Class 11

Lines Written in Early Spring Book Back Answers Class 11 English Guide Chapter 3 Tamilnadu Solutions

Students can Download English Poem 3 Lines Written in Early Spring Questions and Answers, Summary, Activity, Notes, Samacheer Kalvi 11th English Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations. Learn the Samacheer Kalvi 11th English Grammar to enhance your grammar skills like reading comprehension, passage writing, parts of speech, tenses, passive and active voice, and many other concepts in no time.

11th Standard English 3rd Lesson Lines Written in Early Spring Questions and Answers

Warm Up

Question 1.
Do you go for leisurely walks? If you are a city-dweller, what or who would you expect to see on your way?
Answer:
Yes, I do go for morning walks with my classmate Ragu. I live in Chennai. We go to the beach for the walk. We come across policemen, doctors, aged people and some small children too briskly engaged in long walks. They enjoy the morning sun at the back drop of the golden sea. Also I find a host of vendors selling vegetable soups, bittergourd soup and nourishing drinks on the seashore. There are points where pure water is sold in glasses. The spring dug out a few hundred metres near the sea is really sweet. I find one ‘Green volunteer group’ collecting all plastic garbage and cleaning the beach.

Question 2.
If you go to a village, what scenes would you observe?
Answer:
If I go to a village, I will find Water-thirsty lands and their owners longing for rains. I will also . find some farmers trying to coax their borewell owners to provide necessaiy water for their little vegetable garden to help them eke out a living. I will also find young children getting ready to go to school. There would be hens busy searching for their breakfast or chanticleers announcing their supremacy on the roof-tops.

Samacheer Kalvi 11th English Lines Written in Early Spring Textual Questions

1. Find words from the poem that convey the following ideas.

I heard a thousand blended notes
While in a grove I sate reclined,
In that sweet mood when pleasant thoughts
Bring sad thoughts to the mind.

To her fair works did Nature link
The human soul that through me ran;
And much it grieved my heart to think
What Man has made of Man.

Through primrose tufts, in that sweet bower,
The periwinkle trail’d its wreaths;
And ‘tis my faith that every flower
Enjoys the air it breathes.

The birds around me hopp’d and play’d
Their thoughts I cannot measure,
But the least motion which they made
It seem’d a thrill of pleasure.

The budding twigs spread out their fan
To catch the breezy air;
And I must think, do all I can,
That there was pleasure there.

If this belief from heaven be sent,
If such be Nature’s holy plan,
Have I not reason to lament
What Man has made of Man?

(a) connected together
(b) spread over the surface of the ground in a straggling manner
(c) make out or understand
(d) slender woody shoots growing from branches or stems of trees
Answer:
(a) blended
(b) tailed
(c) reason
(d) twigs

2. Complete the summary of the poem by filling in the blanks with the words given below

bower	grove	distressed
pleasant	breezy	peace
sorrow	nature	calm

The speaker says that while sitting in a (1) _____ , his mind is filled with both (2) _____ and sad thoughts. He could associate himself with (3) _____ . But he feels (4) _____ at the fact that human beings are exploiting nature. The atmosphere around is (5) _____ and pleasant with flowers in the sweet (6) _____ The air is (7) _____ and everything seems to be happy. When Nature desires such (8) _____ , it is only the irresponsible act of human beings that brings (9) _____ to other human beings and to nature.
Answer:

1. grove
2. pleasant
3. nature
4. distressed
5. calm
6. bower
7. breezy
8. peace
9. sorrow

3. Read the lines given below and answer the questions that follow.

(i) And ‘tis my faith that every flower
Enjoys the air it breathes…

Question (a)
What is the poet’s faith?
Answer:
The Primrose and Periwinkle share the same bower for their growth. So the poet’s faith is that they enjoy the air they breathe.

Question (b)
What trait of Nature do we see here?
Harmonious relationship of birds, brook, plants, and creepers and willingness to co-exist with one another is the trait evident in nature.

(ii) And I must think, do all I can,
That there was pleasure there…

Question (a)
What did the poet notice about the twigs?
Answer:
The budding twigs spread out their fan To catch the breezy air.

Question (b)
What was the poet’s thought about then?
Answer:
The poet thought that every creature in nature help each other except man.

Question (iii)
If this belief from heaven be sent,
If such be Nature’s holy plan.

Question (a)
What does ‘heaven’ refer to?
Answer:
Heaven refers to the natural source, the heaven, (i.e) God that created life on the earth.

Question (b)
Why does the poet call it ‘holy’?
Answer:
The poet believes that the harmonious, peaceful, and happy co-existence of birds, plants, trees, and brooks soothes the troubled mind of man. So, the poet feels as if he were inside a sacred place when he is in the woods. So, he calls the plan ‘holy’.

4. Explain the following lines with reference to the context in about four to five sentences each.

Question (i)
In that sweet mood when pleasant thoughts
Bring sad thoughts to the mind.
Answer:
Reference: These lines are taken from Poem – “Lines Written in Early Spring”, Poet – “William Wordsworth”.
Context: While sitting in the grove the poet utters these words.
Explanation: When the poet sits in the grove taking rest he observes that all creatures on the earth are connected together in one way or the other. He gets fascinated by the divinity of nature. At that moment the impact of war between two countries and the humans killing each other comes to his mind.

Question (ii)
The birds around me hopp’d and play’d,
Their thoughts I cannot measure.
Answer:
Reference: These lines are from the poem “Lines Written in Early Spring” written by William Wordsworth.
Context: The poet was quite impressed with the beauty and peace that prevailed in the woodland. The birds were oblivious to the presence of the poet. They hopped and chirped around him in absolute bliss. The poet said these words while trying to fathom their thoughts. Explanation: The poet was overwhelmed with delight in the company of birds, plant kingdom and the brook. He tried hard to understand the thoughts of the birds through the bird’s language. But he couldn’t succeed. He simply inferred that they were thrilled and enjoying the jocund company.
Comment: The. lines bring out the nature of the ‘Nature Poet’. .

Question (iii)
Have I not reason to lament
What Man has made of Man?
Answer:
Reference: These lines are taken from Poem – “Lines Written in Early Spring”, Poet – “William Wordsworth”.
Context: The poet laments the behavior of man.
Explanation: The poet feels that as per God’s creation every creature on this earth has its birth to enjoy their life to the fullest. Birds, Flowers, and trees follow this holy plan of nature and make their life filled with happiness forever. It is a man who does not follow the plan of ’’Live and Let Live”. The poet laments about this innate state of man.

5. A. Read the following sets of lines and identify the figures of speech used in each extract.

Question (i)
To her, works did Nature link
Answer:
Personification

Question (ii)
The human soul that through me ran…
Answer:
Metaphor

Question (iii)
And ‘tis my faith that every flower…
Answer:
Personification

Question (iv)
What Man has made of Man?
Answer:
Alliteration man, made, man

B. Read the poem once again. Identify the rhyme scheme and pick out the rhyming pairs of words.

ab, ab is the rhyming scheme of the poem
link – think, wreaths -breathes, measure – pleasure, fan – can, air – there, plan – man, ran – man are some of the rhyming words found in the poem.

6. Based on your reading of the poem, answer the following questions in a sentence or two each.

Question (a)
How does the poet feel while enjoying the beauty of Nature?
Answer:
The poet has both pleasant and sad thoughts in his mind while enjoying the beauty’ of Nature.

Question (b)
Does Nature affect a person’s thoughts and feelings? Explain.
Answer:
Yes, the beauty, harmony, peace, and nature’s pure joy enlivened the poet’s spirits. He couldn’t help comparing the happiness of nature with the self-destructive wars of human beings. He was sad remembering humans.

Question (c)
How do people bring grief and sorrow to one another?
Answer:
They bring grief and sorrow by fighting and being cruel to one another.

Question (d)
Why does the poet think that the birds were happy?
Answer:
The poet thinks that the birds were happy because they hopped and played around him. Their least motion displayed their most joy.

Question (e)
The poet finds joy in various objects of Nature. Explain.
Answer:
The Periwinkle grows around the Primrose and shares the air they breathe. Birds enjoy playing happily. The way in which budding twigs spread their fan to catch the breeze shows that they are happy

Question (f)
Bring out the poet’s thoughts, while comparing Nature with human behaviour.
Answer:
The poet’s joy of witnessing the soul-refreshing joy of plants, flowers, and birds did not last long. He remembered the cruelty with which dictators were throwing bombs and taking away the lives of innocent people. He couldn’t bear the destruction of life and property. He lamented, “What man has made of man?”.

7. Complete the following sentences by choosing the best options.

Question (a)
The poet experiences sadness because _________
(i) the blended notes are jarring
(ii) Nature is filled with negativity
(iii) he is worried about the destruction caused to Nature
(iv) natural calamities occur frequently
Answer:
(iii) he is worried about the destruction caused to Nature

Question (b)
The poem is set in a _________
(i) city
(ii) village
(iii) grove
(iv) park
Answer:
(iii) grove

Question (c)
The poem speaks of _________ .
(i) Man’s plan to shape the destiny
(ii) Man seeking pleasure and riches
(iii) Man indulging in wars and acts of destruction
(iv) Man’s fear of Nature
Answer:
(iii) Man indulging in wars and acts of destruction

8. Answer in a paragraph of about 100-150 words.

Question 1.
Do you think the poet wants to say that man is unhappy because he has lost his link with nature and forgotten how to enjoy nature or because man is cruel to other men?
Answer:
The poet William Wordsworth wants to convey the readiness of nature to teach the art of ‘living together in harmony, peace and bliss. But man has lost his sensitivity to listen to the joyful lessons of nature. His greed and love for possession of territories and abject cruelty to [ fellow humans and nature has disillusioned the poet. He has almost lost faith in the capacity of humans to love and live in harmony with nature, man has gone to the extent of denuding

the forest which really sustains life on earth. Rare species in the forests are on the brink of; destruction. Animals and birds in the red list are growing in number to the great distress of nature lovers. So, I believe Wordsworth is unhappy for both (i.e) man’s losing the link with nature and his infinite capacity to be cruel to other men.

Listening Activity

9. Some phrases have been left out in the poem below. First, read the poem. Then, fill in the missing words on listening to the reading or the recording of it in full. You may listen ’ again, if required.

(For listening to the poem refer to our website wwwfullcircleeducation. in)
“To Autumn” by William Blake (1783)

O Autumn, laden with fruit, and stain’d
’With the blood of the grape, pass not, but sit
Beneath my shady roof; there thou may’st rest,
And tune thy jolly voice to my fresh pipe,
And all the daughters of the year shall dance!
Sing now the lusty song of fruits and flowers.’
“The narrow bud opens her beauties to
The sun, and love runs in her thrilling veins;

Blossoms hang round the brows of Morning,
and Flourish down the bright cheek of modest Eve, .
Till clust’ring Summer breaks forth into singing,
And feather’d clouds strew flowers round her head.
The spirits of the air live in the smells
Of fruit; and joy, with pinions light, roves round
The gardens, or sits singing in the frees.”
Thus sang the jolly Autumn as he sat,
Then rose, girded himself, and o’er the bleak .
Hills fled from our sight; but left his golden load. .

To Autumn:
O Autumn, laden with fruit, and stained
With the blood of the grape, pass not, but sit
Beneath my (1) _____, there thou mayst rest,
And tune thy jolly voice to my (2) _____ ;
And all the daughters of the year shall dance!
Sing now the (3) _____ of fruits and flowers. “
The (4) _____ opens her beauties to
The sun and love runs in her (5) _____ v.;

Blossoms hang round the brows of the morning, and
Flourish down the (6) _____ of modest eve,
Till clustering Summer breaks forth into singing,
And (7) _____ strew flowers round her head.
The spirits of the air live on the smells
Of fruit; and joy, with (8) _____, roves round
The gardens, or sits singing in the trees.”
Thus sang the (9) _____ as he sat,
Then rose girded himself, and o’er the bleak Hills fled from our sight, but left his (10) _____
Answer:

1. shady roof
2. fresh pipe
3. lusty song
4. narrow bud
5. thrilling veins
6. bright cheek
7. feathered clouds
8. pinions of light
9. jolly autumn
10. golden load

Speaking Activity

10. Answer the following Questions 

Question (a)
What scene in nature gives you pleasure? Talk for a minute describing a natural scene that gave you a lot of joy. What did you see, hear, smell, or feel that gave you joy?
Answer:
Every morning I take a walk in the Municipality’s park. The landscaping has been done with an aesthetic mind by gardener Kali. During daybreak, the yellow sun embraces the flowers in the park. They face the sun with coyness befitting a bride. They blush and spread their fragrance. I watch the beauty of the roses and some yellow flowers. I feel refreshed. The morning breeze, the pearl-like mist beads crowning the grass, the swallows which chirp and look for grains or crumbs, all the aged couple walking with empathy for one another fills my heart with joy. These everyday scenes make my day all through the year.

Question (b)
Work in groups of 4-6. Discuss how you would preserve the environment and protect Nature. One or two representatives may share their ideas with the class.
Answer:
Janani: I represent the “Green warriors” group. My group is of the strong opinion that the National Green Corps must wage a war against the ignorance of people. People do not know that’ by cutting woods, they are perpetuating their own poverty. We believe sustainable lumbering is the only way to help poor people and at the same time turn them into guardian angels of the forest.
Karthick: I represent the “Green Earth” group. Could you please throw more light on “Sustainable lumbering”? Do you mean to say that people would use the woods and yet protect them too.

Janani : Thank you for asking a very intelligent question. Poor people who live in the forest villages do not have money to buy gas cylinders. We don’t have enough forest officers to either protect the trees nor the poor animals which are kept even inside the most protected National forest in Kaziranga. Haven’t you heard of Jamuna Tudu, the Lady Tarzan of Jharkhand? In Maturkhan village, Jamuna the newly wedded bride was deeply disturbed by the illegal felling of long tall trees. To her shock, Timber mafias had browbeaten the villagers.

Since 2000, Jamuna spoke to the village women to use dry sticks and twigs for firewood but she made them understand that only if trees survived, there would be rains and villagers will be able to cultivate their lands. She has created 300 forest protection women committees. They protect the forest. About 50 hectares of forests have been reclaimed. Niti Ayog has conferred the “Women transforming India award of 2017”. Seeing Women’s determination to conserve the environment, forest officials and State Government have provided water facilities and schooling facilities, to this remote village.

Karthick : We place on records the valuable information provided by Janani. We would like . to supplement her ideas.
We, the student community can go on a campaign against the rising carbon footprint, pollution, global warming and all man-made evils due to the failure of man to protect the environment.

Because of man’s failure to live in harmony with nature the possibility of the perpetuation of human race is at stake. Let us love nature and protect the environment for making the earth a safer place to live for future generation. Thank you

11. Answer the following in a paragraph of 100-150 words each.

Question (a)
‘Nature can nurture’. Describe how this process happens.
Answer:
Human beings are able to live on earth simply because earth offers them enough food to live on. The plants, trees, flowers, crops, cereals and greens that grow on earth gives all the nutrients necessary for man to survive inclement weather and other challenges. Where there is still heavy rains, we have forest coverage which supports the ‘water cycle’ and periodic rainfall. If forests are well-guarded from timber mafia and stupid people who fell them indiscriminately for firewood, forests would pay back thousand times by pumping out oxygen and taking in carbon-di-oxide.

All of us know that they are free washermen of the air. Earth tries to grow drought-resistent plants and trees where rainfall is poor. With efficient water management. Nature would grow more food for us and nurture us and ensure the continuity of human race on this planet.

Question (b)
When humanity fails to live in harmony with Nature, its effects are felt around the world. Why and how?
Answer:
Man, the worst predator, kills for no reason. Man has to protect forests and live in harmony with nature. Instead, man is callous. He kills elephants for their tusks, Rhinoceros for their home, and polar bears for their fur. Huge trees, in Rainforests, which have been protecting the lives of many

species and insects, are being felled for timber and industrialization. Due to the increase in the denudation of forests, global warming has increased. Water levels in the ocean is increasing. Heatwaves are threatening the lives of people. Polar ice is melting. Scientists fear that if this, persists, there will be hostility caused by water-sharing. Like Karnataka and Tamil Nadu, there will be political unrest and community conflicts demanding a share in drinking water and water for irrigation purposes. In South Africa, zero water day is fast approaching.

