JEE Advanced Exam 2025 - Date, Application Form, Syllabus, Pattern, Eligibility, Preparation Tips, Question Paper

Chemistry: Unit 01

• Concept of atoms and molecules; Dalton’s atomic theory; mole concept; chemical formulae; balanced chemical equations; calculations (based on mole concept and stoichiometry) involving common oxidation-reduction, neutralisation, and displacement reactions
• Concentration in terms of mole fraction, molarity, molality, and normality
• Concept of atoms and molecules; Dalton’s atomic theory; mole concept; chemical formulae; balanced chemical equations; calculations (based on mole concept and stoichiometry) involving common oxidation-reduction, neutralisation, and displacement reactions
• Concentration in terms of mole fraction, molarity, molality, and normality

Chemistry: Unit 02

• Gas laws and ideal gas equation, absolute scale of temperature; deviation from ideality, Van der Waals equation; kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; law of partial pressures
• Diffusion of gases
• Intermolecular interactions: Types, distance dependence, and their effect on properties; liquids: Vapour pressure, surface tension, viscosity
• Gas laws and ideal gas equation, absolute scale of temperature; deviation from ideality, Van der Waals equation; kinetic theory of gases, average, root mean square and most probable velocities and their relation with temperature; law of partial pressures
• Diffusion of gases
• Intermolecular interactions: Types, distance dependence, and their effect on properties; liquids: Vapour pressure, surface tension, viscosity

Chemistry: Unit 03

• Bohr model, spectrum of hydrogen atom; wave-particle duality, De Broglie hypothesis; uncertainty principle; qualitative quantum mechanical picture of hydrogen atom: Energies, quantum numbers, wave function and probability density (plots only)
• Qualitative quantum mechanical picture of hydrogen atom: Shapes of s, p and d orbitals; Aufbau principle; Pauli’s exclusion principle and Hund’s rule
• Bohr model, spectrum of hydrogen atom; wave-particle duality, De Broglie hypothesis; uncertainty principle; qualitative quantum mechanical picture of hydrogen atom: Energies, quantum numbers, wave function and probability density (plots only)
• Qualitative quantum mechanical picture of hydrogen atom: Shapes of s, p and d orbitals; Aufbau principle; Pauli’s exclusion principle and Hund’s rule

Chemistry: Unit 04

• Orbital overlap and covalent bond; hybridisation involving s, p, and d orbitals only; molecular orbital energy diagrams for homonuclear diatomic species (up to Ne2); hydrogen bond; polarity in molecules, dipole moment
• VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral, and octahedral)
• Orbital overlap and covalent bond; hybridisation involving s, p, and d orbitals only; molecular orbital energy diagrams for homonuclear diatomic species (up to Ne2); hydrogen bond; polarity in molecules, dipole moment
• VSEPR model and shapes of molecules (linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral, and octahedral)

Chemistry: Unit 05

• Intensive and extensive properties, state functions, first law of thermodynamics; internal energy, work (pressure-volume only) and heat; enthalpy, heat capacity, standard state, Hess’s law
• Enthalpy of reaction, fusion and vapourization, and lattice enthalpy; second law of thermodynamics; entropy; Gibbs energy; criteria of equilibrium and spontaneity
• Intensive and extensive properties, state functions, first law of thermodynamics; internal energy, work (pressure-volume only) and heat; enthalpy, heat capacity, standard state, Hess’s law
• Enthalpy of reaction, fusion and vapourization, and lattice enthalpy; second law of thermodynamics; entropy; Gibbs energy; criteria of equilibrium and spontaneity

Chemistry: Unit 06

• Law of mass action; significance of ∆G and ∆Gᶱ chemical equilibrium; equilibrium constant (Kp and Kc) and reaction quotient, Le Chatelier’s principle (effect of concentration, temperature and pressure); solubility product and its applications
• Common ion effect, pH and buffer solutions; acids and bases (Bronsted and Lewis concepts); hydrolysis of salts
• Law of mass action; significance of ∆G and ∆Gᶱ chemical equilibrium; equilibrium constant (Kp and Kc) and reaction quotient, Le Chatelier’s principle (effect of concentration, temperature and pressure); solubility product and its applications
• Common ion effect, pH and buffer solutions; acids and bases (Bronsted and Lewis concepts); hydrolysis of salts

