Category: Class 12

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 4 The Summit Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 4 The Summit

12th English Guide The Summit Text Book Back Questions and Answers

Textual Questions:

1. Based on your reading of the text, answer the following questions in one or two sentences each. (Text Book Page No. 116) (Note: IQ → Important Questions)

Question a.
What did Hillary do with his wet boots? (IQ)
Answer:
Hillary cooked his wet boots over the fierce flame of the Primus and managed to soften them.

Question b.
Name equipment and a tool carried by the climbers during their expedition. (IQ)
Answer:
They carried oxygen bottles, ice-ax, and crampons during their expedition.

Question c.
Why did Hillary become clumsy-fingered and slow-moving?
Answer:
After reaching the peak, Hillary ran out of oxygen, he was becoming clumsy-fingered and slow-moving. So, he quickly replaced his oxygen set.

Question d.
What did Hillary find in a tiny hollow? (IQ)
Answer:
Hillary found two oxygen bottles left by Evan and Bourdillon, who had their earlier attempt to reach Mt. Everest.

Question e.
When did Hillary feel a sense of freedom and well being?
Answer:
Their first partly-full bottle of oxygen got exhausted. They had only one oxygen bottle to cany. With reduced load of 20 litre bottle, Hillary cut steps down off the South Summit. So, he felt a sense of freedom and well-being.

Question f.
What did Hillary mean by saying “We had had enough to do the job, but by no means too much”?
Answer:

1. Hillary meant that they carried an exact number of oxygen bottles needed for their expedition.
2. They didn’t even carry a single bottle more.

2. Answer the following questions in two or three sentences each:(Text Book Page No. 116)

Question a.
How did the mountaineers belay?
Answer:
Belaying refers to a variety of techniques used by mountaineers to exert tension on a climbing rope so that a climber does not fall very far. A climbing partner typically applies tension at the other end of the rope whenever the climber is not climbing and removes the tension from the rope when the climber needs a rope to continue to climb.

Question b.
Why was the original zest fading away?
Answer:
Their original zest was fading away as they had to struggle a lot to find the top of Mt. Everest.

Question c.
What did Edmund Hillary do to escape the ’ large overhanging ice cornices?
Answer:
In a number of places, the overhanging ice cornices were very large. In order to escape them, Hillary cut a line of steps down to where the snow met the rocks on the west.

Question d.
What did Tenzing and Edmond Hillary gift to the God of Softy Summit? How did they do it? (IQ)
Answer:

1. Tenzing gifted a bar of chocolate, a packet of biscuits and a handful of lollies whereas Hillary placed a small crucifix given by Colonel Hunt, besides Tenzing’s gifts.
2. They did so by making a little hole in the snow.

Question e.
What did the photograph portray?
Answer:
The photograph portrayed North Col and the old route which had been made famous by the struggles of those great climbers in 1920’s and 1930’s.

Question f.
The soft snow was difficult and dangerous. Why?
Answer:
The soft snow was difficult and dangerous as it sometimes held Hillary’s weight but often fell down suddenly.

Question g.
How did the firm snow at the higher regions fill them with hope?
Answer:
They were a little perturbed by slippery soft snow. But as they reached firmer snow higher up, they felt better. As one bottle of oxygen got exhausted, their load was now less. As Hillary’s ax bit into the first steep slope of the ridge, his high hopes were realized. The snow was crystalline and firm. They were able to make comfortable belays to haul themselves up slowly.

3. Based on the text, answer the following questions in a paragraph of about 100 – 150 words each: (Text Book Page No. 116)

Question a.
How did Hillary and Tenzing prepare themselves before they set off to the summit?
Answer:
They started up their cookers and drank lots of lemon juice and sugar. Then they took sardines and biscuits. Hillary cleaned the ice off the oxygen sets. He rechecked and tested them. He had removed his boots which had become wet the day before. They were now frozen solid. It would be very challenging to start climbing the ice-cold Himalayas with such wet and chilling boots. So, he cooked them over the fierce flame of Primus and managed to soften them up. They were also conscious of the probability of braving snowstorms during the ascent. They fortified their clothing with windproof and also pulled three pairs of gloves silk, woolen, and windproof on to their hands. At 6.30 am they crawled out of their tent into the snow. They hoisted their 30 lb. of oxygen gear on their backs. Connecting their oxygen masks they turned on the valves to bring life-giving oxygen into their lungs. Taking a few deep breaths, They got ready to go.

Question b.
Give an account of the journey to the South Coi from 28,000 feet.
Answer:
They reached a crest of a ridge at about 28000 feet from where the ridge narrowed to a knife-edge. Hillary took over the lead. The route on top of the ridge was filled with soft snow which was both difficult and dangerous. After several hundred feet they reached a tiny hollow where they found two oxygen bottles left by the earlier expeditors. They took it for their use. Hillary took the lead for nearly 400 feet. They made frequent changes of the lead. When Hillary was stamping a trail in deep soft snow, a portion of it gave way and he slipped back. After this, they had a dilemma to proceed further. Still, without losing hope they proceeded further and climbed on to the south peak.

Question c.
Describe the feelings of Edmund Hillary and Tenzing as they reached the top of the Summit.
Answer:
Hillary’s first feelings were of relief on reaching Everest. There were no more ridges to traverse and no more humps to tease them off with the hope of success. He looked at Tenzing. In spite of the balaclava helmet, goggles, and oxygen mask, all encrusted with long icicles, that concealed his face, his delight was visible. He looked around with a grin of delight. They shook hands. Tenzing hugged Hillary and thumped each other till they were breathless. It was 1 .30 am. The ridge had taken them two and a half hours but it seemed like a lifetime.

Question d.
The ridge had taken us two and a half hours, but it seemed like a lifetime. Why?
Answer:
Tenzing and Hillary struggled hard to reach the top of the ridge. They helped each other belaying. After crossing the crack with great struggle, Hillary signaled to Tenzing to come on up who wriggled his way up the crack and collapsed at the top like a giant fish hailing from the sea. Again the ridge curved away to the right and they were unable to find its top. They felt that the ridge seemed never-ending. At this juncture, they lost their original enthusiasm but didn’t give up their try.

Hillary felt at one spot that the ridge seemed to be dropped sharply away instead of rising. Later he found a narrow snow ridge running up to a snowy summit. With the help of the ice-axe they paved the way in the firm snow and reached the top. Though it took two and a half hours for them to reach the top of the ridge, they felt that it took their whole lifetime just because of the struggle they had to reach it.

Question e.
Describe the view from the top. What was the most important photograph?
Answer:
On reaching the peak, Tenzing and Hillary felt a great relief. To the east was their giant neighbour Makalu, unexplored and unclimbed. Far away across the clouds, the great bulk of Kanchenjunga loomed on the horizon. To the west, they could see the unexplored ranges of Nepal stretching off into the distance. The most important photograph was a shot down at the north ridge showed the North Col and the old route. It had been made famous by the famous climbers of 1920’s and 1930’s. It was the breath-taking view of the snow’ clad peak all round.

Question f.
‘There is no height, no depth that the spirit of man, guided by higher Spirit cannot attain’. Discuss the above statement in the context of the achievement of Edmund Hillary and Tenzing.
Answer:
Tenzing and Hillary started with their ascent from 28,000 feet on 29th May. They had undergone many hardships before they reach the summit. The ridge was narrow from 28,000 feet and they had to make their way through soft snow which was both difficult and dangerous. The soft snow gave way suddenly when Hillary had his trail in the deep snow. In spite of his slipping back, he did not give up his effort to move forward. They also found it very difficult to cross the ridge when the snow was firm.

Crossing the narrow crack between the rock and the cornice was really thrilling. It was done by them with fierce determination. Though their energy level went down when they found the ridge to be never-ending, they did not lose hope and proceeded further. It was this strong determination and undying spirit that made them reach the summit successfully. Thus the statement, ‘There is no height, no depth that the spirit of man, guided by the higher spirit cannot attain gets proved.

Paragraph:

Introduction:
Edmund Hillary in his “The Summit” tells how the summit of Everest was reached.

Preparation:
Hillary and his friend Tenzing got ready for the climb from camp-8 on May 29. They drank large quantities of lemon juice and had some biscuits. He softened his boots which became frozen solid. They also wore three pairs of gloves.

Journey:
They reached a crest of a ridge at about 28000 feet which narrowed to a knife-edge. The route on top of the ridge was both difficult and dangerous as it was filled with soft snow without losing hope they proceeded further and crampons on to the south peak.

The struggle:
The snow was crystalline and firm. With the help of his ice-axe he made away and they proceeded further belaying each other. The overhanging ice cornices threatened them. They struggled hard to cross a great cornice which had a forty feet narrow crack between the cornice and the rock. Hillary found a narrow snow ridge running up to a snowy summit. Thus they reached the top. It took nearly two and a half hours for them to/each the top of the ridge.

Sense of fulfillment:
They thumped each other on their back till they became breathless. As they had undergone a huge risk they felt that they had risked their whole lifetime to reach the top. The most important photograph was that of the North ridge. They made a little hole in the snow and placed some offerings to the Gods. From there they safely started descending to the South Col.

Conclusion:
Thus their ascent of Everest depicts the value of teamwork which helps one to overcome any difficulties. The adventure of Hillary and Tenzing enriches the fact that there is no height, no depth, that the spirit of man, guided by a higher spirit cannot attain.

Vocabulary:

Idioms:

I. Given below are some Idiomatic expressions with their meanings. Understand the meaning: (Text Book Page No.117)

1. wait for the dust to settle – to wait for a situation to become clear or certain.
2. get/have all your ducks in a row – to have made all the preparations needed to do something / to be well-organized
3. fetch and carry (for somebody) – to do a lot of little jobs for somebody as if you were their servant
4. do the math – to think carefully about something before doing it, so that you know all the relevant facts or figures
5. round the corner – very near

II. Fill in the blanks with the right idioms. Choose from the above-given idioms: (Text Book Page No.117)

Question a.
The Sherpas are cheerful, gallant men, who________________ tents, oxygen, food etc., for climbers during their ascent of the summit.
Answer:
fetch and carry

Question b.
The team _________________ carefully so as to reach the summit successfully.
Answer:
does the math

Question c.
When they had to climb through deep new snow the party sometimes had to _________________.
Answer:
wait for the dust to settle

Question d.
Each member of the team had all their _________________.
Answer:
get/have all your ducks in a row

Question e.
We could not believe that with a few more whacks of the ice axe in the firm snow we were _______________ to the top.
Answer:
round the corner

III. Understand the meaning of the given idiomatic expression and choose the right one to complete the sentence:
(Text Book Page No.117)

• the icing on the cake — something extra and not essential, but is added to make it even better
• break the ice — to make people more relaxed, especially at the beginning of the meeting

Question a.
The conference room was silent though packed. The chairman introduced an interactive session to _________.
Answer:
break the ice

Question b.
Our headmistress not only promised us to take us for an excursion but also announced that on return we would get a holiday. It was like _________.
Answer:
the icing on the cake

Phrasal Verbs: (Text Book Page No.118)

i. Given below are the phrasal verbs with their meanings. Use the given phrasal verbs in sentences of your own (Text Book Page No.118)

1. I want to turn on the television.
2. Mr. Prem took over charge as manager.
3. The children set off for school.
4.  The meeting was put off to next week.

ii. Given below are some Phrasal Verbs which are frequently used in connection with travelling. Guess the meaning and match: (Text Book Page No.118)

Question a.

Answer:

Question b.

Answer:

Question c.

Answer:

Compound words: (Text Book Page No. 118)

i. Here are some compound words chosen from the text:

I. Match the following with their right field, choosing appropriately from the box given: (Text Book Page No. 119)

Question 1.
snow-board
Answer:
Sports

Question 2.
snow-mobile
Answer:
transportation

Question 3.
snow-chains
Answer:
machinery

Question 4.
snow-storm
Answer:
weather

Question 5.
snow-bird
Answer:
travel

Question 6.
snow-belt
Answer:
geography

Listening:

First, read the following statements. Then, listen to the passage read aloud by your teacher or played on the recorder and complete the statements. You may listen to it again if required. Complete the following: (Text Book Page No. 119)

Question a.
List any three aspects which contributed to the success of the ascent of the summit.

1. ___________
2. __________
3. __________.

Answer:

1. Knowledge gained from other climbers
2. Careful planning
3. Excellence of equipment

Question b.
Without the help of ____________ nothing would have been possible.
Answer:
Teamwork / Sherpas

Question c.
The main idea of the passage is _________
Answer:
reasons for the success of the summit

Question d.
The biggest thing of all is _________.
Answer:
togetherness

Question e.
_________ were cheerful and gallant men.
Answer:
Sherpas

Speaking:

a) Group Activity: (Text Book Page No. 119)

Question i.
Have you ever been on an adventurous trip? If so, share your success story with your friends.
Answer:
I with my brother went on a trip from Tirunelveli to Chennai on a bike. When we were just nearing Chennai, the tire of the bike burst, we did not know what to do. Luckily we managed not to hurt ourselves. We were waiting for someone to help us. Finally, a car came that way. We pleaded with them to help us. They promised to send a mechanic to that place. We waited for nearly two hours. Then the mechanic came and repaired our bike. Later we reached our uncle’s home in Chennai safely.

Question ii.
How will you organize or plan for a trip or an event? Do you have the habit of preparing a check-list? Discuss.
Answer:
I organize a trip with my family to Mysore for four days to visit all the important places. I planned to go by train. So I will book the to and fro tickets to Mysore. I will book a room to stay there in advance, I will prepare a checklist a day before my travel one toothbrush, towel, soap, money, my Id card, medicines, first aid kit. A tourist guide book of Mysore. I will plan everything properly to make my trip safe and pleasant.

b) Individual Activity: (Text Book Page No. 119)

Given below are a few proverbs. Prepare a short speech of two minutes on one of the proverbs:

a) Nothing is impossible:
The word ‘impossible’ means it is possible. You can do anything. “The word impossible is found only in the dictionary of fools,” says Napoleon Bonaparte. In this word, everything is possible on the basis of will power, determination, and sacrifice. To accomplish the most difficult tasks, you need to put in a lot of hard work, extra perseverance, and concentration on a simple objective. You should have determination, dedication, and devotion to attain success. Never bother about the results keep on going even if the pace is slow. Just ensure it remains steady.

b) Where there is a will there’s away.
“Where there is a will there’s a way” is a message of hope and encouragement. Perseverance leads to success. Most of us are endowed with a fair share of intelligence, and all that is needed for success is diligence and perseverance. Some may not be blessed with good health. Some may not be blessed with a sharp intelligence or a retentive memory. Some may be dull. Yet, it is in the will power of all to attain to a certain standard of success. Thus, we may conclude with another saying “Strong Determination is the key to success”.

c) Together we can achieve more.
This means Unity is strength. If people work together, the work is easier and is completed more quickly. This proverb means that you should take advantage of a favourable situation before it changes. It is best to always be honest and tell the truth. By doing so, you will win the trust and respect of others. A country is strong whose citizens are united, a family is strong whose members stay together. Thus unity is very important in each and every sphere of our life.

Giving instructions: (Text Book Page No. 119)
Here are a few instructions are given by a Health Inspector to a group of students, in order to prevent malaria and dengue. Complete the series by adding some more important instructions. (Text Book Page No. 120)

1. Do not allow water to stagnate in and around your house.
2. Keep your surroundings clean.
3. Wear long-sleeved shirts/blouses and long pants/skirts that cover your arms and legs.
4. Do not litter the place with wastes
5. Divide the waste into perishable and non¬perishable and put them in the proper place

Now, write a set of 8 to 10 instructions for the following situations:

1. A doctor instructing a patient regarding a healthy diet and proper care after surgery.

• Eat food at regular intervals.
• Do not take fatty food
• Eat more green vegetables
• Go for a walk daily
• Do not take more sugar and salt

2. A traffic police personnel to the public, as to how to move around in safety, in crowded public places during festival seasons.

