the singing lesson: story summary & analysis · the singing lesson: a commentary the singing...

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ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH Class 12 English Worksheet-8 (Literature) The Singing Lesson: Story Summary & Analysis Plot summary The Singing Lesson, written by Katherine Mansfield, is all about a surprising day of a music teacher’s life. Taken from Katherine’s ‘The Garden Party and Other Stories’ collection, it’s a short story written in third person from an unknown narrator’s perspective. Miss Meadows, a music teacher, receives a letter from her fiancé which states quite plainly that Basil, her fiancé, isn’t ready to marry her and feels that the marriage would fill him with disgust. The word “disgust” is scratched lightly and written above it is the word “regret”. Naturally she’s filled with despair, anger & sadness. And due to her bad mood she sees everyone and everything in a negative light. Her usual calm and cheery demeanor turns gloomy and angry that day and this change doesn’t go unnoticed by her students. During the lesson she’s rather harsh with her students. She tells them that today they would be practicing a lament, without any expression at first. Each stanza, each word, each breath seems like a sob or groan and lament to her gloomy mind. Then she tells them that they must feel the despair, the pain and the sorrow in order to perform the piece perfectly. Though the way she tells them so is not that simple. They are rather frightened by the sudden change in her behavior. During the lesson she’s informed by another colleague that Basil, her fiancé, has sent a telegram for her. Her first thought is that Basil has committed suicide! Yes, you read that right. It’s because the school has a rule; telegram can be sent to the workers during working hours only in case of death or emergency situation. But in the telegram Basil had asked her to ignore the first letter and that he had bought the hat-stand which they had been thinking of lately. In short, the marriage is happening. The content of the telegram definitely lights up her mood and she’s back with her usual cheery demeanor. She returns and continues her class, now practicing a cheerful song, singing with expressions, more loudly and cheerfully than any other student. The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party and Other Stories’ but is still a nice example of Katherine’s talent of capturing real life moments and sentiments in the most beautiful yet simple way. From the starting lines of the story, there’s a slight touch of mystery and lyrical content. The author’s way of making Miss Meadows see the reflection of her own gloomy mood in

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Page 1: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party

ST. XAVIER’S SR. SEC. SCHOOL, CHANDIGARH

Class 12 English Worksheet-8 (Literature)

The Singing Lesson: Story Summary & Analysis

Plot summary

The Singing Lesson, written by Katherine Mansfield, is all about a surprising day of a music

teacher’s life. Taken from Katherine’s ‘The Garden Party and Other Stories’ collection, it’s a

short story written in third person from an unknown narrator’s perspective.

Miss Meadows, a music teacher, receives a letter from her fiancé which states quite plainly that

Basil, her fiancé, isn’t ready to marry her and feels that the marriage would fill him with disgust.

The word “disgust” is scratched lightly and written above it is the word “regret”. Naturally she’s

filled with despair, anger & sadness. And due to her bad mood she sees everyone and everything

in a negative light. Her usual calm and cheery demeanor turns gloomy and angry that day and

this change doesn’t go unnoticed by her students.

During the lesson she’s rather harsh with her students. She tells them that today they would be

practicing a lament, without any expression at first. Each stanza, each word, each breath seems

like a sob or groan and lament to her gloomy mind. Then she tells them that they must feel the

despair, the pain and the sorrow in order to perform the piece perfectly. Though the way she tells

them so is not that simple. They are rather frightened by the sudden change in her behavior.

During the lesson she’s informed by another colleague that Basil, her fiancé, has sent a telegram

for her. Her first thought is that Basil has committed suicide! Yes, you read that right. It’s

because the school has a rule; telegram can be sent to the workers during working hours only in

case of death or emergency situation. But in the telegram Basil had asked her to ignore the first

letter and that he had bought the hat-stand which they had been thinking of lately. In short, the

marriage is happening. The content of the telegram definitely lights up her mood and she’s back

with her usual cheery demeanor.

She returns and continues her class, now practicing a cheerful song, singing with expressions,

more loudly and cheerfully than any other student.

