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MATHEMATICS
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Sets,
Relations and Functions : Sets and their Representations,
Union, intersection and complements of sets, and their
algebraic properties, Relations, equivalence relations,
mappings, one-one, into and onto mappings, composition of
mappings.
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Complex
Numbers : Complex numbers in the form a+ib and their
representation in a plane. Argand diagram. Algebra of complex
numbers, Modulus and Argument (or amplitude) of a complex
number, square root of a complex number. Cube roots of unity,
triangle inequality.
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Matrices
and Determinants : Determinants and matrices of order two
and three, properties of determinants, Evaluation of
determinants. Area of triangles using determinants, Addition
and multiplication of matrices, adjoint and inverse of matrix.
Test of consistency and solution of simultaneous linear
equations using determinants and matrices
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Quadratic
Equations : Quadratic equations in real and complex number system and their
solutions. Relation between roots and co-efficients, nature of roots, formation
of quadratic equations with given roots; Symmetric functions of roots, equations
reducible to quadratic equations – application to practical problems
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Permutations
and Combinations : Fundamental principle of counting;
Permutation as an arrangement and combination as selection,
Meaning of P(n,r) and C(n,r). Simple applications.
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Mathematical
Induction and its Applications
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Binomial
Theorem and its Applications : Binomial Theorem for a
positive integral index; general term and middle term;
Binomial Theorem for any index. Properties of Binomial Co-efficients.
Simple applications for approximations.
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Sequences
and Series : Arithmetic, Geometric and Harmonic
progressions. Insertion of Arithmetic Geometric and Harmonic
means between two given numbers. Relation between A.M., G.M.
and H.M.Special series: Ón, Ón2, Ón3 . Arithmetico-Geometric
Series, Exponential and Logarithmic series.
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Differential
Calculus : Polynomials, rational, trigonometric,
logarithmic and exponential functions, Inverse functions.
Graphs of simple functions. Limits, Continuity;
differentiation of the sum, difference, product and quotient
of two functions. differentiation of trigonometric, inverse
trigonometric, logarithmic, exponential, composite and
implicit functions; derivatives of order upto two.
Applications of derivatives: Rate of change of quantities,
monotonic - increasing and decreasing functions, Maxima and
minima of functions of one variable, tangents and normals,
Rolle’s and Lagrange’s Mean Value Theorems.
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Integral
Calculus : Integral as an anti-derivative. Fundamental
integrals involving algebraic, trigonometric, exponential and
logarithmic functions. Integration by substitution, by parts
and by partial fractions. Integration using trigonometric
identities. Integral as limit of a sum. Properties of definite
integrals. Evaluation of definite integrals; Determining areas
of the regions bounded by simple curves.
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Differential
Equations : Ordinary differential equations, their order
and degree. Formation of differential equations. Solution of
differential equations by the method of separation of
variables. Solution of homogeneous and linear differential
equations, and those of the type d2y/dx2 = f(x)
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Two
Dimensional Geometry : Recall of Cartesian system of
rectangular
co-ordinates in a plane, distance formula, area of a triangle,
condition for the collinearity of three points and section
formula, centroid and in-centre of a triangle, locus and its
equation, translation of axes, slope of a line, parallel and
perpendicular lines, intercepts of a line on the coordinate
axes.
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The
straight line and pair of straight lines: Various
forms of equations of a line, intersection of lines,
angles between two lines, conditions for concurrence of
three lines, distance of a point from a line Equations of
internal and external bisectors of angles between two
lines, coordinates of centroid, orthocentre and
circumcentre of a triangle, equation of family of lines
passing through the point of intersection of two lines,
homogeneous equation of second degree in x and y, angle
between pair of lines through the origin, combined
equation of the bisectors of the angles between a pair of
lines, condition for the general second degree equation to
represent a pair of lines, point of intersection and angle
between two lines.
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Circles
and Family of Circles : Standard form of equation of a
circle, general form of the equation of a circle, its
radius and centre, equation of a circle in the parametric
form, equation of a circle when the end points of a
diameter are given, points of intersection of a line and a
circle with the centre at the origin and condition for a
line to be tangent to the circle, length of the tangent,
equation of the tangent, equation of a family of circles
through the intersection of two circles, condition for two
intersecting circles to be orthogonal.
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Conic
Sections : Sections of cones, equations of conic
sections (parabola, ellipse and hyperbola) in standard
forms, condition for y = mx + c to be a tangent and
point(s) of tangency.