The scarcity of pottable water is going to be a huge humanitarian crisis. As we have failed to protect the national resources, carbon footprint is expanding to alarming levels. Delhi experiences difficulty as planes struggle to land or take off due to thick smog in and around Delhi. As toxic waste is released by Sterlite and other industries people in Thoothukudi are becoming victims of cancer and other lung-related disorders. Atomic power plants also retain potential hazards like radio-activity. Thus humanity’s failure to live in harmony with nature is threatening to wipe out the human race.

Question (c)
Write a letter to the Councillor of your Ward, explaining why a park is necessary for your locality.

XYZ
18.10.2018
From
ABC
18, Mukilan Street,
Nehru Colony,

To
Thiru Mayavan,
Councillor, Ward 1,
Dharmapuri
Sir,
Sub: Request for establishing a Children’s park in Nehru colony in XYZ – reg.
I am living at the above address with my parents. Nehru colony is now fast developing. I am told that the land earmarked for the children’s park is going to be sold for the construction of a shopping mall. Since all the plots have been sold, we children and the aged, need the park for some morning exercises and evening relaxation. I request you to intervene and advise the municipality not to sell the parking space for commercial purposes. Please take steps to establish a park for us.
Thanking you in advance for immediate action.
Yours sincerely,
ABC

To
Thiru Maya van
Councillor, Ward 1
Dharmapuri

Lines Written in Early Spring About the Poet

William Wordsworth and Samuel Taylor Coleridge published together Lyrical Ballads in 1798. It was Wordsworth who broke the myth of writing poetry for an elite audience. It is nothing but ‘a man speaking to man’. He defined poetry as a “spontaneous overflow of powerful feelings” and “emotions recollected in tranquility”. Wordsworth, the nature poet wrote poems easy to be read and enjoyed by common people. His Lucy poems, Michael. Daffodils, The Solitary Reaper, To the cuckoo. Lines composed a few miles above Tintern Abbey have established his reputation as a poet.

Lines Written in Early Spring Summary

Introduction: Wordsworth presents the natural world of birds and flowers as one of calm agreement and pleasure, contrasted with the implied failure of mankind to live up to such a model. What precisely “Man has made of what man” is unstated and that’s probably for the best to explicit about how Wordsworth feels man has failed his fellow men – whether through allowing his fellow humans to starve from poverty and exploitation or through reverting to savage violence. The poem was written against Napoleonic wars, which followed on the hot heels of the reign of terror.

This poem signals the start of the Romantic era and is included in the “preface to lyrical ballads”. It also signals the beginning of a platonic relationship between S.T. Coleridge and William Wordsworth. The poem is in a form of a ballad consisting of six quatrains. The rhyming scheme is ab ab.

In the first quatrain, the divinity of nature is revealed in the phrase “a thousand blended notes” implying almost a pervasive presence of nature akin to the omnipresence of God.

The second quatrain moves briefly away from nature to reminisce on the misery that other humans have caused each other since time immemorial. The poet says man’s state by nature is close to nature “Through primrose tufts, in that green bower. The periwinkle trailed its wreaths; And’tis my faith that every flower enjoys the air it breaths”. The presence of nature as living things strikes. Throughout the poem, Wordsworth builds up the idea of a living, breathing world that is only a fraction removed from humanity. “The hopping birds”, “the budding twigs” enjoy their being there. The plants, creepers and birds fulfill nature’s holy plan of living in harmony with one another. But the poet is quick to add “Have I no reason to lament. What man has made of man!”

Throughout the poem, there was an attempt made by nature to heal the injured soul of the poet. The world of nature untouched by the miseries of humanity continues on while the human soul, bound in its rigid case of mortality and reason, is left behind to experience the misery of the human world.

Lines Written in Early Spring Glossary

Textual:

bower – a pleasant shady place under trees
grieve – mourn or to feel intense sorrow
grove – a small area of land with a group of trees
lament – to express sorrow or unhappiness about something
periwinkle – a trailing plant with large blue flowers
primrose – a wild plant with yellow flowers
recline – lean back in a position of rest
sate – old fashioned spelling for sat
tufts – bunches

Additional:
attempt – effort
celestial – heavenly
chirping – singing
faith – trust
harmony – everywhere
peaceful co-existence
heal – cure
misery – difficulty
pervasive – prevalent

Samacheer Kalvi 11th English Book Solutions Poem

• Once Upon A Time Book Back Answers
• Confessions of a Born Spectator Book Back Answers
• Lines Written in Early Spring Book Back Answers
• Macavity – The Mystery Cat Book Back Answers
• Everest is Not The Only Peak Book Back Answers
• The Hollow Crown Book Back Answers

Forgetting Book Back Answers Class 11 English Guide Chapter 3 Tamilnadu Solutions

Students can Download English Lesson 3 Forgetting Questions and Answers, Summary, Activity, Notes, Samacheer Kalvi 11th English Book Solutions Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus and score more marks in your examinations. Learn the Samacheer Kalvi 11th English Grammar to enhance your grammar skills like reading comprehension, passage writing, parts of speech, tenses, passive and active voice, and many other concepts in no time.

11th Standard English 3rd Lesson Forgetting Questions and Answers

Warm up

Question 1.
How forgetful are you?
Answer:
We are all forgetful at times and would like to find ways of improving our memories.

A. How sharp is your memory?

Take this five-minute memory test. The teacher will read out a series of 30 words, one by one. Some of them will be repeated. Whenever you hear a word for the first time, write ‘N’ (for New) in the corresponding box and when you hear a repeated word write ‘R’ After completing this task, check your results. Compare it with your friends and see where you stand.

A set of 30 words is provided here. You can ask your teacher or a friend to read out the words. Hear carefully and do this activity yourself.

1		11		21
2		12		22
3		13		23
4		14		24
5		15		25
6		16		26
7		17		27
8		18		28
9		19		29
10		20		30

Answer:

1	astonished	11	safety	21	giants
2	available	12	approach	22	reluctant
3	doubt	13	chemist	23	devotee
4	statistical	14	methodical	24	perambulator
5	ordinary	15	doubt	25	memory
6	fortune	16	perfection	26	audacious
7	devotee	17	memory	27	eccentric
8	seldom	18	scarcely	28	common
9	reluctant	19	thousand	29	statistical
10	important	20	visitor	30	efficient

B. Have you ever lost or misplaced anything of value due to forget fulness?

Yes, I have misplaced my hall ticket. I was tensed. My Headmaster asked me not to panic. He identified me to the hall supervisor and allowed me to write my examination in Std X.

At times, instances of forgetfulness may land us in a tight spot or in a difficult situation. Therefore, we need to find ways to remember what we have to do or carry with us. One way is to make a mental check-list that we can verify before starting any activity.

Now discuss with your partner and think of some practical ideas to overcome forgetfulness, in your day-to-day activities.

e.g. setting an alarm

Answer:

e.g. setting an alarm	Keeping a diary
Checklist	Write on calendar
Sticky notes	PDA – Personal Digital Assistant

C. Discuss and share your views with the class on the following. Is forgetfulness a result of carelessness or preoccupation?

Team A : We think it is a result of carelessness. If we really attach great importance to details, we will never forget.
Team B : Perhaps, things you are interested in, you don’t tend to forget.
Team C : We think forgetting is mostly by preoccupation with something. Brain can do , multi-tasking but not always. If your mind is focussed on a serious problem and ways of solving it, the brain shuts down all other memory files for a while. It is purely a temporary issue.
Team A&B : Yes, we agree;with team‘C’.

Samacheer Kalvi 11th English Forgetting Textual Questions

1. Based on your understanding of the essay, answer the following questions in one or two sentences each.

Question (a)
What does lynd actually wonder at?
Answer:
Lynd actually wonders at the efficiency of human memory which remembers many things.

Question (b)
Name a few things that a person remembers easily.
Answer:
A man easily remembers all the items of clothing, shutting the door before leaving the home, turning off lights before going upstairs, etc,

Question (c)
How do psychologists interpret forgetfulness?
Answer:
Psychologists tell us that people forget things because they wish to forget them.

Question (d)
What is the commonest type of forgetfulness, according to Lynd?
Answer:
Commonest type of forgetfulness occurs in the matters of posting letters. The author himself has forgotten to post his own letters many times.

Question (e)
What does the author mean when he says the letter in his pocket leads an unadventurous life?
Answer:
The letter in his pocket leads an unadventurous life as it is kept safe inside his pocket for a long time without him remembering about it.

Question (f)
What are the articles the writer forgets most often?
Answer:
The poet often forgets his books and walking sticks.

Question (g)
Who are the citizens of ‘dreamland’? Why?
Answer:
Sportsmen are the citizens of dreamland because even after returning from their games their mind is still filled with the imagination of playing.

Question (h)
What is common about the ‘angler’ and the ‘poet’?
Answer:
The angler enjoys his sport of fishing so intensely that he forgets his fishing rod. Likewise, the poet, who often roams in his own world of imagination, may forget to post a letter. Both the angler’s and the poet’s loss of memory is a tribute to the intensity of their enjoyment.

2. Based on your reading, answer the following questions in two to four sentences each,

Question (a)
What made people wonder about the absentmindedness of their fellow-beings?
Answer:
The people wondered about the list of articles published for sale which were lost by railway travellers.

Question (b)
What are our memories filled with?
Answer:
Our memories are filled with names of cricketers, footballers, murderers,. actors and actresses. Our memories are filled with many routine activities.

Question (c)
When does human memory work with less than its usual capacity?
Answer:
Human memory works with less than its usual capacity when we forget things as we wish to forget them and when we have antipathy towards something.

Question (d)
Why, according to Lynd, should taking medicines be one of the easiest actions to remember?
Answer:
Taking medicines should be one of the easiest actions to remember because doctor has prescribed the medicine to recover from illness. Besides, there is a need to take it either before or after meals. Everytime one takes meals, one should easily remember medicine.

Question (e)
How,do the chemists make fortunes out of the medicines people forget to take? Similar to the author, many remember to forget medicine as soon as the appointed time arrives.
Answer:
The medicine which is kept for long without swallowing may soon become expiry and cannot be used anymore. Tims chemists make fortunes out of the medicines people forget to take.

Question (f)
The list of articles lost in trains suggest that sportsmen have worse memories than their ordinary serious-minded fellows. Why does Lynd say this?
Answer:
Considerable number of footballs and cricket bats were forgotten by young sportsmen. Serious – minded ordinary citizens forget less. The author Lynd infers that the sportsmen’s forgetfulness is justified as their minds are full of vision of the playing field. Their heads are in the stars and among the clouds. Keeping their hearts in boots, young sportsmen rush home to talk about their exploits and are naturally more absent-minded than serious- minded ordinary folks.

Question (g)
What kind of absent-mindedness is regarded as a virtue by Lynd?
Answer:
The poet forgetting to post a letter is regarded as a virtue by Lynd because this absent-minded as his mind is filled with glorious matter.

Question (h)
Narrate the plight of the baby on its day out.
Answer:
A father offered to take the baby out in a perambulator. On a sunny morning, he was tempted to have a glass of beer. He entered a pub leaving the perambulator in the street opposite to the pub. A little later, his wife found the baby asleep in the perambulator. Her husband was not found anywhere. She took the perambulator home anticipating her husband’s remorse over the stolen baby. But to her obvious dismay, he walked in cheerfully and asked her what was the lunch. He had completely forgotten the baby on its day out.

3. Answer the following in a paragraph of about 100-150 words each.

Question (a)
You have borrowed a branded cricket bat from your reluctant friend for an outstation match. After returning home you realize you have absent-mindedly left it in the hotel room. Write a letter of apology and regret to your friend.

12, Dhandapani Street,
T. Nagar
13.07.2018.

Dear Madhan / Seema,

I’m. fine. I hope this letter finds you in the best of your health. I’m penning this letter to express my profound sorrow for forgetting to bring your branded cricket bat. I have left it behind in the hotel room in Mumbai. I’m terribly sorry. I was late for the train to Chennai. As I rushed to the station, I just forgot the packed bat. I rang up the hotel. I am told that the bat is safe. Next week, my cousin is coming home. I have asked him to bring it from the hotel. Kindly bear with me. Please do forgive my mistake. I shall certainly return your bat in a fortnight.
With deep regrets

Yours loving friend
Arun / Vanitha

To
K. Madhan
S/0 Krishna
17, Valluvar St,
Urappakam

Question (b)
Kahlil Gibran states ‘Forgetfulness is a form of freedom.’ Write an article for your school magazine, linking your ideas logically and giving appropriate examples.
Answer:
“Forgetfulness is a form of freedom”. To a greater extent, this statement is true. Forgetting is the apparent loss of information already encoded and stored in an individual’s long-term memory. It is a gradual process in which old memories are unable to be recalled from memory storage.

There is no use crowding all activities in our minds forever. This may naturally lead to many health hazards. On the other hand, a person with forgetfulness leads a peaceful life because he lives for the present moment without any botheration about the past. Scientists, poets, philosophers, and creative people are most notorious for their absent-minded ways.

Several anecdotes revolve around Albert Einstein and Sir Isaac Newton due to their scattered, forgetful ways. Einstein once called the university he worked at to ask for his own address as he had forgotten it. Persian Poet Sumi says, “Mindlessness help you unite with the divine.” So there is nothing wrong with being forgetful. Far from being is negative, it is a desirable state that not everyone can aspire to.

Question (c)
Will you sympathise or ridicule someone who is intensely forgetful? Write an essay justifying your point of view.
Answer:
Forgetfulness, if deemed a form of freedom, must be welcome. But what one forgets matters. Similar to the father who forgot the baby in the perambulator if one forgets main duties, he would become an anathema to even family members. I wouldn’t be hasty to ridicule a person who “suffers” from acute or intense forgetfulness. I would observe, in the first place, what are the items he forgets routinely. Are they trifles or serious things? If a married man forgets his wife and children and forgets his filial duties, then he deserves chastisement and not ridicule.

If forgetting leads to comic situations like wearing chappals in the wrong foot, or wearing the tie in a funny manner, sometimes a person of extraordinary intelligence may forget his residential address similar to Einstein. Scientists and great philosophers like Socrates and Rabindranath Tagore suddenly went into spells of deep contemplation totally forgetting where they were heading to. Once it so happened that socrates went into a trance on a road. His disciples and friends stood around him the whole day. Night came. Friends bought mats and pillows and slept around him hoping to listen to his words of wisdom as soon as the spell breaks and remembers what he saw in his world of imagination.

Towards dawn, the spell broke. Socrates saw the people sleeping around him. He just carefully walked back home. I have my heart-felt sympathies for my friends who study just before examination and forget what they learnt in the examination hall. I’ve my conviction that those who forget naturally need to be treated with a sympathetic understanding because they really don’t know that they forget. Those who suffer from selective amnesia, I mean politicians who give tall promises before elections but remember to forget them soon after winning the elections need to be ridiculed by funny cartoons and in public places because they have done a breach of trust.

“There is some pleasure even in words, when they bring forgetfulness of present miseries.”

Additional Questions

A Give answers to the following question in 100-150 word each.

Question (a)
Why is Robert Lynd amazed at the efficiency of humans to remember things?
Answer:
Robert Lynd is amazed by the efficiency of human memory. Modem man remembers telephone numbers, names of film stars, cricketers, football champions and even notorious murderers. He remarks with jest that man does not forget a single item of his clothing. No one forgets to shut the door when leaving the house. The institution of family survives in modem cities because ordinary people have efficient memory power. In the ordinary life, man remembers almost everything he is expected to remember like birthdays and Valentine’s day. He remembers appointments for dinner and lunch. He remembers what the weather was in a . long-part August. Not even one in thousand forgets, simple things like switching off lights before going upstairs or a single item of dressing. Almost everybody remembers to do the right things of the right moment till it is time to go to bed.

