JEE ADVANCED Mathematics Syllabus

JEE ADVANCED Mathematics: topic-wise syllabus

1. 1

   Algebra

   ~1 marks

   Sets, Relations, Functions, Equations, Per JEE-ADVANCED Official Notification

   • Sets, Relations, Functions, Venn Diagrams, Inverse, Composition
   • Complex Numbers, Quadratic Equations, Polynomials, Roots, Modulus-Argument Form
   • Sequences and Series — AP, GP, HP, Sum, Mean, Variance, Infinite Series, Binomial
   • Permutation-Combination, Probability, Conditional, Bayes Theorem, Random Variables
   • Matrices and Determinants, System of Equations, Linear Programming, Eigenvalues
   • Logarithms, Partial Fractions, Mathematical Induction, Mathematical Reasoning
   • Boolean Algebra, Logic, Number Theory, Recursion, Mathematical Olympiad
2. 2

   Calculus & Geometry

   ~1 marks

   Differentiation, Integration, Trigonometry, Per JEE-ADVANCED Official Notification

   • Limits, Continuity, Differentiability, Derivatives, Methods
   • Applications of Derivatives — Maxima, Minima, Rate of Change, Tangent, Normal
   • Integration — Definite, Indefinite, Methods, Reduction Formulas, Areas, Volumes
   • Differential Equations — First Order, First Degree, Applications, Higher Order
   • Trigonometric Ratios, Identities, Equations, Inverse Trig, Heights & Distances, Properties
   • Coordinate Geometry — Straight Lines, Circles, Conics, 3D, Vectors
   • Mathematical Reasoning, Statistics, Probability, Linear Algebra, Modern Math
3. 3

   Arithmetic (MBA Quant)

   ~3 marks

   Number System, Percentages, Profit-Loss, SI-CI

   • Number System, HCF-LCM, Indices, Surds, Simplification, Approximation
   • Percentages, Profit-Loss, Discount, SI-CI, Growth Rate, Population Growth
   • Ratio, Proportion, Mixture-Alligation, Partnership, Ages
   • Time-Work, Work-Wages, Pipes & Cisterns, Efficiency
   • Time-Speed-Distance, Trains, Boats, Races, Clocks, Calendar
   • Averages, Mixture Problems, Alligation, Allegation Method
   • Mensuration, Geometry, Coordinate Geometry, Trigonometry
   • Data Interpretation — Tables, Bar, Pie, Line, Caselet, Data Sufficiency
   • Modern Math — Permutation, Combination, Probability, Sets, Functions
   • Commercial Math — Stocks, Shares, Dividends, Brokerage, GST, True Discount
4. 4

   Algebra (MBA Quant)

   ~3 marks

   Equations, Functions, P&C, Probability

   • Linear Equations, Quadratic Equations, Polynomials, Identities
   • Functions, Graphs, Inequalities, Logarithms, Modulus, Domain, Range
   • Sequences and Series, AP, GP, HP, Sum of n terms, Special Series
   • Permutation, Combination, Binomial Theorem, Probability
   • Matrices, Determinants, Linear Programming, System of Equations
   • Set Theory, Relations, Functions, Venn Diagrams, Cardinality
   • Trigonometry — Ratios, Identities, Heights and Distances, Equations
   • Coordinate Geometry — Lines, Circles, Conics, Distance, Slope
   • Calculus — Limits, Derivatives, Integrals, Maxima, Minima, Applications
   • Statistics — Mean, Median, Mode, Variance, Skewness, Correlation, Regression
5. 5

