CBSE 12TH 2018
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Last modified:2018-09-11 09:15:33
CBSE Class 12th Compartment Exam 2018 Registration Begins - Register Here:
Candidates who have appeared for CBSE Class 12th March 2018 Examination as regular candidates from CBSE affiliated institutions and placed as Compartment should approach the school from which they have appeared in CBSE Class 12th 2018 Examination for online submission of their Name. CBSE Class 12 Compartment Exam 2018 is scheduled to be held in July 2018. Only those Candidates whose name is submitted through the online process shall be allowed to appear for Examination to be held in July 2018. Regular candidates who appeared in March 2018 through schools affiliated to the Board and declared as COMPARTMENT are eligible to apply only in one or two subjects in which placed in Compartment. The last date for registration time without late fee is June 21.
Check the Circular for CBSE Class 12 Compartment Exam 2018
Check the fee details for CBSE Class 12 Compartment Exam 2018
Register for CBSE Class 12 Compartment Exam 2018
CBSE Begins Online Application For Revaluation Today; Check Schedule:
CBSE has released the schedule to apply for revaluation, verification of marks, application to obtain photocopy of evaluated answer sheet for 10th and 12th students. The application for re-verification should be submitted from June 1 to June 5, 2018. Students will have to pay Rs. 500 for each subject. Processing charges will be received through Credit/Debit Cards/ Net banking till June 7, 2018. The application process to obtain photocopy of evaluated answer sheets will be accepted from June 15 to June 16, 2018. Processing charges will be received through Credit/Debit Cards/ Net banking till June 18, 2018. The processing charges for class 12th answer sheet is Rs. 700 and for class 10th answer sheet is Rs. 500. The application for re-evaluation will be entertained from June 21 to June 22, 2018. The processing charge for re-evaluation application is Rs. 100. The processing fee will be accepted till June 25, 2018.
CBSE Related Pages updated on 26 Sep 2018
CBSE Class 12th Results declared on May 26, 2018:
Central Board of Secondary Education or CBSE, the national level education board which conducts secondary and higher secondary examinations across India, has released the Class 12th 2018 examination results on the official website cbseresults.nic.in on May 26, 2018.
Check CBSE Class 12th Result 2018
|Govt Jobs||Private Jobs||Free Mock Test||Current Affairs|
|Railway Jobs||Bank Jobs||GK||Result|
CBSE Class 12th Exams in Punjab - Postponed due to "Nationwide Bandh":
CBSE Board Examinations for Class X and XII, which were scheduled for April 2, 2018 Monday, have been postponed as a result of the shutdown call called by a number of Dalit organisations. Schools in Punjab will remain shut and buses will be off the road as well, until the Bharat Bandh gets over. The final practical examinations of classes 10 and 12 of the Punjab School Education Board will be conducted on April 11 instead of April 2, according to the directions of the Education Department.
CBSE Class 12th 2018 Admit Card Released:
CBSE Class 12th Exam Admit Cards 2018 have been released by the Central Board of Secondary Education (CBSE) on its official website - cbse.nic.in. Regular as well as Private candidate's Admit Cards are available online. CBSE Board Exams 2018 for Class 10th and Class 12th are slated to begin on 5th March 2018 and students can access important information like details of their Examination Centre, Roll Number and important instructions from the Admit Cards.
Download the CBSE Class 12th 2018 Admit Card - Regular Candidates | Private Candidates
CBSE Class 12th 2018 Time Table:
Central Board of Secondary Education, CBSE finally released the class 10th and 12th date sheet for 2018 board examinations. The examinations for the class 10th finish on April 4, 2018, and those of class 12 end on April 12 with Home Science paper.
Check the CBSE Class XII 2018 Time Table
CBSE Class 12th Practical Exams In January 2018; Theory Exam Date Sheet Awaited:
Central Board of Secondary Education (CBSE) has begun the process of Class 12th board examinations with the release of exam schedule for practical exams. CBSE Class 12th Practical examinations will begin in January 2018 and may continue till February 2018. Schools have been asked to upload the marks of the students by February, 2018.
CBSE Class 12th board examination comprises of internal or practical exam and external or theory exam. For theory subjects candidates have to obtain 33% marks in order to qualify; however for those subjects which have theory and practical examinations, candidates have to obtain 33% marks in both the exams to qualify; this norm is applicable for senior school certificate exam.
For last academic session, the CBSE Board had released the 10th, 12th Board Examination time table on 9 January 2017. This year, the Board will finalise the exam dates only after the election dates are released for few States.
About CBSE - Exam OverviewThe Central Board of Secondary Education (CBSE) (केंद्रीय माध्यमिक शिक्षा बोर्ड) is a school-level Educational Board at all India level under the Central Government. Besides CBSE there are two other all India level school boards and a number of state level boards.CBSE affiliates all Jawahar Navodaya Vidyalayas (JNV), all Kendriya Vidyalayas (KV), Private Schools, all the schools in the NCT of Delhi and Foreign Schools. The board conducts final examinations for All India Senior School Certificate Examination (AISSCE) for Class X.Every year CBSE conducts the final examinations for Class 10 and Class 12 in the month of March. The results are announced by the end of May. The X results mainly will decide the students to start their career decision towards medical or engineering.The major subjects students want to concentrate is Maths and Science.By Understanding the better concepts students can achieve better results.
Check the official CBSE 12th Exam updates here.
Exam Dates - CBSE 12th ClassThe dates for each subject and with their subject code are tabulated below for candidate's verification.
|CBSE Board Practicals Dates, Depending upon the subjects||-||Second and third week of February 2017|
English Elective – C
|March 2, 2017|
|Physics||042||March 9, 2017|
|Chemistry||043||March 12, 2017|
|Hindi Elective||002||March 14, 2017|
|Biology||044||March 23, 2017|
|March 27, 2017|
|Physical Education||048||March 30, 2017|
The Accountancy subject mainly deals with mathematics and financial subject whereas the topics are mentioned below.
