SYLLABUS
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 (micrometre),
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, ß 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.
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.
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.
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? G and ?G0 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
?G; 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, a, ß, 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 a, ß 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; s and
p-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 hyper conjugation;
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).
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.
