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Chemistry-Physical chemistry: Unit 01

• Matter and its nature, Dalton's atomic theory, concept of atom, molecule, element and compound
• Laws of chemical combination, atomic and molecular masses, mole concept and Avogadro number, molar mass, vapour density-definition
• Relationship between molecular mass and vapour density
• Concept of STP conditions, gram molar volume, percentage composition, empirical and molecular formulae, chemical equations and numerical problems in all these concepts, stoichiometry

Chemistry-Physical chemistry: Unit 02

• Classification of matter-solid, liquid, and gaseous states
• Gaseous state: Gas laws-Boyle's law, Charles's law, Graham's law of diffusion, Avogadro’s law, Dalton's law of partial pressures, Gay Lussac's law of combining volumes, concept of absolute temperature scale, Ideal gas equation
• Gaseous state: Kinetic theory of gases-postulates, concept of average, root mean square and most probable velocities, numerical problems. Ideal and real gases, ideal gas equation, value of R (SI units). Deviation of real gases from the ideal behaviour
• Gaseous state: PV-P curves. Causes for the deviation of real gases from ideal behaviour. Derivation of Van der Waal's equation and interpretation of PV-P curves
• Liquid state: Properties of liquids-vapour pressure, viscosity and surface tension, effect of temperature on them
• Solid state: Classifications of solids-molecular, ionic, covalent and metallic solids, amorphous and crystalline solids, unit cell and lattices, packing in solids (fcc, bcc, and hcp lattices) voids, calculations involving unit cell parameters
• Solid state: Imperfection in solids, electrical and magnetic properties. Band theory of metals, conductors, semiconductors and insulators and n and p type semiconductors

Chemistry-Physical chemistry: Unit 03

• Introduction-constituents of atoms, their charge and mass
• Atomic number and atomic mass
• Wave nature of light, electromagnetic spectrum-emission spectrum of hydrogen-Lyman series, Balmer series, Paschen series, Brackett series and Pfund series
• Rydberg's equation
• Numerical problems involving calculation of wavelength and wave numbers of lines in the hydrogen spectrum
• Atomic model- Bohr's theory, (derivation of equation for energy and radius not required)
• Explanation of origin of lines in hydrogen spectrum
• Limitations of Bohr's theory
• Dual nature of electron-distinction between a particle and a wave
• De Broglie's theory
• Matter-wave equation (derivation)
• Heisenberg's uncertainty principle (qualitative)
• Quantum numbers-n, l, m, and s and their significance and inter relationships
• Concept of orbital-shapes of s, p, and d orbitals
• Pauli's exclusion principle and Aufbau principle
• Energy level diagram and (n+1) rule
• Electronic configuration of elements with atomic numbers from 1 to 54, extra stability of half-filled and completely filled orbitals
• Hund's rule of maximum multiplicity

Chemistry-Physical chemistry: Unit 04

• Kossel-Lewis approach to chemical bond formation, concept of ionic and covalent bonds
• Ionic bonding: Formation of ionic bonds, factors affecting the formation of ionic bonds, calculation of lattice enthalpy
• Covalent bonding: Valence shell electron pair repulsion (VSEPR) theory and shapes of simple molecules, molecular orbital theory (MOT)-linear combination of atomic orbitals (qualitative approach), energy level diagram, rules for filling molecular orbitals
• Covalent bonding: Bonding and anti-bonding molecular orbitals, bond order, electronic configuration of H₂, Li₂, and O₂ non-existence of He₂ and paramagnetism of O₂
• Metallic bonding: Electron gas theory (electron sea model), definition of metallic bond
• Hydrogen bonding: Inter and intra molecular, properties

Chemistry-Physical chemistry: Unit 05

• Methods of expressing concentration of solutions-ppm, molarity, molality, normality, mole fraction, percentage (by volume and wt.)
• Principles of volumetric analysis-standard solution, titrations and indicators-acid-base (phenolphthalein and methyl orange) and redox (diphenylamine) numerical problems
• Vapour pressure of solutions and Raoult's law, ideal and non-ideal solutions, colligative properties of dilute solutions-relative lowering of vapour pressure, depression of freezing point, elevation of boiling point, osmotic pressure
• Calculation of mol. wt. of a solute using colligative properties, Van't Hoff factor and its significance

