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Chemistry: Unit 01

• Measurement in chemistry (precision, significant figures, S.I. 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

Chemistry: Unit 02

• 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
• Kinetic molecular theory of gases (the microscopic model of gas), deviation form ideal behaviour
• 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)

Chemistry: Unit 03

• Constituents of the atom (discovery of electron, rutherford model of the atom)
• Electronics structure of atoms-nature of light and electromagnetic waves, atomic spectra, Bohr’s model of hydrogen, shortcomings of the Bohr's model
• 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, electronics configuration of atoms

Chemistry: Unit 04

• 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

Chemistry: Unit 05

• 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)
• Sources of energy (conservation of energy sources and identification of alternative sources, pollution associated with consumption of fuels, the sun as the primary source)
• First law of thermodynamics, relation between Internal energy and enthalpy, application of first law of thermodynamics
• Second law of thermodynamics-entropy, Gibbs energy, spontaneity of a chemical reaction, Gibbs energy change and chemical equilibrium, Gibbs energy available for useful work

Chemistry: Unit 06

• 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)
• Equilibria involving chemical systems (the law of chemical equilibrium, the magnitude of the equilibrium constant, numerical problems)
• Effect of changing conditions of systems at equilibrium (change of concentration, change of temperature, effect of catalyst-Le Chateliar’s principle)
• 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

Chemistry: Unit 07

• Oxidation and reduction as an electron transfer concept
• Redox reactions in aqueous solutions-electrochemical cells
• e.m.f. of a galvanic cell
• Dependence of e.m.f. 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
• 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

Chemistry: Unit 08

• 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 of Rates of Reactions
• Elementary reactions as steps to more complex reactions
• How fast are chemical reactions?, rate law expression
• Order of a reaction (with suitable examples)
• Units of Rates and Specific Rate Constant
• 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

Chemistry: Unit 09

• Surface: adsorption-physical and chemical adsorption, adsorption isotherms
• Colloids-preparation and general properties, emulsions, micelles
• Catalysis: homogeneous and heterogeneous, structure of catalyst, enzymes, zeolites

Chemistry: Unit 10

• Modern periodic law, types of elements-representatives elements (s and 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

Chemistry: Unit 11

• 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
• 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
• 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

Chemistry: Unit 12

• 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

Chemistry: Unit 13

• 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 fertilizers
• 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

Chemistry: Unit 14

• 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-AlCI3, alums
• Cement
• Biological role of sodium, potassium, magnesium, and calcium

Chemistry: Unit 15

• 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

Chemistry: Unit 16

• 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, electronics 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

Chemistry: Unit 17

• 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 a second and third row transition elements (group wise discussion)
• Preparation and reactions, properties, and uses of potassium dichromate, potassium permanganate
• Inner transition elements: general discussion with special reference to oxidation states, and lanthanide contraction

Chemistry: Unit 18

• Coordination compounds, nomenclature: isomerism in coordination compounds, bonding in coordination compounds, Werner’s coordination theory
• Applications of coordination compounds

Chemistry: Unit 19

• Nature of Radiation from Radioactive Substances
• Nuclear reactions, radio-active disintegration series, artificial transmutation of elements, nuclear fission and nuclear fusion: isotopes and their applications: radio carbon-dating

Chemistry: Unit 20

• Purification (crystallization, sublimation, distillation, differential extraction, chromatography)
• Qualitative analysis, detection of nitrogen, sulphur, phosphorus, and halogens
• Quantitative analysis-estimation of carbon, hydrogen, nitrogen, halogens, sulphur, phosphorus (basic principles only), determination of molecular mass-silver salt method, cholroplatinate salt method, calculation of empirical formula, and molecular formula
• Numerical problems in organic quantitative analysis, modern methods of structure elucidation

Chemistry: Unit 21

• Classification of organic compounds
• Tetravalency of carbon, homologous series
• Functional groups- -C=C-,-C C-, and groups containing halogen, oxygen, nitrogen, and sulphur
• General introduction to naming organic compounds-common names and IUPAC nomenclature of alphatic, aromatic, and cyclic compounds
• Illustration with examples of compounds having not more than three same of different functional groups/atoms
• Isomerism-structural and stereoisomerism (geometrical and optical)
• Chirality-isomerism in compounds having one and two chiral Centres
• Enantiomers, diastereoisomers, recemic forms, recemisation, and resolution
• Covalent bond fission-homolytic and heterolytic: free radicals carbocations and carbanions
• Stability of carbocations and free radicals
• Electrophiles and Nucleophiles
• Electron displacement in a covalent bond-inductive effect, electromeric effect, resonance common types of organic reactions-substitution, addition, elimination, and rearrangement reactions
• Illustration with examples