Chemistry: Unit 07

• Electrochemical cells and cell reactions; standard electrode potentials; electrochemical work, Nernst equation; electrochemical series, EMF of galvanic cells; Faraday’s laws of electrolysis; electrolytic conductance, specific
• Equivalent and molar conductivity, Kohlrausch’s law; batteries: Primary and secondary, fuel cells; corrosion
• Electrochemical cells and cell reactions; standard electrode potentials; electrochemical work, Nernst equation; electrochemical series, EMF of galvanic cells; Faraday’s laws of electrolysis; electrolytic conductance, specific
• Equivalent and molar conductivity, Kohlrausch’s law; batteries: Primary and secondary, fuel cells; corrosion

Chemistry: Unit 08

• Rates of chemical reactions; order and molecularity of reactions; rate law, rate constant, half-life; differential and integrated rate expressions for zero and first order reactions
• Temperature dependence of rate constant (Arrhenius equation and activation energy); catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism
• Rates of chemical reactions; order and molecularity of reactions; rate law, rate constant, half-life; differential and integrated rate expressions for zero and first order reactions
• Temperature dependence of rate constant (Arrhenius equation and activation energy); catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism

Chemistry: Unit 09

• Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ), close packed structure of solids (cubic and hexagonal), packing in fcc, bcc, and hcp lattices
• Nearest neighbours, ionic radii and radius ratio, point defects
• Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ), close packed structure of solids (cubic and hexagonal), packing in fcc, bcc, and hcp lattices
• Nearest neighbours, ionic radii and radius ratio, point defects

Chemistry: Unit 10

• Henry’s law; Raoult’s law; ideal solutions; colligative properties: Lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure; Van’t Hoff factor
• Henry’s law; Raoult’s law; ideal solutions; colligative properties: Lowering of vapour pressure, elevation of boiling point, depression of freezing point, and osmotic pressure; Van’t Hoff factor

Chemistry: Unit 11

• Elementary concepts of adsorption: Physisorption and chemisorption, Freundlich adsorption isotherm; colloids: Types, methods of preparation and general properties; elementary ideas of emulsions, surfactants and micelles (only definitions and examples)
• Elementary concepts of adsorption: Physisorption and chemisorption, Freundlich adsorption isotherm; colloids: Types, methods of preparation and general properties; elementary ideas of emulsions, surfactants and micelles (only definitions and examples)

Chemistry: Unit 12

• Modern periodic law and the present form of periodic table; electronic configuration of elements; periodic trends in atomic radius, ionic radius, ionization enthalpy, electron gain enthalpy, valence, oxidation states
• Periodic trends in electronegativity, and chemical reactivity
• Modern periodic law and the present form of periodic table; electronic configuration of elements; periodic trends in atomic radius, ionic radius, ionization enthalpy, electron gain enthalpy, valence, oxidation states
• Periodic trends in electronegativity, and chemical reactivity

Chemistry: Unit 13

• 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, reactions, use and structure; hydrogen as a fuel
• 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, reactions, use and structure; hydrogen as a fuel

Chemistry: Unit 14

• Alkali and alkaline earth metals-reactivity towards air, water, dihydrogen, halogens, acids; their reducing nature including solutions in liquid ammonia; uses of these elements
• General characteristics of their oxides, hydroxides, halides, salts of oxoacids; anomalous behaviour of lithium and beryllium
• Preparation, properties, and uses of compounds of sodium (sodium carbonate, sodium chloride, sodium hydroxide, sodium hydrogen carbonate) and calcium (calcium oxide, calcium hydroxide, calcium carbonate, calcium sulphate)
• Alkali and alkaline earth metals-reactivity towards air, water, dihydrogen, halogens, acids; their reducing nature including solutions in liquid ammonia; uses of these elements
• General characteristics of their oxides, hydroxides, halides, salts of oxoacids; anomalous behaviour of lithium and beryllium
• Preparation, properties, and uses of compounds of sodium (sodium carbonate, sodium chloride, sodium hydroxide, sodium hydrogen carbonate) and calcium (calcium oxide, calcium hydroxide, calcium carbonate, calcium sulphate)