Chemistry-Physical chemistry: Unit 06

• Meaning of equilibrium, concept of dynamic equilibrium
• Equilibrium involving physical processes: Solid-liquid, liquid-gas and solid-gas equilibria, Henry's law, general characteristics of equilibrium involving physical processes
• Equilibrium involving chemical processes: Law of chemical equilibrium, equilibrium constants (Kp and Kc) and their significance, significance of ∆G and ∆G in chemical equilibria, factors affecting equilibrium, concentration, pressure, temperature
• Equilibrium involving chemical processes: Effect of catalyst, Le Chatelier's principle
• Ionic equilibrium: Electrolytes and non-electrolytes, ionization of electrolytes, electrolysis -Faraday's Laws of electrolysis, numerical problems. Arrhenius theory of electrolytic dissociation, merits and limitations
• Ionic equilibrium: Specific conductivity and molar conductivity-definitions and units. Strong and weak electrolytes with examples. Factors affecting the conductivity. Acid-base theories (Arrhenius, Bronsted-Lowry, and Lewis) and their limitations
• Ionic equilibrium: Acid-base equilibria, ionization constants, strengths of acids and Bases-dissociation constants of weak acids and weak bases
• Ionic equilibrium: Ostwald's dilution law for weak electrolytes (equation derivation)-expression for hydrogen ion concentration of weak acid and hydroxyl ion concentration of weak base-numerical problems. Ionic product of water, pH concept and pH scale
• Ionic equilibrium: pKa and pKb values-numerical problems. Buffers, types of buffers, mechanism of buffer action, Henderson's equation for pH of a buffer (derivation), preparation of buffers of required pH-numerical problems
• Ionic equilibrium: Common ion effect, solubility, expression for Ksp of sparingly soluble salts of types AB, AB2. Relationship between solubility and solubility product of salts of types AB, AB2
• Ionic equilibrium: Applications of common ion effect and solubility product in qualitative analysis, numerical problems

Chemistry-Physical chemistry: Unit 07

• Electronic concept of oxidation and reduction, redox reactions, oxidation number, rules for assigning oxidation number, balancing of redox reactions, electrode potential-definition, factors affecting single electrode potential
• Standard electrode potential, Nernst's equation for calculating single electrode potential, construction of electro-chemical cells, Daniel cell, free energy change during cell reactions (∆G)
• Reference electrodes-standard hydrogen electrode (SHE)-construction, use of SHE for determination of SRP of other single electrodes and pH of solutions, limitations of SHE
• Electrochemical series and its applications, galvanic and electrolytic cells, half-cell and cell reactions, EMF of a galvanic cell and its measurement, Nernst equation and its applications, working principles of dry cell
• Lead acid cell and H₂-O₂ fuel cell

Chemistry-Physical chemistry: Unit 08

• Introduction, commercial importance of rate studies, order of a reaction, factors deciding the order of a reaction-relative concentrations of the reactants and mechanism of the reaction
• First order reaction-equation for rate constant derivation, units
• Half-life period, relation between half-life period and order of a reaction, numerical problems
• Determination of the order of a reaction by the graphical and the Ostwald's isolation method
• Zero order, fractional order and pseudo first order reactions with illustrations
• Effect of temperature on the rate of a reaction, temperature coefficient of a reaction
• Arrhenius interpretation of the energy of activation and temperature dependence of the rate of reaction
• Arrhenius equation
• Influence of catalyst on energy profile
• Numerical problems on energy of activation

Chemistry-Physical chemistry: Unit 09

• Adsorption: Physisorption and chemisorption and their characteristics, factors affecting adsorption of gases on solids, Freundlich and Langmuir adsorption isotherms, adsorption from solutions
• Catalysis: Homogeneous and heterogeneous, activity and selectivity of solid catalysts, enzyme catalysis and its mechanism
• Colloids: Introduction, colloidal system and particle sizes. Types of colloidal systems, lyophilic and lyophobic sols, examples and differences. Preparation of sols by Bredig’s arc method and peptisation. Purification of sols-dialysis and electro dialysis
• Colloids: Properties of sols-Tyndall effect, Brownian movement electrophoresis, origin of charge, coagulation, Hardy and Schulze rule, protective action of sols. Applications of colloids. Emulsions and their characteristics