Question (b)
What according to Robert Lynd are the causes for forgetting?
Answer:
In some matters, the memory is less than perfect, causes could be psychological. We tend to forget things we don’t wish to remember. For example, many people forget to take medicines. Medicine needs to be taken before / after meals. Robert Lynd remarks that chemists make a lot of money because people tend to forget to take medicines. It aggravates the disease and people are forced to buy more and more medicines. It may be due to their antipathy to pills and poisons that many people fail to remember them at the appointed hours. The author is quizzed at the fact as to how a life-long devotee of medicines like himself is forgetful of them as those who take them up unwillingly. He admits that even if he has the pills in his pockets as soon as the time of consumption arrives, he forgets it.

Question (c)
Describe the circumstances leading to the vexation of the mother on the baby’s day out.
Answer:
Once a father took his baby out in a perambulator in the morning. He walked into a pub to have a glass of beer. The child was sitting in the perambulator outside in the street. After sometime his wife came that way for shopping. She was shocked to find her baby sleeping in the perambulator. She decided to teach him a lesson. She took the’baby home. She expected her husband to come and apologize for losing the child. But he just walked in and casually asked his wife cheerfully what was there for lunch. Very few people like Einstein or Socrates would be capable of such absent-mindedness.

Question (d)
What are the observations of Robert Lynd on the capacity of humans to remember and forget things?
Answer:
Robert Lynd is amazed by the efficiency of human memory. Modem man remembers telephone numbers, names of film stars, cricketers, football champions and even notorious murderers. He remarks wittily that man does not forget a single item of his clothing. No one forgets to shut the door when leaving the house. The institution of family survives in modem cities because ordinary people have extraordinary memory power. In some matters, the memory is less than perfect, causes could be psychological. We tend to forget things we don’t wish to remember. For example, many people forget to take medicines.

Medicine needs to be taken before / after meals. Robert Lynd remarks that chemists make a lot of money because people tend to forget to take medicines. It aggravates ithe disease and people are forced to buy more and more medicines. Most people forget to post letters. The author himself would not trust his letters to be posted by others. The author himself never remembered to post letters entrusted to him. He had to apologise for the unposted letters kept with him for long. Likewise, the author forgets his walking sticks often.

Question (e)
How does the author prove that absent-mindedness is a boon as well as a bane?
Answer:
Absent – mindedness of people shocked the author when the Railway department published the list of lost articles. It was startling to note that young people forget bats, balls etc. The author attributes it to the abundant imagination and dreams. They are citizens of dreamland. Anglers also forget their fishing rods. Absent – mindedness is often a blessing in disguise. People can forget their unhappiness and live in a world of Utopia. Great thinkers, poets and philosophers are absent – minded because their minds are full of lofty ideas and imagination. Socrates the philosopher and S.T. Coleridge the poet were absent – minded people. Similarly, Politicians have bad memories. States are yet to produce ideal statesmen. Great writers, composers of music have amazingly great memories.

Memory is half the substance of their art. Once a father took his baby out in a perambulator in the morning. He walked into a pub to have a glass of beer. The child was sitting in the perambulator outside in the street. After sometime, his wife came that way for shopping. She was shocked to find her baby sleeping in the perambulator. She decided to teach her husband a lesson. She took the baby home. She expected her husband to come and apologize for losing the child. But he just walked in and casually asked his wife cheerfully what was there for lunch. Very few people like Einstein or Socrates would be capable of such absent-mindedness. Men should forget unpleasant things and remember pleasant things. Thus Absent – mindedness is both a boon and a bane.

Vocabulary

A. Homonyms and Heteronyms.

Complete the sentences by choosing a suitable word from those given in the brackets.

1. Nobody can say (1) _______ there will be an improvement in the (2) _______ (whether / weather)
2. Your ring is (1) _______ Do not (2) _______ it.(loose / lose) .
3. We found a (1) _______ of biscuits in the old man’s shirt (2) _______ (pocket /packet)
4. When the pole vaulter cleared 28. (1) _______ it was declared a record (2) _______ (feet/feat)
5. Explain the (1) _______ ‘Cut your (2) _______ according to your cloth.’ (coat / quote)
6. The’stranger (1) _______ for a few minutes before he (2) _______ . my house.(paused /passed)
7. The (1) _______ dancer turned (2) _______ after the final performance, (weary /wiry)
8. The chain that I presented to my sister was not made of gold; it was just (1) _______ Iam suffering from a sense of (2) _______ (guilt / gilt)

Answers:

1. whether, weather
2. loose, lose
3. packet, pocket
4. feet, feat
5. quote, coat
6. paused, passed
7. wiry, weary
8. gilt, guilt

Form meaningful sentences using the given words to bring out at least two different meanings.

1. train – You must train yourself to catch the train in time.
2. tear – The tear in the uniform brought tears in the eyes of the student.
3. wind – It is time to wind up the programme because it is very windy and it might rain soon.
4. light – As the bag was very light, the boy was able carry it though there was no light in his street.
5. file – She filed all the documents carefully in a file.
6. bear – The bear couldn’t bear the mischief of the visitor; he took him into the cage and mauled him very badly.

B. Clipped Words
Now, write the clipped and unclipped form of the given words and complete the table.

UNCLIPPED	CLIPPED
chimpanzee	___________
___________	photo
___________	mike
cafeteria	___________
___________	gas
helicopter	___________
telephone	___________
___________	varsity
___________	memo
influenza	___________
___________	hippo
bridegroom	___________
___________	fan
demonstration	___________
refrigerator	___________

Answer:

UNCLIPPED	CLIPPED
chimpanzee	chimp
photograph	photo
microphone	mike
cafeteria	cafe
gasoline	gas
helicopter	copter
telephone	phone
university	varsity
memorandum	memo
influenza	flu
hippopotamus	hippo
bridegroom	groom
ceiling fan or fanatic	fan
demonstration	demo
refrigerator	fridge

C. Refer to a dictionary and match the professions with their relevant job descriptions

	A	B
1.	pathologist	studies languages and their structure
2.	ornithologist	studies atmosphere, weather and climate
3.	entomologist	studies the matter that constitutes the Earth
4.	archaeologist	studies earthquakes
5.	sociologist	studies reptiles and amphibians
6.	geologist	studies functioning of human society
7.	linguist	studies artefacts and. physical remains
8.	seismologist	studies birds
9.	herpetologist	studies insects
10.	meteorologist	studies diseases

Answer:

1. studies diseases
2. studies birds
3. studies insects
4. studies artefacts and physical remains
5. studies functioning of human society
6. studies the matter that constitutes the Earth
7. studies languages and their structure
8. studies earthquakes
9. studies reptiles and amphibians
10. studies atmosphere, weather and climate

D. Fill in the blanks choosing the words from the box. Refer to a dictionary if required. One has been done for you.

(thespian, sadist, polyglot, ambidextrous, philanthropist, misanthrope, bibliophile, nonagenarian, teetotaller, globetrotter, optimist)

(i) Peter always refuses alcohol, when it is offered to him at parties and takes a soft drink instead. He says he always has and always will abstain from alcohol and it is a matter of principle for him. We can call Peter a ________

(ii) Aruna always looks at the bright side of things. Even in the face of misfortune, she firmly believes that everything will workout for the best in the end. What can we call Aruna? ________

(iii) The rich industrialist donated a huge sum of money to set up a public library in his native village. He is a ________ and a social reformer.

(iv) The Chair person of our company keeps travelling all over the world to attend conferences and we call her a ________

(v) Antony has the amazing ability to use both his hands, equally well. He can write, draw and perform various other tasks with equal speed and efficiency with his left as well as his right hand. Antony is ________

(vi) Due to some disturbing incidents in her childhood, Neetu grew into a reclusive adult. She tends to keep aloof and avoids all kinds of social activities. Neetu is a ________

(vii) Tharini serves as an interpreter at meetings between statesmen from different countries. She is also a much sought-after tour guide, as she is well-versed and fluent in multiple languages. Tharini is a ________

(viii) My grandparents are in their nineties. I am glad that this ________ couple are active, cheerful and in good health.

(ix) Richard Burton was a gifted theatre artist. He donned several roles with ease and is especially famous for the Shakespearean parts he played on stage. Mr. Burton is a born ________

(x) The Chairman of this concern seems to derive pleasure from inflicting pain on others. He humiliates and hurts his subordinates for no reason. He is a real ________

Answers:

(i) tee totaller
(ii) optimist
(iii) philanthropist
(iv) globetrotter
(v) ambidextrous
(vi) misanthrope
(vii) polyglot
(viii) nonagenarian
(ix) thespian
(x) sadist

E. Find the antonyms of the following words in the puzzle and shade them with a pencil. The first one has been done for you.

1. seldom,
2. admitted,
3. methodical,
4. reality,
5. virtue,
6. vile,
7. indignant,
8. relish,
9. fact Spot the word

Answers:

1. often
2. denied
3. haphazard
4. fantasy
5. vice
6. good
7. delighted
8. hate
9. fiction

Listening Activity

A. First, read the incomplete sentences given below. Listen to two interesting anecdotes about two scientists that your teacher will read aloud or play on the recorder. Then, based on your understanding, complete the sentences suitably.

(For listening to the passage refer to our website www.fullcircleeducation.in) Thomas Alva Edison stepped from a train in Orange, New Jersey and walked down the platform. The station master knew how forgetful the famous inventor was. Therefore, he would always ask him a customary question. He asked Edison if he had left anything behind. Edison confidently replied that he had not left anything and everything was safe with him. Then, he began taking a count of his suitcases. As he was doing so, he happened to look up at the train. With a start, he dropped his bags and raced back to the car in which he had been travelling. What prompted that burst of activity was the face of his bride, with whom he had just married and returned from a honeymoon trip, staring from a window.

Albert Einstein was working at the Princeton University. One day when he was going back home he forgot his home address. The driver of the cab aid not recognize him. Einstein asked the driver if he knew Einstein’s home. The driver exclaimed that there could be no one who did not know Einstein’s address. He added that everyone in Princeton knew where Einstein lived and asked him if he wanted to meet Einstein. Einstein with a sheepish grin replied that he was Einstein and he had forgotten his residential address. He requested the cabbie if he could take him there. The astonished driver drove him home and dropped him safely. The cabbie considered driving Einstein a great honour and refused to charge him for the service.

1. Edison travelled to New Jersey by ______
2. The station master enquired if Edison ______
3. Edison raced back to the car, when he saw ______
4. Albert Einstein was working in ______
5. One day, when he was going back home, he ______
6. Einstein asked the cab driver if he knew ______
7. The driver was so good that he ______

Answers:

1. a train
2. had left anything behind
3. the face of his bride
4. Princeton university
5. forgot his residential address
6. Einstein’s residence
7. refused to charge him for his

Speaking Activity

Work with a partner and take turns to share your views and suggestions with the class.

Question (i)
You are travelling in a train. When the Train Ticket Examiner enters your compartment, much to your shock, you realize you have forgotten to bring your train ticket. How will you handle the situation?
Answer:
TTE : Please show me your ticket.
Ragu : Oh! sorry! I left my printed ticket on my table.
TTE : Well, this is a reserved compartment, Don’t you know?
Ragu : Sir, I have reserved my ticket. It is 28 UB, S7 in Pandiyan Express.
TTE : Well, what you say might be true. But I want the ticket.
Ragu : Sir, could you please give me five minutes.
TTE : Why?
Ragu : I will ask my sister to scan the ticket and send it to my phone by WhatsApp.
TTE : Okay. But get it in five minutes.
Ragu : Thank you so much sir.

Question (ii)
You forget to wish your best friend on his/her birthday. He gets very angry. How will you try to pacify him/her? Construct a dialogue of about 4 to 5 exchanges and enact a role play.
Answer:
Ramesh : Ravi, aren’t you my best friend?
Ravi : Why do you doubt it?
Ramesh : You didn’t even wish me. Yesterday evening I was waiting for you till 9 pm. Ravi : I’m terribly sorry! I was at the Chepauk stadium watching CSK batting under trying conditions.
Ramesh : Oh! when it comes to cricket, you forget even your weekly tests.
Ravi : Friend, forgive me. Accept my belated wishes.
Ramesh : Okay. Let us forget it and talk about the match.

Question (iii)
‘Forgetfulness is the beginning of happiness’ Do you agree or disagree? Discuss in class.
Answer:
In “Ode to skylark,” Shelly beautifully portrays the human beings’ boundless capacity to worry about dead yesterday, unborn tomorrow and spoil the happiness of a perfectly beautiful present. He says, “We look before and after and pine for what is not. Our sincerest laughter with some pain is fraught”. Human mind has a soft comer for harbouring hurts and pain. It replays them like a broken record often and sustains hostility between individuals. It requires a mature mind to forgive and forget. The road to recovery of any invisible hurt starts the moment one forgives the person and casually forgets all unpleasant memories connected to it. Human mind, according to Robert Lynd, forgets what it chooses to forget. We are in a civilized society because everyone remembers to dress properly and remember the names of friends and relatives. If one develops the attitude to remember only pleasant things, the mind will train itself to forget insignificant bad memories. Thus forgetting is the beginning of real happiness.

Question (iv)
Is there a link between intelligence and absent-mindedness? Share your views on this subject.
Answer:
Of course yes, the person who is smart and extremely intelligent focusses his entire being on an issue or an invention. Thus all other things are abstracted. Great genius like Einstein and philosophers like Tagore tend to forget mundane affairs. Their minds are always preoccupied with lofty ideas and the ills of the society. So, it is believed that eccentricity like absent mindedness is common among very intelligent people. The best example is Einstiein. He sat in the railway coach leaving behind his newly married bride in the car. Only on seeing her furious face, he realized the fact that he forgot to take her along into the railway coach.

Reading Activity

Now, read the following biographical extract on Sujatha Rangarajan, a Science-fiction writer, and answer the questions that follow.

1. Sujatha is the allonym of the Tamil author S. Rangarajan and it is this name that is recognised at Once by the Tamil Sci-Fi reading community. You might have heard of Chitti and his extraordinary exhibition of different qualities in an incredible manner. The robot could excel a human being in any act beyond one’s imagination. Jeeno, a robotic dog which appeared in Sujatha’s science fiction novel “En Iniya Iyandhira” (My Dear Robot) formed the basis of Chitti’s character. Like Chitti, Jeeno was an all-rounder who could cook, clean and fight.

Very high tech computer technology terms are used in the story. Jeeno, a pet robot, plays an important role throughout the story. As the story proceeds, it behaves and starts to think on its own like-a human and instructs Nila, a human being, on how to carry on further.

2. In the preface of ‘En Iniya Iyandhira’,the writer states the reason for his attraction to the genre: “Science gives us the wonderful freedom to analyse thousands and thousands of alternative possibilities. While using it, and while playing with its new games, a writer needs to be cautious only about one thing. The story should draw some parallels or association from the emotions and desires of the present humankind. Only then it becomes interesting. Jeeno, the robot dog, was intelligent.

But the character became popular only because of the robot’s frequently displayed human tendencies. It is no wonder that his works echo these words about him and will reflect in the minds of the readers who enjoy reading his novels to have a lifetime experience.

3. It was Sujatha, who set the trend in sci-fi stories. He had tracked the origin from Mary Shelly’s Frankenstein to his short stories. He has written 50 sci-fi short stories published in various Tamil magazines.

His stories have inspired many readers to extend their reading to English sci-fi writers like Isaac Asimov. The themes were bold even if there was a dependence on very well – established characterisation of English fiction. Sujatha opened up a new world to us with his writings on holograms, computers and works like ‘En Iniya Iyanthira’, inspire many to study computer science.

