**Physics**

**Unit I: Physical World and Measurement**(periods 10)

Physics – scope and excitement; nature of physical laws; Physics, technology and society. Need for measurement: ; systems of units; SI units, fundamental and derived units. Length, mass and time measurements; accuracy and precision of measuring instruments; errors in measurement; significant figures. Dimensions of physical quantities, dimensional analysis and its applications.

Unit II: Kinematics (Periods 30)

Frame of reference. Motion in a straight line: Position-time graph, speed and velocity.Uniform and non-uniform motion, average speed and instantaneous velocity.Uniformly accelerated motion, velocity-time, position-time graphs, relations for uniformly accelerated motion (graphical treatment).Elementary concepts of differentiation and integration for describing motion.Scalar and vector quantities: vectors, notation, Position and displacement vectors, equality of vectors, multiplication of vectors by a real number; addition and subtraction of vectors. Relative velocity. Unit vector; Resolution of a vector in a plane – rectangular components. Motion in a plane. Cases of uniform velocity and uniform acceleration-projectile motion.

Unit III: Laws of Motion (Periods 16)

Intuitive concept of force. Inertia, Newton’s first law of motion; momentum and Newton’s second law of motion; impulse; Newton’s third law of motion. Law of conservation of linear momentum and its applications.

Equilibrium of concurrent forces. Static and kinetic friction, laws of friction, rolling friction. Uniform circular motion, Dynamics of uniform circular motion: Centripetal force, examples of circular motion (vehicle on level circular road, vehicle on banked road).

Unit IV: Work, Energy and Power (Periods 16)

Scalar product of vectors. Work done by a constant force and a variable force; kinetic energy, work-energy theorem, power. Notion of potential energy, potential energy of a spring, conservative forces: conservation of mechanical energy (kinetic and potential energies); non-conservative forces: elementary idea of elastic and inelastic collisions.

Unit V: Motion of System of Particles and Rigid Body (Periods 18)

Centre of mass of a two-particle system, momentum conversation and centre of mass motion. Centre of mass of a rigid body; centre of mass of uniform rod. Vector product of vectors; moment of a force, torque, angular momentum, conservation of angular momentum with some examples.

Equilibrium of rigid bodies, rigid body rotation and equations of rotational motion, comparison of linear and rotational motions; Moment of inertia, radius of gyration. Values of moments of inertia for simple geometrical objects

(no derivation). Statement of parallel and perpendicular axes theorems and their applications.

Unit VI: Gravitation (Periods 14)

Keplar’s laws of planetary motion. The universal law of gravitation.

Acceleration due to gravity and its variation with altitude and depth.

Gravitational potential energy; gravitational potential. Escape velocity. Orbital velocity of a satellite.

Geo-stationary satellites.

Unit VII: Properties of Bulk Matter (Periods 28)

Elastic behaviour, Stress-strain relationship, Hooke’s law, Young’s modulus, bulk modulus, shear, modulus of rigidity.

Pressure due to a fluid column; Pascal’s law and its applications (hydraulic lift and hydraulic brakes). Effect of gravity on fluid pressure. Viscosity, Stokes’ law, terminal velocity, Reynold’s number, streamline and turbulent flow. Bernoulli’s theorem and its applications. Surface energy and surface tension, angle of contact, application of surface tension ideas to drops, bubbles and capillary action.

Heat, temperature, thermal expansion; specific heat – calorimetry; change of state – latent heat. Heat transfer-conduction, convection and radiation, thermal conductivity, Newton’s law of cooling.

Unit VIII: Thermodynamics (Periods 12)

Thermal equilibrium and definition of temperature (zeroth law of thermodynamics). Heat, work and internal energy. First law of thermodynamics. Second law of thermodynamics: reversible and irreversible processes. Heat engines and refrigerators.

Unit IX: Behaviour of Perfect Gas and Kinetic Theory (Periods

Equation of state of a perfect gas, work done on compressing a gas.

Kinetic theory of gases – assumptions, concept of pressure. Kinetic energy and temperature; rms speed of gas molecules; degrees of freedom, law of equipartition of energy (statement only) and application to specific heats of gases; concept of mean free path, Avogadro’s number.

Unit X: Oscillations and Waves (Periods 28)

Periodic motion – period, frequency, displacement as a function of time. Periodic functions.

Simple harmonic motion (S.H.M) and its equation; phase; oscillations of a spring–restoring force and force constant; energy in S.H.M.-kinetic and potential energies; simple pendulum– derivation of expression for its time period; free and forced (damped) oscillations (qualitative ideas only), resonance.

Wave motion. Longitudinal and transverse waves, speed of wave motion. Displacement relation for a progressive wave. Principle of superposition of waves, reflection of waves, standing waves in strings and organ pipes, fundamental mode and harmonics, Beats, Doppler effect.

Practicals

Note: Every student will perform 10 experiments (5 from each section) and 8 activities (4 from each section) during the academic year.

Two demonstration experiments must be performed by the teacher with participation of students. The students will maintain a record of these demonstration experiments.

Evaluation Scheme for Practical Examinations

l One experiment from any one section 8 marks

l Two activities (one from each section) (4+4) 8 marks

l Practical record (experiments & activities) 6 marks

l Record of demonstration experiment & Viva based on these experiments 3 marks

l Viva on experiments & activities 5 marks

Total 30 marks

SECTION A

Experiments

1. Use of Vernier Callipers

(i) to measure diameter of a small spherical/cylindrical body.

(ii) to measure dimensions of a given regular body of known mass and hence find its density.

(iii) to measure internal diameter and depth of a given beaker/calorimeter and hence find its volume.

