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CBSE Class IX SA1 Sample Paper 2014 – Maths


CBSE Class IX SA1 Sample Paper 2014 – Science

NCERT Solutions for Class 8th Hindi Chapter 11 जब सिनेमा ने बोलना सीखा

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NCERT Solutions for Class 8th Hindi Chapter 11 जब सिनेमा ने बोलना सीखा

National Council of Educational Research and Training (NCERT) Book Solutions for Class 8th
Subject: Hindi
Chapter: Chapter 11 – जब सिनेमा ने बोलना सीखा

Class 8th Hindi Chapter 11 जब सिनेमा ने बोलना सीखा NCERT Solution is given below.

NCERT Solutions for Class 8th Hindi
NCERT Solutions for Class 8th Hindi
NCERT Solutions for Class 8th Hindi
NCERT Solutions for Class 8th Hindi

Click Here to view All Chapters Solutions for Class Class 8th Hindi

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NTSE 2013 – Girl toppers

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Anusha Singhaniya and Nandita Mehta from Punjab have cracked National Talent Search Examination organized by NCERT. National Talent Search Exam is an all-India level exam, wherein thousands of students try to bag scholarships for higher studies.

As many as 1,034 students out of 40,000 cleared the exam with Punjab topping the list with 45.

Anusha and Nandita are Class XI (medical) students at Sacred Heart Convent School, Sarabha Nagar.

Nandita Mehta

She scored 98 marks out of 150.  She says, “The result came as a pleasant surprise. It”s a great feeling. I was preparing for NTSE for the past two years and it is extremely tough to manage school studies along with the preparations. But hard work is the ultimate key to success. I worked hard and nailed it.”

Talking about her preparations and tons of hard work put in, Nandita said, “For me it was not just scholarship but the determination to crack the exam. I won”t say that I burnt midnight oil, but I balanced my entire schedule and completed each concept with full determination and total dedication.”

Anusha Singhaniya

She cleared the exam with 94 marks out of 150. While expressing her feelings, Anusha says, “NTSE is one of the most prestigious exam. Being a NTSE scholar is like a life-time achievement for me. It”s a proud feeling to be one of the handful who aced the exam.”

“It was not easy to prepare for the NTSE as there were school studies and examination too. Making a schedule and following it was difficult. My parents and teachers were my supportive system. They encouraged and motivated me to do my best and it is their faith in me that I was bale to crack this exam. I dedicate my success to my parents and teachers.”

Both Anusha and Nandita wish to be doctors in future and will work hard towards achieving this dream.

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NTSE 2013 Topper – Rank 7 – Preetham Upadhyaya

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Preetham Upadhyaya, who secured all India rank (AIR) seven and Karnataka rank two, said preparing for the national-level exam was tough since it involved students who were extremely brilliant. “I did not refer to a lot of books but I did concentrate on the textbooks prescribed by NCERT for mathematics, science and social science from classes nine and ten,” said Preetham.

As many as 64 students from Bangalore have bagged scholarships under the National Talent Search Examination (NTSE), conducted by the National Council of Educational Research and Training (NCERT) in May. The students will now be entitled to a scholarship of Rs 6,000 per year.

The state-level exam was conducted in November 2012. Of the 40,000 students who took the exam from Karnataka, 223 qualified for the national-level scholarship held in May 2013.

NTSE is conducted to identify students with extremely high intellect and academic talent and until 2012, it was conducted for students of class eight. In 2013, NCERT cancelled this and programmed it for students of class ten.

For students pursuing professional courses like engineering, medicine, law and management, financial assistance is provided till postgraduate level and for the ones pursuing basic sciences, social sciences and commerce, assistance up to PhD level is provided.

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National Talent Search Exam (NTSE) Toppers

NCERT Solutions for Class 9th Hindi: Chapter 14 चन्द्र गहना से लौटती बेर

CBSE 2013 – 2014 Class 09 SA1 Question Paper – Social Science

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Central Board of Secondary Education Question Paper

Year: 2013 – 2014
Examination: Summative Assessment I (SA1)
Class: IX
Subject: Social Science

This question paper is provided by Mr. Sumant, Class 9 Student of St. Anselm’s Pink City, Jaipur

Question Paper will be uploaded on 30th Sep 2013. Please visit again on 30th Sep 2013 for Social Science Question Paper.

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CBSE 2013 – 2014 Class 09 SA1 Question Paper – English

Indian Army Medical Standards

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A candidate should have robust physique and good mental health. Chest should be well developed having minimum 5 Cms expansion. Should have normal hearing with each ear and good binocular vision in both eyes. He should be able to read 6/6 in distant vision chart with each eye. Colour vision should be CP-III. Should recognize red and green colours. Should have sufficient number of natural healthy gum and teeth i.e. minimum 14 dental points. Should not have disease like deformity of bones, hydrocele and varicocle or piles.

Physical Fitness Tests(PFT)

To determine the Physical Fitness, the following tests carrying 100 marks are held :-

   (a)  1 Mile Run
(b)  Pull Ups
(c)  Balance
(d)  9 Feet Ditch

Marking system is as follows :-

   (a)  1 MILE RUN

         (i)   5.40 Mins and below                          60 Mks
(ii)   5.41 Mins to 5.50                             48 Mks
(iii)  5.51 Mins to 6 .05                             36 Mks
(iv)  6.06 Mins to 6.20                              24 Mks

   (b)  PULL UPS

          (i)   10 and above                                     40 Mks
(ii)   9                                                     33 Mks
(iii)  8                                                     27 Mks
(iv)  7                                                     21 Mks
(v)   6                                                     16 Mks

   (c)  BALANCE  Should be qualified and no marks are awarded.