The Singing Lesson: A Commentary

The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden

Party and Other Stories’ but is still a nice example of Katherine’s talent of capturing real life

moments and sentiments in the most beautiful yet simple way.

From the starting lines of the story, there’s a slight touch of mystery and lyrical content. The

author’s way of making Miss Meadows see the reflection of her own gloomy mood in

Page 2: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party

everything, even in the sweet greeting from her colleagues and students is quite realistic because

our mood can make us behave in the most peculiar ways at the most wrong times.

In the opening scene, the interaction between the Science Mistress & Miss Meadows is quite

sarcastic and from that we can conclude that Miss Meadows was rather pessimistic. Is it due to

the shock she has received from her fiancé or is it just her general nature? We don’t know. But of

course, towards the end her mood changes and she’s perfectly cheerful, so may be we can say

that the pessimistic way is only due to her bad mood. It’s also safe to say that Miss Meadows

chose to show her feelings and moods through music rather than words.

The story flow is a bit intriguing as well because at first there’s no mention of why Miss

Meadows is in such a bad mood. Readers are left to wonder and assume on their own. But the

answer becomes quite clear at the right time, without making the readers angry or irritated with

all the guess work and questions.

There aren’t many characters but those that are there, are described quite properly and aren’t

exaggerated. Though there’s no mention of the place where it all takes place, we can ascertain

that it’s probably set in the United Kingdom or its provinces, judging from the terms used to

describe the hierarchy of its faculty and the grade levels.

The setting, theme, descriptions, narration of the story is quite simple, lyrical and at times,

comical as well. The author has definitely succeeded in making the reader feel each agitation,

irritation and overwhelming happiness of Miss Meadows. It definitely makes up for a light

reading.

Questions to Do:

1. How does ‘The Singing Lesson’ present a working woman in 19th century?

2. In “The Singing Lesson” it is more atmosphere than plot. Discuss..

3. Bring out the inner turmoil of Miss Meadows in the story “The Singing Lesson”.

4. Comment on the use of interior monologue in The Singing Lesson.

5. Explain the symbolism in the lesson.

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Class 12 Accounts Worksheet-8

CH-2 GOODWILL: CONCEPT AND VALUATION

Theory Questions and Answers

Q-1. Define Goodwill.

Ans- Goodwill means the value of ‘good-name’ or reputation earned by a business through

the hard work and honesty of its owners. So, goodwill enable a business to earn higher

profits in comparison to normal profits earned by other firms in the same trade.

Q-2 Why is Goodwill considered as an Intangible Asset and not a Fictitious Asset?

Ans- Goodwill is not a fictitious asset because it has a realisable value whereas fictitious

assets do not have any realisable value. And it is an intangible asset as it can not be seen and

touched.

Q-3 State any four factors upon which the value of Goodwill of a firm depends

(ISC 2001)

Ans- All factors which help in increasing the profitability of the business, will also affect the

value of goodwill. These factors are:

i. Efficiency of management: A well-managed firm enjoys the advantages of high

productivity and profitability as a result will raise the level of goodwill.

ii. Time factor: A business firm running profitably for a longer period will have more

value of goodwill than a business which has been recently established.

iii. Favourable location: If the business is in a prominent locality having heavy

customer traffic, the goodwill tends to be high.

iv. Capital requirement: If two business firms earn the same rate of profit, the business

with lesser capital requirement shall enjoy more goodwill.

Q-4 On what occasions does the need for valuation of Goodwill arise?

Ans- For partnership firms, the need for valuation of Goodwill arises in the following

circumstances:

i. On the admission of new partner.

ii. On the retirement or death of a partner.

iii. When the business is sold, or partnership is converted into a Joint Stock Company

iv. When two or more firms are amalgamated.

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Q-5 What is meant by Super Profit in the context of valuation of Goodwill in

partnership accounts? (ISC 2009)

Ans- The excess of average profit over normal profit is called super profit.