4. He has been a great writer for more than four decades. He combined reasoning and science in his writings. Being a multifaceted hi-fi and sci-fi humanistic author, he expressed his views distinctively. He was the one who took Tamil novels to the next level. As an MIT alumnus and an engineer at BHEL, he was very good at technology. So, he narrated sci-fi stories, impressively. His readers always enjoyed reading all his detective and sci-fi novels which featured the most famous duo Ganesh and Vasanth.

5. Sujatha has played a crucial role as a playwright for various Tamil movies which have fascinated movie lovers. Hence, it is fathomable that the writer’s perspective of future India enthuses every reader and paves a new way to reading sci-fi stories in English.

A. Answer the following questions in a sentence or two.

Question (i)
How was Jeeno different from other robots?
Answer:
Other robots did tasks only as per the commands issued. But Jeeno frequently displayed human tendencies. It behaved and thought like a human being.

Question (ii)
What precaution should one take while writing Science fiction stories?
Answer
The writer should ensure that the story draws some parallel or association from emotions and desires of the present humankind. Only then the science-fiction would be interesting.

Question (iii)
What inspired Sujatha’s themes?
Answer:
Sujatha had bold trend in sci-fi stories. He had tracked the origin from Mary Shelley’s Frankenstein to his short stories. He opened up a new world to the readers with his writings on holograms, computers, robots who feel and behave like humans, (e.g) “En Iniya Iyanthira”. In short, Sujatha’s themes were inspired by reasoning, science, technology, computers and humanoids.

Question (iv)
Why were Sujatha’s sci-fi stories impressive?
Answer:
Sujatha’s sci-fi stories have really inspired Tamil readers to move on to read Isaac Asimov. He combined reasoning with science in his writings. Being a multi-faceted hi-fi and sci-fi humanistic author, he expressed his views distinctly. Being an alumni of MIT, he was good at technology. Thus his sci-fi stories were always impressive with interesting characters like Chitti, the robot; Jeeno the robot-dog and detective duo Ganesh and Vasanth.

B. Find words from the passage which mean the same as the following.

1. difficult to believe (para 1) incredible
2. a style or category of art, music or literature (para 2) genre
3. having many sides (para 4) multifaceted
4. capable of being understood (para 5) fathomable

Grammar

A. Identify the changes in these pairs of active and passive constructions.

Question 1.
The pilot flew the airplane to Bengaluru.
Answer:
The airplane was flown to Bengaluru by the pilot. In the second sentence, the object has been shifted to the place of subject. It remains passive and allows the work to be done by the noun.

Question 2.
The bananas were eaten by the monkey.
Answer:
The monkey ate the bananas. Here the subject is shifted to the place of object.

B. Change the voice of the following sentences.

Question 1.
Mohammed follows the rules.
Answer:
The rules are followed by Mohammed.

Question 2.
Mohan has completed the course.
Answer:
The course has been completed by Mohan.

Question 3.
Magdalene is singing the prayer.
Answer:
The prayer is being sung by Magdelene.

Question 4.
Who wrote this complaint?
Answer:
By whom was this complaint written?

Question 5.
May God bless you with happiness!
Answer:
May you be blessed with happiness by God.

Question 6.
A house is being constructed by them.
Answer:
They are constructing a house.

Question 7.
Let the door not be slammed.
Answer:
Don’t slam the door.

Question 8.
The team was trained by the coach.
Answer:
The coach trained the team.

C. Make sentences using the passive forms of the verbs.

Question 1.
Tagore/award/Nobel prize/
Tagore was awarded Nobel prize.

Question 2.
IIM Ahmedabad / establish /1961
Answer:
IIM Ahmedabad was established in 1961.

Question 3.
Chhattisgarh/ form / 2000
Answer:
Chhattisgarh was formed in 2000.

Question 4.
First passenger train /inaugurated /India /1853
Answer:
The first passenger train was inaugurated in 1853.

Question 5.
Indian Airlines /set up /1953 ! Indian Airlines was set up in 1953.

D. Look at the newspaper items given below. Use the information in the headlines to complete the sentence.

Question 1.
HEAVY RAINS LASH CHENNAI
______ threw normal life out of gear.
Answer:
Heavy rains threw normal life out of gear.

Question 2.
NEET CLASSES TO BEGIN ON SEPT. 20th
The Centre co-ordinator informed the candidates ______ Sept. 20th
Answer:
The centre coordinator informed the candidates about the commencement of NEET classes on September 20th.

Question 3.
12 INJURED AS BUSES COLLIDE
About at the Dindigul bus terminus here today.
Answer:
About 12 passengers were injured as buses collided at Dindigul.

E. Expand the following news headlines in a sentence.

Question 1.
MUNICIPAL ELECTIONS IN DECEMBER
Answer:
Municipal Elections will be held in December.

Question 2.
TELEPHONE CUSTOMERS TO GET VIDEO PHONE BSNL
Answer:
proposes to give video phone to its customers at a low cost.

Question 3.
CARD LICENSE TO REPLACE PAPER DRIVING LICENSE
Answer:
Transport Minister announced that paper licenses will be replaced with card licenses.

Question 4.
ATM WITHOUT SECURITY GUARD TO CLOSE RBI
Answer:
announced that all ATMS which have no security guard will be closed.

F. Describing a process

1. Complete the passage by filling the blanks with the passive forms of the verbs.

The water should be boiled in a vessel. Then tea leaves and milk (1) _____ to the water. The vessel (2) _____ with a lid. The tea (3) _____ and (4) _____ into the tups. Sugar (5) _____ . and (6) _____ The tea (7) _____ hot.
Answers:

1. should be added
2. must be covered
3. should be filtered
4. poured
5. should be added
6. stirred
7. should be served

2. Here is a recipe to make chocolate cake in a pressure cooker. Rewrite the instructions in passive voice. The first one has been done for you.

Question (i)
First sift the flour, cocoa powder and baking powder in a mixing bowl.
Answer:
The flour, cocoa powder and baking powder are first sifted in a mixing bowl.

Question (ii)
Add butter, sugar, salt, water and vanilla and beat the ingredients using a whisk.
Answer:
Butter, sugar, salt, water, and vanilla should be added and the ingredients must be beaten using a whisk. .

Question (iii)
Add the eggs and beat the batter until it is smooth.
Answer:
The eggs must be added and the batter must be beaten until it is smooth.

Question (iv)
Transfer the batter into the baking tin.
Answer:
The batter must be transferred into the baking tin.

Question (v)
Heat the pressure cooker, covered with the lid but without the pressure, for 3-4 minutes on high heat. Then place the cake tin in the empty cooker (Do not add water in the cooker).
Answer:
The pressure cooker must be heated. It should be covered with the lid but without the pressure. It must be left for 3-4 minutes on high heat. The cake tin must be kept in the empty cooker. (Let not water be added in the cooker)

Question (vi)
Close the lid (without the pressure), lower the flame and let it cook for about 30 minutes.
Answer:
Let the lid be closed without the pressure. The flame must be lowered and it must be let to cook for about thirty minutes.

3. Write the process of wrapping a Christmas gift in a paragraph in passive form, with the help of the pictures given below.

Answers:

1. The gift must be placed in a rectangular box.
2. The required paper must be measured. The gift paper must be placed on the box. It must be wrapped loose end up and over and a cut must be made.
3. The gift paper must be placed face down and centred on the box. The first edge must be brought up and taped in place on to box. Then it must be brought other side up and taped in place.
4. The sides should be folded in against the edges of the box. The diagonal flaps you have created must be creased.
5. The top edge should be folded down. Then bottom edge should be folded up and taped.
6. A gift tag must be added with a bow and ribbon to really class up your Christmas gift and impress recipients of your gift.

Subject and Verb Agreement (Concord)
A. Underline the correct verb in these sentences.

1. The girl and her sisters _______ (watch, watches) television every day.
2. Ravi _______ (doesn’t, don’t) like sports.
3. My classmates _______ (study, studies) before a test.
4. One of the cookies _______ (is, are) missing.
5. A lady with ten cats _______ (live, lives) in that big house.
6. Measles _______ (is, are) very serious.
7. The committee _______ (decide, decides) when to adjourn.
8. Our team _______ (is, are) the best.
9. Everybody _______ (enjoy, enjoys) a good song.
10. Either of these _______ (is, are) suitable.

Answers:

1. watch
2. doesn’t
3. study
4. is
5. lives
6. is
7. decides
8. is
9. enjoys
10. is

B. Correct the following passage.

Where does the deer and the antelope play? One place is Yellowstone National Park. It were created in 1872. Parts of the park is in Wyoming, Montana and Idaho. The park are a safe place for many animals. Bears, moose, buffalo, deer and antelope lives there. Beavers, otters, fish and eagles also enjoys the park. For them, Yellowstone be ‘home sweet home.’
Answer
Where do the deer and the antelope play? One place is Yellowstone National Park. It was created in 1872. Parts of the park are in Wyoming, Montana and Idaho. The park is a safe place for many animals. Bears, moose, buffalo, deer and antelope live there. Beavers, otters, fish and eagles also enjoy the park. For them, Yellowstone is ‘Home, sweet home.’

Writing

Biographical sketch:

A biographical sketch is a brief summary of a person’s life and his achievements. It should include a description of the person’s physical appearance, education, work, achievements and other salient personal traits. The main focus of a biographical sketch is to portray the person in an admirable way.

(a) Given below are hints about a renowned British science fiction writer Arthur C. Clarke. Write a biographical sketch on the author in not more than 80-100 words based on the information given below.

Name	Arthur C. Clarke
Pen names	Charles Willis, E.G.O’Brien
Birth	16 Dec 1917, England
Career	Novelist, Television host, inventor and film screen writer.
Genre	Science Fiction, Television series, film screen play
Awards and Honours	1961, Kalinga Prize – an award given by UNESCO for popularising science Hugo and Nebula Awards Chairman of the Interplanetary Society Highest Civil Honour of Sri Lanka – ‘Sri Lankabhimanya 2005’
Titles	Clarke, Robert Heinlein and Isaac Asimov – ‘Big Three’ of Science Fiction ‘The Prophet of the Space Age’
Famous Works	Childhood’s End 2001: A Space Odyssey Rendezvous with Rana

Arthur C. Clark was bom on 16th December, 1917 in England. He was a novelist, television host, inventor and film screen writer all bundled into one. He gained popularity in science fiction, sensational T.V serials and screen play writing. In recognition of his exceptional skills, he was awarded Kalinga prize for popularising science. This award was given to him by UNESCO in 1961..He was made the chairman of Interplanetary Society and also conferred Hugo and Nebula awards, He was given the highest civilian (award) honour of Sri Lanka ‘Sir Lankabhimanya in 2005’. Clarke is often regarded as one of the triumvirs of sci-fi writers, (i.e) Robert Heinlein, Asimov and himself. He is hailed as “The Prophet of Space Age”. He is widely remembered world over for his famous work “Childhood End”, “2001: A space Odysey”: and “Rendezvous with Rana”.

Report Writing:

Question (a)
You have recently attended a seminar on ‘Science and Literature’ in which writers presented papers on Science Fiction and literature and focused on the creativity of young writers. Write a short report about it for a leading newspaper in about 100-120 words.
Answer:
The seminar on “Science and Literature” was held at American college, Madurai. It was organized in memory of Prof. Vasanth. Students from various colleges, Government Higher Secondary Schools and Matriculation schools were present. Dr. Paul Luv inaugurated the seminar. Students from Manjakkuppam Higher Secondary School talked about novels of Jules Verne-(i.e) Journey to the center of the earth, Twenty thousand leagues under the sea, From earth to the moon, Around the world in eighty days, Five weeks in a balloon, Off on a comet, An Antartic mystery has prophesied man’s potential ability to carryout space travel, explore.

Antarctica, do deep water Research, mission to moon and other celestial bodies. It is mind-boggling to realize that he wrote about these latest developments before 1905. Students were ‘ much impressed by the prolific sci-fi writings of the French novelist more than a century ago.

Prof. Sangeetha spoke on Aldous Huxley’s brave new world which predicted Human genome project and how science can help produce babies with special attributes, size, colour and ’ character traits. All of us, know the cloning of ‘Dolly’. Student from Government Hr. Sec. School D. Kala spoke about Alvin Toffler and how he had predicted revolution due to technological break through in his most famous books. “Future shock”, “The third wave” and “power shift”. He discusses modem technologies including the digital revolution, and the communication revolution. Malathy talked about Sujatha, Tamil Sci-fi writer who influenced large number of children and adults to fall in love with computers and robotics. His imaginary characters Chitti and Jeeno I have endeared him to the masses.

Asimov has written large number of Sci-fi stories in collaboration with Robert A. Heinlein and Arthur C. Clarke. Asimov’s most famous work is the “Foundation series” and Galactic empire”. Asimov has written Lucky start series of Juvenile science-fiction using the pen name Paul French. The seminar ended with the note that many sci-fi writers have greatly contributed to the giant strides science and Technology has made in recent times. Students must read and write sci-fi fiction to influence the development of love for science.

Question (b)
You are the School Pupil Leader. Your school organised an Inter-School Sports event at Nehru Stadium. Write a report on the special events conducted in 100-120 words for the school souvenir.
Answer:
Hon Balakrishna Reddy, the minister for sports inaugurated the sports meet in the presence of state project officer RMSA Dr. V.C. Rameswara Murugan. Mr. Peter the physical director from Salem coordinated all the events. In the track and field events, Meena and Tamilselvi from Ashok Nagar Girl’s School bagged gold and silver medals. In the men’s event, Kandan

Subbu from Government Boys High School, Nungambakkam bagged Gold and Silver medals. Third position was bagged by Presidency School girl Suba. In boy’s event, Ambedkar School Sukumar bagged a silver medal.

Maheswari of Girl’s School, Guduvancherry won the gold in weightlifting. It was heartening to note many Government School students playing tough against even private schools which give special coaching in sports and games. Chandran, the Chief Inspector of Physical Education gave away the prizes to all the winners of various sports and games events.

Forgetting About the Author

Robert Lynd is an Anglo-Irish writer, essayist and a poet. He is respected as one of the greatest essayists of the 20th century. He wrote many articles for leading journals and newspapers like Daily News, the New Statesman and Nation. He wrote under the pseudonym name “Y.Y His essays dealt with interesting and simple topics. His essays arc humourous delightful, ironical and satirical. I le was awarded with an honorary literary Doctorate by Queen’s University. He was confessed silver medal by the Royal Society of Literature.

Forgetting Summary

Robert Lynd is a humorous and delightful essayist. His essays are simple, playful and satirical. His style of writing is elegant and charming. In his essay “Forgetting”, he writes about the root causes of forgetting and also explains what items are usually forgotten by people.

Robert Lynd is amazed by the efficiency of human memory. Modem man remembers telephone numbers, names of film stars, cricketers, football champions and even notorious murderers. He remarks wittily that man does not forget a single item of his clothing; No one forgets to shut the door when leaving the house. The institution of family survives in modem cities because ordinary people have extraordinary memory power. In some matters the memory is less than perfect, causes could be psychological. We tend to forget things we don’t wish to remember.

For example, many people forget to take medicines. Medicine needs to be taken before / after meals. Robert Lynd remarks that chemists make a lot of money because people tend to forget to take medicines. It aggravates the disease and people are forced to buy more and more medicines. Most people forget to post letters. The author himself would not trust his letters to be posted by others. The author himself never remembered to post letters entrusted to him. He had to apologise for the unposted letters kept with him for long. Likewise, the author forgets his walking sticks often.

The Absent-mindedness of people shocked the author when the Railway department published the list of lost articles. It was startling to note that young people forget bats, balls etc. The author attributes it to the abundant imagination and dreams. They are citizens of dreamland. Anglers also forget their fishing rods. Absent-mindedness is often a blessing in disguise. People can forget their unhappiness and live in a world of Utopia. Great thinkers, poets and philosophers are absent-minded because their minds are full of lofty ideas and imagination.

