Mathematics
Algebra : Algebra of complex numbers, modulus and argument,
triangle inequality, nth roots of unity.
Theory of quadratic equations and quadratic expressions, relationship
between the roots and coefficients, sign of a quadratic expression,
greatest and least values of a quadratic expression.
Arithmetic, geometric and harmonic progressions, sums of arithmetic,
geometric and harmonic progressions, Infinite geometric series, sums of
the squares and cubes of the first n natural numbers.
Mathematical induction
Permutations and combinations, Binomial theorem for a positive integral
index.
Determinants of order two and three, solutions of simultaneous linear
equations in two and three variables.
Trigonometry : Trigonometric functions and their graphs,
addition and subtraction formulae, formulae involving multiple and
sub-multiple angles, general solution of trigonometric equations,
relations between the sides and angles of a triangle, properties of a
triangle, solutions of a triangles, heights and distances, trigonometric
functions.
Analytical geometry of two dimensions : 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,
concurrency of lines.
Equation of a circle in various forms, equations of tangent and normal,
intersection of a circle with a straight line, equation of a circle
through the points of intersection of two circles and that of a circle and
a straight line.
Equations of the conic sections in the standard form, focus, directrix,
eccentricity of the conic sections, parametric equations, equations of
tangent and normal.,
Calculus : Into, onto and one-to-one functions, Sum, difference,
product and quotient of two functions, composite function, absolute value,
greatest integer, polynomial, rational, trigonometric, exponential and
logarithmic functions, even and odd functions, inverse of a function.
Limit and continuity of a function, limit and continuity of the sum,
difference, product and quotient of two functions, continuity of composite
function, Derivative of a function, derivative of the sum, difference,
product and quotient of two functions, derivative of composite and
implicit functions, derivatives of polynomial, rational, trigonometric,
inverse trigonometric, exponential and logarithmic functions.
Geometrical interpretation of derivative, tangents and normals,
monotonicity, maximum and minimum values of a function.
Derivatives up to order three.
Integration: As the inverse process of differentiation,
integration by parts, integration by the methods of substitution and
partial fractions.
Definite integral and its applications for the determination of areas,
Properties of definite integrals.
Differential equations : Formation of differential equations, First
order equation, variable separable method and homogeneous equations.
Vectors : Addition of vectors, scalar product, cross product,
scalar and vector products.
Applications in geometry
Top
Physics
Units and dimensions : Displacement, velocity and acceleration,
Kinematics in one and two dimensions, Projectiles, Circular motion,
relative motion.
Newton's laws of motion : Inertial and uniformly accelerated
frames of reference; Force; Spring force; frictional force and
gravitational force. Static and dynamic frictions; Kinetic and potential
energy; Work and Power; Linear Momentum; Conservation of linear momentum
and energy; Linear and angular simple harmonic motions.
Law of gravitation : Gravitational potential and field, Acceleration
due to gravity; Motion of planets and satellites in circular orbits; Kepler's
laws.
Systems of particles : Centre of mass and its motion; Elastic and
inelastic collisions; Rigid bodies; Moment of inertia; Parallel and perpendicular
axes theorems; Moment of inertia of bodies having simple geometrical shapes,
e.g. , uniform ring, disc, thin rod and cylinder; Angular momentum; Torque;
equilibrium of rigid bodies; Conservation of angular momentum.
Hooke's law, Young's modulus, shear and bulk moduli.
Buoyancy : Pressure in a fluid, stream line flow, Bernoulli's theorem.
Wave motion : Concepts of amplitude, frequency and phase; Longitudinal
and transverse waves; Superposition of waves; Progressive and stationary waves;
Vibration of strings and air columns; Resonance; Beats; Speed of sound; echo;
Doppler effect (in sound).
Thermal expansion of solids, liquids and gases : Elements of the Kinetic
theory of gases, absolute temperature, Ideal gas laws, Pressure and temperature
of an ideal gas, Specific heats and their ratio, Isothermal and adiabatic
processes, First law of thermodynamics, Calorimetry, Latent heat, Equivalence
of heat and work.
Heat conduction in one dimension : Elementary concepts of convection
and radiation, Stefan's law of radiation, Wien's displacement law, Newton's
law of cooling, Black body radiation, absorptive and emissive powers,
Kirchhoff's law.
Coulomb's law : Electric field and potential, lines of force.
Capacitance : Dielectric constant, Parallel plate capacitor, 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 applications to networks, Charging
and discharging of capacitor, Heating effect of current.
Ampere's law and Biot-Savart law : Force on a moving charge and on
a current -carrying wire in a magnetic field.
Magnetic moment of a current loop : Effect of a uniform magnetic field
on a current loop, Moving coil galvanometer, voltmeter and ammeter.