Super Profit = Average Profits – Normal Profits

Q-6 What is meant by number of years’ purchase in the valuation of a firm’s

goodwill? (ISC 2014)

Ans- Number of years’ purchase means for how many years, the firm will earn the same

amount of profit because of its past efforts after change of ownership.

Q-6 What is meant by Normal Rate of Return?

Ans- It refers to a return normally earned by an average firm belonging to the same

industry. It is the profit relative to capital investment.

Q-7 Give the formula for calculating Normal Profits.

Ans- Normal Profits = Average Capital Employed X Normal Rate of Return.

Q-8 What is meant by ‘Capitalised value of Average Profits’? Give the formula for

determining it. (Sample Paper 2015)

Ans- Capitalised value of Average Profits means the Capitalised value of future

maintainable profits. Its formula is:

= Average Profits X 100

Normal Rate of Return

Q-9 State two differences between Average Profits and Super Profits.

(ISC 2011)

Average profits

1. It is the average of the profits of the

past few years.

2. The normal rate of return is not

relevant in the calculation of the average

profits

Super Profits

1.It is the excess of the average profits

over the normal profits.

2. The normal rate of return is considered

while calculating super profits.

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Q-10 What is Purchased Goodwill? Give important features of Purchased Goodwill.

Ans- When one business is taken over by another business, the excess of purchase

consideration over its net value(assets-liabilities) is called Purchase Goodwill. Following

are the important features:

i. It arises on purchase of business.

ii. It is recorded in the books of account.

iii. It is shown in the Balance Sheet as an asset.

Q-11 What is Non-purchased Goodwill? Give its important features.

Ans- Non-purchased Goodwill means Internally Generated Goodwill which arises

from several attributes that an ongoing business possesses, for example- favourable

location, time factor, efficiency of management. Its features are:

i. It is generated internally generally over the years.

ii. It is not recorded in the books of accounts as Accounting Standard-26 is followed.

iii. Valuation is the subjective judgement of the valuer.

Q-12 How is Goodwill valued under:

A. Weighted Average Profit Method.

B. Capitalisation of Average Profit Method.

C. Capitalisation of Super Profit Method.

Ans- Refer to ppt-3

Q-13 Is Purchased Goodwill recognised as an asset in the books of accounts? Why?

Ans- As per Accounting Standard-26, Purchased Goodwill is recognised as an asset in

the books of accounts or financial statements because consideration or purchase price has

been paid for it. It is shown on the Asset side of the Balance Sheet and amortised over a

period of time.

Q-14 Is Internally Generated Goodwill recognised as an asset in the books of

accounts? State the reason with your answer.

Ans- Non-purchased or internally generated goodwill or inherent goodwill is not

recognised in the books of accounts because no price has been paid for it. (as per

Accounting Standard-26).

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Assignment: Solve the following questions.

************************************

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Class 12 Commerce Assignment-8

Working capital or circulating capital or revolving capital means Current Assets of

a company that are changed in the ordinary course of business from one form to

another, e.g. from cash to inventories, inventories to receivables, receivables to

cash.

Types of Working Capital

1. Based on Measurement:

Gross Working Capital: Gross working capital refers to the amount of funds

invested in various components of current assets. It consists of raw-material,

work-in-progress, finished-goods, debtors, Short-term Investments

Gross Working Capital = Book Value of current assets

Or Gross working capital =Net working capital + Current Liabilities

Net Working Capital: It represents excess of current assets over current liabilities

over current liabilities. It indicates the soundness of current financial position. It

can be calculated with the help of following formula:

Net Working Capital = Current Assets- Current Liabilities

working capital

Based on Measurement

Gross Working Capital

Net Working Capital

Based on Time Period

Permanent Working Capital

Initial Working Capital

RegularWorking Capital

VariableWorking Capital

Seasonal Working Capital

SpecialWorking capital

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2. Based on Time Period:

Permanent Working Capital: Permanent working capital refers to the minimum

amount of current assets that is required at all times to ensure a minimum level of

uninterrupted business operations. It is of two types:

Initial working capital: It is that part of permanent working capital which is

required at the time of commencement of business. The capital required at

the time commencement of business is usually contributed by owners.