• Do not wear lots of jewels
• Take care of personal belongings.
• Do not allow children to stray away.
• Always follow the queue

3. A mother to her children, on safety measures to be taken before leaving home on vacation.

• Do not go alone
• Carry your belongings safely
• Do not eat from roadside shops
• Do not waste time unnecessarily

Reading:

On the basis of your understanding of the given passage, make notes in any appropriate format:

The Sherpas were nomadic people who first migrated from Tibet approximately 600 years ago, through the Nangpa La pass and settled in the Solukhumbu District, Nepal. These nomadic people then gradually moved westward along salt trade routes. During the 14th century, Sherpa ancestors migrated from Kham. The group of people from the Kham region, east of Tibet, was called “ShyarKhamba”.

The inhabitants of ShyarKhumbu were called Sherpa. Sherpa migrants travelled through O and Tsang, before crossing the Himalayas. According to Sherpa’s oral history, four groups migrated out of Solukhumbu at different times, giving rise to the four fundamental Sherpa clAnswer: Minyagpa, Thimmi, Sertawa, and Chawa. These four groups have since split into the more than 20 different clans that exist today.

Sherpas had little contact with the world beyond the mountains and they spoke their own language. Ang Dawa, a 76-year-old former mountaineer recalled “My first expedition was to Makalu [the world’s fifth highest mountain] with Sir Edmund Hillary’ We were not allowed to got really heavy when wet, and we only got a little salary, but we danced the Sherpa dance, and we were able to buy firewood and make campfires, and we spent a lot of the time dancing and singing and drinking. Today Sherpas get good pay and good equipment, but they don’t have good entertainment. My one regret is that I never got to the top of Everest. I got to the South Summit, but I never got a chance to go for the top.

The transformation began when the Sherpa Tenzing Norgay and the New in 1953. Edmund Hillary took efforts to
build schools and health clinics to raise the living standards of the Sherpas. Thus life in Khumbu improved due to the efforts taken by Edmund Hillary and hence he was known as ‘Sherpa King’.

Sherpas working on the Everest generally tend to perish one by one, casualties of crevasse falls, avalanches, and altitude sickness. Some have simply disappeared on the mountain, never to be seen again. Apart from the bad seasons in 1922, 1970, and 2014 they do not die en masse. Sherpas carry the heaviest loads and pay the highest prices on the world’s tallest mountain. In some ways, Sherpas have benefited from the commercialization of Everest more than any group, earning income from thousands of climbers and trekkers drawn to the mountain. While interest in climbing Everest grew gradually over the decades after the first ascent, it wasn’t until the 1990s that the economic motives of commercial guiding on Everest began.

This leads to an eclipse of the amateur impetus of traditional mountaineering. Climbers looked after each other for the love of adventure and “the brotherhood of the rope” now are tending to mountain businesses. Sherpas have taken up jobs as guides to look after clients for a salary. Commercial guiding agencies promised any reasonably fit person a shot at Everest.

Note Making:

Notes:
Life of Sherpas

I. Nomadic Sherpas migrated from Tibet to Nepal
a) 600 years ago
b) Shyarkhamba
c) 4 Sherpa clans – Minyaagpa, Thimmi, Sertawa, Chawa.

II. Little contact beyond mountains
a) have their own language
b) have no opportunity to reach the top
c) carry things for others
d) Edmund Hillary the ‘Sherpa King’

III. Sherpas die in mountain casualties:
a) carry heaviest loads
b) earn money from climbers
c) 1990s commercial guiding on Everest

Grammar:

Kinds of sentences — Simple, Complex, and Compound:

a) Simple sentence: (Text Book Page No.121)

Task 1:
Pick out the finite verbs in the following sentences: (Text Book Page No. 121)

Question a.
You can solve this problem in different ways.
Answer:
can solve

Question b.
The professor has been working on the last chapter of the book since March.
Answer:
as been working

Question c.
Despite being a celebrity, Ravi mingles easily with everyone.
Answer:
mingles

Question d.
You must speak clearly to make yourself understood.
Answer:
must speak

Question e.
The chairman being away, the clerk is unable to approve the proposal.
Answer:
is

Question f.
Getting down from the car, the Chief Guest walked towards the dais amidst applause.
Answer:
walked

Question g.
The old man struggled to walk without support.
Answer:
struggled

Question h.
In case of emergency, please contact this number.
Answer:
contact

Question i.
The sun having set, the temperature fell rapidly.
Answer:
fell

Question j.
But for your help, I could not have completed the assignment.
Answer:
completed

Task 2:

II. Read the following passage and identify the simple sentences: (Text Book Page No. 121)

Question  1.
Sunflowers turn according to the position of the sun. In other words, they ‘chase the light’. Have you ever wondered what happens on cloudy, rainy days when the sun is completely covered by clouds? If you think the sunflower withers or turns its head towards the ground, you are completely mistaken. Do you know what happens? Sunflowers turn to each other to share their energy. Learning from Nature, we too should support and empower each other.
Answer:
Sunflowers turn according to the position of the sun. In other words, they ‘chase the light’. Have you ever wondered what happens on cloudy, rainy days when the sun is completely covered by clouds? If you think the sunflower withers or turns its head towards the ground, you are completely mistaken. Do you know what happens? Sunflowers turn to each other to share their energy. Learning from Nature, we too should support and empower each other.

b) Complex sentence: (Text Book Page No.122)

Task 1:

Look at the following complex sentences. Circle the Main clauses and underline the Subordinate clauses: (Text Book Page No. I23) 

Question a.
Nobody knows when the power supply will resume.
Answer:
Nobody knows when the power supply will resume.
M.C                                              S.C

Question b.
Please tell me what the time is.
Answer:
Please tell me             what the time is.
M.C                                   S.C

Question c.
The man who directed the film was my schoolmate.
Answer:
The man             who directed the film          was my schoolmate.
M.C                             S.C                                          M.C

Question d.
I believe that all men are basically good.
Answer:
I believe                  that all men are basically good.
M.C                                           S.C

Question e.
No one knows when he will return.
Answer:
No one knows               when he will return.
M.C                                           S.C

Task 2:

Pick out the complex sentences in the following passage: (Text Book Page No. 123)

Question  1.
A man saw a lion in the bush, as he was walking through the forest. He did not know what to do. He was helpless. He was too scared to turn around and run. He just knelt down as if he were getting ready to pray. He closed his eyes, thinking that the lion would pounce on him anytime. Out of the corner of his eye, he saw the lion on its knees too. Shocked, he asked the lion what it was doing. The lion replied that he was praying before he started his meal.
Answer:
A man saw a lion in the bush, as he was walking through the forest. He did not know what to do. He was helpless. He was too scared to turn around and run. He just knelt down as if he were getting ready to pray. He closed his eyes, thinking that the lion would pounce on him anytime. Out of the corner of his eye, he saw the lion on its knees too. Shocked, he asked the lion what it was doing. The lion replied that he was praying before he started his meal.

c) Compound sentence: (Text Book Page No. 123)
Identify the two Main clauses and conjunction in each of the following sentences:

Question a.
It started raining suddenly and people ran for shelter.
Answer:
It started raining suddenly            and                              people ran for shelter.
M.C                                            conjunction                                    M.C

Question b.
Understand the concept well, otherwise, you cannot solve the problem.
Answer:
Understand the concept well,              otherwise,                          you cannot solve the problem.
M.C                                                      conjunction                                            M.C

Question c.
Fifty candidates appeared for the interview, but only five were selected.
Answer:
Fifty cT’rlidates appeared for the interview,                 but                   only five were selected.
M.C                                                                         conjunction                          M.C

Question d.
Ramesh did not know Spanish, so he wanted a translator.
Answer:
Ramesh did not know Spanish,                                so                                        he wanted a translator.
M.C                                                                     conjunction                                           M.C

Question e.
He is a good actor, still, he is not popular.
Answer:
He is a good actor,                   Still,                         he is not popular.
M.C                                       conjunction                          M.C

Task 2:

Pick out the compound sentences in the following passage: (Text Book Page No. 123) 

Question  1.
The food we eat has to be digested and then thrown out of the body. The air we breathe in, has to be thrown out, to help us survive. But we hold negative emotions like insecurity, anger, and jealousy within ourselves for years. If these negative emotions are not eliminated, the mind grows corrupt and diseased. Let us do away with hatred and lead a healthy life filled with peace and joy.
Answer:
The food we eat has to be digested and then thrown out of the body. The air we breathe in, has to be thrown out, to help us survive. But we hold negative emotions like insecurity, anger, and jealousy within ourselves for years. If these negative emotions are not eliminated, the mind grows corrupt and diseased. Let us do away with hatred and lead a healthy life filled with peace and joy.

Task 3:

Complete the sentences choosing the right endings: (Text Book Page No. 124)


Answer:

Conditional clause:

Task 1:

Read the following sentences and fill in the blanks: (Text Book Page No. 124)

Question a.
If I _______ (be) a spider, I would ______ (weave) webs.
Answer:
were, weave

Question b.
If Raj ______ (be) a sculptor, he would ______ (make) beautiful idols.
Answer:
were, make

Question c.
If Mary had an umbrella, she would ______ (lend) it to me.
Answer:
lend

Question d.
Rex would have played with me if he ______ (has) time.
Answer:
had

Question e.
If I were you, I would ______ (accept) this offer.
Answer:
accept

Question f.
We will ______ (select) storybooks for kids if we allow time for storytelling.
Answer:
select

Question g.
The Education Minister will ______ (visit) our school tomorrow if he goes by this way.
Answer:
visit

Question h.
You will be rewarded by the wise if you ______ (stand) for truth.
Answer:
stand

Question i.
If my mother ______ (know) of my poor performance in the exam, she will not allow me to watch a movie.
Answer:
knows

Question j.
If I had won the lottery, I would have ______ (donate) relief materials for the flood victims.
Answer:
donated

Task 2:

Rewrite the following sentences using ‘If’ without changing the meaning: (Text Book Page No. 125)

e.g. Unless you go for a walk regularly, you cannot reduce your weight. (Use ‘If’)
If you do not go for a walk regularly, you cannot reduce your weight.

Question a.
Sindhu would not have won the world championship unless she had single-minded devotion.
Answer:
If Sindhu had not had single-minded devotion, she would not have won the world championship.

Question b.
You will not reach your goal unless you chase your dream.
Answer:
If you do not chase your dream, you will not reach your goal.

Question c.
Unless we plant more trees, we cannot save our planet.
Answer:
If we plant more trees, we can save our planet.

Question d.
The rescue team would not have saved the victims unless they had received the call in time.
Answer:
If the rescue team had received the call in time, they would have saved the victims.

Question e.
The palace cannot be kept clean unless we appoint more people.
Answer:
If we do not appoint more people, the palace cannot be kept clean.

Question f.
The portraits would not have been so natural unless the artist had given his best.
Answer:
If the artist had not given his best, the portraits would not have been so natural.

Question g.
The manager would not have selected Nithiksha unless she exhibited good accounting skills.
Answer:
If she had not exhibited good accounting skills, the manager would not have selected Nithiksha.

Question h.
The policeman would not have arrested the man unless he had violated the rules.
Answer:
If he had not violated the rules, the policeman would not have arrested the man.

Question i.
Mr. Kunaal would not sponsor my higher education unless I studied well.
Answer:
If I studied well, Mr. Kunaal would sponsor my higher education.

Question j.
Kavin will not stop flying kites unless he understands the risk involved in it.
Answer:
If kavin understands the risk involved in it, he will stop flying kites.

Question k.
Tanya would not know the answer unless she referred to the answer key.
Answer:
If she referred to the answer key, Tanya would know the answer.

Question l.
My village cannot achieve a 100 % literacy rate unless the elders of the village cooperate with the education department.
Answer:
If the elders of the village do not cooperate with the education department, my village cannot achieve 100% literacy.

Writing:

Summarizing is to briefly sum up the various points from the notes made from the original passage.

Refer to the reading passage (Text Book Page No. 120). You must have completed reading. Now go through the passage once again and refer to the notes made and do the summarizing.

Rough Copy:
The Sherpas were nomadic people who migrated from Tibet about 600 years ago. They moved to the west. The ancestors from the Kham region were called Shayar khamba. The inhabitants were called Sherpas. There were fundamental clans, sherpas lived beyond the mountains. An old Sherpa Ang Dawa accompanied Edwin Hillary – He was called the Sherpa king, because he took efforts to build schools and health clinics to raise their living standards, Sherpas working on the Everest got perished due to Crevasse falls, Avalanches, and altitude sickness. They can carry heavy loads. They have benefited from the commercialization. Sherpas have taken up to look after clients for a salary. Sherpas’ life is entangled with the mountains.

Fair Copy:

The Sherpas

The Sherpas were nomadic people who migrated from Tibet about 600 years ago. They moved to the west. The ancestors from the Kham region were called Shayar Khamba. The inhabitants were called Sherpas. There were fundamental clans. Sherpas lived beyond the mountains. An old Sherpa Ang Dawa accompanied Edwin Hillary – He was called the Sherpa king because he took efforts to build schools and health clinics to raise their living standards. Sherpas working on the Everest got perished due to Crevasse falls, Avalanches, and altitude sickness. They can cany heavy loads. They have benefited by the commercialization. Sherpas have taken up jobs as guides to look after clients for a salary. Sherpas’ life is entangled with the mountains.

Interpreting non-verbal presentation:

Reading a map:

Let us together scale the summit. Here is a drawing of Everest showing the way to the summit, and the position of the camps with their heights. Trace the trekking trail to reach the summit with the given detail and write an interesting paragraph in about 100 words. (Text Book Page No. 126)

Paragraph about trekking trail to reach the summit:

We started our journey at the base camp. We have sufficient oxygen with us. At the 3rd camp, we suffered a lot due to ice fail. We didn’t come out till the weather was clear. Only three of our team could reach the 8th camp. From here the ridge narrowed to a knife-edged and it was a steep slope. So we had to cut steps and then moved. Since there was a lot of firm snow, we could do it. With great efforts. We reached the 9th camp. One of my friends became sick, I started my challenging journey with my other friend. Having fierce determination, nothing could stop us from reaching the top. When we realized that the ridge ahead of us dropped sharply away, we stood on the summit. It was a splendid joy we shared with each other and shouted, at the height of 28,700 feet.

ஆசிரியரைப் பற்றி:

சர் எட்மெண்ட் பெர்சிவல் ஹிலாரி (Sir Edmund Percival Hillary) (20 ஜீலை 1919 – 11 ஜனவரி 2008) நியூசிலாந்து நாட்டைச் சேர்ந்த மலை ஏறுபவர் (mountaineer), கண்டுபிடிப்பாளர் (explorer) மற்றும் தாராளமான நன்கொடையாளர் (philanthropist). இவர் இரண்டாம் உலகப்போரின் போது “நியூசிலாந்து ராயல் விமானப் படையில்” மாலுமியாக (navigator) பணியாற்றினார்.

எவரெஸ்ட் மலையில் ஏறியதற்கு பின்பு, அவர் தான் உருவாக்கிய “ஹிமாலயன் டிரஸ்ட்” மூலம் நேபாள நாட்டில் உள்ள “ஷெர்பா” (Sherpa) மக்களுக்கு சேவை செய்வதில் தன்னை ஈடுபடுத்திக் கொண்டார். “High Adventure, No Latitude for Error, Nothing Venture, Nothing Win. View from the Summit, The Remarkable Memoir by the First Person to Conquer Everest” ஆகியவை அவருடைய பிரபலமான (famous) புத்தகங்களாகும்.