Course Structure of CBSE 12th AccountancyThe course structure of Accountancy is prescribed below for the candidate's verification.
The Accountancy subject deals with the Commerce group students. Here the detailed Syllabus is prescribed below.
|Part A||Accounting for Partnership Firms and Companies||35|
|Unit 1. Accounting for Partnership Firms||25|
|Unit 2. Accounting for Companies||-|
|Part B||Financial Statement Analysis||-|
|Unit 3. Analysis of Financial Statements||12|
|Unit 4. Cash Flow Statement||8|
|Part C||Project Work||20|
|Part B||Computerized Accounting||-|
|Unit 3. Computerized Accounting||20|
|Part C||Practical Work||20|
Part A: Accounting for Partnership Firms and Companies
Unit 1: Accounting for Partnership Firms
- Partnership: features, Partnership Deed.
- Provisions of the Indian Partnership Act 1932 in the absence of partnership deed.
- Fixed v/s fluctuating capital accounts.Preparation of Profit and Loss Appropriation account- a division of profit among partners, a guarantee of profits.
- Past adjustments (relating to interest on capital, interest on drawing, salary and profit sharing ratio).
- Goodwill: nature, factors affecting and methods of valuation - average profit, super profit, and capitalization.
Accounting for Partnership firms - Reconstitution and Dissolution
- Change in the Profit Sharing Ratio among the existing partners - sacrificing ratio, gaining ratio, accounting for revaluation of assets and reassessment of liabilities and treatment of reserves and accumulated profits. Preparation of revaluation account and balance sheet.
- Admission of a partner - the effect of the admission of a partner on the change in the profit sharing ratio, treatment of goodwill (as per AS 26), treatment for revaluation of assets and reassessment of liabilities, treatment of reserves and accumulated profits, adjustment of capital accounts and preparation of balance sheet.
- Retirement and death of a partner: Effect of retirement/death of a partner on the change in profit sharing ratio, treatment of goodwill (as per AS 26), treatment for revaluation of assets and reassessment of liabilities, adjustment of accumulated profits and reserves, adjustment of capital accounts and preparation of balance sheet. Preparation of loan account of the retiring partner.
Calculation of deceased partner's share of profit till the date of death. Preparation of deceased partner's capital account, executor's account and preparation of balance sheet.
- Dissolution of a partnership: types of dissolution of a firm. Settlement of accounts -preparation of realization account, and other related accounts: capital accounts of partners and cash/bank a/c (excluding piecemeal distribution, sale to a company and insolvency of partners.
Unit-2 Accounting for Companies
Accounting for Share Capital :
- Share and share capital: nature and types.
- Accounting for share capital: issue and allotment of equity shares, private placement of shares, Employee Stock Option Plan (ESOP). Public subscription of shares - over subscription and under subscription of shares; issued at par and at a premium, calls in advance and arrears (excluding interest), issue of shares for consideration other than cash.
- Accounting treatment of forfeiture and re-issue of shares.
- Disclosure of share capital in company's Balance Sheet.
- Debentures: Issue of debentures at par, at a premium and at a discount. The issue of debentures for consideration other than cash; Issue of debentures with terms of redemption; debentures as collateral security-concept, interest on debentures.
- Redemption of debentures: Lump sum, the draw of lots and purchase in the open market (excluding ex-interest and cum-interest). Creation of
- Debenture Redemption Reserve.
Part B: Financial Statement Analysis
Unit 3: Analysis of Financial Statements
- Financial statements of a company: Statement of Profit and Loss and Balance Sheet in the prescribed form with major headings and subheadings (as per Schedule III to the Companies Act, 2013).
- Financial Statement Analysis: Objectives, importance, and limitations.
- Tools for Financial Statement Analysis: Comparative statements, common size statements, cash flow analysis, ratio analysis.
- Accounting Ratios: Objectives, classification, and computation.
- Liquidity Ratios: Current ratio and Quick ratio.
- Solvency Ratios: Debt to Equity Ratio, Total Asset to Debt Ratio, Proprietary Ratio and Interest Coverage Ratio.
- Activity Ratios: Inventory Turnover Ratio, Trade Receivables Turnover Ratio, Trade Payables Turnover Ratio and Working Capital Turnover Ratio.
- Profitability Ratios: Gross Profit Ratio, Operating Ratio, Operating Profit Ratio, Net Profit Ratio and Return on Investment.
Unit 4: Cash Flow Statement
Meaning, objectives, and preparation (as per AS 3 (Revised) (Indirect Method only)
Part B: Computerised Accounting
Unit 3: Computerised Accounting
- Overview of Computerised Accounting System
- Introduction: Application in Accounting.
- Features of Computerised Accounting System.
- Structure of CAS.
- Software Packages: Generic; Specific; Tailored.
Accounting Application of Electronic Spreadsheet
- The concept of an electronic spreadsheet.
- Features offered by an electronic spreadsheet.
- Application in generating accounting information - bank reconciliation statement; asset accounting; loan
- Repayment of loan schedule, ratio analysis
- Data representation - graphs, charts and diagrams.
Using Computerized Accounting System
- Steps in the installation of CAS, codification, and Hierarchy of account heads, the creation of accounts.
- Data: Entry, validation and verification.
- Adjusting entries, preparation of balance sheet, profit and loss account with closing entries and opening entries. Need and security features of the system.
Database Management System (DBMS)
- Concept and Features of DBMS.
- DBMS in Business Application.
- Generating Accounting Information. -
The biology subject deals with the science related units and the course structure is mentioned below.
Course Structure of CBSE 12th BiologyThe course structure of CBSE 12th Biology is prescribed below for candidate's verification.
|VII||Genetics and Evolution||18|
|VIII||Biology and Human Welfare||14|
|IX||Biotechnology and its Applications||10|
|X||Ecology and Environment||14|
The Biology subject is the main subject for the science group students.Here is the brief syllabus of Biology
Unit VI. Reproduction
Reproduction, a characteristic feature of all organisms for the continuation of species; Asexual reproduction Modes of reproduction-Asexual and sexual reproduction; Modes-Binary fission, sporulation, budding, gemmule, fragmentation; vegetative propagation in plants.