   (d)  9 Feet Ditch    Should be qualified and no marks are awarded.

Medical Standards :-

   (a) A candidate should have robust physique and good mental health.

   (b) Chest should be well developed having minimum 5 Cms expension.

   (c) Should have normal hearing with each ear and good binocular vision in both eyes. He should be
able to read 6/6 in distance vision chart with each eye. Colour vision should  be CP-III.

   (d) Should have sufficient number of natural healthy gum and teeth i.e. minimum 14 dental points.

   (e) Should not have diseases like deformity of bones, hydrocele and varicocle or piles.

   (f)  Should recognize red and green colours.

For More Indian Army Career Opportunities Information please click here

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CBSE Class 12 Chemistry Notes: Solutions – Osmosis and Osmotic Pressure

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Osmosis

In osmosis, there is a net flow of solvent molecules from the solvent to the solution or from a less concentrated solution to a more concentrated solution across a semipermeable membrane (membranes of animal origin, membranes made from

Cu2 [Fe (CN) 6], Ca3 (PO4)2 etc.)

Osmosis was first observed by Abbe Nollet in 1748.

Osmotic Pressure

Osmotic pressure is the equilibrium hydrostatic pressure of the column set up as a result of osmosis. It is the minimum pressure that must be applied on the solution to prevent the entry of the solvent into the solution through the semi­permeable membrane. It is the minimum pressure needed to apply on a solution to make its vapour pressure equal to vapour pressure of the solvent.

  • It is denoted by P or π.
  • It is measured by Pfeiffer’s method, Berkely­Hartley’s method, Townsend’s method.

Van’t Hoff equation of osmotic pressure

π = CST
Here, π = Osmotic pressure
C = Concentration of solution in mol/L
S or R = Solution constant

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Class 12 Maths Notes: Probability – 10 Must Solve Objective Problems

ICSE 2013 Class IX and X Syllabus – Commercial Studies

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Aims:

1. To enable students to develop a perceptive, sensitive and critical response to the role of business in a global, national and local context.

2. To allow students to balance the demands of social parameters with individual aspirations.

3. To develop in students an appreciation for the roles of the entrepreneur and the professional manager.

4. To help develop a co-operative attitude through study of the organisation and participation associated with commerce and industry.

5. To provide an appropriate body of knowledge and understanding, and to develop appropriate skills as a basis for further study or work or both.

CLASS IX

There will be one written paper of two hours duration carrying 80 marks and Internal Assessment of 20 marks.

The paper will be divided into two sections A and B.

Section A (Compulsory) will consist of questions requiring short answers and will cover the entire syllabus.

Section B will consist of questions, which will require detailed answers. There will be a choice and candidates will be required to answer four questions from this section.

1. Introduction to commercial organization.

(a) Human activities

Meaning and types – Economic and noneconomic activities – classification of economic activities – business, profession and employment. Comparison between economic and non-economic activities.

(b) Business activities

Meaning and characteristics. Types of business activities – industry – classification of industries on the basis of products. Commerce – types of commerce – trade and aids to trade. Brief description on various types of trade and aids to trade. Inter relationship between industry, commerce and trade needs to be covered.

(c) Non-profit seeking organizations

Meaning and types, comparison between profit seeking and non-profit seeking organisations.

(d) Ownership structures of commercial organization

Sole proprietorship, partnership, Hindu undivided family business, joint stock company, co-operative society, public sector enterprise. (Brief introduction to each ownership structure and its features only. Types, comparison between different ownership structures and their merits and demerits need not be covered).

2. Understanding the functions of a commercial organization.

The following topics should be studied as departments in a typical firm only:

(a) Marketing and Sales.

(b) Finance and Accounting.

(c) Human Resources (personnel, training).

(d) Production.

(e) Purchasing and Stores.

(f) General Administration and Legal.

Students should be explained the concepts and functioning of – Purchasing and Stores, Production, Marketing and Sales, Finance - (manual and computerized accounting system in business organizations). Human Resources (personnel, training), & General Administration and Legal departments, affecting the organisation all through. All the six terms need to be clearly defined and their specific features explained individually. The cross linkages need to be clearly brought out.

This topic should be studied through the medium of a case study or a project. Such tools will make the students appreciate the inter-links. No question is to be set from this topic. Case study or project for this topic can form one of the assignments for “Internal Assessment”.

3. Communication in commercial organization.

Meaning, characteristics, process, importance and different methods of communication.

Different methods of communication (letter, facsimile, e-mail, videoconference, memo, telephonic conversation, etc.). A comparative analysis of these tools need to be undertaken.

4. Introduction to Accounting and Book keeping.

(a) Meaning and objective

Meaning and objective of accounting and book keeping, accounting cycle, distinction between accounting and book keeping.

(b) Basic accounting terminology

The following terms need to be defined and explained – Capital, liability, asset, revenue, expense, purchase, sales, stocks, debtors,
creditors, drawings, debit and credit, discount.

(c) Basic accounting principles and concepts.

Business entity, money measurement, going concern, accounting period, dual aspect and accounting equation, matching principle, principle of full disclosure.

(d) Journal

Meaning and classification of accounts – (conventional and modern), rules of debit and credit.

Meaning, uses and limitations of journal. Recording of transactions in journal. (Simple numericals based on the terminology mentioned in part (b) need to be covered. Compound journal entries including cash discount, bad debts and opening and closing entries need not be covered).

