Mentorship Programme

JEE Mains Syllabus

Mathematics

Unit 1: Sets, Relations and Functions

  • Sets
  • Union, Intersection & Complement
  • Algebra of Sets
  • Power Set
  • Relations
  • Types of Relations
  • Equivalence Relations
  • Functions
  • One-One, Into & Onto Functions
  • Composition of Functions

Unit 2: Complex Numbers and Quadratic Equations

  • Complex Numbers
  • Argand Diagram
  • Algebra of Complex Numbers
  • Modulus & Argument
  • Quadratic Equations
  • Relation Between Roots & Coefficients
  • Nature of Roots
  • Formation of Quadratic Equations



Unit 3: Matrices and Determinants

  • Matrices
  • Types of Matrices
  • Matrix Algebra
  • Determinants
  • Area of Triangle using Determinants
  • Adjoint & Inverse Matrix
  • Linear Equations using Matrices

Unit 4: Permutations and Combinations

  • Fundamental Principle of Counting
  • Permutations
  • Combinations
  • Applications

Unit 5: Binomial Theorem

  • Binomial Expansion
  • General Term
  • Middle Term
  • Applications

Unit 6: Sequence and Series

  • Arithmetic Progression (AP)
  • Geometric Progression (GP)
  • Arithmetic Mean
  • Geometric Mean
  • Relation between AM & GM

Unit 7: Limits, Continuity and Differentiability

  • Functions
  • Graphs of Functions
  • Limits
  • Continuity
  • Differentiability
  • Differentiation
  • Composite & Implicit Functions
  • Second Order Derivatives
  • Applications of Derivatives
  • Rate of Change
  • Increasing & Decreasing Functions
  • Maxima & Minima

Unit 8: Integral Calculus

  • Indefinite Integration
  • Standard Integrals
  • Substitution
  • Integration by Parts
  • Partial Fractions
  • Trigonometric Integrals
  • Definite Integration
  • Fundamental Theorem of Calculus
  • Area Under Curve

Unit 9: Differential Equations

  • Order & Degree
  • Separation of Variables
  • Homogeneous Differential Equations
  • Linear Differential Equations

Unit 10: Coordinate Geometry

  • Cartesian Coordinate System
  • Distance Formula
  • Section Formula
  • Slope of Line
  • Straight Line
  • Angle Between Lines
  • Distance of Point from Line
  • Circle
  • Parabola
  • Ellipse
  • Hyperbola

Unit 11: Three-Dimensional Geometry

  • Coordinates in Space
  • Distance Formula
  • Section Formula
  • Direction Ratios
  • Direction Cosines
  • Equation of Line
  • Skew Lines
  • Shortest Distance

Unit 12: Vector Algebra

  • Scalars & Vectors
  • Vector Addition
  • Components of Vector
  • Scalar Product
  • Vector Product

Unit 13: Statistics and Probability

  • Mean
  • Median
  • Mode
  • Variance
  • Standard Deviation
  • Mean Deviation
  • Probability
  • Addition & Multiplication Theorem
  • Bayes’ Theorem
  • Random Variable

Unit 14: Trigonometry

  • Trigonometric Functions
  • Trigonometric Identities
  • Inverse Trigonometric Functions

Unit 1: Units and Measurements

Unit 2: Kinematics

Unit 3: Laws of Motion

Unit 4: Work, Energy and Power

Unit 5: Rotational Motion

Unit 6: Gravitation

Unit 7: Properties of Solids and Liquids

Unit 8: Thermodynamics

Unit 9: Kinetic Theory of Gases

Unit 10: Oscillations and Waves

Unit 11: Electrostatics

Unit 12: Current Electricity

Unit 13: Magnetic Effects of Current and Magnetism

Unit 14: Electromagnetic Induction and Alternating Current

Unit 15: Electromagnetic Waves

Unit 16: Optics

Unit 17: Dual Nature of Matter and Radiation

Unit 18: Atoms and Nuclei

Unit 19: Electronic Devices

Unit 20: Experimental Skills

Physical Chemistry

Unit 1: Some Basic Concepts in Chemistry

Unit 2: Atomic Structure

Unit 3: Chemical Bonding and Molecular Structure

Unit 4: Chemical Thermodynamics

Unit 5: Solutions

Unit 6: Equilibrium

Unit 7: Redox Reactions and Electrochemistry

Unit 8: Chemical Kinetics

 

