ACCOUNTANCY

1. PREPARATION OF PROJECT REPORT As per the CBSE curriculum guidelines, the students of class XII are required to prepare and submit a Project work for the evaluation of Accountancy Practical. In this regard they are supposed to deal with following practical problem: A Comprehensive project starting with identification of financial transactions of a real business, recording them in journal entries, posting them to the ledger and preparation of Trial balance. Then prepare Trading and Profit and Loss Account and Balance Sheet on the basis of the prepared trial balance. Expenses, incomes and profit (loss), assets and liabilities are to be depicted using pie chart / bar diagram. The Project needs to be presented on A4 size sheets(white/ coloured) with well presented, drafted accounts avoiding any cuttings, doublings or overwritings.

2. Do practice illustrations from NCERT and TS GREWAL for Chapter2,3,4 and 5 3. Learn Accounting formulas for chapter 3 ‘Goodwill: Nature and Valuation’ 4. Prepare a PPT presentation/Chart on any one of the following topics(with min. 8

slides): i) Partnership Basic Theory ii) Profit & Loss Appropriation A/c iii) Types of Capital method iv) Goodwill Valuation Methods v) Revaluation A/c

5. Do following practice questions in holidays’ assignment register:

GURU HARKRISHAN PUBLIC SCHOOL VASANT VIHAR NEW DELHI

HOLIDAYS HOME WORK - 2019-20

CLASS XII

Fundamentals Q.1 State the conditions under which capital balances may change under the system of a

Fixed Capital Account.

Q.2 A is partner in a firm. His capital as on Jan 01, 2007 was Rs. 60,000. He introduced

additional capital of Rs. 20000 on Oct 01 2007. Calculate interest on A’s capital @ 9%

p.a.

Q.3 Alka, Barkha and Charu are partners in a firm having no partnership agreement. Alka,

Barkha and Charu contributed Rs. 20,000, Rs. 30,000 and Rs. 1,00,000 respectively.

Alka and Barkha desire that the profit should be divided in the ratio of capital

contribution. Charu does not agree to this. How will you settle the dispute.

Q.4 A and B are partners in a firm without a partnership deed. A is an active partner and

claims a salary of Rs. 18,000 per month. State with reason whether the claim is valid

or not.

Q.5 Chandar and Suman are partners in a firm without a partnership deed. Chandar’s

capital is Rs. 10,000 and Suman’s capital is Rs. 14,000. Chander has advanced a loan of

Rs. 5000 and claim interest @ 12% p.a. State whether his claim is valid or not.

Q.6 R, S, and T entered into a partnership of manufacturing and distributing educational

CD’s on April 01, 2006. R looked after the business development, S content

development and T financed the project. At the end of the year (31-03-2007) T wanted

an interest of 12% on the capital employed by him. The other partners were not

inclined to this. How would you resolve this within the ambit of the Indian Partnership

Act, 1932?

Q.7 A, B and C are partners in a firm. A withdrew Rs. 1000 in the beginning of each month

of the year. Calculate interest on A’s drawing @ 6% p.a.

Q.8 A, B and C are partners in a firm, B withdrew Rs. 800 at the end of each month of the

year. Calculate interest on B’s drawings @ 6% p.a.

Q.9 A, B and C are partners in a firm. They have omitted interest on capital @ 10 % p.a. for

three years ended 31st march 2007. Their fixed capitals on which interest was to be

calculated through –out were

A Rs. 1,00,000

B Rs. 80,000

C Rs. 70,000

Give the necessary Journal entry with working notes.

Q.10 X, Y, and Z are partners sharing profits and losses in the ratio of 3:2:1. After the final

accounts have been prepared it was discovered that interest on drawings @ 5 % had

not been taken into consideration. The drawings of the partner were X Rs. 15000, Y Rs.

12,600, Z Rs. 12,000. Give the necessary adjusting Journal entry.

Q.11 A, B and C are partners sharing profits and losses in the ratio of 3:2:1. Their fixed

capitals are Rs. 1,50,000, Rs. 1,00,000 and Rs. 80,000 respectively. Profit for the year

after providing interest on capital was Rs. 60,000, which was wrongly transferred to

partners equally. After distribution of profit it was found that interest on capital

provided to them @ 10% instead of 12% . Pass necessary adjustment entry. Show your

working clearly.

Q.12 Ravi and Mohan were partner in a firm sharing profits in the ratio of 7:5. Their

respective fixed capitals were Ravi Rs. 10,00,000 and Mohan Rs. 7,00,000. The

partnership deed provided for the following:- (i) Interest on capital @ 12% p.a.ii) Ravi’s

salary Rs. 6000 per month and Mohan’s salary Rs. 60000 per year. The profit for the

year ended 31-03-2007 was Rs. 5,04,000 which was distributed equally without

providing for the above. Pass an adjustment Entry.

Q.13 Distinguish between fixed capital method and fluctuating capital method.

Q.14 A, B and C were partners in a firm having capitals of Rs. 60,000, Rs. 60,000 and Rs.

80,000 respectively. Their current account balances were A- Rs. 10,000, B- Rs. 5000

and C- Rs. 2000 (Dr.). According to the partnership deed the partners were entitled to

an interest on capital @ 5% p.a. C being the working partner was also entitled to a

salary of Rs. 6,000 p. a. The profits were to be divided as follows:

(i) The first Rs. 20,000 in proportion to their capitals.

(ii) Next Rs. 30,000 in the ratio of 5:3:2.

(iii) Remaining profits to be shared equally.

During the year the firm made a profit of Rs. 1,56,000 before charging any of the above

items.

Prepare the profit and loss appropriation A/C.

Q.15 A and B are partners sharing profits in proportion of 3:2 with capitals of Rs. 40,000

and Rs. 30,000 respectively. Interest on capital is agreed at 5 % p.a. B is to be allowed

an annual salary of Rs. 3000 which has not been withdrawn. During 2001 the profits

for the year prior to calculation of interest on capital but after charging B’s salary

amounted to Rs. 12,000. A provision of 5% of this amount is to be made in respect of

commission to the manager.Prepare profit and loss appropriation account showing the

allocation of profits.