பாடத்தைப் பற்றி:

இப்பாடத்தில் எவரெஸ்ட் சிகரத்தை தொட்ட உலக புகழ் பெற்ற மலைஏறும் வீரர் எட்மண்ட் ஹிலாரி தன் அனுபவத்தை கொடுத்திருக்கிறார். குறிப்பாக மே மாதம் 29ம் தேதி மலையேறும் இறுதி நாளில் நடந்த மெய் சிலிர்க்கும் நிகழ்வை பற்றியும் காலை 4.30 மணி முதல் பிற்பகல் 2 மணி வரை டென்சிங்குடன் சேர்ந்து அவர் எதிர்கொண்ட அபாயங்கள், புத்திசாலித்தனங்கள் பற்றியும் விரிவாக சொல்லப்பட்டு இருக்கிறது. அவர் புரிந்த இந்த அபாயகரமான நிகழ்வை, பாடத்தைப் படித்து விரிவாகக் காண்போம். சாகசங்கள், பயணங்கள் மற்றும் கண்டுபிடிப்புகள் எப்போதும் உற்சாகம் தரக்கூடியவை.

குறிப்பாக அவை எப்பொழுதும் மெய்யானதாகவும் மற்றும் முதன்முதலில் நடப்பதாகவும் இருந்தால் மெய்சிலிப்பேற்றக்கூடியவை. ஒருவர் மனதில் எழும் ஒரே கேள்வி என்னவென்றால், இவ்வாறு அதிகப்படியான ஆபத்துக்கள் அடங்கிய காரியங்களை ஒருவரை செய்யத் தூண்டுவது எது என்பதே ஆகும். இது வலிமைமிக்க துணிகரச் செயலை புரியக்கூடிய மனநிலை மற்றும் தனிச்சிறப்புமிக்க பண்புகளே அவர்களை அத்தகைய உயரங்களை தொடச் செய்கிறது.

The Summit Summary in Tamil

“எவரெஸ்ட்டிற்கு ஏறும் வழி” (The Ascent of Everest) என்னும் ஜான் ஹன்ட் (John Hunt) எழுதிய நூலை சற்று தழுவி இப்பாடப்பகுதி எடுக்கப்பட்டது. எவரெஸ்ட் சிகரம் எவ்வாறு அடையப்பட்டது என்பது சர் எட்மெண்ட் ஹிலாரியின் (Sir Edmund Hillary) சொந்த வார்த்தைகளால் சொல்லப்படுகிறது.

மே 28ல் தெற்கு கணவாயில் போடப்பட்ட முகாமில் 8 பேர் இருந்தனர், முறையே எட்மெண்ட் ஹிலாரி (Edmund Hillary), டென்சிங் (Tenzing), ஜார்ஜ் லோ (George Lowe), அல்பிரட் கிரிகோரி (Albert Gregory) மற்றும் இரண்டு செர்பாக்கள் (Sherpas), பெம்பா (Pemba), அங்க் நியிமா (Ang Nyima). ஆனால் பெம்பா ஏற முடியாத அளவிற்கு உடல்நிலை சரியில்லாமல் இருந்தார். மற்றவர்கள் அதிக சுமையுடன் அன்று 27900 அடி ஏறினர். அங்கே ஹிலாரியும், டென்சிங்கும் சிறிய கூடாரத்தில் இருந்து அவர்களுடன் வந்த மூன்று நபர்கள் முகடுகளில் சறுக்கி தெற்கு கணவாய்க்கு திரும்புவதை கண்டார்கள்.

சூரியன் மறையும் போது, ஹிலாரி மற்றும் டென்சிங் தங்கள் கூடாரத்திற்குள் சென்று, வெப்பம் தரும் (warm clothing) ஆடைகளை அணிந்து, தூங்கும் பைகளுக்குள் நெளிந்து சென்றார்கள். மறுநாள், மே 29ல் காலை 4 மணிக்கு ஏறுவதற்கு அவர்கள் தயாரானார்கள் (ready).

நாங்கள் எங்களது சூட்டடுப்பை (cooker) பற்ற வைத்து, அதிக அளவு எலுமிச்சை சாறையும் (lemon juice), சர்க்கரையும் (sugar) கலந்து குடித்தோம், அதன்பின் எங்களது கடைசி தகரக்குவளையில் உள்ள சார்டின் (sardines) எனப்படும் கடல் உணவையும், பிஸ்கெட்டையும் எடுத்துக் கொண்டோம். நான் எனது ஆக்சிஜன் தொகுப்பு பொருட்களை கூடாரத்தின் உள்ளே இழுத்து, அதன் மேலிருந்த பனிக்கட்டிகளை சுத்தம் செய்து அதனை பரிசோதனை செய்து சோதித்து பார்த்தேன்.

முந்தைய நாள் ஈரமாயிருந்து. இன்று உறைந்து போன (frozen) எனது காலணிகளை கழற்றினேன். எனவே அவைகளை நான் அடுப்பில் இருந்து வரும் புகையினால் சூடேற்றி மென்மையாக்கினேன். எங்களது கீழ் ஆடைக்கு மேலே நாங்கள் காற்று சீராக்கும் ஆடையை அணிந்தும், எங்கள் கைகளில் பட்டு, கம்பளி மற்றும் காற்று சீராக்கும், கையுறைகளையும் (gloves) அணிந்துக் கொண்டோம்.

காலை 6.30 மணியளவில் நாங்கள் எங்கள் கூடராத்தை விட்டு பனிக்குள் (snow) நகர்ந்து வந்து, 30 அளவுடைய ஆக்சிஜன் (oxygen) உருளையை (gear) முதுகில் சுமந்து, முகமூடியை அணிந்து, ஆக்சிஜன் உருளையில் குழாயைத் திறந்து எங்களது நுரையீரலுக்குள் ஆக்சிஜன் வாழ்வை அனுப்பினோம். ஒரு சில சிறந்த ஆழமான சுவாசத்திற்குப் பிறகு நாங்கள் புறப்பட தயாரானோம். எனது உறைந்து போன பாதங்களைப் பற்றி நான் சிறிது கவலைப்பட்டாலும், நான் டென்சிங்கை நகரச் சொன்னேன்.

டென்சிங் நீண்ட மலைமுகட்டை நோக்கி (traverse) செல்லக் கூடிய குறுக்கு பாதையில் நடந்தார். நாங்கள் 28000 அடி பனிக்குவியலை உண்டாக்கிய மலைமுகட்டின் உச்சியை அடைந்தோம். அதன் பிறகு அந்த முகடானது கத்தி போல் கூர்மையான பாதையாக காணப்பட்டது. என் காலகள் இப்போது வெப்பமானதால், நான் டென்சிங்கை முந்தினேன்.

கடினமானதாகவும், ஆபத்தாகவும் இருக்கக்கூடிய மலை முகட்டிற்கு செல்லக்கூடிய பாதையானது மென்பனியால் உருவாகயிருந்தது. அது சில நேரங்களில் என் நிலையிலேயே இருக்க செய்தாலும், அடிக்கடி மேலே செல்ல வழி விட்டது. பல நூறு அடிகளுக்கு அப்புறம் நாங்கள் சிறிய காலியான இடத்திற்கு வந்தோம். அங்கே எவான் மற்றும் போர்டில்லான் ஆகியோரின் முந்தைய முயற்சியில் விட்டுச் சென்ற இரண்டு ஆக்சிஜன் குடுவைகளை கண்டோம்.

மதிப்பு அளவீட்டிலிருந்த பனியை நான் விலக்கி, நாங்கள் அதனை சிக்கனமாக உபயோகித்தால் திரும்ப தெற்கு கணவாய் வரை செல்லத் தேவையான பல நூறு லிட்டர் ஆக்சிஜனை அவை இன்னும் கொண்டுள்ளன என்பதை கண்டறிந்து நிம்மதியானேன்.

நான் தெற்கு உச்சியின் கடைசி 400 அடிக்கு முன்னால் உள்ள மலைமுகட்டிற்கு (ridge) செல்லக்கூடிய பாதையில் தொடர்ந்து பயணமானோம்.

முன்னேறி செல்வதில் நாங்கள் அடிக்கடி (frequent) மாற்றங்களை கொண்டு வந்தோம். நான் எனது அடியை ஆழமான பாதையின் மீதிருந்த ஆழமான பனியில் வைத்த போது, ஒரு பகுதி விலகி சென்றதனால், நான் மூன்று நான்கு அடிகள் பின்னோக்கி வழுக்கினேன். நாங்கள் முன்னேறி செல்வது குறித்து டென்சிங்கிடம் நான் அறிவுரைகளை (advisability) கேட்ட போது, அவர் பனியைக் குறித்து மகிழ்ச்சியற்றுக் காணப்பட்டாலும் அவருடைய வழக்கமான கூற்றான “நீங்கள் விரும்பிய படியே” என்று உரையை முடித்தார்.

நான் முன்னேறிச் செல்வதற்கு முடிவெடுத்தேன் (decided). கடைசியாக நாங்கள் மேலே இருந்த உறுதியான பனியை அடைந்த போது நாங்கள் கடைசியா இருந்த செங்குத்தான சரிவினில் பனியை உடைக்கும் கம்பி கொண்டு பனியை வெட்டி படிகளை உருவாக்கினோம். அப்பொழுது நேரம் காலை 9 மணி.

தெற்கு சிகரத்திற்கு (south summit) கீழே நாங்கள் அமர்வதற்கு ஒரு இருக்கையை வெட்டினோம், பின்பு எங்களது பாதி நிரப்பப்பட்ட முதல் ஆக்சிஜன் குடுவை தீர்ந்திருந்த போது எங்களிடம் ஒரே ஒரு ஆக்சிஜன் நிரம்பிய குடுவை மட்டுமே மீதம் இருந்தது. இப்போது எங்களது உபகரணங்கள் சுமப்பதற்கு இலகுவாகவும், சுமார் 20 க்கு சற்று அதிகமாகவும் தான் எடை கொண்டிருந்தன.

என்னுடைய பனிக் கோடாரி (ice-axe) அந்த முகட்டின் முதல் செங்குத்தான சாய்வினை வெட்டிய போது, என்னுடைய உயர்ந்த நம்பிக்கைகளை (high hopes) நான் உணர்ந்தேன். பனியாகவும் படிகமாகவும் (crystalline), உறுதியானதாகவும் இருந்தது. பனிக்கோடாரியின் இரண்டு அல்லது மூன்று அடிகள் எங்களது பெரிய படிகட்டுகளை (large steps) உண்டு பண்ணியது. பனிக்கோடாரியின் ஒரு உறுதியான அடியானது கைப்பிடியை பாதி வரை மூழ்கச் செய்து, உறுதியான வசதியான மலை ஏற்றத்துக்கு வழி வகுக்கும்.

நாங்கள் ஒரு நேரத்தில் ஒருவர் மட்டுமே நகர்ந்தோம். என்னால் 40 படிகட்டுகளை வெட்ட முடியும், நான் அவ்வாறு வெட்டும் போது என் கயிரை டென்சிங் பிடித்துக் கொண்டு என் எடையைத் தாங்குவார் (belaying). அதன்பின் நான் என் கைப்பிடியை மூழ்கச் செய்து, அதனைச் சுற்றி கயிரால் கண்ணிகள் (loops) போட்டேன். டென்சிங்கோ , உடையும் படிக்கட்டுகளுக்கு எதிராக என்னை நோக்கி நகர்ந்து வந்தார். பின்னர் மறுபடியும் அவர் என் கயிரை பிடித்துக் கொண்டு என் எடையத்ை தாங்கும் போது, நான் வெட்டினேன்.

அதிக இடங்களில் தொங்குகின்ற பனிப்பாறைகள் மிகப் பெரியதாக இருந்ததால், அவற்றிலிருந்து தப்பிக்க நான் பனியின் மேற்பரப்பில் இருந்து பாறை வரையிலும் படிக்கட்டுகளை வெட்டினேன். இந்தப் பெரிய பாறையிலிருந்து நேராக 8000 அடிக்கு கீழாக மேற்கு பள்ளத்தாக்கில் உள்ள முகாம் 4ன் சிறிய கூடாரங்களைப் (tiny tents) பார்த்து சிலிர்ப்பேற்றியது. பாறைகளில் மேலே தவழ்ந்ததாலும் (crawl) பனியில் கைப்பிடிகளை வெட்டியதாலும் எங்களால் இந்த கடினமான பகுதிகளை வேகமாக கடந்து செல்ல முடிந்தது.

அதன் கிழக்குப் பகுதியில் (east side) இன்னொரு பெரிய பனிப்பாதை இருந்தது. அது 40-அடி உயர படியில் உருண்டோடி வந்தது, அங்கே பனிப்பாறைக்கும் பாறைக்கும் இடையே ஒரு விரிசல் (crack) இருந்தது. டென்சிங்கை எவ்வளவு சிறப்பாக என் எடையைத் தாங்க முடியுமோ, அவ்வாறு செய்து விட்டு, நான் அந்த விரிசலுக்குள் ஏறினேன். பின்னர், பின்னோக்கி உதைத்தவாறு என் மலையேறும் கருவியில் இருந்த ஆணிகளை உறைந்த பனியில் முழுவதுமாக மூழ்கச் செய்து நான் தரையில் இருந்து நெம்பியவாறு மேலே எழுந்தேன்.

அங்கிருந்து அனைத்து சிறிய பாறைப்பிடிகளின் துணையோடு, என் மூட்டு, தோள்பட்டை, கைகளால் முடிந்த அளவு பலத்தை திரட்டிக்கொண்டு, பனிப்பாறையுடன் ஒட்டிக்கொள்ள வேண்டும் என்று ஜெபித்துக் (praying) கொண்டே, நான் விரிசலில் மலையேறும் கருவியின் மூலம் பின்புறமாக நகர்ந்தேன்.

எனது முன்னேற்றம் (progress) மெதுவாக இருந்தாலும், நிலையானதாக இருந்தது. டென்சிங் கயிரை விட்டுவிட்டதால், நான் மேல் நோக்கி மெதுமெதுவாக பாறையின் உச்சியைத் தொடும் வரை நகர்ந்து, விரிசலிலிருந்து வெளிவந்து நான் தெற்கு சிகரத்திற்கு படிகளை வெட்டிக் கொண்டிருந்த போது, நான் சுதந்திரமாகவும், நன்றாக இருப்பது போன்றும் உணர்ந்தேன்.

ஒரு சில நிமிடங்களுக்கு நான் மூச்சுவிடுவதற்காக படுத்திருந்தேன். முதன் முறையாக நாங்கள் மலைச் சிகரத்தை அடைவதை எதுவும் தடுக்க முடியாது என்று மிக உறுதியாக உணர்ந்தோம், நான் அந்த தொங்கும் பாறையில் நிலையாக நின்று கொண்டு டென்சிங்கை நோக்கி மேலே வருமாறு கையசைத்தேன் (signed).

நான் அந்த கயிறில் நிம்மதி பெருமூச்சு விட்டபோது, டென்சிங்கோ அந்த விரிசலை நோக்கி மேலே நெளிந்து (wriggled) வந்து கடைசியாக உச்சத்தை அடைந்த போது, மிகப்பெரிய போராட்டத்திற்கு பின், கடலில் இருந்து வெளியே இழுத்து வரப்பட்ட பெரிய இராட்சச மீன் போல் நிலைகுலைந்தார்.