Regular working capital: It is that part of permanent capital which is

required for the day-to-day operations. It ensures sufficient amount of cash to

maintain reasonable quantities of raw material for procession into finished

goods all the times.

Variable Working Capital: The temporary or variable working capital varies

with the volume of operations. This is the additional working capital required from

time to time over and above the permanent working capital. This is of two types:

Seasonal working capital: It refers to liquid capital needed during a

particulars season. During the peak season, business enterprises have to

increase the purchase of raw materials e.g. wool for woollen mills and

employ more people to convert them into finished goods

Special working capital: It is that part of variable capital which needed for

financing special operations due to some unforeseen contingencies like

strikes, natural calamities, increased prices etc.

Difference between Fixed capital and Working Capital

Basis of Difference Fixed Capital Working Capital

Meaning It is that part of total capital

which is invested in fixed

assets such as land,

building, furniture ,

machinery etc.

It is the money available for

daily operations of a business

enterprise. Working capital =

Current Assets- Current

Liabilities

Time period It is required for long-term It is required for short-term

Source Issue of shares, debenture,

long-term loan etc.,

Can be raised by means of

short-term loan, trade credit

etc.,

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Assignment:

Short answer questions: 1. Why is working capital known as circulating capital?

2. Distinguish between gross working capital and net working capital

Long answer questions: 1. Discuss any four factors that affect the working capital requirements of a

company.

2. You are finance manager of a newly established company. The directors

have asked you to determine the amount of fixed capital requirement for

the company. Explain any four factors that you will consider while

determining the fixed capital requirement for the company

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Class 12 Economics Worksheet-8

TOPIC- BANKS: COMMERCIAL BANKS AND CENTRAL BANKS

Read the text given below and answer the following questions:

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Page 15: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party
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Page 17: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party

Very Short Answer Questions (2 marks)

Question 1. Give two methods of credit control .

Question 2. What is variable reserve ratio ?.

Question 3. What is meant by monetary policy ?.

Short Answer Questions (3 marks)

Question 1.Distinguish between CRR and SLR?.

Long Answer Questions (6 marks) Question- Distinguish between quantitative and qualitative methods of credit control. Briefly explain the main quantitative credit control instruments.

**************

Page 18: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party

Class 12 Maths Worksheet-8

PROPERTIES OF DETERMINANTS (CONTD)…………..

Students, you must have observed that in applying properties , we tend to apply operations along rows

and columns in such a way that we get a common factor or 1’s so that 1’s can be made zeros.

ILLUSTRATION 27:

1 𝛼 𝛼2 + 𝛽𝛾

1 𝛽 𝛽2 + 𝛾𝛼

1 𝛾 𝛾2 + 𝛼𝛽

= 2( 𝛼 − 𝛽)(β –γ ) ( γ – α)

Solution: Since we already have 1’s , so its very easy to make them zeros by applying

R1 → R1 – R2 and R2 → R2- R3 [we can apply max two operations at a time]

0 𝛼 − 𝛽 𝛼2 + 𝛽𝛾 − 𝛽2 − 𝛾𝛼

0 𝛽 − 𝛾 𝛽2 + 𝛾𝛼 − 𝛾2 − 𝛼𝛽

1 𝛾 𝛾2 + 𝛼𝛽

=

0 𝛼 − 𝛽 (𝛼 − 𝛽)(𝛼 + 𝛽) − 𝛾(𝛼 − 𝛽)

0 𝛽 − 𝛾 (𝛽 − 𝛾)(𝛽 + 𝛾) − 𝛼(𝛽 − 𝛾)

1 𝛾 𝛾2 + 𝛼𝛽

0 𝛼 − 𝛽 (𝛼 − 𝛽)(𝛼 + 𝛽 − 𝛾)

0 𝛽 − 𝛾 (𝛽 − 𝛾)(𝛽 + 𝛾 − 𝛼)

1 𝛾 𝛾2 + 𝛼𝛽

= ( 𝛼 − 𝛽)(β –γ )

0 1 𝛼 + 𝛽 − 𝛾0 1 𝛽 + 𝛾 − 𝛼

1 𝛾 𝛾2 + 𝛼𝛽

Now expanding this determinant along C1 because we have two zeros along it.