Chemistry: Unit 15

• Oxidation state and trends in chemical reactivity of elements of groups 13-17; anomalous properties of boron, carbon, nitrogen, oxygen, and fluorine with respect to other elements in their respective groups
• Group 13: Reactivity towards acids, alkalis, and halogens; preparation, properties, and uses of borax, orthoboric acid, diborane, boron trifluoride, aluminium chloride, and alums; uses of boron and aluminium
• Group 14: Reactivity towards water and halogen; allotropes of carbon and uses of carbon; preparation, properties, and uses of carbon monoxide, carbon dioxide, silicon dioxide, silicones, silicates, zeolites
• Group 15: Reactivity towards hydrogen, oxygen, and halogen; allotropes of phosphorus; preparation, properties, and uses of dinitrogen, ammonia, nitric acid, phosphine, phosphorus trichloride, phosphorus pentachloride
• Group 15: Oxides of nitrogen and oxoacids of phosphorus
• Group 16: Reactivity towards hydrogen, oxygen, and halogen; simple oxides; allotropes of sulfur; preparation/ manufacture, properties, and uses of dioxygen, ozone, sulfur dioxide, sulfuric acid; oxoacids of sulfur
• Group 17: Reactivity towards hydrogen, oxygen, and metals; preparation/ manufacture, properties, and uses of chlorine, hydrogen chloride and interhalogen compounds; oxoacids of halogens, bleaching powder
• Group 18: Chemical properties and uses; compounds of xenon with fluorine and oxygen
• Oxidation state and trends in chemical reactivity of elements of groups 13-17; anomalous properties of boron, carbon, nitrogen, oxygen, and fluorine with respect to other elements in their respective groups
• Group 13: Reactivity towards acids, alkalis, and halogens; preparation, properties, and uses of borax, orthoboric acid, diborane, boron trifluoride, aluminium chloride, and alums; uses of boron and aluminium
• Group 14: Reactivity towards water and halogen; allotropes of carbon and uses of carbon; preparation, properties, and uses of carbon monoxide, carbon dioxide, silicon dioxide, silicones, silicates, zeolites
• Group 15: Reactivity towards hydrogen, oxygen, and halogen; allotropes of phosphorus; preparation, properties, and uses of dinitrogen, ammonia, nitric acid, phosphine, phosphorus trichloride, phosphorus pentachloride
• Group 15: Oxides of nitrogen and oxoacids of phosphorus
• Group 16: Reactivity towards hydrogen, oxygen, and halogen; simple oxides; allotropes of sulfur; preparation/ manufacture, properties, and uses of dioxygen, ozone, sulfur dioxide, sulfuric acid; oxoacids of sulfur
• Group 17: Reactivity towards hydrogen, oxygen, and metals; preparation/ manufacture, properties, and uses of chlorine, hydrogen chloride and interhalogen compounds; oxoacids of halogens, bleaching powder
• Group 18: Chemical properties and uses; compounds of xenon with fluorine and oxygen

Chemistry: Unit 16

• Oxidation states and their stability; standard electrode potentials; interstitial compounds; alloys; catalytic properties; applications; preparation, structure, and reactions of oxoanions of chromium and manganese
• Oxidation states and their stability; standard electrode potentials; interstitial compounds; alloys; catalytic properties; applications; preparation, structure, and reactions of oxoanions of chromium and manganese

Chemistry: Unit 17

• Lanthanoid and actinoid contractions; oxidation states; general characteristics
• Lanthanoid and actinoid contractions; oxidation states; general characteristics