CHANGE IN PROFIT SHARING RATIO (1) R & T are partners in a firm sharing profits in the ratio of 3:2. S joins the firm, R surrenders 1/4th of his share and T 1/5th of his share in favour of “S”. (2) A and B are partners sharing profits & losses in the ratio of 3:2. They admit C for 1/5th of his share from A and 4/5th share from B. (3) A & B are partners. They admit C for 1/4th share. In future, the ratio between A & B would be 2:1. Calculate new ratio & sacrificing ratio (4) X,Y and Z are partners in the ratio of 3:2:1. W joins the firm as a new partner for 1/6th share in

profits. Z would retain his original share. Calculate new ratio & sacrificing ratio (5) A and B are equal partners. They admit C and D as partners with 1/5th and 1/6th share respectively. Calculate new ratio & sacrificing ratio. (6) A and B are partners sharing profits/losses in the ratio of 3:2. C is admitted for 1/4th share. A and B decide to share equally in future. Calculate new ratio & sacrificing ratio. (7) X and Y shared profits in the ratio of 7:3. Z was admitted as a partner. X surrendered 1/7th of his share and Y 1/3rd of his share in favour of Z. Calculate new ratio & sacrificing ratio.

BIOLOGY

Q.1 Draw well labelled diagrams of the followings-

a) Cellular structure of anther

b) Development of pollen grains from microspore

c) Megasporogenesis

d) Sectional view of semineferous tubule

e) Structure of sperm

f) Menstrual cycle

g) Structure of ovary

Q.2 Explain co dominance with an example?

Q. 3 Explain mohybrid and dihybrid cross by punnet square method?

Q.4 Draw chart on sex determination in:-

a) Human being

b) Birds

c) Insects

d) Honey bee

Q.5 Make pictorial project with explanation on the followings:-

a) Griffith experiment

b) Harshey and Chase experiment

c) Meselson and Stahl experiment

d) Salient features of human genome

Q6. Make a project report on any topic of Biology.

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BUSINESS STUDIES

Q.1 Explain in brief the characteristics of Management.

Q.2. What are the objectives of Management. Discuss in brief.

Q.3.”Anything minus Management is nothing”. In the light of this statement, discuss the

importance of Management.

Q.4. Illustrate the concept of Functional foremanship with the help of diagram.

Q.5. Explain how changes in political policies can put impact on business environment.

Illustrate with examples.

Q.6. XYZ Ltd. target is to produce 10,000 shirts per month at a cost of Rs.100 per shirt. The

production manager achieved the target at a cost of Rs, 90 per shirt, Do you think the

‘production manager’ is effective and efficient? Give reasons in support of your answer.

Q.7. In oneof the principle of scientific management, Taylor emphasis that there should be

equal division of work and responsibility between workers and management and

management should work almost side by side with workers helping them.

(i) Identify the principle

(ii) State any other two scientific principles.

Q.8. How would you argue that the success of business enterprise is significantly influenced

by its environment.?

Q.9. What is meant by social environment? Give two examples how it effects our business

organization.

Q.10. In a manufacturing unit , the purchase department purchased 50 tonnes of raw

material for production department. Although only 40 tonnes was needed by the

production department. Due to this, goods were over produced and not accepted by sales

department. As a result, some goods remain unsold.

(i) Which aspect of manage is lacking above? Name and explain it.

(ii) Explain any two points of importance of that aspect.

Q.11. In a factory, the tool box was kept under the table of every worker, whenever worker

need tools he had to bend to take out tool from tool box and keep it back after use. The

newly appointed supervisor observed it and suggested to keep a tool near every worker’s

chair where tool box can be placed, so that workers do not waste their energy in bending

again and again.

(i) Which technique of scientific management is used by new supervisor? Explain it.

(ii) State the objectives of the above study.

PROJECT WORK

As per CBSE Guidelines, prepare a project report on any one of the following topics

assigned to you:

(i) Fayol’s principles of management. (ii) Taylor’s scientific principles of management. (iii) Business Environment :

Child labour

Women Empowerment

Packaging (shift from unpacked to packed, change in style of packaging)

Inclination towards GYM

Impact on business after Demonetization

Goods and Services Tax on products

Boom in Android (iv) Marketing Management :

Jewellery

Stationary

Watches

Bakery items

Shoes, etc.

CHEMISTRY

Q1: Write short note on the following :

1. Riemer Tiemann Reaction

2. Kolbe’s Reaction

3. HVZ Reaction

4. Aldol Condensation

5. Cannizzaro Reaction

6. Wolff Kishner Reduction

7. Hoffmann bromamide Reaction

8. Sandmeyer’s Reaction

9. SN1 and SN2 Mechanism

10. Carbylamine Reaction’

11. Rosenmund Reduction

12. Coupling Reaction

13. Williamson’s Synthesis

Q2 : Account For The Following

1. Chlorobenzene is less reactive than chloroethane towards nucleophilic substitution

reaction.

2. Phenol has higher value of Ka than ethanol.

3. Acidic strength of alcohols follows the order 1o > 2o >3o.

4. Ethanol is more reactive than propanone towards nucleophilic addition reaction.

5. Carboxylic acid have low pka value than phenol.

6. Amines have higher BPT than alkyl halides.

7. Aniline has lower KB value than ethanamine.

8. Nitration of aniline form significant amount of m-Nitro aniline.

9. Alcohols have higher BPT than Alkyl Halides of comparable molecular mass.

10. Basic strength of aqueous amines follow the order 2o > 1o > 3o for methyl amines

Q3 : How will you distinguish between the following pair of compounds

1. Chloro benzene and chloro ethane.

2. Phenol and propan-1-ol.

3. 2-methyl propan-1-ol.

4. Propan-2-ol.

5. Ethanal and propanone.

6. Propanal and benzaldehyde.

7. Benzaldehyde and propanone.

8. Ethanoic acid and phenol.

9. Ethanamine and n-methyl ethanamine.

10. Ethanal and benzaldehyde.

Q4: Write the mechanism for the following.

1. When two molecules of ethanol react in the presence of conc. H2SO4 at 413k.

2. When ethanoic acid reacts with methanol in the presence of conc. Sulphuric acid.

Q5 : How will you form :

1. Benzoic acid from propyl benzene.

2. Propane from propanone.

3. Propan-2-ol from propanone.

4. 4-Aminobenzoic acid from Toluene.

5. Sulphanilic acid from Nitrobenzene.

Q6 : (a) What are Analgesics? Classify them and give 1 example of each type.

(b) Differentiate between antiseptics and disinfectants. Give Example

(c) Define antibiotics. Give different types with example.

(d) How the use of artificial sweetener is beneficial to us.

(e) Explain detergents and its types with example.

Q7 : Write the monomer / Monomers of following polymers. Classify them on the basis of

mode of polymerisation and as copolymers or homo polymers.