மலை முகடுகள் முன்பு போலவே தொடர்ந்தன, பெரிய பனிப்பாறையின் (giant cornices) வலது புறமும், கூர்மையான மலைச் சரிவுகள் இடது புறமும் இருந்தன. அந்த மலைமுகடானது வலது புறமாக வளைந்து (curved) சென்றதால் எங்களுக்கு மலை உச்சி எங்கு இருக்கிறது என்று தெரியாமல் போனது. நான் (கூனல்) திமிலின் பின்புறத்தை வெட்டும் போது அடுத்த திமில் கண்ணில் தென்படும். நேரம் செலவழிந்து கொண்டே இருந்தது, மலைமுகடுகளும் முடிவது போலத் தோன்றவில்லை.

எங்களது உண்மையான பேரார்வம் சிறிது விலகியது. இது ஒரு கடுமையான போராட்டமாகவே மாறியது. எங்களுக்கு முன்னே இருந்த பனிப்பாறை (snowy summit) எழுவதற்குப் பதிலாக, கிழே விழ ஆரம்பித்ததை நான் அதன்பின் உணர்ந்தேன். ஒரு குறுகலான பனிமுகடு (ice-axe) ஒரு மலை உச்சியை நோக்கி ஓடுவதைப் பார்க்க நான் மேல் நோக்கி பார்த்தேன்.

இதிலிருந்து விடுபட வேண்டும் (relief) என்பதே என் முதல் உணர்வாக இருந்தது. மேலும் இனிமேல் வெட்டுவதற்கு படிகட்டுகளோ, கடப்பதற்கு மலை முகடுகளோ, வென்றுவிடலாம் என்ற நம்பிக்கைக்கு ஏமாற்றம் அளிக்கும் மலை அங்கே காணப்படவில்லை. நான் டென்சிங்கை நோக்கினேன்.

மறைக்கக்கூடிய தலைகவசத்தையும் (balaclavahelmet), பனிக் கண்ணாடியையும், ஆக்சிஜன் வாயு முகமூடியையும் அணிந்திருந்தால் அனைத்தும் ஈட்டி போன்ற கூர்மையான வடிவுடைய பனிக்கட்டியும் சேர்த்து அவருடைய முகத்தை மறைத்தாலும், அவரைச் சுற்றிலும் அவர் பார்த்து விட்டு சந்தோஷத்தினால் சிரித்ததை எதையும் மறைக்கவில்லை.

நாங்கள் இருவரும் கை குலுக்கிக் கொண்டோம். டென்சிங் அவரது கையை என் தோள்மேல் போட்டுக் கொண்டார், கிட்டத்தட்ட மூச்சு முட்டும் வரை நாங்கள் இருவரும் முதுகில் தட்டிக் கொண்டோம். அப்போது நேரம் காலை 11,30 மணியாய் இருந்தது. இந்த மலை முகடு 2 1/2 மணி நேரத்தை எடுத்துக் கொண்டது, அது எங்களுக்கு ஒரு ஆயுட்காலமாகவே தோன்றியது.

எங்களுக்கு கிழக்கில் இதுவரை கண்டறியப்படாத ஏற்படாத பெரிய இராட்சச (giant) அண்டையரான மக்காலு (makalu) இருந்தது. மேகங்களுக்கிடையில் மிகத் தூரத்தில் கஞ்சன்சங்காவின் (Kanchenjunga) மிகப்பெரும் பகுதி அடிவானத்தில் நிழல் போல அச்சுறுத்தும் விதமாக காணப்பட்டது. மேற்கில் இதுவரை கண்டறியப்படாத நேபாளத்தின் மலைப்பகுதிகள் தூரத்திற்கு நீண்டு கிடந்ததை எங்களால் பார்க்க முடிந்தது.

வடக்கு மலைமுகட்டுக்கு கிழே உள்ள வடக்கு கணவாயையும் (North Col), 1920 மற்றும் 1930 களில் மலை ஏறுபவர்களால் போராடி பிரபலமாக்கப்பட்ட பழைய பாதையையும் (old route) காட்டும் மிக முக்கியமான புகைப்படமாக (photograph) நான் கருதும் புகைப்படம் அப்போது எடுக்கப்பட்டது. பத்து மணித்துளிகளுக்கும் பின், நான் மெதுவாக நகர்பவனாகவும் என் விரல்கள் வளைவுத் தன்மையற்றும் மாறின அதனால் நான் உடனே என் ஆக்சிஜன் உபகரணத்தை மாற்றினேன்.

இந்த வேளையில் (meanwhile), டென்சிங் பனியின் நடுவே ஒரு சிறிய துளையிட்டு (hole), அதனுள் – பலதரப்பட்ட சிறிய உணவுப் பொருட்களான (articles), சாக்லேட், பிஸ்கட், குச்சிமிட்டாய் (lollies) போன்றவற்றை வைத்தார். உண்மையில் இவை சிறிய படைப்புகள் தான் ஆனாலும் இந்த உயரமான மலைச்சிகரத்தை இருப்பிடமாக கொண்டுள்ளதாக நம்பும் அனைத்து பக்திமயமான புத்தமதத்தவர்களின் கடவுள்களுக்கு (devout Buddhists) ஒரு சிறு அடையாளப் பரிசாக இருக்கும்.

2 நாட்கள் முன்னதாக நாங்கள் தெற்கு கணவாயில் ஒன்றாக இருந்த போது, கர்னல் ஹன்ட் (Colonel Hunt) என்னிடம் ஒரு சிறிய சிலுவையை (crucifix) கொடுத்து, அதனை மலை உச்சிக்கு எடுத்துச் செல்லுமாறு கேட்டுக் கொண்டார். நானும் பனியில் சிறிய துளையிட்டு, டென்சிங்கின் பரிசுப்பொருட்களுக்கு அருகில் அந்த சிலுவையை வைத்தேன்.

15 நிமிடங்களுக்கு பிறகு, நான் உச்சியிலிருந்து எங்களது படிக்கட்டுகளை நோக்கி கீழே இறங்கினேன். ஆக்ஸிஜன் ‘ குறைந்து கொண்டிருப்பதன் அவசரத்தால் தூண்டப்பட்ட நாங்கள் நேரத்தை வீணாக்காமல் எங்கள் பாதையில் முன்னேறி சென்றோம் (cramponed). நாங்கள் மிக கவனமாக பாறையின் குறுக்கே தவழ்ந்து கடந்து, வழுக்கக்கூடிய பனிப்பகுதியில் ஒருவர் பின் ஒருவராக நகர்ந்து, கடைசியாக எங்களின் படிக்கட்டுகளில் மலையேறினோம் மேலும் திரும்பவும் தெற்கு வந்தோம்.

அப்போது நாங்கள் மிகவும் களைப்பாக இருந்தோம், ஆனாலும், நாங்கள் முகட்டில் சேமித்து வைத்திருந்த உருளைகளை (cylinders) நோக்கி கீழே நகர்ந்தோம். நாங்கள் எங்கள் முகாமை விட்டு மிக குறுகிய தூரத்தில் இருந்தாலும், எங்களது சொந்த குடுவைகளில் மிகச் சிறிய அளவே ஆக்சிஜன் மீதமிருந்ததாலும், நாங்கள் கூடுதல் உருளைகளை சுமந்து எதிர்பார்க்க முடியாத தரைத்தளத்தை (crazy platform) உடைய எங்களது கூடாரத்தை மதியம் 2 மணி அளவில் அடைந்தோம்.

எங்களுக்கு இதுவரை எல்லாவித தேவைகளுக்கும் நன்றாக உதவிய முகாமை கடைசியாக ஒருமுறை பார்த்த படி, நாங்கள் கீழ்நோக்கி திரும்பி, எங்கள் கால்களை இழுத்த படியே, மலை முகட்டிலிருந்து தெற்கு கணவாய்க்கு பாதுகாப்பாக கீழறங்கும் வேலையில் எங்களை ஈடுபடுத்திக் கொண்டோம்.

கனவைப் (dream) போலவே நேரம் கடந்தது முகாமிற்கு 200 அடிக்கு மேலே எங்களை நோக்கி வந்த இருவர் எங்களை சந்தித்தன. அவர்கள் சூடான சூப்பையும், நெருக்கடி கால ஆக்சிஜனையும் சுமந்து கொண்டிருந்த ஜரர்ஜ் லோ மற்றும் வில்பிரட் நாய்ஸ் ஆவார்கள். உயரத்திற்கு மிக அருகில் வந்த போது எனது ஆக்ஸிஜன் தீர்ந்தது. எங்களது வேலையை முடிப்பதற்கு போதுமான அளவு ஆக்ஸிஜனை நாங்கள் வைத்திருந்தோம், ஆனால் கொஞ்சம் கூட தேவைக்கு அதிகமாக இல்லை.

நாங்கள் எங்கள் கூடாரத்திற்குள் தவழ்ந்து வந்து, மகிழ்ச்சிப் பெருமூச்சு விட்டு (delight), எங்கள் தூங்கும் பைகளின் (sleeping bags) மேல் நிலை குலைந்து விழுந்த போது எங்களின் கூடாரங்கள் முடிவில்லாத தெற்கு கணவாயில் காற்றினால் சிறகடித்து (flapped) விழுந்து எங்களை பொட்டலம் போல் பொதிந்தது.

எங்களது பிரயாணத்தை வழிநடத்திய ஜான் ஹண்ட் என்பார் இவ்வாறு கூறுகிறார், “இது ஒரு மறக்க முடியாத நாளாக இருந்தது”. அவர்கள் உச்சியை ஏறி அடைந்தார்கள். அங்கே சந்தோஷ கூச்சலும், கைகலக்கல்களும், அரவணைப்புகள் இந்த இரண்டு கதாநாயகர்களுக்காக காணப்பட்டன. அவர்களது சந்தோஷமும் பெருமிதமும் டென்சிங் மற்றும் ஹிலாரியால் மிகச் கச்சிதமாக முடிக்கப்பட்ட இந்த சாலையை அவர்கள் எவ்வாறு பகிர்ந்து கொண்டார்கள், என்பதை காண்பித்தது. சாகசமானது (adventure) நிறைவுக்கு (concluded) வந்தது.

ஆபத்து மற்றும் கடினமான சூழ்நிலைகளில் உருவாக்கப்பட்ட குழுப்பணியும் (teamwork), தோழமை உணர்வும், ஒன்றையொன்று சந்தித்து, ஒன்றாக வென்றது தான் எவரெஸ்ட் சிகரத்தை ஏறிய கதையாகும், அவர்கள் இந்த பெரிய மலையின் உச்சியில் ஏறிய பிறகும், மற்றவர்களுக்கு அவர்களுடைய சொந்த “எவரெஸ்ட்களை” கண்டறியும் வண்ணம்.

சாகசத்திற்கான நிறைய சந்தர்ப்பங்கள் இன்னனமும் உள்ளன. அவற்றுள் சில, கைக்கு மிக அருகாமையிலும், மற்றவை வேறு நிலங்களில் வெகு தூரத்திலும் உள்ளன. அனைத்து சாகசங்களும் உற்சாகமளிப்பதில்லை. அதுபோல மலையில், மட்டுமே சாகசங்கள் புரியப்படுவதில்லை. நம்முடைய அன்றாட வாழ்க்கையிலும், கடவுளின் உன்னத சக்தியால் மேலே ஏறுவதற்கு எவெரெஸ்ட்கள் உள்ளன.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.5 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.5

Question 1.
A bridge has a parabolic arch that is 10 m high in the centre and 30 m wide at the bottom. Find the height of the arch 6 m from the centre, on either sides.
Solution:

PQ = 2a = 30 m
a = 15 m
Point Q be (15 , -10)
Equation of the parabola
x² = -4 ay …….. (1)
Q lies on parabola
15² = -4a( -10)
a = \(\frac {225}{40}\)
(1) ⇒ x² = -4(\(\frac {225}{40}\))y
x² = \(\frac {225}{10}\)y
Let B(6, y) lies on parabola
6² = \(\frac {225}{10}\) y₁
y₁ = –\(\frac {36×10}{225}\) = \(\frac {-8}{5}\) = \(\frac {8}{5}\) m
AB = AC – BC = 10 – \(\frac {8}{5}\)
= \(\frac {50-8}{5}\) = \(\frac {42}{5}\)
AB = 8.4 m
∴ The height of the arch 6 m from the centre is 8.4 m.

Question 2.
A tunnel through a mountain for a four lane highway is to have a elliptical opening. The total width of the highway (not the opening) is to be 16 m and the height at the edge of the road must be sufficient for a truck 4 m high to clear if the highest point of the opening is to be 5 m approximately. How wide must the opening be?
Solution:

Let the equation of the ellipse be
\(\frac {x^2}{a^2}\) + \(\frac {y^2}{b^2}\) = 1
Length of semi minor axis b = 5
i,e., \(\frac {x^2}{a^2}\) + \(\frac {y^2}{5^2}\) = 1
Let BB’ be the road width and AA’ be the end points of the opening of the tunnel.
Let CB = 8, BD = 4
∴ D is (8, 4) lies on the ellipse
\(\frac {8^2}{a^2}\) + \(\frac {4^2}{5^2}\) = 1
⇒ a² = \(\frac {25}{9}\) × 64
⇒ a = \(\frac {40}{3}\)
The width AA’ = 2a
= \(\frac {80}{3}\) = 26.66 m
The required width is 26.66 m.

Question 3.
At a water fountain, water attains a maximum height of 4 m at horizontal distance of 0.5 m from its origin. If the path of water is a parabola, find the height of water at a horizontal distance of 0.75 m from the point of origin.
Solution:

Let the equation of parabola be
(x – h)² = -4a (y – k)
Here vertex B (0.5, 4)
∴ Equation of parabola
(x – 0.5)² = -4a(y – 4)
Parabola passes through origin (0, 0)
(0 – 0.5)² = -4a(0 – 4)
(-\(\frac {1}{2}\))² = 16a
∴ \(\frac {1}{4}\) = 16a ⇒ a = \(\frac {1}{64}\)
∴ Equation of parabola
(x – 0.5)² = -4(\(\frac {1}{64}\))(y- 4)
This Parabola passes again through D(0.75, y₁)
∴ (0.75 – 0.5)² = –\(\frac {1}{16}\) (y₁ – 4)
(0.25)² = –\(\frac {1}{16}\) (y₁ – 4)
(\(\frac {1}{4}\))² = –\(\frac {1}{16}\) (y₁ – 4)
\(\frac {1}{16}\) = –\(\frac {1}{16}\) (y₁ – 4)
1 = -y₁ + 4
y₁ = 3
Height of water at a horizontal distance of 0.75 m is 3 m.

Question 4.
An engineer designs a satellite dish with a parabolic cross section. The dish is 5 m wide at the opening and the focus is placed 1.2 m from the vertex
(a) Position a co-ordinate system with the origin at the vertex and the x-axis on the parabola’s axis of symmetry and find an equation of the parabola.
(b) Find the depth of the satellite dish at the vertex.
Solution:

(a) Consider the satellite dish is open rightward parabola
y² = 4 ax ……….. (1)
Clearly a = 1.2m
(1) ⇒ y² = 4(1.2)
y² = 4.8x
(b) Use the point (x₁, 2.5) in (1)
(2.5)² = 4(1.2)x₁
\(\frac{(2.5)^{2}}{4(1.2)}\) = y₁
x₁ = 1.3 m
∴ The depth of the satellite dish at vertex is 1.3 m

Question 5.
The parabolic cable of a 60 m portion of the roadbed of a suspension bridge are positioned as shown below. Vertical cables are to be spaced every 6 m along this portion of the roadbed. Calculate; the lengths of first two of these vertical cables: from the vertex.

