of borax, boric acid, boron hydride, silicones, preparation and uses, preparation, properties and uses of nitrogen, ammonia, nitric acid and oxides of nitrogen, phosphorus – allotropic forms, preparation and properties of phosphine,

phosphorus pentachloride and phosphorus trichloride, preparation, properties and uses of oxygen and ozone,  hydrides and halides of 16 group elements, their structure and nature, allotropic forms of sulphur- their preparation, preparation, properties and uses of sulphur dioxide, industrial preparation of oxo-acids of sulphur, preparation and properties of halogen and halogen acids, inter halogen compounds, pseudohalide ions. Oxo-acids of halogens, their structure and nature, preparation, properties and uses of xenon fluorides, oxides of xenon and xenon oxo fluorides.

 

15.

The d – and f- Block Elements: General introduction, electronic configuration and general trend in the properties of  first row transition metals like metallic character, ionization enthalpy, oxidation states, ionic radii, coloured ion formation, catalytic properties, magnetic properties, oxides, halides and sulphides of first row transition metals, complex compound formation etc. Preparation, properties and structures of KMnO4 and K2Cr2 O7, lanthanoids and actinoids.

 

16.

Co-ordination Compounds and organometallics:  Meaning of co-ordination compounds, Werner’s theory, ligands – their types, IUPAC nomenclature of co- ordination compounds, isomerism, bonding in co-ordination compounds, colour, magnetic properties and, stabilities  of co-ordination compounds. Chemical and biological importance of  co-ordination compounds, metal carbonyls: preparation, properties and bonding, organometallic  compounds and their classification.

 

17.

Organic Chemistry : Some  Basic Principles and  Techniques: General Classification of organic compounds, Shapes of organic compounds-Hybridisation(sp, sp2,sp3), Structural representation of  organic molecules, Functional groups, Homologous, series. Common or trivial names, nomenclature of aliphatic, aromatic and substituted aromatic compounds.

            Isomerism :  Structural and Stereo isomerism, Enantiomerism, Diasteriomers, Meso compounds and reacemic mixture, Fundamental Concepts in Reaction Mechanism: Cleavage of covalent bond, Types of attacking species, electron movement in organic reactions,  electronic displacement in a covalent bond and types of organic reactions.

            Methods of purification of organic compounds: Qualitative analysis, Quantitative analysis., estimation of the elements and determination  of empirical and molecular formula, Cyanides & Iso cyanides, diazonium salts

 

18.

Hydrocarbons: Classification of hydrocarbons.

Alkanes: Conformations (Newmann and Sawhorse formulae), Physical  properties, Chemical reactions

Cycloalkanes: Preparation, physical and chemical properties, stability of cycloalkanes(Bayer strain theory), chair and boat forms of cyclohexane.

Alkenes:, structure of double bond, geometrical isomerism, physical properties, methods of preparation, chemical reactions.

Alkadienes: Classification of  dienes, Preparation of conjugated dienes, Chemical properties(1,2 and 1,4- addition to conjugated dienes).

Alkynes:, structure of triple bond, physical properties, methods of preparation Chemical properties, Acidic nature of alkynes

Aromatic Hydrocarbons:, Structure of benzene, resonance, aromaticity (Huckel’s rule) Chemical properties, mechanism of electrophilic substitution direct influence of substituents in monosubustituted benzene.

 

19.

Environmental Chemistry: Environmental pollution, Atmospheric pollution, Tropospheric pollution(Air pollution), Major air pollutants, Control of air pollution, Smog(Chemical and Photochemical smog), Stratospheric pollution: Ozone layer and its depletion, Acid rain, Green House Effect and Global warming, Water pollution, Soil pollution and Industrial waste. Green chemistry as an alternative tool for reducing pollution, strategies for control of pollution

 

20.

Haloalkanes and Haloarenes: Classification, methods of preparation of haloalkanes and  haloarenes, their  physical properties, tests to distinguish between alkyl and aryl halides, mechanism of SN1 and SN2 reactions, elimination  reactions (Saytzeff Rule, E1 & E2 mechanism).Poly halogen compounds: Preparation and properties.

 

 

21.

Alcohols, Phenols and Ethers: Classification,  preparation,  properties and uses, tests to distinguish between primary, secondary and tertiary alcohols. Distinctions between alcohols and phenols. Preparation of ethers , physical and chemical properties.

 

22.

Aldehydes, Ketones  and  Carboxylic Acids: Structure of carbonyl group, preparation of aldehydes and ketones, physical , Chemical properties and uses, tests to distinguish between aldehydes and ketones .Preparations of carboxylic acids preparation properties and uses.

 

23.

Amines (Organic compounds containing nitrogen ): Classification, Structure of amino group, preparation, Physical, Chemical properties, tests to distinguish between  primary, secondary and tertiary amines

 

24.

Polymers: Polymerization, Classification of polymers based on : origin, structure, molecular forces, mode of polymerization. Addition polymerization Condensation polymerization(Step-growth polymerization) Preparation of condensation polymers Synthetic and natural rubber and vulcanization, Determination of molecular mass of polymers:. Poly dispersity index(PDI). Bio-degradable polymers like PHBV.

 

25.

Biomolecules(Biochemistry):Carbohydrates: Classification of carbohydrates , Structural determination of glucose and fructose on the basis of  their chemical properties, Open chain (Fischer) structure, cyclic structure(Haworth form), a and b forms of glucose, Mutarotation, anomers and epimers, Chemical reactions of glucose, Reducing and non-reducing sugars, Configuration of glucose and fructose. Disaccharides Sucrose, Haworth representation of disaccharides, Polysaccharides, Starch, Cellulose, and amylopectin structures, Functions of Carbohydrates in living organisms. Carbohydrate metabolism, glycolysis, electron-transport  chain,

Proteins: Amino acids, Zwitter ion, Iso-electric point, peptides and peptide bond, Fibrous proteins, Globular proteins and their functions, Primary, Secondary(Helix and pleated sheet structures) and tertiary structure of proteins, denaturation and renaturation, Enzymes, specificity and mechanism of enzyme activity , coenzymes, applications of enzymes.

