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### CBSE Class 12 Mathematics Syllabus

Units & Marks:

RELATIONS AND FUNCTIONS - 10 Marks
ALGEBRA - 13 Marks
CALCULUS - 44 Marks
VECTORS AND THREE - DIMENSIONAL GEOMETRY - 17 Marks
LINEAR PROGRAMMING - 06 Marks
PROBABILITY - 10 Marks

Total : 100 Marks
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) Period
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 functions.Concept of exponential and logarithmic functions.
Derivatives of logarithmic and exponential functions. 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 interpretation.

2. Applications of Derivatives: (10) Periods
Applications of derivatives: rate of change of bodies, increasing/decreasing functions, tangents and normals, use of derivatives in 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 variety of functions by substitution, by partial fractions and by parts, simple integrals 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, 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 or constant
+ px = q, where p and q are functions of y or constant
UNIT-IV: VECTORS AND THREE-DIMENSIONAL GEOMETRY

1. Vectors: (12) Periods
Vectors and scalars, magnitude and direction of a vector. Direction cosines and direction ratios of a vector. 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. Scalar triple product of vectors.

2. Three - dimensional Geometry: (12) Periods
Direction cosines and direction 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, 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
Conditional probability, multiplication theorem on probability. independent events, total probability, Baye's theorem, Random variable and its probability distribution, mean and variance of random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
Recommended Textbooks:

1) Mathematics Part I - Textbook for Class XI, NCERT Publication
2) Mathematics Part II - Textbook for Class XII, NCERT Publication

### CBSE Class 12 Physics Syllabus

Time: 3 Hours
Marks: 70
Unit I : Electrostatics - 08
Unit II : Current Electricity - 07
Unit III : Magnetic effect of current & Magnetism - 08
Unit IV : Electromagnetic Induction and Alternating current - 08
Unit V : Electromagnetic Waves - 03
Unit VI : Optics - 14
Unit VII : Dual Nature of Matter - 04
Unit VIII : Atoms and Nuclei - 06
Unit IX : Electronic Devices - 07
Unit X : Communication Systems - 05

Total : 70
Unit I: Electrostatics (Periods 25)

Electric Charges; Conservation of charge, Coulomb’s law-force between two point charges, forces between multiple charges; superposition principle and continuous charge distribution. Electric field, electric field due to a point charge, electric field lines, electric dipole, electric field due to a dipole, torque on a dipole in uniform electric fleld.

Electric flux, statement of Gauss’s theorem and its applications to find field due to infinitely long straight wire, uniformly charged infinite plane sheet and uniformly charged thin spherical shell (field inside and outside). Electric potential, potential difference, electric potential due to a point charge, a dipole and system of charges; equipotential surfaces, electrical potential energy of a system of two point charges and of electric dipole in an electrostatic field. Conductors and insulators, free charges and bound charges inside a conductor. Dielectrics and electric polarisation, capacitors and capacitance, combination of capacitors in series and in parallel, capacitance of a parallel plate capacitor with and without dielectric medium between the plates, energy stored in a capacitor. Van de Graaff generator.
Unit II: Current Electricity (Periods 22)

Electric current, flow of electric charges in a metallic conductor, drift velocity, mobility and their relation with electric current; Ohm’s law, electrical resistance, V-I characteristics (linear and non-linear), electrical energy and power, electrical resistivity and conductivity. Carbon resistors, colour code for carbon resistors; series and parallel combinations of resistors; temperature dependence of resistance. Internal resistance of a cell, potential difference and emf of a cell,combination of cells in series and in parallel.

Kirchhoff’s laws and simple applications. Wheatstone bridge, metre bridge. Potentiometer - principle and its applications to measure potential difference and for comparing emf of two cells; measurement of internal resistance of a cell.
Unit III: Magnetic Effects of Current and Magnetism (Periods 25)