Chapter-2: Sexual Reproduction in Flowering Plants
Flower structure; Development of male and female gametophytes; Pollination-types, agencies, and examples; Outbreeding devices; Pollen-Pistil interaction; Double fertilization; Post fertilization events-Development of endosperm and embryo, Development of seed and formation of fruit; Special modes-apomixis, parthenocarpy, polyembryony; Significance of seed and fruit formation.
Chapter-3: Human Reproduction
Male and female reproductive systems; Microscopic anatomy of testis and ovary; Gametogenesis-spermatogenesis & oogenesis; Menstrual cycle; Fertilisation embryo development upto blastocyst formation, implantation; Pregnancy and placenta formation (Elementary idea); Parturition (Elementary idea); Lactation (Elementary idea).
Chapter 4: Reproductive Health
Need for reproductive health and prevention of sexually transmitted diseases (STD); Birth control – Need and Methods, Contraception and Medical Termination of Pregnancy (MTP); Amniocentesis; Infertility and assisted reproductive technologies - IVF, ZIFT, GIFT (Elementary idea for general awareness).
Unit VII. Genetics and Evolution
Chapter-5: Principles of Inheritance and Variation
Mendelian Inheritance; Deviations from Mendelism-Incomplete dominance, Co-dominance, Multiple alleles and Inheritance of blood groups, Pleiotropy; Elementary idea of polygenic inheritance; Chromosome theory of inheritance; Chromosomes and genes; Sex determination - in humans, birds, honey bee; Linkage and crossing over; Sex linked inheritance - Haemophilia, Colour blindness; Mendelian disorder in humans-Thalassemia; Chromosomal disorders in humans; Down's syndrome, Turner's and Klinefelter's syndromes.
Chapter-6: Molecular Basis of Inheritance
Search for genetic material and DNA as genetic material; Structure of DNA and RNA; DNA packaging; DNA replication; Central dogma; Transcription, genetic code, translation; Gene expression and regulation - Lac Operon; Genome and human genome project; DNA fingerprinting.
Origin of life; Biological evolution and evidence for biological evolution (Paleontological, comparative anatomy, embryology and molecular evidence); Darwin's contribution, Modern Synthetic theory of Evolution; Mechanism of evolution - Variation (Mutation and Recombination) and Natural Selection with examples, types of natural selection; Gene flow and genetic drift; Hardy - Weinberg's principle; Adaptive Radiation; Human evolution.
Unit VIII. Biology and Human Welfare
Chapter-8: Human Health and Diseases
Pathogens; parasites causing human diseases (Malaria, Filariasis, Ascariasis, Typhoid, Pneumonia, common cold, amoebiasis, ring worm); Basic concepts of immunology - vaccines; Cancer, HIV and AIDs; Adolescence, drug and alcohol abuse.
Chapter-9: Strategies for Enhancement in Food Production
Improvement in food production: Plant breeding, tissue culture, single cell protein, Biofortification, Apiculture and Animal husbandry.
Chapter-10: Microbes in Human Welfare
In household food processing, industrial production, sewage treatment, energy generation and as biocontrol agents and biofertilizers. Antibiotics; production and judicious use.
Unit IX. Biotechnology and Its Applications
Chapter-11: Biotechnology - Principles and Processes
Genetic engineering (Recombinant DNA technology).
Chapter-12: Biotechnology and its Application
Application of Biotechnology in health and agriculture: Human insulin and vaccine production, gene therapy; Genetically modified organisms-Bt crops; Transgenic Animals; biosafety issues, biopiracy, and patents.
Download your official CBSE 12th Class Biology syllabus
The Business Studies is the important subject for the Commerce Students.Here is the course structure are mentioned below.
Course structure of CBSE 12th Business Studies
|Part A||Principles and Functions of Management||-|
|1||Nature and Significance of Management||16|
|2||Principles of Management|
|Part B||Business Finance and Marketing|
|Part C||Project Work||20|
CBSE 12th Syllabus for Business Studies
Part A: Principles and Functions of Management
Unit I: Nature and Significance of Management
- Management - concept, objectives, and importance
- Management as Science, Art, and Profession
- Levels of management
- Management functions - planning, organizing, staffing, directing and controlling
Coordination - concept, characteristics, and importance.
Unit 2: Principles of Management
- Principles of Management - concept, nature, and significance
- Fayol’s principles of management
- Taylor’s Scientific Management - principles and techniques.
- Business Environment - concept and importance
- Dimensions of Business Environment - Economic, Social, Technological, Political and Legal
- Impact of Government policy changes on business with special reference to liberalization, privatization, and globalization in India.
Unit 4: Planning
- Concept, importance, and limitations
- Planning process
- Single use and Standing Plans - Objectives, Strategy, Policy, Procedure, Method, Rule, Budget and Programme.
Unit 5: Organising
- Concept and importance.
- Organizing Process.
- Structure of organization - functional and divisional.
- Formal and informal organization.
- Delegation: concept, elements and importance.
- Decentralization: concept and importance.
Unit 6: Staffing
- Concept and importance of staffing
- Staffing as a part of Human Resource Management
- Staffing process: Recruitment - sources; Selection - process
- Training and Development - Concept and importance. Methods of training- on the job and off the job- Induction training, vestibule training, apprenticeship training and internship training.
Unit 7: Directing
- Concept and importance
- Elements of Directing: - Supervision - concept, functions of a supervisor.; - Motivation - Concept, Maslow’s hierarchy of needs; Financial and non-financial incentives.; - Leadership - concept, styles - authoritative, democratic and laissez faire.; - Communication - concept, formal and informal communication; barriers to effective; communication, how to overcome the barriers.