Inorganic Chemistry

Unit 9: Classification of Elements and Periodicity in Properties

Unit 10: p-Block Elements

Unit 11: d- and f-Block Elements

Unit 12: Coordination Compounds

Organic Chemistry

Unit 13: Purification and Characterisation of Organic Compounds

Unit 14: Some Basic Principles of Organic Chemistry

Unit 15: Hydrocarbons

Unit 16: Organic Compounds Containing Halogens

Unit 17: Organic Compounds Containing Oxygen

Unit 18: Organic Compounds Containing Nitrogen

Unit 19: Biomolecules

Unit 20: Principles Related to Practical Chemistry

JEE Advance Syllabus

Mathematics

1. Sets, Relations and Functions

  • Sets and their representations; union, intersection, complement and algebraic properties of sets
  • Power set
  • Relations: types of relations, equivalence relations
  • Functions: one-one, into, onto; composition of functions

2. Algebra

  • Complex numbers: algebra, conjugation, polar form, modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations
  • Quadratic equations (real coefficients): roots and coefficients relation, forming equations from given roots, symmetric functions of roots
  • Progressions: AP, GP, HP; AM, GM, HM; sums of finite AP and GP; infinite GP; sums of squares and cubes of first n natural numbers
  • Logarithms and their properties
  • Permutations and combinations
  • Binomial theorem (positive integral index) and properties of binomial coefficients

3. Matrices

  • Equality, addition, scalar multiplication, product, transpose
  • Determinant of a square matrix (order up to 3)
  • Inverse of a square matrix (order up to 3)
  • Diagonal, symmetric and skew-symmetric matrices
  • Solving simultaneous linear equations in two or three variables

4. Probability and Statistics

  • Addition and multiplication rules, conditional probability, Bayes’ theorem, independence of events
  • Probability using permutations and combinations
  • Mean, median, mode, mean deviation, variance, standard deviation (grouped and ungrouped data)

5. Trigonometry

  • Trigonometric functions, periodicity and graphs
  • Addition and subtraction formulae; multiple and sub-multiple angles
  • General solution of trigonometric equations
  • Sine rule, cosine rule, half-angle formula, area of a triangle
  • Inverse trigonometric functions (principal value only)

6. Analytical Geometry

  • Two dimensions
    • Cartesian coordinates, distance, section formulae, shift of origin
    • Straight line: various forms, angle between lines, distance of a point from a line, lines through intersection of two lines, angle bisectors, concurrency
    • Centroid, orthocentre, incentre, circumcentre of a triangle
    • Circle: various forms, tangent, normal, chord, parametric equations, intersection with a line or circle, family of circles through intersection points
    • Parabola, ellipse, hyperbola: standard forms, foci, directrices, eccentricity, parametric equations, tangent and normal
    • Locus problems
  • Three dimensions
    • Direction cosines and direction ratios
    • Equation of a line in space
    • Equation of a plane
    • Distance of a point from a plane

7. Differential Calculus

  • Functions: real-valued functions; into, onto, one-one; sum, difference, product, quotient; composite; absolute value, polynomial, rational, trigonometric, exponential, logarithmic; even and odd; inverse of a function
  • Limits and continuity: continuity of composite functions, intermediate value property, L’Hospital’s rule
  • Derivatives: chain rule; derivatives of standard functions; implicit functions; derivatives up to order two
  • Applications: geometrical meaning, tangents and normals, increasing and decreasing functions, maxima and minima, Rolle’s theorem, Lagrange’s mean value theorem

8. Integral Calculus

  • Indefinite integrals of standard functions
  • Definite integrals, properties, fundamental theorem of integral calculus
  • Integration by parts, substitution, partial fractions
  • Area involving simple curves
  • Differential equations: formation, homogeneous equations, variable separable, linear first-order equations