Socrates the philosopher and S.T. Coleridge the poet were absent-minded people. Similarly, Politicians have bad memories. States are yet to produce ideal Statesmen. Great writers, composers of music have amazingly great memories . Memory is half the substance of their art. Once a father took his baby out in a perambulator in the morning. He walked into a pub to have a glass of beer. The child was sitting in the perambulator outside in the street. After sometime, his wife came that way for shopping. She was shocked to find her baby sleeping in the perambulator.

She decided to teach her husband a lesson. She took the baby home. She expected her husband to come and apologize for losing the child. but he just walked in and casually asked his wife cheerfully what was there for the lunch. Very few people like Einstein or Socrates would be capable of such absent-mindedness. Men should forget unpleasant things and remember pleasant things.

Textual:

• abstracted – lacking concentration on what is
• happening around
• antipathy – strong dislike
• audacious – bold and daring
• delinquent – a young person who is regularly
• involved in wrongdoing
• eccentric – tending to act strangely
• exploits – daring or heroic acts or actions, feats
• fallible – capable of making mistakes
• fortunes – huge sums of money
• indignant – being very angry.
• mediocre – not very good, ordinary
• prosaic – dull
• quivering – trembling, shivering
• reluctant -unwilling
• sieve – strainer or filter
• vexation – irritation, annoyance
• vintage – wine of high quality produced in a particular year

Additional:

• Antipathy – dislike
• Magnificent – spectacular
• Prosaic – dull

Forgetting Synonyms

Choose the most appropriate synonym for the underlined word. (Exam model)

Question 1.
The ordinary man seldom forgets things.
(a) frequently
(b) rarely
(c) never
(d) often
Answer:
(b) rarely

Question 2.
A very methodical man remembers to take medicine.
(a) chaotic
(d) organized
(c) disarrayed
(d) inefficient
Answer:
(d) organized

Question 3.
I am always reluctant to trust a visitor to post my letters.
(a) willing
(b) unwilling
(c) like
(d) hatred
Answer:
(b) unwilling

Question 4.
It is because of their antipathy to pills.
(a) love
(b) affinity
(c) like
(d) aversion
Answer:
(d) aversion

Question 5.
Chemists make their fortunes out of medicines people forget to take.
(a) riches/wealth
(b) poverty
(c) paucity
(d) luck
Answer:
(a) riches/wealth

Question 6.
A long chain of circumstances leads to a number of embarrassing questions.
(a) comfortable
(b) interesting.
(c) anxious
(d) awkward
Answer:
(d) awkward

Question 7.
I am no delinquent in such matters.
(a) activist
(b) wrongdoer
(c) volunteer
(d) strategist
Answer:
(b) wrongdoer

Question 8.
I dare not carry an umbrella because I forget it often.
(a) believe
(b) refuse
(c) accept
(d) fear
Answer:
(d) fear

Question 9.
He did not even have the grimmest jawed umbrella.
(a) pleasant
(b) charming
(c) beautiful
(d) unpleasant
Answer:
(d) unpleasant

Question 10.
An absent-minded angler is good at inventing magnificent lies.
(a) dull
(b) drab
(c) cluster
(d) spectacular
Answer:
(d) spectacular

Question 11.
One has no time to remember the mediocre.
(a) great
(b) exceptional
(c) ordinary
(d) excellent
Answer:
(c) ordinary

Question 12.
He has a memory like sieve.
(a) glass
(b) filter
(c) fitter
(d) sleeve
Answer:
(d) sleeve

Question 13.
He is an audacious perverter of the truth.
(a) daring / bold
(b) timid
(c) frightened
(d) alarmed
Answer:
(a) daring / bold

Question 14.
We regard a person who does not possess a good memory as eccentric.
(a) usual
(b) conventional
(c) controversial
(d) strange / queer
Answer:
(d) strange / queer

Question 15.
Being indignant at her husband’s behaviour, she decided to teach him a lesson.
(a) cool
(b) calm
(c) anxious
(d) angry
Answer:
(d) angry

Question 16.
She anticipated her husband’s white face with quivering lips confessing the theft of the child.
(a) solid
(b) daring
(c) trembling
(d) cold.
Answer:
(c) trembling

Question 17.
Her husband’s cheerful entry and enquiry about lunch and forgetting the baby was her vexation.
(a) joy
(b) bliss
(c) ecstasy
(d) annoyance / irritation
Answer:
(d) annoyance / irritation

Question 18.
Most of us are bom with prosaically efficient memories.
(a) elated
(b) cheerfully
(c) normally
(d) dull
Answer:
(d) dull

Question 19.
They are abstracted from the world outside them.
(a) actual
(b) distracted
(c) stupid
(d) concrete
Answer:
(b) distracted

Question 20.
Men with fallible memories try to make out a case for their superiority.
(a) infallible
(b) valuable
(c) error-prone
(d) malicious
Answer:
(c) error-prone

Forgetting Antonyms

Choose the most appropriate antonym for the underlined word. (Exam model)

Question 1.
Many people who read the list of lost articles in the trains would be astonished.
(a) unexpected
(b) unpredictable
(c) surprised
(d) expected
Answer:
(d) expected

Question 2.
Modem man remembers even telephone numbers.
(a) recalls
(b) retrieves
(c) recollects
(d) forgets
Answer:
(d) forgets

Question 3.
The ordinary man seldom forgets to turn off lights.
(a) rarely
(b) almost never
(c) scarcely
(d) frequently
Answer:
(d) frequently

Question 4.
Moral giants remember to take medicines regularly.
(a) periodically
(b) intermittently
(c) irregularly
(d) continuously
Answer:
(c) irregularly

Question 5.
The fact remains.
(a) truth
(b) verity
(c) veracity’
(d) lie / fiction
Answer:
(d) lie / fiction

Question 6.
Some forget pills due to their antipathy.
(a) strong dislike
(b) aversion
(c) hostility
(d) affinity
Answer:
(d) affinity

Question 7.
Chemists make their fortunes out of the medicines forgotten to take.
(a) luck
(b) wealth
(c) bounty
(d) misfortunes
Answer:
(d) misfortunes

Question 8.
I am always reluctant to trust a visitor to post my letters.
(a) unwilling
(b) indisposed
(c) ill-disposed
(d) willing
Answer:
(d) willing

Question 9.
I put it for safety into one of my pockets.
(a) protection
(b) danger
(c) defence
(d) asylum
Answer:
(b) danger

Question 10.
I get weary of holding it in my hands.
(a) exhausted
(b) tired
(c) depleted
(d) energetic / fresh
Answer:
(d) energetic / fresh

Question 11.
A methodical man always remembers everything.
(a) organized
(b) disciplined
(c) chaotic/unorganized
(d) regular
Answer:
(c) chaotic/unorganized

Question 12.
A long chain of circumstances leads to a number of embarrassing questions’.
(a) awkward
(b) uneasy
(c) comforting
(d) discomforting
Answer:
(c) comforting

Question 13.
I am no great delinquent in such matters.
(a) irresponsible
(b) careless
(c) responsible
(d) negligent
Answer:
(c) responsible

Question 14.
I dare not carry an umbrella.
(a) defy
(b) fear
(c) avoid / dodge
(d) encounter
Answer:
(c) avoid / dodge

Question 15.
Memories prevent them from doing prosaic things.
(a) dull
(b) drab
(c) interesting
(d) boring
Answer:
(c) interesting

Question 16.
The angler who invents magnificent lies after a day’s fishing is bound to be absent-minded.
(a) spectacular
(b) fabulous
(c) weak / feeble
(d) strong
Answer:
(c) weak / feeble

Question 17.
Absent’ – minded great people have no time to remember the mediocre.
(a) average
(b) drab
(c) common
(d) exceptional / excellent
Answer:
(d) exceptional / excellent

Question 18.
People with fallible memories occasionally assert their superiority.
(a) likely to do mistakes
(b) infallible
(c) insatiable
(d) inscrutable
Answer:
(b) infallible

Question 19.
Memory is half the substance of their art.
(a) remembrance
(b) forgetfulness
(c) recollection
(d) retrieval
Answer:
(b) forgetfulness

Question 20.
He is an audacious perverter of truth.
(a) bold
(b) daring
(c) diligent
(d) timid
Answer:
(d) timid

Question 21.
A man who does not possess a good memory is often regarded eccentric.
(a) strange
(b) queer
(c) unconventional
(d) ordinary / conventional
Answer:
(d) ordinary / conventional

Question 22.
What was her vexation?
(a) worry
(b) annoyance
(c) regret
(d) pleasure
Answer:
(d) pleasure

Question 23.
Great Statesmen have the genius of memory and intellect combined.
(a) mental ability
(b) dunce
(c) sharp witted
(d) brilliance
Answer:
(b) dunce

Question 24.
She was indignant at her husband’s behaviour.
(a) furious
(b) ruffled
(c) angry
(d) contented / composed
Answer:
(d) contented / composed

Question 25.
She arrived home anticipating with angry relish the white face and quivering lips.
(a) enjoyment
(b) like
(c) dislike
(d) pleasure
Answer:
(c) dislike

Samacheer Kalvi 11th English Book Solutions Prose

• The Portrait of a Lady Book Back Answers
• The Queen of Boxing Book Back Answers
• Forgetting Book Back Answers
• Tight Corners Book Back Answers
• The Convocation Address Book Back Answers
• The Accidental Tourist Book Back Answers

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2

Question 1.
Without expanding the determinant, prove that
Solution:

Question 2.
Show that
Solution:

Question 3.
Prove that
Solution:
LHS
Taking a from C₁, b from C₂ and c from C₃ we get

Expanding along R₁ we get
(2c) (abc) (1) [ab + ab] = abc (2c) (2ab)
1 = (abc) (4abc) = 4a²b²c²
= RHS

Question 4.

Solution:

Question 5.
Prove that
Solution:

Question 6.
Show that
Solution:

Question 7.
Write the general form of a 3 × 3 skew-symmetric matrix and prove that its determinant is 0.
Solution:

Question 8.

Solution:

we get – (aα² + 2bα + c) [ac – b²]
So Δ = 0 ⇒ (aα² + 2bα + c) (ac -b²) = – 0 = 0
⇒ aα² + 2bα + c = 0 or ac – b² = 0
(i.e.) a is a root of ax² + 2bx + c = 0
or ac = b²
⇒ a, b, c are in G.P.

Question 9.
Prove that
Solution:

Question 10.
If a, b, c are p^th, q^th and r^th terms of an A.P., find the value of
Solution:
We are given a = t_p,b = t_q and c = t_r
Let a be the first term and d be the common difference

Question 11.
Show that is divisible by x⁴
Solution:

Multiplying R₁ by a, R₂ by b and R₃ by c and
taking out a from C₁ b from C₂ and c from C₃ we get
==

Question 12.
If a, b, c are all positive, and are p^th, q^th and r^th terms of a G.P., show that

Solution:

Question 13.
Find the value of if x, y, z ≠ 1.
Solution:
Expanding the determinant along R₁

Question 14.

Solution:

Question 15.
Without expanding, evaluate the following determinants:

Solution:

Question 16.
If A is a square matrix and |A| = 2, find the value of |AA^T|.
Solution:
Given |A| = 2
[Property 1: The determinant of a matrix remains unaltered if its rows are changed into columns and columns. That is, |A| = |A^T|]

|A^T| = |A| = 2
∴ |A A^T| = |A| |A^T|
= 2 × 2 = 4

Question 17.
If A and B are square matrices of order 3 such that |A| = -1 and |B| = 3, find the value of |3AB|.
Solution:
Given A and B are square matrices of order 3 such that |A| = -1 and |B| = 3
[It A is a square matrix of order n then det ( kA) = |kA| = kⁿ |A|.]
A and B are square matrices of order 3. Therefore,
AB is also a square matrix of order 3.
|3 AB| = 3³ |AB|
= 27 |A| |B|
= 27 × – 1 × 3
|3 AB| = – 81

Question 18.
If λ = -2, determine the value of
Solution:
Given λ = -2
∴ 2λ = -4; λ² = (-2)²; 3λ² + 1 = 3 (4) + 1 = 13
6λ – 1 = 6(-2) – 1 = -13

expanding along R₁
0(0) + 4 (0 + 13) + 1 (-52 + 0) = 52 – 52 = 0
Aliter: The determinant value of a skew-symmetric matrix is zero

Question 19.
Determine the roots of the equation
Solution:

Given the determinant value is 0
⇒ 30(1 + x) (2 – x) = 0
⇒ 1 + x = 0 or 2 – x = 0
⇒ x = -1 or x = 2
So, x = -1 or 2.

Question 20.
Verify that det (AB) = (det A) (det B) for
Solution:


{(-20)(52) (-19) + (10)(38)(—49) + (2)(64)(-17)} – {(-49)(52) (2) + (-17)(38)(-20) + (-19)(64)(10)}
= (19760 – 18620 – 2176) – (-5096 + 12920 – 12160)
= (19760 + 5096 + 12160) – (18620 + 2176 + 12920)
= 37016 – 33716 = 3300 ….(3)
Now (1) × (2) = (3)
(i.e.,) (-33) (-100) = 3300
⇒ det (AB) = (det A), (det B)

Question 21.
Using cofactors of elements of the second row, evaluate |A|, where
Solution:

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.2 Additional Problems

Question 1.

Solution:

Question 2.

Solution:

Question 3.

Solution:

Question 4.

Solution:

Question 5.

Solution:

Question 6.

Solution:

Question 7.

Solution:

Question 8.

Solution:

Question 9.

Solution:

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4

Question 1.
Find the area of the triangle whose vertices are (0, 0), (1, 2) and (4, 3)
Solution:
Area of triangle with vertices

∴ Area of A with vertices (0, 0), (1, 2) and (4, 3) is

(as the area cannot be negative).

Question 2.
If (k, 2), (2, 4) and (3, 2) are vertices of the triangle of area 4 square units then determine the value of k.
Solution:

Question 3.
Identify the singular and non-singular matrices:

Solution:
(i) For a given square matrix A,
1. If |A| = 0 then it is a singular matrix.
2. If |A| ≠ 0 then it is a non singular matrix.

⇒ A is a singular matrix.

Which is a skew symmetric matrix
∴ |A| = 0 ⇒ A is a singular matrix.

Question 4.
Determine the value of a and b so that the following matrices are singular:

Solution:

expanding along R₁
b(4 + 4) + 7 (-6 – 1) = 0 (given)
8b + 7 (-7) = 0
(i.e.,) 8b – 49 = 0 ⇒ 8b = 49 ⇒ b = 49/8

Question 5.
If cos 2θ = 0, determine \(\left[\begin{array}{ccc}{\theta} & {\cos \theta} & {\sin \theta} \\ {\cos \theta} & {\sin \theta} & {0} \\ {\sin \theta} & {0} & {\cos \theta}\end{array}\right]^{2}\)
Solution:

Question 6.
Find the value of the product;
Sol:

Samacheer Kalvi 11th Maths Solutions Chapter 7 Matrices and Determinants Ex 7.4 Additional Problems

Question 1.
Identify the singular and non-singular matrix.

Solution:
If the determinant value of a square matrix is zero it is called a singular matrix. Otherwise it is non-singular.

Question 2.
Show that
Solution:

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.2

Question 1.
Verify whether the following ratios are direction cosines of some vector or not.