Chemistry: Unit 18

• Werner’s theory; nomenclature, cis-trans and ionization isomerism, hybridization and geometries (linear, tetrahedral, square planar, and octahedral) of mononuclear coordination compounds; bonding [VBT and CFT (octahedral and tetrahedral fields)]
• Magnetic properties (spin-only) and colour of 3D-series coordination compounds; ligands and spectrochemical series; stability; importance and applications; metal carbonyls
• Werner’s theory; nomenclature, cis-trans and ionization isomerism, hybridization and geometries (linear, tetrahedral, square planar, and octahedral) of mononuclear coordination compounds; bonding [VBT and CFT (octahedral and tetrahedral fields)]
• Magnetic properties (spin-only) and colour of 3D-series coordination compounds; ligands and spectrochemical series; stability; importance and applications; metal carbonyls

Chemistry: Unit 19

• Metal ores and their concentration; extraction of crude metal from concentrated ores: Thermodynamic (iron, copper, zinc) and electrochemical (aluminium) principles of metallurgy; cyanide process (silver and gold); refining
• Metal ores and their concentration; extraction of crude metal from concentrated ores: Thermodynamic (iron, copper, zinc) and electrochemical (aluminium) principles of metallurgy; cyanide process (silver and gold); refining

Chemistry: Unit 20

• Groups I to V (only Ag²⁺ , Hg²⁺, Cu²⁺+, Pb²⁺, Fe³⁺, Cr³⁺, Al³⁺, Ca²⁺, Ba²⁺, Zn²⁺, Mn²⁺ and Mg²⁺); nitrate, halides (excluding fluoride), carbonate and bicarbonate, sulphate, and sulphide
• Groups I to V (only Ag²⁺ , Hg²⁺, Cu²⁺+, Pb²⁺, Fe³⁺, Cr³⁺, Al³⁺, Ca²⁺, Ba²⁺, Zn²⁺, Mn²⁺ and Mg²⁺); nitrate, halides (excluding fluoride), carbonate and bicarbonate, sulphate, and sulphide

Chemistry: Unit 21

• Atmospheric pollution; water pollution; soil pollution; industrial waste; strategies to control environmental pollution; green chemistry
• Atmospheric pollution; water pollution; soil pollution; industrial waste; strategies to control environmental pollution; green chemistry

Chemistry: Unit 22

• Hybridisation of carbon; σ and π-bonds; shapes of simple organic molecules; aromaticity; structural and geometrical isomerism
• Stereoisomers and stereochemical relationship (enantiomers, diastereomers, meso) of compounds containing only up to two asymmetric centres (R, S and E,Z configurations excluded)
• Determination of empirical and molecular formulae of simple compounds by combustion method only; IUPAC nomenclature of organic molecules (hydrocarbons, including simple cyclic hydrocarbons and their mono-functional and bi-functional derivatives only)
• Hydrogen bonding effects; inductive, resonance, and hyperconjugative effects; acidity and basicity of organic compounds; reactive intermediates produced during homolytic and heterolytic bond cleavage
• Formation, structure and stability of carbocations, carbanions, and free radicals
• Hybridisation of carbon; σ and π-bonds; shapes of simple organic molecules; aromaticity; structural and geometrical isomerism
• Stereoisomers and stereochemical relationship (enantiomers, diastereomers, meso) of compounds containing only up to two asymmetric centres (R, S and E,Z configurations excluded)
• Determination of empirical and molecular formulae of simple compounds by combustion method only; IUPAC nomenclature of organic molecules (hydrocarbons, including simple cyclic hydrocarbons and their mono-functional and bi-functional derivatives only)
• Hydrogen bonding effects; inductive, resonance, and hyperconjugative effects; acidity and basicity of organic compounds; reactive intermediates produced during homolytic and heterolytic bond cleavage
• Formation, structure and stability of carbocations, carbanions, and free radicals

Chemistry: Unit 23

• Homologous series; physical properties (melting points, boiling points, and density) and effect of branching on them; conformations of ethane and butane (Newman projections only); preparation from alkyl halides and aliphatic carboxylic acids
• Reactions: Combustion, halogenation, (including allylic and benzylic halogenation) and oxidation
• Homologous series; physical properties (melting points, boiling points, and density) and effect of branching on them; conformations of ethane and butane (Newman projections only); preparation from alkyl halides and aliphatic carboxylic acids
• Reactions: Combustion, halogenation, (including allylic and benzylic halogenation) and oxidation