1. Nylon6,6

2. Buna-N

3. Terylene

4. Bake lite

5. Melamine polymer

6. Neoprene

7. Urea formaldehyde resin

8. PHBV

9. Teflon

10. Nylon-2-Nylon-6

Q8. (1) Define carbohydrates. What do you understand by polysaccharides? Give example.

(2) Give reaction of glucose with

(a) NH2-OH

(b) Br2 water

(c) Acetic anhydride

(d) Nitric Acid

(3) Represent glucose by Haworth structure and mention alpha and beta anomer.

(4) What do you get on hydrolysis of

(a) Maltose

(b) Lactose

(c) Sucrose

(5) Define Proteins and classify them on the basis of molecular shape. Give example

of each type

(6) What are essential amino acid? Give example?

(7) (A) Differentiate between DNA and RNA?

(B) If one strand of DNA is

GGA ATT CAT AAT

What will be the sequence in DNA and RNA Stand?

(8) Write the source and deficiency disease caused by

(a) Vitamin B12 (b) Vitamin B6

(c) Vitamin (d) Vitamin D

Q9. Define Vitamins and classify them based upon their solubility.

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GURU HARKRISHAN PUBLIC SCHOOL VASANT VIHAR HOLIDAYS ‘ HOME WORK (2019-20)

CLASS XII

NATIOAL INCOME AND RELATED AGGREGATES

A Read the following statement carefully. Write true or false with reasons. (i) Intermediate goods are included in the estimation of GDP.

(ii) A stock is a quantity measured at a specified period of time.

(iii) Population of a country and number of births both are stock variables.

(iv)Domestic product can be more then national product.

(v) Salaries to Indian residents working in German embassy in India is included in domestic

income of india.

(vi) Both value added and value of output are identical concepts.

(vii) Retirement pensions are included in the estimation of national income.

(viii) Prize won in a lottery is included in the national income.

B. Very short answer type question

1 Define depreciation

2. Define indirect taxes

3. What is an externality/external effect in relation to national income

4. What do you understand by GDP deflator

C. Answer the following questions.

1 Distinguish between intermediate goods and final goods.

2. Classify the following into intermediate and final goods by giving reasons.

1. Cheese purchased by DOMINO’S

2. A tractor purchased by a farmer

3. Fruits and vegetables purchased by restaurant

4. Car purchased by Government for military use

5. Stationary purchased by a student

6. Milk purchased by a hotel

3. (i)Explain the concept of normal resident of a country

(ii)Classify the following into normal residents of india and non –residents of india.

(a)An Indian working in Dubai on 11 months VISA.

(b)An Indian working in Indian Embassy in Russia.

(c)A Chinese working in a Taj hotel in India for a period of 2 years.

(d)An Indian working at the United Nations in New Delhi.

4. Explain the concept of value added

5. Calculate net value added at FC

(Rs in Lakhs)

(i)Excise duty 25

(ii) Consumption of fixed capital 40

(iii) Closing stock 10

(iv) Sales 800

(v) Subsidies 5

(vi) Intermediate consumption 300

(vii) Opening stock 20

(viii) Operating surplus 60

(ix) Purchase of raw material 200

6. Find out the intermediate consumption. (Rs in Crores)

(i) GVA 300

(ii) Consumption of fixed capital 100

(iii) Sales tax 40

(iv) Subsidies 20

(v) Closing stock 150

(vi) Opening stock 70

(vii) Value of output 6500

7. How are externalities a limitation of GDP as an index of welfare

8. How is national income measured with the help of value added method or output

method

9. How is national income measured by expenditure method

10. From the following data, calculate GDPmp and National income:

Item (Rs in Crores)

(i) Wages and salaries 800 (ii) Rent 300

(iii) Profit after tax 700 (iv) Consumption of fixed capital 80

(v) Mixed income 600

(vi) COE paid by government 500 (vii) NFIA -50

(viii) Interest 500 (ix) NIT 150

(x) Employer’s contribution to SS Scheme 50

(xi) Direct taxes paid by household 70 (xii) Corporation tax 100

11. From the following data, calculate National Income:

Items (Rs in Crores)

(i) Compensation of employees 1200

(ii) Rent 400 (iii) Profit 800

(iv) Consumption of fixed capital 300 (v) Mixed income 1000

(vi) Private income 3600

(vii) NFIA -50 (viii) Net retained earnings of private enterprises 200

(ix) Interest 250 (x) NIT 350

(xi) Net export -60 (xii) Direct taxes 150

(xiii) Corporation tax 100

12. Calculate Gross National Product at market price by product method and income

method.

Items (Rs in C rores (i) Value of output of primary sector 1000

(ii) Indirect taxes 200

(iii) Compensation of employees 780

(iv) Net factor income from abroad 100 (v) Intermediate purchase by all the sectors 2900

(vi) Rent 300 (vii) Value of output of secondary sector 2000

(viii) Subsidies 50

(ix) Interest 600 (x) Consumption of fixed capital 120

(xi) Value of output of tertiary sector 3000 (xii) Profit 320

(xiii) Mixed income of self –employed 830

13. Calculate National income method and expenditure method.

Item (Rs in Crores) (i) Profit 200

(ii) Private final consumption expenditure in home country

350

(iii) Government final consumption expenditure 250 (iv) Wages and salaries 350

(v) Gross domestic capital formation 90 (vi) Consumption of fixed capital 20

(vii) Net export -20

(viii) Interest 60 (ix) Rent 70

(x) Net factor income from abroad 50 (xi) Net indirect taxes 60

(xii) Expenditure of NPISHs 30 (xiii) Direct purchase made by resident households

abroad 100

(xiv) Purchase made by non-residents in home country 10

14. How will the following be treated while estimating national income of india? Give

reasons.

(i) Dividend received by an Indian from his investment in shares of a foreign

company.

(ii) Money received by a family in India from relatives working abroad.

(iii) Interest received on loans given to a friend for purchasing a car.

(iv) Profits earned by an Indian bank from its branches abroad.

(v) Salaries paid to non –resident Indians working in Indian embassy in America.

(vi) Payment of interest on a loan taken by an employee from the employer.

(vii) Dividend received by a foreigner from investment in shares of an Indian

company.

(viii) Payment of interest by a government firm.

(ix) Scholarship given to Indian students studing in india by a foreign company.

(x) Family members working free on the farm owned by the family.

(xi) Rent free house from an employer.