(e) Ledger

Meaning, posting and balancing of ledger accounts. (Ledger posting on the basis of simple journal entries).

(f) Trial balance

Meaning, objectives and preparation of trial balance with the given set of ledger account balances.

(Re-drafting of trial balance need not be covered.)

(g) Cash Book

Meaning, types of cash books, preparation of single column cash book.

5. Trade

(a) Trade – Home Trade and International trade

Meaning and types of trade

Home trade – functions of retailers and wholesalers, types of retailers and wholesalers (features only).

International trade – meaning, types, advantages and disadvantages of international trade.

(b) Issues of the Environment

(i) Types of pollution – air, water, soil, radiation and noise.

Air pollution due to vehicles, industries, brick kilns, etc.

Water pollution: industrial waste, oil spills, urban- commercial and domestic waste.

(ii) Effects of pollution on environment and human health.

Bhopal Gas Tragedy; Chernobyl Disaster.

(iii) Abatement of pollution

Air: setting standards and implementing them, using technical devices to reduce pollution.

Water: Proper collection and disposal of domestic sewage, treatment of industrial waste to yield safe effluents, etc.

(iv) Management of waste in industrial and commercial establishments.

Sources of waste – domestic, industrial, agricultural, commercial and other establishments.

Domestic waste: paper, glass, plastic, rags, kitchen waste, etc.

Industrial: mining operations, cement factories, oil refineries, construction units.

Agricultural: plant remains, animal waste, processing waste.

Municipal: sewage, degradable and nondegradable waste from offices, etc.

(v) Methods of safe disposal of waste.

Basic understanding of: segregation, dumping, composting, drainage, treatment of effluents before discharge.

CLASS X

There will be one written paper of two hours duration carrying 80 marks and Internal Assessment of 20 marks.

The paper will be divided into two sections A and B.

Section A (Compulsory) will consist of questions requiring short answers and will cover the entire syllabus. There will be no choice of questions.

Section B will consist of questions, which will require detailed answers. There will be a choice and candidates will be required to answer four questions from this section.

1. Stakeholders in commercial organisations

(a) Distinction between stakeholders and customers.

Explain all the six stakeholders of a firm - shareholder, creditor, supplier, employee, government and society.

It should be stressed that customer, though very important for any firm is not a stakeholder as he does not have a stake in the
firm.

(b) Internal and external stakeholders.

Stakeholders within and outside the firm need to be explained. The six stakeholders need to be classified as internal and external stakeholders.

(c) Expectations of stakeholders – employers (owners and managers), employees, associates, and the general public.

The student must understand that each of these stakeholders is equally important and any one of them cannot be satisfied at the cost of the other one.

2. Communication

(a) Meaning and types

Verbal and non-verbal communication, formal and informal communication. (merits, demerits and suitability).

(b) Interpersonal skills in communication

Skills required for effective communication and barriers causing breakdown in communication and measures to overcome the
barriers.

3. Marketing

(a) Marketing

Meaning, objectives, importance and functions of marketing.

(b) Product and service

Meaning, types and difference between a product and a service (with examples).

(c) Marketing research

Meaning, role and methods of marketing research.

(d) Advertising and sales promotion

Advertising – meaning, importance of advertising, merits and demerits, difference between advertising and publicity, advertising
media. Code of conduct for advertisers.

Sales promotion – meaning and techniques.

Brand and Trademarks – their meaning, brand promotion – meaning and techniques, brand equity and brand loyalty.

(e) Sales and the selling process, including the difference between marketing and sales, qualities of a good salesman. Consumer Protection Act – 1986, need for consumer protection, features of the Act and rights of the consumer.

Explanation and examples.

4. Finance and accounting

(a) Capital and revenue

Capital and revenue receipts, capital and revenue expenditure and deferred revenue expenditure.

(b) Final accounts of a sole trader

Meaning and preparation of Trading account, Profit and Loss account and Balance sheet based on the given trial balance with the adjustment of closing stock only. (Preparation of manufacturing account, profit and loss on sale of assets, intangibleand fictitious assets, prepaid and accrued expenses and incomes are excluded.)

(c) Non-profit organizations

Simple understanding of receipts and payments account, income and expenditure account and balance sheet. Only features and comparison with final accounts of trading organization. No numerical problems.

(d) Fundamental concept of Cost (direct, variable, etc.)

Classification of costs needs to be explained, based on behaviour (fixed, variable, semivariable), nature (direct, indirect), controllability and functionality.

(e) Budgeting

Meaning and utility of budgeting, comparison between budgeting and forecasting, budgets – (meaning and types).

(f) Banking – functions of the Central Bank and commercial banks, types of accounts and documents used in banking transactions.

Central Bank and commercial banks: role in the economic development. Types of commercial banks now present in India (public sector commercial banks, private sector commercial banks, foreign commercial banks); the types of accounts and some basic documents used in banking transactions ( pass book, cheques, pay-in-slips, bank drafts, traveller’s cheques, debit and credit cards),
ATM need to be clearly explained. Credit Control measures used by the Central Bank to be excluded.

5. Human Resources

(a) Recruitment, selection and training.

(i) Recruitment – meaning, sources, advantages and disadvantages of different sources,

(ii) Selection- meaning and steps, types of selection test,

(iii) Training – meaning, objectives, importance, types and methods of training (performance appraisal is excluded).