Chemistry-Physical chemistry: Unit 10

• Concepts of System and types of systems, surroundings, work, heat, energy, extensive and intensive properties, state functions
• Spontaneous and non-spontaneous processes, criteria for spontaneity-tendency to attain a state of minimum energy and maximum randomness
• First law of thermodynamics-internal energy and enthalpy, heat capacity and specific heat, measurement of ΔU and ΔH, Hess's law of constant heat summation, enthalpy of bond dissociation, combustion, formation, atomization, sublimation, phase transition
• Ionization, solution and dilution
• Entropy-a measure of randomness, change in entropy, unit of entropy
• Entropy and spontaneity
• Second law of thermodynamics, Gibbs' free energy as a driving force of a reaction, Gibbs' equation, prediction of feasibility of a process in terms of ∆G, standard free energy change and its relation to Kp
• Numerical problem

Chemistry-Inorganic chemistry: Unit 01

• Periodic table-periods and groups
• Modern periodic law and present form of periodic table, s, p, d, and f block elements, atomic radii (Van der Waal and covalent) and ionic radii, comparison of size of cation and anion with the parent atom, size of isoelectronic ions
• Ionization energy, electron affinity, electronegativity-definition with illustrations, Fajan's rules
• Variations of atomic radius, ionization energy, electron affinity, electronegativity down the group and along the period and their interpretation

Chemistry-Inorganic chemistry: Unit 02

• Modes of occurrence of elements in nature, minerals, ores, steps involved in the extraction of metals-concentration, reduction (chemical and electrolytic) and refining with reference to the extraction of Al, Cu, Zn, and Fe
• Thermodynamic and electrochemical principles involved in the extraction of metals

Chemistry-Inorganic chemistry: Unit 03

• Isotopes, preparation, properties, and uses of hydrogen
• Physical and chemical properties of water and heavy water, structure, preparation, reactions, and uses of hydrogen peroxide, classification of hydrides-ionic, covalent and interstitial, hydrogen as a fuel

Chemistry-Inorganic chemistry: Unit 04

• General introduction, electronic configuration and general trends in physical and chemical properties of elements, anomalous properties of the first element of each group, diagonal relationships
• Preparation and properties of NaOH, NaCl, Na₂CO₃, and NaHCO₃
• Industrial use of lime, limestone, plaster of Paris and cement, biological significance of Na, K, Mg, and Ca

Chemistry-Inorganic chemistry: Unit 05

• General electronic configuration and general trends in physical and chemical properties of elements across the periods and groups, unique behaviour of first element in each group
• Group 13: Preparation, properties, and uses of boron and aluminium, structure, properties and uses of borax, boric acid, diborane, boron trifluride, aluminium chloride and alums
• Group 14: Tendency for catenation, structure, properties, and uses of allotropes and oxides of carbon, silicon tetrachloride, silicates, zeolites and silicones
• Group 15: Properties and uses of nitrogen and phosphorus, allotropic forms of phosphorus, preparation, properties, structure and uses of ammonia, nitric acid, phosphine and phosphorus halides (PCl3, PCl5)
• Group 15: Structures of oxides and oxoacids of nitrogen and phosphorus
• Group 16: Preparation, properties, structures, and uses of ozone, allotropic forms of sulphur, preparation, properties, structure and uses of sulphuric acid, structures of oxoacids of sulphur
• Group 17: Preparation, properties, and uses of hydrochloric acid, trends in the acidic nature of hydrogen halides, structures of interhalogen compounds and oxides and oxoacids of halogens
• Group 18: Occurrence and uses of noble gases. Structures of fluorides and oxides of xenon

Chemistry-Inorganic chemistry: Unit 06

• Transition elements, electronic configuration, occurrence and characteristics, general trends in properties of 3d series-electronic configurations, size, variable oxidation states, colour, magnetic properties, catalytic behaviour, complex formation
• Interstitial compounds and alloy formation
• Preparation, properties and uses of K₂Cr₂O₇ and KMnO₄
• Lanthanoids: Electronic configuration, oxidation states and lanthanoid contraction
• Actinoids: Electronic configuration, oxidation states and comparison with lanthanoids