2. Use of screw gauge

(i) to measure diameter of a given wire, (ii) to measure thickness of a given sheet

(iii) to measure volume of an irregular lamina

3. To determine radius of curvature of a given spherical surface by a spherometer.

4. To find the weight of a given body using parallelogram law of vectors.

5. Using a simple pendulum, plot L-T and L-T2 graphs. Hence find the effective length of second’s pendulum using appropriate graph.

6. To study the relationship between force of limiting friction and normal reaction and to find co-efficient of friction between a block and a horizontal surface.

7. To find the downward force, along an inclined plane, acting on a roller due to gravitational pull of the earth and study its relationship with the angle of inclination by plotting graph between force and sin?.

Activities

1. To make a paper scale of given least count, e.g. 0.2cm, 0.5cm.

2. To determine mass of a given body using a metre scale by principle of moments.

3. To plot a graph for a given set of data, with proper choice of scales and error bars.

4. To measure the force of limiting friction for rolling of a roller on a horizontal plane.

5. To study the variation in range of a jet of water with angle of projection.

6. To study the conservation of energy of a ball rolling down on inclined plane (using a double inclined plane).

SECTION B

Experiments

1. To determine Young’s modulus of elasticity of the material of a given wire.

2. To find the force constant of a helical spring by plotting graph between load and extension.

3. To study the variation in volume with pressure for a sample of air at constant temperature

by plotting graphs between P and V, and between P and I/V.

4. To determine the surface tension of water by capillary rise method.

5. To determine the coefficient of viscosity of a given viscous liquid by measuring terminal velocity of a given spherical body.

6. To study the relationship between the temperature of a hot body and time by plotting a cooling curve.

7. (i) To study the relation between frequency and length of a given wire under constant tension using sonometer.

(ii) To study the relation between the length of a given wire and tension for constant frequency using sonometer.

8. To find the speed of sound in air at room temperature using a resonance tube by two resonance positions.

9. To determine specific heat of a given (i) solid (ii) liquid, by method of mixtures.

Activities

1. To observe change of state and plot a cooling curve for molten wax.

2. To observe and explain the effect of heating on a bi-metallic strip.

3. To note the change in level of liquid in a container on heating and interpret the observations.

4. To study the effect of detergent on surface tension by observing capillary rise.

5. To study the factors affecting the rate of loss of heat of a liquid.

6. To study the effect of load on depression of a suitably clamped metre scale loaded

(i) at its end

(ii) in the middle.

Recommended Textbooks.

1. Physics Part-I, Textbook for Class XI, Published by NCERT

2 . Physics Part-II, Textbook for Class XI, Published by NCERT

Class XI CHEMISTRY (Theory)

One Paper Time: 3 Hours 70 marks

Unit No. Title Marks

Unit I Some Basic concepts of chemistry 3

Unit II Structure of Atom 6

Unit III Classification of Elements and Periodicity in Properties 4

Unit IV Chemical Bonding and molecular Structure 5

Unit V States of Matter: Gases and Liquids 4

Unit VI Thermodynamics 6

Unit VII Equilibrium 6

Unit VIII Redox Reactions 3

Unit IX Hydrogen 3

Unit X S-Block Elements 5

Unit XI Some P-Block Elements 7

Unit XII Organic Chemistry: some basic Principles and Techniques 7

Unit XIII Hydrocarbons 8

Unit XIV Environmental Chemistry 3

Total 70

Unit I: Some Basic Concepts of Chemistry (Periods 14)

General Introduction: Importance and scope of chemistry.

Historical approach to particulate nature of matter, laws of chemical combination. Dalton’s atomic theory: concept of elements, atoms and molecules.

Atomic and molecular masses. Mole concept and molar mass: percentage composition,empirical and molecular formula; chemical reactions, stoichiometry and calculations based on Stoichiometry.

Unit II: Structure of Atom (Periods 16)

Discovery of electron, proton and neutron; atomic number, isotopes and isobars. Thomson’s model and its limitations, Rutherford’s model and its limitations. Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, De Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers, shapes of s, p, and d orbitals, rules for filling electrons in orbitals – Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

Unit III: Classification of Elements and Periodicity in Properties (Periods 8)

Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements –atomic radii, ionic radii. Ionization enthalpy, electron gain enthalpy, electro negativity, valence.

Unit IV: Chemical Bonding and Molecular Structure (Periods 16)

Valence electrons, ionic bond, covalent bond: bond parameters. Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital; theory of homo nuclear diatomic molecules (qualitative idea only), hydrogen bond.

Unit V: States of Matter: Gases and Liquids (Periods 14)

Three states of matter. Intermolecular interactions, type of bonding, melting and boiling points.

Role of gas laws in elucidating the concept of the molecule, Boyle’s law. Charles law, Gay Lussac’s law, Avogadro’s law. Ideal behaviour, empirical derivation of gas equation, Avogadro’snumber. Ideal gas equation. Derivation from ideal behaviour, liquefaction of gases, critical temperature.

Liquid State – Vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations).

Unit VI: Thermodynamics (Periods16)

Concepts Of System, types of systems, surroundings. Work, heat, energy, extensive and intensive properties, state functions.

First law of thermodynamics – internal energy and enthalpy, heat capacity and specific heat, measurement of DU and DH, Hess’s law of constant heat summation, enthalpy of: bond dissociation, combustion, formation, atomization, sublimation. Phase transformation, ionization,

and solution.

Introduction of entropy as a state function, free energy change for spontaneous and nonspontaneous processes, criteria for equilibrium.