Concept of magnetic field, Oersted’s experiment.
Biot - Savart law and its application to current carrying circular loop. Ampere’s law and its applications to infinitely long straight wire. Straight and toroidal solenoids, Force on a moving charge in uniform magnetic and electric fields. Cyclotron. Force on a current-carrying conductor in a uniform magnetic field. Force between two parallel current-carrying conductors-definition of ampere. Torque experienced by a current loop in uniform magnetic field; moving coil galvanometer-its current sensitivity and conversion to ammeter and voltmeter. Current loop as a magnetic dipole and its magnetic dipole moment. Magnetic dipole moment of a revolving electron. Magnetic field intensity due to a magnetic dipole (bar magnet) along its axis and perpendicular to its axis. Torque on a magnetic dipole (bar magnet) in a uniform magnetic field; bar magnet as an equivalent solenoid, magnetic field lines; Earth’s magnetic field and magnetic elements. Para-, dia- and ferro - magnetic substances, with examples. Electromagnets and factors affecting their strengths. Permanent magnets.
Unit IV: Electromagnetic Induction and Alternating Currents (Periods 20)

Electromagnetic induction; Faraday’s laws, induced emf and current; Lenz’s Law, Eddy currents. Self and mutual induction.
Alternating currents, peak and rms value of alternating current/voltage; reactance and impedance; LC oscillations (qualitative treatment only), LCR series circuit, resonance; power in AC circuits,
wattless current.
AC generator and transformer.
Unit V: Electromagnetic waves (Periods 4)

Need for displacement current, Electromagnetic waves and their characteristics (qualitative ideas only). Transverse nature of electromagnetic waves. Electromagnetic spectrum (radio waves, microwaves, infrared, visible, ultraviolet, X-rays, gamma rays) including elementary facts about their uses.
Unit VI: Optics (Periods 30)

Reflection of light, spherical mirrors, mirror formula. Refraction of light, total internal reflection and its applications, optical fibres, refraction at spherical surfaces, lenses, thin lens formula, lensmaker’s formula. Magnification, power of a lens, combination of thin lenses in contact combination of a lens and a mirror. Refraction and dispersion of light through a prism. Scattering of light - blue colour of sky and reddish apprearance of the sun at sunrise and sunset. Optical instruments : Human eye, image formation and accommodation correction of eye defects (myopia, hypermetropia) using lenses. Microscopes and astronomical telescopes (reflecting and refracting) and their magnifying powers.

Wave optics: Wave front and Huygen's principle, relection and refraction of plane wave at a plane surface using wave fronts. Proof of laws of reflection and refraction using Huygen's principle. Interference Young's double slit experiment and expression for fringe width, coherent sources and sustained interference of light. Diffraction due to a single slit, width of central maximum. Resolving power of microscopes and astronomical telescopes. Polarisation, plane polarised light Brewster's law, uses of plane polarised light and Polaroids.
Unit VII: Dual Nature of Matter and Radiation (Periods 8)

Dual nature of radiation. Photoelectric effect, Hertz and Lenard’s observations; Einstein’s photoelectric equation-particle nature of light. Matter waves-wave nature of particles, de Broglie relation. Davisson-Germer experiment (experimental details should be omitted; only conclusion should be explained).
Unit VIII: Atoms & Nuclei (Periods 18)

Alpha-particle scattering experiment; Rutherford’s model of atom; Bohr model, energy levels, hydrogen spectrum.
Composition and size of nucleus, atomic masses, isotopes, isobars; isotones. Radioactivityalpha, beta and gamma particles/rays and their properties; radioactive decay law.
Mass-energy relation, mass defect; binding energy per nucleon and its variation with mass number; nuclear fission, nuclear fusion.
Unit IX: Electronic Devices (Periods 18)

Energy bands in solids (Qualitative ideas only) conductors, insulator and semiconductors; semiconductor diode – I-V characteristics in forward and reverse bias, diode as a rectifier; I-V characteristics of LED, photodiode, solar cell, and Zener diode; Zener diode as a voltage regulator. Junction transistor, transistor action, characteristics of a transistor, transistor as an amplifier (common emitter configuration) and oscillator. Logic gates (OR, AND, NOT, NAND and NOR). Transistor as a switch.
Unit X: Communication Systems (Periods 10)

Elements of a communication system (block diagram only); bandwidth of signals (speech, TV and digital data); bandwidth of transmission medium. Propagation of electromagnetic waves in the atmosphere, sky and space wave propagation. Need for modulation. Production and detection of an amplitude-modulated wave. Practicals Every student will perform atleast 15 experiments (7 from section A and 8 from Section B) The
activities mentioned here should only be for the purpose of demonstration. One Project of three marks is to be carried out by the students.