Chemistry-Inorganic chemistry: Unit 07

• Werner's theory-ligands, coordination number, denticity, chelation, IUPAC nomenclature of mononuclear coordination compounds, isomerism, bonding-valence bond approach. Importance of coordination compounds in qualitative analysis
• Extraction of metals and in biological systems

Chemistry-Inorganic chemistry: Unit 08

• Environmental pollution-atmospheric, water and soil; atmospheric pollution-tropospheric and stratospheric; tropospheric pollutants-gaseous pollutants: Oxides of carbon, nitrogen and sulphur, hydrocarbons, their sources, harmful effects, and prevention
• Greenhouse effect and global warming, acid rain; particulate pollutants-smoke, dust, smog, fumes, mist, their sources, harmful effects, and prevention
• Stratospheric pollution-formation and breakdown of ozone, depletion of ozone layer, its mechanism and effects; water pollution-major pollutants such as pathogens, organic wastes and chemical pollutants, their harmful effects and prevention
• Soil pollution-major pollutants such as pesticides (insecticides, herbicides, and fungicides) their harmful effects and prevention; strategies to control environmental pollution

Chemistry-Organic chemistry: Unit 01

• Purification: Crystallization, sublimation, distillation, differential extraction and chromatography-principles and their applications; qualitative analysis-detection of nitrogen, sulphur, phosphorus and halogens
• Purification: Quantitative analysis-basic principles involved in the estimation of carbon, hydrogen, nitrogen, halogens, sulphur, and phosphorus; calculations of empirical formulae and molecular formulae, numerical problems in org. quantitative analysis

Chemistry-Organic chemistry: Unit 02

• Tetravalency of carbon, shapes of simple molecules-hybridization (s and p), classification of organic compounds based on functional groups, compounds containing halogens, oxygen, nitrogen and sulphur
• Homologues series, isomerism-structural and stereoisomerism
• Nomenclature: Covalent bond fission-homolytic and heterolytic, free radicals, carbocations and carbanions. Stability of carbocations and free radicals, electrophiles and nucleophiles
• Electronic displacement in a covalent bond: Inductive effect, electromeric effect, resonance and hyperconjugation
• Types of organic reactions: Substitution, addition, elimination and rearrangement

Chemistry-Organic chemistry: Unit 03

• Classification, isomerism, IUPAC nomenclature, general methods of preparation, properties and reactions
• Alkanes: Conformers, Sawhorse and Newman projections of ethane, mechanism of halogenation of alkanes, combustion and pyrolysis
• Alkenes: Geometrical isomerism, mechanism of electrophilic addition, addition of hydrogen, halogens, water, hydrogen halides-Markownikoff's and peroxide effect, ozonolysis and polymerization
• Alkynes: Acidic character, addition of hydrogen, halogens, water and hydrogen halides
• Aromatic hydrocarbons: Nomenclature, benzene-structure and aromaticity, mechanism of electrophilic substitution, halogenation, nitration, Friedel-Craft's alkylation and acylation, directive influence of functional group in mono-substituted benzene

Chemistry-Organic chemistry: Unit 04

• General methods of preparation, properties, and reactions
• Nature of C-X bond, mechanisms of substitution reactions, uses, environmental effects of chloroform, iodoform, freons and DDT

Chemistry-Organic chemistry: Unit 05

• General methods of preparation, properties, and reactions
• Alcohols, phenols, and ethers: Alcohols-identification of primary, secondary, and tertiary alcohols, mechanism of dehydration
• Alcohols, phenols, and ethers: Ethers-structures
• Aldehyde and ketones: Nature of carbonyl group, nucleophilic addition to >C=O group, relative reactivities of aldehydes and ketones, important reactions such as nucleophilic addition (addition of HCN, NH3 and its derivatives), Grignard reagents, oxidation
• Aldehyde and ketones: Reduction (Wolf Kishner and Clemmensen), acidity of α–hydrogen, aldol condensation, Cannizzaro reaction, Haloform reaction, chemical tests to distinguish between aldehydes and ketones
• Carboxylic acids: Acidic strength and factors affecting it