Unit 8: Controlling
- Concept, nature, and importance
- Relationship between planning and controlling
- Steps in the process of control.
Part B: Business Finance and Marketing
Unit 9: Financial Management
- Concept and objectives of financial management.
- Financial decisions: investment, financing and dividend and factors affecting.
- Financial planning - concept and importance.
- Capital Structure - concept and factors affecting.
- Fixed and Working Capital - concept and factors affecting their requirements.
- Financial Markets: concept and types.
- Money market and its instruments.
- Capital market and its types (primary and secondary).
- Stock Exchange - functions and training procedure. Depository Services and D'mat Account.
Unit 11: Marketing Management
- Marketing - concept, and functions.
- Marketing management philosophies.
- Marketing Mix - concept
- Product - concept, branding, labeling, and packaging. Price - factors determining the price.
- Physical distribution- concept, channels of distribution: types, choice of channels.
- Promotion -concept, and elements; advertising- concept, role, objections against advertising, personal selling - concept and qualities of a good salesman, sales promotion - concept and techniques, public relations - concept and role.
Unit 12: Consumer Protection
- Concept and importance of consumer protection.
- Consumer Protection Act 1986
- Meaning of consumer and consumer protection.
- Rights and responsibilities of consumers
- Who can file a complaint and against whom?
- Redressal machinery.
- Remedies available.
- Consumer awareness - Role of consumer organizations and Non-Governmental Organizations (NGOs).
Chemistry is an important scoring subject in the science. The course structure is mentioned below.
Course structure of CBSE 12th Chemistry
The course structure of chemistry is prescribed below
|VI||Isolation of Elements||19|
|VIII||d- and f-Block Elements|
|X||Haloalkanes and Haloarenes||28|
|XI||Alcohols, Phenols, and Ethers|
|XII||Aldehydes, Ketones and Carboxylic Acids|
|XIII||Organic Compounds containing Nitrogen|
|XVI||Chemistry in Everyday Life|
CBSE 12th Class Syllabus for Chemistry
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 I: Solid State
Unit II: Solutions
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, vant Hoff factor.
Unit III: Electrochemistry
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 -electrolytic 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
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, Arrhenius equation.
Unit V: Surface Chemistry
Adsorption - physisorption and chemisorption, factors affecting adsorption of gases on solids, catalysis, homogeneous 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
Principles and methods of extraction - concentration, oxidation, reduction -electrolytic method and refining; occurrence and principles of extraction of aluminum, copper, zinc, and iron.
Unit VII: p - Block Elements
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 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, classification of 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
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, color, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K2Cr2O7 and KMnO4.
Unit IX: Coordination Compounds
Coordination compounds - Introduction, ligands, coordination number, color, magnetic properties and shapes, IUPAC nomenclature of mononuclear coordination compounds. Bonding, Werner's theory, VBT, and CFT; structure and stereoisomerism, the importance of coordination compounds (in qualitative inclusion, extraction of metals and biological system).
Unit X: Haloalkanes and Haloarenes
- Haloalkanes: Nomenclature, nature of the 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
- 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, electrophilic substitution reactions, uses of phenols.
- Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses.
- Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, the 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
- 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
- Carbohydrates - Classification (aldoses and ketoses), monosaccharides (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, the 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
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
- Chemicals in medicines - analgesics, tranquilizers antiseptics, disinfectants, antimicrobials, antifertility drugs, antibiotics, antacids, antihistamines.
- Chemicals in food - preservatives, artificial sweetening agents, elementary idea of antioxidants.
- Cleansing agents - soaps and detergents, cleansing action.
Economics is a general subject for the Commerce Group students. Here the course structure is mentioned below.
Course structure of CBSE 12th EconomicsThe course structure of CBSE 12th Economics is mentioned below.
|Part A: Introductory Microeconomics||-|
|Consumer Equilibrium and Demand||16|
|Producer Behaviour and Supply||16|
|Forms of Market and Price Determination||12|
|Part B: Introductory Macroeconomics||-|
|National Income and Related Aggregates||15|
|Money and Banking||8|
|Determination of Income and Employment||12|
|Government Budget and the Economy||8|
|Balance of Payments||7|
CBSE Class 12th Syllabus for Economics
Unit 2: Consumer Equilibrium and Demand
- Consumer's equilibrium – meaning of utility, marginal utility, the 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 and its slope, movement along and shifts in the demand curve; price elasticity of demand - factors affecting price elasticity of demand; measurement 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.
- Production function - Short-Run and Long-Run
- 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 cost; Average fixed cost, average variable cost and marginal cost-meaning and their relationship.
- Revenue - total, average and marginal revenue - meaning and their relationship.
- Producer's equilibrium-meaning and its conditions in terms of marginal revenue-marginal cost.
Unit 4: Forms of Market and Price Determination
- 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.
- Simple Applications of Demand and Supply: Price ceiling, price floor.
Part B: Introductory Macroeconomics
Unit 5: National Income and related aggregates
- Some basic concepts: consumption goods, capital goods, final goods, intermediate goods; stocks and flows; gross investment and depreciation.
- The 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 6: Money and Banking
- 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.
- The Central bank and its functions ( an example of the Reserve Bank of India): Bank of the issue, Govt. Bank, Banker's Bank, Controller of Credit through Bank Rate, CRR, SLR, Repo Rate and Reverse Repo Rate, Open Market Operations, Margin requirement.
Unit 7: Determination of Income and Employment
- Aggregate demand and its components. The 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, taxes and money supply.
Unit 8: Government Budget and the Economy
- 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.
- The balance of payments account - meaning and components; the balance of payments deficit-meaning.
- Foreign exchange rate - the meaning of fixed and flexible rates and managed to float.
- Determination of exchange rate in a free market.
The Engineering Graphics mainly related to the diagram related topics and also with the practical. The course structure is mentioned below.