   Data Interpretation

   ~3 marks

   Charts, Tables, Caselets, Data Sufficiency

   • Table DI — Direct, Calculation-Based, Multi-Step
   • Bar Graph DI — Single, Double, Stacked, Comparison
   • Pie Chart DI — Sector Angle, Percentage, Comparison, Multiple Pie
   • Line Graph DI — Trend, Multiple Lines, Comparison, Growth Rate
   • Caselet DI — Story-Based, Multi-Step, Verbal Reasoning with Data
   • Data Sufficiency — Two-Statement, Three-Statement, Multi-Condition
   • Comparison DI — Ratio, Percentage, Difference, Growth Rate
   • Missing Data DI — Find the Missing Value, Estimate, Calculate
   • Quant-Based DI — Averages, Ratios in Data, Business Scenarios, HR Data
   • Radar, Web, Mixed Chart DI, Business Scenarios — Revenue, Cost, Profit, Market Share
6. 6

   English

   ~3 marks

   Verbal Ability, Grammar, Vocabulary, RC

   • Reading Comprehension — Factual, Inferential, Critical, Editorial, Business
   • Cloze Test, Fill in the Blanks, Sentence Completion
   • Spotting Errors, Sentence Correction, Sentence Improvement
   • Para Jumbles, Sentence Rearrangement, Paragraph Completion
   • Vocabulary — Synonyms, Antonyms, One-Word Substitutes, Idioms, Phrasal Verbs
   • Grammar — Tenses, Voice, Narration, Prepositions, Articles, Modals
   • Word Usage, Foreign Words, Root Words, Etymology, Confusables
   • Essay Writing, Letter Writing, Email Writing, Report, Précis
   • Business Reading — Business News, Annual Reports, Strategies, Case Studies
   • Critical Reading — Argument Analysis, Flaw Identification, Strengthen/Weaken
7. 7

   Logical Reasoning

   ~3 marks

   Puzzles, Arrangements, Logic, Decisions

   • Seating Arrangement — Linear, Circular, Square, Rectangular, Hexagonal
   • Floor/Ladder Puzzles, Box Puzzles, Scheduling (Day/Month/Year)
   • Venn Diagrams, Sets, Family Tree, Blood Relations, Direction
   • Number Series, Letter Series, Coding-Decoding, Pattern Recognition
   • Syllogisms, Statement-Conclusion, Assumption, Inference, Course of Action
   • Critical Reasoning, Paradox, Brainteasers, Logic Games
   • Decision Making, Selection, Prioritization, Optimization, Negotiation
   • Data Sufficiency, Input-Output, Scheduling, Ranking
   • Verbal Reasoning — Analogies, Classification, Odd-Man-Out, Series
   • Visual Reasoning, Pattern Completion, Embedded Figures, Mirror, Water
8. 8

   Mechanics (Physics)

   ~4 marks

   Kinematics, Dynamics, Rotational Motion, Gravitation

   • Kinematics — Motion in 1D/2D/3D, Projectile, Circular, Relative Motion
   • Newton's Laws of Motion, Friction, Pseudo Forces, Constraint Motion
   • Work, Energy, Power, Kinetic and Potential Energy, Conservation
   • Circular Motion, Banking of Roads, Conical Pendulum, Vertical Circle
   • Rotational Mechanics — Torque, Angular Momentum, Moment of Inertia, Rolling
   • Gravitation — Kepler's Laws, Universal Law, Gravitational Field, Satellite
   • Elasticity — Stress, Strain, Hooke's Law, Young's Modulus, Bulk Modulus, Shear Modulus
   • Fluid Mechanics — Pressure, Buoyancy, Bernoulli's Theorem, Viscosity, Surface Tension
   • Mechanical Waves — SHM, Oscillations, Spring, Pendulum, Wave Motion, Sound
   • Properties of Matter, Units, Dimensions, Error Analysis, Significant Figures
9. 9

   Heat & Thermodynamics (Physics)

