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Chemistry: Unit 01

• General introduction: Importance and scope of chemistry
• Historical approach to particulate nature of matter, laws of chemical combination
• Dalton’s atomic theory: Concept of elements, atoms, and molecules
• Atomic and molecular masses mole concept, and molar mass: Percentage composition, empirical and molecular formula chemical reactions, stoichiometry and calculations based on stoichiometry

Chemistry: Unit 02

• Classification of solids based on different binding forces: molecular, ionic, covalent, and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices
• Classification of solids based on different binding forces: Calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties

Chemistry: Unit 03

• Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties-relative lowering of vapour pressure, elevation of boiling point, depression of freezing point
• Osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass

Chemistry: Unit 04

• Discovery of electron, proton, and neutron; atomic number, isotopes, and isobars
• Thomson’s model and its limitations, Rutherford’s model, and its limitations
• Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p, and d orbitals
• Rules for filling electrons in orbitals-Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals

Chemistry: Unit 05

• Significance of classification, brief history of the development of periodic table, modern periodic law, and the present form of periodic table, periodic trends in properties of elements-atomic radii, ionic radii
• Ionization enthalpy, electron gain enthalpy, electro negativity, valence

Chemistry: Unit 06

• Valence electrons, ionic bond, covalent bond: Bond parameters
• Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR (valence shell electron pair repulsion) theory, concept of hybridization
• Involving s, p, and d orbitals and shapes of some simple molecules, molecular orbital; theory of homonuclear diatomic molecules (qualitative idea only), hydrogen bond

Chemistry: Unit 07

• Three states of matter
• Intermolecular interactions, type of bonding, melting, and boiling points
• Role of gas laws in elucidating the concept of the molecule, Boyle’s law
• Charles law, Gay Lussac’s law, Avogadro’s law
• Ideal behaviour, empirical derivation of gas equation, Avogadro’s number
• Ideal gas equation
• Derivation from ideal behaviour, liquefaction of gases, critical temperature
• Liquid state-vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations)

Chemistry: Unit 08

• Concepts of system, types of systems, surroundings
• Work, heat, energy, extensive and intensive properties, state functions
• First law of thermodynamics-internal energy and enthalpy, heat capacity and specific heat, measurement of DU and DH, Hess’s law of constant heat summation, enthalpy of: Bond dissociation, combustion, formation, atomization, sublimation
• Phase transformation, ionization, and solution
• Introduction of entropy as a state function, free energy change for spontaneous, and non-spontaneous processes, criteria for equilibrium

Chemistry: Unit 09

• Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium-Le Chatelier’s principle; ionic equilibrium-ionization of acids and bases
• Strong and weak electrolytes, degree of ionization, concept of pH
• Hydrolysis of salts
• Buffer solutions, solubility product, common ion effect

Chemistry: Unit 10

• Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions

Chemistry: Unit 11

• Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties, and uses of hydrogen; hydrides-ionic, covalent, and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxide-preparation
• Properties and structure; hydrogen as a fuel

Chemistry: Unit 12

• Group 1 and group 2 elements: General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship
• Group 1 and group 2 elements: Trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen, and halogens; uses

Chemistry: Unit 13

• Sodium carbonate, sodium chloride, sodium hydroxide, and sodium hydrogen carbonate, biological importance of sodium and potassium
• CaO, CaCO₃, and industrial use of lime and limestone, biological importance of Mg and Ca

Chemistry: Unit 14

• General introduction to p-block elements: Group 13 elements-general introduction, electronic configuration, occurrence. Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group
• General introduction to p-block elements: Group 13 elements-boron-physical and chemical properties, some important compounds: Borax, boric acids, boron hydrides. Aluminum: Uses, reactions with acids, and alkalies

Chemistry: Unit 15

• General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behavior of first element, carbon-catenation, allotropic forms, physical and chemical properties
• Uses of some important compounds: Oxides
• Important compounds of silicon and a few uses: Silicon tetrachloride, silicones, silicates, and zeolites

Chemistry: Unit 16

• Some basic principles and techniques: General introduction, methods of qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds, electronic displacements in a covalent bond: Inductive effect
• Some basic principles and techniques: Electronic displacements in a covalent bond-electromeric effect, resonance and hyper conjugation. Homolytic and heterolytic fission of a covalent bond: Free radicals, carbocations, carbanions
• Some basic principles and techniques: Electrophiles and nucleophiles, types of organic reactions