(b) Simple understanding of industrial relations and the role of trade unions. Concept of Social Security – including brief reference to Provident Fund, Gratuity, Pension, Group Insurance and Maternity Benefits. Self-explanatory.

(Acts are not required).

6. Logistics and Insurance

(a) Transportation

Means of transportation (land, air and water), merits, demerits and suitability.

(b) Warehousing

Meaning, importance, types and documents used.

(c) Insurance

Meaning, importance and principles.

(d) Striving for a better environment

(i) Community participation and public awareness programmes for ecological restoration and conservation like The Chipco Andolan (Movement).

(ii) Use of efficient and eco-friendly technology and the sustainable use of resources.

Eco efficiency would mean reduction in the amount of raw material used, reduction in energy used, reducing pollution, recycling material, renewable materials and ensuring that goods are durable. Judicious use of resources keeping the future in mind.

(iii) Environmental values and ethics

Choose to carry cloth bags, use organic manure. Clean surroundings, respect for other people’s things. developing an ethical environmental consciousness e.g. refusing use of polybags, styrofoam containers, etc; reusing: plastic and glass containers; recycling: e.g. paper – this will reduce demand on wood and save trees.

INTERNAL ASSESSMENT

A minimum of three assignments are to be done during the year, as assigned by the teacher.

EVALUATION

The project work is to be evaluated by the subject teacher and by an External Examiner. The External Examiner shall be nominated by the Head of the school and may be a teacher from the faculty, but not teaching the subject in the relevant section/class. For example, a teacher of Commerce/Accounts of Class XI may be deputed to be the External Examiner
for Class X Commercial Studies project work.

The Internal Examiner and the External Examiner will assess the candidate’s work independently.

Award of marks (20 marks)

Subject Teacher (Internal Examiner) 10 marks

External Examiner 10 marks

The total mark obtained out of 20 are to be sent to the Council by the Head of the school.

The Head of the school will be responsible for the entry of marks on the mark sheets provided by the Council.

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CBSE Class 12 Chemistry Notes: Solutions – Raoult’s Law

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Raoult’s Law for Volatile Solutes

Raoult’s law states that in a solution, the vapour pressure of a component at a given temperature is equal to the mole fraction of that component in the solution multiplied by the vapour pressure of that component in the pure state.

The total vapour pressure P of a solution containing two components A and B is

Raoult’s Law for Non-Volatile Solutes

Raoult’s law states that the relative lowering of vapour pres­sure of a solution containing a non­volatile solute is equal to the mole fraction of the solute in the solution.

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CBSE Class 12 Chemistry Notes: Solutions – Elevation in Boiling Point


Jharkhand Board Class X Sample Papers 2013 – SCIENCE THEORY

HBCSE National Olympiad Programme State I – National Standard Examinations (NSEs)

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National Standard Examinations constitute the first stage of selection of students in the National Olympiad Programme. Every student aspiring to go through successive stages of the programme must enroll for the NSEs.

Eligibility

Physics, Chemistry, Biology (NSEP, NSEC, NSEB):

All Indian students who are born on or after July 1, 1993 and, in addition, are in Class XII or lower as of November 30, 2012, are eligible to appear for NSEP, NSEC, and NSEB 2012-2013. If they qualify in NSEP/NSEC/NSEB they will be eligible for subsequent stages leading to participation in International Olympiads for Physics/Chemistry/Biology 2013 respectively.

Junior Science (NSEJS):

All Indian students who are born on or after January 1, 1998 and, in addition, are in Class X or lower as of November 30, 2012, are eligible to appear in NSEJS 2012–2013. If they qualify in the NSEJS, they will be eligible for subsequent stages leading to participation in International Junior Science Olympiad 2013.

Astronomy (NSEA):

All Indian students who are born on or after January 1, 1994 and, in addition, are in Class XII or lower as of November 30, 2012, are eligible to appear for NSEA 2012–2013. If they qualify in the NSEA they will be eligible for subsequent stages leading to participation in International Olympiad in Astronomy and Astrophysics 2013.

It is the student’s responsibility to determine that he/she satisfies eligibility norms. If at some later stage it is found that the student does not meet eligibility norms, he/she may face disqualification from the programme.

Syllabus

The syllabus for NSEs in Physics, Chemistry and Biology is broadly equivalent to the senior secondary level (Class XI and Class XII) of CBSE. The syllabus for NSEA is broadly equivalent to senior secondary level (Class XI and Class XII) of CBSE. There will be greater emphasis on physics and mathematics and elementary astronomy.

The syllabus for NSEJS is broadly equivalent to secondary school level (up to Class X) of CBSE. All the basic subjects of science (Physics, Chemistry, Biology) and Mathematics will have roughly equal emphasis.The schedule for the NSEs is described herewith.

National Standard Examination in Physics (NSEP)

Date of exam : 24th November 2012 (Saturday)
Time of exam : 09.30 am – 11.30 am
Last Date of Enrollment : 15 th September 2012

Part A 50 multiple choice questions consisting of (A1) 40 questions, each with only one of the four
options correct, and (A2) 10 questions, each with one or more than one option  correct. To get credit, all correct option(s) and no incorrect option(s) should be marked.

Part B 5 or 6 short answer- type questions or problems.

Language English

(However, NSEP question papers may be available in Hindi and some other regional languages provided there are at least 300 students opting for that language. Please see the IAPT website: http://www.iapt.org.in in this connection.)