Nucleic acids : Nucleosides, Nucleotides, Structure of ATP, Photosynthesis(Light and dark reactions)  Primary and Secondary structure of DNA(Double Helix structure) , biological functions of nucleic acids, Replication, Protein synthesis (Transcription, Translation, mutation), genetic code, genetic errors, Vitamins, classification, diseases caused by the deficiency of vitamins, Hormones (steroid hormones and non-steroid hormones) and their functions.

26.

Chemistry in Everyday life: Drugs and medicines -  designing a drug, drug metabolism, classification of drugs, enzymes as drug targets, action of drug through drug receptor interaction, types of drugs: Antipyretics, Analgesics, antiseptics, disinfectants, tranquilizers, antimicrobials, antibiotics(Narrow spectrum and broad spectrum antibiotics), antifertility drugs, antihistmmines,  antacids. Chemicals in food, Food preservatives, artificial sweetening agents, Soaps and detergents, Preparation soaps(Saponification) and detergents, cleansing action of soaps,  advantages of detergents over soaps, Deodorants, Edible colours,  antioxidants.

 

 

 

  

 

SYLLABUS FOR WRITTEN EXAMINATION FOR PGT(COMMERCE)

 

PART – I

BUSINESS STUDIES AND MANAGEMENT

 

·          Introduction to Business– Concepts, characteristics, objectives. Classification of business as industry and commerce. Distinctive features of business - Business, profession and employment. Choice of Form of Organization .Large Scale and Small Scale Business-.Assistance by Government to Small Scale Sector.            

 

·          Form of Business Organization – Sole Proprietors, Joint Hindu Family, Partnership, Joint Stock Company and its formation, Cooperative organization.  

 

·          Business ownership– Private, public and Joint sector. Public Enterprises, Role-dynamics of Public Sector, Global Enterprises (Multinational Companies), Joint Ventures.                                                                                                                 

 

·          Business Services – banking, insurance, transportation, warehousing, communication, Impact of Technology on Business Services.                             

 

·          Trade: Internal Trade  Retail and Wholesale trade, Emerging modes of business-franchisee, E-business and Outsourcing.  International Business–Export-Import – Procedure and documentation, EPZ/SEZ . International Trade Institutions and Agreements – WTO, UNCTAD, World-Bank, IMF.                                             

 

·          Business Finance:  Sources  – owners and borrowed fund, Sources of raising finance, Equity and preference Shares, GDR,ADR, Debentures, Bonds – Retained Profit, Public Deposits, Loan from Financial Institutions and commercial banks, Credit-rating and rating agencies, Trade credit, Micro-credit.                               

 

·          Social Responsibility of Business, Business Ethics, Environment protection.      

 

·          Management – concept, objectives, nature of management as Science, Art and Profession, levels, Principles of Management  general and scientific.                   

 

 

·          Business Environment – meaning, importance, dimensions, changing business environment–special reference to liberalization, privatization and globalization, Business - a Futuristic vision.                                                                                  

 

·          Management Function – Planning, organizing, staffing, directing, controlling and coordination                                                                                                            

 

  • Business Finance: Financial Management – meaning, scope, role and objectives, financial planning, Capital structure, leverage, Fixed and working capital – meaning and factors affecting its requirements.   FCCB’S, Factoring, Lease financing, commercial papers

                                              

 

·          Financial Market – Money Market-nature, instruments, Capital Market- Primary and secondary, Stock exchange, NSEI, OTCEI, Procedures, SEBI.                      

 

·          Human Resource Management– meaning , importance, man-power estimation , Recruitment and selection, Training and development , Compensation, Performance Evaluation                                                                                         

 

·          Marketing – meaning, functions and role, Levels of Marketing , Changing facets of marketing , Product-mix, Marketing-mix.                                                

·          Organizational Behaviors : Individual behaviors , Motivation–concepts and applications, Personality perception, Learning and attitude, Leadership and its approaches, Communication.                                                    

 

 

·          Consumer Protection – Meaning, importance, consumers’ rights, Consumers’ responsibilities, Consumer awareness and Legal redressal with special reference to consumer Protection Act, Role of consumer organization and NGOs.              

 

PART –II


FINANCIAL ACCOUNTING AND FINANCIAL STATEMENT ANALYSIS

 

·          Accounting: Meaning, objectives, qualitative characteristics of Accounting information, Accounting Principles, Accounting concepts, Accounting standards, Cash and Accrual Basis of Accounting.                                                               

 

·          Process of Accounting :Voucher, transaction ,Accounting Equation, Rules of Debit and Credit, Book of original entry-Journal and Special Purpose Books, Ledger ,posting from Journal and subsidiary  books, Balancing of Accounts, Trial Balance and Rectification of Errors .Bank Reconciliation Statement.        

 

·          Accounting for depreciation ,Provisions and Reserves ,Bills of Exchange, Non-Profit  Organization , Partnership Firms  -  Reconstitution of Partnership (Admission ,Retirement ,Death and Dissolution),Account of Incomplete Records.