Chemistry: Unit 17

• Classification of hydrocarbons: Alkanes-nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion, and pyrolysis
• Classification of hydrocarbons: Alkenes-nomenclature, structure of double bond (ethene) geometrical isomerism, physical properties, methods of preparation; chemical reactions: Addition of hydrogen, halogen, water, hydrogen halides
• Classification of hydrocarbons: Alkenes-(Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition
• Classification of hydrocarbons: Alkynes-nomenclature, structure of triple bond (ethyne), physical properties. Methods of preparation, chemical reactions: Acidic character of alkynes, addition reaction of-hydrogen, halogens, hydrogen halides, and water
• Classification of hydrocarbons: Aromatic hydrocarbons-introduction, IUPAC nomenclature; benzene: Resonance, aromaticity; chemical properties: Mechanism of electrophilic substitution-nitration, sulphonation, halogenation
• Classification of hydrocarbons: Aromatic hydrocarbons-Friedel-Craft’s alkylation and acylation: Directive influence of functional group in mono-substituted benzene; carcinogenicity and toxicity

Chemistry: Unit 18

• Conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s law, electrolysis and laws of electrolysis (elementary idea), dry cell-electrolytic cells and galvanic cells
• Lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion

Chemistry: Unit 19

• Rate of a reaction (average and instantaneous), factors affecting rate of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant
• Integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)

Chemistry: Unit 20

• Adsorption-physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis: Homogenous and heterogeneous, activity and selectivity: Enzyme catalysis; colloidal state: Distinction between true solutions
• Colloidal state: Colloids, and suspensions, lyophilic, lyophobic, multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion-types of emulsions

Chemistry: Unit 21

• Principles and methods of extraction-concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc, and iron

Chemistry: Unit 22

• Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen-preparation, properties, and uses
• Group 15 elements: Compounds of nitrogen-preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); phosphorous-allotropic forms; compounds of phosphorous: Preparation and properties of phosphine
• Group 15 elements: Compounds of phosphorous-halides (PCl₃, PCl₅) and oxoacids

Chemistry: Unit 23

• General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: Preparation, properties, and uses; simple oxides; ozone
• Sulphur-allotropic forms; compounds of sulphur: Preparation, properties, and uses of sulphur dioxide; sulphuric acid: Industrial process of manufacture, properties, and uses, oxoacids of sulphur (structures only

Chemistry: Unit 24

• General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: Preparation, properties, and uses of chlorine and hydrochloric acid, interhalogen compounds
• Compounds of halogens: Oxoacids of halogens (structures only)

Chemistry: Unit 25

• General introduction, electronic configuration
• Occurrence, trends in physical and chemical properties, uses

Chemistry: Unit 26

• General introduction, electronic configuration, occurrence, and characteristics of transition metals, general trends in properties of the first row transition metals-metallic character, ionization enthalpy, oxidation states, ionic radii
• Colour catalytic property, magnetic properties, interstitial compounds, alloy formation preparation and properties of K²Cr²O⁷ and KMnO⁴
• Lanthanoids-electronic configuration, oxidation states, chemical reactivity, and lanthanoid contraction
• Actinoides-electronic configuration, oxidation states

Chemistry: Unit 27

• Coordination compounds-introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds
• Bonding; isomerism, importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems)

Chemistry: Unit 28

• Haloalkanes: Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions
• Haloarenes: Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only) uses and environmental effects of-dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT

Chemistry: Unit 29

• Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary, and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol
• Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols
• Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses

Chemistry: Unit 30

• Aldehydes and ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses
• Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses

Chemistry: Unit 31

• Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary, and tertiary amines
• Cyanides and isocyanides-will be mentioned at relevant places in context
• Diazonium salts: Preparation, chemical reactions, and importance in synthetic organic chemistry

Chemistry: Unit 32

• Carbohydrates-classification (aldoses and ketoses), monosaccharide (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance
• Proteins-elementary idea of á-amino acids, peptide bond, polypeptides, proteins, structure of amines-primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes
• Vitamins-classification and functions
• Nucleic acids: DNA and RNA

Chemistry: Unit 33

• Classification-natural and synthetic, methods of polymerization (addition and condensation), copolymerization
• Some important polymers: Natural and synthetic like polythene, nylon, polyesters, bakelite, rubber