National Standard Examination in Chemistry (NSEC)

Date of exam : 24th November 2012 (Saturday)
Time of exam : 12.30 pm – 02.30 pm
Last Date of Enrollment : 15th September 2012

The question paper consists of 80 multiple choice questions, each with only one of the four options correct.

Language : English only

National Standard Examination in Biology (NSEB)

Date of exam : 24th November 2012 (Saturday)
Time of exam : 03.00 pm – 05.00 pm
Last Date of Enrollment : 15th September 2012

The question paper consists of 80 multiple choice questions, each with only one of the four options correct.
Language : English only

National Standard Examination in Astronomy (NSEA)

Date of exam : 24th November 2012 (Saturday)
Time of exam : 03.00 pm – 05.00 pm
Last Date of Enrollment : 15th September 2012

The question paper consists of 80 multiple choice questions, each with only one of the four options correct.
Language : English only

National Standard Examination in Junior Science (NSEJS)

Date of exam : 24th November 2012 (Saturday)
Time of exam : 03.00 pm – 05.00 pm
Last Date of Enrollment : 15th September 2012

The question paper consists of 80 multiple choice questions, each with only one of the four options correct.
Language : English only

HBCSE National Olympiad Programme

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Class 11 Chemistry Notes Stocihiometry – Oxidation and Reduction

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Oxidation Number:

It is the charge (real or imaginary) which an atom appears to have when it is in combination. It may be a whole no. or fractional. An element may have different values of oxidation number depending. It depends on nature of compound in which it is present. There are some operational rules to determine oxidation number.

Oxidation:

Addition of oxygen, removal of hydrogen, addition of electro-negative element, removal of electropositive element, loss of electrons, increase in oxidation number (de – electro nation).

Reduction:

Removal of oxygen, addition of hydrogen, removal of electronegative element, addition of electro positive element, gain of electrons, decrease inoxidation number (electro nation).

Redox Reactions:

A reaction in which oxidation & reduction occur simultaneously.

Oxidising Agents:

(oxidants, oxidizers). They oxidise others, themselves are reduced & gain electrons. Eq. O2, O3, HNO3, MnO2, H2O2, halogens, KMnO4, K2Cr2O7, KIO3, CIO3, FeCl3, NaOCl hydrogen ions.
[Atoms are present in their higher oxidation state.

Reducing Agents:

H2, molecular form is weak reducing agent but Nascent hydrogen is powerful. C, CO, H2S, SO2, SnCl2, sodium thio Sulphate, Al, Na, CaH2, NaBH4, LiAlH4. They reduce others, themselves get oxidised & lose electrons. Also called reductants or reducers.
[Atoms are present in their lower oxidation state.]

Both oxidizing & Reducing Agents:

SO2, H2O2, O3, NO2, etc.

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ICSE 2013 Class IX and X Syllabus – Technical Drawing Applications

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Aims:

1. To develop competence among the students to pursue technical courses like Engineering, Architecture, Draftsmanship Surveying and other professional courses.

2. To understand basic principles of instrumental drawing drawn to scale and to acquire basic skills in the use of traditional drafting methods which would also be helpful in understanding computer  aided designs.

3. To acquire the basic knowledge in their applications in various fields.

CLASS IX

There will be one written paper of three hours  duration carrying 100 marks and Internal Assessment of 100 marks.

The paper will be divided into two sections, Section I and Section II.

Section I (40 marks) shall consist of compulsory short answer questions chosen from the entire syllabus.

Section II (60 marks) shall contain questions which require longer answers. There will be a choice of questions.

THEORY – 100 Marks

1. Types of lines

(i) Border lines.

(ii) Outlines.

(iii) Dashed/ Dotted lines.

(iv) Centre lines.

(v) Extension lines or Projection lines.

(vi) Dimension lines.

(vii) Construction lines.

(viii) Cutting-Plane lines.

(ix) Section or Hatching lines.

(x) Short break lines.

(xi) Long break lines.

The names of different lines and their uses to be matched with the correct thickness and shade

2. Dimensioning

(i) Aligned system.

(ii) Unidirectional System.

3. Lettering and Numbering

Upright capitals and small, freehand, single stroke, as used in Engineering drawing, and between, the correct guide lines.

4. Sheet Layout

Basic – draw border lines, title block with name, sheet number, title etc.

5. Geometrical Constructions

(a) Bisector of line segment.

(b) Division of a line segment into required number of parts/ proportional parts.

(c) Perpendicular and parallel lines.

(d) Bisection of an angle, trisection of a right angle/ straight angle.

(e) Congruent angle.

(f) To find the centre of an arc.

(g) Regular polygons up to six sides with simple methods using T-square and setsquares.

Point, Lines and Angles: Definitions of the various terms used in relation to, a point, different types of lines and different types of angles to be used only in construction.

  •   Bisecting a line.
  • Drawing a perpendicular to a line from a point, in/above / away from the end of, the line.
  • Bisecting an angle when the lines meet.
  •  Trisecting a right angle.
  • Making an angle equal to a given angle.
  •  Draw parallel line to a given line touching given point away from the line by using correct instruments such as set squares/compasses.
  •  Draw parallel line to a given line at a given distance.
  •  Locating a point equally distant from two points, away from the line
  •  Dividing a straight line into any required number of given parts.
  •  Draw two lines, from two points outside a given straight line, to meet at a point in the line, making equal angles with it.
  •  Constructing angles of 90, 45, 22½, 135, 67½, 60, 120, 30, 52½, 105, 75, 37½. degrees.

Triangles: Definition of a triangle, the terms (with their definitions) relating to the different parts of a triangle, classifying the different kinds of triangles, according to their sides / angles.

