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.

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).

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.

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.

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

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 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

First law of thermodynamics and its applications (only for ideal gases)

Specific heats (Cv and Cp for monoatomic and diatomic gases)Blackbody radiation: absorptive and emissive powers; Kirchhoff's law Wien's displacement law, Stefan's law.

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.

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.

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,

neutralization, and displacement

reactions

Concentration in terms of mole fraction,

molarity, molality and normality.

Absolute scale of temperature, ideal gas

equation

Deviation from ideality, van der Waals

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

Bohr model, spectrum of hydrogen atom, quantum numbers

Wave-particle duality, de

BrogliEhypothesis

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).

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.

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.

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.

Rates of chemical reactions

Order of reactions

Rate constant

First order reactions

Temperature dependence of the rate

constant (Arrhenius equation)

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

Raoult’s law

Molecular weight determination from lowering of vapour pressure, elevation of boiling point and depression of freezing point.

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

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

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

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.

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)

Oxides and chlorides of tin and lead

Oxides, chlorides and sulphates of Fe2+

pressure-volume workCu2+ and Zn2+

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

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).

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.

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

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.

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.

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

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).

Classification

Mono- and di-saccharides (glucose and sucrose)

Oxidation, reduction, glycoside formation and hydrolysis of sucrose.

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.

Understanding and appreciation of three-dimensional forms with building elements, colour, volume and orientation.Visualization through structuring objects in memory