Electromagnetic induction : Faraday's law, Lenz's law, Self and mutual
inductance, Growth and decay of current in an LR circuit, LC oscillation.
Rectilinear propagation of light : Reflection and refraction at
plane and curved surfaces, Total internal reflection, Deviation and
dispersion of light by a prism, Thin lenses, Combinations of mirrors and
thin lenses, spherical aberration, Magnification, Microscope and
telescope.
Wave nature of Light : Interference, Young's double slit
experiment, Fringe width.
Elementary concepts of diffraction by a single slit.
Alpha, beta and gamma radiations: law of radioactive decay, Decay
constant, Half-life and mean life, Photoelectric effect, DeBroglie
wavelength, Bohr's theory of hydrogen like atoms, Characteristic and
continuous X- rays.
Properties of X-rays. Atomic nucleus, binding energy and its
calculation, Fission and fusion processes, energy calculations in these
processes.
Elementary concepts of metals, insulators and semiconductors, Intrinsic
and extrinsic semi conductors p-n junction as a rectifier; transistors:
quantitative application as amplifier (in common emitter mode} and
oscillator.
Top
Chemistry
The concept of atoms and molecules : laws of chemical
combination, Mole concept, Chemical Formulae, Balanced Chemical equations,
Concentration in terms of mole fraction, Molarity, molality and normality.
Calculations involving common oxidation-reduction, neutralisation, and
displacement reactions.
Gaseous, liquid and solid states : Absolute scale of temperature,
Ideal gas equation, Deviation from ideality (compression factor, Z}; Van Der
Waal's equation; diffusion of gases, Kinetic theory of gases, Average, Root
mean square and most probable velocities and their relation with temperature,
law of partial pressure, Vapour pressure, surface tension and viscosity, Classification
of solids, crystalline state, seven crystal systems (only cell parameters
a, b, c, a, b, and g close packed structure of solids-only cubic}.
Packing fcc, bcc, hcp, nearest neighbours, simple ionic compounds,
point defects.
Atomic structure : Rutherford model, Spectrum of hydrogen atom,
Bohr model, de-Broglie relations, uncertainty principle, Quantum numbers,
Electronic configuration of elements (upto atomic number 36), Aufbau
Principle, Pauli's exclusion principle and Hund's rule, shapes of s, p,
and d orbitals.
Periodicity of properties of elements : Classification of
elements in s, p and d block, Periodicity in properties with respect to
atomic and ionic radii, Ionisation energy , Electron affinity,
Electronegativity , Oxidation state, Metallic and non-metallic character
and trends in reactivity .
Bonding and molecular structure : Lewis structures, Orbital
overlap and covalent bond, Hybridisation involving s, p and d orbitals
only, Co- ordinate covalent bond, Ionic bond, Hydrogen bond: Orbital
energy diagrams for diatomic species, polarity in molecules, dipole moment
(qualitative aspects only), VSEPR model, Molecular shape, linear, Angular,
Planar, pyramidal, Tetrahedral, and Octahedral, Square planar.
Energetics: First law of thermodynamics, Second law of
thermodynamics, Internal energy, Enthalpy, Hess's law, Heat of reaction,
fusion and vaporisation.
Chemical equilibrium : Chemical Equilibria, law of mass action,
Reaction quotient, Equilibrium constant, Relation between kp
and Kq, Le- chatelier's principle and its applications,
Dependence on concentration, Temperature and pressure, Solubility product,
Common ion effect.
Significance of DGo and
DGo
in chemical equilibrium, common ion effect, pH and buffer solutions, acids
and bases (Bronsted and Lewis), hydrolysis of salts.
Electrochemistry : Faraday's laws of electrolysis, Electrochemical
cells and cell reactions, Standard electrode potential and electrochemical
series, E.M.F. of a galvanic cell.
Nernst equation and DG.
Solutions : Raoult's law, molecular weight determination from lowering
of vapour pressure, elevation of boiling point and depression of freezing
point.
Chemical kinetics : Rates of chemical reactions, Order of reaction,
Rate constant, Effect of concentration and temperature.
Kinetics of first order reactions, Arrhenius equation.
Surface Chemistry : Elementary concepts in adsorption (excluding
adsorption isotherms), colloids, emulsions, surfactants and micelles
(definitions and examples only).
Nuclear chemistry : Radioactivity, properties of
a,
b and g rays, kinetics of radioactive
decay (decay series excluded), stability of nuclei with respect to
proton-neutron ratio.
Isolation/preparation and properties of the non-metals :
Nitrogen, phosphorus, oxygen, sulphur, fluorine, chlorine, bromine and
iodine. Properties of allotropes of carbon (graphite and diamond only);
preparation and properties of ozone.