Unit VII: Equilibrium (Periods 16)

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – ionization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts (elementary idea). Buffer solutions, solubility product, common ion effect (with illustrative examples).

Unit VIII: Redox Reactions (Periods 6)

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

Unit IX : Hydrogen (Periods 8)

Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides – ionic, covalent and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxide-preparation, properties and structure; hydrogen as a fuel.

Unit X: s-Block Elements (Alkali and Alkaline earth metals) (Periods 14)

Group 1 and Group 2 elements:

General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses.

Preparation and properties of some important compounds:

Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of sodium and potassium. CaO, CaCO3 and industrial use of lime and limestone, biological importance of Mg and Ca

Unit XI: Some p-Block Elements (Periods 16)

General Introduction to p-Block Elements

Group 13 elements: General introduction, electronic configuration, occurrence. Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron- physical and chemical properties, some important compounds: borax, boric acids, boron hydrides. Aluminium: uses, reactions with acids and alkalies.

Group 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element, Carbon – catenation, allotropic forms, physical and chemical properties; uses of some important compounds: oxides.

Important compounds of silicon and a few uses: silicon tetrachloride, silicones, silicates and zeolites.

Unit XII: Organic Chemistry – Some Basic Principles and Techniques

(Periods 14)

General introduction, methods of qualitative and quantitative analysis, classification and IUPAC

nomenclature of organic compounds Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation.

Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions

Unit XIII: Hydrocarbons (Periods 16)

Classification of hydrocarbons

Alkanes – Nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including halogenation, free radical mechanism, combustion and pyrolysis.

Alkenes – Nomenclature, structure of double bond (ethene) geometrical isomerism, physical properties, methods of preparation; chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition.

Alkynes – Nomenclature, structure of triple bond (ethyne), physical properties. Methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of – hydrogen, halogens, hydrogen halides and water.

Aromatic hydrocarbons: Introduction, IUPAC nomenclature; Benzene: resonance aromaticity ; chemical properties: mechanism of electrophilic substitution. – nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation: directive influence of functional group in mono-substituted benzene; carcinogenicity and toxicity.

Unit XIV: Environmental Chemistry (Periods 6)

Environmental pollution – air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming – pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of environmental pollution.

CBSE Board Syllabus Class XI-XII

CHEMISTRY (Code No. 043)

Rationale

Higher Secondary is the most crucial stage of school education because at this juncture specialized discipline based, content-oriented courses are introduced. Students reach this stage after 10 years of general education and opt for Chemistry with a purpose of pursuing their career in basic sciences or professional courses like medicine, engineering, technology and study courses in applied areas of science and technology at tertiary level. Therefore, there is a need to provide learners with sufficient conceptual background of Chemistry, which will make them competent to meet the challenges of academic and professional courses after the higher secondary stage.

The new and updated curriculum is based on disciplinary approach with rigour and depth taking care that the syllabus is not heavy and at the same time it is comparable to the international level. The knowledge related to the subject of Chemistry has undergone tremendous changes during the past one decade. Many new areas like synthetic materials, bio-molecules, natural resources, industrial chemistry are coming in a big way and deserve to be an integral part of chemistry syllabus at senior secondary stage At international level, new formulations and nomenclature of elements and compounds, symbols and units of physical quantities floated by scientific bodies like IUPAC and CGPM are of immense importance and need to be incorporated in the updated syllabus. The revised syllabus takes care of all these aspects. Greater emphasis has been laid on use of new nomenclature, symbols and formulations, teaching of fundamental concepts, applications of concepts in chemistry to industry/ technology, logical sequencing of units, removal of obsolete content and repetition etc.

OBJECTIVES

The broad objectives of teaching Chemistry at Senior Secondary Stage are to help the learners:

to promote understanding of basic facts and concepts in chemistry while retaining the excitement of chemistry.

to make students capable of studying chemistry in academic and professional courses (such as medicine, engineering, technology) at tertiary level.

to expose the students to various emerging new areas of chemistry and apprise them with their relevance in their future studies and their application in various spheres of chemical sciences and technology.

to equip students to face various changes related to health, nutrition, environment, population, weather, industries and agriculture.

to develop problem solving skills in students.

to expose the students to different processes used in industries and their technological applications.

to apprise students with interface of chemistry with other disciplines of science such as physics, biology, geology, engineering etc.

to acquaint students with different aspects of chemistry used in daily life.

to develop an interest in students to study chemistry as a discipline.

COURSE STRUCTURE

Class XI (Theory)

——————————————————————————————————————————————————-

One Paper Time: 3 Hours 70 marks

——————————————————————————————————————————————————

Unit No. Title Marks

Unit I Some Basic concepts of chemistry 3

Unit II Structure of Atom 6

Unit III Classification of Elements and Periodicity in Properties 4

Unit IV Chemical Bonding and molecular Structure 5

Unit V States of Matter: Gases and Liquids 4

Unit VI Thermodynamics 6

Unit VII Equilibrium 6

Unit VIII Redox Reactions 3

Unit IX Hydrogen 3

Unit X S-Block Elements 5

Unit XI Some P-Block Elements 7

Unit XII Organic Chemistry: some basic Principles and Techniques 7

Unit XIII Hydrocarbons 8

Unit XIV Environmental Chemistry 3

Total : 70

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Unit: Some Basic Concepts of Chemistry (Periods 14)

General Introduction: Importance and scope of chemistry.

Historical approach to particulate nature of matter, laws of chemical combination. Dalton’s atomic theory: concept of elements, atoms and molecules.

Atomic and molecular masses mole concept and molar mass: percentage composition, empirical and molecular formula chemical reactions, stoichiometry and calculations based on stoichiometry.