PROJECT WORK

As per the CBSE curriculum guidelines, the students of class XII are required to prepare and submit a Project work for the evaluation of Economics. In this you are supposed to follow given instructions: Guidelines

1. Every student will complete one project on separate topic as given by teacher.

2. It should be hand written and not more than 3500 to 4000 words.

3. Sequence of the project file in the following way:

4. Page 1 – Economics Project Name of the topic Page 2 : Name of the student, board roll no. Page 3: Certificate Page 4 : Acknowledgement Page 5: Index Page 6: Objectives Page 7: Introduction of the topic/title

Identifying the causes, consequences and remedies

Critical analysis of the topic

Various stakeholders and effect on each of them

Conclusion

Students’ own views/perception/opinion and learning from the work Last page : Bibliography (name of the book, Magazine, Extract, General and name of the Site from where you have taken your content).

ENGLISH

Q1 Cut advertisements from the ‘classified ads’ of newspapers and paste them under the

following heads in your notebooks.

A. Situation vacant

B. Sale and purchase (property/vehicles/household goods)

C. To-Let

D. Lost and found

E. Educational institutions/courses

F. Missing persons/pet animals

G. Tours and travel

Q2 Select two interesting articles from the editorial page of any national daily and paste

them in your notebook.

Q3 Write ‘ Article’ in about 150-200 words on the following topics:-

1. Environment pollution

2. Elderly care

3. Role of youth in combating corruption

4. Education for all

Q4 Write different types of poetic devices along with their definitions. Quote at least 5

examples of each from the poems prescribed in the syllabus (flamingo).

Q5. Revise the work done in the class.

GEOGRAPHY

Note:- Answer all the questions .

1 Explain the three school of thoughts in human geography and give two characteristics of each school of thoughts.

2 Explain the three components of population change. 3. Give a detailed account of the factors influencing the distribution of population in

the world. 4. What is migration? Explain the factors causing migration.

5. Explain the different trends of population growth in the world from early period to the present day.

6. Explain the three stages of population change with the help of a diagram. 7. Explain the factors responsible for imbalances in the male female ratio found in

different parts of the world. 8. What is the significance of age sex pyramid. Explain. 9. Define Human Development. 10. Explain the various approaches to human development. 11. How is Human Development measured? Explain in detail. 12. Read chapter 5 and 6 ‘Primary Activities’ and Secondary Activities’ and prepare ten

short answer questions from each chapter. Also write their correct answers. 13. On the outline map of World show the following features. (i) Areas under Nomadic Herding. (ii) Areas under Intensive subsistence farming. (III) Areas under Commercial animal rearing. 14. Prepare a project on Conservation of Environment. 15. Complete your Geography Practical File from Chapter 1 to 5.

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INFORMATIC PRACTICES

1. (a) Identify the odd one out of the following : Optical Fiber/Coaxial Cable/Bluetooth/Twisted Pair Cable Give reason for your answer. (b) How is it easier to diagnose fault in Star topology than in Bus topology ? (c) What is the purpose of logical address of computer ? (d) Does open source software only mean that the software is free of cost ? Give reason for your answer. (e) Which of the following are valid IP addresses ? Give reason(s) if invalid. (i) 121.23.1.45 (ii) 192.168.0.254 1 (iii) 192.168.0.1 (f) Mr. Ravi, an IT Help Desk executive needs to remotely login a customer’s PC to provide him technical support. Suggest a remote access software to him.

(g)Identify the fastest wired media out of the following: Ethernet cable, Optical fiber, Co-axial cable (h)Mention any two main advantages of star topology over bus topology. (i) Discuss the significance of Bluetooth technology. 2. (a) Write MySql command to create the table DEPARTMENT with given constraints. Table DEPARTMENT COLUMN_NAME DATATYPE(SIZE) CONSTRAINT DepartmentID int(4) Primary key DepName varchar(50) Not Null ManagerID char(4) Location varchar(30) (b) In a Database, there are two tables given below :

Table : EMPLOYEE

EMPLOYEEID NAME SALES JOBID

E1 SAMITA SINHA 1100000 102

E2 VIJAY SINGH TOMAR

1300000 101

E3 AJAY RAJPAL 1400000 103 E4 MOHIT RAMNANI 1250000 102

E5 SHAILJA SINGH 1450000 103

Table : JOB

JOBID JOBTITLE SALARY 101 President 200000

102 Vice President 125000 103 Assitant 80000

104 Accounting Manager 70000 105 Accountant 65000

`106 Sales Manager 80000

Write SQL Queries for the following :

(i) To display employee ids, names of employees, job ids with corresponding job titles.

(ii) To display names of employees, sales and corresponding job titles who have achieved sales more than 1300000. (iii) To display names and corresponding job titles of those employee who have ‘SINGH’ (anywhere) in their names. (iv) Identify foreign key in the table EMPLOYEE. (v) Write SQL command to change the JOBID to 104 of the Employee with ID as E4 in the table ‘EMPLOYEE’. 3. (a) Write one advantage and one disadvantage of e-learning to students. 4. (a) Write one similarity and one difference between CHAR and VARCHAR data types. (b) Consider the following table named “GARMENT”. Write command of SQL for (i) to (iv) and output for (v) to (vii). Table : GARMENT

GCODE GNAME SIZE COLOUR PRICE 111 TShirt XL Red 1400.00

112 Jeans L Blue 1600.00

113 Skirt M Black 1100.00 114 Ladies Jacket XL Blue 4000.00

115 Trousers L Brown 1500.00 116 Ladies Top L Pink 1200.00

(i) To display names of those garments that are available in ‘XL’ size. (ii) To display codes and names of those garments that have their names starting with ‘Ladies’. (iii) To display garment names, codes and prices of those garments that have price in the range 1000.00 to 1500.00 (both 1000.00 and 1500.00 included). (iv) To change the colour of garment with code as 116 to “Orange”. (v) SELECT COUNT(DISTINCT (SIZE)) FROM GARMENT; (vi) SELECT AVG (PRICE) FROM GARMENT; (vii) SELECT GNAME FROM GARMENT WHERE SIZE IN (‘M’, ‘L’) AND PRICE > 1500; (c) What is the degree and cardinality of ‘Garment’ table ? 5(a) What precaution must be taken with regard to making payments while shopping online ? (b) Write down any two benefits of net banking. (c)Mr. Sanjay, a banking professional want to enroll himself in an e-Learning course. Mention him any two challenges of e-Learning.

