IIT JEE Advanced Syllabus 2024

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Sections

JEE Advanced Topics

Sets, Relations, and 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, 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, special functions (polynomial, trigonometric, exponential, logarithmic, power, absolute value, greatest integer etc.), sum, difference, product and composition of functions.

Algebra

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.

Matrices

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.

Probability and Statistics

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.

Trigonometry

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.

Analytical Geometry

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; 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.

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, equation of a circle through the points of intersection of two circles and those of a circle and a straight line.

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, angle between two planes, angle between a line and the plane, coplanar lines.

Differential Calculus

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.

Integral Calculus

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.

Vectors

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

Sections

JEE Advanced Topics

General

General Units and dimensions, dimensional analysis; least count, significant figures; Methods of measurement and error analysis for physical quantities pertaining to the following experiments: Experiments based on using Vernier calipers and screw gauge (micrometer), Determination of g using simple pendulum, Young’s modulus - elasticity of the material Surface tension of water by capillary rise and effect of detergents. Specific heat of a liquid using calorimeter, focal length of a concave mirror and a convex lens using u-v method, Speed of sound using resonance column, Verification of Ohm’s law using voltmeter and ammeter, and specific resistance of the material of a wire using meter bridge and post office box

Mechanics

Kinematics in one and two dimensions (Cartesian coordinates only), projectiles; Uniform circular motion; Relative velocity.

Newton’s laws of motion; Inertial and uniformly accelerated frames of reference; Static and dynamic friction; Kinetic and potential energy; Work and power; Conservation of linear momentum and mechanical energy. Systems of particles; Centre of mass and its motion; Impulse; Elastic and inelastic collisions. Rigid body, moment of inertia, parallel and perpendicular axes theorems, moment of inertia of uniform bodies with simple geometrical shapes; Angular momentum; Torque; Conservation of angular momentum; Dynamics of rigid bodies with fixed axis of rotation; Rolling without slipping of rings, cylinders and spheres; Equilibrium of rigid bodies; Collision of point masses with rigid bodies.

Forced and damped oscillation (in one dimension), resonance. Linear and angular simple harmonic motions. Hooke’s law, Young’s modulus. Law of gravitation; Gravitational potential and field; Acceleration due to gravity; Kepler’s law, Geostationary orbits, Motion of planets and satellites in circular orbits; Escape velocity. Pressure in a fluid; Pascal’s law; Buoyancy; Surface energy and surface tension, angle of contact, drops, bubbles and capillary rise. Viscosity (Poiseuille’s equation excluded), Modulus of rigidity and bulk modulus in mechanics.

Stoke’s law; Terminal velocity, Streamline flow, equation of continuity, Bernoulli’s theorem and its applications. Wave motion (plane waves only), longitudinal and transverse waves, superposition of waves; Progressive and stationary waves; Vibration of strings and air columns; Resonance; Beats; Speed of sound in gases; Doppler effect (in sound)

Thermal Physics

Thermal expansion of solids, liquids and gases; Calorimetry, latent heat; Heat conduction in one dimension; Elementary concepts of convection and radiation; Newton’s law of cooling; Ideal gas laws; Specific heats (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 and its applications (only for ideal gases); Second law of thermodynamics, reversible and irreversible processes, Carnot engine and its efficiency; Blackbody radiation: absorptive and emissive powers; Kirchhoff’s law; Wien’s displacement law, Stefan’s law.

Electricity and Magnetism

Coulomb’s law; Electric field and potential; Electrical potential energy of a system of point charges and of electrical dipoles in a uniform electrostatic field; Electric field lines; Flux of electric field; Gauss’s law and its application in simple cases, such as, to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell.

Capacitance; Parallel plate capacitor with and without dielectrics; Capacitors in series and parallel; Energy stored in a capacitor. Electric current; Ohm’s law; Series and parallel arrangements of resistances and cells; Kirchhoff’s laws and simple applications; Heating effect of current. Biot–Savart’s law and Ampere’s law; Magnetic field near a current-carrying straight wire, along the axis of a circular coil and inside a long straight solenoid; Force on a moving charge and on a current-carrying wire in a uniform magnetic field. Magnetic moment of a current loop; Effect of a uniform magnetic field on a current loop; Moving coil galvanometer, voltmeter, ammeter and their conversions.

Electromagnetic induction: Faraday’s law, Lenz’s law; Self and mutual inductance; RC, LR, LC and LCR(in series) circuits with D.C. and A.C. sources.