Unit II: Structure of Atom (Periods 16)

Discovery of electron, proton and neutron; atomic number, isotopes and isobars. Thomson’s model and its limitations, Rutherford’s model and its limitations. Bohr’s model and its limitations, concept of shells and subshells, dual nature of matter and light, de Broglie’s relationship, Heisenberg uncertainty principle, concept of orbitals, quantum numbers,

shapes of s, p, and d orbitals, rules for filling electrons in orbitals – Aufbau principle, Pauli exclusion principle and Hund’s rule, electronic configuration of atoms, stability of half filled and completely filled orbitals.

Unit III: Classification of Elements and Periodicity in Properties (Periods 8 )

Significance of classification, brief history of the development of periodic table, modern periodic law and the present form of periodic table, periodic trends in properties of elements -atomic radii, ionic radii. Ionization enthalpy, electron gain enthalpy, electro negativity, valence.

Unit IV: Chemical Bonding and Molecular Structure (Periods 16)

Valence electrons, ionic bond, covalent bond: bond parameters. Lewis structure, polar character of covalent bond, covalent character of ionic bond, valence bond theory, resonance, geometry of covalent molecules, VSEPR theory, concept of hybridization, involving s, p and d orbitals and shapes of some simple molecules, molecular orbital; theory of homo nuclear diatomic molecules (qualitative idea only), hydrogen bond.

Unit V: States of Matter: Gases and Liquids (Periods 14)

Three states of matter. Intermolecular interactions, type of bonding, melting and boiling points. Role of gas laws in elucidating the concept of the molecule, Boyle’s law. Charles law, Gay Lussac’s law, Avogadro’s law. Ideal behaviour, empirical derivation of gas equation, Avogadro’s number. Ideal gas equation. Derivation from ideal behaviour,

liquefaction of gases, critical temperature.

Liquid State – Vapour pressure, viscosity and surface tension (qualitative idea only, no mathematical derivations).

Unit VI: Thermodynamics (Periods16)

Concepts Of System, types of systems, surroundings. Work, heat, energy, extensive and intensive properties, state functions.

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 transformation, ionization, and solution.

Introduction of entropy as a state function, free energy change for spontaneous and nonspontaneous processes, criteria for equilibrium.

Unit VII: Equilibrium (Periods 16)

Equilibrium in physical and chemical processes, dynamic nature of equilibrium, law of mass action, equilibrium constant, factors affecting equilibrium – Le Chatelier’s principle; ionic equilibrium – ionization of acids and bases, strong and weak electrolytes, degree of ionization, concept of pH. Hydrolysis of salts (elementary idea). Buffer solutions, solubility product, common ion effect (with illustrative examples).

Unit VIII: Redox Reactions (Periods 6)

Concept of oxidation and reduction, redox reactions, oxidation number, balancing redox reactions, applications of redox reactions.

Unit IX : Hydrogen (Periods 8 )

Position of hydrogen in periodic table, occurrence, isotopes, preparation, properties and uses of hydrogen; hydrides – ionic, covalent and interstitial; physical and chemical properties of water, heavy water; hydrogen peroxide-preparation, properties and structure; hydrogen as a fuel.

Unit X: s-Block Elements (Alkali and Alkaline earth metals) (Periods 14)

Group 1 and Group 2 elements:

General introduction, electronic configuration, occurrence, anomalous properties of the first element of each group, diagonal relationship, trends in the variation of properties (such as ionization enthalpy, atomic and ionic radii), trends in chemical reactivity with oxygen, water, hydrogen and halogens; uses.

Preparation and properties of some important compounds:

Sodium carbonate, sodium chloride, sodium hydroxide and sodium hydrogen carbonate, biological importance of sodium and potassium.

CaO, CaCO3 and industrial use of lime and limestone, biological importance of Mg and Ca

Unit XI: Some p-Block Elements (Periods 16)

General Introduction to p-Block Elements

Group 13 elements: General introduction, electronic configuration, occurrence. Variation of properties, oxidation states, trends in chemical reactivity, anomalous properties of first element of the group; Boron- physical and chemical properties, some important compounds:

borax, boric acids, boron hydrides. Aluminium: uses, reactions with acids and alkalies.

Group 14 elements: General introduction, electronic configuration, occurrence, variation of properties, oxidation states, trends in chemical reactivity, anomalous behaviour of first element, Carbon – catenation, allotropic forms, physical and chemical properties; uses of some important compounds: oxides.

Important compounds of silicon and a few uses: silicon tetrachloride, silicones, silicates and zeolites.

Unit XII: Organic Chemistry – Some Basic Principles and Techniques (Periods 14)

General introduction, methods of qualitative and quantitative analysis, classification and IUPAC nomenclature of organic compounds

Electronic displacements in a covalent bond: inductive effect, electromeric effect, resonance and hyper conjugation.

Homolytic and heterolytic fission of a covalent bond: free radicals, carbocations, carbanions; electrophiles and nucleophiles, types of organic reactions

Unit XIII: Hydrocarbons (Periods 16)

Classification of hydrocarbons

Alkanes – Nomenclature, isomerism, conformations (ethane only), physical properties, chemical reactions including free radical mechanism of halogenation, combustion and pyrolysis.

Alkenes – Nomenclature, structure of double bond (ethene) geometrical isomerism, physical properties, methods of preparation; chemical reactions: addition of hydrogen, halogen, water, hydrogen halides (Markovnikov’s addition and peroxide effect), ozonolysis, oxidation, mechanism of electrophilic addition.