Solution:

From the diagram, the equation is x² = 4 ay and it passes through C(30, 13)
Equation of Parabola x² = 4ay.
30² = 4a × 13
4a = \(\frac {30^2}{13}\)
∴ Equation of the parabola is
x² = \(\frac {30^2}{13}\)y
(i) Let VG = 6 and GE = y
∴ E is (6, y) and it lies on the parabola
36 = \(\frac {30^2}{13}\)y
⇒ y = 0.52
Gable from the road = 3 + 0.52
= 3.52 m.

(ii) Let VH = 12 and HF = y
∴ F (12, y) lies on the parabola
12² = \(\frac {30^2}{13}\)y
⇒ y = \(\frac {144×13}{900}\)
= \(\frac {208}{100}\)y
y = 2.08
Cable from the road = 3 + 2.08 = 5.08
The heights of the first two vertical cables from the vertex are 3.52 m and 5.08 m

Question 6.
Cross-section of a Nuclear cooling tower is in the shape of a hyperbola with equation \(\frac {x^2}{30^2}\) – \(\frac {y^2}{44^2}\) = 1. The tower is 150 m tall and the distance from the top of the tower to the centre of the hyperbola is half the distance from the base of the tower to the centre of the hyperbola. Find the diameter of the top and base of the tower.

Solution:

Equation of hyperbola is \(\frac {x^2}{30^2}\) – \(\frac {y^2}{44^2}\) = 1
Given OC = \(\frac {1}{2}\) OD and CD = 150
∴ OC = 50 m and OD = 100 m
Let the Radius of top of the tower be x₁ and bottom of the tower be x₂.
∴ Points A(x₁, 50) and B(x₂, 100)
Hyperbola passes through A(x₁, 50)

∴ Radius of the top = 45.41 m.
Diameter of the top = 90.82 m
Also
The hyperbola again passes through B(x₂, 100)

∴ Radius of the base = 74.48 m.
Diameter of the base = 148.96 m
∴ Diameter of the top and base of the tower are 90.82 m and 148.96 m.

Question 7.
A rod of length 1.2 m moves with its ends always touching the co-ordinate axes. The locus of a point P on the rod, which is
0. 3 m from the end in contact with x axis is an ellipse. Find the eccentricity.
Solution:

Length of rod BD = 1.2 m
Let P(x, y) be any point on the Rod such
that PB = 0.3 m
∴ PD = 1.2 – 0.3 = 0.9 m
Let ΔPAB and ΔPCD are similar triangles
In ΔPAB sin θ = \(\frac {y}{0.3}\)
In A PCB cos θ = \(\frac {y}{0.9}\)
We know that sin² θ + cos² θ = 1

Question 8.
Assume that water’issuing from the end of a horizontal pipe, 7.5 m. above the ground, describes a parabolic path. The vertex of the parabolic path is at The end of the pipe. At position 2.5 in below the line of the pipe, the flow of water has curved outward 3 m beyond the vertical, line through the end of the pipe. How far beyond this vertical line will the water strike the ground?
Solution:

Equation of the water path is
x² = – 4 ay
Use the point (3, – 2.5) in (1)
(3)² = – 4a(- 2.5)
9 = 10a
a = \(\frac{9}{10}\) substituting in (1)
(1) ⇒ x² = -4\(\frac{9}{10}\)y …………. (2)
Use the point (x₁, -7.5) in (2)
(2) ⇒ x₁² = -4 \(\frac{9}{10}\)(-7.5) ⇒ x₁² = 30(\(\frac{9}{10}\))
x₁ = \(\sqrt{3 \times 9}\)
x₁ = \(3 \sqrt{3}\) m
∴ The water strikes the ground \(3 \sqrt{3}\) m beyond the vertical line.

Question 9.
On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 in when it is 6 m away from the point of projection. Finally, it reaches the ground 12 in away from the starting-point. Find the angle of! projection.
Solution:

Equation of the parabola be x² = – 4ay ……. (1)
B(6, -4) lies on parabola
6² = -4a(-4)
\(\frac {36}{16}\) = a ⇒ a = \(\frac {9}{4}\)
(1) ⇒ x² = -(\(\frac {9}{4}\))y
x² = -9y ………. (2)
Now need tofind slope at (-6, -4)
Diff (2) w.r.to x
2x = -9 \(\frac {dy}{dx}\)
\(\frac {dy}{dx}\) = \(\frac {2x}{-9}\)
At(-6, -4), \(\frac {dy}{dx}\) = \(\frac {2(-6)}{-9}\) = \(\frac {12}{9}\) = \(\frac {4}{3}\)
tan θ = \(\frac {4}{3}\)
θ = tan^-1(\(\frac {4}{3}\))

Question 10.
Points A and B are 10 km apart and it is determined from the sound of an explosion heard at those points at different times that the location of the explosion is 6 km closer to A than 5. Show that the location of the explosion is restricted to a particular curve and find an equation of it.
Solution:
As shown in figure, A and B are on both sides of x-axis at Co-ordinates (-5, 0) and (5, 0)
The distance between A and B is 10. A point C is on the graph at Co-ordinates (x, y)
C is 6 km closer to A than B.

Squaring on both sides we get,
(x – 5)² + y² = 36 + (x + 5)² + y² + 12(\(\sqrt {(x+5)^2+y^2}\))
x² + 25 – 10x + y² = x² + 10x + y² + 36 + 25 + 12\(\sqrt {(x+5)^2+y^2}\)
-20x – 36 = 12\(\sqrt {(x+5)^2+y^2}\)
(÷ by 4) ⇒ -5x – 9 = 3\(\sqrt {(x+5)^2+y^2}\)
Squaring both sides we get,
25x² + 81 + 90x = 9(x² + 25 + 10x + y²)
25x² + 81 + 90x – 9x² – 90x – 9y² – 225 = 0
16x² – 9y² – 144 = 0
16x² – 9y² = 144
(÷ by 144) ⇒ \(\frac {x^2}{9}\) – \(\frac {y^2}{16}\) = 1 is the required equation of hyperbola.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 3 In Celebration of Being Alive Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 3 In Celebration of Being Alive

12th English Guide In Celebration of Being Alive Text Book Back Questions and Answers

Textual Questions:

1. Answer the following questions in one or two sentences based on your understanding of the lesson: (P.No. 70)(Note: IQ —> Important Questions)

Question a.
What thoughts troubled Dr. Christiaan Barnard as he neared the end of his career as a heart surgeon?
Answer:
Towards the end of his career, Dr. Christiaan Barnard was troubled by the suffering of people and especially of young children. He could not accept the fact that 12 million children are unlikely to reach the age of one and about 6 million children die annually before reaching the age of five.

Question b.
What were Dr. Barnard’s feelings when he was hospitalized after an accident?
Answer:
Dr. Barnard had a feeling about why his wife and himself had to suffer.

Question c.
When and where did the accident occur? (IQ)
Answer:
He and his wife were crossing the road after a lovely meal. A car hit him and knocked him into his wife. His wife was thrown into the other lane and was struck by a car coming in the opposite direction.

Question d.
How did the hospitalization of Dr. Barnard and his wife affect their routine?
Answer:
Dr. Barnard was not able to attend to the patients who were waiting for him to operate on them. His wife was not able to take care of her young baby.

Question e.
How was Dr. Barnard’s attitude to suffering different from that of his father’s?
Answer:
Dr. Barnard’s father accepted suffering as God’s will. He also believed that suffering ennobles humans. But Dr. Barnard found no meaning in the agony and suffering of patients and especially of the young children.

Question f.
How was the unattended trolley put to use? (IQ)
Answer:
The unattended trolley was used as a car for a race (Grand Prix of Cape Town’s Red cross children’s’ hospital) within the hospital.

Question g.
What roles did the duo take up?
Answer:

1. The two boys took the roles of a driver and a mechanic
2. The blind boy was the mechanic and the boy with on arm was the driver.

Question h.
Why did the choice of roles prove to be easy for them?
Answer:
The mechanic provided motor power by galloping along behind the trolley with his head down. The driver steered the trolley by scraping his foot on the floor. The choice of the roles was easy because the mechanic was totally blind and the driver had only one arm.

Question i.
Who encouraged them and how?
Answer:
The other patients encouraged them by laughing and shouting.

Question j.
What does Dr. Barnard compare this entertainment to?
Answer:
Dr. Barnard compared the trolley race as much better entertainment than anything anyone puts on at the Indianapolis 500 car race.

Question k.
What happened in the grand finale? (IQ)
Answer:
The grand finale led to the scattering of plates and silverware placed on the trolley.

Question l.
How does Dr. Barnard know the boy who played the trolley’s driver?
Answer:
Dr. Barnard knew the trolley’s driver better. He had successfully closed a hole in his heart a few years back.

Question m.
What was the profound lesson that Dr. Barnard learned from the boys?
Answer:
The profound lesson that Dr.Barnard learned was that the business of living in the celebration of being alive.

2. Answer the following questions in three or four sentences: (Text Book Page No. 71)

Question a.
Detail the statistics Dr. Barnard has provided in his speech.
Answer:
Of the 125 million children bom that year, 12 million are unlikely to reach the age of one. Another six million will die before the age of five. Among the rest, many will end up as mental or physical cripples.

Question b.
What happened when the doctor couple was crossing the street?
Answer:
When they were crossing the street a car hit him and knocked him into his wife. She was thrown into the
other lane and struck by a car coming from the opposite direction.

Question c.
What injuries did they sustain in the accident?
Answer:
Dr. Barnard had eleven broken ribs. A lung was profoundly perforated. His wife had a badly fractured shoulder.

Question d.
Dr. Barnard couldn’t find any nobility in suffering. Why?
Answer:
Dr.Barnard couldn’t find any nobility in suffering because a sufferer would move restlessly with his mind filled with agony.

Question e.
Why does Dr. Barnard find the suffering of children heartbreaking?
Answer:
He has always found the suffering of young children heart-breaking. Especially because they have total faith in doctors. They believe doctors will help. They don’t complain even after undergoing a mutilating surgery.

Question f.
How did the boy who played the mechanic lose his eyesight?
Answer:

1. One night his mother and father were drunk.
2. His mother threw a lantern at his father which missed and broke over the child’s head and shoulders.
3. He suffered severe third-degree burns on the upper part of his body and lost both his eyesight.

Question g.
Why does Dr. Barnard describe the blind boy as a ‘walking horror’?
Answer:
At the time of the Grand Prix, the boy was a walking horror. His face was disfigured. A long flap of skin was hanging from the side of his neck to his body. As the wound healed around his neck, his lower jaw became gripped in a mass of fibrous tissue. The only way he could open his mouth was to raise his head.

Question h.
What were the problems the trolley driver suffered from?
Answer:

1. The trolley driver had a hole in his heart which was successfully closed by Dr.Barnard.
2. He also suffered from a malignant tumour of the bone because of which his shoulder and arm were amputated.

3.Answer the following in a paragraph of 100 – 150 words each: (P.No. 71)

Question a.
Give an account of the medical problems for which the two boys were hospitalized.
Answer:
The seven years old mechanic suffered third-degree bums on the upper part of his body. He had lost both his eyes. He was literally a walking horror. He was disfigured. A long flap of skin was hanging from the side of his neck to his body. As the wound healed around his neck, his lower jaw became gripped in a mass of fibrous tissue. The trolley driver had a malignant tumour of the bone. A few days before the race, his shoulder and arm were amputated. There was little hope of his recovery. If two adults had similar ailments, they would have got dejected with life. But the boys were just happy celebrating the joy of being alive.

Question b.
“These two children had given me a profound lesson …” Elucidate.
(or)
Question c.
Describe the ‘Grand Prix’ at Cape Town’s Red Cross Children’s Hospital.
(or)
Question d.
How did a casual incident in a hospital help Dr. Barnard perceive a new dimension of life?
Answer:
The author describes the event as “the Grand Prix of Cape Town’s Red Cross Children’s’ Hospital”. A nurse had left a breakfast trolley unattended. Very soon this trolley was commandeered by a daring crew of two, a driver and a mechanic. The mechanic provided motor power by galloping along behind the trolley head down. While the driver, seated on the lower deck held on with one hand and steered it by scrapping his foot on the floor. The choice of roles wags easily because the mechanic was totally blind and the driver had only one arm. It was better than the Indianapolis 500 car race. Patients shouted and cheered the boys. There was a grand finale of scattered plates and silverware before the nurse and ward sister took control of the situation.

Question e.
Life is unjust and cruel to certain people. Do they all resign themselves to their fate? Can you think of some who have fought their disabilities heroically and remained a stellar example for others? (for e.g. the astrophysicist Stephen Hawking, a paraplegic). Give an account of one such person and his/her struggle to live a fruitful life.
Answer:
It is a true fact that life is unjust and cruel to certain people. But they all do not resign themselves to their fate. In this context it is worth mentioning Divij Shah who is a one-handed cycling champion, He lost his right hand in an accident when he was four. Determined not to define that mishap in his life, he has experienced way more than the average person with two hands. In his teens, he played for West Bengal’s U-16 cricket team. Constantly looking for challenges, he also took upcycling. After meticulous practice, he bagged silver at the Asian Para-cycling championships that took place a few months ago. At present, Divij has his eyes set on becoming a champion in the 2020 Paralympics.

Paragraph:

Introduction:
In celebration of being alive is an extract of Christiaan Barnard’s speech wherein he narrates an incident which took place in his hospital. It is this incident which made him look at the positive aspect of life. He and his wife met with an accident a few years back. They both were affected very badly. Barnard had eleven broken ribs and a perforated lung and his wife had a badly fractured shoulder. He had a bad feeling about why his wife and himself had to suffer.

4 Better person:
He remembered his father’s words who was of the view that suffering ennobles one and makes one a better person. Barnard found the suffering of children heartbreaking.

In the hospital:
A ‘Grand Prix’ of cape town’s red cross children’s hospital made him perceive a new dimension of life. A nurse had left a breakfast trolley unattended which was taken possession of by two bold and daring boys. One acted as a driver and the other a mechanic.

The mechanic who was seven years old suffered severe third-degree burns on the upper part of his body and lost both his eyes. The trolley’s driver had a hole in his heart which was successfully closed by Dr. Barnard. Later he was hospitalized again because he had a malignant tumour of the bone out of which his shoulder and arm were amputated.

Life lesson:
The patients encouraged them by their shouts and laughter. It was a much better entertainment the result of which was the scattered plates and silverware placed on the trolley. After the Grand Prix, the driver who had a little hope of recovery proudly informed Dr. Barnard that the trolley’s wheels were not properly oiled but he was a good driver and he had full confidence in the mechanic.