Electromagnetic Waves

Electromagnetic waves and their characteristics. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, x-rays, gamma rays) including elementary facts about their uses

Optics

Rectilinear propagation of light; Reflection and refraction at plane and spherical surfaces; Total internal reflection; Deviation and dispersion of light by a prism; Thin lenses; Combinations of mirrors and thin lenses; Magnification.

Wave nature of light: Huygen’s principle, interference limited to Young’s double slit experiment. Diffraction due to a single slit. Polarization of light, plane polarized light; Brewster's law, Polaroids.

Modern Physics

Atomic nucleus; α, β and γ radiations; Law of radioactive decay; Decay constant; Half-life and mean life; Binding energy and its calculation; Fission and fusion processes; Energy calculation in these processes. Photoelectric effect; Bohr’s theory of hydrogen-like atoms; Characteristic and continuous X-rays, Moseley’s law; de Broglie wavelength of matter waves.

Sections

JEE Advanced Topics

General Topics                                                                                   

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.

States of Matter: Gases and Liquids

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.

Atomic Structure

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), shapes of s, p and d orbitals; Aufbau principle; Pauli’s exclusion principle and Hund’s rule.

Chemical Bonding and Molecular Structure

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).

Chemical Thermodynamics

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.

Chemical and Ionic Equilibrium

Law of mass action; Significance of ΔG and ΔG0 in 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.

Electrochemistry

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.

Chemical Kinetics`

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.

Solid State

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

Solutions

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.

Surface Chemistry

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).

Classification of Elements and Periodicity in Properties

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

Hydrogen

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.

s-Block Elements

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).

Sections

JEE Advanced Topics

Isolation/preparation and properties of the following non-metals

Boron, silicon, nitrogen, phosphorus, oxygen, sulphur and halogens

Properties of allotropes of carbon (only diamond and graphite), phosphorus and sulphur

Preparation And Properties of The Following Compounds

Oxides, peroxides, hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium, potassium, magnesium and calcium

Boron: diborane, boric acid and borax

Aluminium: alumina, aluminium chloride and alums

Carbon: oxides and oxyacid (carbonic acid)

Silicon: silicones, silicates and silicon carbide

Nitrogen: oxides, oxyacids and ammonia

Phosphorus: oxides, oxyacids (phosphorus acid, phosphoric acid) and phosphine

Oxygen: ozone and hydrogen peroxide

Sulphur: hydrogen sulphide, oxides, sulphurous acid, sulphuric acid and sodium thiosulphate

Halogens: hydrohalic acids, oxides and oxyacids of chlorine, bleaching powder

Xenon fluorides.

Transition Elements 3D Series

Definition, general characteristics, oxidation states and their stabilities, colour (excluding the details of electronic transitions) and calculation of spin-only magnetic moment

Coordination compounds: nomenclature of mononuclear coordination compounds, cistrans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar and octahedral).

Preparation And Properties of The Following Compounds

Oxides and chlorides of tin and lead

Oxides, chlorides and sulphates of Fe2+, Cu2+ and Zn2+

Potassium permanganate, potassium dichromate, silver oxide, silver nitrate, silver thiosulphate.

Ores and Minerals

Commonly occurring ores and minerals of iron, copper, tin, lead, magnesium, aluminium,

zinc and silver.

Extractive Metallurgy

Chemical principles and reactions only (industrial details excluded), Carbon reduction method (iron and tin), Self reduction method (copper and lead), Electrolytic reduction method (magnesium and aluminium), Cyanide process (silver and gold).

Principles of Qualitative Analysis

Groups I to V (only Ag+ , Hg2+, Cu2+, Pb2+, Bi3+, Fe3+, Cr3+, Al3+, Ca2+, Ba2+, Zn2+, Mn2+ and Mg2+)

Nitrate, halides (excluding fluoride), sulphate and sulphide.

Sections

Topics

Concepts

Hybridisation of carbon, σ and π-bonds, Shapes of simple organic molecules, Structural and geometrical isomerism

Optical isomerism of compounds containing up to two asymmetric centers, (R,S and E,Z nomenclature excluded),

IUPAC nomenclature of simple organic compounds (only) hydrocarbons, mono-functional and bi-functional compounds), Conformations of ethane and butane (Newman projections), Resonance and hyperconjugation, Keto-enol tautomerism,

Determination of empirical and molecular formulae of simple compounds (only combustion method), Hydrogen bonds, Definition and their effects on physical properties of alcohols and carboxylic acids, Inductive and resonance effects on acidity and basicity of organic acids and bases, Polarity and inductive effects in alkyl halides, Reactive intermediates produced during homolytic and heterolytic bond cleavage

Formation, structure and stability of carbocations, carbanions and free radicals.