   ~4 marks

   Heat Transfer, Laws, Kinetic Theory

   • Heat and Temperature — Scales, Thermometry, Thermal Expansion
   • Calorimetry — Specific Heat, Latent Heat, Heat Capacity
   • Heat Transfer — Conduction, Convection, Radiation, Thermal Conductivity
   • Thermodynamics — Zeroth, First, Second, Third Law, PV Diagram, Work, Heat
   • Kinetic Theory of Gases — Pressure, RMS Speed, Mean Free Path, Degrees of Freedom
   • Gas Laws — Boyle's, Charles', Gay-Lussac's, Ideal Gas Equation, Real Gases
   • Thermodynamic Processes — Isothermal, Adiabatic, Isobaric, Isochoric, Cyclic
   • Heat Engines, Refrigerators, Carnot Cycle, Entropy
   • Calorimetry, Phase Changes, Latent Heat, Triple Point, Critical Point
   • Thermal Radiation, Black Body, Stefan-Boltzmann Law, Wien's Displacement Law
10. 10

    Optics & Modern Physics

    ~4 marks

    Light, EM Waves, Relativity, Quantum, Nuclear

    • Ray Optics — Reflection, Refraction, Total Internal Reflection, Prism
    • Lenses and Mirrors — Image Formation, Formulae, Power, Combination
    • Optical Instruments — Microscope, Telescope, Magnifying Glass, Camera
    • Wave Optics — Interference, Diffraction, Polarization, Young's Double Slit
    • Electromagnetic Waves — EM Spectrum, Properties, Maxwell's Equations
    • Photoelectric Effect — Einstein's Equation, Work Function, Threshold Frequency
    • Bohr's Atomic Model, Hydrogen Spectrum, Atomic Structure
    • Nuclear Physics — Atomic Structure, Radioactivity, Half-Life, Decay
    • Modern Physics — Photoelectric Effect, X-rays, Lasers, Optical Fibers
    • Semiconductor Physics — Diode, Transistor, Logic Gates, Communication
11. 11

    Electrostatics & Current Electricity

    ~4 marks

    Charges, Fields, Circuits, EM

    • Electrostatics — Coulomb's Law, Electric Field, Electric Potential, Equipotential
    • Capacitance, Capacitors, Series-Parallel, Energy Stored, Dielectrics
    • Current Electricity — Ohm's Law, Resistance, Resistivity, Conductivity
    • Circuits — Series, Parallel, Combination, Kirchhoff's Laws, Wheatstone Bridge
    • DC Circuits, EMF, Internal Resistance, Potentiometer, Meter Bridge
    • Heating Effect of Current, Joule's Law, Electric Power, Commercial Units
    • Magnetic Effects — Biot-Savart Law, Ampere's Law, Solenoid, Cyclotron
    • Electromagnetic Induction — Faraday's Law, Lenz's Law, Self/Mutual Induction
    • AC Circuits — RLC, Resonance, Impedance, Transformer, Generator, AC
    • EM Waves, Maxwell's Equations, Communication Systems, Modulation
12. 12

    Modern Physics

    ~4 marks

    Quantum, Nuclear, Solid State, Electronics

    • Quantum Mechanics — Wave-Particle Duality, De Broglie Wavelength, Heisenberg
    • Schrodinger Equation (Qualitative), Quantum Numbers, Atomic Orbitals
    • Nuclear Physics — Nuclear Structure, Binding Energy, Mass Defect
    • Radioactivity — Alpha, Beta, Gamma Decay, Half-Life, Decay Constant
    • Nuclear Reactions — Fission, Fusion, Chain Reaction, Atomic Reactor
    • Particle Physics — Quarks, Leptons, Bosons, Hadrons, Standard Model
    • Solid State Physics — Crystal Structure, Band Theory, Semiconductors
    • Electronics — Diodes, Transistors, Amplifiers, Oscillators, Logic Gates
    • Digital Electronics — Boolean Algebra, Logic Families, Flip-Flops
    • Communication — AM, FM, AM Modulation, Antenna, Propagation of EM Waves
13. 13