Course Structure of Engineering Graphics
The course structure of Engineering Graphics are mentioned below
|Unit||Topic / Chapter||Marks|
|I||Isometric Projections of Solids||25|
|A. Drawing of Machine parts||-|
|B. Assemble Drawing and Dis-assembly drawings||-|
Unit I: Isometric Projection of Solids
- (i) Construction of isometric scale showing main divisions of 10 mm and smaller divisions of 1 mm, also showing the leading angles. Drawing helping views such as triangles, pentagon, hexagon, etc., using an isometric scale.
- (ii) Isometric projections (drawn to isometric scale) of solids such as cube, regular prism and pyramids (triangular, square, pentagonal and hexagonal), cone, cylinder, sphere, hemisphere, frustum of right regular pyramids (triangular, square, pentagonal, hexagonal) and cone, when they are cut by a plane parallel to the base. The axis and the base side of the solid should be either perpendicular to HP / VP or parallel to HP and VP. (Indicate the direction of viewing)
- (iii) Combination of two solids (except "frustum" of Pyramids and Cone) Keeping the base side parallel or perpendicular to HP/VP and placed centrally together, axis of both the solids should not be given parallel to HP.
(1) Question on frustum will be asked in the vertical position only.
(2) Hidden lines are not required in isometric projection.
Unit II: Machine Drawing
A. Drawing of machine parts
(i) Drawing to full-size scale with instruments.
(Internal choice will be given between any two of the following).
Introduction of threads: Standard profiles of screw threads square, knuckle, B.S.W., Metric (external and internal). Bolts (Square, Hexagonal, Tee, and Hook); Nuts: (Square and Hexagonal), Plain washer, a combination of nut and bolt with or without a washer for assembling two parts together, Single riveted lap joint with standard dimensions.
(ii) Freehand sketches
(Internal choice will be given between any two of the following).
Conventional representation of external and internal threads; studs (plain, square-neck, and collar), screws (round-head, cheesehead, 900 flat countersunk-head, hexagonal socket head and grub-screw). Types of rivets:- snap head, pan head-without tapered neck, flat head and 600 countersunk flat head. Types of sunk-keys (rectangular taper, Woodruff and double-head feather key with gib head on both ends).
B. Assembly drawings and Dis-Assembly drawings
(Internal choice will be given between an Assembly drawing and a Dis-Assembly drawing).
1. In all Assembly drawings, the half sectional front view will be asked. Side/End view or Top View/Plan will be drawn without section.
2. In all the Dis-assembly drawings, only two orthographic views (one of the two views may be half in section or full in section) of any two parts.
3. (a) In all sectional views, hidden lines/edges are not to be shown. (b) In all full views, hidden /edges are to be shown.
- (i) Open-Bearing
- (ii) Bushed-Bearing
- (i) Cotter-joints for circular-rods (socket and spigot joint)
- (ii) Cotter-joints for round-rods (sleeve and cotter joint)
- (iii) Cotter-joints for square rods (Gib and cotter-joint)
- (i) Turnbuckle
- (ii) Flange pipe joint
- (i) Unprotected Flange Coupling (having socket and spigot arrangement)
- (ii) Protected Flange Coupling
Download your CBSE 12th Class Engineering Graphics Syllabus.
The English language which plays a very important role in language papers recently.The course structure of English Core is mentioned below.
Course structure of English Core
The Course structure of English core is given below as
|Section||Unit/Area of Learning||Marks|
|C||Literature & Long Reading Text||40|
|(i) Flamingo + Value Based||-|
|(ii) Supplementary Reader - Vistas|
- Two unseen passages with a variety of very short answer / short answer or MCQ type questions to test comprehension, interpretation, and inference. Vocabulary such as word formation and inference of meaning will also be tested.
- The total length of the two passages will be between 1100 and 1200 words.
- a. Factual passages, e.g., instructions, descriptions, reports.
- b. Descriptive passages involving opinion, e.g., argumentative, persuasive or interpretative text.
- c. Literary passages, e.g., extract from fiction, drama, poetry, essay or biography. A poem could be of 28-35 lines.
- The passages can be literary, factual or discursive to test comprehension. The length of one passage should be between 600-700 words.
- The third passage of 400-500 words for note-making and abstraction.
- Short Answer Questions, e.g., advertisement and notices, designing or drafting posters, writing formal and informal invitations and replies.
- Long Answer Questions: Letters based on the verbal/visual input.
- Letter types include
- Business or official letters (for making inquiries, registering complaints, asking for and giving information, placing orders and sending replies)
- Letters to the editor (giving suggestions or opinion on issues of public interest.
- Application for a job
- Very Long Answer Questions: Two compositions based on visual and/or verbal Input may be descriptive or argumentative in nature such as an article, a debate or a speech.
- Flamingo and Vistas
- Very Short Answer Questions - Based on an extract from poetry to test comprehension and appreciation.
- Short Answer Questions - Based on prose/drama/poetry from both the texts.
- Long Answer Question - Based on texts to test global comprehension and extrapolation beyond the texts to bring out the key messages and values.
- Long Answer Question - Based on texts to test global comprehension along with analysis and extrapolation.
- Long Answer Question - Based on the theme, plot, and incidents from the prescribed novels.
- Long Answer Question - Based on understanding appreciation, analysis and interpretation of the character sketch.
- Prescribed Books
- Flamingo: English Reader published by NCERT
- Vistas: Supplementary Reader published by NCERT.
Course structure of English Elective
The course structure of English Elective is mentioned as
|B||Writing Skills and Grammar||40|
|C||Literary Texts & Long Reading||40|
Section A: Reading Skills
Very short answer / Short answer and MCQ type questions:
Two unseen passages (including poems) with a variety of questions including 04 marks for vocabulary such as word formation and inferring meaning. The total range of the two passages including a poem or a stanza should be around 1000-1100 words to assess comprehension, analysis, inference, evaluation and literary appreciation.
