JOINT ENTRANCE EXAMINATION ADVANCED (JEE ADVANCED) Syllabus 

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JOINT ENTRANCE EXAMINATION (ADVANCED)

CHEMISTRY
Physical chemistry
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.
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.
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).

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.
Organic chemistry
Concepts: Hybridisation of carbon;  and -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.
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.
MATHEMATICS
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.
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.
Addition and multiplication rules of probability, conditional probability, Bayes
Theorem, independence of events, computation of probability of events using
permutations and combinations.
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, halfangle
formula and the area of a triangle, inverse trigonometric functions
(principal value only).
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.
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.
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.
Vectors
Addition of vectors, scalar multiplication, dot and cross products, scalar triple
products and their geometrical interpretations.
PHYSICS
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.
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.
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; 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.
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; Viscosity (Poiseuille’s equation excluded), 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); 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 and LC circuits with d.c. and a.c. sources.
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.
Modern physics
Atomic nucleus; α, β and
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.