    Units, Measurement & Practical Physics

    ~4 marks

    • Units and Dimensions — SI Units, Dimensional Analysis, Conversion
    • Measurement — Vernier Caliper, Screw Gauge, Significant Figures, Errors
    • Vectors — Addition, Subtraction, Dot Product, Cross Product, Resolution
    • Kinematics — 1D, 2D, 3D Motion, Projectile, Relative Velocity, Circular
    • Newton's Laws — Inertia, F=ma, Action-Reaction, Free Body Diagrams
    • Friction, Work, Energy, Power, Collisions (Elastic, Inelastic)
    • Gravitation — Universal Law, g, Escape Velocity, Kepler's Laws, Satellites
    • Properties of Matter — Elasticity, Fluid Statics, Surface Tension, Viscosity
    • Oscillations and Waves — SHM, Wave Motion, Sound, Doppler Effect
    • Practical Physics — Lab Equipment, Experiments, Error Analysis, Data Interpretation
14. 14

    Electromagnetism

    ~4 marks

    Magnetic, EM Induction, AC, Communication

    • Magnetic Effects — Magnetic Field, Oersted, Ampere, Biot-Savart, Right-Hand Rule
    • Magnetic Materials — Dia, Para, Ferromagnetic, Hysteresis, Curie Temperature
    • Earth's Magnetism — Magnetic Declination, Dip, Magnetic Maps, Compass
    • Electromagnetic Induction (EMI) — Faraday's Experiments, Faraday's Law, Lenz's Law
    • Eddy Currents, Self-Inductance, Mutual Inductance, Inductors, Transformers
    • AC Generator, Motor, Alternating Current, RMS, Peak Value, Phase
    • AC Circuits — R, L, C, RLC Series/Parallel, Resonance, Impedance, Power Factor
    • EM Waves — Generation, Properties, Spectrum, Applications, Communication
    • Communication Systems — Modulation (AM, FM, PM), Antenna, Propagation
    • Modern Physics Applications — X-ray, Laser, Fibre Optics, Solar Cell
15. 15

    Atomic Structure & Chemical Bonding

    ~4 marks

    Quantum, Periodic Table, Bonds

    • Atomic Structure — Bohr's Model, Quantum Numbers, Electronic Configuration, Shapes
    • Atomic Models — Thomson, Rutherford, Bohr, Schrodinger (Qualitative), Heisenberg
    • Photoelectric Effect, Wave-Particle Duality, de Broglie Wavelength, Heisenberg
    • Periodic Table — Periodicity, Atomic Radius, Ionization Energy, Electronegativity
    • Chemical Bonding — Ionic, Covalent, Coordinate, Hydrogen Bonding, Metallic
    • Hybridization — sp, sp2, sp3, sp3d, sp3d2 with Examples (CH4, NH3, H2O)
    • VSEPR Theory, VBT (Valence Bond Theory), MOT (Molecular Orbital Theory)
    • Bond Parameters — Bond Length, Angle, Energy, Polarity, Dipole Moment
    • Resonance, Hyperconjugation, Inductive Effect, Mesomeric Effect, Electromeric
    • Lattice Energy, Born-Haber Cycle, Fajan's Rules, Polarizing Power
16. 16

    States of Matter & Solutions

    ~4 marks

    Gas, Liquid, Solid, Solutions, Colloids

    • Gas Laws — Boyle's Law, Charles' Law, Gay-Lussac's Law, Avogadro's Law, Ideal Gas
    • Kinetic Molecular Theory — Postulates, Derivation of Gas Laws, RMS Speed
    • Real Gases — van der Waals Equation, Critical Constants, Liquefaction
    • Liquid State — Properties, Vapor Pressure, Surface Tension, Viscosity
    • Solid State — Crystalline, Amorphous, Crystal Systems, Bravais Lattices
    • Unit Cell, Coordination Number, Packing Efficiency, Density Calculations
    • Imperfections in Solids — Point Defects, Schottky, Frenkel, F-Centers
    • Solutions — Types, Concentration (Molarity, Molality, Normality, Formality)
    • Colligative Properties — Lowering of VP, Elevation of BP, Depression of FP, Osmotic
    • Colloids — Types, Preparation, Properties, Emulsions, Gels, Tyndall Effect
17. 17