Chemistry: Unit 34

• Environmental pollution-air, water, and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone, and its reactions, effects of depletion of ozone layer
• Greenhouse effect and global warming-pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution

Chemistry: Unit 35

• Chemicals in medicines-analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines
• Chemicals in food-preservatives, artificial sweetening agents
• Cleansing agents-soaps and detergents, cleansing action

Biology (Botany and Zoology): Unit 01

• Nature and scope of biology
• Methods of biology
• Our place in the universe
• Laws that govern the universe and life
• Level of organization
• Cause and effect relationship
• Being alive
• What does it mean? present approaches to understand life processes, molecular approach; life as an expression of energy; steady state and homeostasis; self duplication and survival; adaptation; death as a positive part of life
• Origin of life and its maintenance
• Origin and diversity of life
• Physical and chemical principles that maintain life processes
• The living crust and interdependence
• The positive and negative aspects of progress in biological sciences
• The future of the living world, identification of human responsibility in shaping our future

Biology (Botany and Zoology): Unit 02

• Cell as a unit of life
• Small biomolecules; water, minerals, mono and oligosaccharides, lipids, amino acids, nucleotides and their chemistry, cellular location and function
• Macromolecules in cells-their chemistry, cellular location, and functional significance
• Polysaccharides, proteins, and nucleic acids
• Enzymes; chemical nature, classification, mechanism in action-enzyme complex, allosteric modulation (brief), irreversible activation
• Biomembranes; fluid mosaic model of membrane, role in transport, recognition of external information (brief)
• Structural organization of the cell; light and electron microscopic views of cell, its organelles, and their functions; nucleus mitochondria, chloroplasts, endoplasmic reticulum
• Golgi complex, lysosomes, microtubules, cell wall, cilia and flagella, vacuoles, cell inclusions
• A general account of cellular respiration
• Fermentation, biological oxidation (a cycle outline), mitochondrial electron transport chain, high energy bonds, and oxidative phosphorylation, cell reproduction; process of mitosis and meiosis

Biology (Botany and Zoology): Unit 03

• Introduction
• The enormous variety of living things, the need for classification to cope with this variety; taxonomy and phylogeny; shortcomings of a two kingdom classification as plants and animals; the five kingdom classification, monera, protista, plantae
• Fungi, and animalia; the basic features of five kingdom classification
• Modes of obtaining nutrition-autotrophs and heterotrophs
• Life style producers, consumers, and decomposers
• Unicellularity and multicellularity, phylogenetic relationships
• Concepts of species, taxon, and categories-hierarchical levels of classification; binomial nomenclature; principles of classification and nomenclature; identification and nature of viruses and bacteriophages
• Kingdom monera-archeabacteria-life in extreme environments; bacteria, actinomycetes, cyanobacteria
• Examples and illustration of autotrophic and heterotrophic life; mineralizes-nitrogen fixers; monera in cycling matter; symbiotic forms; disease producers
• Kingdom protista-eukaryotic unicellular organisms, development of flagella and cilia; beginning of mitosis; syngamy and sex
• Various life styles shown in the major phyla
• Evolutionary precursors of complex life forms
• Diatoms, dinoflagellates, slime moulds, protozons; symbiotic forms
• Plant kingdom-complex autotrophs, red brown, and green algae; conquest of land, bryophytes, ferns, gymnosperms and angiosperms
• Vascularization; development of flower, fruit, and seed
• Kingdom fungi-lower fungi (zygomycetes), higher fungi (ascomycetes and basidiomycetes); the importance of fungi
• Decomposers; parasitic forms; lichens and mycorrhizae
• Animal kingdom-animal body pattern, and symmetry
• The development of body cavity in invertebrate vertebrate physia
• Salient features with reference to habitat and example of phylum porifera, coelenterata, helminthis, annelids, mollusca, arthropoda, echinoderms; chordata-(classes-fishes, amphibians, reptiles, birds and mammals) highlighting major characters

Biology (Botany and Zoology): Unit 04

• Species: Origin and concept of species population, interaction between environment and population community
• Biotic community, interaction between different species, biotic stability
• Changes in the community
• Succession
• Ecosystem; interaction between biotic and abiotic components; major ecosystems, manmade ecosystem-agroecosystem
• Biosphere; flow of energy, trapping of solar energy, energy pathway, food chain, food web, biogeochemical cycles, calcium, and sulphur, ecological imbalance, and its consequences
• Conservation of natural resources; renewable and non-renewable (in brief)
• Water and land management, wasteland development
• Wild life and forest conservation; causes for the extinction of some wild life, steps taken to conserve the remaining species, concept of endangered species-Indian examples, conservation of forests; Indian forests, importance of forests
• Hazards of deforestation, concept of afforestation
• Environmental pollution; air and water pollution, sources, major pollutants of big cities of our country, their effects and methods of control, pollution due to nuclear fallout and waste disposal, effect and control, noise pollution; sources and effects