Chemistry-Organic chemistry: Unit 06

• General methods of preparation, properties, reactions, and uses
• Amines: Nomenclature, classification, structure, basic character and identification of primary, secondary, and tertiary amines
• Diazonium salts: importance in synthetic organic chemistry

Chemistry-Organic chemistry: Unit 07

• General introduction and classification of polymers, general methods of polymerization-addition and condensation, copolymerization, natural and synthetic rubber and vulcanization
• Some important polymers with emphasis on their monomers and uses-polyethylene, nylon 6, 6; polyester and bakelite

Chemistry-Organic chemistry: Unit 08

• General introduction and importance of biomolecules
• Carbohydrates: Classification-aldoses and ketoses, monosaccharides (glucose and fructose) and constituent monosaccharides of oligosaccharides (sucrose, lactose, and maltose), polysaccharides (starch, cellulose, glycogen) importance
• Proteins: Elementary idea of amino acids, peptide bond, polypeptide, proteins-primary, secondary, tertiary, and quaternary, denaturation of proteins, enzymes, hormones
• Vitamins: Classification and functioning
• Nucleic acids: Chemical constitution of DNA and RNA, biological functions of nucleic acids

Chemistry-Organic chemistry: Unit 09

• Chemicals in medicine-analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines-their meaning and common examples
• Chemicals in food-preservatives, artificial sweetening agents, common examples
• Cleansing agents-soaps and detergents, cleansing action

Chemistry-Organic chemistry: Unit 10

• Detection of extra elements (N, S, halogens) in organic compounds, detection of the functional groups-hydroxyl (alcoholic and phenolic), carbonyl (aldehyde and ketone), carboxyl and amino groups in organic compounds
• Chemistry involved in the titrimetric exercises: Acid-base titrations, use of indicators, redox titrations and their indicators
• Chemical principles involved in the qualitative salt analysis: Cations-Pb²+, Cu²+, Al³+, Fe³+, Zn²+, Ni²+, Ca²+, Ba²+, Mg²+ , NH⁴+; anion-CO₃²¯, S²¯, SO₄²¯, NO₃¯ , NO₂¯, Cl¯, Br¯, and I¯

Mathematics: Unit 01

• Sets: Sets and their representations. Empty set. Finite and infinite sets. Equal sets. Subsets. Subsets of the set of real numbers especially intervals (with notations). Power set. Universal set. Venn diagrams. Union and intersection of sets
• Sets: Difference of sets. Complement of a set, properties of complement sets
• Relations and functions: Ordered pairs, Cartesian product of sets. Number of elements in the Cartesian product of two finite sets. Cartesian product of the reals with itself (upto R × R × R)
• Relations and functions: Definition of relation, pictorial diagrams, domain, co-domain, and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function
• Relations and functions: Domain, co-domain, and range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus
• Relations and functions: Signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions
• Relations and functions: Types of relations-reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations. Partial fractions, logarithms and its related properties
• Trigonometric functions: Positive and negative angles. Measuring angles in radians and in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle
• Trigonometric functions: Truth of the identity sin2x + cos2x = 1 , for all x. Signs of trigonometric functions and sketch of their graphs. Expressing sin (x+y) and cos (x+y) in terms of sin x, sin y, cos x and cos y
• Trigonometric functions: Deducing the identities like following- tan (x ± y)= tan x ± tan y / 1 ± tan x tan y; cot (x Ŧ y) = cot x cot y Ŧ 1 / cot y Ŧ cot x, sin x + sin y = 2 sin (x+y/2) cos (x-y/2); cos x + cox y = 2 cos (x + y/2) cos (x-y/2)
• Trigonometric functions: Deducing the identities like following- sin x - sin y = 2 cos (x+y/2) sin (x-y/2); cos x - cos y = -2 sin (x=y/2) sin (x-y/2)
• Trigonometric functions: Identities related to sin2x ,cos2x, tan2x ,sin3x ,cos3x, and tan3. General solution of trigonometric equations of the type sinθ = sinα , cosθ = cosα, tanθ = tanα. Proofs and simple applications of sine and cosine formulae
• Inverse trigonometric functions: Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions

Mathematics: Unit 02

• Principle of mathematical induction: Process of the proof by induction, motivating the application of the method by looking at natural numbers as the least inductive subset of real numbers. The principle of mathematical induction and simple applications
• Complex numbers and quadratic equations: Introduction, complex numbers, algebra of complex numbers, brief description of algebraic properties of complex numbers, the modulus and the conjugate of complex number, Argand plane and polar representation
• Complex numbers and quadratic equations: Fundamental theorem of algebra. Solution of quadratic equations in the complex number system, square root of a complex number
• Linear inequalities: Linear inequalities, algebraic solutions of linear inequalities in one variable and their representation on the number line. Graphical solution of linear inequalities in two variables
• Linear inequalities: Solution of system of linear inequalities in two variables-graphically
• Permutations and combinations: Fundamental principle of counting. Factorial n. Permutations and combinations derivation of formulae and their connections, simple applications
• Binomial theorem: History, statement and proof of the binomial theorem for positive integral indices. Pascal's triangle, general and middle term in binomial expansion, simple applications
• Sequence and series: Sequence and series. Arithmetic progression (A.P.), Arithmetic mean (A.M.), geometric progression (G.P.), general term of a G.P., sum of n terms of a G.P. Arithmetic and geometric series, infinite G.P. and its sum
• Sequence and series: Geometric mean (G.M.). Relation between A.M. and G.M. Sum to n terms of the special series: n∑k k=1,n ∑k² k=1,n ∑k³ k=1
• Matrices: Concept, notation, order, equality, types of matrices, zero matrix, transpose of a matrix, symmetric and skew symmetric matrices. Addition, multiplication and scalar multiplication of matrices, simple properties of addition
• Matrices: Multiplication and scalar multiplication. Non-commutativity of multiplication of matrices and existence of non-zero matrices whose product is the zero matrix (restrict to square matrices of order 2)
• Matrices: Concept of elementary row and column operations. Invertible matrices and proof of the uniqueness of inverse, if it exists; (here all matrices will have real entries)
• Determinants: Determinant of a square matrix (up to 3 × 3 matrices), properties of determinants, minors, cofactors and applications of determinants in finding the area of a triangle. Adjoint and inverse of a square matrix
• Determinants: Consistency, inconsistency and number of solutions of system of linear equations by examples, solving system of linear equations in two or three variables (having unique solution) using inverse of a matrix

Mathematics: Unit 03

• Straight lines: Brief recall of 2-D from earlier classes, shifting of origin. Slope of a line and angle between two lines. Various forms of equations of a line: Parallel to axes, point-slope form, slope-intercept form, two-point form
• Straight lines: Various forms of equations of a line-intercepts form and normal form. General equation of a line. Equation of family of lines passing through the point of intersection of two lines. Distance of a point from a line
• Conic sections: Sections of a cone-circles, ellipse, parabola, hyperbola, a point, a straight line and pair of intersecting lines as a degenerated case of a conic section. Standard equations and simple properties of parabola, ellipse and hyperbola
• Conic sections: Standard equation of a circle
• Vectors: Vectors and scalars, magnitude and direction of a vector. Direction cosines/ ratios of vectors. Types of vectors (equal, unit, zero, parallel, and collinear vectors), position vector of a point, negative of a vector, components of a vector
• Vectors: Addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Scalar (dot) product of vectors, projection of a vector on a line. Vector (cross) product of vectors
• Vectors: Scalar triple product
• Three-dimensional geometry: Coordinate axes and coordinate planes in three dimensions. Coordinates of a point. Distance between two points and section formula. Direction cosines/ ratios of a line joining two points
• Three-dimensional geometry: Cartesian and vector equation of a line, coplanar and skew lines, shortest distance between two lines. Cartesian and vector equation of a plane. Angle between-(i) two lines, (ii) two planes, (iii) a line and a plane
• Three-dimensional geometry: Distance of a point from a plane