 

 

·          Accounting of Joint stock Companies: Share capital types of shares, accounting for issue, allotment forfeiture and re-issue of shares. Debentures –types, issue and method of redemption .                                                                                 Final  Accounts of  Sole proprietor and Joint Stock Companies. Emerging trends of presentation of Final Accounts.                                                                       

 

·          Financial Statement Analysis: Meaning, significance, limitation .Tools for Financial Statement Analysis-comparative statements, common size statements, Trend analysis, accounting ratios.                                                                       

 

·          Cash Flow Statement: Meaning, objectives, preparation as per revised standard issued by ICAI.                                            

 

·          Cost Accounting- Nature, functions . Job costing, Process costing, Marginal costing, Cost-volume-profit relationship. Cost control and cost reduction techniques                                                                                                            

 

·          Computers In Accounting: Introduction to Computers and Accounting Information System, Application of Computers in Accounting, Automation of Accounting process, designing accounting reports, MIS reporting, data exchange with other information  system. Ready made , customized and tailor made Accounting Systems.                                                                                           

·          Accounting And Database Management System –meaning, concept of entity and relationship in an accounting system, Data Base Management System(DBMS) in accounting.                                                                                                             

 

 

 

 

Syllabus for written examination for PGT(ECONOMICS)

PART – A

Introductory Micro Economics and Macro Economics

 

1.      Introduction: Central problems of an economy, production possibility curve and opportunity cost.

2.      Consumer Behaviour and Demand: Consumer’s Equilibrium - meaning and attainment of equilibrium through Utility Approach and Indifference Approach, Demand, market demand, determinants of demand, demand curve, movement along and shifts in demand curve. Law of demand and its exceptions. Price elasticity of demand, measurement of price elasticity of demand - percentage, total expenditure and geometric method.

3.      Producer Behaviour & Supply: Agents of production. Production function. Cost and Revenue- meaning and various types of costs and revenue. Returns to a factor and returns to scale. Supply, market supply, determinants of supply, supply curve, movement along and shifts in supply curve, price elasticity of supply and its measurement.

4.      Forms of Market and Price Determination: Forms of market – meaning and features. Price determination under perfect competition, monopoly and imperfect competitions, effects of shifts in demand and supply, Oligopoly market form (Features). 

5.       National Income and related aggregates: Macroeconomics: Meaning. Circular flow of income, concepts of GDP, GNP, NDP, NNP (at market price and factor cost), National Disposable Income, Private Income, Personal Income and Personal Disposable Income. Measurement of National Income by income Expenditure, Value added method.

6.      Determination of Income and Employment: Aggregate demand, Aggregate supply and their components. Propensity to consume and propensity to save.  Involuntary unemployment and full employment. Determination of income and employment. Concept of investment multiplier and its working. Problems of excess and deficient demands Measures to correct excess and deficient demands - availability of credit, change in Government spending. Inflation: meaning, causes and remedies

 

(a)    Money and Banking: Money - meaning, evolution and functions. Central bank - meaning and functions. Commercial banks - meaning and functions. Recent significant reforms and issues in Indian Banking System-privatisation and modernization,  Measurement of supply of money, Problems of Barter system.

7.      Government Budget and the Economy: Government budget - meaning and its components. Objectives of government budget. Classification of receipts; classification of expenditure. Types of budget. Revenue deficit, fiscal deficit and primary deficit: meaning and implications; measures to contain different deficits. Downsizing the role of government.

 

8.      Balance of Payments: Foreign exchange rate- meaning (Fixed and Flexible), merits and demerits; Determination through demand and supply. Balance of payments accounts - meaning and components                                         

9.      International Economics: IMF – The World Bank and its associates. WTO.

 

10.  Concepts of shares, debentures, SEBI, NSEW, BSE and various indices.

 


 

PART-B

Statistics and Indian Economic Development

 

(a)    Introduction and collection, organization of data: Meaning, scope and importance of statistics in Economics. Collection and organisation of data. Census of India and National Sample Survey Organisation.   

Statistical Tools and Interpretation: Measures of Central Tendency. Measures of Dispersion. Lorenz Curve: Meaning and its application. Correlation – meaning. Measures of correlation - Karl Pearson’s method, Spearman’s rank correlation. Time series analysis. Introduction to Index Numbers - meaning, types - wholesale price index, consumer price index and index of industrial production, uses of index numbers; Inflation and index numbers. Arithmetic  Mean, Weighted    mean,  Median Mode, Partition values.

1.      Development Policies and Experience: A brief introduction of the state of Indian economy on the eve of independence. Common goals of Five Year Plans, major controversies on planning in India. Main features, problems and policies of agriculture, industry and foreign trade.

2.      Economic Reforms since 1991: Need & main features - liberalisation, globalisation and privatisation; an appraisal of LPG policies

3.      Current challenges facing Indian Economy: Poverty and programmes for poverty alleviation. Rural development: Key issues - credit and marketing - role of cooperatives; agricultural diversification; alternative farming - organic farming. Human Capital Formation. Growth of Education Sector in India. Employment: opportunities and other related issues. Infrastructural Problems and policies. Sustainable Economic Development: Meaning; Effects of Economic Development on Resources and Environment.                                                              

4.      Development Experience of India: A comparison with neighbours India and Pakistan, India and China, Issues: growth, population, sectoral development and other developmental indicators.

 

 

 

  

 

SYLLABUS FOR WRITTEN EXAMINATION FOR PGT (ENGLISH)

 

Section A

READING COMPREHENSION

 

Ability to comprehend, analyze and interpret unseen texts.

Three/four unseen reading passages may be set. Note making can be added to test organization of the contents in various forms.

 

      Section B

GRAMMAR AND USAGE

Ability to apply the knowledge of syntax and grammatical items & use them accurately in  the context provided .

The following grammatical structures will be tested through error correction / editing/ gap filling / sentence completion / multiple choice questions :

1.      Determiners

2.      Tenses

3.      Clauses

4.      Modals

5.      Voice

6.      Reported Speech.

 

Section C

LITERATURE

ü        Romantic period (e.g. Shelley, Wordsworth, Keats, Coleridge etc)

ü        19th and 20th Century American and English Literature (e.g. Robert Frost, Hemmingway, Whitman, Hawthorne, Emily Dickinson , Bernard Shaw, Arthur Miller etc. )

ü        Modern Indian Writing in English (e.g. Anita Desai, Vikram Seth, Nissin Ezekiel, K N Daruwala, Ruskin Bond, R K Narayan, Mulk Raj Anand, Khushwant Singh etc)

Modern writing in English from other parts of the world e.g. / Africa / South Asia, )    Glossary of Literary terms may be added  2) Prosody and rhetoric may be added.

T.S. Eliot,  D.H. Lawrence,( Oedipus Complex) William Blake may be added.