550-600 words in length (for note-making and summarising)
450-500 words in length (to test comprehension)
The passage could be of any one of the following types:
Factual passages, e.g., illustrations, description, reports
Discursive passages involving opinion, e.g., argumentative, persuasive
Literary passages, e.g., poems, extracts from fiction, biography, autobiography, travelogue, etc. In the case of a poem, the text may be shorter than the prescribed word limit.
Section B: Writing Skills and Grammar
Short Answer Question: Notices, advertisements, factual description of people, places and objects, drafting posters, drafting, accepting and declining invitations.
Long Answer Question: Letter of any of the following types based on a verbal or visual input:
a) Official letters for making inquiries, suggesting changes - registering and responding to complaints, asking for and giving information, placing orders and sending replies.
b) Letters to the editor on various social, national and international issues.
c) Application for a job including CV (Curriculum Vitae) / Resumé.
Very Long Answer Question: Sustained writing task such as writing a speech, an article for a magazine or a report based on the verbal/visual input.
A variety of questions, as listed below may be asked, involving the application of grammar items in context (i.e., not in isolated sentences). The grammar syllabus will be sampled each year. Though only models, determiners, voice and tense forms have been dealt with in class XI, however, other grammar items such as prepositions, verb forms, connectors which have been learned earlier would also be included.
Very Short Questions and Multiple Choice Questions
Reordering of words and sentences
Composing a dialogue based on a given input
Error correction in sentences
Drafting questions/questionnaires based on given input
Section C: Literature: Prescribed Books and Long Reading Text (Novel)
- Questions to test comprehension at different levels and of different kinds - local, global, interpretative, inferential, evaluative and extrapolation.
- Very Short and Short Answer Questions: Two based on out of three extracts from different poems to test theme, setting and literary devices.
- Short Answer Questions: Based on different prose/drama/poetry/pieces from the Literature Reader; to test local and global comprehension of ideas and languages used in the text.
- Long Answer Question: Extended questions based on one of the prose texts or play in the Literature Reader to test global comprehension and for extrapolation beyond the text.
- Long Answer Questions: To test understanding, appreciation, analysis, inference in a plot and writing a character sketch.
Note: Values based questions for 4 marks may be asked in Sections - B or C
1. Language Skills book - Class XII English Elective CBSE published by Central Board of Secondary Education, Delhi.
2. Literature Reader - Class XII English Elective CBSE published by Central Board of Secondary Education, Delhi.
3. Novel (either one)
- i) The Invisible Man (Unabridged) by H.G. Wells
- ii) Silas Marner (Unabridged) by George Eliot.
Geography subject mainly deals with countries and their capitals and also a deatiled study about the regions.The course structure of
Geography is mentioned below.
Course Structure of Geography
The course structure of Geography is below
|A||Fundamentals of Human Geography||35|
|Unit 1||Human Geography||-|
|Unit 3||Human Activities||-|
|Unit 4||Transport, Communication, and Trade||-|
|Unit 5||Human settlements||-|
|B||India: People and Economy||35|
|Unit 7||Human Settlements||-|
|Unit 8||Resources and Development||-|
|Unit 9||Transport, Communication, and International Trade||-|
|Unit 10||Geographical Perspective on selected issues and problems||-|
|Unit 1||Processing of Data and Thematic Mapping||15|
|Unit 2||Field study or Spatial Information Technology||10|
|Unit 3||Practical Record Book and Viva Voce||5|
A. Fundamentals of Human Geography
Unit 1: Human Geography: Nature and Scope
Unit 2: People
Population-distribution,density and growth
Population change-spatial patterns and structure; determinants of population change;
Age-sex ratio; rural-urban composition;
Human development - concept; selected indicators, international comparisons
Unit 3: Human Activities
Primary activities - concept and changing trends; gathering, pastoral, mining, subsistence agriculture, modern agriculture; people engaged in agricultural and allied activities - some examples from selected countries.
Secondary activities-concept; manufacturing: types - household, small scale, large scale; agro-based and mineral based industries; people engaged in secondary activities - some examples from selected countries.
Tertiary activities-concept; trade, transport, and tourism; services; people engaged in tertiary activities - some examples from selected countries.
Quaternary activities - concept; people engaged in quaternary activities - a case study from selected countries.
Unit 4: Transport, Communication & Trade
Land transport - roads, railways; trans-continental railways.
Water transport - inland waterways; major ocean routes.
Air transport - Intercontinental air routes.
Oil and gas pipelines.
Satellite communication and cyberspace- Importance and usage for geographical information; use of GPS.
International trade-Bases and changing patterns; ports as gateways of international trade, the role of WTO in International trade.
Ocean: National rights and international treaties.
Unit 5: Human settlements
Settlement types - rural and urban; morphology of cities (case study); distribution of megacities; problems of human settlements in developing countries.
Map Work on the identification of features based on 1-5 units on the outline/Physical/Political Map of World.
B. India: People and Economy
Unit 6: People
Population: distribution, density, and growth; composition of the population - linguistic, religious; sex, rural-urban and occupational-regional variations in the growth of population.
Migration: international, national-causes and consequences.
Human development: selected indicators and regional patterns.
Population, environment, and development.
Unit 7: Human Settlements
Rural settlements - types and distribution.
Urban settlements - types, distribution and functional classification.
Unit 8: Resources and Development
Land resources - general land use; agricultural land use, Geographical conditions and distribution of major crops (Wheat, Rice, Tea, Coffee, Cotton, Jute, Sugarcane, and Rubber), agricultural development and problems.
Water resources - availability and utilization-irrigation, domestic, industrial and other uses; scarcity of water and conservation methods -rain water harvesting and watershed management.
Mineral and energy resources - distribution of metallic (Iron ore, Copper, Bauxite, Manganese); non-metallic (Mica, Salt) minerals; conventional (Coal, Petroleum, Natural gas and Hydroelectricity) and non-conventional energy sources (solar, the wind, biogas) and conservation.