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Three
Dimensional Geometry : Coordinates of a point in
space, distance between two points; Section formula, direction
ratios and direction cosines, angle between two intersecting
lines. Skew lines, the shortest distance between them and its
equation. Equations of a line and a plane in different forms;
intersection of a line and a plane, coplanar lines, equation
of a sphere, its centre and radius. Diameter form of the
equation of a sphere.
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Vector
Algebra : Vectors and Scalars, addition of vectors,
components of a vector in two dimensions and three dimensional
space, scalar and vector products, scalar and vector triple
product. Application of vectors to plane geometry.
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Measures
of Central Tendency and Dispersion : Calculation of Mean,
median and mode of grouped and ungrouped data. Calculation of
standard deviation, variance and mean deviation for grouped
and ungrouped data.
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Probability
: Probability of an event, addition and multiplication
theorems of probability and their applications; Conditional
probability; Bayes’ Theorem, Probability distribution of a
random variate; Binomial and Poisson distributions and their
properties.
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Trigonometry
: Trigonometrical identities and equations. Inverse
trigonometric functions and their properties. Properties of
triangles, including centroid, incentre, circum- centre and
orthocentre, solution of triangles. Heights and Distances
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Statics
: Introduction, basic concepts and basic laws of
mechanics, force, resultant of forces acting at a point,
parallelogram law of forces, resolved parts of a force,
Equilibrium of a particle under three concurrent forces,
triangle law of forces and its converse, Lami’s theorem and
its converse, Two parallel forces, like and unlike parallel
forces, couple and its moment.
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Dynamics
:Speed and velocity, average speed, instantaneous speed,
acceleration and retardation, resultant of two velocities.
Motion of a particle along a line, moving with constant
acceleration. Motion under gravity. Laws of motion, Projectile
motion.
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PHYSICS
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Units
and Measurement : Units for measurement, system of units
– S.I., fundamental and derived units. Dimensions and their
applications.
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Description
of Motion in One Dimension : Motion in a straight line,
uniform and non-uniform motion, their graphical
representation. Uniformly accelerated motion, and its
applications
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Description
of Motion in Two and Three Dimensions : Scalars and
vectors, vector addition, a real number, zero vector and its
properties. Resolution of vectors. Scalar and vector products,
uniform circular motion and its applications projectile
motion.
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Laws
of Motion : Force and inertia – Newton ’s Laws of
Motion. Conservation of linear momentum and its applications,
rocket propulsion, friction – laws of friction
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Work,
Energy and Power : Concept of work, energy and power.
Energy – kinetic and potential. Conservation of energy and
its applications, Elastic collisions in one and two
dimensions. Different forms of energy.
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Rotational
Motion and Moment of Inertia : Centre of mass of a
two-particle system. Centre of mass of a rigid body, general
motion of a rigid body, nature of rotational motion, torque,
angular momentum, its conservation and applications. Moment of
Inertia, parallel and perpendicular axes theorem, expression
of moment of inertia for ring, disc and sphere.
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Gravitation
: Acceleration due to gravity, one and two-dimensional
motion under gravity. Universal law of gravitation, variation
in the acceleration due to gravity of the earth. Planetary
motion, Kepler’s laws, artificial satellite –
geostationary satellite, gravitational potential energy near
the surface of earth, gravitational potential and escape
velocity.
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Solids
and Fluids : Inter-atomic and Inter-molecular forces,
states of matter. (A) Solids : Elastic properties,
Hook’s law, Young’s modulus, bulk modulus, modulus of
rigidity. (B) Liquids : Cohesion and adhesion. Surface
energy and surface tension. Flow of fluids, Bernoulli’s
theorem and its applications. Viscosity, Stoke’s Law,
terminal velocity.
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Oscillations
: Periodic motion, simple harmonic motion and its equation
of motion, energy in S.H.M., Oscillations of a spring and
simple pendulum.
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Waves
: Wave motion, speed of a wave, longitudinal and
transverse waves, superposition of waves, progressive and
standing waves, free and forced Oscillations, resonance,
vibration of strings and air-columns, beats, Doppler effect.
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Heat
and Thermodynamics : Thermal expansion of solids, liquids
and gases and their specific heats, Relationship between Cp
and Cv for gases, first law of thermodynamics, thermodynamic
processes. Second law of thermodynamics, Carnot cycle,
efficiency of heat engines.