B. Evaluation Scheme for Practical Examination: Total Periods : 60
Two experiments one from each section : 8+8 Marks
Practical record (experiments & activities) : 6 Marks
Project : 3 Marks
Viva on experiments & project : 5 Marks
SUGGESTED INVESTIGATORY PROJECTS: CLASS XII

1 To study various factors on which the internal resistance/emf of a cell depends.

2. To study the variations, in current flowing, in a circuit containing a LDR, because of a variation.
(a) in the power of the incandescent lamp, used to 'illuminate' the LDR. (Keeping all the lamps at a fixed distance).
(b) in the distance of a incandescent lamp, (of fixed power), used to 'illuminate' the LDR.

3. To find the refractive indices of (a) water (b) oil (transparent) using a plane mirror, a equiconvex lens, (made from a glass of known refractive index) and an adjustable object needle.

4. To design an appropriate logic gate combinatin for a given truth table.

5. To investigate the relation between the ratio of
(i) output and input voltage and
(ii) number of turns in the secondary coil and primary coil of a self designed transformer.

6. To investigate the dependence, of the angle of deviation, on the angle of incidence, using a hollow prism filled, one by one, with different transparent fluids.

7. To estimate the charge induced on each one of the two identical styro foam (or pith) balls suspended in a vertical plane by making use of Coulomb's law.

8. To set up a common base transistor circuit and to study its input and output characteristic and to calculate its current gain.

9. To study the factor, on which the self inductance, of a coil, depends, by observing the effect of this coil, when put in series with a resistor/(bulb) in a circuit fed up by an a.c. source of adjustable frequency.

10. To construct a switch using a transistor and to draw the graph between the input and output voltage and mark the cut-off, saturation and active regions.

11. To study the earth's magnatic field using a tangent galvanometer.
Recommended Textbooks.

### CBSE Class 12 Chemistry Syllabus

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, packing efficiency, voids, number of atoms per unit cell in a cubic unit cell, point defects, electrical and magnetic properties. Band theory of metals, conductors, semiconductors and insulators and n & p type semiconductors.
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, Raoult's law, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass, van't Hoff factor.
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 law of electrolysis (elementary idea), dry cell - lectrolytic cells and Galvanic cells, lead accumulator, EMF of a cell, standard electrode potential, Nernst equation and its application to chemical cells, Relation between Gibbs energy change and emf of a cell, 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). Activation energy, Arrhenious equation.
Unit V: Surface Chemistry (Periods 8)

Adsorption - physisorption and chemisorption, factors affecting adsorption of gases on solids, catalysis, homogenous and heterogenous activity and selectivity; enzyme catalysis colloidal state distinction between true solutions, colloids and suspension; 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 & uses ; compounds of nitrogen, preparation and properties of ammonia and nitric acid, oxides of nitrogen (Structure only) ; Phosphorus - allotropic forms, compounds of phosphorus: 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, classification of oxides, Ozone, Sulphure -allotropic forms; compounds of sulphure: 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 (Periods 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 reactvity and lanthanoid contraction and its consequences. Actinoids - Electronic configuration, oxidation states and comparison with lanthanoids.
Unit IX: Coordination Compounds (Periods 12)

Coordination compounds - Introduction, ligands, coordination number, colour, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT, and CFT; structure and stereo isomerism, importance of coordination compounds (in qualitative inclusion, extraction of metals and biological system).
Unit X : Haloalkanes and Haloarenes. (Periods 12)
Haloalkanes: Nomenclature, nature of C -X bond, physical and chemical properties, mechanism of substitution reactions, optical rotation.
Haloarenes: Nature of C -X bond, substitution reactions (Directive influence of halogen in 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 with special reference to 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 nucleophillic 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), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen) importance. Proteins -Elementary idea of α - amino acids, peptide bond, polypeptides, proteins, structure of proteins - primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea excluding structure. 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. Biodegradable and non-biodegradable polymers.
Unit XVI: Chemistry in Everyday life (Periods 8)

Chemicals in medicines - analgesics, tranquilizers antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines. Chemicals in food - preservations, artificial sweetening agents, elementary idea of antioxidants. Cleansing agents- soaps and detergents, cleansing action.
Practicals (Marks)
Volumetric Analysis : 10
Salt Analysis : 8
Content Based Experiment : 6
Class record, project work and viva : 6

Total : 30
PRACTICAL SYLLABUS

Micro-chemical methods are available for several of the practical experiments. Wherever possible, such techniques should be used.
A. Surface Chemistry (Periods 5)
(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) Dialysis of sol-prepared in (a) above.
(c) Study of the role of emulsifying agents in stabilizing the emulsion 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 (HCI) and strong base (NaOH).
iii) Determination of enthaply change during interaction (Hydrogen bond formation) between acetone and chloroform.