Industries - types, factors of industrial location; distribution and changing pattern of selected industries-iron and steel, cotton textiles, sugar, petrochemicals, and knowledge based industries; the impact of liberalization, privatization, and globalization on industrial location; industrial clusters.
Planning in India - target group area planning (case study); the idea of sustainable development (case study).
Unit 9: Transport, Communication, and International Trade
Transport and communication-roads, railways, waterways, and airways: oil and gas pipelines; Geographical information and communication networks.
International trade - changing pattern of India's foreign trade; seaports and their hinterland and airports.
Unit 10: Geographical Perspective on selected issues and problems
Environmental pollution; urban - waste disposal.
Urbanisation, rural-urban migration; problems of slums.
Map work on locating and labeling of features based on above units on an outline map of India.
C. Practical Work
Unit 1: Processing of Data and Thematic Mapping
Unit 2: Field study or Spatial Information Technology.
Download your CBSE 12th Class Geography Syllabus
Course Structure of History
The course structure of History is mentioned below
|Units 1 - 4||Themes in Indian History Part - I||25|
|Units 5 - 9||Themes in Indian History Part - II||25|
|Units 10 - 15||Themes in Indian History Part - III||25|
|Unit 16||Map Work||5|
Syllabus of CBSE 12th History
The syllabus of CBSE 12th History is prescribed below.
Themes in Indian History Part-I
1. The Story of the First Cities: Harappan Archaeology
2. Political and Economic History: How Inscriptions tell a story
3. Social Histories: Using the Mahabharata
4. A History of Buddhism: Sanchi Stupa
Themes in Indian History Part-II
5. Agrarian Relations: The Ain-i- Akbari
6. The Mughal Court: Reconstructing Histories through Chronicles
7. New Architecture: Hampi
8. Religious Histories: The Bhakti-Sufi tradition
9. Medieval Society Through Travellers' Accounts
Themes in Indian History Part-III
10. Colonialism and-Rural Society: Evidence from Official Reports
11. Representations of 1857
12. Colonialism and Indian Towns: Town Plans and Municipal Reports
13. Mahatma Gandhi through Contemporary Eyes
14. Partition through Oral Sources
15. The Making of the Constitution
Unit 16: Map Work
Download your CBSE 12th Class History Syllabus.
Home Science subject deals with the is the science of a home and it includes all the things that concern the person, home, family members, and resources. It is the education for "better living" and the core of this education is the family ecosystem.
Course Structure of Home Science
The course structure of Home Science is prescribed below
|I||Human Development: Lifespan Approach (Part II)||30|
|II||Nutrition for Self, Family, and Community|
|III||Money Management and Consumer Education||35|
|IV||Apparel: Designing, Selection, and Case|
|V||Community Development and Extension (Part II)||5|
|VI||Career Option after Home Science Education|
Unit I: Human Development: Lifespan Approach (Part II)
A. Adolescence (12 - 18 years)(i) Growth & Development - Domains and principles.
(ii) Meaning, characteristics, and needs.
(iii) Influences on identity formation
(a) Biological and Physical changes-early and late mature. (Role of heredity and environment)
(b) Social, culture and media.
(c) Emotional changes.
(d) Cognitive changes.
(iv) Specific issues and concerns
(a) Eating disorders-Causes, consequences, and management - Anorexia Nervosa, Bulimia.
(c) Substance Abuse
(d) Related to sex
(e) Handling stress and peer pressure.
(i) Young & middle adulthood: Understanding and management of new responsibilities, carrier marriage, and family.
(ii) Late Adulthood/Old age:
(a) Health and Wellness: physical, social, emotional, financial, recreational needs
(b) Care for elderly (at home and outside - old age home)
(c) Anger management
Unit II: Nutrition for Self, Family and Community
(a) Meal Planning: Meaning and importance, principles and factors affecting meal planning; Nutritional needs, food preferences and modifications of diets in different age groups: infants, children, adolescents, adults, elderly and in special conditions: pregnancy and lactation (including traditional foods given in these conditions)
- (i) Use of basic food groups (ICMR) and serving size in meal planning
- (ii) Factors influencing selection of food: culture, family food practices, media, peer group, availability of foods, purchasing power, individual preference & health.
- (b) Food safety and quality:
- (i) Safe food handling (personal, storage, kitchen, cooking and serving).
- (ii) Safety guards against food adulteration, definition and meaning of food adulteration as given by FSSAI (Food Safety and Standard Authority of India).
- (iii) Common adulterants present in cereals, pulses, milk and milk products, fats and oils, sugar, jaggery, honey, spices and condiments.
- (iv) Effects of some of the adulterants present in the foods: kesari dal, metanil yellow, argemone seeds.
- (v) Food standards (FPO, Agmark, ISI).
- (c) Therapeutic modification of normal diet with respect to consistency, frequency, foodstuffs, nutrients and methods of cooking.
- (d) Modification of diet according to common ailments: diarrhoea, fever, jaundice, hypertension, diabetes and constipation. Physiological changes, clinical symptoms, requirements and dietary requirements in each condition.
Unit III: Money Management and Consumer Education
(a) Family Income:
- (i) Various sources of family income:
- money income
- real income, (direct and indirect)
- psychic income
- (ii) Supplementing family income-need and ways; need and procedure for maintaining household accounts (daily, weekly and monthly).
(b) Savings and Investment:
- (i) Meaning and importance of savings.
- (ii) The basis for selection of investment methods: risk, security, profit, tax saving.
- (iii) Ways/methods of investment -
- Bank schemes (saving, fixed, recurring);
- Post Office schemes (savings, recurring deposit, monthly income scheme, National saving certificate, Senior citizen scheme);
- Insurance schemes (whole life, mediclaim);
- Public Provident Fund (PPF), Provident Fund (PF).
- (iv) Consumer Protection and Education: Meaning, problems faced by the consumer, Consumer Protection Amendment Act (2011); Consumer aids: labels, standardization marks, (ECO Mark, Hallmark, Woolmark, Silk mark), advertising, leaflets, and Consumer redressal forum, Internet.