Solution:

Question 2.
Find the direction cosines of a vectors whose direction ratios are
(i) 1, 2, 3
(ii) 3, -1, 3
(iii) 0, 0, 7
Solution:

Question 3.
Find the direction cosines and direction ratios for the following vectors

Solution:

Question 4.
A triangle is formed by joining the points (1, 0, 0), (0, 1, 0) and (0, 0, 1). Find the direction cosines of the medians.
Solution:

Question 5.
If \(\frac{1}{2}, \frac{1}{\sqrt{2}}\), a are the direction cosines of some vector, then find a.
Solution:

Question 6.
If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c.
Solution:
Given (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0) then find a set of values of a, b, c.
Let the given points be A (1, 0, 0) and B (0, 1, 0)
[The direction ratios of the line joining the points A (x₁, y₁, z₁) and B (x₂, y₂, z₂) are x₂ – x₁, y₂ – y₁, z₂ – z₁ or x₁ – x₂, y₂ – y₂, z1,  z₁ – z₂ j
The direction ratios of the line joining the points A(1, 0, 0) and B(0, 1, 0) are
(0 – 1, 1 – 0, 0 – 0)
(- 1, 1, 0) ………. (1)
Also the direction ratios are
(1 – 0, 0 – 1, 0 – 0)
(1, -1, 0) ………. (2)
Given the direction ratios are
(a, a + b , a + b + c) ………. (3)
Comparing (1) and (3) we have
(-1, 1, 0) = (a, a + b, a + b + c)
a = -1, a + b = 1 ⇒ – 1 + b = 1 ⇒ b = 2
a + b + c = 0 ⇒ – 1 + 2 + c = 0 ⇒ c = – 1
Comparing (2) and (3) we get
a = 1 , a + b = – 1 ⇒ 1 + b = – 1 ⇒ b = – 2
a + b + c = 0 ⇒ 1 – 2 + c = 0 ⇒ c = 1
∴ The required set of values of a, b, c are
a = -1, b = 2, c = – 1 and
a = 1, b = – 2, c = 1

Question 7.
Show that the vectors \(2 \hat{i}-\hat{j}+\hat{k}, 3 \hat{i}-4 \hat{j}-4 \hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}\) form a right angled triangle.
Sol:

⇒ The given vectors form the sides of a right-angled triangle.

Question 8.
Find the value of k for which the vectors \(\vec{a}=3 \hat{i}+2 \hat{j}+9 \hat{k}\) and \(\vec{b}=\hat{i}+\lambda \hat{j}+3 \hat{k}\) are parallel.
Solution:

Question 9.
Show that the following vectors are coplanar.

Solution:
Let the given three vectors be \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\). When we are able to write one vector as a linear combination of the other two vectors, then the given vectors are called coplanar vectors.




We are able to write \(\vec{a}\) as a linear combination of \(\vec{b}\) and \(\vec{c}\)
∴ The vectors \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are coplanar

Question 10.
Show that the points whose position vectors and are coplanar
Solution:
Let the given points be A, B, C and D. To prove that the points A, B, C, D are coplanar, we have to prove that the vectors \(\overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AC}}\) and \(\overrightarrow{\mathrm{AC}}\) are coplanar



∴ we are able to write one vector as a linear combination of the other two vectors ⇒ the given vectors \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) are coplanar.
(i.e.,) the given points A, B, C, D are coplanar.

Question 11.
If \(\vec{a}=2 \hat{i}+3 \hat{j}-4 \hat{k}\), \(\vec{b}=3 \hat{i}-4 \hat{j}-5 \hat{k}\) and \(\vec{c}=-3 \hat{i}+2 \hat{j}+3 \hat{k}\), find the magnitude and direction cosines of
(i) \(\vec{a}+\vec{b}+\vec{c}\)
(ii) \(3 \vec{a}-2 \vec{b}+5 \vec{c}\)
Solution:

>

Question 12.
The position vectors of the vertices of a triangle are and . Find the perimeter of the triangle
Solution:
Let A, B, C be the vertices of the triangle ABC,

Question 13.
Find the unit vector parallel to and
Solution:

Question 14.
The position vector \(\vec{a}\), \(\vec{b}\), \(\vec{c}\) three points satisfy the relation \(2 \vec{a}-7 \vec{b}+5 \vec{c}=\overrightarrow{0}\). Are these points collinear?
Solution:

Question 15.
The position vectors of the points P, Q, R, S are and respectively. Prove that the line PQ and RS are parallel.
Solution:

Question 16.
Find the value or values of m for which \(m(\hat{i}+\hat{j}+\hat{k})\) is a unit vector
Solution:

Question 17.
Show that points A(1, 1, 1), B(1, 2, 3), and C(2, -1, 1) are vertices of an isosceles triangle.
Solution:

Samacheer Kalvi 11th Maths Solutions Chapter 8 Vector Algebra – I Ex 8.2 Additional Problems

Question 1.
Show that the points whose position vectors given by


Solution:

Question 2.
Find the unit vectors parallel to the sum of \(3 \hat{i}-5 \hat{j}+8 \hat{k}\) and \(-2 \hat{j}-2 \hat{k}\)
Solution:

Question 3.
The vertices of a triangle have position vectors Prove that the triangle is equilateral.
Solution:

Question 4.
Prove that the points form an equilateral triangle.
Solution:

Question 5.
Examine whether the vectors are coplanar
Solution:


⇒ We are not able to write one vector as a linear combination of the other two vectors
⇒ the given vectors are not coplanar.

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 1 Sets Ex 1.4

Question 1.
For the curve y = x³ given in Figure, draw
(i) r = -x³
(ii) y = x³ + 1
(iii) y = x³ – 1
(iv) y = (x + 1)³ with the same scale.





Solution:
(i) It is the reflection on y axis
(ii) The graph of y = x³ + 1 is shifted upward to 1 unit.
(iii) The graph of y = x³ – 1 is shifted downward to 1 unit.
(iv) The graph of y = (x + 1)³ is shifted to the left for 1 unit.

Question 2.

Solution:

Question 3.
Graph the functions f(x) = x³ and g(x) = \(\sqrt[3]{x}\) on the same coordinate plane. Find fog and graph it on the plane as well. Explain your results.
Solution:

Question 4.
Write the steps to obtain the graph of the function y = 3(x – 1)² + 5 from the graph y = x².
Solution:
Draw the graph of y = x²
To get y = (x – 1)² we have to shift the curve 1 unit to the right.
Then we have to draw the curve y = 3(x – 1)² and finally, we have to draw y = 3(x – 1)² + 5

Question 5.
From the curve y = sin x, graph the functions
(i) y = sin(-x)
(ii) y = -sin(-x)
(iii) y = sin (\(\frac{\pi}{2}\) + x) which is cos x
(iv) y = sin (\(\frac{\pi}{2}\) – x) which is also cos x (refer trigonometry)
Solution:
First we have to draw the curve y = sin x

(i) y = sin (-x) = – sin x = f(x)

(ii) y = -sin(-x) = -[-sin x] = sin x

Question 6.
From the curve y = x, draw
(i) y = -x
(ii) y = 2x
(iii) y = x + 1
(iv) y = \(\frac{1}{2}\)x + 1
(v) 2x + y + 3 = 0. 2
Solution:
y = x

(i) y = -x

(ii) y = 2x


y = 2x the graph moves away from the x-axis, as multiplying factor is 2 which is greater than one.

(iii) y = 2x + 1

(iv) y = 1/2x + 1


y = \(\frac{1}{2}\)x moves towards x – axis by a side factor \(\frac{1}{2}\) which is less than y = \(\frac{1}{2}\)x + 1 upwards by 1 unit.

(v) y = -2x – 3

Question 7.
From the curve y = |x|, draw
(i) y= |x – 1| + 1
(ii) y = |x + 1| – 1
(iii) y = |x + 2| – 3.
Solution:
Given, y = |x|
If y = x

If y = -x

(i) y = |x – 1| + 1
y = x – 1 + 1
y = -x + 1 + 1 = x

(ii) y = |x + 1| – 1
y = x + 1 – 1 = x
y = -x -1 – 1
y = -x – 2
y = – (x + 2)

(iii) y = |x + 2| – 3
y = x + 2 – 3 ⇒ x – 1
y = -x – 2 + 3 = 1 – x
y = -(x – 1)

Question 8.
From the curves = sin x, draw y = sin |x| (Hint: sin(-x) = -sin x.)
Solution:
y = sin |x|
∴ y = sin x
∴ y = sin (-x) = – sin x
y = – sin x

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 5 Binomial Theorem, Sequences and Series Ex 5.3

Question 1.
Find the sum of the first 20-terms of the arithmetic progression having the sum of first 10 terms as 52 and the sum of the first 15 terms as 77.
Solution:
Let ‘a’ be the first term and d be the common difference of A.P.

Question 2.

Solution:

Question 3.
Compute the sum of first n terms of the following series:
(i) 8 + 88 + 888 + 8888 + ……
(i) 6 + 66 + 666 + 6666 + …..
Solution:

Question 4.
Compute the sum of first n terms of 1 + (1 + 4) + (1 + 4 + 4²) + (1 + 4 + 4² + 4³) + ……..
Solution:

Question 5.
Find the general term and sum to n terms of the sequence \(1, \frac{4}{3}, \frac{7}{9}, \frac{10}{27}, \ldots \ldots \ldots\)
Solution:

Denominator 1, 3, 9, 27, which is a G.P. a = 1, r = 3

It is an arithmetico Geometric series. Here the n^th term is t_n = [a + (n – 1)d]r^{n – 1} where a = 1, d = 3 and r = 1/3
Now the sum to n terms is

Question 6.

Solution:

Question 7.
Show that the sum of (m + n)^th and (m – n)^th term of an A.P. is equal to twice the m^th term.
Solution:
The n^th term of an A.P is T_n = a + (n – 1) d
T_m+n = a + (m + n – 1) d
T_m-n = a + (m – n – 1) d
T_m+n + T_m-n = a + (m + n – 1) d + a + (m – n – 1)d
= 2a + [m + n – 1 + m – n – 1) d
= 2a + [2m – 2] d
= 2a + 2 (m – 1) d
= 2 [a + (m – 1] d
T_m+n + T_m-n = 2T_m
Hence the sum of the ( m + n)^th term and ( m – n)^th term of A.P is equal to twice the m^th term.

Question 8.
A man repays an amount of ₹ 3250 by paying ₹ 20 in the first month and then increases the payment by ₹ 15 per month. How long will it take him to clear the amount?
Solution:
a = 20, d = 15, S_n = 3250 to find n.

3n² + 5n – 1300 = 0
3n² – 60n + 65n – 1300 = 0
3n (n – 20) + 65 (n – 20) = 0
(3n + 65) (n – 20) = 0
n = – 65/3 or 20
n = – 65/3 is not possible
∴ n = 20
So he will take 20 months to clear the amount.

Question 9.
In a race, 20 balls are placed in a line at intervals of 4 meters with the first ball 24 meters away from the starting point. A contestant is required to bring the balls back to the starting place one at a time. How far would the contestant run to bring back all balls?
Solution:
t₁ = 24 × 2 = 48, t₂ =48 + 8 = 56 or (24 + 4)2, t₃ =(28 + 4)2 = 64 which is an A.P.
Here a = 48,
d = 56 – 48 = 8

The contestant has to run 2480 m to bring all the balls.

Question 10.
The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of the 2^nd hour, 4^th hour, and n^th hour?
Solution:
Number of bacteria present initially = 30
Number of bacteria at the end of 1 hour = 2 × 30 = 60
Number of bacteria at the end of two hours = 2 × 60 = 120
Number of bacteria at the end of three hours = 2 × 120 = 240
Number of bacteria at the end of four hours = 2 × 240 = 480

∴ The sequence of a number of bacterias at the end of every hour is
30, 60, 120, 240, 480, …………………………..
30, 30 × 2, 30 × 4, 30 × 8, 30 × 16, …………………
30, 30 × 2, 30 × 2², 30 × 2³, 30 × 2⁴, …………………
This sequence is a Geometric sequence with first term a = 30, common ratio r = 2
Number of bacteria at the end of n^th hour t_n+1 = a. rⁿ
t_n+1 = 30(2ⁿ)
Number of bacteria at the end of 2^nd hour = 120
Number of bacteria at the end of 4^th hours = 480
Number of bacteria at the end of n^th hour = 30(2ⁿ)

Question 11.
What will ₹ 500 amount to in 10 years after its deposit in a bank which pays an annual interest rate of 10% compounded annually?
Solution:

Question 12.
In a certain town, a viral disease caused severe health hazards upon its people disturbing their normal life. It was found that on each day, the virus which caused the disease spread in Geometric Progression. The amount of infectious virus particle gets doubled each day, being 5 particles on the first day. Find the day when the infectious virus particles just grow over 1,50,000 units?
Solution:
a = 5, r = 2, t_n >150000, To find ‘n’

On the 15^th day it will grow over 150000 units.

Samacheer Kalvi 11th Maths Solutions Chapter 5 Binomial Theorem, Sequences and Series Ex 5.3 Additional Questions

Question 1.
If the ratio of the sums of m terms and n terms of an A.P. be m² : n², prove that the ratio of its m^th and n^th terms is (2m – 1) : (2n – 1).
Solution:
Let ‘a’ be the first term and d be the common difference of A.P.

⇒ 2an + (mn – n)d = 2am + (mn – m)d
⇒ 2an – 2am = (mn – m – mn + n)d
⇒ 2a(n – m) = (n – m)d ⇒ d = 2a, [n – m ≠ 0, as n ≠ m]

Hence, the required ratio is (2m – 1) : (2n – 1)

Question 2.
Determine the number of terms of geometric progression {a_n} if a₁ = 3, a_n = 96, S_n = 189.
Solution:

Question 3.
The sum of first three terms of a G.P. is to the sum of the first six terms as 125 : 152. Find the common ratio of the G.P.
Solution:

Hence, the common ratio of the G.P. is \(\frac{3}{5}\)

Question 4.
Find the sum to n terms the series: (x + y) + (x² + xy + y²) + (x³ + x²y + xy² + y³) + …
Solution:
(x + y) + (x² + xy + y²) + (x³ + x²y + xy² + y³) + … to n terms

Question 5.
Sum the series: (1 + x) + (1 + x + x²) + (1 + x + x² + x³) + … up to n terms
Solution:

Question 6.
Sum up to n terms the series: 7 + 77 + 777 + 7777 + …
Solution:
S = 1 + 77 + 777 + 7777 + … to n terms

Question 7.
If S₁, S₂, S₃ be respectively the sums of n, 2n, 3n, terms of a G.P. , then prove that S₁(S₃ – S₂) = (S₂ – S₁)₂.
Solution:
Let a be the first term and r be the common ratio of G.P.

Question 8.
If the sum of the n terms of a G.P be S, their product P and the sum of their reciprocals R, the prove that \(P^{2}=\left(\frac{S}{R}\right)^{n}\)
Solution:
Let a be the first term and r be the common ratio of the G.P.

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 4 Combinatorics and Mathematical Induction Ex 4.5

Question 1.
The sum of the digits at the 10th place of all numbers formed with the help of 2, 4, 5, 7 taken all at a time is ……..
(a) 432
(b) 108
(c) 36
(d) 18
Solution:
(b) 108
Hint.
The given digits are 2, 4, 5 ,7
The unit place can be filled with the digit 2. Then the remaining Ten’s , hundred’s, Thousand’s place can be filled with the remaining three digits 4, 5, 7 in 3P₃ ways.
∴ There will be 3 × 2 × 1 = 6 four digit numbers whose unit place is 2.
Similarly, there are 6 four digit numbers whose unit place is 4 , 6 four digit numbers whose unit place is 5 and 6 four digit numbers whose unit place is 7.
∴ Total in the unit place
= 6 × 2 + 6 × 4 + 6 × 5 + 6 × 7
= 6 × (2 + 4 + 5 + 7)
= 6 × 18 = 108
Sum of the digit at the unit place = 108
∴ Sum of the digit at the tens place = 108

Question 2.
In an examination, there are three multiple-choice questions and each question has 5 choices. A number of ways in which a student can fail to get all answer correct is ……..
(a) 125
(b) 124
(c) 64
(d) 63
Solution:
(b) 124
Hint.
Each question has 5 options in which 1 is correct.
So the number of ways of getting the correct answer for all three questions is 5³ = 125
So the number of ways in which a student can fail to get all answer correct is < 125 (i.e.) 125 – 1 = 124

Question 3.
The number of ways in which the following prize be given to a class of 30 boys first and second in mathematics, first and second in physics, first in chemistry and first in English is ……….
(a) 30⁴ × 29²
(b) 30³ × 29³
(c) 30² × 29⁴
(d) 30 × 29⁵
Solution:
(a) 30⁴ × 29²
Hint.
Number of students = 30
First prize can be given to any one of 30 students
= 30 × 30 × 30 × 30 = 30⁴ ways
Second prize can be given to anyone of the remaining 29 students = 29 × 29 = 29² ways
∴ Total number of ways prizes can be given = 30⁴ × 29² ways

Question 4.
The number of 5 digit numbers all digits of which are odd is ………
(a) 25
(b) 5⁵
(c) 5⁶
(d) 625
Solution:
(b) 5⁵
Hint. The odd number are 1, 3, 5, 7, 9
Number of odd numbers = 5
We need a five-digit number So the number of five-digit number = 5⁵

Question 5.
In 3 fingers, the number of ways four rings can be worn is …… ways.
(a) 4³ – 1
(b) 3⁴
(c) 68
(d) 64
Solution:
(b) 3⁴
Hint.
Number of rings = 4
Each finger can be worn rings in 4 ways.
∴ Number of ways of wearing four rings in three fingers
= 4 × 4 × 4
= 64

Question 6.