(d) James works for a Garments company. He has created a form for the employees. Help him choose most appropriate controls from ListBox, ComboBox, TextField, TextArea, RadioButton, Checkbox, Label and Command Button for the following entries : i. To enter first name of employee ii. To select gender (M/F) iii. To choose category of employee (Permanent/Temporary) iv. To allow entering remarks about the employee in the form of paragraph. (e)Mention any two example of common Database Management System (f)Write the full forms of the following: i. DDL ii. DML 6.(a) the following code using switch case: int day=Integer.parseInt(jTextField1.getText()); if(day>=1 && day<=5) jOptionPane1.showMessageDialog(this, "Working Day"); else if(day>=6 && day<=7) jOptionPane1.showMessageDialog(this, "Off Day"); else jOptionPane1.showMessageDialog(this, "Invalid Entry"); (b) Deepti works as a programmer in a travel company. She has developed the following code to display travel detail according to user’s choice. Help her in rewriting the same code using SWITCH CASE: if(choice==1) jTextField1.setText(“New Delhi to Goa”); else if(choice==2) jTextField1.setText(“New Delhi to Paris”); else if(choice==3) jTextField1.setText(“New Delhi to Bangkok”); else jTextField1.setText(“Pl. choose valid option”); 7(a) Mention any two example of common Database Management System. (b) Write the full forms of the following: i. DDL ii. DML

(c) Ms. Archana, a class XI student has just started learning MySQL. Help her in understanding the basic difference between Alter and Update command with suitable example. Also suggest her suitable command for the following purpose: i. To display the list of the database already existing in MySQL. ii. To use the database named City. iii. To remove the pre-existing database named Clients. iv. To remove all the records of the table named “Club” at one go along with its structure permanently. Q8.Differentiate unary and binary operators. Q9.Name the text interaction methods used in Java and explain the purpose of their use with the help of example. Q10.How entry control loop is different from an exit control loop. Q11.Compare and contrast the following : a)JTextfield and Jlabel . b)Jlistbox and Jcombo button c)Jradio button and Jcheckbox. Q12Name atleast 5 computer threats and their preventive measures.

HOME WORK FOR PRACTICAL

PREPARE A PRACTICAL FILE AS EXPLAINED IN THE CLASS-ROOM WITH THE FOLLOWING

CONTENTS :

1)Certificate. 2)Acknowledgement. 3)25 Java IDE Programmes using different controls (print out of coding,form,output) 4)5 tables of SQL having 5 queries for each table. NOTE : Practical file should contain printouts of all the above mentioned contents.

Use A4 sheets for file.

COMPUTER SCIENCE

Q1.Name the header files inwhich the following belong to : a)random( ) b)read( ) c)isalpha ( ) d)strcmp( ) e)abs ( ) f) clrscr ( )

Q2.What is the difference between Public and Private members of a class ?

Q3.Define a class named STREAM in C++ with the following descriptions:

Private Members :

AD_NO Integer

NAME Array of 25 characters

FEES Float

Public Members :

Function Read_data( ) to input AD_NO,NAME and Percentage .

Function Display( ) to Display the details after calling the function select_Stud( ) of an

objct .

Function Select_Stud( ) to choose students for different streams depending on their

percentage and display the fees they have to deposit.

Percentage Stream Fees Percentage > = 90 Computer 18000

Percentage > = 80 but < =90

Biology 14000

Percentage < 80 but >= 70

Commerce 12000

Otherwise No Stream 0

Q4.Answer the questions (i) to (iv) based on the following code : class shop {char category[10]; char date_of_Manufacturer[10]; char Company [20]; public : shop( ); void enterditails ( ) ; void showdatails ( ) ; }; Class BigShop ; public Shop

{ protected : int tax ; public : float Price ; BigShop( ) ; void enterBigdetails ( ) ; void showBigdetails ( ) ; }; class Mall : public BigShop { int no_of_floors ; public : Mall ( ); void enterdetails ( ) ; void showdetails( ) ; }; (i)How many bytes will be required by an object of class Shop and an object of class Mall respectively ? (ii)Write names of all the member functions accessible from the objects of class Mall. (iii)Write names of all the members accessible from member functions of class Bigshop. (iv)Write names of all the data members which are accessible from the objects of class Mall. Q5.Define the following : (i)Degree (ii)Cardinality (iii)Primary Key (iv)Alternate Key (v)Candidate Key Q6.What Is function overloading ? Q7.When a function is overloaded,there are multiple definitions of the functions .What makes the various definitions of the function different from each other ?Give an example. Q8.What is Encapsulation and data hiding ?How are they implemented in c++ ?Explain with the help of an example. Q9.What are the different types of inheritance .Explain by giving examples for each type of inheritance . Q10.What is a class and an object ?

PRACTICAL HOME WORK

Q1.Make a Practical file containing A4 size sheets and the following contents :

(i)Certificate. (ii)Acknoledgement

(iii)20 c++ programs and their outputs from different topics like arrays,classes,function overloading,inheritance etc. (iv)5 SQL Tables with 10 queries from each table (5 queries and 5 output statements)

PHYSICAL EDUCATION

Prepare PHYSICAL EDUCATION PRACTICAL FILE as given per the CBSE Syllabus 2019-20 constituting the following :

1) Practical 1: Fitness test administration of all items (AAHPER TEST (CHAP-6 :TEST AND

MEASUREMENT IN SPORTS)

2) Practical 2 : Procedure of ASANAS, benefits and contraindications for any 2 ASANAS for EACH LIFE STYLE DISEASE given in the book (CHAP-3 : YOGA AND LIFESTYLE)

3) Practical 3: Procedure for administering SENIOR CITIZEN FITNESS TEST AND

CONDUCT IT UPON 5 ELDERLY MEMBERS

(CHAP-6 :TEST AND MEASUREMENT IN SPORTS)

4) Practical 4 :ANY 1 GAME OF YOUR CHOICE listed below (LABELLED DIAGRAM OF FIELD & EQUIPMENTS, RULES, SKILLS AND TERMINOLOGIES (INTERNET or ANY BOOK ON THE SPECIALISED GAME)

GAMES :

BASKETBALL

FOOTBALL

KABADDI

KHO-KHO

VOLLEYBALL

HANDBALL

HOCKEY

CRICKET

BOCCE

UNIFIED BASKETBALL

All topics are covered in new revised book of HEALTH AND PHYSICAL EDUCATION,

Saraswati Publishers (2019-20) (CHAP-3 : YOGA AND LIFESTYLE, CHAP-6 :TEST AND

MEASUREMENT IN SPORTS)

PHYSICS

Chapter – 1 : Electric Charges and Fields

Theory Based Questions:

Q1. (a) State Coulomb’s law of force between charges at rest. Express the same in SI units.

