NVS PGT SYLLABUS AND EXAM PATTERN 2020

NVS PGT SYLLABUS AND EXAM PATTERN

NVS PGT SYLLABUS AND EXAM PATTERN

Welcome TO Sarkari syllabus.com

 today we are going to discuss the detailed syllabus and exam pattern of Navodaya Vidyalaya Sangathan NVS PGT geography syllabus and exam pattern.

 first thing must be come first so let’s get started with exam pattern.

NVS PGT EXAM PATTERN

exam pattern has  02 stage examination,

 first stage written examination

 second stage interview

 later I will discuss the details syllabus of the stage first as well as some important things regarding the interview also.

TESTComponent of the testQUESTIONMARKS
Part-IReasoning Ability1515
Part-IIGeneral Awareness1515
Part-IIITeaching Aptitude2020
Part-IVSubject Knowledge (YOUR SUBJECT)100100
TOTAL150150
Part-VLanguage Competency Test
(General English and General
Hindi-15 marks each subject).
This part is qualifying in nature
only with minimum 33 1/3rd
marks in each language.

I would like to cover few more important points.

  1.  the final merit list will be made on the basis of Mark’s score in the written examination as well as an interview.
  2. The ratio of marks will be 85:15 Where 85% marks will be count from written examination and 15% marks will be count from an interview test the written examination will be a total of 150 marks.
  3.  and the interview will be 60 marks.
  4.  there is no negative marking in the written examination.
  5.  later I will tell you the detailed written examination syllabus in which you will be able to understand the maximum marks questions will be asked from your relevant discipline relevant subject by which you are appearing for a PGT exam
  6.  100 questions will be asked from your biology topic so prepare well for your concern subject

Language Competency Test

  1. Synonyms
  2. Homonyms
  3. Antonyms
  4. Spelling
  5. Word formation
  6. Idioms and phrases
  7. Fill in suitable words
  8. Grammar
  9. Spotting errors
  10. Sentence correction
  11. Active/ passive voice
  12. Phrases and idioms
  13. Direct and indirect speech
  14. Reading Comprehension
  15. Passage completion
  16. Theme detection
  17. Deriving conclusion
  18. Rearrangement of passage

Language Competency Test General Hindi

  1. विपरीतार्थकशब्द.
  2. पर्यायवाचीशब्द.
  3. मुहावरेतथालोकोक्तियां.
  4. गुढार्थी (क्लोजटाइप) प्रकारकागद्यांश.
  5. वाक्यक्रमव्यवस्थापन.
  6. वाक्योंमेंत्रुटियाँ.
  7. वाक्योंमेंरिक्त-स्थानोंकीपूर्ति.
  8. वर्तनीअशुद्धियाँ.
  9. वाक्यांशकेलिएएकशब्द.
  10. अपठितगद्यांश.

Reasoning Ability

  1. Analogy
  2. Classification
  3. Word formation
  4. Statement and conclusions
  5. Syllogism
  6. Statement and assumptions
  7. Statement and arguments
  8. Coding decoding
  9. Blood relations
  10. Passage and conclusions
  11. Alphabet test
  12. Series test
  13. Number, ranking and time sequence
  14. Direction sense test
  15. Decision-making test
  16. Figure series
  17. Input/output
  18. Assertion and reasoning
  19. Sitting arrangement
  20. Odd figure out
  21. Analogy
  22. Series test
  23. Miscellaneous test.

General Awareness

  1. Science – Inventions & Discoveries
  2. Indian Constitution
  3. Geography
  4. Budget and Five Year Plans
  5. History
  6. Scientific Research
  7. Important Financial & Economic News
  8. Culture
  9. Economy Current Affairs – National & International
  10. India and its neighboring countries
  11. General Politics
  12. Sports
  13. Economy, Banking, and Finance
  14. Knowledge of Current Events
  15. Countries & Capitals

NVS PGT GEOGRAPHY SYLLABUS

Topic I:

Geography as a disciplineGeographical ideas in ancient, medieval & modern periods:

the contributions of Varenius, Kant, Reine, Humboldt and Ritter.

Influence of Richthofen and Darwin.

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. Marxist Geography and critical social theory. Development in Indian Geography.

Topic-2 Origin and Evolution of the Earth

Introduction to the solar system, Motions of Earth: Rotation, Revolution.

The 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 NVS PGT GEOGRAPHY

Interior of the Earth and Distribution of oceans and continentsConstitution 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 LandformsMineral 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 and Thornthwaite Schemes classification). 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 SoilClimate: 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 disastersCauses,

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.

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) 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 NVS PGT GEOGRAPHY

Geographical perspective on selected issues and problems Environmental pollution-Land, Water, Air, Noise, Global Warning, Poverty, Food Security; Sustainable Development.

Topic -18 NVS PGT GEOGRAPHY

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.

INTERVIEW TIPS NVS PGT

Interview for PGT post is very important and Critical things because it is scoring as well as mandatory also.

 you have to good score in interview.

 if you have good marks in your interview then there are more chances to get selected for the PGT post because the merit list is based on written exam + interview.

OFFICIAL WEBSITE-CLICK HERE

NVS PGT CHEMISTRY SYLLABUS

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, the concept of limiting reagent

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 behavior, 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, energy band, band gaps, semiconductors, magnetic and dielectric properties.

stoichiometric and non- stoichiometric defects in solids.

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.

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, 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.

Surface Chemistry:

Adsorption, absorption, sorption, Physical adsorption, Chemisorption adsorption, isotherms ( Freundlich, Langmuir), application of adsorption.

types of 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.

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).

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.

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 nonvolatile solute, Ideal and nonideal solution.

Colligative properties, abnormal molecular masses and Van’t Hoff factor.

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.

Thermodynamics: NVS PGT CHEMISTRY SYLLABUS

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.

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.

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.NVS PGT SYLLABUS

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.

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.

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.

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 coordination compounds, metal carbonyls:

preparation, properties and bonding, organometallic compounds and their classification.

Organic Chemistry : NVS PGT CHEMISTRY SYLLABUS

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 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.

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).NVS PGT SYLLABUS

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.

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.

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.

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.

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.

Amines (Organic compounds containing nitrogen ):

Classification, Structure of amino group, preparation, Physical, Chemical properties, tests to distinguish between primary, secondary and tertiary amines

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.

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),  and  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.NVS PGT SYLLABUS

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.

the cleansing action of soaps, advantages of detergents over soaps, Deodorants, Edible colors, antioxidants.

NVS PGT physics SYLLABUS

Syllabus for written examination for PGT ( PHYSICS )

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 NVS PGT physics SYLLABUS

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 NVS PGT physics SYLLABUS

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.

The first law of thermodynamics. The 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.NVS PGT SYLLABUS

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.

the 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, a 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.NVS PGT SYLLABUS

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.

Compton effect, deffraction of X- rays ,Bragg’s law ,Hall effect. 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.

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.

NVS PGT Mathematics SYLLABUS

Syllabus for written examination for PGT ( Mathematics )

Sets :NVS PGT SYLLABUS

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: NVS PGT Mathematics SYLLABUS

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

Complex Numbers:NVS PGT Mathematics SYLLABUS

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:NVS PGT Mathematics SYLLABUS

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 GramSchmidt 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.

SOME OTHER TOPICS NVS PGT Mathematics SYLLABUS

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.

Leave a Reply