9. Vectors

  • Addition of vectors, scalar multiplication
  • Dot and cross products
  • Scalar triple product and geometrical interpretations

1. General

  • Units and dimensions, dimensional analysis
  • Least count, significant figures
  • Error analysis for these experiments:
    • Vernier calipers and screw gauge
    • Determination of g using a simple pendulum
    • Young’s modulus by Searle’s method
    • Specific heat of a liquid using a calorimeter
    • Focal length of concave mirror and convex lens (u-v method)
    • Speed of sound using resonance column
    • Ohm’s law verification; specific resistance using meter bridge and post office box

2. Mechanics

  • Kinematics: 1D and 2D (Cartesian only), projectiles, uniform circular motion, relative velocity
  • Laws of motion: Newton’s laws, inertial and uniformly accelerated frames, static and dynamic friction
  • Work, energy and power: kinetic and potential energy, conservation of momentum and mechanical energy
  • Systems of particles: centre of mass, impulse, elastic and inelastic collisions
  • Gravitation: law of gravitation, potential and field, g, satellites in circular orbits, escape velocity
  • Rigid body: moment of inertia, parallel and perpendicular axes theorems, torque, angular momentum and its conservation, fixed axis rotation, rolling without slipping, equilibrium, collision of point masses with rigid bodies
  • Oscillations: linear and angular SHM
  • Elasticity: Hooke’s law, Young’s modulus
  • Fluids: pressure, Pascal’s law, buoyancy, surface energy and surface tension, capillary rise, viscosity (Poiseuille’s equation excluded), Stokes’ law, terminal velocity, streamline flow, equation of continuity, Bernoulli’s theorem
  • Waves: plane waves, longitudinal and transverse, superposition, progressive and stationary waves, strings and air columns, resonance, beats, speed of sound in gases, Doppler effect (sound)

3. Thermal Physics

  • Thermal expansion of solids, liquids and gases
  • Calorimetry, latent heat
  • Heat conduction in one dimension; elementary convection and radiation
  • Newton’s law of cooling
  • Ideal gas laws; Cv and Cp for monoatomic and diatomic gases
  • Isothermal and adiabatic processes, bulk modulus of gases
  • Equivalence of heat and work; first law of thermodynamics (ideal gases only)
  • Blackbody radiation: absorptive and emissive powers, Kirchhoff’s law, Wien’s displacement law, Stefan’s law

4. Electricity and Magnetism

  • Electrostatics: Coulomb’s law, field and potential, potential energy of point charges and dipoles, field lines, flux, Gauss’s law (infinite wire, infinite plane sheet, thin spherical shell)
  • Capacitance: parallel plate capacitor with and without dielectrics, series and parallel, stored energy
  • Current electricity: Ohm’s law, series and parallel resistances and cells, Kirchhoff’s laws, heating effect
  • Magnetism: Biot-Savart law, Ampere’s law, field near a straight wire, axis of a circular coil, inside a solenoid; force on a moving charge and on a current-carrying wire
  • Magnetic moment of a current loop, torque on a loop, moving coil galvanometer, voltmeter and ammeter conversions
  • Induction: emf in a moving wire, Faraday’s law, Lenz’s law, self and mutual inductance
  • RC, LR and LC circuits with DC and AC sources

5. Electromagnetic Waves

  • Characteristics and transverse nature
  • Electromagnetic spectrum (radio waves to gamma rays) and elementary uses

6. Optics

  • Ray optics: rectilinear propagation, reflection and refraction at plane and spherical surfaces, total internal reflection, prism deviation and dispersion, thin lenses, combinations of mirrors and lenses, magnification
  • Wave optics: Huygens’ principle, interference (limited to Young’s double slit experiment)

7. Modern Physics

  • Atomic nucleus, α, β, γ radiations
  • Radioactive decay law, decay constant, half-life, mean life
  • Binding energy, fission and fusion, energy calculations
  • Photoelectric effect
  • Bohr’s theory of hydrogen-like atoms
  • Characteristic and continuous X-rays, Moseley’s law
  • de Broglie wavelength