 

 

 

 

Syllabus for Written Examination for PGT (Geography)

 

 

Topic I: Geography as a discipline-

 

Geographical ideas in ancient, medieval & modern periods: the Kant, Humboldt and Ritter, Videl-da-la Blache, F. Ratzel etc.

Contemporary geography: Post Second World War, Environmentalism, Areal Differentiation, spatial organization, Behavioural and perceptual Geography. Positivism in Geography. Humanistic Geography. Development in Indian Geography.

 

Topic-2 Origin and Evolution of the Earth-

 

Introduction to the solar system,

Motions of Earth: Rotation, Revolution, Occurrence of Day and Night; change of seasons; Latitudes and Longitudes; Finding time.

Earth’s Interior: Origin of contents and ocean basis Wagener’s Continental drift theory, Theory of Plate Tectonics Earthquakes and Volcanoes, Folding and faulting

Origin of the Earth: Nebular hypothesis (old Theory) and Big-Bang Theory. Evolution of continents, atmosphere and oceans.

 

Topic-3 Interior of the Earth and Distribution of oceans and continents-

 

Constitution of Earth’s interior (based on Seismic Evidences), origin of the continents and ocean basins. Wegner’s theory of Continental drift and Plate Tectonics. Plate movements and interactions-Volcanism and seismicity.

 

Topic-4 Landforms-

 

Mineral and rocks- classification of rocks, rock cycle. Important minerals geomorphic process of denudation Endogenic and Exogenic processes. Mass Wasting, Landslide, Work of River, Glacier Wind, Sea Waves etc, processes of soil formation.

 

Topic-5 Climate:

 

Atmosphere: Composition and structure. Insolation and temperature, Atmospheric pressure and winds, Atmospheric moisture, cyclones, classification of climate (Koeppen). Global climatic changes: Causes and effects.

 

Topic-6 Water (Ocean)

 

Geomorphology of the ocean floor, submarine relief features of Atlantic, Pacific and Indian Ocean. Movement of ocean water: Currents, tides and waves. Marine deposits and coral reefs.

 

 

Topic -7 Life on the Earth

 

Approaches in environmental Geography, landscape, ecosystem and perception approaches, Man and the Biosphere: Interactive and dynamic relationship. Human impact on biogeochemical cycles.

 

Topic-8 India:

 

Geographical basis of Indian State-territory; location, extent, shape and size.

 

Topic-9 Physiography:

 

Structure, Physiographic divisions, Drainage system and its evolution.

 

Topic-10 Climate, Vegetation and Soil-

 

Climate: factors controlling climate of India

Origin and mechanism of Indian monsoon; Seasons of India, Classification of climate of India (Koeppen’s, Thornthwaite, Triwartha).

Soils: Type and distribution (I.C.A.R.), Soil problems, conservation of soil

Vegetation- Types & Distribution; conservation

Wild Life- its conservation.

 

Topic-11 Natural Hazards and disasters-

 

Causes, Consequences and management in India Environmental Hazards: Floods, droughts, cyclones, earthquakes and landslides; human adjustment to hazards; hazards perception and mitigation; environmental institutions and legislation in India.

 

Tsunami, Man made disasters – Fires, Road, Rail traffic accidents, Terrorist attacks, chemical and industrial accidents, Epidemic.

 

 

Topic-12 Human Geography: Nature and Scope.

 

Nature and scope of Human Geography, Approaches to the Human Geography, Determinism, Environmental Determinism, Possibilism, Neo-determinism, ecological and Behaviouralism.

 

Topic -13 People (World and India)

 

 Trends and patterns of population growth: determinants and patterns of population distribution; theories, demographic transition; Human migration, Patterns of human development.

 

Topic-14 Human Activities: (World and India)     

 

Influence of LPG on industrial development especially in India.

 

 

Primary: -Hunting, gathering, Herding (Nomadic & Commercial) Lumbering fishing, mining and agriculture; Agricultural practices; some major crops.

Secondary: - Industries: Classification, Theories of localization, major Industries, recent trends in industries, world comparisons.

Tertiary:-(Services)

Quaternary-Quinary activities

Planning in India: target area planning, idea of sustainable development

 

Topic-15 Transport, Communication and Trade(World and India)

Transport and communication Roads, railways, waterways and airways; oil and gas pipelines, national electric grids. Communication networking-radio, television, satellite and Internet.

International Trade-Basis and components, trade balance, major trading organizations, changing pattern of India’s foreign trade, sea-routes, inland water-ways, sea ports and their hinter-land.

 

Topic-16 Human settlements (World and India)

 

Unstable and stable settlements, rural settlements: origin, types and patterns; Urban settlements: Origin and growth of towns; functional classification of towns. Problems of urbanization in the world; urbanization in India; Urban slums and squatters. Morphology of cities; distribution of Mega-cities, problems of human settlements in Developing countries.

 

Topic -17 Geographical perspective on selected issues and problems

 

Environmental pollution-Land, Water, Air, Noise, Global Warning, Poverty, Food Security; Sustainable Development.

 

Topic  -18  General Cartography (Practicals)

 

Elements and classification of maps, scales, map-projections, finding directions, latitudes, longitudes and calculation of local & standard time, Identification & Analysis of relief forms: Topographical Maps and interpretation. Weather-instruments and interpretation of weather maps. Digital mapping, Remote sensing, Visual interpretation. Processing of Data, Thematic mapping, representing statistical data by various diagrams-Bar, Histogram, Pie etc.

Spatial Information technology: GIS, GPS, Computers-Software and Hardware components, Data format, Raster and Vector, editing and topology etc.

Spatial Analysis; Overlay, Buffer and Proximity analysis.

Field Survey, Field Survey procedures: Defining the problem, objectives, Scope, Tools and Techniques.

 

19.       Water Resources

 

            Causes, Consequences of water Scarcity and deterioration of water quality shortcomings of MPP’s. Rain water Harvesting

 

 

  

 

 

SYLLABUS FOR WRITTEN EXAMINATION FOR PGT HISTORY

          INDIAN HISTORY

          Harappan Civilization –   a. Town Planning                              

                                              b. Religion   

                                              c. Economic - Social Crafts-Scripts

                                        d. Script Writing

                                          e. Decline-Cunningham And John Marshall discoveries.