Alkynes - Nomenclature, structure of triple bond (ethyne), physical properties. Methods of preparation, chemical reactions: acidic character of alkynes, addition reaction of – hydrogen, halogens, hydrogen halides and water.

Aromatic hydrocarbons: Introduction, IUPAC nomenclature; benzene: resonance aromaticity; chemical properties: mechanism of electrophilic substitution. – nitration sulphonation, halogenation, Friedel Craft’s alkylation and acylation: directive influence of functional group in mono-substituted benzene; carcinogenicity and toxicity.

Unit XIV: Environmental Chemistry (Periods 6)

Environmental pollution – air, water and soil pollution, chemical reactions in atmosphere, smog, major atmospheric pollutants; acid rain, ozone and its reactions, effects of depletion of ozone layer, greenhouse effect and global warming – pollution due to industrial wastes; green chemistry as an alternative tool for reducing pollution, strategy for control of

environmental pollution.

Practicals

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Evaluation Scheme for Examination Marks

Volumetric Analysis 10

Salt Analysis 6

Content Based Experiment 4

Class Record and Viva 5

Investigatory project 5

Total 30

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PRACTICALS SYLLABUS Total Periods 60

A. Basic Laboratory Techniques (Periods 2)

1. Cutting glass tube and glass rod

2. Bending a glass tube

3. Drawing out a glass jet

4. Boring a cork

B. Characterization and purification of chemical substances (Periods 6)

1. Determination of melting point of an organic compound

2. Determination of boiling point of an organic compound

3. Crystallization of impure sample of anyone of the

following: Alum, copper sulphate, Benzoic acid.

C. Experiments related to pH change (Periods 6)

(a) Anyone of the following experiments:

Determination of pH of some solutions obtained from fruit juices, varied concentrations of acids. ,bases and salts using pH paper or universal indicator.

Comparing the pH of solutions of strong and weak acid of same concentration.

Study the pH change in the titration of a strong base using universal indicator.

b) Study of pH change by common-ion effect in case of weak acids and weak bases.

D. Chemical equilibrium (Periods 4)

One of the following experiments:

(a) Study the shift in equilibrium between ferric ions and thiocyanate ions by increasing/ decreasing the concentration of either ions.

(b) Study the shift in equilibrium between [Co(H2O)6]2+ and chloride ions by changing the concentration of either of the ions.

E. Quantitative estimation (Periods 16)

Using a chemical balance.

Preparation of standard solution of oxalic acid.

Determination of strength of a given solution of sodium hydroxide by titrating it against standard solution of oxalic acid.

Preparation of standard solution of sodium carbonate.

Determination of strength of a given solution of hydrochloric acid by titrating it against standard sodium carbonate solution.

F. Qualitative analysis (Periods 16)

Determination of one anion and one cation in a given salt

(Note: Insoluble salts excluded)

G. Detection of nitrogen, sulphur, Chlorine (Periods 10)

bromine and iodine in an organic compound.

PROJECT (Periods 10)

Scientific investigations involving laboratory testing and collecting information from other sources.

A Few suggested Projects

Checking the bacterial contamination in drinking water by testing sulphide ion.

Study of the methods of purification of water.

Testing the hardness, presence of iron, fluoride, chloride etc. depending upon the regional variation in drinking water and the study of causes of presences of these ions above permissible limit (if any).

Investigation of the foaming capacity of different washing soaps and the effect of addition of sodium carbonate on them.

Study of the acidity of different samples of the tea leaves.

Determination of the rate of evaporation of different liquids.

Study of the effect of acids and bases on the tensile strength of fibers.

Analysis of fruit and vegetable juices for their acidity.

Note: Any other investigatory project, which involves about 10 period of work, can be chosen with the approval of the teacher.

Recommended Textbooks.

1. Chemistry Part – I, Published by NCERT

2. Chemistry Part – II, Published by NCERT

COURSE STRUCTURE

Class XII (Theory)

——————————————————————————————————————————————————-

One Paper Time: 3 Hours 70 marks

——————————————————————————————————————————————————

Unit No. Title Marks

Unit I Solid State 4

Unit II Solutions 5

Unit III Electrochemistry 5

Unit IV Chemical kinetics 5

Unit V Surface chemistry 4

Unit VI General principles and processes of Isolation of Elements 3

Unit VII p-Block Elements 8

Unit VIII d- and f- Block Elements 5

Unit IX Coordination Compounds 3

Unit X Haloalkanes and Haloarenes 4

Unit XI Alcohols, Phenols and Ethers 4

Unit XII Aldehydes, Ketones and Carboxylic acids 6

Unit XIII Organic Compounds containing Nitrogen 4

Unit XIV Biomolecules 4

Unit XV Polymers 3

Unit XVI Chemistry in Everyday life 3

Total : 70

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Unit I: Solid State (Periods 12)

Classification of solids based on different binding forces: molecular, ionic, covalent and metallic solids, amorphous and crystalline solids (elementary idea), unit cell in two dimensional and three dimensional lattices, calculation of density of unit cell, packing in solids, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties.

Unit II: Solutions (Periods 12)

Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions, colligative properties – relative lowering of vapour pressure, elevation of Boiling Point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass.

Unit III: Electrochemistry (Periods 14)

Redox reactions, conductance in electrolytic solutions, specific and molar conductivity variations of conductivity with concentration, Kohlrausch’s Law, electrolysis and laws of electrolysis (elementary idea), dry cell – electrolytic cells and Galvanic cells; lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, fuel cells; corrosion.