(a) 7 and 11
(b) 6 and 7
(c) 2 and 11
(d) 2 and 6
Solution:
(b) 6 and 7

Question 7.
The product of r consecutive positive integers is divisible by ………
(a) r!
(b) (r – 1)!
(c) (r + 1)!
(d) r!
Solution:
(a) r!
Hint.
The product of r consecutive positive integers is
1 × 2 × 3 × …………… × r = r!
which is divisible by r!
Also, 1 × 2 × 3 × …………… × r = r!
= ( r – 1) ! × r
which is divisible by (r – 1) !

Question 8.
The number of 5 digit telephone numbers which have none of their digits repeated is
(a) 90000
(b) 10000
(c) 30240
(d) 69760
Solution:
(d) 69760
Hint.
The number of 5 digit telephone numbers which have none of their digits repeated is ¹⁰P₅ = 30240
Thus the required telephone number is 10⁵ – 30240 = 69760

Question 9.
If a² – ^aC₂ = a² – ^aC₄ then the value of ‘a’ is ….
(a) 2
(b) 3
(c) 4
(d) 5
Solution:
(b) 3
Hint.
a₂ – a = 2 + 4 = 6
a₂ – a – 6 = 0
(a – 3) (a + 2) = 0 ⇒ a = 3

Question 10.
There are 10 points in a plane and 4 of them are collinear. The number of straight lines joining any two points is ……..
(a) 45
(b) 40
(c) 39
(d) 38
Solution:
(b) 40
Hint.

Question 11.
The number of ways in which a host lady invite 8 people for a party of 8 out of 12 people of whom two do not want to attend the party together is
(a) 2 × ¹¹C₇ + ¹⁰C₈
(b) ¹¹C₇ + ¹⁰C₈
(c) ¹²C₈ – ¹⁰C₆
(d) ¹⁰C₆ + 2!
Solution:
(c) ¹²C₈ – ¹⁰C₆
Hint.
Number of the way of selecting 8 people from 12 in ¹²C₈
∴ out of the remaining people, 8 can attend in ¹⁰C₈
The number of ways in which two of them do not attend together = ¹²C₈ – ¹⁰C₆

Question 12.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of three parallel lines …….
(a) 6
(b) 9
(c) 12
(d) 18
Solution:
(d) 18
Hint.
Number of parallelograms = ⁴C₂ × ³C₂ = 6 × 3 = 18

Question 13.
Everybody in a room shakes hands with everybody else. The total number of shake hands is 66. The number of persons in the room is …….
(a) 11
(b) 12
(c) 10
(d) 6
Solution:
(b) 12
Hint.

Question 14.
The number of sides of a polygon having 44 diagonals is ……….
(a) 4
(b) 4!
(c) 11
(d) 22
Solution:
(c) 11
Hint:

Question 15.
If 10 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then the total number of points of intersection are ………
(a) 45
(b) 40
(c) 10!
(d) 2¹⁰
Solution:
(a) 45
Hint:

Question 16.
In a plane there are 10 points are there out of which 4 points are collinear, then the number of triangles formed is …….
(a) 110
(b) ¹⁰C₃
(c) 120
(d) 116
Solution:
(d) 116
Hint:

Question 17.
In ²ⁿC₃ : ⁿC₃ = 11 : 1 then n is ………
(a) 5
(b) 6
(c) 11
(d) 1
Solution:
(b) 6
Hint.

Question 18.
^{(n – 1)}C_r + ^{(n – 1)}C_{(r – 1)} is ………
(a) ^{(n + 1)}C_r
(b) ^{(n – 1)}C_r
(c) ⁿC_r
(d) ⁿC_{r – 1}
Solution:
(c) ⁿC_r

Question 19.
The number of ways of choosing 5 cards out of a deck of 52 cards which include at least one king is …….
(a) ⁵²C₅
(b) ⁴⁸C₅
(c) ⁵²C₅ + ⁴⁸C₅
(d) ⁵²C₅ – ⁴⁸C₅
Solution:
(d) ⁵²C₅ – ⁴⁸C₅
Hint.
Selecting 5 from 52 cards = ⁵²C₅
selecting 5 from the (non-king cards 48) = ⁴⁸C₅
∴ Number of ways is ⁵²C₅ – ⁴⁸C₅

Question 20.
The number of rectangles that a chessboard has ……
(a) 81
(b) 99
(c) 1296
(d) 6561
Solution:
(c) 1296
Hint. Number of horizontal times = 9
Number of vertical times = 9
Selecting 2 from 9 horizontal lines = ⁹C₂
Selecting 2 from 9 vertical lines = ⁹C₂

Question 21.
The number of 10 digit number that can be written by using the digits 2 and 3 is ……..
(a) ¹⁰C₂ + ⁹C₂
(b) 2¹⁰
(c) 2¹⁰ – 2
(d) 10!
Solution:
(b) 2¹⁰
Hint.
Selecting the number from (2 and 3)
For till the first digit can be done in 2 ways
For till the second digit can be done in 2 ways ….
For till the tenth digit can be done in 2 ways
So, total number of ways in 10 digit number = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁰

Question 22.
If P_r stands for ^rP_r then the sum of the series 1 + P₁ + 2P₂ + 3P₃ + … + nP_n is ……..
(a) P_{n + 1}
(b) P_{n + 1} – 1
(c) P_{n – 1} + 1
(d) ^{(n + 1)}P_{(n – 1)}
Solution:
(b) P_{n + 1} – 1
Hint:
1 + 1! + 2! + 3! + … + n!
Now 1 + 1 (1!) = 2 = (1 + 1)!
1 + 1 (1!) + 2(2!) = 1 + 1 + 4 = 6 = 3!
1 + 1(1!) + 2(2!)+ 3(3!) = 1 + 1 + 4 + 18 = 24 = 4!
1 + 1(1!) + 2(2!) + 3(3!) ….+ n(n!) = (n + 1) ! – 1
= ^{n + 1}P_{n + 1} – 1 = P_{n + 1} – 1

Question 23.
The product of first n odd natural numbers equals …….

Solution:

Hint:

Question 24.
If ⁿC₄, ⁿC₅, ⁿC₆ are in AP the value of n can be ………..
(a) 14
(b) 11
(c) 9
(d) 5
Solution:
(a) 14
Hint:

30 + n² – 9n + 20 – 12n + 48 = 0
n² – 21 n + 98 = 0
(n – 7) (n – 14) = 0
n = 7 (or) 14

Question 25.
1 + 3 + 5 + 7 + + 17 is equal to ………
(a) 101
(b) 81
(c) 71
(d) 61
Solution:
(b) 81
Hint:

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 4 Combinatorics and Mathematical Induction Ex 4.2

Question 1.
If ^{(n – 1)} P₃ : ⁿP₄, find n:
Solution:

Question 2.
If ¹⁰P_{r – 1} = 2 × ⁶P_r, find r.
Solution:

Question 3.
(i) Suppose 8 people enter an event in a swimming meet. In how many ways could the gold, silver, and bronze prizes be awarded?
Solution:
Number people enter in a swimming meet = 8 Prizes awarded = Gold, silver, bronze.
The gold medal can be awarded to any one of the 8 people in 8 ways. The silver medal can be awarded to any one of the remaining 7 people in 7 ways. The bronze medal can be awarded to any one of the remaining 6 people in 6 ways,
∴ Total number of ways of awarding the prizes = 8 × 7 × 6 = 336

(ii) Three men have 4 coats, 5 waistcoats, and 6 caps. In how many ways can they wear them?
Solution:
Selecting and arranging 3 coats from 4 can be done in ⁴P₃ ways
Selecting and arranging 3 waistcoats from 5 can be done in ⁵P₃ ways Selecting and arranging 3 caps from 6 can be done in ⁶P₃ ways
∴ Total number of ways = ⁴P₃ × ⁵P₃ × ⁶P₃ = 172800 ways

Question 4.
Determine the number of permutations of the letters of the word SIMPLE if all are taken at a time?
Solution:
Number of letters in the word SIMPLE = 6
The total number of the word is equal to the number of arrangements of these letters, taken all at a time
∴ Total number of words = 6P₆ = 6!
= 6 × 5 × 4 × 3 × 2 × 1
= 720

Question 5.
A test consists of 10 multiple-choice questions. In how many ways can the test be answered if

(i) Each question has four choices?
Solution:
Total number of questions = 10
Each question has four choices.
Each question can be answered in 4 ways.
∴ The total number of ways of answering 10 questions
= 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4
= 4¹⁰

(ii) The first four questions have three choices and the remaining have five choices?
Solution:
The first four questions have three choices and the remaining have five choices
First, four questions have three choices.
∴ The number of ways of answering the first four questions is = 3 × 3 × 3 × 3 = 3⁴
The remaining six questions have 5 choices
∴ The number of ways of answering the remaining 6 questions is = 5 × 5 × 5 × 5 × 5 × 5 = 5⁶
∴ The total number of ways of answering the questions = 3⁴ × 5⁶

(iii) Question number n has n + 1 choices?
Solution:
Question number n has n + 1 choices.
The first question has a 1 + 1 choice.
∴ Number of ways of answering the first question = 2
The second question has 2 + 1 choices
∴ Number ways of answering second question = 3

Tenth question has (10 + 1) choices
∴ Number of ways of answering tenth question = 11
∴ A total number of ways of answering the given 10 questions = 2 × 3 × 4 × ……. × 11 = 11!

Question 6.
A student appears in an objective test which contain 5 multiple-choice questions. Each question has four choices out of which one correct answer.

(i) What is the maximum number of different answers can the students give?
Solution:
Number multiple-choice questions = 5
Number of ways of answering each question = 4
∴ The total number of ways of answering the five questions = 4 × 4 × 4 × 4 × 4 = 45
Hence, the maximum number of different answers = 4⁵

(ii) How will the answer change if each question may have more than one correct answers?
Solution:
When each question has more than 1 correct answer.
Selecting the correct choice from the 4 choice can be done is ⁴C₁ or ⁴C₂ or ⁴C₃ or ⁴C₄ ways.

Each question can be answered in 15 ways.
Number of questions = 5
∴ Total number of ways = 15⁵

Question 7.
How many strings can be formed from the letters of the word ARTICLE, so that vowels occupy the even places?
Solution:
The given word is ARTICLE
Number of letters in the word = 7
Vowels in the given word = A, I, E
Number of vowels in the given word = 3

∴ Number of even places = 3
3 Vowels can occupy the 3 even places in 3P3 = 3! ways
The remaining 4 letters can occupy the remaining places in
4P₄ = 4! ways
Hence a total number of ways of arrangement = 4! × 3! = 4 × 3 × 2 × 3 × 2 = 144

Question 8.
8 women and 6 men are standing in a line.
(i) How many arrangements are possible if any individual can stand in any position?
Solution:
Total number of persons in a line = 8 + 6 = 14
The number of ways of standing 14 persons in a line in any position = 14P₁₄ = 14!

(ii) In how many arrangements will all 6 men be standing next to one another?
Solution:
Consider 6 men as one unit.
8 women + 6 men as one unit = 9 can be arranged in 9! ways.
6 men can among themselves be arranged in 6! ways.
∴ A total number of ways of arrangement = 9! × 6!

(iii) In how many arrangements will no two men be standing next to one another?
Solution:
Since no two men be together they have to be placed between 8 women and before and after the women.
w | w | w | w | w | w | w | w
There are 9 places so the 6 men can be arranged in the 9 places in ⁹P₆ ways.
After this arrangement, the 8 women can be arranged in 8! ways.
∴ Total number of arrangements = (⁹P₆) × 8!

Question 9.
Find the distinct permutations of the letters of the word MISSISSIPPI?
Solution:
MISSISSIPPI
Number of letters = 11
Here M – 1 time
I – 4 times
S – 4 times
P – 2 times

Question 10.
How many ways can the product a2b3c4 be expressed without exponents?
Solution:
a²b³c⁴ = aabbbcccc
Number of letters = 9
a = 2 times,
b = 3 times,
c = 4 times,

Question 11.
In how many ways 4 mathematics books, 3 physics books, 2 chemistry books and 1 biology book can be arranged on a shelf so that all books of the same subjects are together.
Solution:
Number of subjects = 4
4 subjects can be arranged in the shelf in 4! ways Number of mathematics books = 4
4 Mathematics books keeping together can be arranged in 4! ways
Number of physics books = 3
3 Physics books keeping together can be arranged in 3! ways.
Number of chemistry books =2
2 Chemistry books keeping together can be arranged in 2! ways.
Number of biology books = 1
1 biology book can be arranged in 1! way
Hence, the total numbers of ways of arranging the books
= 4! × 4! × 3! × 2! × 1!
= (4 × 3 × 2 × 1) (4 × 3 × 2 × 1) × (3 × 2) (2 × 1)
= 24 × 24 × 6 × 2
= 6912

Question 12.
In how many ways can the letters of the word SUCCESS be arranged so that all Ss are together?
Solution:
The given word is SUCCESS
Number of letters other than S = 4
Treating all S’s together as one letter
Total number of letters in the word = 5
Number of U’s = 1
Number of C’s = 2
Number of E’s = 1
Number of S’s (treated as one letter ) = 1
Number of ways of arranging = \(\frac{5 !}{2 ! \times 1 ! \times 1 ! \times 1 !}\)
= \(\frac{5 \times 4 \times 3 \times 2 \times 1}{2 \times 1}\)
= 5 × 4 × 3
= 60 ways

Question 13.
A coin is tossed 8 times,

(i) How many different sequences of heads and tails are possible?
Solution:
Number of coins tossed = 8
Number of outcome for each toss = 2
Total number of outcomes = 28

(ii) How many different sequences containing six heads and two tails are possible?
Solution:
Getting 6 heads and 2 tails can be done in ⁸P₆ or ⁸P₂ ways

Question 14.
How many strings are there using the letters of the word INTERMEDIATE, if

(i) The vowels and consonants are alternative
Solution:
INTERMEDIATE

The number of ways in which vowels and consonants are alternative = \(\frac{6 ! 6 !}{3 ! 2 !}=\) 43200

(ii) All the vowels are together
Solution:
The number of arrangements:
Keeping all the vowels as a single unit. Now we have 6 + 1 = 7 units which can be arranged in 7! ways.
Now the 6 consonants can be arranged in \(\frac{6 !}{2 !}\) (T occurs twice) ways in vowels, I – repeats thrice
and E – repeats twice

(iii) Vowels are never together (and) (iv) No two vowels are together.
Solution:
Vowels should not be together = No. of all arrangements – No. of all vowels together

So number of ways in which No two vowels are together = 19958400 – Number of ways in which vowels are together = 19958400 – 151200 = 19807200

Question 15.
Each of the digits 1,1, 2, 3, 3 and 4 is written on a separate card. The seven cards are then laid out in a row to form a 6-digit number.