A. Physical Chemistry

1. General topics

  • Atoms and molecules, Dalton’s atomic theory, mole concept
  • Chemical formulae, balanced equations, yield calculations
  • Equivalent concept, redox reactions, disproportionation
  • Concentration terms: mole fraction, molarity, molality, normality

2. Gaseous and liquid states

  • Absolute scale of temperature, ideal gas equation
  • Deviation from ideality, van der Waals equation
  • Kinetic theory: average, RMS and most probable velocities
  • Law of partial pressures, vapour pressure, diffusion

3. Atomic structure and chemical bonding

  • Bohr model, hydrogen spectrum, quantum numbers
  • Wave-particle duality, de Broglie hypothesis, uncertainty principle
  • Shapes of s, p, d orbitals; electronic configuration up to Z = 36; Aufbau, Pauli, Hund
  • Orbital overlap and covalent bond; hybridisation (s, p, d)
  • Orbital energy diagrams for homonuclear diatomic species
  • Hydrogen bond; polarity and dipole moment (qualitative)
  • VSEPR and shapes of molecules

4. Energetics

  • First law, internal energy, work, heat, pressure-volume work
  • Enthalpy, Hess’s law, heat of reaction, fusion and vaporisation
  • Second law, entropy, free energy, criterion of spontaneity

5. Chemical equilibrium

  • Law of mass action, equilibrium constant, Le Chatelier’s principle
  • Significance of ΔG and ΔG° in equilibrium
  • Solubility product, common ion effect, pH, buffers
  • Acids and bases (Brønsted and Lewis), hydrolysis of salts

6. Electrochemistry

  • Cells and cell reactions, standard electrode potentials
  • Nernst equation and relation to ΔG, electrochemical series, emf
  • Faraday’s laws of electrolysis
  • Conductance (specific, equivalent, molar), Kohlrausch’s law
  • Concentration cells

7. Chemical kinetics

  • Rates of reaction, order, rate constant, first-order reactions
  • Arrhenius equation and activation energy
  • Catalysis: homogeneous, heterogeneous, enzyme catalysis

8. Solid state

  • Classification of solids, crystalline state, seven crystal systems
  • Close packing (cubic), fcc, bcc, hcp
  • Nearest neighbours, ionic radii, simple ionic compounds, point defects

9. Solutions

  • Raoult’s law
  • Molecular weight from vapour pressure lowering, boiling point elevation, freezing point depression

10. Surface chemistry

  • Adsorption (isotherms excluded)
  • Colloids: types, preparation, general properties
  • Emulsions, surfactants, micelles (definitions and examples)

11. Nuclear chemistry

  • Isotopes and isobars, properties of α, β, γ rays
  • Kinetics of radioactive decay (decay series excluded), carbon dating
  • Nuclear stability and n/p ratio, fission and fusion