Unit IV: Chemical Kinetics (Periods 12)

Rate of a reaction (average and instantaneous), factors affecting rate of reaction; concentration, temperature, catalyst; order and molecularity of a reaction; rate law and specific rate constant, integrated rate equations and half life (only for zero and first order reactions); concept of collision theory (elementary idea, no mathematical treatment)

Unit V: Surface Chemistry (Periods 8 )

Adsorption – physisorption and chemisorption; factors affecting adsorption of gases on solids; catalysis : homogenous and heterogeneous, activity and selectivity: enzyme catalysis; colloidal state: distinction between true solutions, colloids and suspensions; lyophilic, lyophobic, multimolecular and macromolecular colloids; properties of colloids; Tyndall effect, Brownian movement, electrophoresis, coagulation; emulsion – types of emulsions.

Unit VI: General Principles and Processes of Isolation of Elements (Periods 8 )

Principles and methods of extraction – concentration, oxidation, reduction electrolytic method and refining; occurrence and principles of extraction of aluminium, copper, zinc and iron.

Unit VII: p-Block Elements (Periods 14)

Group 15 elements: General introduction, electronic configuration, occurrence, oxidation states, trends in physical and chemical properties; nitrogen – preparation, properties and uses; compounds of nitrogen: preparation and properties of ammonia and nitric acid, oxides of nitrogen (structure only); Phosphorous-allotropic forms; compounds .of phosphorous: preparation and properties of phosphine, halides (PCl3, PCl5) and oxoacids (elementary idea only)

Group 16 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; dioxygen: preparation, properties and uses; simple oxides; Ozone. Sulphur – allotropic forms; compounds of sulphur: preparation, properties and uses of sulphur dioxide; sulphuric acid: industrial process of manufacture, properties and uses, oxoacids of sulphur (structures only).

Group 17 elements: General introduction, electronic configuration, oxidation states, occurrence, trends in physical and chemical properties; compounds of halogens: preparation, properties and uses of chlorine and hydrochloric acid, interhalogen compounds, oxoacids of halogens (structures only).

Group 18 elements: General introduction, electronic configuration. Occurrence, trends in physical and chemical properties, uses.

Unit VIII: d and f Block Elements (Period 14)

General introduction ,electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, colour catalytic property, magnetic properties, interstitial compounds, alloy formation preparation and properties of K2Cr2O7 and KMnO4.

Lanthanoids – electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction.

Actinoids – Electronic configuration, oxidation states.

Unit IX: Coordination Compounds (Period 12)

Coordination compounds – Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. bonding; isomerism, importance of coordination compounds (in qualitative analysis, extraction of metals and biological systems).

Unit X: Haloalkanes and Haloarenes. (Periods 12)

Haloalkanes:

Nomenclature, nature of C-X bond, physical and chemical properties, mechanism of substitution reactions.

Haloarenes:

Nature of C-X bond, substitution reactions (directive influence of halogen for monosubstituted compounds only)

Uses and environmental effects of – dichloromethane, trichloromethane, tetrachloromethane, iodoform, freons, DDT.

Unit XI: Alcohols, Phenols and Ethers (Periods 12)

Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only); identification of primary, secondary and tertiary alcohols; mechanism of dehydration, uses of methanol and ethanol.

Phenols : Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophillic substitution reactions, uses of phenols.

Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses.

Unit XII: Aldehydes, Ketones and Carboxylic Acids (Periods 12)

Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties mechanism of nucleophilic addition, reactivity of alpha hydrogen in aldehydes; uses.

Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.

Unit XIII: Organic compounds containing Nitrogen (Periods 10)

Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, identification of primary, secondary and tertiary amines.

Cyanides and Isocyanides – will be mentioned at relevant places in context.

Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry.

Unit XIV: Biomolecules (Periods 12)

Carbohydrates – Classification (aldoses and ketoses), monosaccahrides (glucose and fructose), oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); importance.

Proteins – Elementary idea of α – amino acids, peptide bond, polypeptides, proteins, structure of amines-primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes.

Vitamins -Classification and functions.

Nucleic Acids: DNA and RNA .

Unit XV: Polymers (Periods 8 )

Classification – natural and synthetic, methods of polymerization (addition and condensation), copolymerization. Some important polymers: natural and synthetic like polythene, nylon, polyesters, bakelite, rubber.

Unit XVI: Chemistry in Everyday life: (Period 8 )

1. Chemicals in medicines – analgesics, tranquilizers, antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.

2. Chemicals in food – preservatives, artificial sweetening agents.

3. Cleansing agents – soaps and detergents, cleansing action.

Practicals

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Evaluation Scheme for Examination Marks

Volumetric Analysis 10

Salt Analysis 6

Content Based Experiment 4

Class Record and Viva 5

Investigatory project 5

Total 30

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PRACTICALS SYLLABUS Total Periods 60

A. Surface Chemistry. (Periods 6)

(a) Preparation of one lyophilic and one lyophobic sol.

Lyophilic sol – starch, egg albumin and gum

Lyophobic sol – aluminium hydroxide, ferric hydroxide, arsenous sulphide.

(b) Study of the role of emulsifying agents in stabilizing the emulsions of different oils.

B. Chemical Kinetics (Periods 4)

(a) Effect of concentration and temperature on the rate of reaction between sodium thiosulphate and hydrochloric acid.

(b) Study of reaction rates of any one of the following:

(i) Reaction of iodide ion with hydrogen peroxide at room temperature using different concentration of iodide ions.

(ii) Reaction between potassium iodate, KIO3 and sodium sulphite: (Na2SO3) using starch solution as indicator (clock reaction).

