JEE Advanced 2021 syllabus is important for students to understand and comprehend in order to crack JEE Advanced 2021. JEE Advanced is required to be qualified to get admissions in IITs across the country. Thousands of students qualify JEE Main and appear for JEE Advanced. Those who qualify for JEE Advanced require rigorous practice and dedicated hard work to ace the JEE Advanced 2021 exam. To begin with, one has to have a clear idea of the syllabus for the exam. JEE Advanced Syllabus 2021 is comprehensive and far-reaching which requires understanding and complete awareness of the topics.
Sections | Topics |
Algebra | Modulus and principal argument, conjugation, multiplication, triangle inequality, geometric interpretations. polar representation. Algebra of complex numbers, addition, cube roots of unity. Quadratic equations, the formation of quadratic equations, roots and coefficients, symmetric functions., infinite geometric series, sums of squares and cubes of the first n natural numbers. Logarithms, Arithmetic, geometric and harmonic progressions, mean, sum, Permutations and combinations, binomial theorem properties of binomial coefficients. |
Matrices | A rectangular array of real numbers, addition, multiplication by a scalar and product of matrices, transpose of a matrix, Determinant of a square matrix, inverse of a square matrix, properties of matrix operations, diagonal, and their properties, solutions of simultaneous linear equations in two or three variables. equality of matrices, symmetric and skew-symmetric matrices |
Probability | Bayes Theorem, Addition and multiplication rules of probability, conditional probability, probability of events using permutations and combinations, independence of events. |
Trigonometry | Periodicity and graphs,, addition and subtraction formulae, sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, The general solution of trigonometric equations. inverse trigonometric functions (principal value only). formulae involving multiple and sub-multiple angles |
Analytical Geometry | Equation of a circle. Parametric equations, equation of a circle through the points of intersection Equations of a parabola, hyperbola ellipse and in standard form, foci, eccentricity. Locus problems. Direction cosines and ratios, equation of a straight line in space, a distance of a point from a plane. equation of a plane Cartesian coordinates, section formulae, a shift of origin. Equation of a straight line, the angle between two lines, equation of the bisector of the angle between two lines, concurrency of lines; Centroid, orthocentre, Lines through the point of intersection of two given lines, incentre and circumcentre of a triangle |
Differential Calculus | Limit & continuity, Rolle’s theorem, Tangents and normals, continuous functions, Ls hospital rule, polynomial, Lagrange’s theorem, chain rule, even and odd functions, inverse trigonometric, logarithmic function, increasing functions, decreasing functions, derivatives, an intermediate value of the continuous function, absolute value, onto, one-one functions, other types of functions |
Integral Calculus | Integration by substitution, partial fractions, fundamental theorem of calculus, the inverse process of differentiation, application of definite integrals for finding area, homogenous equations, linear first-order equations, separation of variables, indefinite integrals, definite integrals |
Vectors | Scalar triple products, Geometrical interpretations if scaler triple product, dot and cross product, the addition of vectors, Scalar multiplication |
Sections | Topics |
General | Vernier callipers, screw gauge, Determination of g using a simple pendulum, Young’s modulus, Speed of sound, Verification of Ohm’s law, the specific resistance of the material x, Units and dimensions. Methods of measurement and error analysis, Specific heat of a liquid, the focal length of a concave mirror and a convex lens using the u-v method, Dimensional analysis, |
Thermal Physics | Thermal expansion of solids Elementary concepts of convection and radiation, Newton's law of cooling, Kirchhoff’s law Specific heats (Cv and Cp for monoatomic and diatomic gases) Ideal gas laws Equivalence of heat and work, Stefan’s law. The first law of thermodynamics Blackbody radiation: absorptive and emissive powers Wien’s displacement law Isothermal and adiabatic processes, the bulk modulus of gases |
Optics | Rectilinear propagation of light; The different phenomenon of light, Wave nature of light |