Preparation, Properties and Reactions of Alkanes

Homologous series, physical properties of alkanes (melting points, boiling points and density), Combustion and halogenation of alkanes, Preparation of alkanes by Wurtz reaction and decarboxylation reactions.

Preparation, Properties and Reactions of Alkenes and Alkynes

Physical properties of alkenes and alkynes (boiling points, density and dipole moments), Acidity of alkynes, Acid catalysed hydration of alkenes and alkynes (excluding the stereochemistry of addition and elimination), Reactions of alkenes with KMnO4 and ozone, Reduction of alkenes and alkynes; Preparation of alkenes and alkynes by elimination reactions, Electrophilic addition reactions of alkenes with X2, HX, HOX and H2O (X=halogen), Addition reactions of alkynes; Metal acetylides.

Reactions of Benzene

Structure and aromaticity, Electrophilic substitution reactions: halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation, Effect of o-, m- and p-directing groups in monosubstituted benzenes.

Phenols

Acidity, electrophilic substitution reactions (halogenation, nitration and sulphonation), Reimer-Tieman reaction, Kolbe reaction.

Characteristic Reactions of The Following (including those mentioned above)

Alkyl halides: rearrangement reactions of alkyl carbocation, Grignard reactions, nucleophilic substitution reactions

Alcohols: esterification, dehydration and oxidation, reaction with sodium, phosphorus halides, ZnCl2/concentrated HCl, conversion of alcohols into aldehydes and ketones

Ethers: Preparation by Williamson’s Synthesis

Aldehydes and Ketones: oxidation, reduction, oxime and hydrazone formation

Aldol condensation, Perkin reaction

Cannizzaro reaction

Haloform reaction and nucleophilic addition reactions (Grignard addition)

Carboxylic acids: formation of esters, acid chlorides and amides, ester hydrolysis

Amines: basicity of substituted anilines and aliphatic amines, preparation from nitro compounds, reaction with nitrous acid, azo coupling reaction of diazonium salts of aromatic amines, Sandmeyer and related reactions of diazonium salts; carbylamine reaction

Haloarenes: nucleophilic aromatic substitution in haloarenes and substituted haloarenes (excluding Benzyne mechanism and Cine substitution).

Carbohydrates

Classification

Mono- and di-saccharides (glucose and sucrose)

Oxidation, reduction, glycoside formation and hydrolysis of sucrose.

Amino Acids And Peptides

General structure (only primary structure for peptides) and physical properties

Properties And Uses of Some Important Polymers

Natural rubber, cellulose, nylon, teflon and PVC.

Practical Organic Chemistry

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

Chemical methods of separation of mono-functional organic compounds from binary mixtures.

Topic

Marks

Weightage in %

Capacitance

6

4.84%

Current Electricity

8

6.45%

Electromagnetic Field

3

2.42%

Electromagnetic Induction

11

8.87%

Topic

Marks

Weightage in %

Calorimetry & Thermal Expansion

3

2.42%

Heat Transfer

10

8.06%

KTG & Thermodynamics

3

2.42%

Topic

Marks

Weightage in %

Circular Motion

6

4.84%

Elasticity & Viscosity

3

2.42%

Error in Measurement

7

5.65%

Rigid Body Dynamic

11

8.87%

Unit & Dimension

4

3.23%

Topic

Marks

Weightage in %

Modern Physics

23

18.55%

Topic

Marks

Weightage in %

Geometrical Optics & Physical Optics

14

11.25%

Wave Optics

4

3.23%

Topic

Marks

Weightage in %

SHM

4

3.23%

Sound Waves

4

3.23%

Topic

Marks

Chemical Bonding

8

Coordination Compounds

6

Metallurgy

4

P-Block

11

Qualitative Analysis

7

Total

36

Topic

Marks

Amines

11

Aromatic Compounds

6

Biomolecules

4

Carbonyl compounds

3

General Organic Chemistry

8

Polymers

7

Stereoisomerism

6

Total

45

Topic

Marks

Atomic Structure & Nuclear Chemistry

3

Chemical Equilibrium

6

Chemical Kinetics

8

Electrochemistry

3

Gaseous State

3

Mole Concept

9

Solution & Colligative Properties

4

Surface Chemistry

3

Solid State

4

Total

43

Topic

Marks

Binomial Theorem

3

Complex Numbers

7

Coordinate Geometry

18

Differential & Integral Calculus

38

Fundamentals of Mathematics

5

Probability

9

Matrices

14

Permutation & Combination

3

Quadratic Equation

3

Sequence & Series

3

Trigonometry

10

Vector & 3D

11