(b) Name and define the SI unit of charge.

(c) Write Coulomb’s law in vector form. What is the importance of expressing it in vector

form?

Q2. Define dielectric constant of a medium in terms of force between electric charges, electric

field & electrical permittivity.

Q3. Define electric field intensity and derive an expression for it at a point on the axial line of

a dipole. Also determine its direction.

Q4. Define electric dipole moment. Derive an expression for the electric field intensity at any

point along the equatorial line of an electric dipole.

Q5. (a) Derive an expression for the torque acting on an electric dipole, which is held in

uniform electric field, when the axis of the dipole makes an angle with the electric

field. Hence define electric dipole moment.

(b) What happens when an electric dipole is held in a non-uniform electric field? What will

be the force and the torque when the dipole is held parallel or antiparallel to the

electric field?

Q6. Sketch the lines of force of

(i) a point charge q > 0,

(ii) a point charge q < 0,

(iii) an electric dipole or two equal and opposite charges separated by a small distance,

(iv) two equal positive charges placed small distance apart in air, and

(v) a positively charged plane conductor.

Q7. State Gauss’s theorem in electrostatics. Using this theorem, derive an expression for the

.

Q8. (a) Define electric flux.

(b) A point charge is placed at the centre of spherical Gaussian surface. How will electric

flux change if

(i) the sphere is replaced by a cube of same or different volume,

(ii) a second charge is placed near, and outside, the original sphere,

(iii) a second charge is placed inside the sphere, and

(iv) the original charge is replaced by an electric dipole?

Q9. Using Gauss Theorem derive an expression for the electric field intensity at a point near a

thin infinite plane sheet of charge density .

Q10. Apply Gauss theorem to calculate the electric field due to a uniformly charged spherical

shell at a point

(a) outside the shell, (b) on the shell and (c) inside the shell.

Draw a graph showing the variation of electric field E with distance r from the centre of a

uniformly charged thin spherical shell.

Numerical Questions :

Q1. Which is bigger – a coulomb or a charge on an electron? How many electronic charges

form one coulomb of charge?

Q2. A charge q is placed at the centre of the line joining two equal charges Q. Show that the

system of three charges will be in equilibrium if q = – Q/4.

Q3. Two similar balls each having mass m and charge q are hung from a silk thread of length l,

prove that equilibrium separation

3/1

0

2

2

mg

lqx

when each thread makes a small angle with the vertical.

Q4. Two small spheres each having mass m kg and charge q coulomb are suspended from a

point by insulating threads each I metre long but of negligible mass. If is the angle,

each thread makes with the vertical when equilibrium has been attained, show that

0

222 ε 4π tanθθ sin mgl 4q

Q5. Two point charges q1 = + 0.2C and q2 = + 0.4 C are placed 0.1 m apart. Calculate the

electric field at (a) the midpoint between the charges. (b) a point on the line joining q1

and q2 such that it is 0.05 m away from q2 and 0.15 m away from q1.

Q6. ABCD is a square of side 5m. Charges of +50 C, – 50 C and + 50 C are placed at A, C and D

respectively. Find the resultant electric field at B.

Q7. Electric field in is directed along + X direction and given by

BAxEx

25 , where E is in 1NC and x is in metre, A and 1NC 1mB are constants with dimensions. Talking A = 10

and B = 5 1NC , calculate

(i) the electric flux through the cube.

(ii) net charge enclosed within the cube.

Q8. Two small identical electrical dipoles AB and CD, each of

dipole moment ‘p’ are kept at an angle of 120o as shown in

Fig. What is the resultant dipole moment of this

field ⃗⃗ ⃗⃗ ⃗⃗ combination? If this system is subjected to electric

directed along + X direction, what will be the magnitude

and direction of the torque acting on this?

Q9. (a) Two point charges placed at a distance r in air exert a force F on each other. At what

distance will these charges experience the same force F in a medium of dielectric

constant K?

(b) A force F is acting between two charges placed some distance apart in vacuum. If a

brass rod is placed between these two charges, how does the force change?

Q10. (a) An infinite line charge produces a field of 9 at a distance of 2 cm.

Calculate the linear charge density.

(b) Two large, thin metal plates are parallel and close to each other. On their inner faces,

the plates have surface charge densities of opposite signs and of magnitude

. What is E (a) to the left of the plates, (b) to the right of the

plates, and (c) between the plates?

(c) A spherical rubber balloon carries a charge that is uniformly distributed over its

surface. As the balloon is blown up; how does E vary for points (i) inside the balloon,

(ii) on the surface of the balloon and (iii) outside the balloon?

Chapter – 2: Electrostatic Potential & capacitance

Theory Based Questions:

Q1. (a) Define electric potential. Derive an expression for the electric potential at a distance r

from a point charge q.

(b) Draw graphs showing the variations of (i) electrostatic potential V and (ii)

electrostatic field E with distance r from a charge q.

Q2. Derive an expression for the electric potential due to an electric dipole at any general

point.

Q3. (a) What is an equipotential surface? Give an example.

(b) Show that the amount of work done in moving a test charge over an equipotential

surface is zero.

(c) Sketch equipotential surface for

(i) a positive point charge

(ii) two equal and opposite charges separated by a small distance.

(iii) two equal and positive charges separated by a small distance.

(iv) a uniform electric field.

Q4. Derive an expression for the potential energy of a dipole in a uniform electric field. Hence

discuss the conditions of its stable and unstable equilibrium.

Q5. (a) Derive an expression for the capacitance of a parallel plate capacitor.

(b) What are the factors on which the capacitance of a parallel plate capacitor depends?

Q6. Derive an expression for the energy stored in a parallel plate capacitor. Hence show that

electric field E is a source of energy with energy density

.

Q7. Two capacitors with capacity and are charged to potentials and respectively

and then connected in parallel. Calculate the common potential across the combination,

the charge on each capacitor, the electrostatic energy stored in the system and the

change in the electrostatic energy from its initial value.

Q8. (a) How does a dielectric develop a net dipole moment in an external electric field when it

has (i) non-polar molecules and (ii) polar molecules?

(b) Explain why the polarization of a dielectric reduces the electric field inside the

dielectric. Hence define dielectric constant.

Q9. (a) Define polarisation density. How is it related to the induced surface charge density?

(b) Define electric susceptibility. Deduce the relation between dielectric constant and

electric susceptibility.

Q10. What is a dielectric? A dielectric slab of thickness t is kept between the plates of a

parallel plate capacitor separated by distance d. Derive the expression for the

capacitance of the capacitor for t << d.