Mathematics: Unit 04

• Limits and derivatives: Derivatives introduced as rate of change both as that of distance function and geometrically. Intuitive idea of limit lim(X->0) logₑ (1+x)/x, lim(X->0) eˣ-1 /x . Limits of trigonometric functions
• Limits and derivatives: Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference
• Limits and derivatives: Product and quotient of functions. Derivatives of polynomial of trigonometric functions
• Continuity and differentiability: Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function. Concepts of exponential, logarithmic functions
• Continuity and differentiability: Derivatives of logₑ z and eᶻ. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives
• Continuity and differentiability: Rolle's and Lagrange's mean value theorems (without proof) and their geometric interpretations
• Applications of derivatives: Rate of change, increasing/ decreasing functions, tangents and normal, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool)
• Applications of derivatives: Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations)
• Integrals: Integration as inverse process of differentiation. Integration of a variety of functions by substitution, by partial fractions and by parts, only simple integrals of the type ʃ dx/ x² ± a², ʃ dx/ √x² ± a², ʃ dx/ √ a² - x², ʃ dx/ ax² + bx + c
• Integrals: Only simple integrals of the type ʃ dx/ √ ax² + bx + c, ʃ (px + q)dx/ ax² + bx + c, ʃ (px + q)dx/ √ax² + bx + c, ʃ √ x² - a² dx, ʃ √ ax² + bx + c dx, and ʃ (px+q) √ ax² + bx + c dx
• Integrals: Definite integrals as a limit of a sum. Fundamental theorem of calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals
• Applications of the integrals: Applications in finding the area under simple curves, especially lines, arcs of circles/ parabolas/ ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable)
• Differential equations: Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given
• Differential equations: Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree
• Differential equations: Solutions of linear differential equation of the type-dy/dx+Py=Q where P and Q are functions of x or constant, dx/dy+Px=Q where P and Q are functions of y or constant

Mathematics: Unit 05

• Mathematically acceptable statements
• Connecting words/ phrases-consolidating the understanding of 'if and only if (necessary and sufficient) condition', 'implies', 'and/or', 'implied by', 'and', or, 'there exists' and their use through variety of examples related to real life and mathematics
• Validating the statements involving the connecting words-difference between contradiction, converse and contrapositive

Mathematics: Unit 06

• Statistics: Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/ grouped data. Analysis of frequency distributions with equal means but different variances
• Probability: Random experiments-outcomes, sample spaces (set representation). Events: Occurrence of events, 'not', 'and', and 'or' events, exhaustive events, mutually exclusive events. Axiomatic (set theoretic) probability
• Probability: Connections with the theories of earlier classes. Probability of an event, probability of 'not', 'and, and 'or' events. Multiplications theorem on probability. Conditional probability, independent events, total probability. Baye's theorem
• Probability: Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution

Mathematics: Unit 07

• Introduction, related terminology such as constraints, objective function, optimization, different types of linear programming (L.P.) problems, mathematical formulation of L.P. problems, graphical method of solution for problems in two variables
• Feasible and infeasible regions, feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constrains)

English: Unit 01

• Use of proper tense and sequence of tense

English: Unit 02

• Have to/ had to, must, should, need, ought to and their negative form

English: Unit 03

English: Unit 04

English: Unit 05

English: Unit 06

• Commands and requests, statements, questions

English: Unit 07

• Noun clauses, adverb clauses of condition and time, relative clauses

English: Unit 08

English: Unit 09

English: Unit 10

• Synonyms, antonyms, spellings, one word substitutions

Maths: Unit 01

Maths: Unit 02

Maths: Unit 03

Maths: Unit 04

Maths: Unit 05

Maths: Unit 06

Maths: Unit 07

English: Unit 01

English: Unit 02

English: Unit 03

English: Unit 04

English: Unit 05

English: Unit 06

English: Unit 07

English: Unit 08

English: Unit 09

English: Unit 10

Chemistry: Unit 01

Chemistry: Unit 02

Chemistry: Unit 03

Chemistry: Unit 04

Chemistry: Unit 05

Chemistry: Unit 06

Chemistry: Unit 07

Chemistry: Unit 08

Chemistry: Unit 09

Chemistry: Unit 10

Chemistry: Unit 11

Chemistry: Unit 12

Chemistry: Unit 13

Chemistry: Unit 14

Chemistry: Unit 15

Chemistry: Unit 16

Chemistry: Unit 17

Chemistry: Unit 18

Chemistry: Unit 19

Chemistry: Unit 20

Chemistry: Unit 21

Chemistry: Unit 22

Chemistry: Unit 23

Chemistry: Unit 24

Chemistry: Unit 25

Chemistry: Unit 26

Chemistry: Unit 27

Chemistry: Unit 28