IIT-JEE Advanced-2021- Syllabus

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

Matrices as a rectangular array of real numbers

Equality of matrices

Addition and 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

Probability

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 and 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)

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

In centre 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 and 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's 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, its geometrical and physical significance

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

Definite integrals and their properties

Fundamental theorem of integral calculus

Integration by parts

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

Physical chemistry

General topics

Concept of atoms and molecules

Dalton's atomic theory

Mole concept

Chemical formula

Balanced chemical equations

Calculations 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

Orbital energy diagrams for homonuclear diatomic species

Hydrogen bond

Polarity in molecules

Dipole moment

VSEPR model and shapes of molecules

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

Chemical equilibrium

Law of mass action

Equilibrium constant

Le Chatelier's principle

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 conductivity

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 rate constant (Arrhenius equation)

Solid state

Solid state: Classification of solids

Crystalline state

Seven crystal systems (cell parameters a, b, c, α, β, γ)

Close packed structure of solids

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

Elevation of boiling point and depression of freezing point

Surface chemistry

Elementary concepts of adsorption

Colloids: types, methods of preparation and general properties

Elementary ideas of emulsions, surfactants and micelles

Nuclear chemistry

Radioactivity

Isotopes and Isobars

Properties of α, β and γ rays

Kinetics of radioactive decay

Carbon dating

Stability of nuclei with respect to proton-neutron ratio

Brief discussion on fission and fusion reactions

Inorganic chemistry

Isolation/preparation and properties of the following non-metals

Boron

Silicon: silicones, silicates and silicon carbide

Nitrogen

Phosphorus

Oxygen

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

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

Properties of allotropes

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

Preparation and properties of 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

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 thiosulfate

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

Co-ordination compounds: nomenclature of mononuclear coordination compounds, cistrans and ionisation isomerisms, hybridization and geometries of mononuclear coordination compounds (linear, tetrahedral, square planar 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

Carbon reduction method (iron and tin)

Self-reduction method copper (copper and lead)

Electrolytic reduction method (magnesium and aluminium)

Cyanide process (silver and gold)

Principles of qualitative analysis

Groups I to V elements (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

Σ and π-bonds

Shapes of simple organic molecules

Structural and geometrical isomerism

Optical isomerism of compounds containing up to two asymmetric centres

IUPAC nomenclature of simple organic compounds

Conformations of ethane and butane

Resonance and hyper conjugation

Keto-enol tautomerism

Determination of empirical and molecular formulae of simple compounds

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

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

Acidity of alkynes

Acid catalysed hydration of alkenes and alkynes

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 mono substituted benzenes

Phenols

Acidity

Electrophilic substitution reactions, halogenation, nitration, sulphonation, Friedel-Crafts alkylation and acylation

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

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

Physics

General

Units and dimensions

Dimensional analysis

Least count

Significant figures

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on using Vernier callipers and screw gauge

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on determination of g using simple pendulum

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on young's modulus by Searle's method

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on specific heat of a liquid using calorimeter

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on focal length of a concave mirror and a convex lens using u-v method

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on speed of sound using resonance column

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on verification of ohm's law using voltmeter and ammeter

Methods of measurement and error analysis for physical quantities pertaining to the experiments based on specific resistance of the material of a wire using meter bridge and post office box

Mechanics

Kinematics in one and two dimensions

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

Stoke's law

Terminal velocity

Streamline flow

Equation of continuity

Bernoulli's theorem and its applications

Wave motion, phase, amplitude and velocity of wave

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

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 (current electricity)

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, self and mutual induction

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 theory for propagation of light and rectilinear propagation of light

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

Architecture aptitude test

Freehand drawing

This would comprise of simple drawing depicting the total object in its right form and proportion, surface texture, relative location and details of its component parts in appropriate scale

Common domestic or day-to-day life usable objects like furniture, equipment etc. from memory

Geometrical drawing

Exercises in geometrical drawing containing lines, angles, triangles, quadrilaterals, polygons, circles, etc.

Study of plan

Elevation of simple solid objects like prisms, cones, cylinders, cubes, splayed surface holders, etc.

Three-dimensional perception

Understanding and appreciation of three-dimensional forms with building elements, colour, volume and orientation

Visualization through structuring objects in memory

Imagination and aesthetic sensitivity

Composition exercise with given elements

Context mapping

Creativity check through innovative uncommon test with familiar objects

Sense of colour grouping or application

Architectural awareness

General interest and awareness of famous architectural creations – both national and international, places and personalities (architects, designers, etc.) in the related domain