Construction of Triangles when the following is given:

  •  the base, altitude and one side.
  • all three sides.
  •  the base angles and the altitude.
  •  the base and the base angles.
  •  the perimeter and the proportion of the sides.
  •  the base and the ratio of the angles.
  •  the perimeter and the base angles.

Construction of Isosceles Triangles when the following is given:

  •  the altitude and the base.
  • the base and one side.
  • a base angle and an equal side.
  •  the altitude and an equal side.

Construction of Right angled triangles when the following is given:

  •  the hypotenuse and the base.
  • the hypotenuse and an acute angle.
  •  The base and height.

Quadrilaterals :D efinitions of a quadrilateral / different kinds of quadrilaterals, e.g. a square, a rectangle, a rhombus and a trapezium to be used only in the construction of

  •  a rectangle: when the diagonal and one side is given or two sides are given.
  •  a square: when one side or the diagonal is given.
  •  a rhombus: when one side and one angle is given/when two diagonals are given.
  •  a trapezium: when the diagonal and the equal sides are given/when two parallel sides and distance between them is given.

Polygons: Definition of a polygon ( regular and irregular) and the terms relating to it only to be used in construction methods and Special construction methods of regular polygons (up to eight sides) when the following is given:

  •  the length of a side
  • the length of sides and necessary angles are given.

Circles and tangents: Definition of a circle / tangent, and the different parts contained in a circle, e.g. center, circumference, diameter, radius, arc, chord, sector and segment. Concentric circles only to be used in construction methods for:

  • finding the center of a circle.
  •  obtaining its circumference, radius given.
  •  obtaining the length of any given arc.
  •  drawing an arc /a circle to pass through 2 / 3 given points.
  •  drawing a tangent to an arc / a circle from a point in / outside the arc / circle.
  •  drawing two tangents, at a given inclination to each other, to a given circle.
  •  drawing a tangent to a circle, parallel to a given line.
  •  drawing a common exterior tangent to two circles of equal diameter.
  •  drawing a common exterior tangent to two circles of unequal diameter, when the circles touch / do not touch / cut one another.
  •  drawing a common interior tangent to two circles of equal / unequal diameter when the circles touch/do not touch one another.

6. Basic facility in Orthographic Projections

(a) Projection of points.

(b) Projection of lines (in 1st quadrant/ 3rd quadrant / contained by reference plane)

(i) line parallel to both the reference planes.

(ii) line parallel to one of the reference planes and perpendicular to the other plane.

(iii) line inclined to one of the reference planes and parallel to the other plane.

(iv) line inclined to both the reference planes.

(v) To find the true length of the line from the given projections.

(c) Projections of Surfaces/ Areas: such as regular polygons and circular lamina (1st angle and 3rd angle).

(i) surface perpendicular to both the reference planes.

(ii) surface perpendicular to one of the reference planes and parallel to the other.

(iii) Surface inclined to one of the surface planes and perpendicular to the other.

(iv) Conversion of simple pictorial views into orthographic views (1st angle / 3rd angle method) ELEVATION (F.V) PLAN
(T.V.) END VIEW: LHS/RHS.

Its definition. The complete explanation with demonstration of viewing objects, placed within the First and Third quadrant (the planes of projections), and obtaining the different views, i.e. the front elevation, visible end elevations and plan, and drawing them, accordingly, using the, First angle or the Third angle, method of projection. Hidden end elevation to be excluded. Layout of drawing sheet, i.e. the Orthographic views (First / Third angle method), inserting the required projection lines, center lines, leader  lines, dimension lines, dimensioning from the  Pictorial (Isometric / Oblique view) of the object.

7. Isometric drawing

Copying the given isometric figure (simple and basic).

Their definition and their uses, the correct method of drawing them, along with the correct use of the appropriate, basic, drawing instruments.

The difference between the Isometric  projection and the Isometric view.

  •  drawing the Isometric view / projection, of straight lined objects, showing isometric planes.
  •   drawing the isometric view of cylindrically shaped objects, e.g. round bars / pipes / washers.

8. Free hand sketching

Domestic items, appliances and tools, such as cup with a saucer, an electric bulb, a fountain pen with the cap removed, a tooth brush, a hammer (ball / claw pein), , a woodsaw, a hacksaw, a screwdriver, a spanner, pliers, chisel, tri-square, calipers (internal and external) a pair of scissors, a pair of compasses, divider, knife, water tap etc.

Draw free hand sketches of these tools keeping the proportion of various parts.

PART II – INTERNAL ASSESSMENT

Minimum fifteen drawing assignments to be done during the year as assigned by the teacher.

CLASS X

There will be one written paper of three hours duration carrying 100 marks and Internal Assessment of 100 marks.

The paper will be divided into two sections, Section I and Section II

Section I will consist of a number of questions covering Section A of the syllabus. The candidates are to attempt three questions out of five.

Section II will consist of questions covering Section B of the syllabus. The candidates are to attempt two questions out of three.

THEORY – 100 Marks
        SECTION A

1. Geometrical Constructions based on Plane Geometry

(i) Division of a line into equal or proportional parts: Construction of a triangle/ quadrilateral when its perimeter and the ratio of the lengths of its sides are given.

(ii) Division of a circle into equal parts (4, 6, 8, 12) using set square or compasses.

(iii) To find the length of an arc/circumference of a circle.

(iv) An angle and a circle touching its sides.

(v) A circle of given radius passing through two given points.