⇒ ( 𝛼 − 𝛽)(β –γ ) 1 𝛼 + 𝛽 − 𝛾1 𝛽 + 𝛾 − 𝛼

= ( 𝛼 − 𝛽)(β –γ ) [ (β + γ - α) – ( α + β – γ) ]

⇒ ( 𝛼 − 𝛽)(β –γ ) [ 2 γ - 2α ] = 2( 𝛼 − 𝛽)(β –γ ) ( γ – α) Hence proved.

36. Using properties of determinants prove that 1 𝑎 𝑎3

1 𝑏 𝑏3

1 𝑐 𝑐3

= (a-b)(b-c)(c-a)(a+b+c)

[Hint: use a3-b3= (a-b)(a2 +b2+ab)]

37. Using properties prove that 𝑎 𝑎 + 𝑏 𝑎 + 2𝑏

𝑎 + 2𝑏 𝑎 𝑎 + 𝑏𝑎 + 𝑏 𝑎 + 2𝑏 𝑎

= 9 (a+b) b2 [Hint: R1 →R1+R2 +R3 ]

38. Prove that 𝑎 𝑏 − 𝑐 𝑐 − 𝑏

𝑎 − 𝑐 𝑏 𝑐 − 𝑎𝑎 − 𝑏 𝑏 − 𝑎 𝑐

= ( a+b-c)( b+c-a)(c+a-b) [Hint: C1 →C1+C2, C2 → C2+C3]

39. Prove using properties ; 𝑎2 + 2𝑎 2𝑎 + 1 12𝑎 + 1 𝑎 + 2 1

3 3 1

= (a-1) 3 [Hint: R1 → R1 –R2 , R2 → R2 –R3 ]

Page 19: The Singing Lesson: Story Summary & Analysis · The Singing Lesson: A Commentary The Singing Lesson is a bit weak in tone as compared to its 15 counterparts from ‘The Garden Party

ILLUSTRATION 28: 𝑏2 + 𝑐2 𝑎𝑏 𝑎𝑐

𝑏𝑎 𝑐2 + 𝑎2 𝑏𝑐𝑐𝑎 𝑐𝑏 𝑎2 + 𝑏2

= 4 a2 b2 c2 ---------------(1)

Solution : It is very important to see in such problems that all the elements are not in same format or it

means to say that few are in squares and few are in product. So our first effort will be to bring all to same

format

Multiplying first row by a, second row by b and third row by c [obviously when we multiply,

division will also take place automatically, therefore abc’s division factor will be written outside]

⇒ 1

𝑎𝑏𝑐

𝑎(𝑏2 + 𝑐2) 𝑎2𝑏 𝑎2𝑐

𝑏2𝑎 𝑏(𝑐2 + 𝑎2) 𝑏2𝑐

𝑐2𝑎 𝑐2𝑏 𝑐(𝑎2 + 𝑏2)

[See multiplication and division go simultaneously]

Now taking a common along C1, b common along C2 and c common along C3

Remember : if we multiply a, b, c along Rows , then we should take a,b, c common along columns or

vice versa.

⇒ 𝑎𝑏𝑐

𝑎𝑏𝑐

𝑏2 + 𝑐2 𝑎2 𝑎2

𝑏2 𝑐2 + 𝑎2 𝑏2

𝑐2 𝑐2 𝑎2 + 𝑏2

------------------------------------------------------(2)

See the difference in (1) and (2) , now all elements have come in same format i.e. squares.