Conclusion:
Thus the action of the two children made Dr. Barnard realize the fact that the business of living is the celebration of being alive. He also realized that what is important is what you’ve left and not what you’ve lost.
Learn to live in the sufferings

Vocabulary:
Go through the lesson and spot the words which mean the same as the following: (Text Book Page No. 71)

Question 1.
profession (para 1)
Answer:
Career

Question 2.
sorrowful (para 2)
Answer:
Gloomy

Question 3.
decency (para 5)
Answer:
Noble

Question 4.
destiny (para 6)
Answer:
Fate

Question 5.
hijacked (para 8)
Answer:
Commandeered

Question 6.
motivation (para 9)
Answer:
Encouragement

Question 7.
serious (para 10)
Answer:
Severe

Question 8.
significant (para 13)
Answer:
Important

b) Go through the lesson and spot the words opposite to the meaning of the following:
Question 1.
rare (para 1)
Answer:
prevalent

Question 2.
primitive (para 6)
Answer:
sophisticated

Question 3.
fiction (para 7)
Answer:
witness / fact

Question 4.
fearful (para 8)
Answer:
intrepid

Question 5.
benign (para 11)
Answer:
malignant
Question 6.
diffidence (para 11)
Answer:
hope, confidence

Question 7.
boredom (para 12)
Answer:
amusement/recreation

Question 8.
criticize (para 13)
Answer:
appreciate.

c) Frame illustrative sentences to distinguish the meaning of the words in the following clusters: (Text Book Page No. 72)

1. career — carrier — courier
2. patients — patience — patents
3. accident — incident — incidence
4. scraping — scrapping — scrubbing
5. accept — except — expect
6. lesson — lessen — lesion
7. severe — sever — sewer
8. raise — rise— rice
9. quiet — quite — quit
10. final — finale — feline

Answer:

d) Fill in the blanks with the words given in brackets: (Text Book Page No. 72)
[profound, amusement, confidence, agony, solace, intrepid, disfigured, perforated]

Question 1.
Theatrical plays were a main source of ___________ before the advent of television.
Answer:
amusement

Question 2.
The __________ warriors of the Spartan Army marched into battle against a powerful enemy.
Answer:
intrepid

Question 3.
The ___________ of parents finally came to an end when their lost child was found with the help of police.
Answer:
agony

Question 4.
Social media has brought about a ________ impact on the lives of millennials.
Answer:
profound

Question 5.
The tires of the car got ________ when the vehicle rolled over the rusted nails scattered on the road.
Answer:
perforated

Question 6.
Thomas Alva Edison did not lose his, ________ even after facing a series of experimental failures in his quest to discover tungsten.
Answer:
confidence

Question 7.
Many victims of the pipeline explosion in an oil refinery were left permanently ________.
Answer:
disfigured

Question 8.
The old lady found ________ in the company of the children in the neighbourhood.
Answer:
solace

e) Form a phrase with each of the following pairs of nouns given below: (Text Book Page No. 72)

Here is an example from the lesson:
fibre + tissue — fibrous tissue

Question 1.
muscle + pain
Answer:
Muscular pain

Question 2.
skeleton + system
Answer:
skeletal system

Question 3.
nerve + disorder
Answer:
nervous disorder

Question 4.
digestion + enzymes
Answer:
digestive enzymes

Question 5.
surgery + instruments
Answer:
surgical instruments

Question 6.
agony + experience
Answer:
agonic experience

Question 7.
glory + victory
Answer:
glorious victory

Question 8.
fancy + idea
Answer:
fanciful idea

Question 9.
emotion + song
Answer:
emotional song

Question 10.
sense + issue
Answer:
sensible issue / sensitive issue.

f) Fill the empty boxes with suitable words under each word class: (Text Book Page No. 73)

Answer:

g) Spot the errors in the following sentences and rewrite them correctly: (Text Book Page No. 73) 

Question 1.
My grandfather is well-known in the village for his noble deeds.
Answer:
noble

Question 2.
I had my evening meals in a restaurant near my office.
Answer:
meal

Question 3.
The Boss had full confidence in his Manager for the successful completion of the project.
Answer:
in

Question 4.
After the complicated surgery, the patient hoped to complete recovery.
Answer:
for

Question 5.
The new health care scheme announced by the Government will bring relief to the children suffering with acute tuberculosis.
Answer:
from

Question 6.
In spite of his poverty and setbacks, was able to launch his dream carrier.
Answer:
career.

Listening: (Text Book Page No. 73)

Listen to the passage being readout. Based on your understanding, complete the statements given below with appropriate answers:

Question 1.
Boredom occurs when a person is unable to ________.
Answer:
stay attentive

Question 2.
________ and ________ are emotional consequences of boredom.
Answer:
Anger, frustration

Question 3.
Two physical signs of acute boredom are ________, ________.
Answer:

• eyelids droop
•  the frown on the face

Question 4.
How does boredom affect the quality of work a person does?
Answer:
A bored person commits a lot of errors in his work.

Question 5.
Mention two ways by which one can overcome boredom.
Answer:

• exercise
• set goals and work for them

Speaking: (Text Book Page No. 73)

Question 1.
You are rushing to attend to important work and you witness an accident on your way. Will you go to the rescue of the injured person? Share your views with the class.
Answer:
It is human nature to help the suffering. If I happen to see an accident while going on important work, I would go to the rescue of the injured person. While I was going out on important work, I happened to see an accident on the road. An old lady who was crossing the road was knocked down by a car. She fell down on the road with bleeding injuries. I immediately went to her, tied a cloth around the injured place to stop bleeding, and took her to a nearby hospital in, an auto-rickshaw. The doctors treated her injuries and her life was saved. I informed her relatives about the accident and they rushed to the hospital. They thanked me for helping the old lady.

Question 2.
Every person should take up the responsibility to serve society in his or her own way. Discuss the various ways in which you can serve society.
Answer:
Every citizen has the responsibility to serve society. There are many ways of helping the needy. Plastic has ruined the environment. The government is taking various, steps to ban the use of plastic. Awareness should be created among the public about the dangers of using plastic. I would form a small group of my friends and try to bring awareness to the public by meeting members of every household in my locality. Planting trees is very important. I will contact people, try to plant saplings wherever it is possible. I would meet the children in the locality and their parents and request them to inculcate healthy habits in their children regarding personal hygiene.

Dialogue: (Text Book Page No. 73)

Here is a conversation between a student who wishes to open an account and a bank clerk. (Text Book Page No. 74)

Student: Good morning, madam.
Bank Clerk: Good morning, what can I do for you?
Student: I would like to open an account in your bank.
Bank Clerk: Are you a student of a school or a college?
Student: I am a student of Govt. Hr. Sec. School, Tirunelveli.
Bank Clerk: Why do you want to open an account?
Student: My class teacher advised me to open an account to receive the monetary benefits from government schemes.
Bank Clerk: Here is an application form to open an account in our bank. Fill it up.
Student: Should I enclose any document with the form?
Bank Clerk: Yes. You should enclose a valid identity proof and an address proof that are approved by the government.
Student: Madam, can I submit the form and documents tomorrow?
Bank Clerk: Okay. You need to make an initial deposit of Rs. 500/- to open an account.
Student: Sure Madam, Thank you.
Bank Clerk: You are welcome.

a) Pair work: Practise the dialogue with another student. Then write a similar dialogue between a student and the class teacher regarding an educational trip: (Text Book Page No. 74)

Student: Good morning Mam.
Teacher: Yes, Good morning what about our educational trip?
Student: Yes Mam, I have come to speak about that.
Teacher: Did you inform all the students about it?
Student: Yes, Mam. I have informed all the students. But some of them are not willing to come.
Teacher: Why? Any problem?
Student: Yes Mam, Money is the only problem for them.
Teacher: OK, Give me the list of the students who are willing to participate in the educational trip.
Student: Yes Mam, I will give it at once.
Teacher: OK, see you in the classroom.

.
b) Build a conversation for the following situations with a minimum of five exchanges: (Text Book Page No. 74)

1. A passenger and a railway staff regarding the cancellation of the reserved tickets:
Passenger: Good Morning Sir.
Staff: Good morning, what can I do for you?
Passenger: Sir, I want to cancel my reserved ticket.
Staff: Why? What ¡s the reason?
Passenger: My grandfather is dead. So I am unable to go now.
Staff: 0k, It’s all right.
Passenger: Will you refund the money, Sir?
Staff: Yes, please fill the cancellation form.
Passenger: Sure sir, Thank you very much.
Staff: You are welcome.

2. Two friends about the NSS camp which they are going to attend:
Ramu: Hai Rahul, How are you?
Raghul: I am fine. How are you?
Ramu: lam fine. Are you coming to the NSS camp?
Raghul: Yes, I will come. What about you?
Ramu: Yeah! I will also come.
Raghul: Are you willing to participate in any programme?
Ramu: Yes, I will.
Raghul: Shall we speak about the danger of plastics?
Ramu: OK. It’s a good idea.
Raghul: OK, Ram we shall meet in the NSS camp.

3. A salesman and a customer at an electronic shop:
Salesman: You are welcome Sir. what do you want?
Customer: May I have a mixie?
Salesman: Yes, off course. which company do you want sir?
Customer: I want to buy preethi sir.
Salesman: Please come to this side.
Customer: what is the price of it?
Salesman: It is only Rs.3500 sir.
Customer: Does it have any warranty
Salesman: Yes, sir It has 10 years warranty.
Customer: 0K sir, I take this one.

4. A father and his daughter about the advantages of the habit of newspaper- reading:
Father: Do you read any newspaper regularly?
Daughter: Yes dad, I am reading the newspaper daily.
Father: Ws nice. Do you think reading newspaper is essential?
Daughter: Certainly. In fact, it is a storehouse of knowledge.
Father: What can you learn from it?
Daughter: I can learn about world trade, commerce, politics, films, games, and sports, etc from it.
Father Now, what is your suggestion for others?
Daughter: I want to say that everybody should read at least one newspaper daily.
Father: Okay, It is a good habit, and keeps going.
Daughter: Thank you, Dad.

c) Extend the conversation with two more relevant exchanges: (Text Book Page No. 75)

1. Receptionist: Good evening, sir. Welcome to Chennai.
Traveller: I would like to book a deluxe room in your hotel for 3 days.
Receptionist: Single room or double room?
Traveller: Double room, please
Receptionist: Sir, give me your Aadhar card.
Traveller: I have my driving license only
Receptionist: 0k. That will do sir.

2. Student: Good morning, sir. May I come in?
Teacher: Good morning, why are you late today?
Student: My bus broke down on the way. So I had to walk to school.
Teacher: Go and inform the HM.
Student: Yes sir, I will inform him.
Teacher: Get his permission and then enter the classroom

Reading:

Reading Comprehension: (Text Book Page No. 75)

Read the passage given below and answer the questions that follow:

Humans have long been fascinated by fiction. We experience the excitement in assigning supernatural power to
imaginary characters in fictional stories and so we have Spiderman, Batman, He-man, Titans, and many more. The ‘Cyborg’ was an offshoot of such wild imagination of humans to invest our species with superhuman powers. Today, the Cyborg is no more an imaginary organism. We are living in a world where a sizeable population of humans has merged their bodies with technological implants. The term Cyborg, short for ‘cybernetic organism’ was coined to describe a man, whose body is implanted with technological devices to supplement and substitute body functions.

Cyborgs include people with cardiac pacemakers, contact lenses, bionic ears and eyes, prosthetics, and so on. In other words, a cyborg is partly human and partly machine. The technological innovations in the field of medicine and healthcare augment humans with machines, producing a beta version of the human body. The advent of brain-machine interfaces is certain to blur the boundary between humans and machines. Scientists are working hard to find a technique for age reversal too. People do not want to die, so mankind is striving to get to the final frontier, which is the development of machines and devices that would accord man immortality.

The needs of humans are not limited. As time passes, food habits change, thinking patterns change, and even appearances change. We are about to travel by driverless, fully automated vehicles. Computers and smartphones have become our masters. The more we depend and merge with technological advancements, the more the humanness in us slowly erodes. Intelligence is sought to be infused into machines and robotics are designed in such a way to give the man a virtual human companion. The field of artificial intelligence is overtaking the human brain and many fear that it could even harm the human race. Despite certain limitations and potential threats, many believe that cyborgs will be the next step in the evolution of mankind. The amalgamation of man and machine is sure to add a new dimension to the life of mankind and this will prove to be the biggest evolution in Biology’ since the emergence of life, four billion years ago.

Question a.
Account for the popularity of characters with supernatural powers. (Text Book Page No. 76)
Answer:
Humans have long been fascinated by fiction. We experience the excitement in assigning supernatural power to imaginary characters in fictional stories

Question b.
Who is referred to as a ‘Cyborg’?
Answer:
The ‘Cyborg’ was an offshoot of such wild imagination of humans to invest our species with superhuman powers. Today, the Cyborg is no more an imaginary organism. We are living in a world where a sizeable population of humans have merged their bodies with technological implants.

Question c.
What is expected to happen with the advent of the brain-machine interface?
Answer:
The advent of brain-machine interfaces is certain to blur the boundary between humans and machines.

Question d.
The needs of humans are not limited. How is this statement elaborated in the passage?
Answer:
The needs of humans are not limited. As time passes, food habits change, thinking patterns change, and even appearances change. We are about to travel by driverless, fully automated vehicles. Computers and smartphones have become our masters.

Question e.
How can a machine turn into a virtual companion for humans?
Answer:
The more we depend and merge with technological advancements, the more the humanness in us slowly erodes. Intelligence is sought to be infused into machines and robotics are designed in such a way to give man a virtual human companion.

Question f.
Explain the flip side of the rapid technological advancement.
Answer:
Scientists are working hard to find a technique for age reversal too. People do not want to die, so mankind is striving to get to the final frontier, which is development of machines and devices that would accord man immortality.

Question g.
Identify the word in para 1 which means ‘everlasting life’.
Answer:
Long – immortality

Question h.
Which of the following words is synonymous with ‘amalgamation’?
Answer:
a) recreation
b) integration
c) exploration
d) proposition

Question i.
Which of the following options is the antonym of the word ‘advent’?
Answer:
a) drawback
b) dispute
c) departure
d) danger

Question j.
Find out the word which is the antonym of ‘natural’ in para 2.
Answer:
Artificial.

Active and Passive voice: (Text Book Page No. 76)

Task 1:
Change the following sentences into Passive Voice: (Text Book Page No. 77)

Question a.
Governor inaugurated the exhibition at ten o’clock.
Answer:
The exhibition was inaugurated by the Governor at ten o’clock.

Question b.
The crowd expected their leader to arrive early in the morning.
Answer:
Their leader was expected to arrive early in the morning by the crowd.

Question c.
Who taught her Computer Science?
Answer:
By whom she was taught computer science?

Question d.
They unanimously named Ravi the captain of the team.
Answer:
Ravi was named the captain of the team unanimously by them.

Question e.
The President gave the commander an award.
Answer:
The commander was given an award by the president.

Question f.
Do not tell a lie.
Answer:
Let not a fie be fold.

Question g.
Please open the door.
Answer:
Let the door be opened.

Question h.
It is time to stop work.
Answer:
Let the work be stopped by this time / It is time the work is stopped.

Question i.
They say he is a spy.
Answer:
It is said by them that he is supposed to be a spy.

Question j.
One should keep one’s promise.
Answer:
One’s promises should be kept.

Question k.
People burn a great deal of wood in winter.
Answer:
A great deal of wood is burned by people in winter.

Question l.
Where had you kept the book?
Answer:
Where had the book been kept by you?

Question m.
When did you feel the tremors?
Answer:
When was the tremors felt by you?

Question n.
How did you do the experiment?
Answer:
How was the experiment done by you?

Question o.
Whose car did someone park in front of your gate?
Answer:
Whose car was parked by someone in front of your gate?

Change the following sentences into Active Voice: (Text Book Page No. 78)

Question a.
The smuggler has been nabbed by the police.
Answer:
The police have nabbed the smuggler.

Question b.
By whom were you interviewed?
Answer:
Who interviewed you?

Question c.
Why were you scolded by your parents?
Answer:
Why did your parents scold you?

Question d.
Not a word was spoken by the convict in self¬defence.
Answer:
The convict did not speak a word in self defence.

Question e.
Good news is expected shortly.
Answer:
They expect Good news shortly.

Question f.
The mail has just been received.
Answer:
They have just received the mail.

