The Syllabus for 2005 Joint Entrance Exam. It is common for the Screening Test and the Main Examination.
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 uv 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; Circular
motion (uniform and nonuniform); 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.
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 monatomic 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.
BiotSavart law and Ampere's law, magnetic field near a currentcarrying straight wire, along the axis of a
circular coil and inside a long straight solenoid; Force on a moving charge and on a currentcarrying 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 doubleslit experiment.
Modern physics: Atomic nucleus; Alpha, beta and gamma radiations; Law of radioactive decay; Decay
constant; Halflife and mean life; Binding energy and its calculation; Fission and fusion processes; Energy
calculation in these processes.
Photoelectric effect; Bohr's theory of hydrogenlike atoms; Characteristic and continuous Xrays, Moseley's
law; de Broglie wavelength of matter waves.
Chemistry
 Physical chemistry
 General topics: The 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;
Waveparticle duality, de Broglie hypothesis; Uncertainty principle; Quantum mechanical picture of hydrogen
atom (qualitative treatment), 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, pressurevolume 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 DG and DGo 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; Electrode potentials; Nernst equation and its
relation to DG; Electrochemical series, emf of galvanic cells; Faraday's laws of electrolysis; Electrolytic
conductance, specific, equivalent and molar conductance, 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, a, b,
g), 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 vapor 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 a, b and g rays; Kinetics of radioactive
decay (decay series excluded), carbon dating; Stability of nuclei with respect to protonneutron ratio;
Brief discussion on fission and fusion reactions.
Inorganic Chemistry
Isolation/preparation and properties of the following nonmetals: 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; Fertilizers: commercially available (common) NPK type.
Transition elements (3d series): Definition, general characteristics, oxidation states and their stabilities,
colour (excluding the details of electronic transitions) and calculation of spinonly 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).
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, sulphide and sulphite.
 Organic Chemistry
 Concepts: Hybridisation of carbon; Sigma and pibonds; Shapes of molecules; Structural and geometrical
isomerism; Optical isomerism of compounds containing up to two asymmetric centers, (R,S and E,Z
nomenclature excluded); IUPAC nomenclature of simple organic compounds (only hydrocarbons, mono
functional and bifunctional compounds); Conformations of ethane and butane (Newman projections);
Resonance and hyperconjugation; Ketoenol tautomerism; Determination of empirical and molecular formula
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, FriedelCrafts alkylation and acylation; Effect of o, m and pdirecting 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/
conc.HCl, conversion of alcohols into aldehydes and ketones; 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 disaccharides (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 monofunctional 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 skewsymmetric matrices and their properties, solutions of simultaneous linear equations in two or
three variables.
Addition and multiplication rules of probability, conditional probability, 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 submultiple 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 onetoone 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,
applications of 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, application of the 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, variables
separable method, linear first order differential equations.
 Vectors: Addition of vectors, scalar multiplication, scalar products, dot and cross products, scalar triple
products and their geometrical interpretations.