Now we apply a suitable operation so as to get 1’s or 0’s

R1 → R1 – R2 – R3 gives us 0 −2𝑐2 −2𝑏2

𝑏2 𝑐2 + 𝑎2 𝑏2

𝑐2 𝑐2 𝑎2 + 𝑏2

Now (-2) can be taken common from R1

= ( -2 ) 0 𝑐2 𝑏2

𝑏2 𝑐2 + 𝑎2 𝑏2

𝑐2 𝑐2 𝑎2 + 𝑏2

Now operate R2 → R2- R1 and R3 → R3 –R1 [ The purpose is get as many 0’s as we can]

⇒ 0 𝑐2 𝑏2

𝑏2 𝑎2 0𝑐2 0 𝑎2

Now we can expand along R1

we get (-2) [ -c2 ( b2 a2 – 0 ) + b2 ( 0 – c2 a2 ) ] = (-2) ( - 2 a2 b2 c2 ) = 4 a2 b2 c2 Hence proved.

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40. Using properties of determinants prove that 𝑎2 + 1 𝑎𝑏 𝑎𝑐

𝑏𝑎 𝑏2 + 1 𝑏𝑐𝑐𝑎 𝑐𝑏 𝑐2 + 1

= a2 + b2 + c2 +1

ILLUSTRATION 29: Using properties prove that

𝑥 𝑥2 1 + 𝑝𝑥3

𝑦 𝑦2 1 + 𝑝𝑦3

𝑧 𝑧2 1 + 𝑝𝑧3

= ( 1+ pxyz) (x-y)(y-z)(z-x)

Solution: By using property no. 4 the given determinant can be split into two determinants as:

𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

+

𝑥 𝑥2 𝑝𝑥3

𝑦 𝑦2 𝑝𝑦3

𝑧 𝑧2 𝑝𝑧3

( Take p common out from C3 )

⇒ 𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

+ p 𝑥 𝑥2 𝑥3

𝑦 𝑦2 𝑦3

𝑧 𝑧2 𝑧3

( Now taking x, y , z common from R1, R2, R3 respectively)

⇒ 𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

+ p xyz 1 𝑥 𝑥2

1 𝑦 𝑦2

1 𝑧 𝑧2

( Now interchanging C1 ↔ C3 and then C2 ↔ C1 )

⇒ 𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

+ p xy z 𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

= ( 1+ pxyz) 𝑥 𝑥2 1𝑦 𝑦2 1

𝑧 𝑧2 1

Now applying R1 → R1 – R2 and R2 → R2 – R3 we get

= (1 + pxyz) 𝑥 − 𝑦 𝑥2 − 𝑦2 0

𝑦 − 𝑧 𝑦2 − 𝑧2 0

𝑧 𝑧2 1

= ( 1+ pxyz)

𝑥 − 𝑦 (𝑥 − 𝑦)(𝑥 + 𝑦) 0

𝑦 − 𝑧 (𝑦 − 𝑧)(𝑦 + 𝑧) 0

𝑧 𝑧2 1

= ( 1+ pxyz) (x-y ) ( y-z)

1 𝑥 + 𝑦 01 𝑦 + 𝑧 0

𝑧 𝑧2 1

Now we can expand along C3 because it has two zeros

= ( 1+ pxyz) (x-y)(y-z) [ (y +z) - (x+y) ]

= (1+ pxyz) (x-y)(y-z)( z-x) Hence Proved.

41. If x, y and z are all different and

𝑥 𝑥2 1 + 𝑥3

𝑦 𝑦2 1 + 𝑦3

𝑧 𝑧2 1 + 𝑧3

= 0 , show that ( 1+ xyz) = 0

[ Hint: Same as illustration 29. , reach the step ( 1+ xyz) 1 x x2

1 y y2

1 z z2

= 0

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SOLVING THE DETERMINANT EQUATION

ILLUSTRATION 30: Using properties of determinants, solve for ‘x’.