    Thermodynamics, Equilibrium, Kinetics

    ~4 marks

    Energetics, Rate, Ionic

    • Thermodynamics — System, Surroundings, Internal Energy, Enthalpy, Entropy, Gibbs
    • First Law of Thermodynamics — Work, Heat, Energy Conservation, Enthalpy
    • Thermochemistry — Enthalpy of Formation, Combustion, Neutralization, Solution
    • Second Law of Thermodynamics — Entropy, Spontaneity, Carnot Cycle
    • Chemical Equilibrium — Equilibrium Constant (Kc, Kp), Le Chatelier's Principle
    • Ionic Equilibrium — Acids, Bases, pH, Buffer Solutions, Indicators, Solubility Product
    • Chemical Kinetics — Rate Law, Order, Molecularity, Integrated Rate Equations
    • Arrhenius Equation, Activation Energy, Catalysis, Collision Theory
    • Electrochemistry — Cells, EMF, Nernst Equation, Electrolysis, Faraday's Laws
    • Colligative Properties of Electrolytes — van't Hoff Factor, Osmotic Pressure
18. 18

    Inorganic Chemistry

    ~4 marks

    Periodic Table, s/p/d/f Block, Coordination, Metallurgy

    • Periodic Table — Classification, Periodicity, Properties, s/p/d/f Block Elements
    • Hydrogen, s-Block Elements — Properties, Compounds, Uses (Na, K, Ca, Mg)
    • p-Block Elements — Group 13-18, Properties, Compounds, Allotropes
    • Boron, Carbon, Nitrogen, Oxygen, Phosphorus, Sulfur, Halogen Families
    • Noble Gases — Properties, Compounds, Clathrates, Xenon Compounds
    • d-Block / Transition Elements — Properties, Variable Valency, Catalysis
    • f-Block Elements — Lanthanides, Actinides, Properties, Uses
    • Coordination Compounds — Werner's Theory, IUPAC, Isomerism, Bonding
    • Metallurgy — Ore, Mineral, Extraction, Refining, Alloys, Properties
    • Environmental Chemistry, Pollution, Green Chemistry, Bioinorganic Chemistry
19. 19

    Organic Chemistry I

    ~4 marks

    Basic, Hydrocarbons, Functional Groups, Reactions

    • Organic Chemistry Basics — Tetravalent Carbon, Hybridization, Bonding, Isomerism
    • IUPAC Nomenclature — Alkanes, Alkenes, Alkynes, Functional Groups
    • Isomerism — Structural (Chain, Position, Functional, Metamerism, Tautomerism)
    • Stereoisomerism — Geometrical (cis-trans), Optical (d, l, meso), E/Z, R/S
    • Alkanes — Properties, Reactions (Substitution, Combustion, Cracking, Reforming)
    • Alkenes — Properties, Reactions (Addition, Polymerization, Markownikoff, Peroxide)
    • Alkynes — Properties, Reactions (Addition, Acidity, Ozonolysis, Polymerization)
    • Aromatic Hydrocarbons — Benzene, Aromaticity, Electrophilic Substitution (EAS)
    • Alkyl/Aryl Halides — Properties, Reactions (Substitution, Elimination, Grignard)
    • Alcohols, Phenols, Ethers — Properties, Reactions, Acidity, Preparation
20. 20

    Organic Chemistry II

    ~4 marks

    Aldehydes, Amines, Biomolecules, Polymers, Practical

    • Aldehydes and Ketones — Carbonyl Compounds, Nucleophilic Addition, Aldol
    • Carboxylic Acids — Properties, Acidity, Reactions, Derivatives (Esters, Amides)
    • Amines — Properties, Basicity, Reactions, Diazonium Salts, Aniline
    • Amino Acids, Peptides, Proteins — Structure, Properties, Zwitterions, Isoelectric
    • Carbohydrates — Mono, Di, Polysaccharides, Glucose, Fructose, Starch, Cellulose
    • Lipids, Fats, Oils, Waxes, Phospholipids, Steroids, Cholesterol
    • Vitamins, Hormones, Enzymes, Nucleic Acids (DNA, RNA), Genetic Code
    • Polymers — Natural, Synthetic, Addition, Condensation, Plastics, Rubber, Fibers
    • Chemistry in Everyday Life — Drugs, Food Preservatives, Cleansing Agents, Cosmetics
    • Practical Organic Chemistry — Qualitative Analysis, Quantitative Analysis, Lab Tests
21. 21