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Transference
of Heat : Modes of transference of heat. Thermal
conductivity. Black body radiations, Kirchoff’s Law, Wien’s
law, Stefan’s law of radiation and Newton ’s law of
cooling.
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Electrostatics
: Electric charge – its unit and conservation, Coulomb’s
law, dielectric constant, electric field, lines of force,
field due to dipole and its behaviour in a uniform electric
field, electric flux, Gauss’s theorem and its applications.
Electric potential, potential due to a point charge.
Conductors and insulators, distribution of charge on
conductors. Capacitance, parallel plate capacitor, combination
of capacitors, energy of capacitor.
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Current
Electricity : Electric current and its unit, sources of
energy, cells- primary and secondary, grouping of cells
resistance of different materials, temperature dependence,
specific resistivity, Ohm’s law, Kirchoff’s law, series
and parallel circuits. Wheatstone Bridge with their
applications and potentiometer with their applications.
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Thermal
and Chemical Effects of Currents : Heating effects of
current, electric power, simple concept of thermo-electricity
– Seeback effect and thermocouple, Chemical effect of
current – Faraday’s laws of electrolysis.
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Magnetic
Effects of Currents : Oersted’s experiment, Bio-Savert’s
law, magnetic field due to straight wire, circular loop and
solenoid, force on a moving charge in a uniform magnetic field
(Lorentz force), forces and torques on currents in a magnetic
field, force between two current carrying wires, moving coil
galvanometer and conversion to ammeter and voltmeter.
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Magnetostatics
: Bar magnet, magnetic field, lines of force, torque on a
bar magnet in a magnetic field, earth’s magnetic field, para,
dia and ferro magnetism, magnetic induction, magnetic
susceptibility.
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Electromagnetic
Induction and Alternating Currents : Induced e.m.f.,
Faraday’s Law, Lenz’s Law, Self and Mutual Inductance,
alternating currents, impedance and reactance, power In a.c.
Circuits with L.C. And R Series Combination, resonant
circuits. Transformer and A.C. generator.
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Ray
Optics : Reflection and refraction of light at plane and
curved surfaces, total internal reflection, optical fibre;
deviation and dispersion of light by a prism; Lens formula,
magnification and resolving power; microscope and telescope.
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Wave
Optics : Wave nature of light; Interference – Young’s
double slit experiment. Diffraction - diffraction due to a
single slit. Elementary idea of polarization.
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Electromagnetic
Waves : Electromagnetic waves and their characteristics,
Electromagnetic wave spectrum from gamma to radio waves –
propagation of EM waves in atmosphere.
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Electron
and Photons : Charge on an electron, e/m for an electron,
photoelectric effect and Einstein’s equation of
photoelectric effect.
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Atoms,
Molecules and nuclei : Alpha - particles scattering
experiment, Atomic masses, size of the nucleus; radioactivity;
Alpha, beta and gamma particles/ rays and their properties,
radioactive decay law, half life and mean life of radio-active
nuclei, binding energy, mass energy relationship, nuclear
fission and nuclear fusion.
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Solids
and Semi-conductors Devices : Energy bands in solids,
conductors, insulators and semi-conductors, pn junction,
diodes, diode as rectifier, transistor action, transistor as
an amplifier.
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CHEMISTRY
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Some
Basic Concepts : Measurement in chemistry (Precision,
significant figures, SI units, Dimensional analysis). Laws of
chemical combination. Atomic Mass, Molecular Mass, mole
concept, Molar Mass, determination of Molecular formula.
Chemical equation, stoichiometry of Chemical reactions.
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States
of Matter : Gaseous state, measurable properties of gases,
Boyle’s Law, Charle’s Law and absolute scale of
temperature, Avogadro’s hypothesis, ideal gas equation,
Dalton’s law of partial pressures.
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Kinetic
molecular theory of gases (the microscopic model of gas),
deviation form ideal behaviour.
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The
solid state (classification of solids, X-ray studies of
crystal lattices and unit cells, packing of constituent
particles in crystals). Imperfection in solids, electrical,
magnetic and dielectic properties of solids. Liquid state
(Properties of liquids, Vapour pressure, Surface tension,
Viscosity).
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Atomic
Structure : Constituents of the atom (discovery of
electron, rutherford model of the atom).