𝑥 + 2 𝑥 + 6 𝑥 − 1𝑥 + 6 𝑥 − 1 𝑥 + 2𝑥 − 1 𝑥 + 2 𝑥 + 6

= 0

Solution: Operate R1 → R1 + R2 + R3 , We get

3𝑥 + 7 3𝑥 + 7 3𝑥 + 7𝑥 + 6 𝑥 − 1 𝑥 + 2𝑥 − 1 𝑥 + 2 𝑥 + 6

= 0 [ The purpose of this operation is to get common factor]

(3x+7) 1 1 1

𝑥 + 6 𝑥 − 1 𝑥 + 2𝑥 − 1 𝑥 + 2 𝑥 + 6

= 0

[After getting 1’s, we make them zero]

Therefore C1 → C1 –C2 and C2 → C2 –C3

(3x+7) 0 0 17 −3 𝑥 + 2

−3 −4 𝑥 + 6 = 0

Now since we have two 0’s in first row, therefore we expand the determinant along R1

(3x+7) (1) 7 −3

−3 −4 = 0 or (3x+7) (-28-9) = 0 or 3x+7= 0 or x = -

7

3

42. Solve using properties of determinants;

𝑎 + 𝑥 𝑎 − 𝑥 𝑎 − 𝑥𝑎 − 𝑥 𝑎 + 𝑥 𝑎 − 𝑥𝑎 − 𝑥 𝑎 − 𝑥 𝑎 + 𝑥

= 0

[Hint: Apply R1 → R1 + R2 +R3 or C1 → C1 + C2 + C3 ] Ans: x = 0, 3a

43. Solve 3𝑥 − 8 3 3

3 3𝑥 − 8 33 3 3𝑥 − 8

= 0 [Hint: R1 → R1 + R2 +R3 ] Ans: 2

3 ,

11

3 ,

11

3

44. Solve using properties of determinants; 15 − 2𝑥 11 1011 − 3𝑥 17 16

7 − 𝑥 14 13 = 0

[ Hint: Apply R1 → R1 –R2, R2 → R2 –R3 ] Ans: 4

More Problems on Properties of Determinants Contd……. in Worksheet-9

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Class 12 Physical Education Worksheet-7

FOOTBALL

Goal keeping: Goal keeper, often shortened to keeper or goalie, is one of the major

positions of football. It is the most specialized position in the sport. The goalkeeper’s

primary role is to prevent the opposing team from successfully moving the ball over the

defended goal-line (between the goal posts and under the crossbar)

Goal keeper usually performs goal kicks, and also gives commands to their defense

during corner kicks, direct and indirect free kicks, and marking

Goal keeper clothing and equipments:

A goal keeper must wear a different colour uniform that distinguishes him from

the rest of the team, as well as the opposing team and referees.

Just like field players, goal keeper must wear appropriate stocking, shin guards

and football shoes.

Wear gloves to improve their grip on the ball (though gloves are not mandatory

attire).

Jewellery is not allowed.

Skills of the Goal keeper:

Catching.

Throwing and fisting

Punting

Dribbling and dodging

Diving for the ball and covering it

Stance and balance.

The position of the following while conducting a tie breaker in the game of football:

The ball: must be placed on the placed on the penalty mark.

Defending goal keeper: must remain on his goal line,

facing the kicker, between the goalposts until the ball has been kicked.

Players other than the kicker must be located:

Inside the field of play.

Outside the penalty area and penalty arc.

Behind the penalty mark.

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At least 10 yards (9.15 M), away from

the penalty mark or in the center of the field of play (on the half way line).

Referee: Near to the ball.

Attacking Goal keeper: near the junction of the goal line and the penalty area.

Terminology:

Advantage: advantage is a wonderful clause in the rules in which whistling the

foul would actually be hurting the team being fouled by not letting play continue.

Zonal marking: Zonal marking s a defensive strategy where defenders cover an

area of the pitch rather than marking a specific opponent.

Sliding tackle: Tackle in football where one let extended to push the ball away

from the opposite player.

Through pass: It is a pass sent between two back defenders, or “through” a gap in

the defense, into open space behind the defenders and out of the reach of the

goalkeeper.

Man to man marking: It is a system of marking in which each player is responsible

for an opposing player rather than an area of the field.