 

1)      Rise of Magadh in relation to 16 Mahajanpadas                     

2)      Rise of Heterodox sects with special reference to     Buddhism, Jainism –

                                          a. Rise

                                          b. Teaching

                                                 c. Comparison

                                               d. Effect on society, trade &commerce

3)      The Mauryas

                                  a. Causes for its rise                                                                                                                                         

                                  b. Chandragupta Maurya Administration

                                  c. Contribution of Ashoka the Great (all

                                      aspects)

                                    d. Decline and fall of Mauryan Empire

4)      The Guptas

a.        16 Mahajanapadas, Rise of Magadha, Chandragupta Maurya,

Administration, Gupta Administration, Ashoka The Great,

Society, Trade, Commerce Towns, Limitations of Inscriptions.

b.   Samudra Gupta                                                                              

                                        c.   Chandragupta Vikramaditya etc

                                        d. Administration, Religion, Trade & Commerce

 

6)      The Defeat of Hindu kingdom

 

Early Societies, Mahabharata, Kinship, Marriage System, Gotra, Caste System ,Jatis, Untouchables, Gender Access To Property , Social Differences – Handling Texts, Historians And Mahabharata .

 

Polyandry, Sanchi Stupa –Vedic Sacrifices, Rise Of Buddhism And Jainism, Buddha, Mahavira, Teachings, Sangha, Stupas Sculpture, Hinayana And Mahayana, Hinduism, Shaivism, Temple Architecture.

 

Medieval Travelers –Al –Biruni,   Ibn Battuta , Francios  Bernier Description Of Indian Society.

 

Integration Of Cults –Bhakti Movement – Sufism-Nayanars, Alvars, Virashaivism, Kabir ,Guru  Nanak, Mirabai, Sultanate Period – Architecture And  Administration.

 

Discoveries Of Hampi, Nayakas, Rayas, Sultans-Decline Of The Vijayanagara Capital Selection, Forts, Water Resources Royal Centre, MahanavamiDibba-Vijayanagara Architecture.

 

Peasants, Agriculture, Village Community, Caste, Panchayat System, Women In Agrarian Society, Forests And  Tribes ,Zamindars, Land Revenue System, Currency , Abul Fazl Allami-Ain I Akbari.

 

Mughals From 1526-1707,Polity, Administration  Court ,Society, Economy , Akbar- Administration, Religion, Akbar Nama.

 

Advent Of Europeans And Establishment Of British Rule, Bengal Zamindars-Permanent Settlement, Ryotwari And  Mahalwari Systems, Jotedars, 5th Committee Report, Santhals , Pahariyas, Bombay Deccan Riots, Money Lenders.

 

7)      Mughal Period – 1526 to 1707(all aspects)                              

                                             a. Polity

                                             b. Administration

                                             c. Society

                                             d. Economy

 

8)      Medieval Period – Society and Culture with special  Reference to Bhakti Movement and Sufism

9)            Medieval Architecture – Delhi Sultanate ’n Mughal Period

10)        The Advent of Europeans and the establishment of   5 British rule                                                                        

11)         British rule and its impact on Indian economy               

12)        Revolt 1857 –            a. Nature                                                      

                                           b. Causes

                                           c.  Leaders

                                             d.  Awadh In Revolt.

                                             e. Events

                                             f. Consequences

                                                        g. Causes of defeat

                                           h. Impact

                                             i. Vision Of Unity,

        j. Sources And Images Of The Revolt.

Pre Colonial Cities- Bombay, Madras Calcutta.

 

13)         The socio – religious reform movements and the rise  of nationalism                                                                   

14)         The Indian freedom movement - 1885 to 1947   

Mahatma Gandhi From 1917 to 1947.

 

Partition, Why Partition?  Riots, Gendering Partition.

           

15)       Constitution –            a. Framing                                                                                                                              b. Features

                                       c. Working of the Constitution

                                       d. Adoption of the Constitution

HISTORY OF THE WORLD                                                                                                  

1)      Rise of Ancient Civilizations with special reference to         

          Mesopotamia         a. Urbanization

                                    b. Script    

                                         c. Trade

                                         d. Calendar

 

2)       Roman and Greek civilization                                                                                          a. Rise of the empire

                                        b. Administration        

                                        c. Society

3)       Rise of Islam –     a. Teachings                                                                                                                                                                             

       b. Culture                                         
       c. Crusades

       d. Abbasid Revolution,

       e. Khaliphs,

       f.  Architecture,

       g. Literacy.

       h. Language.

4)       Nomadic people of Central Asia                                               

5)      The Dark age - Feudalism in Europe                                                

                                                a. Manor State

                                              b. Decline

6)   Renaissance ’n Reformation period in Europe                                                     

7) Capitalism and Mercantilism                                                  

        a. Industrial Revolution

        b. Imperialism and colonialism

8) China Since 1840 to 1949              

                                                                                                                                                                                                           

9)      Japan since 1840 to 1949   

America And Australia.

 

Syllabus for written examination for PGT(Mathematics)

 

Sets :

Sets and their representations. Empty set. Finite & Infinite sets. Equal sets. Subsets. Subsets of the set of real numbers. Power set. Universal set. Venn diagrams. Union and Intersection of sets. Difference of sets. Complement of a set.

 

Relations & Functions:

Ordered pairs, Cartesian product of sets. Number of elements in the cartesian product of two finite sets. Cartesian product of the reals with itself (upto R x R x R). Definition of relation, pictorial diagrams, domain. co-domain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation a function, domain, co-domain & range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions. Sets and their Representations. Union, intersection and complements of sets, and their algebraic properties, Relations, equivalence relations, mappings, one-one, into and onto mappings, composition of mappings.

 

Principle of Mathematical Induction:

Processes of the proof by induction. The principle of mathematical induction.