Biology (Botany and Zoology): Unit 05

• Form and function
• Tissue system in flowering plants; meristematic and permanent
• Mineral nutrition-essential elements, major functions of different elements, passive and active uptake of minerals
• Modes of nutrition, transport of solutes, and water in plants
• Photosynthesis; photochemical and biosynthetic phases, diversity in photosynthetic pathways, photosynthetic electron transport, and photophosphorylation, photorespiration
• Transpiration and exchange of gases
• Stomatal mechanism
• Osmoregulation in plants: Water relations in plant cells, water potential
• Reproduction and development in angiosperms; asexual and sexual reproduction
• Structure and functions of flower: Development of male and female gametophytes in angiosperms, pollination, fertilization, and development of endosperm, embryo seed, and fruit
• Differentiation and organ formation
• Plant hormones and growth regulation; action of plant hormones in relation to seed dormancy and germination, apical dominance, senescence, and abscission
• Applications of synthetic growth regulators
• A brief account of growth and movement in plants

Biology (Botany and Zoology): Unit 06

• Animal tissues, epithelial, connective, muscular, nerve
• Animal nutrition, organs of digestion, and digestive process, nutritional requirements for carbohydrates, proteins, fats, minerals, and vitamins; nutritional imbalances and deficiency diseases
• Gas exchange and transport: Pulmonary gas exchange and organs involved, transport of gases in blood, gas exchange in aqueous media circulation: Closed and open vascular systems, structure and pumping action of heart, arterial blood pressure, lymph
• Excretion and osomoregulation
• Ammonotelism, ureotelism, urecotelism, excretion of water, and urea with special reference to man
• Role of kidney in regulation of plasma, osmolarity on the basis of nephron structure, skin, and lungs in excretion
• Hormonal coordination; hormones of mammals, role of hormones as messengers and regulators
• Nervous coordination, central autonomic and peripheral nervous systems, receptors, effectors, reflex action, basic physiology of special senses, integrative control by neuroendocrinal systems
• Locomotion: Joints, muscle movements, types of skeletal muscles according to types of movement, basic aspects of human skeleton
• Reproduction; human reproduction, female reproductive cycles
• Embryonic development in mammals (up to three germs layers), growth, repair, and ageing

Biology (Botany and Zoology): Unit 07

• Heredity and variation: Introduction, Mendel’s experiments with peas and concepts of factors
• Mendel’s laws of inheritance
• Genes: Packaging of heredity material in prokaryotes-bacterial chromosome and plasmid; and eukaryote chromosomes
• Extra nuclear genes, viral genes
• Linkage (genetic) maps
• Sex determination and sex linkage
• Genetic material and its replication, gene manipulation
• Gene expression; genetic code, transcription, translation, gene regulation
• Molecular basis of differentiation

Biology (Botany and Zoology): Unit 08

• Origin of life: Living and non-living, chemical evolution, organic evolution; Oparin ideas, Miller-Urey experiments
• Interrelationship among living organisms and evidences of evolution: Fossil records including geological scale, morphological evidence-hematology, vestigial organs, embryological similarities, and biogeographical evidence
• Darwin’s two major contributions
• Common origin of living organisms and recombination as source of variability, selection and variation, adaptation (Lederberg’s replica plating experiment for indirect selection of bacterial mutants), reproductive isolation, speciation
• Role of selection, change and drift in determining composition of population
• Selected examples: Industrial melanism; drug resistance, mimicry, malaria in relation to G-6-PD deficiency and sickle cell disease
• Human evolution: Paleontological evidence, man’s place among mammals
• Brief idea of dryopithecus, australopithecus, homo erectus, H.neanderthlensis, Cro-Magnon man and homo sapiens
• Human chromosomes, similarity in different racial groups
• Comparison with chromosomes of nonhuman primates to indicate common origin; cultural vs. biological evolution
• Mutation: Origin and types of mutation, their role in speciation