D. Electrochemistry (Periods 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 2)
Preparation of any one of the following compounds
i) Acetanilide
ii) Di -benzal acetone
iii) p-Nitroacetanilide
iv) Aniline yellow or 2 - Naphthol aniline dye.

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.
Cation - Pb2+, Cu2+, As3+,
A3l , Fe3+,Mn2+, Zn2+, Co2+, Ni2+, Ca2+, Sr2+, Ba2+, Mg2+, NH+ 4
Anions - Co2- 3, S2-, SO2- 3, SO2- 4, NO- 2, NO- 3, Cl-, Br-, I-, PO3- 4, C2O2- 4, CH3COO- (Note: Insoluble salts excluded)
PROJECT

Scientific investigations involving laboratory testing and collecting information from other sources.
A few suggested Projects.
• Study of the 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 power, 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.

### CBSE Class 12 Computer Science Syllabus

UNIT 1: OBJECT ORIENTED PROGRAMMING IN C++

REVIEW: C++ covered In Class -XI, Object Oriented Programming:
Concept of Object Oriented Programming - Data hiding, Data encapsulation, Class and Object, Abstract class and Concrete class, Polymorphism (Implementation of polymorphism using Function overloading as an example in C++); Inheritance, Advantages of Object Oriented Programming over earlier programming methodologies,

Implementation of Object Oriented Programming concepts in C++:
Definition of a class, Members of a class - Data Members and Member Functions (methods), Using Private and Public visibility modes, default visibility mode (private); Member function definition: inside class definition and outside class definition using scope resolution operator (::); Declaration of objects as instances of a class; accessing members from object(s), Objects as function arguments - pass by value and pass by reference;

Constructor and Destructor:
Constructor: Special Characteristics, Declaration and Definition of a constructor, Default Constructor, Overloaded Constructors, Copy Constructor, Constructor with default arguments; Destructor: Special Characteristics, Declaration and definition of destructor;

Inheritance (Extending Classes):
Concept of Inheritance, Base Class, Derived Class, Defining derived classes, protected visibility mode; Single level inheritance, Multilevel inheritance and Multiple inheritance, Privately derived, Publicly derived and Protectedly derived class, accessibility of members from objects and within derived class(es);

Data File Handling:
Need for a data file, Types of data files - Text file and Binary file;
Text File : Basic file operations on text file: Creating/Writing text into file, Reading and Manipulation of text from an already existing text File (accessing sequentially); Binary File: Creation of file, Writing data into file, Searching for required data from file, Appending data to a file, Insertion of data in sorted file, Deletion of data from file, Modification of data in a file; Implementation of above mentioned data file handling in C++;

Components of C++ to be used with file handling: Header file:
fstream.h; ifstream, ofstream, fstream classes; Opening a text file in in, out, and app modes;
Using cascading operators (>> <<)for writing text to the file and reading text from the file; open(),
get(), put(), getline() and close() functions; Detecting end-of-file (with or without using eof() function);
Opening a binary file using in, out, and app modes;
open(), read(), write() and close() functions; Detecting end-of-file (with or without using eof()
function); tellg(), tellp(), seekg(), seekp() functions.