Chemistry: Unit 24

• Physical properties (boiling points, density, and dipole moments); preparation by elimination reactions; acid catalysed hydration (excluding the stereochemistry of addition and elimination); metal acetylides; reactions of alkenes with KMnO4 and ozone
• Reduction of alkenes and alkynes; electrophilic addition reactions of alkenes with X2, HX, HOX, (X=halogen); effect of peroxide on addition reactions; cyclic polymerization reaction of alkynes
• Physical properties (boiling points, density, and dipole moments); preparation by elimination reactions; acid catalysed hydration (excluding the stereochemistry of addition and elimination); metal acetylides; reactions of alkenes with KMnO4 and ozone
• Reduction of alkenes and alkynes; electrophilic addition reactions of alkenes with X2, HX, HOX, (X=halogen); effect of peroxide on addition reactions; cyclic polymerization reaction of alkynes

Chemistry: Unit 25

• Structure; electrophilic substitution reactions: Halogenation, nitration, sulphonation, Friedel crafts alkylation and acylation; effect of directing groups (monosubstituted benzene) in these reactions
• Structure; electrophilic substitution reactions: Halogenation, nitration, sulphonation, Friedel crafts alkylation and acylation; effect of directing groups (monosubstituted benzene) in these reactions

Chemistry: Unit 26

• Physical properties; preparation, electrophilic substitution reactions of phenol (halogenation, nitration, sulphonation); Reimer-Tiemann reaction, Kolbe reaction; esterification; etherification; aspirin synthesis
• Oxidation and reduction reactions of phenol
• Physical properties; preparation, electrophilic substitution reactions of phenol (halogenation, nitration, sulphonation); Reimer-Tiemann reaction, Kolbe reaction; esterification; etherification; aspirin synthesis
• Oxidation and reduction reactions of phenol

Chemistry: Unit 27

• Rearrangement reactions of alkyl carbocation; Grignard reactions; nucleophilic substitution reactions and their stereochemical aspects
• Rearrangement reactions of alkyl carbocation; Grignard reactions; nucleophilic substitution reactions and their stereochemical aspects

Chemistry: Unit 28

• Physical properties; reactions: Esterification, dehydration (formation of alkenes and ethers); reactions with: Sodium, phosphorus halides, ZnCl2/ concentrated HCl, thionyl chloride; conversion of alcohols into aldehydes, ketones, and carboxylic acids
• Physical properties; reactions: Esterification, dehydration (formation of alkenes and ethers); reactions with: Sodium, phosphorus halides, ZnCl2/ concentrated HCl, thionyl chloride; conversion of alcohols into aldehydes, ketones, and carboxylic acids

Chemistry: Unit 29

• Preparation by Williamson’s synthesis; C-O bond cleavage reactions
• Preparation by Williamson’s synthesis; C-O bond cleavage reactions

Chemistry: Unit 30

• Preparation of: Aldehydes and ketones from acid chlorides and nitriles; aldehydes from esters; benzaldehyde from toluene and benzene; reactions: Oxidation, reduction, oxime, and hydrazone formation; aldol condensation, Cannizzaro reaction
• Haloform reaction; nucleophilic addition reaction with RMgX, NaHSO3, HCN, alcohol, amine
• Preparation of: Aldehydes and ketones from acid chlorides and nitriles; aldehydes from esters; benzaldehyde from toluene and benzene; reactions: Oxidation, reduction, oxime, and hydrazone formation; aldol condensation, Cannizzaro reaction
• Haloform reaction; nucleophilic addition reaction with RMgX, NaHSO3, HCN, alcohol, amine

Chemistry: Unit 31

• Physical properties; preparation: From nitriles, Grignard reagents, hydrolysis of esters and amides; preparation of benzoic acid from alkylbenzenes; reactions: Reduction, halogenation, formation of esters, acid chlorides, and amides
• Physical properties; preparation: From nitriles, Grignard reagents, hydrolysis of esters and amides; preparation of benzoic acid from alkylbenzenes; reactions: Reduction, halogenation, formation of esters, acid chlorides, and amides

