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, N_{2 }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 ( C_{2} , C_{3},
C_{4}, 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,
K_{c} and K_{p}
, 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 KMnO_{4} and K_{2}Cr_{2}
O_{7}, 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,
sp^{2},sp^{3}), 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 SN^{1} and SN^{2} reactions,
elimination reactions (Saytzeff Rule, E_{1} & E_{2}
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, 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)
·
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
·
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.
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
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
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
4.
Development Experience of
SYLLABUS FOR WRITTEN EXAMINATION FOR PGT (ENGLISH)
Section A
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
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.
LITERATURE
ü
Romantic period (e.g. Shelley, Wordsworth,
Keats, Coleridge etc)
ü
19^{th} and 20^{th} 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. /
T.S.
Eliot, D.H.
Lawrence,( Oedipus Complex) William Blake may be added.
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.
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
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
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
Origin and mechanism of Indian monsoon; Seasons of India, Classification
of climate of
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
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
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
Influence of LPG on industrial
development especially in
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
Topic-15 Transport, Communication and Trade(World and
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
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
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
Administration, Gupta Administration, Ashoka The Great,
Society, Trade,
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,
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, Mahanavami –Dibba-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,
Advent
Of Europeans And Establishment Of British Rule,
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 –
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-
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
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.
b.
Decline
6) Renaissance ’n Reformation period in
7)
Capitalism and Mercantilism
a. Industrial Revolution
b. Imperialism and colonialism
8)
9)
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.
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.
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.
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,
second law of motion; impulse;
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,
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.
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;
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.