 

Permutations & Combinations:

Fundamental principle of counting. Factorial n. Permutations and combinations, derivation of formulae and their connections, simple applications.

 

Complex Numbers:

Complex numbers, Algebraic properties of complex numbers, Argand plane and polar representation of complex numbers, Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system. Modulus and Argument of a complex number, square root of a complex number. Cube roots of unity, triangle inequality.

Linear Inequalities:

Linear inequalities. Algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables. Solution of system of linear inequalities in two variables- graphically. Absolute value, Inequality of means, Cauchy-Schwarz Inequality, Tchebychef’s Inequality.

 

Binomial Theorem:

Statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, general and middle term in binomial expansion, simple applications. Binomial Theorem for any index. Properties of Binomial Co-efficients. Simple applications for approximations.

Sequence and Series:

Sequence and Series. Arithmetic, Geometric and Harmonic progressions (G.P.), General terms and sum to n terms of A.P., G.P. and H.P. Arithmetic Mean (A.M.), Geometric Mean (G.M.), and Harmonic Mean (H.M.), Relation between A.M., G.M. and H.M. Insertion of Arithmetic, Geometric and Harmonic means between two given numbers. Special series, Sum to n terms of the special series. . Arithmetico-Geometric Series, Exponential and Logarithmic series.

Elementary Number Theory:

Peano’s Axioms, Principle of Induction; First Principle, Second Principle, Third Principle, Basis Representation Theorem, Greatest Integer Function Test of Divisibility, Euclid’s algorithm, The Unique Factorisation Theorem, Congruence, Sum of divisors of a number . Euler’s totient function, Theorems of Fermat and Wilson.

 

Quadratic Equations:
Quadratic equations in real and complex number system and their solutions. Relation between roots and co-efficients, nature of roots, formation of quadratic equations with given roots; Symmetric functions of roots, equations reducible to quadratic equations – application to practical problems.

 

Polynomial functions, Remainder & Factor Theorems and their converse, Relation between roots and coefficients, Symmetric functions of the roots of an equation. Common roots.

 

Matrices and Determinants:
Determinants and matrices of order two and three, properties of determinants, Evaluation of determinants. Area of triangles using determinants, Addition and multiplication of matrices, adjoint and inverse of matrix. Test of consistency and solution of simultaneous linear equations using determinants and matrices.

 

Two dimensional Geometry:
Cartesian system of rectangular co-ordinates in a plane, distance formula, section formula, area of a triangle, condition for the collinearity of three points, centroid and in-centre of a triangle, locus and its equation, translation of axes, slope of a line, parallel and perpendicular lines, intercepts of a line on the coordinate axes.

Various forms of equations of a line, intersection of lines, angles between two lines, conditions for concurrence of three lines, distance of a point from a line, Equations of internal and external bisectors of angles between two lines, coordinates of centroid, orthocentre and circumcentre of a triangle, equation of family of lines passing through the point of intersection of two lines, homogeneous equation of second degree in x and y, angle between pair of lines through the origin, combined equation of the bisectors of the angles between a pair of lines, condition for the general second degree equation to represent a pair of lines, point of intersection and angle between two lines.

Standard form of equation of a circle, general form of the equation of a circle, its radius and centre, equation of a circle in the parametric form, equation of a circle when the end points of a diameter are given, points of intersection of a line and a circle with the centre at the origin and condition for a line to be tangent to the circle, length of the tangent, equation of the tangent, equation of a family of circles through the intersection of two circles, condition for two intersecting circles to be orthogonal.

Sections of cones, equations of conic sections (parabola, ellipse and hyperbola) in standard forms, condition for y = mx + c to be a tangent and point(s) of tangency.

 

Trigonometric Functions:

Positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. Graphs of trigonometric functions. Expressing sin (x+y) and cos (x+y) in terms of sinx, siny, cosx & cosy. Identities related to     sin2x, cos2x, tan 2x, sin3x, cos3x and tan3x. Solution of trigonometric equations, Proofs and simple applications of sine and cosine formulae. Solution of triangles. Heights and Distances.

Inverse Trigonometric Functions:

Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

 

Differential Calculus:
Polynomials, rational, trigonometric, logarithmic and exponential functions, Inverse functions. Graphs of simple functions. Limits, Continuity and differentiability; Derivative, Geometrical interpretation of the derivative, Derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions, Derivative of composite functions; chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Exponential and logarithmic functions and their derivatives. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle's and Lagrange's Mean Value Theorems and their geometric interpretations.

 

Applications of Derivatives:

Applications of derivatives: rate of change, increasing / decreasing functions, tangents & normals, approximation, maxima and minima.

 

Integral Calculus:
Integral as an anti-derivative. Fundamental integrals involving algebraic, trigonometric, exponential and logarithmic functions. Integration by substitution, by parts and by partial fractions. Integration using trigonometric identities. Definite integrals as a limit of a sum, Fundamental Theorem of Calculus. Basic Properties of definite integrals and evaluation of definite integrals; Applications of definite integrals in finding the area under simple curves, especially lines, areas of circles / Parabolas / ellipses, area between the two curves.

Differential Equations:
Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation.

Vectors:

Vectors and scalars, magnitude and direction of a vector. Direction cosines / ratios of vectors. Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a

line. Vector (cross) product of vectors.

 

Three dimensional Geometry:
Coordinates of a point in space, distance between two points; Section formula, Direction cosines / ratios of a line joining two points. Cartesian and vector equationof a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between (i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane. Scalar and vector triple product. Application of vectors to plane geometry. Equation of a sphere, its centre and radius. Diameter form of the equation of a sphere.

 

Statistics:

Calculation of Mean, median and mode of grouped and ungrouped data. Measures of dispersion; mean deviation, variance and standard deviation of ungrouped / grouped data. Analysis of frequency distributions with equal means but different variances.