Numerical Questions:

Q1. Twenty seven drops of same size are charged at 220 V each. They coalesce to form a

bigger drop. Calculate the potential of the bigger drop.

Q2. Calculate the electric potential at the centre of a square of side √ having charges 100

and at the four corners of the square.

Q3. An infinite plane sheet of charge density is held in air. In this situation how far

apart are two equipotential surfaces, whose p.d. is 5V?

Q4. An electric dipole of length 4cm, when placed with its axis making an angle of 60o with a

uniform electric field experiences a torque of 4 √ Nm. Calculate the (i) magnitude of the

electric field, (ii) potential energy of the dipole, if the dipole has charges of 8 nC.

Q5. An electric dipole consists of two opposite charges each of magnitude 1 separated by

2 cm. The dipole is placed in an external electric field of . Find (i) the maximum

torque exerted by the field on the dipole (ii) the work which the external agent will have

to do in turning the dipole through 180o starting from the position .

Q6. A parallel plate capacitor of 300 is charged to 200 V. If the distance between its plates

is halved, what will be the potential difference between the plates and what will be the

change in stored energy?

Q7. Two parallel plate capacitors, X and Y, have the

same area of plates and same separation between

them. X has air between the plates while Y contains

a dielectric medium of

(i) Calculate capacitance of each capacitor

if equivalent capacitance of the combination is 4

(ii) Calculate the potential difference between the plates of X and Y.

(iii) What is the ratio of electrostatic energy stored in X and Y?

Q8. Keeping the voltage of the charging source constant, what would be the percentage

change in the energy stored in a parallel plate capacitor if the separation between its

plates were to be decreased by 10%?

Q9. (a) Calculate the capacitance of the capacitor shown in

the figure.

(b) Find the capacitance of the infinite network between

points A and B.

Q10. Calculate equivalent capacitance between A & B. Also, calculate charge and voltage across

each capacitor.

(i) (ii)

(iii)

C1 = C2 = C4 = 5pF C3 = C5 = 10 pF

Chapter – 3 : Current Electricity

Theory Based Questions:

Q1. Give some important points of differences between electromotive force and potential

difference.

Q2. Define the terms drift velocity and relaxation time. Derive an expression for the drift

velocity of free electrons in a conductor in terms of relaxation time.

Q3.(a) Derive ohm’s law on the basis of the theory of electron drift.

(b) Derive an expression for the resistivity of a conductor in terms of number density of

free electrons and relaxation time.

Q4. Define internal resistance of a cell. Prove that RV

Er

1 , where R = external

resistance.

Q5. Derive the condition for obtaining maximum current through an external resistance

connected across a series combination of cells.

Q6. Derive the condition for obtaining maximum current through an external resistance

connected across a parallel combination of cells.

Q7. Derive the condition for obtaining maximum current through an external resistance

connected across a mixed grouping of cells.

Q8. State Wheatstone bridge principle. Deduce the condition for which Wheatstone bridge is

balanced.

Q9. Define potential gradient. With the help of a circuit diagram, explain how a potentiometer

can be used to compare the emfs of two primary cells.

Q10. State the principle of a potentiometer. With the help of a circuit diagram, describe a

method to find the internal resistance of a primary cell.

Numerical Questions:

Q1. A current of 2mA is passed through a colour coded carbon resistor with first, second &

third rings of yellow, green and orange colours. What is the voltage drop across the

resistor?

Q2.(a) A wire has a resistance of 16 . It is melted and drawn into a wire of half its length.

Calculate the resistance of the new wire. What is the percentage change in its

resistance?

(b) The resistance of a wire is R ohms. What will be its new resistance if it is stretched to

‘n’ times its original length?

Q3. Two wires X, Y have the same resistivity, but their cross – sectional areas are in the ratio 2

: 3 and lengths in the ratio 1 : 2. They are first connected in series and then in parallel to a

d.c. source. Find out the ratio of the drift speeds of the electrons in the two wires for the

two cases.

Q4.(a) A set of n identical resistors, each of resistance R , when connected in series have an

effective resistance R & when connected in parallel, their effective resistance is Y .

Find relation between R, X and Y.

(b) A wire of uniform cross section and length has a resistance of 16 . It is cut into four

equal parts. Each part is stretched uniformly to length l and all the four stretched

parts are connected in parallel. Calculate the total resistance of the combination so

formed. Assume that stretching of wire does not cause any change in the density of its

material.

Q5.(a) Calculate the current shown by the ammeter A in the circuit shown in figure.

(b) A battery of emf 10V is connected to resistance as shown in figure. Find the potential

difference between points A and B, R1 = R4 = 1 , R2 = R3 = 3 .

Q6. Calculate equivalent resistance between A & B.

(i) (ii)

Q7. (a) The reading on a high resistance voltmeter when a cell is connected across it is 2.2V.

When the terminals of the cell are also connected to a resistance of 5 , the voltmeter

reading drops to 1.8V. Find the internal resistance of the cell.

(b) A battery of emj ‘E’ & internal resistance ‘r’ gives a current of 0.5A with an external

resistor of 12 & a current of 0.25 A with an external resistor of 25 . Calculate

internal resistance of the cell & emf of the cell.

Q8. Three cells of emf 2V, 1.8V, 1.5V are connected in series. Their internal resistances are

0.05 , 0.7 & 1 respectively. If the battery is connected to an external resistance of

4 via a very low resistance ammeter, what would be the reading in the ammeter?

Q9. Two identical cells of emf 1.5V each joined in parallel provide supply to an external circuit

consisting of two resistances of 17 each joined in parallel. A very high resistance

voltmeter reads the terminal voltage of cells to be 1.4V. Calculate the internal resistance

of each cell.

Q10. 12 cells, each of emf 1.5V & internal resistance 0.5 are arranged in m rows each

containing n cells connected in series. Calculate the values of n and m for which this

combination would send maximum current through an external resistance of 1.5 .

Q11.(a) Using kirchoff’s laws, calculate the potential difference across the 8 resistor shown

in the figure.

(b) Determine the current in each branch of the

network shown in the figure.

(c) In the circuit shown in figure, E, F, G & H are cells

of emf 2V, IV, 3V and IV & their internal

resistances are 2 , 1 , 3 & 1

respectively. Calculate

(i) potential difference between B and D.

(ii) potential difference across the terminals of each

of the cells G and H.

Q12. (a) A galvanometer of 15 resistance is connected across

BD. Calculate the current through the

galvanometer when a potential difference of 10V is maintained across AC.