Unit IV: Apparel: Designing, Selection, and Care
- (i) Application of elements of art and principles of design in designing apparel.
- (ii) Selection and purchase of fabrics- purpose, cost, season, quality, durability, ease of maintenance and comfort.
- (iii) Selection of apparel- factors influencing the selection of apparel- age, size, climate, occupation, figure, occasion, fashion, drape cost and workmanship.
- (iv) Care and maintenance of clothes: Cleansing agents: soaps and detergents (basic differences and their utility); General principles of stain removal, stain removal of tea, coffee, lipstick, ball pen, Grease, Curry and Blood.
- (v) Storage of clothes.
Unit V: Community Development and Extension (Part II)
- (i) Water safety: Safe drinking water-importance of potable water for good health, and its qualities, simple methods of making water safe for drinking; boiling, filtering (traditional and modern technology), use of alum, chlorine.
- (ii) Salient features of income generating schemes
- DWCRA (Development of Women and Children in Rural Area)
- MGNREGA (Mahatma Gandhi National Rural Employment Guarantee Act, 2005)
Unit VI: Career Options after Home Science Education
Career options for self and wage employment of various fields of Home Science.
Download your CBSE 12th class Home Science Syllabus
Mathematics subject deals with the problems and important topics which are common to all the groups. The course structure of Mathematics is prescribed below.
Course Structure of Mathematics
The course structure of Mathematics is prescribed below.
|I.||Relations and Functions||10|
|IV.||Vectors and 3D Geometry||17|
Syllabus of CBSE 12th Class MathematicsUnit I: Relations and Functions
1. Relations and Functions
Types of relations: reflexive, symmetric, transitive and equivalence relations. One to one and onto functions, composite functions, the inverse of a function. Binary operations.
2. Inverse Trigonometric Functions
Definition, range, domain, principal value branch. Graphs of inverse trigonometric functions. Elementary properties of inverse trigonometric functions.
Unit II: Algebra
The concept, notation, order, equality, types of matrices, zero and identity matrix, the transpose of a matrix, symmetric and skew-symmetric matrices. Operation on matrices: Addition and multiplication and multiplication with a scalar. 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).The 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).
The 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 a number of solutions of a system of linear equations by examples, solving system of linear equations in two or three variables (having a unique solution) using the inverse of a matrix.
Unit III: Calculus
1. Continuity and Differentiability
Continuity and differentiability, a derivative of composite functions, chain rule, derivatives of inverse trigonometric functions, derivative of implicit functions. The 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
Applications of derivatives: the 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).
Integration as an inverse process of differentiation.Integration of a variety of functions by substitution, by partial fractions and by parts, Evaluation of simple integrals of the following types and problems based on them.
4. Applications of the Integrals
Applications in finding the area under simple curves, especially lines, circles/parabolas/ellipses (in standard form only), Area between any of the two above said curves (the region should be clearly identifiable).
5. Differential Equations
Definition, order, and degree, general and particular solutions of a differential equation.Formation of the differential equation whose general solution is given.A solution of differential equations by the method of separation of variables solutions of homogeneous differential equations of first order and first degree. Solutions of the linear differential equation of the type:
dy/dx + py = q, where p and q are functions of x or constants.
dx/dy + px = q, where p and q are functions of y or constants.
Unit IV: Vectors and Three-Dimensional Geometry
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, the addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio. Definition, Geometrical Interpretation, properties, and application of the scalar (dot) product of vectors, vector (cross) product of vectors, a scalar triple product of vectors.
2. Three-Dimensional Geometry
Direction cosines and direction ratios of a line joining two points.Cartesian equation and vector equation of a line, coplanar and skew lines, the shortest distance between two lines.Cartesian and vector equation of a plane.The angle between (i) two lines, (ii) two planes, (iii) a line and a plane.The distance of a point from a plane.
Unit V: Linear Programming
1. Linear Programming
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 (bounded and unbounded), feasible and infeasible solutions, optimal feasible solutions (up to three non-trivial constraints).
Unit VI: Probability
Conditional probability, multiplication theorem on probability. independent events, total probability, Bayes theorem, Random variable and its probability distribution, mean and variance of a random variable. Repeated independent (Bernoulli) trials and Binomial distribution.
Download your CBSE 12th Class Mathematics Syllabus
Syllabus of CBSE 12th class for Physics
The syllabus of CBSE 12th Class for physics are mentioned below
Section A : Very Short Answers
Section B: Short Answers
Section C: Very Big Questions
Section D: Large Answers
Download your CBSE 12th Class Physics Syllabus.
Syllabus of CBSE 12th Class for Political Science
The syllabus of CBSE 12th Class for Political Science are mentioned below
Section A : Very Short Answer
Section B : Short Answer
Section C: Long Answers
Section D : Map-Based Questions
Download your CBSE 12th Class Political Science Syllabus.
Syllabus of CBSE 12th Class for Psychology
The syllabus of CBSE 12th class for Psychology are mentioned below
Section A : Learning Outcomes and Testing Techniques
Section B : Very Short Answer
Section C : Short Answer
Section D : Long Answer
Download your CBSE 12th Class Psychology Syllabus.
Syllabus of CBSE 12th Class for Sociology
Section A : Learning Outcomes and Testing Techniques
Section B : Very Short Answer
Section C : Short Answer
Section D : Long Answer
Download your CBSE 12th class for Sociology
Syllabus of CBSE 12th Class for Language Subjects
The syllabus of CBSE 12th Class for Language Subjects namely Assamese, Bengali, Bodo, Gujarati, Kannada, Marathi, Malayalam, Manipuri , Odia,Punjabi,Tamil etc are mentioned below.
Section A : Learning Outcomes and Testing Techniques
Section B : Very Short Answer
Section C : Short Answer
Section D : Long Answer
Download your CBSE 12th class for Language /Volume II Subjects.
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