Question g.
Sundari has been taken to the hospital by her husband.
Answer:
The husband has taken Sundari to the hospital.

Question h.
Our television is being repaired now.
Answer:
He is repairing our television now.

Question i.
Sweets have not been distributed to children by the organisers.
Answer:
The organisers have not distributed sweets to children.

Question j.
Prizes were being given by the chief guest.
Answer:
The chief guest was giving the prizes.

Question k.
Nobody has been seen in the library this week.
Answer:
I have seen nobody in the library this week.

Question l.
Nobody would have known the truth if you had not disclosed it.
Answer:
The truth would not have been known if it had not been disclosed by you.

Question m.
You are advised to help the poor and needy.
Answer:
You have to help the poor and needy.

Question n.
You are requested to make a cup of tea for the guest.
Answer:
Please make a cup of tea for the guest.

Question Tags: (Text Book Page No. 79)

Task 1:
Add suitable question tags to the following sentences and punctuate properly: (Text Book Page No.81)

Question 1.
The children are very happy today.
Answer:
Aren’t they?

Question 2.
You have not returned my books yet.
Answer:
Have you?

Question 3.
We enjoyed the trip very much.
Answer:
Didn’t we?

Question 4.
Let’s clean the shelves this weekend.
Answer:
Shall we?

Question 5.
My mother rarely travels by bus.
Answer:
Does she?

Question 6.
Somebody must bell the cat.
Answer:
Mustn’t someone?

Question 7.
Anita never comes late to the office.
Answer:
Does she?

Question 8.
I am always the winner.
Answer:
Aren’t I?

Question 9.
Don’t commit this mistake again.
Answer:
Will you?

Question 10.
There is a pharmacy near that bus stand.
Answer:
Isn’t there?

Question 11.
Bacteria can never survive in extreme weather conditions.
Answer:
Can they?

Question 12.
I am not as smart as you are.
Answer:
Am I?

Question 13.
The boys broke the windowpane last evening.
Answer:
Didn’t they?

Question 14.
Leaves wither during autumn.
Answer:
Don’t they?

Question 15.
You should add a little salt to the buttermilk.
Answer:
Shouldn’t you?

Task 2:
Correct the error found in the question tag in each of the following: (Text Book Page No.81) 

Question 1.
The evildoers cannot cross the path of truth, can’t they?
Answer:
Can they?

Question 2.
The vegetables in the fridge are still fresh, aren’t it?
Answer:
aren’t they?

Question 3.
The village head understood the intention of the politician, doesn’t he?
Answer:
didn’t he?

Question 4.
I claim to be a person of faith and prayer, aren’t I?
Answer:
don’t I?

Question 5.
The employees are seldom allowed to meet their boss, aren’t they?
Answer:
are they?

Question 6.
Let’s organize a trip to Goa, can we?
Answer:
shall we?

Question 7.
The landlady will charge me for the damage, shan’t she?
Answer:
won’t she?

Question 8.
Both the sisters have left for Canada, aren’t they?
Answer:
haven’t they?

Question 9.
That’s definitely not the right thing to do in this situation, isn’t that?
Answer:
is that?

Question 10.
We needn’t apply for a bank loan, do we?
Answer:
need we?

Question 11.
The Chief Guest spoke a few words, did he?
Answer:
didn’t he?

Question 12.
The rhinoceros has a horn made of keratin, haven’t they?
Answer:
hasn’t it?

Story writing: (Text Book Page No. 82)

Task 1:
Expand the following outlines into complete stories and supply a suitable title for each: (Text Book Page No. 83)

Exercise: (Text Book Page No. 84)

1. Big cotton merchant – owned a factory – many employees – one day a heap of cotton stolen – no due – merchant’s secretary assured to find out – asked him to host dinner – invite all workers – merchant agreed – middle of the feast – secretary suddenly shouted – cotton sticking to hair of thieves – the guilty dusted their heads – tried to clear – caught in the trap – punished.

The Clever Secretary

Once upon a time, there was a big cotton merchant. He owned a factory. Many employees were working on it. One day a bale of cotton was stolen. The merchant had no clue as to who might have stolen the baie of cotton. The merchant’s secretary assured him that she will find out the thief. She asked him to host a dinner and invite all the workers. Merchant agreed. When the feast was in progress, the secretary shouted suddenly, There is cotton sticking on to the hair of the thieves. The guilty ones dusted their heads to clear it. They ‘ .ere caught. They were punished.

2. Mr. X, a rich businessman – runs a company – always very busy with office work – one day his son – 10 years old – approaches dad and asks – how much he earns in one hour – father gets furious – boy persuades – father says Rs. 500 – immediate son asks for Rs. 300 – father shouts – wasting money on toys – son leaves to his room crying – father feels bad – thinks might need some stationery – enters boy’s room and gives money – boy becomes happy – takes some crumpled notes – under his pillow – counts everything together – total Rs.500 – gives it to dad – wants to buy – one hour of his time – father realizes his mistake – feels sorry and guilty – hugs son – closes all office files – takes him on a picnic – decides to spend more time with near and dear ones.

Sons Love for his father

Mr. X is a rich businessman. He runs a company. He is always busy with his office work. Like a snail, he carries his office workers everywhere. His young son one day asks him, “How much do you earn in an hour?”. The father gets furious and refuses to reply. But the son coaxes him to give the answer. The father grudgingly says, “Rs. 500/- an hour”. Immediately the boy asks his dad to give him three hundred rupees. He reprimands his son for trying to waste his hard-earned money. The boy cries and goes to the bedroom without dinner. The father feels guilty. He realizes that the boy might really need the money for buying some stationery. He gives him three hundred rupees. The next moment, the boy collected all the crumpled notes from under his pillow. Dad asks, “why did you ask for money when you have so much?”. Without replying the boy handed him Rs. 500/- and said, “This is the amount you earn in an hour, I have given you that money. Now will you spend an hour with me?”. The father realizes his mistake. He takes the boy out on a picnic. Then onwards he regularly spends time with him.

Task 2:
Continue and complete the following stories and suggest suitable titles for the same: (Text Book Page No. 85)

1. A rich man had a neighbour who was suffering from acute poverty. The rich man was proud of
his wealth and treated his poor neighbour with disrespect and derision. One day, a fortune-teller told the rich man that all his wealth would be possessed by his neighbour within a month. The rich man became greatly worried and spent sleepless nights. He did not know how to safeguard his wealth round the clock.

Suddenly he thought of a plan. He disposed of everything he had and with all that money, he bought a large, precious diamond. He sewed up the diamond in his turban. He proudly said to himself, “Now, there’s no way. My poor neighbour can never secure my wealth. The words of the fortune-teller will prove false.” …………………….

The rich man used to have the turban on his head securely always. One 0ay a strong wind blew the turban away. It was carried by a monkey which ran away, jumping on to trees. The rich man ran behind it. He could not keep pace with it. However, he found the turban near his house. He frantically searched for the diamond. But it was not there. The monkey searched for some food in the turban and in the process threw the diamond in the poor neighbour’s house. After many days the neighbour found the diamond, sold it, and became rich. Thus the astrologer’s prediction came true.

2. Four friends decided to go to a restaurant for dinner. They ordered an extra-large pizza with
grated cheese and other choice toppings. The next 20 minutes seemed to be too long a time. Their eyes widened and their mouth watered, when the server brought the steaming hot pizza and placed it on the table. They could barely control the drool. Simultaneously, all the four hands pulled at a slice from the plate, their faces beaming with a victorious grin. Silence prevailed as they were absorbed in the taste of their favourite food. They relished every mouthful to the core and savoured the taste of each topping with a smile of approval.

Soon, the plate was empty and clean with no trace. The boys dabbed their mouths and wiped their hands with tissues. Mission accomplished, they leaned back with immense joy and satisfaction not knowing, it would be short¬lived. The waiter arrived with the bill. Joseph, who had brought the others to the restaurant for a treat casually slipped his hand into his pocket to get his wallet. He gave a soft shriek accompanied by an expression of dismay and utter disbelief. He exclaimed, “It’s not there! Someone has pinched my wallet! What are we to do now?” ………….

Joseph tried to convince the manager of the hotel about the theft of the purse. He refused to accept their version and asked them to pay the bill. Joseph asked his friends to stay in the hotel and he went home, brought money and paid at the hotel, for the relief of all.

ஆசிரியரைப் பற்றி:

கிறிஸ்டியன் நீத்லிங் பெர்னார்டு (Christiaan Neethling Barnard) 1922ல் தென் ஆப்ரிக்காவில் ஓர் ஏழ்மையான பெற்றோருக்கு 4வது குழந்தையாகப் பிறந்தார். கல்வியில் அதிக நாட்டம் காட்டிய இவர், தனது சகோதரரை இதய நோயினால் (a cardiac ailment) இழந்த பிறகு மருத்துவம் (medicine) படிக்க தீர்மானித்தார். இவர் கல்வி உதவித்தொகை மூலமாக இதய அறுவை சிகிச்சையில் (cardiac surgery) மேற்படிப்பு பயின்றார்.

இதய அறுவை சிகிச்சை வல்லுநரான பெர்னார்டு, அக்காலத்தில் குணப்படுத்த இயலாத பிறவி மற்றும் சிக்கலான இதயக் கோளாறுகளில் கவனம் (focussed) செலுத்தினார். விலங்குகளிடம் இதயமாற்று அறுவை சிகிச்சை (heart transplantation) செய்து, பின்னர் 1967ல் உலகின் முதன்முதலில் மனிதர்களுக்கிடையே இதய மாற்று அறுவை சிகிச்சை செய்தார்.

இதனால் இவர் உலக அளவில் அடையாளங்காணப்பட்டு, இன்று வரை ஏற்றுக்கொள்ளக்கூடிய அறுவை சிகிச்சை உத்திகளை (techniques) வகுத்தார். இவர் 14 புத்தகங்களை எழுதியுள்ளார். இவரின் 235 அறிவியல் கட்டுரைகள், புகழ்பெற்ற பத்திரிக்கைகளில் பிரசுரமாகியுள்ளன. “ஒரே வாழ்க்கை ”, “ஆரோக்கியமான இதயத்திற்கு 50 வழிகள்”, “மிகச்சிறந்த மருந்து”, மற்றும் “நம்பிக்கை ‘ என்பன இவர் எழுதிய புத்தகங்களுள் சில இதய அறுவை சிகிச்சையில் முன்னோடியான இவர் கேப்டவுன் பல்கலைகழகத்தில் (University of Cape), மருத்துவத்துறையில் முனைவர் (Doctorate) பட்டம் பெற்றார்.

அதன் பிறகு உலகின் பல்வேறு பல்கலைக்கழகங்கள் இவருக்கு 11 கௌரவ டாக்டர் பட்டம் வழங்கின. இவர் 36 சர்வதேச விருதுகளைப் (International Awards) பெற்றுள்ளார். இவரின் கடைசி காலத்தில் இவர் “கிறிஸ்டியன் பெர்னார்டு அறக்கட்டளையை நிறுவி உலகம் முழுவதும் உள்ள பின்தங்கிய குழந்தைகளுக்கு (underprivileged) சேவை செய்யவும், அவர்களின் நிலையை உயர்த்த காரணமாகவும் இருந்தார். இவர் தனது 78ம் வயதில் 2001ல் மறைந்தார்.

பாடத்தைப் பற்றி:

“நாம் அனைவருக்கும் முதன் முதலில் இதய மாற்று அறுவை சிகிச்சை செய்த மருத்துவர் கிறிஸ்டியன் பெர்னான்ட் அறிவோம். இங்கே அவருடைய பேச்சின் சாரம்சம் கொடுக்கப்பட்டுள்ளது, இதில் வாழ்க்கையை குறித்து அவர் கொண்டிருந்த தோற்றத்தை மாற்றிய அவரது அனுபவத்தை விளக்குகிறார்”.

கொடுக்கப்பட்ட பாடத்தில் ஒரு மருத்துவமனையில் செவிலியர் (Nurse) ஒருவர் காலைச் சிற்றுண்டி வண்டியை கவனிக்காமல் விட்டுவிட்டனர். ஆனால் கை துண்டிக்கப்பட்ட சிறுவனும் இயந்திர வல்லுனரும் அதை நகர்த்தி நோயாளிகளுக்கு உணவு பரிமாறுகின்றனர். இருவரும் நல்ல பாடத்தை போதிக்கின்றனர். இப்படி ஒரு வியத்தகு மாற்றத்தை உண்டு பண்ணியது என்ன என்பதை இங்கே கண்டரிவோம்.

In Celebration of Being Alive Summary in Tamil

ஒரு இதய சிகிச்சை நிபுணராக என்னுடைய வேலையின் (career – பணி) இறுதியை நெருங்க நெருங்க என் மக்கள் ஏன் வேதனைப்பட வேண்டும் என்பதை நோக்கி என் எண்ணங்கள் (thoughts) திரும்பின. இன்று இவ்வுலகில் அதிகப்படியான மக்கள் மிக கொடூரமாக (cruelly) வேதனைப்படுகிறார்கள்.

இந்த ஆண்டு பிறக்கக்கூடிய 125 மில்லியன் குழந்தைகளில், 12 மில்லியன் குழந்தைகள் தங்களது ஒரு வயதை அடைவதே கடினம் மற்றும் அடுத்த 6 மில்லியன் குழந்தைகளில் 5 வயதை எட்டுவதே இல்லை என்பது உங்களுக்கு தெரியுமா! மீதமுள்ளவர்களில் நிறைய பேர் மனம் (mental) அல்லது உடல் ஊனமுற்றவர்களாகவே (physical cripples) ஆகின்றனர்.

சில வருடங்களுக்கு முன்னால் நான் சந்தித்த விபத்திலிருந்து எனக்கு இந்த இருண்ட எண்ணங்கள் (gloomy thoughts) தோன்றியிருக்கலாம் (stem). அருமையான உணவிற்கு பின் நான் என் மனைவியுடன் ஒரு நிமிடம் தெருவை தாண்டி சென்று கொண்டிருந்தேன். மறு நிமிடம் ஒரு கார் என்னை இடித்து (hit) என் மனைவியின் மீது தள்ளியது (knocked), அவளோ அடுத்த பாதையில் தூக்கி வீசப்பட்டு எதிரே வந்த காரினால் அடிப்பட்டாள் (struck).

அடுத்த சில நாட்கள் நான் மருத்துவமனையில் மிகுந்த மன வேதனையையும் (agony), பயத்தையும் (fear) மட்டும் அனுபவிக்கவில்லை கூடவே கோபத்தையும் (anger) உணர்ந்தேன். நானும் என் மனைவியும் ஏன் வேதனைப்பட வேண்டும் என என்னால் புரிந்து கொள்ள முடியவில்லை . என்னுடைய 11 விலா எலும்புகள் (ribs) உடைந்தன மற்றும் எனது நுரையீரலிலும் (lung) அடிபட்டு துளைகள் விழுந்தன. எனது மனைவியின் தோல்பட்டையும் நொறுங்கியது. ஏன் எங்களுக்கு இவ்வாறு நடக்க வேண்டும்? என மீண்டும் மீண்டும் நான் எனக்குள்ளே கேட்டுக்கொண்டேன்.