Biology (Botany and Zoology): Unit 09

• Introduction, role of biology, in the amelioration of human problems
• Domestication of plant-a historical account, improvement of crop plants; principles of plant breeding and plant introduction
• Use of fertilizers, their economic, and ecological aspects
• Use of pesticides: Advantages and hazards
• Biological methods of pest control
• Crops today
• Current concerns, gene pools, and genetic conservation
• Underutilized crops with potential uses of oilseeds, medicines, beverages, spices, fodder, new crops-leucaena (subabul), jojoba, guayule, winged bean, etc
• Biofertilizers-green manure, crop residues, and nitrogen fixation (symbiotic, non symbiotic)
• Applications of tissue culture and genetic engineering in crops
• Domestication and introduction of animals
• Livestock, poultry, fisheries (fresh water, marine, aquaculture)
• Improvement of animals: Principles of animal breeding
• Major animal diseases and their control
• Insects and their products (silk, honey, wax, and lac)
• Bioenergy-biomass, wood (combustion; gasification, ethanol)
• Cow dung cakes, gobar gas, plants as sources of hydrocarbons for producing petroleum, ethanol from starch, and lignocellulose
• Biotechnology, application in health and agriculture, genetically modified (GM) organisms, biosafety issues
• A brief historical account-manufacture of cheese
• Yoghurt, alcohol, yeast, vitamins, organic acids, antibiotics, steroids, dextrins
• Scaling up laboratory findings to industrial production, sewage treatment
• Production of insulin, human growth hormones, interferon
• Communicable diseases including STD and diseases spread through blood transfusion (hepatitis, AIDS, etc) Immune response, vaccine, and antisera
• Allergies and inflammation
• Inherited diseases and dysfunctions, sex-linked diseases, genetic incompatibilities, and genetic counseling
• Cancer-major types, causes, diagnosis, and treatment
• Tissue and organ transplantation
• Community health services and measures; blood banks; mental health, smoking, alcoholism, and drug addiction-physiological symptoms and control measures
• Industrial wastes, toxicology, pollution-related diseases
• Biomedical engineering-spare parts for man, instruments for diagnosis of diseases and care
• Human population related diseases
• Human population, growth, problems and control, inequality between sexes, control measures; test-tube babies aminocentesis
• Future of biology

Mathematics: Unit 01

• Sets: Sets and their representations. Empty set. Finite and Infinite sets. Equal sets. Subsets, subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets
• Sets: Difference of sets. Complement of a set
• Relations and 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, types of relations-reflexive, symmetric
• Relations and functions: Transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations, pictorial representation of a function, domain. Codomain and range of a relation
• Relations and functions: Function as a special kind of relation from one set to another. Real valued function of the real variable, domain, and range of these functions, constant, identity, polynomial, rational, modulus
• Relations and functions: Signum and greatest integer functions with their graphs. Sum, difference, product, and quotients of functions
• Trigonometric functions: Positive and negative angles. Measuring angles in radians and in degrees, and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle
• Trigonometric functions: Truth of the identity sin²x + cos²x=1, for all x. Signs of trigonometric functions, and sketch of their graphs. Expressing sin (x+y) and cos (x+y) in terms of sinx, siny, cosx and cosy
• Trigonometric functions: Deducing the identities like the following- tan(x ± y)= tan x ± tan y/ 1 ± tan x tan y, cot (x ± y)= cot x cot y ± 1/ cot y ± cot x, cos x + cos y = 2 cos x + y/ 2 cos x -y/ 2,
• Trigonometric functions: Deducing the identities like the following- sin x – sin y = 2cos (x + y)/ 2 sin (x – y)/ 2, cos x - cos y = -2 sin x+y/ 2 sin (x – y)/ 2. Identities related to sin2x, cos2x, tan2x, sin3x, cos3x, and tan3x
• Trigonometric functions: General solution of trigonometric equations of the type sin è ?= sin á, cos è ?= cos á ?, and tan è ?= tan á
• Inverse trigonometric functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions. Properties of triangles, including centroid, incentre
• Inverse trigonometric functions: Circum-centre and orthocentre, solution of triangles. Heights and distances