Pointers: Introduction to Printer, Declaration and Initialization of Pointers; Dynamic memory allocation/ deallocation operators: new, delete; Pointers and Arrays: Array of Pointers, Pointer to an array (1 dimensional array) Function returning a pointer, Reference variables and use of alias; Function call by reference. Pointer to structures: Deference operator: *, ->; self referencial structures;
UNIT 2: DATA STRUCTURES

Introduction to data structure, primitive and non-primitive data structure, linear and non-linear structure, static and dynamic data structure.
Arrays: One and two Dimensional arrays: Sequential allocation and address calculation;
One dimensional array: Traversal, Searching (Linear, Binary Search), Insertion of an element in an array, deletion of an element from an array, Sorting (Insertion, Selection, Two-dimensional arrays: Traversal, Finding sum/difference of two NxM arrays containing numeric values, Interchanging Row and Column elements in a two dimensional array;

Stack (Array and Linked implementation of Stack):
Operations on Stack (PUSH and POP) and its Implementation in C++, Converting expressions from INFIX to POSTFIX notation and evaluation of Postfix expression;
Queue: (Circular Array and Linked Implementation): Introduction to Queue (FIFO - First in First out operations) Operations on Queue (Insert and Delete) and its Implementation in C++.
UNIT 3: DATABASES AND SQL

Database Concepts: Introduction to data base concepts and its need.
Relational data model: Concept of domain, tuple, relation, key, primary key, alternate key, candidate key;
Relational algebra: Selection, Projection, Union and Cartesian product;

Structured Query Language: General Concepts: Advantages of using SQL, Data Definition Language and Data Manipulation Language;

Data types: NUMBER/DECIMAL, CHARACTER/VARCHAR/VARCHAR2, DATE;
SQL commands: CREATE TABLE, DROP TABLE, ALTER TABLE, UPDATE...SET..., INSERT, DELETE; SELECT, DISTINCT, FROM, WHERE, IN, BETWEEN, GROUP BY, HAVING, ORDER BY;
SQL functions: SUM, AVG, COUNT, MAX and MIN; Obtaining results (SELECT query) from 2 tables using equi-join, Cartesian Product and Union
Note: Implementation of the above mentioned commands could be done on any SQL supported software on one or two tables.
UNIT 4: BOOLEAN ALGEBRA

Role of Logical Operations in Computing.
Binary-valued Quantities, Logical Variable, Logical Constant and Logical Operators: AND, OR, NOT;
Truth Tables; Closure Property, Commutative Law, Associative Law, Identity law, Inverse law, Principle of Duality, Idem potent Law, Distributive Law, Absorption Law, Involution law, DeMorgan's Law and their applications;
Obtaining Sum of Product (SOP) and Product of Sum (POS) form from the Truth Table, Reducing Boolean Expression (SOP and POS) to its minimal form, Use of Karnaugh Map for minimization of Boolean expressions (up to 4 variables);

Application of Computing Logic:
Building up logic circuits using basic Logic Gates (NOT, AND, OR, NAND, NOT)
Use of Boolean operators (NOT, AND, OR) in SQL SELECT statements
Use of Boolean operators (AND, OR) in search engine queries.
UNIT 5: COMMUNICATION AND OPEN SOURCE CONCEPTS COMMUNICATION TECHNOLOGIES

Evolution of Networking: ARPANET, Internet, Interspace Different ways of sending data across the network with reference to switching techniques (Circuit, Message and Packet switching)
Data Communication terminologies: Concept of Channel, Baud, Bandwidth (Hz, KHz, MHz) and Data transfer rate (bps, kbps, Mbps, Gbps, Tbps)
Network devices: Modem, RJ45 connector, Ethernet Card, Hub, Switch, Gateway
Network Topologies and types: Bus, Star, Tree; PAN, LAN, WAN, MAN
Network Protocol: TCP/IP, File Transfer Protocol (FTP), PPP, Remote Login (Telnet), Internet Wireless/Mobile Communication protocol such as GSM, CDMA, GPRS, WLL, 1G, 2G and 3G Electronic mail protocols such as SMTP, POP3 Protocols for Chat and Video Conferencing VoIP protocols such as Wi-Fi and WiMax

Network Security Concepts: Threats and prevention from Viruses, Worms, Trojan horse, Spams Use of Cookies, Protection using Firewall; India IT Act, Cyber Law, Cyber Crimes, IPR issues, Hacking. WebServices: WWW, Hyper Text Markup Language (HTML), eXtensible Markup Language (XML); Hyper Text Transfer Protocol (HTTP); Domain Names; URL; Protocol Address; Website, Web browser, Web Servers; Web Hosting, Web Scripting - Client side (VB Script, Java Script, PHP) and Server side (ASP, JSP, PHP), Web 2.0 (for social networking) Open Standards Introduction to open standards and its advantage in development of inter-operable environment. Open Source Concepts Proprietory and Open Source Software, Freeware, Shareware, FLOSS/FOSS, GNU,FSF, OSI, W3C
Practicals:

1. Programming in C++ 10 - One programming problem in C++ to be developed and tested in Computer during the examination. Marks are allotted on the basis of following:

Logic : 5 Marks
Documentation/Indentation : 2 Marks
Output presentation : 3 Marks

Notes: The types of problems to be given will be of application type from the following topics.
Arrays (One dimensional and two dimensional)
Array of structure
Stack using arrays and linked implementation
Queue using arrays (circular) and linked implementation
Binary File operations (Creation, Displaying, Searching and modification)
Text File operations (Creation, Displaying and modification)

2. SQL Commands 05 - Five Query questions based on a particular Table/Reaction to be tested practically on Computer during the examination. The command along with the result must be written in the answer sheet.

3. Project Work 05 - The project has to be developed in C++ language with Object Oriented Technology and also should have use of Data files. (The project is required to be developed in a group of 2-4 students)
Presentation on the computer
Project report (Listing, Sample, Outputs, Documentation
Viva

4. Practical File 05 - Must have minimum 20 programs from the following topics
Arrays (One dimensional and two dimensional, sorting, searching, merging, deletion'& insertion of elements)
Arrays of structures,
Stacks using arrays and linked implementation
Queues using arrays (linear and circular) and linked implementation
File (Binary and Text) operations (Creation, Updation, Query)
Any computational based problems
15 SQL commands along with the output based on any table/relation: 3 Marks

5. Viva Voce 05 - Viva will be asked from syllabus covered in class XII and the project developed by student.
GUIDELINES FOR PROJECTS (Class XI and XII)

1. Preamble:
1.1 The academic course in Computer Science includes one Project in each year. The Purpose behind this is to consolidate the concepts and practices imparted during the course and to serve as a record of competence.
1.2 A group of 2-4 students as team may be allowed to work on one project.

2. Project content
2.1 Project for class XI can be selected from the topics mentioned in the syllabus or domains on the similar lines
2.2 Project for class XII should ensure the coverage of following areas of curriculum:
a. Problem Solving
b. Data Structure
c. Object Oriented Programming in C++
d. Data File Handling

Theme of the project can be
Any subsystem of a System Software or Tool
Any Scientific or a fairly complex algorithmic situation.
School Management, Banking, Library information system, Hotel or Hospital management system, Transport query system
Quizzes/Games;
Tutor/Computer Aided Learning Systems

2.3 The aim of the project is to highlight the abilities of algorithmic formulation, modular programming, optimized code preparation, systematic documentation and other associated aspects of Software Development.

2.4 The assessment would be through the project demonstration and the Project Report, which should portray Programming Style, Structured Design, Minimum Coupling, High Cohesion, Good documentation of the code to ensure readability and ease of maintenance.
Suggested Reference Books:

Computer Fundamentals and Boolean Algebra
1. Rajaraman, FUNDAMENTALS OF COMPUTERS 4th Edition, Prentice Hall of India.
2. Peter Norton, INTRODUCTION TO COMPUTER 4th Edition, Tata McGraw Hill
3. Thomas C. Bartee, DIGITAL COMPUTER FUNDAMENTALS, McGraw Hill International.

Problem Solving and Programming in C++
Note: Prior knowledge of C is not required in the learning of C++, eventhough reference about C are made in some of the books.
1. Robert Lafore, OBJECT ORIENTED PROGRAMMING IN TURBO C++, Galgotia Publications Pvt. Ltd.
2. David Parsons, OBJECT ORIENTED PROGRAMMING WITH C++, BPB Publications.
3. Bjarne Stroutrup, THE C++ PROGRAMMING LANGUGE, Adison Wesley.

Data Structures
1. M.A. Weiss, Data Structures and Algorithm Analysis in C++. the Benjamin/Cummings Pub. Co., Inc.
2. Sartaj & Sahni, Fundamentals of Data Structure, Galgotia Book Source

Database Management System and SQL
1. C.J. Date, DATABASE PRIMER, Adison Wesley.