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Electronic
structure of atoms – nature of light and electromagnetic
waves, atomic spectra, bohr’s model of hydrogen,
shortcomings of the bohr model
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Dual
nature of matter and radiation. de-Broglie relation. The
uncertainty principle, Quantum Mechanical Model of the atom,
Orbitals and Quantum numbers. Shapes of orbitals. Aufbau
principle, Pauli Exclusion Principle, Hund’s Rule,
Electronic Configuration of atoms.
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Solutions
: Types of solutions, Units of concentration, Vapour-pressure
of solutions and Raoult’s law. Colligative properties.
Determination of molecular mass. Non-ideal solutions and
abnormal molecular masses. Volumetric analysis-concentration
unit.
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Chemical
Energetics and Thermodynamics : Energy changes during a
chemical reaction, Internal energy and Enthalpy, Internal
energy and Enthalpy changes, Origin of Enthalpy change in a
reaction, Hess’s Law of constant heat summation, numericals
based on these concepts. Enthalpies of reactions(Enthalpy of
neutralization, Enthalpy of combustion, Enthalpy of fusion and
vaporization).
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Sources
of energy (conservation of energy sources and identification
of alternative sources, pollution associated with consumption
of fuels. The sun as the primary source).
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First
law of thermodynamics; Relation between Internal energy and
Enthalpy, application of first law of thermodynamics.
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Second
law of thermodynamics : Entropy, Gibbs energy, Spontaneity
of a chemical reaction, Gibbs energy change and chemical
equilibrium, Gibbs energy available for useful work.
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Chemical
Equilibrium : Equilibria involving physical changes
(solid-liquid, liquid-gas equilibrium involving dissolution of
solids in liquids, gases in liquids, general characteristics
of equilibrium involving physical processes).
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Equilibria
involving chemical systems (the law of chemical equilibrium,
the magnitude of the equilibrium constant, numerical
problems).
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Effect
of changing conditions of systems at equilibrium (change of
concentration, change of temperature, effect of catalyst-Le
Chateliar’s principle).
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Equilibria
involving ions — ionization of electrolytes, weak and strong
electrolytes, acid-base equilibrium, various concepts of acids
and bases, ionization of water, pH scale, solubility product,
numericals based on these concepts.
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Redox
Reactions and Electrochemistry : Oxidation and reduction
as an electron transfer concept. Redox reactions in aqueous
solutions-electrochemical cells. EMF of a galvanic cell.
Dependence of EMF on concentration and temperature (NERNST
equation and numerical problems based on it). Electrolysis,
Oxidation number (rules for assigning oxidation number, redox
reactions in terms of oxidation number, nomenclature).
Balancing of oxidation-reduction equations.
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Electrolytic
conduction. Molar conductivity, Kohlrausch’s Law and its
applications, Voltaic cell, Electrode potential and
Electromotive force, Gibb’s energy change and cell
potential. Electrode potential and products of electrolysis,
Fuel cells, corrosion and its prevention.
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Rates
of Chemical Reactions and Chemical Kinetics : Rate of
reaction, Instantaneous rate of reaction and order of
reaction. Factors affecting rates of reactions - factors
affecting rate of collisions encountered between the reactant
molecules, effect of temperature on the reaction rate, concept
of activation energy, catalyst. Effect of light on rates of
reactions. Elementary reactions as steps to more complex
reactions. How fast are chemical reactions?
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Rate
law expression. Order of a reaction (with suitable examples).
Units of rates and specific rate constants. Order of reaction
and effect of concentration (study will be confined to first
order only). Temperature dependence of rate constant – Fast
reactions (only elementary idea). Mechanism of reaction (only
elementary idea). Photochemical reactions.
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Surface
Chemistry : Surfaces : Adsorption – Physical and
chemical adsorption, adsorption isotherms Colloids –
Preparation and general properties, Emulsions, Micelles
Catalysis : Homogeneous and heterogeneous, structure of
catalyst, Enzymes, Zeolites
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Chemical
Families – Periodic Properties : Modern periodic law,
Types of elements – Representative elements (s & p
block), Transition elements –d-block elements, inner
transition elements – f-block elements). Periodic trends in
properties – ionization enthalpy, electron gain enthalpy,
atomic radii, valence, periodicity in properties of
compounds).
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Chemical
Bonding and Molecular Structure : Chemical bonds and Lewis
structure, shapes of molecules (VSEPR theory). Quantum theory
of the covalent bond, hydrogen and some other simple
molecules, carbon compounds, hybridization, Boron and
Beryllium compounds.