Mathematics: Unit 02

• Principle of mathematical induction: Processes of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications
• Complex numbers and quadratic equations: Need for complex numbers, especially-1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers
• Complex numbers and quadratic equations: Argand plane and polar representation of complex numbers. Statement of fundamental theorem of algebra, solution of quadratic equations in the complex number system
• 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
• Linear inequalities: Solution of system of linear inequalities in two variables-graphically
• Permutations and combinations: Fundamental principle of counting. Factorial n. (n!). Permutations and combinations, derivation of formulae and their connections, simple applications
• Binomial theorem: History, statement, and proof of the binomial theorem for positive integral indices. Pascal’s triangle, general and middle term in binomial expansion, simple applications
• Sequence and series: Sequence and series. Arithmetic progression (AP). arithmetic mean (AM) geometric progression (GP), general term of a GP, sum of n terms of a GP, geometric mean (GM), relation between AM and GM
• Sequence and series: Sum to n terms of the special series Ón, Ón², and Ón³
• Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric, and skew symmetric matrices. Addition, multiplication, and scalar multiplication of matrices, simple properties of addition
• Matrices: Multiplication and scalar multiplication. Non commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
• Matrices: Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists
• Determinants: Determinant of a square matrix (up to 3 x 3 matrices), properties of determinants, minors, cofactors, and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix
• Determinants: Consistency, inconsistency, and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

Mathematics: Unit 03

• Straight lines: Slope of a line and angle between two lines. Various forms of equations of a line: Parallel to axes, point-slope form, slope-intercept form, two-point form, intercepts form and normal form. General equation of a line
• Straight lines: Distance of a point from a line
• Conic sections: Sections of a cone-circle, ellipse, parabola, hyperbola, a point, a straight line, and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse, and hyperbola
• Conic sections: Standard equation of a circle
• Introduction to three-dimensional geometry: Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula

Mathematics: Unit 04

• Limits and derivatives: Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference
• Limits and derivatives: Product and quotient of functions. Derivatives of polynomial and trigonometric functions
• Continuity and differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function
• Continuity and differentiability: Concept of exponential and logarithmic functions, and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives
• Continuity and differentiability: Rolle’s and Lagrange’s mean value theorems (without proof) and their geometric interpretations
• Applications of derivatives: Applications of derivatives-rate of change, increasing/ decreasing functions, tangents, and normals, approximation
• Applications of derivatives: Maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems
• Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions, and by parts; only simple integrals of the type to be evaluated. Definite integrals as a limit of a sum
• Integrals: Only simple integrals of the type-∫ dx/ x ± a, ∫ dx/ √ x ± a, ∫ dx/ √ a - x, ∫ dx/ ax + bx + c, ∫ dx/ √ ax + bx + c, ∫ (px + q)/ √ax + bx + c dx, ∫ √ a ± x dx and ∫ √ x - a dx to be evaluated
• Integrals: Definite integrals as a limit of a sum, fundamental theorem of calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals
• Applications of the integrals: Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ ellipses (in standard form only), area between the two above said 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
• Differential equations: Homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type: dy/ dx+py = q, where p and q are functions of x

Mathematics: Unit 05

• 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
• Vectors: 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: Direction cosines/ ratios of a line joining two points. Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane
• Three-dimensional geometry: Angle between-(i) two lines, (ii) two planes. (iii) a line and a plane. Distance of a point from a plane

Mathematics: Unit 06

• Linear programming: Introduction, definition of related terminology such as constraints, objective function, optimization, different types of linear programming (LP) problems, mathematical formulation of LP problems
• Linear programming: Graphical method of solution for problems in two variables, feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints)

Mathematics: Unit 07

• Mathematical reasoning: Mathematically acceptable statements. Connecting words/ phrases-consolidating the understanding of 'if and only if (necessary and sufficient) condition', 'implies', 'and/ or', 'implied by', 'and', 'or'
• Mathematical reasoning: 'there exists' and their use through variety of examples related to real life and mathematics. Validating the statements involving the connecting words, difference between contradiction, converse, and contra positive

Mathematics: Unit 08

• Statistics: Measures of central tendency, mean, median, and mode from ungrouped/ grouped data. Measures of dispersion, mean deviation, variance, and standard deviation from ungrouped/ grouped data. Correlation, regression lines
• Probability: Random experiments: outcomes, sample spaces (set representation). Events: Occurrence of events, 'not', 'and' and 'or' events, exhaustive events, mutually exclusive events axiomatic (set theoretic) probability, probability of an event
• Probability: Probability of 'not', 'and' and 'or' events. Multiplication theorem on probability. Conditional probability, independent events, total probability, Bayes’s theorem, random variable and its probability distribution
• Probability: Mean and variance of stochastic variable. Repeated independent (Bernoulli) trials and binomial distribution