B. Inorganic Chemistry

  • Non-metals: isolation, preparation and properties of boron, silicon, nitrogen, phosphorus, oxygen, sulphur, halogens; allotropes of carbon (diamond, graphite), phosphorus, sulphur
  • Compounds of s-block and p-block elements
    • Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of Na, K, Mg, Ca
    • Boron: diborane, boric acid, borax
    • Aluminium: alumina, aluminium chloride, alums
    • Carbon: oxides, carbonic acid
    • Silicon: silicones, silicates, silicon carbide
    • Nitrogen: oxides, oxyacids, ammonia
    • Phosphorus: oxides, oxyacids, phosphine
    • Oxygen: ozone, hydrogen peroxide
    • Sulphur: H₂S, oxides, sulphurous acid, sulphuric acid, sodium thiosulphate
    • Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder
    • Xenon fluorides
  • Transition elements (3d series): definition, general characteristics, oxidation states and stability, colour, spin-only magnetic moment
  • Coordination compounds: nomenclature of mononuclear compounds, cis-trans and ionisation isomerism, hybridisation and geometry (linear, tetrahedral, square planar, octahedral)
  • Compounds of other metals: oxides and chlorides of tin and lead; oxides, chlorides and sulphates of Fe²⁺, Cu²⁺, Zn²⁺; KMnO₄, K₂Cr₂O₇, silver oxide, silver nitrate, silver thiosulphate
  • Ores and minerals: iron, copper, tin, lead, magnesium, aluminium, zinc, silver
  • Extractive metallurgy (chemical principles only)
    • Carbon reduction (iron, tin)
    • Self reduction (copper, lead)
    • Electrolytic reduction (magnesium, aluminium)
    • Cyanide process (silver, gold)
  • Qualitative analysis
    • Cations: Ag⁺, Hg²⁺, Cu²⁺, Pb²⁺, Bi³⁺, Fe³⁺, Cr³⁺, Al³⁺, Ca²⁺, Ba²⁺, Zn²⁺, Mn²⁺, Mg²⁺
    • Anions: nitrate, halides (excluding fluoride), sulphate, sulphide

C. Organic Chemistry

1. Basic concepts

  • Hybridisation of carbon, σ and π bonds, shapes of simple molecules
  • Structural and geometrical isomerism
  • Optical isomerism (up to two asymmetric centres; R,S and E,Z nomenclature excluded)
  • IUPAC nomenclature (hydrocarbons, mono- and bi-functional compounds)
  • Conformations of ethane and butane (Newman projections)
  • Resonance, hyperconjugation, keto-enol tautomerism
  • Empirical and molecular formula (combustion method only)
  • Hydrogen bonding and physical properties of alcohols and carboxylic acids
  • Inductive and resonance effects on acidity and basicity
  • Reactive intermediates: carbocations, carbanions, free radicals

2. Alkanes

  • Homologous series, physical properties
  • Combustion, halogenation
  • Preparation by Wurtz reaction and decarboxylation

3. Alkenes and alkynes

  • Physical properties, acidity of alkynes
  • Acid-catalysed hydration (stereochemistry excluded)
  • Reactions with KMnO₄ and ozone, reduction
  • Preparation by elimination
  • Electrophilic addition (X₂, HX, HOX, H₂O), addition reactions of alkynes, metal acetylides

4. Benzene

  • Structure and aromaticity
  • Electrophilic substitution: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation
  • Directing effects of o-, m-, p- directing groups

5. Phenols

  • Acidity, electrophilic substitution (halogenation, nitration, sulphonation)
  • Reimer-Tiemann reaction, Kolbe reaction

6. Characteristic reactions of functional groups

  • Alkyl halides: carbocation rearrangement, Grignard reactions, nucleophilic substitution
  • Alcohols: esterification, dehydration, oxidation, reaction with sodium, phosphorus halides, ZnCl₂/conc. HCl; conversion to aldehydes and ketones
  • Ethers: Williamson synthesis
  • Aldehydes and ketones: oxidation, reduction, oxime and hydrazone formation, aldol condensation, Perkin reaction, Cannizzaro reaction, haloform reaction, nucleophilic addition (Grignard)
  • Carboxylic acids: esters, acid chlorides, amides, ester hydrolysis
  • Amines: basicity of anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling, Sandmeyer and related reactions, carbylamine reaction
  • Haloarenes: nucleophilic aromatic substitution (benzyne mechanism and cine substitution excluded)

7. Biomolecules and polymers

  • Carbohydrates: classification, glucose and sucrose, oxidation, reduction, glycoside formation, hydrolysis of sucrose
  • Amino acids and peptides: general structure, primary structure of peptides, physical properties
  • Polymers: natural rubber, cellulose, nylon, teflon, PVC (properties and uses)

8. Practical organic chemistry

  • Detection of N, S and halogens
  • Identification of hydroxyl (alcoholic, phenolic), carbonyl (aldehyde, ketone), carboxyl, amino and nitro groups
  • Chemical separation of mono-functional organic compounds from binary mixtures

Mentorship Programme