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Coordinate
covalent bond, ionic bond as an extreme case of polar covalent
bond, ionic character of molecules and polar molecules.
Bonding in solid state ionic, molecular and covalent solids,
metals). Hydrogen bond, Resonance.
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Molecules:
Molecular orbital. Theory – bond order and magnetic
properties of H2, O2, N2, F2 on the basis of MOT.
Hybridisation involving s, p and d orbitals (including shapes
of simple organic molecules), Dipole moment and structure of
molecules.
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Chemistry
of Non-metals – I : Hydrogen ( unique position in
periodic table, occurrence, isotopes, properties, reactions
and uses), Hydrides – molecular, soline and interstitial
Oxygen (occurrence, preparation, properties and reactions,
uses), simple oxides; ozone. Water and hydrogen peroxide,
structure of water molecule and its aggregates, physical and
chemical properties of water, hard and soft water, water
softening, hydrogen peroxide – preparation, properties,
structure and uses. Nitrogen – Preparation, properties,
uses, compounds of Nitrogen – Ammonia, Oxides of Nitrogen,
Nitric Acid – preparation, properties and uses.
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Chemistry
of Non-Metals – II : Boron – occurrence, isolation,
physical and chemical properties, borax and boric acid, uses
of boron and its compounds. Carbon, inorganic compounds of
carbon – oxides, halides, carbides, elemental carbon.
Silicon – occurrence, preparation and properties, oxides and
oxyacids of phosphorus, chemical fertililzers. Sulphur –
occurrence and extraction, properties and reactions, oxides,
Sulphuric acid – preparation, properties and uses, sodium
thiosulphate. Halogens – occurrence, preparation,
properties, hydrogen halides, uses of halogens.
Noble gases – discovery, occurrence and isolation, physical
properties, chemistry of noble gases and their uses.
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Chemistry
of Lighter Metals : Sodium and Potassium – occurrence
and extraction, properties and uses. Important compounds –
NaCl, Na2CO3, NaHCO3, NaOH, KCI, KOH. Magnesium
and calcium – occurrence and extraction, properties and
uses. Important compounds MgCl2, MgSO4, CaO, Ca(OH)2, CaCO3,
CaSO4, plaster of paris , Bleaching Powder. Aluminium –
occurrence, extraction, properties and uses, compounds –
AlCl3, alums. Cement. Biological role of Sodium,
Potassium, Magnesium and Calcium.
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Heavy
Metals : Iron – Occurrence and extraction, compounds of
iron, oxides, halides, sulphides, sulphate, alloy and steel.
Copper and silver – occurrence and extraction, properties
and uses, compounds – sulphides, halides and sulphates,
photography. Zinc and Mercury –occurrence and extraction,
properties and uses, compounds -oxides, halides; sulphides and
sulphates Tin and Lead– occurrence and extraction,
properties and uses, compounds – oxides, sulphides, halides.
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Chemistry
of Representative Elements : Periodic properties –
Trends in groups and periods (a) Oxides-nature (b)
Halides-melting points (c) Carbonates and sulphates –
solubility. The chemistry of s and p block elements,
electronic configuration, general characteristic properties
and oxidation states of the following:- Group 1 elements –
Alkali metals Group 2 elements – Alkaline earth
metals Group 13 elements – Boron
family Group 14 elements – Carbon
family Group 15 elements – Nitrogen
family Group 16 elements – Oxygen
family Group 17 elements – Halogen family Group
18 elements – Noble gases and Hydrogen
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Transition
Metals including Lanthanides : Electronic configuration:
General characteristic properties, oxidation states of
transition metals. First row transition metals and general
properties of their compounds-oxides, halides and sulphides.
General properties of second and third row transition elements
(Groupwise discussion). Preparation and reactions,
properties and uses of Potassium dichromate and Potassium
permanganate.
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Inner
Transition Elements: General discussion with special
reference to oxidation states and lanthanide contraction.
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Coordination
Chemistry and Organo Metallics : Coordination compounds,
Nomenclature : Isomerism in coordination compounds; Bonding in
coordination compounds, Werner’s coordination theory.
Applications of coordination compounds.
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Nuclear
Chemistry : Nature of radiations from radioactive
substances. Nuclear reactions; Radioactive disintegration
series; Artificial | | |