Mathematics: Unit 09

• Introduction, basic concepts, and basic laws of mechanics, force, resultant of forces acting at a point, parallelogram law of forces, resolved parts of a force, equilibrium of a particle under three concurrent forces
• Triangle law of forces and its converse, Lami’s theorem and its converse, two parallel forces, like and unlike parallel forces, couple, and its moment

Mathematics: Unit 10

• Speed and velocity, average speed, instantaneous speed, acceleration and retardation, resultant of two velocities
• Motion of a particle along a line, moving with constant acceleration
• Motion under gravity
• Laws of motion, projectile motion

Agriculture: Unit 01

• Agrometerology: Elements of weather-rainfall, temperature, humidity, wind velocity, sunshine weather forecasting, climate change in relation to crop production
• Genetics and plant breeding: (a) Cell and its structure, cell division-mitosis, and meiosis and their significance, (b) organisation of the genetic materials in chromosomes, DNA and RNA, (c) Mendel’s laws of inheritance
• Genetics and plant breeding: (c) Reasons for the success of Mendel in his experiments, absence of linkage in Mendel’s experiments. (d) quantitative inheritance, continuous and discontinuous variation in plants, (e) monogenic and polygenic inheritance
• Genetics and plant breeding: (f) Role of genetics in plant breeding, self and cross-pollinated crops, methods of breeding in field crops-introduction, selection, hybridization, mutation, and polyploidy, tissue and cell culture
• Genetics and plant breeding: (g) Plant biotechnology-definition and scope in crop production
• Biochemistry: PH and buffers, classification, and nomenclature of carbohydrates; proteins; lipids; vitamins and enzymes
• Microbiology: Microbial cell structure, microorganisms-algae, bacteria, fungi, actinomycetes, protozoa and viruses. Role of microorganisms in respiration, fermentation and organic matter decomposition

Agriculture: Unit 02

• Scope and importance: (a) Importance of livestock in agriculture and industry, white revolution in India, (b) important breeds Indian and exotic, distribution of cows, buffaloes, and poultry in India
• Care and management: (a) Systems of cattle and poultry housing, (b) principles of feeding, feeding practices, (c) balanced ration-definition and ingredients, (d) management of calves, bullocks
• Care and management: (g) Pregnant and milch animals as well as chicks crockrels, and layers, poultry, (e) signs of sick animals, symptoms of common diseases in cattle and poultry, rinderpest, black quarter, foot and mouth
• Care and management: (e) Mastitis and haemorrhagic septicaemia coccidiosis, fowl pox, and ranikhet disease, their prevention, and control
• Artificial insemination: Reproductive organs, collection, dilution, and preservation of semen, and artificial insemination, role of artificial insemination in cattle improvement. Livestock products: Processing and marketing of milk, and milk products

Agriculture: Unit 03

• Introduction: (a) Targets and achievements in foodgrain production in India since independence and its future projections, sustainable crop production, commercialization of agriculture, and its scope in India
• Introduction: (b) Classification of field crops based on their utility-cereals, pulses, oils seeds, fibre, sugar, and forage crops
• Soil, soil fertility, fertilizers, and manures: (a) Soil, soil pH, soil texture, soil structure, soil organisms, soil tilth, soil fertility and soil health, (b) essential plant nutrients, their functions, and deficiency symptoms
• Soil, soil fertility, fertilizers, and manures: (c) Soil types of India and their characteristics, (d) organic manure, common fertilizers including straight, complex, fertilizer mixtures, and biofertilizers; integrated nutrient management system
• Irrigation and drainage: (a) Sources of irrigation (rain, canals, tanks, rivers, wells, tube wells), (b) scheduling of irrigation based on critical stages of growth, time interval, soil moisture content, and weather parameters
• Irrigation and drainage: (c) Water requirement of crops, (d) methods of irrigation and drainage, (e) watershed management
• Weed control: Principles of weed control, methods of weed control (cultural, mechanical, chemical, biological, and integrated weed management)
• Crops: Seed bed preparation, seed treatment, time and method of sowing/ planting, seed rate; dose, method and time of fertilizer application, irrigation, interculture, and weed control; common pests and diseases, caused by bacteria
• Crops: Fungi virus and nematode, and their control, integrated pest management, harvesting, threshing, post harvest technology: Storage, processing and marketing of major field crops-rice, wheat, maize, sorghum, pearl millet, groundnut, mustard
• Crops: pigeon-pea, gram, sugarcane, cotton, and berseem

