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.
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.
Wave nature of light: Huygen’s principle, interference limited to Young’s double-slit experiment.
Photoelectric effect;
Bohr’s theory of hydrogen-like atoms; Characteristic and continuous
X-rays, Moseley’s law; de Broglie wavelength of matter waves.
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 ΔG° 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, γ), 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 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.
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; Sigma and pi-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-enol tautomerism; 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 (X=halogen) and H2O; 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 Syllabus
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, 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, 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.