(b) Calculate equivalent resistance across points A and B.

Q13. (a) In the following

circuit, a metre

bridge is shown in

its balanced

state. The meter bridge wire has a resistance

of 1 ohm/cm. Calculate the value of ‘X’ and the

current drawn from the battery of negligible

internal resistance.

(b) In a metre bridge, the null point is found at ‘l1’, from A.

If now a resistance ‘X’ is connected in parallel

with ‘S’, the null point occurs at ‘l2’ from A. Obtain

formula for X in terms of ,1l

2l and S.

Q14. (a) Two cells of emfs, E1 & E2 (E1 < E2) are connected as shown in figure

When a potentiometer is connected between A & B, the balancing length of the

potentiometer wire is 300 cm. On connecting the same potentiometer between A &

C, the balancing length is 100cm. Calculate the ratio of E1 & E2.

Q15. In a potentiometer, a standard cell of emf 5V & of negligible resistance maintains a steady

current through the potentiometer wire of length 5m. Two primary cells of emfs E1 & E2

are joined in series with (i) same polarity & (ii) opposite polarity. The combination is

connected through a galvanometer& a jockey to the potentiometer. The balancing

lengths in the two cases are found to be 350cm and 50cm respectively.

(i) Draw the necessary circuit diagram.

(ii) Find the value of the emfs of the two cells.

--X--

POLITICAL SCIENCE

Read& revise following chapters;

1) Cold war era

2) US Hegemony in world politics

3) Alternative centres of power

4) The end of bipolarity

5) Map questions;

a) Countries belonging to NATO & WARSAW Pact

b) Founding members of NAM

c) Allied & Axis powers of WW1 WW2

d) A nation that was invaded by SU in 1979

e) Nation that came into existence after the socialist revolution in 1917

f) Nation that suffered due to civil war for 10 years i.e. upto 2001

g) Countries that came into existence after 1991

h) Identify two major Oil and Gas producers of S.U.

i) Two countries that were declared founder members of Commonwealth and

Independent states

j) Identify four older members of E.U. & two new members of E.U.

k) Locate and label any 5 countries of ASEAN

l) Revise cartoon given on Pg no.37

m) Questions related to

Cartoons given on Pg no.55,57,59,60

Pictures given on Pg no.52 & 56.

PROJECT FILE :-

Project file

Handwritten work

Simple and easy topic

Five pages of topic content

4 to 5 pages of other things look like title page , acknowledgment , certificate , bibliography

etc. – in total let it be approximately 10 pages

PROJECT WORK :-

E.U. as alternative centre of power

UN – an indispensable organisation

Geopolitics - over oil and water

Demands for statehood in India

RTI – watchdog of democracy

Evolution of election system in India

Rise of China

One party dominance – BJP past 2014

India's relationship with its neighbours

Role of regional parties

Separist movement – Kashmir

Relevance of NAM and SAARC

Naxalite movement

Politics of reservation in India

Cold war 2 – USA and China

PUNJABI

1) ,

ਲਈ ।

2) ਲ ਲ ਲ :-

ੳ) ) ੲ) ।

3) ਲ ਲ ਲ ਲ

ਲਈ ਲ

4) ਲ - ਲ ਈ ਲ ਲ

5)

:- ।

--X--

12

2019-2020

1 - 5

2 । -5

3 ।

4 ।

5 - ।

( )

।

( ) ।

( ) ।

( ) औऱ

।

( ) , -

।

6 ।

7 ।

8 ।

--x--

MATHEMATICS

INVERSE TRIGONOMETRY

1.Express each of the following in the simplest term:

(i) tan ― 1 {√ √

√ √ }

(ii) cos ― 1 (

)

(iii) sin ― 1 (

)

(iv) (

√ )

(v) ( √

)

1. Simplify the following:

(i) sin ― 1 { √ √ √ }

(ii) sin ― 1 { √

√ }

(iii) sin { √

}

(iv) tan ― 1 { √ }

(v) tan ― 1 {

√ }

(vi) {√ √

}

(vii) {

(

) (

) } + {

(

) (

)}

(viii) (

) (

)

2. If a > b > c > 0. Prove, (

) + (

) + (

) = π

3. Prove that: (√

) = 2 (√

)

4. If y = (√ ) ― (√ ) , then prove that = tan2 (

)

5. If (

) + (

) = α, then prove that

―

cos α +

= sin2 α.

6. If cos―1 + cos―1 + cos―1 z = , then prove that 2 + 2 + z2 + 2 z = 1.

7. If cos―1 (

) + cos―1 (

) = α, then prove that 9 2 ― 12 cos α + 4 2 =

36 sin2 α.

8. If (

) ― (

) = (

) , then prove that =

.

9. If ―

, solve for .

10. Prove that: 2 (

) = (

).

11. Write the range of one branch of , other than the Principle Branch.

12. Solve for : + + = .

13. Solve the equation for : ― + =

, where > 0.

14. Solve the equation: ― 3

― 4

+ 2

=

.

15. What is the range of the principle branch of defined on the domain R ― [ ]

16. Show that + +

DIFFERENTIATION

1. If = + , prove that 2 =

2. If = log (

), prove that 2 =

3. If = log ( √ ) , prove that 2 + 1 = 0

4. If = [ √ ]

, show that 2 + 1 ― = 0

5. If = a , = a , find

6. If = (

) , show that 2 + 1 = 0

7. If = a , = a , prove 2 =

8. If = a , = , prove that

=

at

9. If = , prove that 2 ― 2 1 + 2 = 0

10. If = , show that 2 ― 4 1 + 4 = 0

11. If = a ― , = a + , prove that 2 = ―

12. If = , prove that 2 + 1 + = 0

13. If = , = , prove that 2 ― 1 + = 0

14. If = , prove that 2 ― 1 ― 2 = 0

15. If = , prove that 2 + 1 = 0

16. If = , prove that 2 + 2 1 = 2

17. If = ( √ ) , show that 2 + 1 = 0

18. If = , prove that 2 + 1 + = 0 , where = +

19. If = (

) , show that 2 ― 1 ― = 0

20. If = (

) , prove that

=

21. If √ + √ = 1, prove that

= ― √

.

22. If = ( √ √ ) , then prove that

=

√ +

√ .

23. If = , show that

=

.

24. If + = , prove that

=

.

25. If = , prove that

=

.

26. If = , prove that

=

.

27. If = , prove that (i)

=

and (ii)

= 0 .

28. If = , prove that

=

.

29. If = and = , 0 < <

, find

,

.