Chemistry: Unit 32

• Preparation from nitro compounds, nitriles and amides; reactions: Hoffmann bromamide degradation, Gabriel phthalimide synthesis; reaction with nitrous acid, Azo coupling reaction of diazonium salts of aromatic amines
• Sandmeyer and related reactions of diazonium salts; Carbylamine reaction, Hinsberg test, Alkylation and acylation reactions
• Preparation from nitro compounds, nitriles and amides; reactions: Hoffmann bromamide degradation, Gabriel phthalimide synthesis; reaction with nitrous acid, Azo coupling reaction of diazonium salts of aromatic amines
• Sandmeyer and related reactions of diazonium salts; Carbylamine reaction, Hinsberg test, Alkylation and acylation reactions

Chemistry: Unit 33

• Reactions: Fittig, Wurtz-Fittig; nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding benzyne mechanism and cine substitution)
• Reactions: Fittig, Wurtz-Fittig; nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding benzyne mechanism and cine substitution)

Chemistry: Unit 34

• Carbohydrates: Classification; mono- and disaccharides (glucose and sucrose); oxidation; reduction; glycoside formation and hydrolysis of disaccharides (sucrose, maltose, lactose); anomers
• Proteins: Amino acids; peptide linkage; structure of peptides (primary and secondary); types of proteins (fibrous and globular)
• Nucleic acids: Chemical composition and structure of DNA and RNA
• Carbohydrates: Classification; mono- and disaccharides (glucose and sucrose); oxidation; reduction; glycoside formation and hydrolysis of disaccharides (sucrose, maltose, lactose); anomers
• Proteins: Amino acids; peptide linkage; structure of peptides (primary and secondary); types of proteins (fibrous and globular)
• Nucleic acids: Chemical composition and structure of DNA and RNA

Chemistry: Unit 35

• Types of polymerization (addition, condensation); homo and copolymers; natural rubber; cellulose; nylon; teflon; bakelite; PVC; biodegradable polymers; applications of polymers
• Types of polymerization (addition, condensation); homo and copolymers; natural rubber; cellulose; nylon; teflon; bakelite; PVC; biodegradable polymers; applications of polymers

Chemistry: Unit 36

• Drug-target interaction; therapeutic action, and examples (excluding structures), of antacids, antihistamines, tranquilizers, analgesics, antimicrobials, and antifertility drugs; artificial sweeteners (names only); soaps, detergents, and cleansing action
• Drug-target interaction; therapeutic action, and examples (excluding structures), of antacids, antihistamines, tranquilizers, analgesics, antimicrobials, and antifertility drugs; artificial sweeteners (names only); soaps, detergents, and cleansing action

Chemistry: Unit 37

• Detection of elements (N, S, halogens); detection and identification of the following functional groups: Hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino, and nitro
• Detection of elements (N, S, halogens); detection and identification of the following functional groups: Hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl, amino, and nitro

Mathematics: Unit 01

• Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection
• De-Morgan’s laws on difference (for finite number of sets) and practical problems based on them
• Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation
• Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions
• Function as a special case of special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc), sum, difference, product and composition of functions
• Sets and their representations, different kinds of sets (empty, finite and infinite), algebra of sets, intersection, complement, difference and symmetric difference of sets and their algebraic properties, De-Morgan’s laws on union, intersection
• De-Morgan’s laws on difference (for finite number of sets) and practical problems based on them
• Cartesian product of finite sets, ordered pair, relations, domain and codomain of relations, equivalence relation
• Function as a special case of relation, functions as mappings, domain, codomain, range of functions, invertible functions, even and odd functions, into, onto and one-to-one functions
• Function as a special case of special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc), sum, difference, product and composition of functions

Mathematics: Unit 02

• Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations
• Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots
• Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers
• Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients
• Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations
• Statement of fundamental theorem of algebra, quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots
• Arithmetic and geometric progressions, arithmetic and geometric means, sums of finite arithmetic and geometric progressions, infinite geometric series, sum of the first n natural numbers, sums of squares and cubes of the first n natural numbers
• Logarithms and their properties, permutations and combinations, binomial theorem for a positive integral index, properties of binomial coefficients