    Organic Chemistry III

    ~4 marks

    Spectroscopy, Biomolecules, Polymers, Chemistry in Action

    • Spectroscopy — UV, IR, NMR (Principles, Applications to Organic Compounds)
    • Reaction Mechanisms — SN1, SN2, E1, E2, Addition, Elimination, Substitution
    • Named Reactions — Aldol, Cannizzaro, Perkin, Reformatsky, Wittig, Diels-Alder
    • Reagents — Grignard, LDA, NaBH4, LiAlH4, PBr3, SOCl2, KMnO4, K2Cr2O7
    • Heterocyclic Compounds — Furan, Pyrrole, Thiophene, Pyridine, Indole, Quinoline
    • Biomolecules — Amino Acids, Proteins, Enzymes, Carbohydrates, Nucleic Acids
    • Drugs and Pharmaceuticals — Analgesics, Antipyretics, Antibiotics, Antiseptics
    • Polymers — Classification, Polymerization, Natural and Synthetic Polymers
    • Chemistry in Industries — Petroleum, Petrochemicals, Pharmaceuticals, Dyes, Paints
    • Environmental Chemistry — Pollution, Water Treatment, Green Chemistry, Waste
22. 22

    Algebra (Advanced)

    ~4 marks

    Sets, Relations, Functions, Complex Numbers, P&C

    • Sets, Relations, Functions, Venn Diagrams, Equivalence Relations
    • Complex Numbers — Algebra, Argand Plane, Modulus-Argument, De Moivre's
    • Quadratic Equations, Polynomials, Identities, Factorization, Remainder Theorem
    • Sequences and Series — AP, GP, HP, Sum, Special Series, Method of Differences
    • Permutations and Combinations, Binomial Theorem, Multinomial Theorem
    • Probability — Conditional, Bayes, Independent Events, Random Variables
    • Matrices and Determinants — Types, Operations, Inverse, Cramer's Rule
    • Linear Algebra — Vector Spaces, Eigenvalues, Linear Programming, Graph Theory
    • Logarithms, Antilogarithms, Partial Fractions, Induction, Mathematical Reasoning
    • Number Theory — Divisibility, Modular Arithmetic, Fermat's, Wilson's Theorem
23. 23

    Trigonometry (Advanced)

    ~4 marks

    Ratios, Identities, Equations, Inverse, Heights

    • Trigonometric Ratios (sin, cos, tan, cot, sec, cosec) — Sign Conventions
    • Trigonometric Identities — Pythagorean, Sum-Difference, Product-to-Sum
    • Trigonometric Equations — General Solutions, Specific Solutions
    • Inverse Trigonometric Functions — sin^-1, cos^-1, tan^-1, Properties
    • Heights and Distances — Angle of Elevation, Depression, Problems
    • Properties of Triangles — Sine Rule, Cosine Rule, Half-Angle, Napier Analogy
    • Trigonometric Series — Taylor Series, Maclaurin Series for sin, cos
    • Multiple and Sub-multiple Angles — sin 2θ, cos 2θ, sin 3θ, cos 3θ
    • Conditional Trigonometric Identities, Maxima and Minima
    • Heights and Distances — Bearing, Compass, Survey Problems, Real-World Applications
24. 24

    Coordinate Geometry (Advanced)

