Jee Advanced Syllabus

One of the Indian Institute of Technology would conduct the Joint Entrance Examination under the guidance of Joint Admission Board (JAB) for admissions into the most prestigious engineering colleges of the country. The JEE ADVACNCED exam is a door to get into the Bachelor’s or Integrated Master’s Programme’s of IITs and some other Institutes. Only those students are allowed to attempt JEE ADVANCED who have cleared the JEE MAINS exam conducted by the National Testing Agency. The application for the exam will begin after the result of JEE MAIN is announced. The exam is now conducted in ONLINE mode and is available only in Hindi and English.

Syllabus of JEE ADVANCED is divided into three sections namely PHYSICS, CHEMISTRY and MATHEMATICS. Section wise syllabus is given below:

1. Physics

1.1 Mechanics:

Kinematics in one and two dimensions (Cartesian coordinates only)
Projectile Motion, 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, Impulse
Systems of particles
Centre of mass and its motion
Elastic and inelastic collisions
Law of gravitation, Gravitational Potential and Field
Acceleration due to gravity, Motion of planets and satellites in circular orbits
Escape velocity
Rigid body moment of inertia
Parallel and perpendicular axes theorems
Moment of inertia of uniform bodies with simple geometrical shapes
Angular momentum, Conservation of angular momentum
Equilibrium of rigid bodies
Dynamics of rigid bodies with fixed axis of rotation
Torque
Rolling without slipping of rings
Cylinders and Spheres
Collision of point masses with rigid bodies
Linear and angular simple harmonic motions
Hooke’s law, Young’s modulus
Pressure in a fluid, Pascal’s law, Buoyancy
Surface energy and surface tension
Capillary rise
Stoke’s law, Viscosity (Poiseuille’s equation excluded)
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 gas, Doppler Effect;

1.2 Thermal Physics:

Thermal expansion of solids, liquids and gases;
Calorimetry, Latent Heat
Heat conduction in one dimension
Newton’s law of cooling;
Elementary concepts of convection and radiation;
Ideal gas laws, Specific heats (Cv and Cp for monoatomic and diatomic gases)
Bulk modulus of gases;
Isothermal and adiabatic processes, Equivalence of heat and work;
First law of thermodynamics and its applications (only for ideal gases);
Blackbody radiation: absorptive and emissive powers;
Kirchhoff’s law;
Wien’s displacement law, Stefan’s law;

1.3 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
RC, LR and LC circuits with d.c. and a.c. sources.
Effect of a uniform magnetic field on a current loop;
Self and mutual inductance
Moving coil galvanometer, voltmeter, ammeter and their conversions;
Electromagnetic induction: Faraday’s law, Lenz’s law;

1.4 Optics:

Rectilinear propagation of light;
Total internal reflection;
Reflection and refraction at plane and spherical surfaces;
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

1.5 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;
de Broglie wavelength of matter waves;
Characteristic and continuous X-rays, Moseley’s law;

1.6 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 by Searle’s method, 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

2. CHEMISTRY

2.1 Physical Chemistry

(a). General topics

Concept of atoms and molecules, Dalton’s atomic theory, Mole concept; Chemical formulae, Balanced chemical equations
Calculations (based on mole concept) involving common oxidation-reduction,
Neutralisation and Displacement Reactions
Concentration in terms of Mole Fraction, Molarity, Molality and Normality

(b). Gaseous and liquid states

Absolute scale of temperature, ideal gas equation
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, Vapour pressure, Diffusion of gases;

(c). Atomic structure and chemical bonding

Bohr model, spectrum of hydrogen atom, quantum numbers;
Wave-particle duality, de Broglie hypothesis;
Uncertainty principle,
Qualitative quantum mechanical picture of hydrogen atom, shapes of s, p and d orbitals; Electronic configurations of elements (up to atomic number 36);
Aufbau principle, Pauli’s exclusion principle and Hund’s rule;
Orbital overlap and covalent bond
Hybridisation involving s, p and d orbitals only
Orbital energy diagrams for homonuclear diatomic species; Hydrogen bond;
Polarity in molecules, dipole moment (qualitative aspects only)
VSEPR model and shapes of molecules:
(linear, angular, triangular, square planar, pyramidal, square pyramidal, trigonal bipyramidal, tetrahedral and octahedral).

(d). Energetics

First law of thermodynamics
Internal energy, work and heat, pressure-volume work; Enthalpy, Hess’s law
Heat of reaction, fusion and vapourization;
Second law of thermodynamics;
Entropy;
Free energy
Criterion of spontaneity

(e). 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;

(f). 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;
Concentration cells;
Electrolytic conductance, specific, equivalent and molar conductivity, Kohlrausch’s law;

(g). Chemical kinetics

Rates of chemical reactions;
Order of reactions
Rate constant;
First order reactions
Temperature dependence of rate constant (Arrhenius equation)

(h). 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 neighbor,
Ionic radii,
Simple ionic compounds
Point Defects

(i). Solutions

Raoult’s law;
Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point

(j). 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)

(k). 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
Brief discussion on fission and fusion reactions

2.2 Organic Chemistry

(a). 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.

(b). 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

(c). 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

(d). 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.

(e).Phenols

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

(f). 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).

(g). Carbohydrates

Classification; mono- and di-saccharides (glucose and sucrose)
Oxidation, reduction, glycoside formation and hydrolysis of sucrose

(h). 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.

(i). 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

2.3 Inorganic Chemistry

(a). 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

(b). 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

(c). 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)

(d). 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

(e). Ores and minerals

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

(f). Extractive metallurgy

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

(g). 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

3. Mathematics

3.1 Algebra

Algebra of complex numbers, addition, multiplication, conjugation, polar representation, properties of modulus and principal argument, triangle inequality, cube roots of unity, geometric interpretations.
Quadratic equations with real coefficients, relations between roots and coefficients, formation of quadratic equations with given roots, symmetric functions of roots
Arithmetic, geometric and harmonic progressions, arithmetic, geometric and harmonic means, sums of finite arithmetic and geometric progressions, infinite geometric series, 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

3.2 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,
Determinant of a square matrix of order up to three, 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

3.3 Probability

Addition and multiplication rules of probability,
Conditional probability
Bayes Theorem and independence of events
Computation of probability of events using permutations and combinations

3.4 Trigonometry

Trigonometric functions, their periodicity and graphs, addition and subtraction formulae, formulae involving multiple and sub-multiple angles, general solution of trigonometric equations
Relations between sides and angles of a triangle, sine rule, cosine rule, half-angle formula and the area of a triangle, inverse trigonometric functions (principal value only)

3.5 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: Direction cosines and direction ratios, equation of a straight line in space, equation of a plane, distance of a point from a plane.

3.6 Differential Calculus

Real valued functions of a real variable, into, onto and one-to-one functions, sum, difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions
Limit and 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
Even and odd functions, inverse of a function, 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
Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals, increasing and decreasing functions, maximum and minimum values of a function, Rolle’s theorem and Lagrange’s mean value theorem

3.7 Integral Calculus

Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals 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 involving simple curves
Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, linear first order differential equations

3.8 Vectors

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