(i) How many distinct 6-digit numbers are there?
Solution:
The given digits are 1, 1, 2, 3, 3, 4
The 6 digits can be arranged in 6! ways
In which 1 and 3 are repeated twice.

(ii) How many of these 6-digit numbers are even?
Solution:
To find the number even numbers
The digit in unit place is 2 or 4 which can be filled in 2 ways

(iii) How many of these 6-digit numbers are divisible by 4?
Solution:
To get a number -f- by 4 the last 2 digits should be -r- by 4 So the last two digits will be 12 or 24 or 32.
When the last 2 digits are 1 and 2.

When the last 2 digits are 3 and the number of 6 digit numbers (remaining number 1, 1, 3, 4)
So there of 6 digit numbers ÷ by 4 = 12 + 6 + 12 = 30

Question 16.
If the letters of the word GARDEN are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, then find the ranks of the words
(i) GARDEN
(ii) DANGER.
Solution:
The given letters are GARDEN.
To find the rank of GARDEN:
The given letters in alphabetical order are A D E G N R

The rank of GARDEN is 379
To find the rank of DANGER

(ii) The No. of words starting with A = 5! =120

Question 17.
Find the number of strings that can be made using all letters of the word THING. If these words are written as in a dictionary, what will be the 85^th string?
Solution:
(i) Number of words formed = 5! = 120
(ii) The given word is THING
Taking the letters in alphabetical order G H I N T
To find the 85^th word

Question 18.
If the letters of the word FUNNY are permuted in all possible ways and the strings thus formed are arranged in the dictionary order, find the rank of the word FUNNY.
Solution:
The given word is FUNNY

Question 19.
Find the sum of all 4-digit numbers that can be formed using digits 1, 2, 3, 4, and 5 repetitions not allowed?
Solution:
The given digits are 1, 2, 3, 4, 5
The no. of 4 digit numbers

Sum of the digits = 1 + 2 + 3 + 4 + 5 = 15
Sum of number’s in each place = 24 × 15 = 360

Question 20.
Find the sum of all 4-digit numbers that can be formed using digits 0, 2, 5, 7, 8 without repetition?
Solution:
The given digits are 0, 2, 5, 7, 8
To get the number of 4 digit numbers
1000’s place can be filled in 4 ways (excluding 0)
100’s place can be filled in 4 ways (excluding one number and including 0)
10’s place can be filled in (4 – 1) = 3 ways
and unit place can be filled in (3 – 1) = 2 ways
So the number of 4 digit numbers = 4 × 4 × 3 × 2 = 96

To find the sum of 96 numbers:

In 1000’s place we have the digits 2, 5, 7, 8. So each number occurs \(\frac{96}{4}\) = 24 times.
Now in 100’s place 0 come 24 times. So the remaining digits 2, 5, 7, 8 occurs 96 – 24 = \(\frac{72}{4}\) = 18 times
Similarly in 10’s place and in-unit place 0 occurs 24 times and the remaining digits 2, 5, 7, 8 occurs 18 times.
Now sum of the digits = 2 + 5 + 7 + 8 = 22
Sum in 1000’s place = 22 × 24 = 528
Sum in 100’s, 10’s and in unit place = 22 × 18 = 396
∴ Sum of the 4 digit numbers is

Samacheer Kalvi 11th Maths Solutions Chapter 4 Combinatorics and Mathematical Induction Ex 4.2 Additional Questions

Question 1.

Solution:

Question 2.
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7 if no digit is repeated?
Solution:
Here total number of digits = 6
The unit place can be filled with any one of the digits 2, 4, 6.

Question 3.
Find n if ^{n – 1}P₃ : ⁿP₄ = 1 : 9
Solution:

Question 4.
How many words can be formed by using the letters of the word ORIENTAL so that A and E always occupy the odd places?
Solution:
[Hint: There are 4 odd places in the word]

Now the remaining 6 places filled with remaining 6 letters

Hence the total number of permutations = 12 × 720 = 8640

Question 5.
Out of 18 points in a plane, no three are in the same line except five points which are collinear. Find the number of lines that can be formed joining the points.
Solution:
Total number of points = 18
Out of 18 numbers, 5 are collinear and we get a straight line by joining any two points.
∴ Total number of straight-line formed by joining 2 points out of 18 points = ¹⁸C₂
Number of straight lines formed by joining 2 points out of 5 points = ⁵C₂
But 5 points are collinear and we get only one line when they are joined pairwise.
So, the required number of straight lines are

Hence, the total number of straight lines = 144

Question 6.
We wish to select 6 person from 8 but, if the person A is chosen, then B must be chosen. In how many ways can selections be made?
Solution:
Total number of persons = 8
Number of persons to be selected = 6
Condition is that if A is chosen, B must be chosen

Case I: When A is chosen, B must be chosen
Number of ways = ⁶C₄
[∴ A and B are set to be choosen]

Case II: When A is not chosen, then B may be chosen
∴ Number of ways = ⁷C₆

Hence, the required number of ways = 22

Question 7.
How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?
Solution:
For 3-digit even numbers, the unit’s place can be occupied by one of the 3 digits 2, 4 or 6. The remaining 5 digits can be arranged in the remaining 2 places in ⁵P₂ ways.

∴ By the multiplication rule, the required number of 3-digit even numbers is 3 × ⁵P₂ = 3 × 5 × 4 = 60.

Question 8.
Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?
Solution:
For 4 digit numbers, we have to arrange the given 5 digits in 4 vacant places. This can be done in ⁵P₄ = 5 × 4 × 3 × 2 = 120 ways.

For 4-digit even numbers, the unit’s place can be occupied by one of the 2 digits 2 or 4. The remaining 4 digits can be arranged in the remaining 3 places in ⁴P₃ ways.
∴ By the multiplication rule, the required number of 4-digit even numbers is 2 × ⁴P₃ = 2 × 4 × 3 × 2 = 48.

Question 9.
Find r if

(i) ⁵P_r = 2 ⁶P_{r – 1} 4
Solution:

(ii) ⁵P_r = ⁶P_{r – 1}

⇒ 42 – 13r + r² = 6 ⇒ r² – 13r + 36 = 0
⇒ (r – 4)(r – 9) = 0 ⇒ r = 4, 9
Now, we know that ⁿP_r is meaningful only when r ≤ n.
∴ ⁵P_r and ⁶P_{r – 1} are meaningless when r ≤ 9.
∴ Rejecting r = 9, we have r = 4

Question 10.
How many words, with or without meaning, can be made from the letters of the word MONDAY, assuming that no letter is repeated, if

(i) 4 letters are used at a time
(ii) all letters are used at a time
(iii) all letters are used but first letter is a vowel?
Solution:
The word MONDAY has 6 distinct letters.

(i) 4 letters out of 6 can be arranged in ⁶P₄ ways.
∴ The required number of words = ⁶P₄ = 6 × 5 × 4 × 3 = 360

(ii) 6 letters can be arranged among themselves in 6P6 ways.
∴ The required number of words = ⁶P₆ = 6! = 1 × 2 × 3 × 4 × 5 × 6 = 720.

(iii) The first place can be filled by anyone Of the two vowels O or A in 2 ways. The remaining 5 letters can be arranged in the remaining 5 places II to VI in ⁵P₅ = 5! ways.
∴ By the multiplication rule, the required number of words = 2 × 5! = 2 × 1 × 2 × 3 × 4 × 5 = 240

You can Download Samacheer Kalvi 11th Maths Book Solutions Guide Pdf, Tamilnadu State Board help you to revise the complete Syllabus and score more marks in your examinations.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 6 Two Dimensional Analytical Geometry Ex 6.2

Question 1.
Find the equation of the lines passing through the point (1, 1)
(i) With y-intercept (- 4)
(ii) With slope 3
(iii) And (-2, 3)
(iv) And the perpendicular from the origin makes an angle 60° with x-axis.
Solution:
(i) Given y intercept = – 4,
Let x intercept be a

(ii) with slope 3
The equation the line passing through the point (x₁, y₁) and having slope m is
y – y₁ = m(x – x₁)
Given (x₁, y₁) = (1, 1), m = 3
∴ The required equation of the line is
y – 1 = 3(x – 1)
y – 1 = 3x – 3
3x – y – 3 + 1 = 0
3x – y – 2 = 0

(iii) Passing through (1, 1) and (-2, 3)

Question 2.
If P (r, c) is mid point of a line segment between the axes, then show that \(\frac{x}{r}+\frac{y}{c}=\) 2.
Solution:
P (r, c) is the midpoint of AB.
⇒ A = (2r, 0) and B = (0, 2c)
(i.e) x intercept = 2r and
y intercept = 2c .

Question 3.
Find the equation of the line passing through the point (1, 5) and also divides the co-ordinate axes in the ratio 3 : 10.
Solution:
Let x-intercept be 3a and y-intercept be 10a

Question 4.
If p is length of perpendicular from origin to the line whose intercepts on the axes are a and b, then show that \(\frac{1}{p^{2}}=\frac{1}{a^{2}}+\frac{1}{b^{2}}\)
Solution:

Question 5.
The normal boiling point of water is 100°C or 212°F and the freezing point of water is 0°C or 32°F.
(i) Find the linear relationship between C and F
(ii) Find the value of C for 98.6° F and
(iii) The value of F for 38°C.
Solution:
Given when C = 100, F = 212 and when C = 0, F = 32

Question 6.
An object was launched from a place P in constant speed to hit a target. At the 15th second, it was 1400m away from the target and at the 18th second 800m away. Find
(i) The distance between the place and the target
(ii) The distance covered by it in 15 seconds,
(iii) Time is taken to hit the target.
Solution:
Taking time = x and distance = y
We are given at x = 15, y = 1400 and at x = 18, y = 800

Question 7.
The population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant).
Solution:
Taking the year as x and population as y
We are given when x = 2005,
y = 1,35,000 and
when x = 2010,
y = 1,45,000

y – 135000 = 2000 (x – 2005)
y = 2000(x – 2005) + 135000
At x = 2015, y = 2000 (2015 – 2005) + 135000
(i.e) y = 2000 (10) + 135000 = 20000 + 135000 = 1,55,000
The approximate population in the year 2015 is 1,55,000

Question 8.
Find the equation of the line, if the perpendicular drawn from the origin makes an angle 30° with x – axis and its length is 12.
Solution:
The equation of the line is x cos α + y sin α = p

Question 9.
Find the equation of the straight lines passing through (8, 3) and having intercepts whose sum is 1.
Solution:
Given sum of the intercepts = 1 ⇒ when x-intercept = a then y-intercept = 1 – a

8 (1 – a) + 3a = a (1 – a)
8 – 8a + 3a = a – a²

Question 10.

Solution:

⇒ The points A, B, C lie on a line
⇒ The points A, B, C are collinear

Question 11.
A straight line is passing through the point A (1, 2) with slope \(\frac{5}{12}\). Find points on the line which are 13 units away from A.
Solution:

Question 12.
A 150m long train is moving with a constant velocity of 12.5 m/s. Find
(i) The equation of the motion of the train,
(ii) Time taken to cross a pole,
(iii) The time taken to cross the bridge of length 850 m is?
Solution:
(i) Now m = \(\frac{y}{x}\) = 12.5m / second,
The equation of the line is y = mx + c ….(1)
Put c = -150, m = 12.5 m,
The equation of motion of the train is y = 12.5x – 150

(ii) To find the time taken to cross a pole we take y = 0 in (1)
⇒ 0 = 12.5x – 150 ⇒ 12.5x = 150

(iii) When y = 850 in (1)
850 = 12.5 x – 150 ⇒ 12.5x = 850 + 150 = 1000

Question 13.
A spring was hung from a hook in the ceiling. A number of different weights were attached to the spring to make it stretch, and the total length of the spring was measured each time shown in the following table.

(i) Draw a graph showing the results.
(ii) Find the equation relating the length of the spring to the weight on it.
(iii) What is the actual length of the spring.
(iv) If the spring has to stretch to 9 cm long, how much weight should be added?
(v) How long will the spring be when 6 kilograms of weight on it?
Solution:
Taking weight (kg) as x values and length (cm) as y values we get (x₁, y₁) = (2, 3), (x₂, y₂) = (4, 4)

The equation of the line passing through the above two points is

(iii) When x = 0, 2y = 4 ⇒ y = 2 cm

(iv) When y = 9 cm, x – 18 = – 4
x = -4 + 18 = 14 kg

(v) When x = 6 (kg), 6 – 2y = – 4, -2y = -4 – 6 = -10
⇒ 2y = 10 ⇒ y = 10/2 = 5 cm.

Question 14.
A family is using Liquefied petroleum gas (LPG) of weight 14.2 kg for consumption. (Full weight 29.5 kg includes the empty cylinders tare weight of 15.3 kg.). If it is used at a constant rate then it lasts for 24 days. Then the new cylinder is replaced
(i) Find the equation relating the quantity of gas in the cylinder to the days.
(ii) Draw the graph for the first 96 days.
Solution:

Question 15.
In a shopping mall, there is a hall of cuboid shape with dimension 800 × 800 × 720 units, which needs to be added the facility of an escalator in the path as shown by the dotted line in the figure. Find
(i) The minimum total length of the escalator,
(ii) The heights at which the escalator changes its direction,
(iii) The slopes of the escalator at the turning points.

Solution:
(i) the minimum total length of the escalator.
Shape of the hall in the shopping mall is cuboid. When you open out the cuboid, the not of the cuboid will be as shown in the following diagram.

The path of the escalator is from OA to AB to BC to CD

The minimum length = 3280 units

(ii) The height at which the escalator changes its direction.

(iii) Slope of the escalator at the turning points

Since ∆OAE = ∆ABB’ = ∆BCC’ = ∆CAD
Slope at the points B, C will be \(\frac{9}{40}\)

Samacheer Kalvi 11th Maths Solutions Chapter 6 Two Dimensional Analytical Geometry Ex 6.2 Additional Questions Solved

Question 1.
Find the equation of a straight line on which length of the perpendicular from the origin is four units and the line makes an angle of 120° with the positive direction of the x-axis.
Solution:

Question 2.
Find the equation of the line which passes through the point (- 4, 3), and the portion of the line intercepted between the axes is divided internally in the ratio 5 : 3 by this point.
Solution:
Let AB be a line passing through a point (-4, 3) and meets the x-axis at A (a, 0) and the y-axis at B (0, b).

Question 3.
If the intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1 : 2, then find the equation of the line.
Solution:
Let a and b be the intercepts on the given line.


Hence, the required equation is 8x – 5y + 60 = 0

Question 4.
Find the equation of the straight line which passes through the point (1, -2) and cuts off equal intercepts from axes.
Solution:
Intercept form of a straight line is \(\frac{x}{a}+\frac{y}{b}\) = 1, where a and b are the intercepts on the axis

If equation (1) passes through the point (1, -2) we get

So, equation of the straight line is x v

Hence, the required equation x + y + 1 = 0

Question 5.
Find the distance of the line 4x – y = 0 from the point P(4, 1) measured along the line making an angle 135° with the positive x-axis
Solution:
The equation in distance form of the line passing through P(4, 1) and making an angle of 135° with the positive x-axis

Question 6.
The line 2x – y = 5 turns about the point on it, whose ordinate and abscissa are equal, through an angle of 45° in the anti-clockwise direction, find the equation of the line in the new position.
Solution:
If the line 2x – y = 5 makes an angle θ with the x-axis.
Then, tan θ = 2. Let P (α, α) be a point on the line 2x – y = 5.
Then, 2 α – α = 5 ⇒ α = 5

So, the coordinates of P are (5, 5). If the line 2x – y – 5 = 0 is rotated about point
P through 45° in an anti-clockwise direction, then the line in its new position makes angle θ + 45° with the x-axis.
Let m’ be the slope of the line in its new position. Then,

Thus, the line in its new pdsition passes through P (5, 5) and has slope m’ = -3
So, its equation y – 5 = m’ (x – 5) or, y – 5 = -3 (x – 5) or, 3x + y – 20 = 0