C. Thermochemistry (Periods 4)

Any one of the following experiments

i) Enthalpy of dissolution of copper sulphate or potassium nitrate.

ii) Enthalpy of neutralization of strong acid (HC1) and strong base (NaOH)

iii) Determination of enthalpy change during interaction (Hydrogen bond formation) between acetone and chloroform

D. Electrochemistry (Period 2)

Variation of cell potential in Zn/Zn2+||Cu2+/Cu with change in concentration of electrolytes (CuSO4 or ZnSO4) at room temperature.

E. Chromatography (Periods 2)

i) Separation of pigments from extracts of leaves and flowers by paper chromatography and determination of Rf values.

ii) Separation of constituents present in an inorganic mixture containing two cations only (constituents having large difference in Rf values to be provided).

F. Preparation of Inorganic Compounds (Periods 4)

i) Preparation of double salt of ferrous ammonium sulphate or potash alum.

ii) Preparation of potassium ferric oxalate.

G. Preparation of Organic Compounds (Periods 4)

Preparation of any two of the following compounds

i) Acetanilide

ii) Di-benzal acetone

iii) p-Nitroacetanilide.

iv) Aniline yellow or 2 – Napthol aniline dye.

v) Iodoform

H. Tests for the functional groups present in organic compounds: (Periods 6)

Unsaturation, alcoholic, phenolic, aldehydic, ketonic, carboxylic and amino (primary) groups.

I. Characteristic tests of carbohydrates, fats and proteins in pure samples and their detection in given food stuffs. (Periods 4)

J. Determination of concentration/molarity of KMnO4 solution by titrating it against a standard solution of: (Periods 8 )

i) Oxalic acid,

ii) Ferrous ammonium sulphate (Students will be required to prepare standard solutions by weighing themselves).

K. Qualitative analysis (Periods 14 )

Determination of one cation and one anion in a given salt.

(Note: Insoluble salts excluded)

PROJECT

Scientific investigations involving laboratory testing and collecting information from other sources.

A few suggested Projects.

Study of presence of oxalate ions in guava fruit at different stages of ripening.

Study of quantity of casein present in different samples of milk.

Preparation of soybean milk and its comparison with the natural milk with respect to curd formation, effect of temperature, etc.

Study of the effect of potassium bisulphate as food preservative under various conditions (temperature, concentration, time etc.) :

Study of digestion of starch by salivary amylase and, effect of pH and temperature on it.

Comparative study of the rate of fermentation of following materials: wheat flour, gram flour, potato juice, carrot juice etc.

Extraction of essential oils present in Saunf (aniseed), Ajwain (carum), Illaichi (cardamom).

Study of common food adulterants in fat, oil, butter, sugar, turmeric powder, chilli powder and pepper.

Note: Any investigatory project, which involves about 10 periods of work, can be chosen with the approval of the teacher.

Recommended Textbooks.

1. Chemistry Part – I, Published by NCERT

2. Chemistry Part – II, Published by NCERT

MATHEMATICS (Code No 041)

The Syllabus in the subject of Mathematics has undergone changes from time to time in accordance with growth of the subject and emerging needs of the society. Senior Secondary stage is a launching stage from where the students go either for higher academic education in Mathematics or for professional courses like engineering, physical and Bioscience, commerce or computer applications. The present revised syllabus has been designed in accordance with National Curriculum Frame work 2005 and as per guidelines given in Focus Group on Teaching of Mathematics 2005 which is to meet the emerging needs of all categories of students. Motivating the topics from real life situations and other subject areas, greater emphasis has been laid on application of various concepts.

Objectives

The broad objectives of teaching Mathematics at senior school stage intend to help the pupil:

to acquire knowledge and critical understanding, particularly by way of motivation and visualization, of basic concepts, terms, principles, symbols and mastery of underlying processes and skills.

to feel the flow of reasons while proving a result or solving a problem.

to apply the knowledge and skills acquired to solve problems and wherever possible, by more than one method.

to develop positive attitude to think, analyze and articulate logically.

to develop interest in the subject by participating in related competitions.

to acquaint students with different aspects of mathematics used in daily life.

to develop an interest in students to study mathematics as a discipline.

to develop awareness of the need for national integration, protection of environment, observance of small family norms, removal of social barriers, elimination of sex biases.

to develop reverence and respect towards great Mathematicians for their contributions to the field of Mathematics.

COURSE STRUCTURE

Class XI

One Paper Three Hours Max Marks. 100

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Units Marks

I. SETS AND FUNCTIONS 29

II. ALGEBRA 37

III. COORDINATE GEOMETRY 13

IV. CALCULUS 06

V. MATHEMATICAL REASONING 03

VI. STATISTICS AND PROBABILITY 12

Total 100

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UNIT-I: SETS AND FUNCTIONS

1. Sets : (12) Periods

Sets and their representations. Empty set. Finite & 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. Difference of sets. Complement of a set.

2. Relations & Functions: (14) Periods

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 x R x R). Definition of relation, pictorial diagrams, domain. codomain and range of a relation. Function as a special kind of relation from one set to another. Pictorial representation of a function, domain, co-domain & range of a function. Real valued function of the real variable, domain and range of these functions, constant, identity, polynomial, rational, modulus, signum and greatest integer functions with their graphs. Sum, difference, product and quotients of functions.

3. Trigonometric Functions: (18) Periods

Positive and negative angles. Measuring angles in radians & in degrees and conversion from one measure to another. Definition of trigonometric functions with the help of unit circle. 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 sinx, siny, cosx & cosy. Deducing the identities like the following:

Identities related to sin 2x, cos2x, tan 2x, sin3x, cos3x and tan3x. General solution of trigonometric equations of the type sinθ = sin α, cosθ = cos α and tanθ = tan α.