Chemistry: Unit 22

• Classification
• Sources of hydrocarbons: alkanes-general methods of preparation (from unsaturated hydrocarbons, alkylhalides, aldehydes, ketones, and carburoxylic acids)
• Physical properties and reactions (substitution), oxidation, and miscellaneous)
• Conformations of alkanes (ethane, popane butane) and cyclohexane, sawhorse and Newman projections)-mechanism of halogaration of alkanes
• Alkanes and alkynes-general methods of preparation, physical peorperties, chemical reactions-mechanism of electrophilic addition reactions in alkenes-Markowni Koff’s rule, peroxide effect
• Acidic character of Alkynes
• Polymerisation of alkenes
• Aromatic hydrocarbons-benzene and its homologues, isomerism, chemical reactions of benzene
• Structure of benzene, resonance
• Directive influence of substituents
• Petroleum-hydro carbons from petroleum, cracking, and reforming, quality of gasoline, octane number, gasoline additives

Chemistry: Unit 23

• Haloakanes and haloarenes-methods of preparation, physical properties, and reactions
• Preparation, properties, and uses of chloroform, and lodoform

Chemistry: Unit 24

• General methods of preparation, correlation of physical properties with their structures, chemical properties, and uses of alchols, polyhydric alcohols, ethers, aldehydes, ketones, carboxylic acids, and their derivatives, phenol
• Benzaldehyde and benzoic acid-their important methods of preparation and reactions
• Acidity of carboxylic acids and phenol effect of substituents on the acidity of carboxylic acids

Chemistry: Unit 25

• Cyanides, isocyanides, nitrocompounds and amines-nomenclature and classification of amines, cyanides, isocyanides, nitrocompounds, and their methods of preparation, correlation of their physical properties with structure
• Chemical reactions and uses-basicity of amines

Chemistry: Unit 26

• Classification on polymers, natural, and synthetic polymers (with stress on their general methods of preparation), and important uses of the following-Teflon, PVC, polystyrene, nylon-66, terylene, bakelite

Chemistry: Unit 27

• The cell and energy cycle, carbohydrates: monosaccharides, disaccharides, polysaccharides, amino acids and peptides-structure and classification
• Proteins and enzymes-structure of proteins, role of enzymes
• Nucleic acids-DNA and RNAm, biological functions of nucleic acids-protein synthesis and replication
• Lipids-structure, membranes, and their functions

Chemistry: Unit 28

• Dyes, chemicals in medicines (antipyretic, analgesic, antibiotics, and tranquilisers), rocket propellants
• Structural formulae non-evaluative

Chemistry: Unit 29

• Environmental pollutants, soil, water, and air pollution, major atmospheric pollutants, acid rain, ozone, and its reactions causing ozone layer depletion, effects of the depletion of ozone layer, industrial air pollution

Mathematics: Unit 01

• 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

Mathematics: Unit 02

• 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

Mathematics: Unit 03

• 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

Mathematics: Unit 04

• 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

Mathematics: Unit 05

• Fundamental principle of counting, permutation as an arrangement and combination as selection, meaning of P (n,r) and C (n,r)
• Simple applications

Mathematics: Unit 06

• 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

Mathematics: Unit 07

• 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: Sn,Sn2 ,Sn3
• Arithmetico-geometric series, exponential, and logarithmic series

Mathematics: Unit 08

• 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

Mathematics: Unit 09

• Integral as an anti-derivative
• Fundamental integrals involving algebraic, trigonometric, exponential, and logarithmic functions
• Integration by substitution, by parts, and 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

Mathematics: Unit 10

• 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)

Mathematics: Unit 11

• Recall of Cartesian system of rectangular coordinates in a plane, distance formula, area of a triangle, condition of the collinearity of three points, and section formula, centroid, and incentre 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
• The straight line and pair of straight lines: various forms of equations of a line, intersection of line, 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, orthocenter, 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 a represent a pair of lines, point of intersection, and angle between two lines
• 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 conditions 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
• 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

Mathematics: Unit 12

• 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

Mathematics: Unit 13

• 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

Mathematics: Unit 14

• Calculation of mean, median, and mode of grouped, and ungrouped data
• Calculation of standard deviation, variance, and mean deviation for grouped, and ungrouped data

Mathematics: Unit 15

• Probability of an event, addition, and multiplication theorems of probability, and their application, conditional probability, Bayes' theorem, probability distribution of a random variate, binomial and poisson distributions, and their properties

Mathematics: Unit 16

• Trigonometrical identities and equations
• Inverse trigonometric functions and their properties
• Properties of triangles, including centroid, incentre, circum-centre, and orthocenter, solution of triangles
• Heights and distances

Computer awareness: Unit 01

• Organization of a computer, central processing unit (CPU), structure of instructions in CPU, input/output devices, computer memory, back-up devices

Computer awareness: Unit 02

• Representation of characters, integers and fractions, binary and hexadecimal representations, binary arithmetic: addition, subtraction, multiplication, division, simple arithmetic, and two's complement arithmetic, floating point representation of numbers
• Boolean algebra, truth tables, Venn diagram