 

Probability:

Random experiments: outcomes, sample spaces. Events: occurrence of events, exhaustive events, mutually exclusive events, Probability of an event, probability of 'not', 'and' & 'or' events., Multiplication theorem on probability. Conditional probability, independent events,, Baye's theorem, Random variable and its probability distribution, Binomial and Poisson distributions and their properties.

 

Linear Algebra

Examples of vector spaces, vector spaces and subspace, independence in vector spaces, existence of a Basis, the row and column spaces of a matrix, sum and intersection of subspaces. Linear Transformations and Matrices, Kernel, Image, and Isomorphism, change of bases, Similarity, Rank and Nullity. Inner Product spaces, orthonormal sets and the Gram-Schmidt Process, the Method of Least Squares. Basic theory of Eigenvectors and Eigenvalues, algebraic and geometric multiplicity of eigen value, diagonalization of matrices, application to system of linear differential equations. Generalized Inverses of matrices, Moore-Penrose generalized inverse.

 

Real quadratic forms, reduction and classification of quadratic forms, index and signature, triangular reduction of a pair of forms, singular value decomposition, extrema of quadratic forms. Jordan canonical form, vector and matrix decomposition.

 

Field extensions, fundamental theorem of Galois theory, splitting fields, algebraic closure and normality, Galois group of a polynomial, finite fields, separability, cyclic extensions, solvability by radicals.

 

Abstract Algebra

Groups. semigroups, monoids and groups cyclic groups cosets and Lagrange’s Theorem, normality, quotient groups, and homomorphisms, symmetric, alternating, and dihedral groups, direct products and direct sums free groups, free products, generators and relations. The structure of groups, free abelian groups, finitely generated abelian groups, group actions on a set, Sylow Theorem, nilpotent and solvable groups ,Jordan-Hölder Theorem.  Rings and homomorphisms ,subrings and ideals integral domains, principal ideal domains and Euclidean domains factorization in commutative rings, rings of quotients, rings of polynomials, factorization in polynomial rings.

 

Analysis

Monotone functions and functions of bounded variation. Real valued functions, continuous functions, Absolute continuity of functions, standard properties. Uniform continuity, sequence of functions, uniform convergence, power series and radius of convergence. Riemann-Stieltjes integration, standard properties, multiple integrals and their evaluation by repeated integration, change of variable in multiple integration. Uniform convergence in improper integrals, differentiation under the sign of integral - Leibnitz rule.

 

Dirichlet integral, Liouville’s extension. Introduction to n-dimensional Euclidean space, open and closed intervals (rectangles), compact sets, Bolzano-Weierstrass theorem, Heine-Borel theorem. Maxima-minima of functions of several variables, constrained maxima-minima of functions. Analytic function, Cauchy-Riemann equations, singularities, Statement of Cauchy theorem and of Cauchy integral formula with applications, Residue and contour integration. Fourier and Laplace transforms, Mellin’s inversion theorem.

 

Conformal Mapping,Elliptic Function.Elementary Functions (Exponential, Logarithm, Complex Exponents, Trigs, Hyperbolic Functions) Integrals (Definite Integrals, Antiderivatives, Cauchy Goursat Theorem, Cauchy Integral Formula, Liouville's Theorem, Fundamental Theorem of Algebra, Maximum Modulus Principle) Series (Sequences, Convergence of Series, Taylor Series, Laurent Series, Absolute and Uniform Convergence, Power Series techniques) Residues and Poles (Residues, Cauchy's Residue Theorem, Residue at Infinity, Zeros of Analytic Functions

 

Functional Analysis

Normed space,Hann Banach theorem, Banach Space,Inner Product Space,Measure Theory,Hilbert Space, ,Holders Inequality,Bessel Inequality

 

Topology

Set theory. Orderings.  Cardinals and ordinals.Equivalence of the various forms of Zorns’s lemmaTransfinite induction and  construction.Topologicalspaces.Neighborhood system of a point; closure, interior and boundary.Bounded Variation, bases and subbases.Connectedness,arcwiseconnectedness, local connectedness. Filters.  Directed sets and nets, subnets and cluster points  Embedding and Metrization.  Existence of continuous functions, Tietze’s theorem.  Embedding in cubes.  Metric spaces.  Completeness.  Baire category theorem.  Urysohn metrization theorem.  Compactness and localcompactness.Tychonoff’stheorem.Compactification (Alexandroff one-point and Stone-Cech).  Lebesgue’s covering lemma.  Paracompactness Homotopy theory.  The fundamental group, functorial properties,.  Covering spaces: unique path lifting, the universal cover, relation between covering spaces and fundamental group. Homology theory.  Basic properties of homology groups.  Chain complexes and homotopy.

 

Syllabus for written examination for PGT (Phy)

 

Unit I: Physical World and Measurement

Need for measurement: Units of measurement; systems of units; SI units, fundamental

and derived units. Length, mass and time measurements; accuracy and precision of

measuring instruments; errors in measurement; significant figures.

dimensional analysis and its applications.

 

Unit II: Kinematics

Frame of reference. Motion in a one ,two and three dimension: Position-time graph, speed and velocity.

Uniform and non-uniform motion, average speed and instantaneous velocity.

Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion .Vectors :Position and displacement vectors .addition and subtraction of vectors. Relative velocity.scalar product of vectors,Vector product of vectors.

Unit vector; Resolution of a vector in a plane - rectangular components. Motion in a

plane. Cases of uniform velocity and uniform acceleration-projectile motion.

 

Unit III: Laws of Motion

Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s

second law of motion; impulse; Newton’s third law of motion. Law of conservation of

linear momentum and its applications.

Equilibrium of concurrent forces. Types of friction, laws of friction, .Dynamics of uniform circular motion .

 

Unit IV: Work, Energy and Power

Work done by a constant force and a variable force; kinetic

energy, work-energy theorem, power.

Notion of potential energy, potential energy of a spring, conservative forces: conservation

of mechanical energy (kinetic and potential energies); non-conservative forces: elastic

and inelastic collisions in one and two dimensions.

 

Unit V: Motion of System of Particles and Rigid Body

Centre of mass of a two-particle system, momentum conversation and centre of mass

motion. Centre of mass of a rigid body; centre of mass of uniform rod.