Preparation and properties of the following compounds : Oxides,
hydroxides, carbonates, bicarbonates, chlorides and sulphates of sodium,
potassium, magnesium and calcium, alumina, aluminium chloride and alums,
hydrogen peroxide, carbon, oxides and carbides, nitrogen, oxides, oxyacids
and ammonia, phosphorus: oxides and oxyacids (meta- and orthophosphoric
acids), Boron, diborane, boric acid and borax, Silicon, silicones, silicon
carbides, silicates, Sulphur, oxides, sulphurous and sulphuric acids,
sodium thiosulphate and hydrogen sulphide, Halogens, hydrohalic acids,
oxyacids of chlorine, bleaching powder.
Fertilizers : commercially available (common) NPK type; Tin and lead,
Oxides and chlorides, Preparation and properties of XeF2 , XeF4
and XeF6 . Tansition elements (only the first row, 3d series):
Definition, Werners approach to coordination compounds, general characteristic
properties (viz. , variable oxidation states , colour (excluding the details
of electronic transition)] , calculation of spin-only magnetic moment, formation
of complexes (stereochemistry excluded) , nomenclature of simple coordination
compounds , valence bond approach to define geometries of coordination compounds
of linear, tetrahedral, octahedral and square planar geometries.
Preparation and properties of the following compounds : Ferrous sulphate,
ferric chloride, Potassium Permanganate, Potassium dichromate, Mohr's salt,
ferric oxide, copper sulphate, oxide and sulphate of zinc, Silver oxide, silver
nitrate, silver bromide, silver thiosulphate.
Principles of qualitative analysis : Group I to V excluding interfering
radicals.
Ores and minerals : Commonly occurring ores of iron, copper,
lead, magnesium and aluminium, tin and silver.
Extractive metallurgy (Chemical principles and reactions only,
industrial details excluded) : Carbon reduction method (iron, tin ), Self
reduction method (copper and lead), Electrolytic reduction method
(magnesium and aluminium) .
Cyanide process (silver, gold).
Concepts of hybridisation of Carbon : Sigma and pi-bonds; Resonance.
Homologous series. Structural and geometrical isomerism, Optical
isomerism of compounds containing one asymmetric centres only. Ketoenol
tautomerism IUPAC nomenclature of simple organic compounds (hydrocarbons
and mono functional compounds for Screening Test only).
Bifunctional compounds. Determination of empirical and molecular
formula of simple compounds (combustion method).
Inductive and resonance effects on acidity and basicity of acids and
bases respectively.
Hydrogen bonds and their effects on physical properties of alcohols and
carboxylic acids.
Polarity and inductive effects in alkyl halides : Reactive intermediates
produced during homolytic and heterolytic bond cleavage, Formation, structure
stability and reactivity of Alkyl carbocations and free radicals.
Physical properties of alkanes (mp, bp and density) : Combustion
and halogenation of alkanes. Preparation of alkanes by Wurtz coupling and
decarboxylation reaction.
Conformation of ethane.
Structure and physical properties of alkenes and alkynes (bp,
density, dipole moment) : Acidity of alkynes; Preparation of alkenes and
alkynes by elimination reaction. Electrophilic addition reaction of
alkenes with Br2, HBr, HOCl, and add catalyzed hydration
(Stereochemistry of addition and elimination excluded), Reactions of
alkene with KMnO4 and Ozone, Reactions of alkynes, Metal
acetylides, reduction and hydration
Benzene : Structure and aromaticity, Electrophilic substitution reactions,
bromination, nitration, sulfonation (orientation excluded for Screening test
only), Phenols, acidity, electrophilic reaction (halogenation, nitration and
sulphonation).
Friedel Crafts alkylation and acylation. Effect of 0, m, p directing
groups in mono substituted benzenes.
Characteristic reactions of the following : Alcohol (esterification,
dehydration and oxidation), Reaction of alcohols with sodium, phosphorus
halides, ZnCl2/Conc.HCl.Alkyl halides (nucleophilic
substitution reactions), rearrangement of alkyl carbocations), Aldehydes
and ketones (oxidation, reduction, oxime and hydrazone formation, Aldol
condensation, Perkin reaction, Canizzaro reaction, haloform and Grignard
reaction only), Carboxylic acids (formation of esters, acid chlorides and
amides).
Phenol : Acidity of phenols, halogenation, nitration, sulfonation
and Riemer-tiemann reaction. Amines: Basicity of aniline and aliphatic amine,
Preparation from nitro compounds, reaction with nitrous acid, formation and
reactions of diazonium salts, and its coupling with, phenols, carbylamine
reaction. Nucleophilic aromatic substitution in haloarenes and substituted
haloarenes (excluding Benzyne mechanism and Cine substitution).
Carbohydrates : Classification -mono, di and polysaccharides (glucose,
sucrose and starch only), hydrolysis of sucrose.
Top