    ~4 marks

    2D/3D, Conics, Vectors, Transformations

    • Straight Lines — Slope, Equation, Distance, Angle Between Lines, Family of Lines
    • Circles — Standard Form, General Form, Tangent, Normal, Chord of Contact, Pole-Polar
    • Conic Sections — Parabola, Ellipse, Hyperbola (Standard Forms, Focus, Directrix, Eccentricity)
    • 3D Coordinate Geometry — Distance, Section Formula, Direction Cosines, Ratios
    • Plane and Line in 3D — Equation, Angle, Distance, Symmetric Form
    • Sphere, Cone, Cylinder — Equations, Tangent Plane, Generator, Curved Surface
    • Vectors — Types, Addition, Subtraction, Dot, Cross, Triple Product
    • Vector Algebra — Position Vector, Section Formula, Projection, Resolution
    • Coordinate Transformations — Translation, Rotation, Reflection, Scaling
    • Locus, Curve Tracing, Parametric Equations, Applications to Motion
25. 25

    Calculus (Advanced)

    ~4 marks

    Limits, Derivatives, Integration, Differential Equations

    • Limits — Algebraic, Trigonometric, Logarithmic, Exponential, L'Hopital's Rule
    • Continuity, Discontinuity, Types of Discontinuity, Intermediate Value Theorem
    • Differentiation — First Principles, Product, Quotient, Chain Rule, Implicit
    • Applications of Derivatives — Tangent, Normal, Maxima, Minima, Rate of Change
    • Higher-Order Derivatives, Successive Differentiation, Leibnitz Theorem
    • Integration — Indefinite, Definite, Methods (Substitution, Parts, Partial Fractions)
    • Applications of Integration — Areas, Volumes, Arc Length, Surface Area
    • Differential Equations — First Order, First Degree, Second Order, Exact Equations
    • Differential Equations Applications — Population Growth, Newton's Law of Cooling
    • Integral Calculus — Beta, Gamma Functions, Multiple Integrals, Improper Integrals
26. 26

    Probability & Statistics (Advanced)

    ~4 marks

    Probability, Stats, Linear Programming

    • Probability — Classical, Axiomatic, Conditional, Independent Events, Bayes
    • Random Variables — Discrete, Continuous, PMF, PDF, Expectation, Variance
    • Probability Distributions — Binomial, Poisson, Normal, Geometric, Exponential
    • Statistics — Mean, Median, Mode, Standard Deviation, Variance, Skewness, Kurtosis
    • Correlation and Regression — Pearson, Spearman, Least Squares, Coefficient
    • Sampling Methods — Random, Stratified, Systematic, Cluster, Multistage
    • Hypothesis Testing — Null, Alternative, t-test, z-test, Chi-square, F-test, ANOVA
    • Linear Programming — Formulation, Graphical Method, Simplex Method, Duality
    • Game Theory — Pure, Mixed Strategy, Saddle Point, Dominance, Two-Person Zero-Sum
    • Operations Research — Transportation, Assignment, Sequencing, Replacement, Inventory
27. 27

    Modern Mathematics

    ~4 marks

    Sets, Relations, Boolean Algebra, Number Theory

    • Sets, Relations, Functions, Equivalence Relations, Partial Order
    • Boolean Algebra — Boolean Operations, Laws, Simplification, Karnaugh Maps
    • Logic — Propositional, Predicate, Quantifiers, Truth Tables, Inference Rules
    • Graph Theory — Types, Euler, Hamiltonian, Coloring, Planar, Trees, BFS, DFS
    • Number Theory — Primes, GCD, LCM, Modular Arithmetic, Fermat, Wilson, Euler
    • Combinatorics — Permutation, Combination, Pigeonhole, Inclusion-Exclusion
    • Group Theory — Definitions, Subgroups, Cyclic, Permutation, Lagrange, Cosets
    • Mathematical Induction, Recurrence Relations, Generating Functions
    • Linear Algebra — Matrices, Determinants, Eigenvalues, Eigenvectors, Systems
    • Topology (Basic) — Open Sets, Closed Sets, Continuity, Compactness