Agriculture: Unit 04

• Importance of fruits and vegetables in human diet, crop diversification, and processing industry
• Orchard location and layout, ornamental gardening and kitchen garden
• Planting system, training, pruning, intercropping, protection from frost and sunburn
• Trees, shrubs, climbers, annuals, perennials-definition and examples
• Propagation by seed, cutting, budding, layering, and grafting
• Cultivation practices, processing and marketing of: (i) Fruits-mango, papaya, banana, guava, citrus, grapes, (ii) vegetables-radish, carrot, potato, onion, cauliflower, brinjal, tomato, spinach, and cabbage
• Cultivation practices, processing and marketing of: (iii) Flowers-gladiolus, canna, chrysanthemums, roses, and marigold
• Principles and methods of fruit and vegetable preservation
• Preparation of jellies, jams, ketchup, chips, and their packing

Plant sciences: Unit 01

Plant sciences: Unit 02

Plant sciences: Unit 03

Plant sciences: Unit 04

Plant sciences: Unit 05

Physical science: Unit 01

Physical science: Unit 02

Physical science: Unit 03

Physical science: Unit 04

Physical science: Unit 05

Entomology and nematology: Unit 01

Entomology and nematology: Unit 02

Entomology and nematology: Unit 03

Entomology and nematology: Unit 04

Entomology and nematology: Unit 05

Agronomy: Unit 01

Agronomy: Unit 02

Social science: Unit 01

Social science: Unit 02

Social science: Unit 03

Social science: Unit 04

Statistical science: Unit 01

Statistical science: Unit 02

Statistical science: Unit 03

Horticulture: Unit 01

Horticulture: Unit 02

Horticulture: Unit 03

Horticulture: Unit 04

Horticulture: Unit 05

Horticulture: Unit 06

Forestry/ agroforestry and silviculture: Unit 01

Forestry/ agroforestry and silviculture: Unit 02

Forestry/ agroforestry and silviculture: Unit 03

Forestry/ agroforestry and silviculture: Unit 04

Forestry/ agroforestry and silviculture: Unit 05

Forestry/ agroforestry and silviculture: Unit 06

Forestry/ agroforestry and silviculture: Unit 07

Forestry/ agroforestry and silviculture: Unit 08

Agricultural engineering and technology: Unit 01

Agricultural engineering and technology: Unit 02

Agricultural engineering and technology: Unit 03

Agricultural engineering and technology: Unit 04

Agricultural engineering and technology: Unit 05

Water science and technology: Unit 01

Community science (formerly home science): Unit 01

Community science (formerly home science): Unit 02

Community science (formerly home science): Unit 03

Community science (formerly home science): Unit 04

Community science (formerly home science): Unit 05

Animal biotechnology: Unit 01

Animal biotechnology: Unit 02

Veterinary medicine: Unit 01

Veterinary medicine: Unit 02

Veterinary medicine: Unit 03

Veterinary medicine: Unit 04

Veterinary medicine: Unit 05

Veterinary medicine: Unit 06

Veterinary medicine: Unit 07

Veterinary medicine: Unit 08

Veterinary medicine: Unit 09

Veterinary medicine: Unit 10

Veterinary medicine: Unit 11

Veterinary medicine: Unit 12

Animal science: Unit 01

Animal science: Unit 02

Animal science: Unit 03

Animal science: Unit 04

Animal science: Unit 05

Animal science: Unit 06

Animal science: Unit 07

Animal science: Unit 08

Animal science: Unit 09

Animal science: Unit 10

Fisheries science: Unit 01

Fisheries science: Unit 02

Fisheries science: Unit 03

Fisheries science: Unit 04

Fisheries science: Unit 05

Fisheries science: Unit 06

Fisheries science: Unit 07

Fisheries science: Unit 08

Fisheries science: Unit 09

Fisheries science: Unit 10

Fisheries science: Unit 11

Fisheries science: Unit 12

Dairy science: Unit 01

Dairy science: Unit 02

Dairy technology: Unit 01

Dairy technology: Unit 02

Food science technology: Unit 01

Food science technology: Unit 02

Agri-business management: Unit 01

Agri-business management: Unit 02