UNIT-II: ALGEBRA

1. Principle of Mathematical Induction: (06) Periods

Processes 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.

2. Complex Numbers and Quadratic Equations: (10) Periods

Need for complex numbers, especially , to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.

3. Linear Inequalities: (10) Periods

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. Solution of system of linear inequalities in two variables- graphically.

4. Permutations & Combinations: (12) Periods

Fundamental principle of counting. Factorial n. (n!)Permutations and combinations, derivation of formulae and their connections, simple applications.

5. Binomial Theorem: (08) Periods

History, statement and proof of the binomial theorem for positive integral indices. Pascal’s triangle, General and middle term in binomial expansion, simple applications.

6. Sequence and Series: (10) Periods

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., geometric mean (G.M.), relation between A.M. and G.M. Sum to n terms of the special series Σn, Σn2 and Σn3.

UNIT-III: COORDINATE GEOMETRY

1. Straight Lines: (09) Periods

Brief recall of 2D from earlier classes. 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, twopoint form, intercepts form and normal form. General equation of a line. Distance of a point from a line.

2. Conic Sections: (12) Periods

Sections of a cone: circle, 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. Standard equation of a circle.

3. Introduction to Three -dimensional Geometry (08) Periods

Coordinate axes and coordinate planes in three dimensions. Coordinates of a point.

Distance between two points and section formula.

UNIT-IV: CALCULUS

1. Limits and Derivatives: (18) Periods

Derivative introduced as rate of change both as that of distance function and geometrically, intuitive idea of limit. Definition of derivative, relate it to slope of tangent of the curve, derivative of sum, difference, product and quotient of functions. Derivatives of polynomial and trigonometric functions.

UNIT-V: MATHEMATICAL REASONING

1. Mathematical Reasoning: (08) Periods

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 wordsdifference between contradiction, converse and contrapositive.

UNIT-VI: STATISTICS & PROBABILITY

1. Statistics: (10) Periods

Measure of dispersion; mean deviation, variance and standard deviation of ungrouped/grouped data. Analysis of frequency distributions with equal means but different variances.

2. Probability: (10) Periods

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, connections with the theories of earlier classes. Probability of an event, probability of ‘not’, ‘and’ & ‘or’ events.

Recommended Textbooks.

1) Mathematics Part I – Textbook for Class XI, NCERT Publication

2) Mathematics Part II – Textbook for Class XI, NCERT Publication

COURSE STRUCTURE

Class XII

One Paper Three Hours Max Marks. 100

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Units Marks

I. RELATIONS AND FUNCTIONS 10

II. ALGEBRA 13

III. CALCULUS 44

IV. VECTORS AND THREE – DIMENSIONAL GEOMETRY 17

V. LINEAR PROGRAMMING 06

VI. PROBABILITY 10

Total 100

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UNIT I. RELATIONS AND FUNCTIONS

1. Relations and Functions : (10) Periods

Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, inverse of a function. Binary operations.

2. Inverse Trigonometric Functions: (12) Periods

Definition, range, domain, principal value branches. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.

UNIT-II: ALGEBRA

1. Matrices: (18) Periods

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, 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). 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).

2. Determinants: (20) Periods

Determinant of a square matrix (up to 3 x 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. 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.

UNIT-III: CALCULUS

1. Continuity and Differentiability: (18) Periods

Continuity and differentiability, derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit function.Concept of exponential and logarithmic functions and their derivative. Logarithmic differentiation. Derivative of functions expressed in parametric forms. Second order derivatives. Rolle’s and Lagrange’s Mean Value Theorems (without proof) and their geometric interpretations.

2. Applications of Derivatives: (10) Periods

Applications of derivatives: rate of change, increasing/decreasing functions, tangents & normals, approximation, maxima and minima (first derivative test motivated geometrically and second derivative test given as a provable tool). Simple problems (that illustrate basic principles and understanding of the subject as well as real-life situations).

3. Integrals: (20) Periods

Integration as inverse process of differentiation. Integration of a variaty of functions by substitution, by partial fractions and by parts, only simple integrals of the type to be evaluated.

Definite integrals as a limit of a sum, Fundamental Theorem of Calculus (without proof). Basic properties of definite integrals and evaluation of definite integrals.

4. Applications of the Integrals: (10) Periods

Applications in finding the area under simple curves, especially lines, areas of circles/ parabolas/ellipses (in standard form only), area between the two above said curves (the region should be clearly identifiable).

5. Differential Equations: (10) Periods

Definition, order and degree, general and particular solutions of a differential equation. Formation of differential equation whose general solution is given. Solution of differential equations by method of separation of variables, homogeneous differential equations of first order and first degree. Solutions of linear differential equation of the type:

dy/dx+ py = q, where p and q are functions of x.

UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

1. Vectors: (12) Periods

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, 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.

2. Three – dimensional Geometry: (12) Periods

Direction cosines/ratios of a line joining two points. 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. Distance of a point from a plane.

UNIT-V: LINEAR PROGRAMMING

1. Linear Programming: (12) Periods

Introduction, definition of 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 constraints).

UNIT-VI: PROBABILITY

1. Probability: (18) Periods

Multiplication theorem on probability. Conditional probability, independent events, total probability, Baye’s theorem, Random variable and its probability distribution, mean and variance of haphazard variable. Repeated independent (Bernoulli) trials and Binomial distribution.

Recommended Textbooks.

1) Mathematics Part I – Textbook for Class XII, NCERT Publication

2) Mathematics Part II – Textbook for Class XII, NCERT Publication