Mathematics: Unit 03

• Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three
• Adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables
• Matrices as a rectangular array of real numbers, equality of matrices, addition, multiplication by a scalar and product of matrices, transpose of a matrix, elementary row and column transformations, determinant of a square matrix of order up to three
• Adjoint of a matrix, inverse of a square matrix of order up to three, properties of these matrix operations, diagonal, symmetric and skew-symmetric matrices and their properties, solutions of simultaneous linear equations in two or three variables

Mathematics: Unit 04

• Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes theorem
• Computation of probability of events using permutations and combinations
• Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation and variance of grouped and ungrouped data, analysis of the frequency distribution with same mean but different variance, random variable
• Mean and variance of the random variable
• Random experiment, sample space, different types of events (impossible, simple, compound), addition and multiplication rules of probability, conditional probability, independence of events, total probability, Bayes theorem
• Computation of probability of events using permutations and combinations
• Measure of central tendency and dispersion, mean, median, mode, mean deviation, standard deviation and variance of grouped and ungrouped data, analysis of the frequency distribution with same mean but different variance, random variable
• Mean and variance of the random variable

Mathematics: Unit 05

• Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations
• Inverse trigonometric functions (principal value only) and their elementary properties
• Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations
• Inverse trigonometric functions (principal value only) and their elementary properties

Mathematics: Unit 06

• Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin. Equation of a straight line in various forms, angle between two lines, distance of a point from a line
• Two dimensions: Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; centroid, orthocentre, incentre and circumcentre of a triangle
• Two dimensions: Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle
• Two dimensions: Equation of a circle through the points of intersection of two circles and those of a circle and a straight line
• Two dimensions: Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus problems
• Three dimensions: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines
• Three dimensions: Angle between two planes, angle between a line and the plane, coplanar lines
• Two dimensions: Cartesian coordinates, distance between two points, section formulae, shift of origin. Equation of a straight line in various forms, angle between two lines, distance of a point from a line
• Two dimensions: Lines through the point of intersection of two given lines, equation of the bisector of the angle between two lines, concurrency of lines; centroid, orthocentre, incentre and circumcentre of a triangle
• Two dimensions: Equation of a circle in various forms, equations of tangent, normal and chord. Parametric equations of a circle, intersection of a circle with a straight line or a circle
• Two dimensions: Equation of a circle through the points of intersection of two circles and those of a circle and a straight line
• Two dimensions: Equations of a parabola, ellipse and hyperbola in standard form, their foci, directrices and eccentricity, parametric equations, equations of tangent and normal. Locus problems
• Three dimensions: Distance between two points, direction cosines and direction ratios, equation of a straight line in space, skew lines, shortest distance between two lines, equation of a plane, distance of a point from a plane, angle between two lines
• Three dimensions: Angle between two planes, angle between a line and the plane, coplanar lines

Mathematics: Unit 07

• Limit of a function at a real number, continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions
• Continuity of composite functions, intermediate value property of continuous functions
• Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions
• Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems
• Derivatives up to order two of implicit functions, geometric interpretation of derivatives
• Limit of a function at a real number, continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L’Hospital rule of evaluation of limits of functions
• Continuity of composite functions, intermediate value property of continuous functions
• Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions
• Tangents and normals, increasing and decreasing functions, derivatives of order two, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem, geometric interpretation of the two theorems
• Derivatives up to order two of implicit functions, geometric interpretation of derivatives

Mathematics: Unit 08

• Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integral and their properties, fundamental theorem of integral calculus
• Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas bounded by simple curves
• Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, linear first order differential equations
• Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals as the limit of sums, definite integral and their properties, fundamental theorem of integral calculus
• Integration by parts, integration by the methods of substitution and partial fractions, application of definite integrals to the determination of areas bounded by simple curves
• Formation of ordinary differential equations, solution of homogeneous differential equations of first order and first degree, separation of variables method, linear first order differential equations

Mathematics: Unit 09

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