(vi) An arc passing through three noncollinear points.

(vii) A continuous arc passing through not more than 5 non-collinear points.

(viii) A regular polygon (3, 4 5 6 sides) with special methods (side given).

(ix) Construction of a regular octagon in a square (side of the square = distance between parallel sides of a octagon).

(x) More than one polygon (sides 3, 4, 5, 6, 7, 8) on a common base on the same side/opposite sides.

(xi) Inscribing/Circumscribing a circle on a regular polygon (3, 4, 5, 6 sides).

(xii) Inscribe/Circumscribe a circle of given radius by a regular polygon up to six sides.

(xiii) In a regular polygon to draw the same number of equal circles as the sides of the polygon each circle touching one /two sides of the polygon and two of the other circles externally.

(xiv) Outside a regular polygon to draw the same number of equal circles as the sides of the polygon each touching one side of the polygon and two of the other circles externally.

(xv) Regular hexagon and 3 equal circles inside it touching one side/ two sides of the hexagon and the other two circles externally.

(xvi) A circle and (3, 4, 5, 6,) equal circles inside it touching internally and touching each other externally.

(xvii) Tangents to a circle at a point on the circumference.

(xviii) Direct common tangents/Transverse common tangents to two equal/unequal circles. Also to measure and record their lengths.

(xix) Drawing (not more than three) circles touching each other externally and also touching two converging lines (radius of one of the circles is given).

2. Area constructions

(i) Constructions based on the application of area theorems (area of polygons).

(ii) Converting the given polygon into a triangle having equal/half/double the area of the polygon.

(iii) Changing given triangles (2 or 3) into a single triangle having the area equal to the sum of the areas of the given triangles.

Methods for constructing:

  • a scalene triangle / isosceles triangle /a right angled triangle equal to the area / half the area / twice the area of any given quadrilateral.
  • a parallelogram equal in area to any given triangle.
  •   a triangle equal in area to the sum of any two / three given triangles.
  • a triangle equal in area / half the area to any given regular pentagon / hexagon.
  •   a triangle of a given base / altitude, equal in area to another given triangle.
  • a triangle equal in area to ½ or twice the area of any given triangle.
  •   a square equal in area to any given parallelogram / triangle / rectangle.
  • a square, equal in area to any given regular pentagon / hexagon.

3. Templates as an application of geometrical constructions and other constructions such as:

(i) Arc of a given radius touching a given line and passing through a given point.

(ii) Arc of given radius touching two intersecting straight lines.

(iii) Arc of given radius touching a given arc and a straight line.

(iv) Arc of a given radius touching two given arcs (externally/internally).

(To redraw the given figure and insert the dimensions).

Applying the construction methods, involving  circles, tangential, circles / arcs /straight lines and points, for constructing TEMPLATES of various shapes.

4. Scales

(i) To find the R.F. (Representative Fraction) and the scale length from the given data by showing neat working.

(ii) Construction of a plain scale/diagonal scale.

(iii) Use of constructed scale in the preparation of field drawing scale diagram (Enough data to be provided).

Definition of R.F. formula. Finding the Representative Fraction (R. F.) and the Scale length by the given data by showing neat working/lettering. Construction of Plain and Diagonal Scales in different units of linear measurements, and marked and numbered accordingly. Transferring the required  measurements, from the constructed scale, to create finished Scaled drawings, of: field drawings / templates / Orthographic projections / plane geometrical constructions.

5. Engineering Curves

An ellipse, a parabola

Engineering Curves (construction only) as used in
manhole covers, arches, dams, monuments etc.

(i) Ellipse: (major and minor axes given)

(a) by arcs of circles method.
(b) by the concentric circles method.
(c) by oblong method.

(ii) Parabola (base and axis given)

(a) by rectangle method.
(b) by tangent method

6. Solids

(i) Orthographic projections of right solids such as regular prisms and pyramids with bases as regular polygons up to six sides, cylinder and cone.

(a) Axis perpendicular to one of the reference planes and parallel to the other.
(b) Axis parallel to both the reference planes(prism/cylinder only).
(c) Axis inclined to one of the reference planes and parallel to the other. Use of auxiliary plane may be included.(Auxiliary elevation and auxiliary plan).

(ii) Development of surfaces of the right solids (Parallel and Radial).

(iii) Determination of true length of line when inclined to both the reference planes e.g. slant edge of a pyramid.

Right Solids, such as, Prisms (triangular, square, pentagonal and hexagonal )

Pyramids (triangular, square, pentagonal and hexagonal bases.), Cylinders and Cones:

Simple word problems on

(i) orthographic projections of right solids.

  •  with its axis, perpendicular to one plane, and, parallel to the other plane.
  • with its axis, parallel to both planes
  •   with its axis, parallel to one plane, and, inclined to the other plane.

(ii) Parallel and Radial Development of lateral surfaces of right solids with axis perpendicular to H.P. and parallel to V.P.

(iii) Determination of true length of the slant edge of a pyramid when the slant edge is inclined to both H.P. and V.P.

(iv) Auxiliary views:

Figure showing auxiliary inclined plane should be given with the word problem.

–– Auxiliary elevation of right solid with axis parallel to H.P. and inclined to V.P.

–– Auxiliary plan of a right solid with axis inclined to H.P. and parallel to V.P.

7. Oblique drawing

Conversion of given orthographic views to oblique view (circular parts in top view to be excluded).Circular parts only in one view either in front view or in the side view. The angle of inclination with the receding axis to be given

SECTION B

8. Sections of right solids (prism, pyramid, cylinder and cone)

(i) Sectional views of cut solids with axis perpendicular to H.P. and parallel to V.P.