; moment of a force, torque, angular momentum, conservation

of angular momentum with some examples.

Dynamics of rigid bodies, comparison of linear and rotational motions; moment of inertia, radius of gyration.

Values of moments of inertia for geometrical objects. Parallel and perpendicular axis theorems and their applications.

 

Unit VI: Gravitation

Keplar’s laws of planetary motion. The universal law of gravitation.

Variation of Acceleration due to gravity and with altitude,latitude and depth.

Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity

of a satellite. Geo-stationary satellites.

 

Unit VII: Properties of Bulk Matter

Elastic behaviour, Stress-strain relationship, Hooke’s law,modulus of elasticity .

Pressure due to a fluid column; Pascal’s law and its applications

Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent

flow. Bernoulli’s theorem and its applications.

Surface energy and surface tension, application of surface tension ideas

to drops, bubbles and capillary rise.

Heat, temperature, thermal expansion; specific heat - calorimetry; change of state - latent

heat.

Heat transfer-conduction, convection and radiation, thermal conductivity, Newton’s law

of cooling.

 

Unit VIII: Thermodynamics

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat,

work and internal energy. First law of thermodynamics.

Second law of thermodynamics: reversible and irreversible processes. Heat engines and

refrigerators.carnot cycle and carnot’s theorem.

Equation of state of a perfect gas, work done on compressing a gas.

Kinetic theory of gases ,degrees of freedom, law of equipartition of energy  and application to specific heats of gases; concept of mean free path, Avogadro’s

number.

 

 

 

Unit IX: Oscillations and Waves

Periodic motion - period, frequency, displacement as a function of time. Periodic functions.Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring–restoring force and force constant; energy in S.H.M.-kinetic and potential energies; simple pendulum–derivation of expression for its time period; free, forced and damped oscillations, resonance.

 

Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement

relation for a progressive wave. Principle of superposition of waves, reflection of waves,

standing waves in strings and organ pipes, fundamental mode and harmonics, Beats,

Doppler effect.

 

Unit X: Electrostatics

Electric Charges; Conservation of charge, Coulomb’s law and its application,force between two point charges,

forces between multiple charges; superposition principle and continuous charge distribution.

Electric field, electric field due to a point charge, electric field lines; electric dipole, electric

field due to a dipole; torque on a dipole in uniform electric field.

Gauss’s theorem and its applications

Electric potential, potential difference, electric potential due to a dipole

and system of charges; equipotential surfaces, electrical potential energy of a system of

two point charges and of electric dipole in an electrostatic field.

Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics

and electric polarisation, capacitors and capacitance, combination of capacitors, capacitance of a parallel plate capacitor with and without dielectric medium

between the plates, energy stored in a capacitor. Van de Graaff generator.

 

Unit XI: Current Electricity

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility

and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics

(linear and non-linear), electrical energy and power, electrical resistivity and conductivity.

Carbon resistors, colour code for carbon resistors; series and parallel combinations of

resistors; temperature dependence of resistance.

Internal resistance of a cell, potential difference and emf of a cell, combination of cells in

series and in parallel.

Kirchhoff’s laws and its applications..

Potentiometer - principle and its applications

Thermal and chemical effect of current.

Unit XII: Magnetic Effects of Current and Magnetism

Biot - Savart law and its application

Ampere’s law and its applications to infinitely long straight wire, straight and toroidal

solenoids.

Lorentz’s force. Cyclotron,synchrotron.

Interaction of a current-carrying conductor with magnetic field. Force between two

parallel current-carrying conductors. Torque experienced by a current

loop in uniform magnetic field and its application;

Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole momentof a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet)

along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a

uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s

magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with

examples. Electromagnets and factors affecting their strengths. Permanent magnets.

 

Unit XIII: Electromagnetic Induction and Alternating Currents

Electromagnetic induction; Faraday’s law, induced emf and current; Lenz’s Law, Eddy

currents. Self and mutual inductance.

Need for displacement current.

Alternating currents and its measurement  reactance and

impedance; LC oscillations, LCR series circuit, resonance;

power in AC circuits,.

generator , motors and transformer.

 

UnitXIV: Optics

 Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal

reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin

lens formula, lens-maker’s formula. Magnification, power of a lens, combination of thin

lenses in contact. Refraction and dispersion of light through a prism.

Scattering of light  and its application.

Optical instruments: Human eye-eye defects and its correction. Microscopes

and astronomical telescopes and their magnifying powers.

Wave optics: wave front and Huygens’ principle, reflection and refraction of plane wave at

a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygens’

principle. Interference, Young’s double slit experiment and expression for fringe width,

coherent sources and sustained interference of light. Diffraction due to a single slit, width of

central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation,

plane polarised light; Brewster’s law, uses of plane polarised light and Polaroids.

 

Unit XV: Modern Physics

Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s

photoelectric equation-particle nature of light., deffraction of X- rays ,Bragg’s law.

Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment.

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy

levels, hydrogen spectrum.

Composition and size of nucleus,  packing fraction and magnetic moment, atomic masses, isotopes, isobars; isotones. Radioactivity-alpha,

beta and gamma particles/rays and their properties; radioactive decay law.

Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; liquid drop model of nucleus, nuclear fission and fusion.,critical mass ,chain reaction and fission reaction, ionization chamber,Geiger counter and scinitillation counter,linear accelerator.

Elements of a communication system ,bandwidth of signals (speech, TV

and digital data); bandwidth of transmission medium.

 

Unit XVI: Electronic Devices

Semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias,

diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode;

Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of

a transistor; transistor as an amplifier (common emitter configuration) and oscillator. Logic gates and its combination. Transistor as a switch.

Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave  Wein’s displacement law, stefan’s law,Qualititave ideas of Black body radiations

Energy band diagrams in solids Conductors, semiconductors And insulators

 

In addition to the above,  an MCQ  on practical skills based on the experiments of XI and XII  syllabus  may be included.