Extra time: Additional period, normally two halves of 15 minutes, used to

determine the winner in some tied cup matches.

Nut Meg: When a player intentionally plays the ball between an opponent’s legs,

runs past the opponent, and collects their own pass.

One-on-one: A situation where the only player between an attacking player and

the goal is the opponent’s goalkeeper.

Step over: Skill move performed by an attacking player in which the player with

the ball will move their foot over the ball without making contact with it. The

intent of the move is to confuse a defender into thinking that the attacking player

is moving with the ball in a certain direction; when the defender changes direction,

the attacker will quickly change direction.

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Technical area: An area within which the manager must remain while coaching

their team during a match, marked by white lines at the side3 of the field.

Half volley: A pass or shot in which the ball is struck just as, or just after, it

touches the ground.

Attacker: Usually refers to a striker but can be used to describe any player close to

the opposing team’s goal line.

Defender: Defenders are positioned in front of the goal keeper and have the

principal role of keeping the opposition away from their goal.

Mid fielder: the playing position for players those are responsible for linking play

between attackers and defenders.

Strikers: An attacking player whose job is to finish attacking plays by scoring a

goal.

Chip: It is a high trajectory shot, hit with the intention of the ball going over the

goalkeeper and into the goal.

Cross: A cross pass is given into the penalty area by the attacking team, usually

from the area between the penalty area and the touchline.

One touch pass: A pass in which the ball is played on with a player’s first touch.

Lob: A kick to the ball over (an opponent)| in a high arc.

Banana kick: A banana kick is an off-center kick that makes the ball curve or

suddenly change direction before dropping to the ground.

Bicycle kick: move made by a player with their back to the goal. The player

throws their body into the air, makes a shearing movement with the legs to get one

leg in front of the other, and attempts to play the ball backwards over their own

head, all before returning to the ground. Also known as an overhead kick.

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Wall pass: The player who is running with the ball avoids a tackle from an

opponent by passing to a stationary or running team mate, who acts as a wall by

bouncing the ball back to the player who has now run clear.

Goal line Technology (GLT): A system to determine whether the ball has crossed

the line for a goal or not.

Center spot: The spot marked at the center of the field from which the kickoff is

made.

Corner flag: The flag marking each of the four corners of the field.

Foul: any kind of illegal play.

National and International governing bodies:

All India Football Federation (AIFF): The All India Football Federation, also simply

known as the AIFF, is the governing body of association football in India. The AIFF was

officially funded on 23 June, 1937.

Objectives of AIFF:

To improve and popularize the game of football constantly and promote it

throughout India.

To organize its annual domestic and International Competitions.

To draw up regulations and provisions and ensure their enforcement.

To control every type of Association Football including Friendly matches by

taking appropriate steps to prevent infringements of Statues, regulations or

decisions of FIFA, AIFF or of the Laws of the Game.

Members of the AIFF General Body:

One football association in each of state or union territory as defined bgy7 the

constitution of India.

Services Sports Control Board and Railways Sports Promotion Board.

Women’s Committee.

Federation International de Football Association: (FIFA):

It was formed on May 21, 1904. The federation international de football

association (FIFA) is an association which describes itself as an international

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governing body of association football. FIFA is responsible for organizing

football’s main International Tournaments. Now its membership comprises 211

associations. Although it does not control the rules of football.

International Football Association Board (IFAB): It is the body that determines the laws

of the game of association football. It was formed in 1886. The board meets twice a year,

once to decide on possible changes to the rules governing the game of football.

IMPORTANT TOURNAMENTS:

National Tournaments:

Santosh trophy

B.C. Roy trophy

Durand cup

Stafford cup

DCM trophy

Rovers cup

G.U. Raja Memorial Trophy

International Tournaments:

FIFA World cup

UEFA European Football championship

FIFA club World Cup

CONMEBOL Copa America

FIFA Confederation Cup

CAF Africa Cup of Nations

CONCACAF Gold Cup

UEFA Champions League.