Modern Physics | Atomic nucleus Bohr’s theory of hydrogen-like atoms; Photoelectric effect; Moseley’s law; Characteristic and continuous X-rays, de Broglie wavelength of matter waves. |
Electricity and Magnetism | Topics related to Coulomb’s law, Capacitance and related concepts; Electric current Biot–Savart’s law and Ampere’s law; Magnetic field by different objects The magnetic moment of different objects, Electromagnetic induction and related topics. |
Mechanics | Kinematics in one and two dimensions, Newton’s laws of motion and related topics, Systems of particles Law of gravitation, Escape velocity. Rigid body, parallel and perpendicular axes theorems, a moment of inertia of uniform bodies momentum; Dynamics of rigid bodies; cylinders and spheres; Equilibrium of rigid bodies; Linear and angular simple harmonic motions. The vibration of strings Pressure in a fluid; Pascal’s law, Stoke’s law; Bernoulli’s theorem and its applications. Wave motion (plane waves only), Progressive and stationary waves; Speed of sound in gases; Doppler effect (in sound). Torque; Conservation of angular momentum, Rolling without slipping of rings, Collision of point masses with rigid bodies, Hooke’s law, Young’s modulus. Terminal velocity, Streamline flow, equation of continuity, longitudinal and transverse waves, superposition of waves; |
Sections | Topics |
General Topics | Dalton’s atomic theory Chemical formulae Concept of atoms and molecules Balanced equations oxidation-reduction, neutralization, and displacement reactions Mole concept mole fraction, molarity, molality and normality. |
Gaseous and Liquid State | Deviation from ideality, van der Waals equation Kinetic theory of gases Law of partial pressures Diffusion of gases. ideal gas equation The absolute scale of temperature, |
Atomic Structure and Chemical Bonding | The spectrum of the hydrogen atom, Wave-particle duality, Bohr model, Qualitative quantum mechanical picture of the hydrogen atom, Aufbau principle de Broglie hypothesis Uncertainty principle Hybridisation Orbital energy diagrams for homonuclear diatomic species Hydrogen bond Pauli’s exclusion principle and Hund’s rule Orbital overlap and covalent bond Polarity in molecules, dipole moment (qualitative aspects only) VSEPR model |
Energetics | The first law of thermodynamics The second law of thermodynamics The criterion of spontaneity. Internal energy, work and heat, pressure-volume work Enthalpy, Hess’s law The heat of reaction, fusion and vapourization Entropy Free energy |
Chemical Equilibrium | Law of mass action Equilibrium constant, Le Chatelier’s principle (effect of concentration, temperature and pressure) Significance of ΔG and ΔG0 in chemical equilibrium Solubility product, 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 Nernst equation and its relation to ΔG Electrochemical series, emf of galvanic cells Faraday’s laws of electrolysis Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law Concentration cells. |
Chemical Kinetics | Rates of chemical reactions Order of reactions Rate constant First-order reactions Temperature dependence of the rate constant (Arrhenius equation). |
Solid State | Classification of solids, crystalline state, seven crystal systems (cell parameters a, b, c, α, β, γ), the close-packed structure of solids (cubic), packing in fcc, bcc and hcp lattices Nearest neighbours, ionic radii, simple ionic compounds, point defects. |
Solutions | Raoult’s law Molecular weight determination from lowering of vapour pressure, the elevation of boiling point and depression of freezing point. |
Surface Chemistry | Elementary concepts of adsorption (excluding adsorption isotherms) Colloids: types, methods of preparation and general properties Elementary ideas of emulsions, surfactants, and micelles (only definitions and examples). |
Nuclear Chemistry | Radioactivity Isotopes and isobars Properties of α, β and γ rays Kinetics of radioactive decay (decay series excluded), carbon dating Stability of nuclei with respect to proton-neutron ratio A brief discussion on fission and fusion reactions. |
Sections | 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 |
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. |
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. |
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). |
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 centres, (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-enoltautomerism 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. |
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