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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).

**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 (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 rate constant

(Arrhenius equation).

**Solid state:** Classification of solids, crystalline state, seven crystal systems (cell

parameters a, b, c, α, β, ), 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, 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

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.

**Inorganic chemistry**

**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, cis-trans

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.

**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.

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).

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.

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.

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.

Addition of vectors, scalar multiplication, dot and cross products, scalar triple

products and their geometrical interpretations.

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.

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