(a) V.T. (Vertical Trace) parallel to or inclined to H.P.
(b) H.T. (Horizontal Trace) parallel/inclined to V.P. (Figure showing V.T and H.T should be given) Questions based on word problems should be excluded.

(ii) Axis parallel to both the reference planes  (prism and cylinder only) with H.T .or V.T. of cutting plane shown in the figure.

(iii) Development of lateral surfaces of cut solids (parallel, radial): Prism, Pyramid, cylinder, cone.

(iv) Development of pipe joints as elbow joints, exhaust pipes etc. and the objects made of sheet metals in the shape of cylinders.

(v) True shape of a section.

(vi) Auxiliary views (A.F.V. /A.T.V.) of cut solids with axis perpendicular to H.P and parallel to V.P with

(a) Auxiliary plane parallel to the cutting plane.
(b) Auxiliary plane inclined to H.P at a given angle q.

Sections of Right Solids, such as, Prisms, Cylinders, Pyramids and Cones.

Sectional views, of cut / truncated solids,

  •  with its axis, perpendicular to the H.P. and parallel to the V.P., when the cutting plane is parallel / inclined to H.P. or, to  the V.P. (only one cutting plane to be  expressed in the figure)
  • with its axis, parallel to both planes ( prisms and cylinders only), with not more than one cutting plane shown in the figure.

 

Developments of the lateral surfaces of:

  •   Cut Solids / Truncated Solids (parallel and radial), such as, Prisms, Cylinders, Pyramids and Cones with one cutting plane shown in the figure.
  •  Cylindrical pipe joints, as used for constructing, Chimneys, Ventilators,  exhaust pipes, etc., as application of  development of lateral surfaces of cut/truncated cylinders with one/more than one cutting plane shown in the figure.

 

Auxiliary view, of cut / truncated solids such as prism / pyramids / cylinder / cone, when the axis is perpendicular to the H.P. and parallel to the V.P. with the Auxiliary plane;

  •   parallel to the cutting plane.
  •   at an inclination to the H.P

Auxiliary plane should be shown in the figure.

and

The True Shape of the, cut / truncated, surface of right solids such as prism / pyramid / cylinder / cone when axis is perpendicular to H.P. and parallel to V.P.

9. Isometric Drawing (Use of scale to draw isometric drawing may be included. e.g. 2:1 or 1:2 only).

(a) Copy the given isometric figure.

(b) Conversion of the given orthographic view into isometric drawing.

(c) Isometric projection by constructing and making use of an isometric scale.

Isometric Drawing: In full scale and maybe in the scale of 2:1 or 1:2.

  • • Drawing the Isometric view, from a given,Isometric view.
  •  Drawing the Isometric view, by reading and visualizing the same, from the given Orthographic views
  •  Drawing the Isometric projection from either a given pictorial view or the Orthographic views, by constructing and using the Isometric Scale.

10. Sectional Orthographic views (1st and 3rd angle methods)

(a) Conversion of given pictorial view (Isometric/oblique into sectional/half sectional orthographic views).

(b) Conversion of a given orthographic view into sectional/half sectional views and adding the missing view.

The Orthographic Projection, First and Third, angle methods: (at least one of the views as sectional view).

  • Drawing the Orthographic views / full sectional views / half-sectional views of an object shown in a given pictorial view: Isometric / Oblique with cutting plane / planes shown.
  •  Converting the given Orthographic view / views into Sectional views, full / half according to the Cutting plane line / lines marked in a given view / views.
  •  Dimensioning the Orthographic views showing the cutting plane, naming the views.

PART II- INTERNAL ASSESSMENT – 100 MARKS
                                      

1. To prepare a file containing minimum 15 drawing assignments. The drawing assignments should cover entire syllabus of class X. One / two assignments on each units of syllabus should be prepared on half imperial size drawing paper.

2. To make a three dimensional model with stiff cartridge paper / chart paper involving the  application of the development of solids such as a prism / pyramid.

3. To make a model with thermocol involving the application of the true shape of the section of truncated solids such as a prism / pyramid / cylinder / cone.

EVALUATION

The assignments/project work is to be evaluated by the subject teacher and by an External Examiner. The External Examiner may be a teacher nominated by the  Head of the school, who could be from the faculty, but not teaching the subject in the section/class.

The Internal Examiner and the External Examiner will assess the assignments independently.

Award of marks (100 marks)

Subject Teacher (Internal Examiner): 50 marks
External Examiner: 50 marks

The total marks obtained out of 100 are to be sent to  the Council by the Head of the school. The Head of the school will be responsible for the entry of the marks on the mark sheets provided by the Council.

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CBSE Class 12 Maths Notes: Matrices – Ad joint of a Square Matrix

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Let A = [aij] be a square matrix of order n and let Cij be cofactor of a­ij in A. Then the transpose of the matrix of cofactors of elements of A is called the adjoint of A and is denoted by adj A.

Thus, adjA = [Cij]T  => (adj A)ij = Cji

Properties of Inverse of a Matrix:

(i).       (Reversal Law) If A and B are invertible matrices of the same order, then AB is invertible and (AB)-1 = B-1A-1. In general, if A, B, C are invertible matrices then

(ABC…..)-1 =…..C-1B-1A-1

(ii).       The inverse of the inverse of the matrix is the original matrix itself, i.e. (A–1)–1 = A.

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