Computer Network
1. A.S. Tanenbaum, Computer Network 4th Edition, Prentice Hall of India P. Ltd.
2. Williams Stalling, Data Communication and Networks 5th Edition, Prentice Hall of India P. Ltd.
3. Hancock, Network Concept and Architectures, BPB Publications.

### CBSE Class 12 Economics Syllabus

Part A : Introductory Microeconomics

Unit 1: Introduction 10 Periods
Meaning of microeconomics and macroeconomics
What is an economy? Central problems of an economy : what, how and for whom to produce; concepts of production possibility frontier and opportunity cost.

Unit 2: Consumer Equilibrium and Demand 32 Periods
Consumer's equilibrium – meaning of utility, marginal utility, law of diminishing marginal utility, conditions of consumer's equilibrium using marginal utility analysis. Indifference curve analysis of consumer's equilibrium-the consumer's budget (budget set and budget line), preferences of the consumer (indifference curve, indifference map) and conditions of consumer's equilibrium.
Demand, market demand, determinants of demand, demand schedule, demand curve, movement along and shifts in the demand curve; price elasticity of demand - factors affecting price elasticity of demand; measurenment of price elasticity of demand – (a) percentage-change method and (b) geometric method (linear demand curve); relationship between price elasticity of demand and total expenditure.

Unit 3: Producer Behaviour and Supply 32 Periods
Production function: Total Product, Average Product and Marginal Product.
Returns to a Factor.
Cost and Revenue: Short run costs - total cost, total fixed cost, total variable cost; Average fixed cost, average variable cost and marginal cost-meaning and their relationship.
Revenue - total, average and marginal revenue.
Producer's equilibrium-meaning and its conditions in terms of marginal revenue-marginal cost.
Supply, market supply, determinants of supply, supply schedule, supply curve, movements along and shifts in supply curve, price elasticity of supply; measurement of price elasticity of supply – (a) percentagechange method and (b) geometric method.

Unit 4: Forms of Market and Price Determination 22 Periods
Perfect competition - Features; Determination of market equilibrium and effects of shifts in demand and supply.
Other Market Forms - monopoly, monopolistic competition, oligopoly - their meaning and features.

Unit 5: Simple applications of Tools of demand and supply 8 Periods (not to be examined)
Part B : Introductory Macroeconomics

Unit 6: National Income and related aggregates 30 Periods
Some basic concepts: consumption goods, capital goods, final goods, intermediate goods; stocks and flows; gross investment and depreciation.
Circular flow of income; Methods of calculating National Income – Value Added or Product method,
Expenditure method, Income method.
Aggregates related to National Income:
Gross National Product (GNP), Net National Product (NNP), Gross and Net Domestic Product (GDP and NDP) - at market price, at factor cost; National Disposable Income (gross and net), Private Income, Personal Income and Personal Disposable Income; Real and Nominal GDP. GDP and Welfare
Unit 7: Money and Banking 18 Periods

Money – its meaning and functions.
Supply of money – Currency held by the public and net demand deposits held by commercial banks.
Money creation by the commercial banking system.
Central bank and its functions (example of the Reserve Bank of India).

Unit 8: Determination of Income and Employment 25 Periods
Aggregate demand and its components.
Propensity to consume and propensity to save (average and marginal).
Short–run equilibrium output; investment multiplier and its mechanism.
Meaning of full employment and involuntary unemployment.
Problems of excess demand and deficient demand; measures to correct them - change in government spending, availability of credit.

Unit 9: Government Budget and the Economy 17 Periods
Government budget - meaning, objectives and components.
Classification of receipts - revenue receipts and capital receipts; classification of expenditure - revenue expenditure and capital expenditure.
Measures of government deficit - revenue deficit, fiscal deficit, primary deficit:their meaning.
Fiscal Policy and its role (non evaluative topic)

Unit 10: Balance of Payments 14 Periods
Balance of payments account - meaning and components; balance of payments deficit-meaning.
Foreign exchange rate – meaning of fixed and flexible rates and managed floating.
Determination of exchange rate in a free market.
Recommended textbooks

1. Indian Economic Development, Class XI, NCERT
2. Introductory Micro Economics, Class XII, NCERT
3. Macro Economics, Class XII, NCERT
4. Supplimentary Reading Material in Economics, Class XII, CBSE
Note : The above publications are also available in Hindi Medium