எல்லாவற்றிற்கும் மேலாக நான் எனது வேலையையும் பார்க்க வேண்டியதிருந்தது. என்னிடம் சிகிச்சை பெற நோயாளிகள் (patients) காத்து கொண்டிருந்தனர். எங்களின் சிறு வயது குழந்தைக்கு என் மனைவியின் அரவணைப்பு தேவைப்பட்டது.
எனது தந்தை இப்போது உயிரோடிருந்தால் அவர் இவ்வாறு தான் கூறியிருப்பார். “மகனே, இது கடவுளின் விருப்பம், அவர் இவ்வாறு தான் உன்னை சோதிப்பார். சோதனைகளே உன்னை மேன்மையாக்கி, ஒரு சிறந்த மனிதனாக உன்னை உருவாக்கும் (ennobles)”.

ஆனால், ஒரு மருத்துவராக வேர்வையால் நனைந்த படுக்கையில் (sweatsoaked bed) வலியால் துடித்துக் கொண்டும், மனம் நிறைய கடுந்துயராலும் நிரப்பப்பட்ட நோயாளிடம் எந்தவொரு பெருந்தன்மையையும் (noble) என்னால் காண இயலவில்லை. இரவில் மருத்துவமனையில் தனிமையில் படுக்கையில் அழுது கொண்டிருக்கும் குழந்தையிடமும் என்னால் எந்தவொரு பெருந்தன்மையையும் (nobility) காண இயலவில்லை.

அக்காலத்தில் அதிநவீன (sophisticated) இதய அறுவை சிகிச்சை முறைகள் கிடையாது. குழந்தைகள் வேதனையடைவதைக் கண்டுநான் மனமுடைந்து போயிருக்கிறேன். ஏனென்றால் அவர்கள் தங்களின் முழு நம்பிக்கையையும் (trust) மருத்துவர்கள் மற்றும் செவிலியர்கள் மீது வைப்பார்கள். நீங்கள் அவர்களுக்கு உதவுவீர்கள் என்று அவர்கள் நம்புவார்கள்.

உங்களால் முடியவில்லை என்றால் அவர்கள் தங்கள் விதியைக் கூட ஏற்றுக் கொள்ள (believe) மாட்டார்கள். உருவச்சிதைவு அடையக்கூடிய அறுவைச்சிகிச்சை (mutilating surgery) செய்த பிறகு கூட அவர்கள் குறைகூற மாட்டார்கள்.

பல வருடங்களுக்கு முன்னால் ஒரு நாள் காலையில் நான் கண்டதை கேட்டவுடன் நகரின் செஞ்சிலுவை (Red cross) சிறுவர் மருத்துவமனையில் மோட்டார் வாகன ஓட்டப் பந்தயம் (Grand Prix) என்றே அழைப்பேன். அந்நிகழ்வு வேதனையைக் குறித்து நான் எண்ணிவந்ததில், ஒரு உண்மையை நான் விட்டிருந்ததை குறித்து அது என் கண்களைத் திறந்தது. அது எனக்கு ஒரு பெரிய ஆறுதலாக (solace) இருந்தது.

அந்த காலை அங்கு என்ன நடந்தது என்றால், காலை உணவு தள்ளுவண்டியை (breakfast trolley) செவிலியர் எடுக்கவில்லை. அடுத்தகணமே அந்த தள்ளுவண்டியானது இரு துணிச்சலான (intrepid), தைரியமான ஓட்டுநர் மற்றும் இயந்திர வல்லுநரால் வழி நடத்தப்பட்டது.

இயந்திர வல்லுநரோ தலையை குனிந்தவாறு தள்ளுவண்டியை பின்புறமிருந்து விரைந்து தள்ளி அதற்கு இயந்திர சக்தியளித்தனர் (provided), அதே வேளையில் ஓட்டுநரோ, தள்ளுவண்டியின் முன்புறம் அமர்ந்து கொண்டு ஒருகையால் வண்டியைப் பிடித்து காலால் தரையை உரசி (scraping) தள்ளுவண்டியை ஓட்டினார். அவர்கள் தேர்ந்தெடுத்த வேடங்கள் மிக எளிது ஏனென்றால் இயந்திர வல்லுநரோ கண்ணிழந்தவன் (blind), ஓட்டுநரோ ஒரு கை (arm) மட்டுமே கொண்டவன்.

அன்று அவர்கள் ஒரு பெரிய நிகழ்ச்சியையே நடத்தினார்கள். மீதமிருந்த நோயாளிகளிடமிருந்து அவர்களுக்கு கிடைத்த உற்சாகத்தையும் (encouragement) சிரிப்பையும் பார்த்த போது இண்டியானா போலிஸில் (Indiana Polis) நடைபெறும் 500 கார்களின் ஓட்டப்பந்தயத்தை (race) விட இவர்களின் நிகழ்ச்சி மிகச்சிறந்தது என தோன்றியது. அவர்களை செவிலியர்கள் பிடித்து, திட்டி, படுக்கைக்கு திரும்ப அனுப்பும் வரை, அங்கு சிதறிய தட்டுகள் மற்றும் சில்வர் பாத்திரங்களின் இறுதிச் சுற்று (grand finale) நடந்தது.

அவ்விருவர்களைப் பற்றி நான் கூறுகிறேன். இயந்திர வல்லுநரோ 7 வயதானவன். ஒரு நாள் அவனது தாயும் தந்தையும் குடித்து விட்டு சண்டையில், அவனது தாய் விளக்கை (lantern) எடுத்து தந்தை மீது எறியும் போது அது தவறி குழந்தையின் தலை மற்றும் தோள் பகுதியின் மீது விழுந்தது. இதனால் அதிகப்படியான மூன்றாம் நிலை காயங்களால் அவனது மேலுடல் பாதிக்கப்பட்டது, அவனது இரண்டு கண்களும் பார்வை இழந்தன.

வாகன ஓட்டப்பந்தயத்தின் போது அவன் ஒரு நடமாடும், பயமூட்டும் (horror) பொருளாக, அதாவது உருக்குலைந்த (disfigured) முகத்தோடும், ஒரு நீண்ட சதை மடிப்பு கழுத்திலிருந்து தொங்கிய வண்ணமும் காணப்பட்டான்.

அவனது கழுத்தைச் சுற்றி காயம் ஆறிக்கொண்டிருந்த வேளையில், அவனுடைய கீழ்த்தாடை நரம்புத் திசுக்களினால் (tissue) இறுகப்பற்றிக் கொள்ளப்பட்டது. அவன் தனது தலையை உயர்த்தினால் (raise) மட்டுமே அவனால் தனது வாயைத் திறக்க முடியும். அந்த பந்தயம் முடிந்து நான் அவளை சந்தித்த போது “நாங்கள் வென்று விட்டோம். உங்களுக்கு தெரியுமா?” என்று சிரித்துக்கொண்டே கூறினான்.

அந்த தள்ளுவண்டியின் ஓட்டுநரை (trolley’s driver) எனக்கு நன்றாக தெரியும். சில வருடங்களுக்கு முன்னால். அவன் இதயத்தில் இருந்த ஓட்டையை நான் வெற்றிகரமாக அடைத்தேன். அவன் எலும்பில் இருந்த வீரியமான (malignant tumour) கட்டியின் காரணமாக அவன் மறுபடியும் மருத்துவமனைக்கு அழைத்து வரப்பட்டான். பந்தயத்திற்கு சில நாட்கள் முன்னதாக அவனது தோள்பட்டையும், கையும் சிகிச்சையின் மூலம் வெட்டி எடுக்கப்பட்டது (amputated).

அவன் குணமடைவதற்கான (recovery) நம்பிக்கை குறைவாகவே காணப்பட்டது. பந்தயத்திற்குப் பின் அவன் என்னிடம், தள்ளுவண்டியின் சக்கரங்கள் சரியாக எண்ணெய் இடப்படவில்லை என்றும், அவன் ஒரு சிறந்த ஓட்டுநர் என்றும், தான் இயந்திர வல்லுநரிடம் முழு நம்பிக்கை கொண்டிருந்ததாகவும் கூறினான்.

திடீரென, வாழ்க்கையை வாழ்வதற்கான ஒரு ஆழமான பாடத்தை (profound lesson) இவர்கள் இருவரும் எனக்கு கற்று கொடுத்ததாகவே உணர்ந்தேன் (realized). ஏனென்றால் வாழ்வது என்பது இனிமைக்காவோ, பொழுது போக்கிற்காகவோ, மனமகிழ்ச்சிக்காகவோ நாம் செய்யும் ஏதோ ஒன்று அல்ல, மாறாக மகிழ்ச்சி என்ற வார்த்தையின் உண்மையான உணர்வே ஆகும். வாழ்வதென்பது உயிரோடிருப்பதின் கொண்டாட்டமே (celebration).

நான் வேதனைப்படுவதை தவறான (wrong) முறையிலிருந்தே பார்த்து கொண்டிருந்தேன். நீங்கள் வேதனை அடைவதால் மட்டும் சிறந்த மனிதராக முடியாது. ஆனால் வேதனையை அனுபவித்து (experience) இருக்கிறீர்கள் என்றால் உங்களால் ஒரு சிறந்த மனிதனாக முடியும். இருளைப் பற்றி அறியாவிட்டால், நம்மால் ஒளியைப் பாராட்ட இயலாது.

கடுங்குளிரால் பாதிக்கப்படாமல் நம்மால் வெதுவெதுப்பை பாராட்ட இயலாது. நீங்கள் இழந்தது எதுவோ அது முக்கியமில்லை (important), உங்களிடம் மீதமிருப்பது (left) எதுவோ அதுவே மிக முக்கியம் என்று இச்சிறுவர்கள் எனக்கு உணர்த்தி விட்டார்கள்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.4

Question 1.
Find the equations of the two tangents that can be drawn from (5, 2) to the ellipse 2x² + 7y² = 14.
Solution:
2x² + 7y² = 14
(÷ by 14) ⇒ \(\frac{x^{2}}{7}+\frac{y^{2}}{2}\) = 1
comparing this equation with \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1
we get a² = 7 and b² = 2
The equation of tangent to the above ellipse will be of the form
y = mx + \(\sqrt{a^{2} m^{2}+b^{2}}\) ⇒ y = mx + \(\sqrt{7 m^{2}+2}\)
Here the tangents are drawn from the point (5, 2)
⇒ 2 = 5m + \(\sqrt{7 m^{2}+2}\) ⇒ 2 – 5m = \(\sqrt{7 m^{2}+2}\)
Squaring on both sides we get
(2 – 5m)² = 7m² + 2
25m² + 4 – 20m – 7m² – 2 = 0
18m² – 20m + 2 = 0
(÷ by 2) ⇒ 9m² – 10m + 1 = 0
(9m – 1) (m – 1) = 0
‘ m = 1 (or) m = 1/9
When m = 1, the equation of tangent is
y = x + 3 or x – y + 3 = 0
When m = \(\frac{1}{9}\) the equation of tangent is 9
y = \(=\frac{x}{9}+\sqrt{\frac{7}{81}+2}\) (i.e.) y = \(\frac{x}{9}+\frac{13}{9}\)
9y = x + 13 or x – 9y + 13 = 0

Question 2.
Find the equations of tangents to the hyperbola \(\frac {x^2}{16}\) – \(\frac {y^2}{64}\) = 1 which are parallel to 10x – 3y + 9 = 0.
Solution:
Equation of Hyperbola \(\frac {x^2}{16}\) – \(\frac {y^2}{64}\) = 1
∴ a² = 16, b² = 64
Tangent is parallel to the line
10x – 3y + 9 = 0 is
10x – 3y + k = 0
∴ 3y = 10x + k
y = \(\frac {10}{3}\)x + \(\frac {k}{3}\)
∴ m = \(\frac {10}{3}\) c = \(\frac {k}{3}\)
Condition that the line y = mx + c to be tangent to the hyperbola is
c² = a²m² – b²

k² = 1024
k = ±32
∴ Equation of tangent
⇒ 10x – 3y ± 32 = 0

Question 3.
Show that the line x – y + 4 = 0 is a tangent to the ellipse x² + 3y² = 12. Also find the co-ordinates of the point of contact.
Solution:
The given ellipse is x² + 3y² = 12
(÷ by 12) ⇒ \(\frac{x^{2}}{12}+\frac{y^{2}}{4}\) = 1
(ie.,) Here a² = 12 and b² = 4
The given line is x – y + 4 = 0
(ie.,) y = x + 4
Comparing this line with y = mx + c
We get m = 1 and c = 4
The condition for the line y = mx + c
To be a tangent to the ellipse \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1 is c² = a²m² + b²
LHS = c² = 4² = 16
RHS: a²m² + b² = 12( 1 )² + 4 = 16
LHS = RHS The given line is a tangent to the ellipse. Also the point of contact is
\(\left(\frac{-a^{2} m}{c}, \frac{b^{2}}{c}\right)=\left[-\left(\frac{12(1)}{4}\right), \frac{4}{4}\right]\) (i.e.,) (-3, 1)

Question 4.
Find the equation of the tangent to the parabola y² = 16x perpendicular to 2x + 2y + 3 = 0.
Solution:
Equation of the parabola
y² = 16x
4 a = 16
a = 4
Tangent is perpendicular to the line
2x + 2y + 3 = 0 is 2x – 2y + k = 0
2x – 2y + k = 0
2y = 2x + k
y = x + \(\frac {k}{2}\)
m = 1 c = \(\frac {k}{2}\)
Condition that the line y = mx + c to be tangent to the parabola is
c = \(\frac {a}{m}\)
\(\frac {k}{2}\) = \(\frac {4}{1}\)
k = 8
Equation of the tangent
2x – 2y + 8 = 0
÷ by 2 ⇒ x – y + 4 = 0

Question 5.
Find the equation of the tangent at t = 2 to the parabola y² = 8x (Hint: use parametric form).
Solution:
y² = 8x
Comparing this equation with y² = 4ax
we get 4a = 8 ⇒ a = 2
Now, the parametric form for y² = 4ax is x = at², y = 2at
Here a = 2 and t = 2
⇒ x = 2(2)² = 8 and y = 2(2) (2) = 8
So the point is (8, 8)
Now eqution of tangent to y² = 4 ax at (x₁, y₁) is yy₁ = 2a(x + x₁)
Here (x₁, y₁) = (8, 8) and a = 2
So equation of tangent is y(8) = 2(2) (x + 8)
(ie.,) 8y = 4 (x + 8)
(÷ by 4) ⇒ 2y = x + 8 ⇒ x – 2y + 8 = 0
Aliter
The equation of tangent to the parabola y² = 4ax at ‘t’ is
yt = x + at²
Here t = 2 and a = 2
So equation of tangent is
(i.e.,) y(2) = x + 2(2)²
2y = x + 8 ⇒ x – 2y + 8 = 0

Question 6.
Find the equations of the tangent and normal to hyperbola 12x² – 9y² = 108 at θ = \(\frac {π}{3}\) .
(Hint: use parametric form)
Solution:
(i) Equation of the tangent to hyperbola be

⇒ 4x – 3y = 6
⇒ 4x – 3y – 6 = 0

(ii) Equation of the normal to hyperbola be

⇒ 3x + 4y – 42 = 0

Question 7.
Prove that the point of intersection of the tangents at ‘t₁‘ and ‘t₂‘ on the parabola y² = 4ax is [at₁t₂, a(t₁ + t₂)].
Solution:
Equation of the tangent of parabola y² = 4ax be
at t₁ yt₁ = x + at₁² ……….. (1)
at t₂ yt₂ yt = x + at₂² ……….. (2)
(1) – (2) ⇒ y(t₁ – t₂) = a(t₁² – t₂²)
y(t₁ – t₂) = a(t₁ + t₂)(t₁ – t₂)
y = a(t₁ + t₂)
(1) ⇒ t₁a(t₁ + t₂) = x + at₁²
x = at₁² + at₁t₂ – at₁²
x = at₁t₂
Point of intersection be [at₁t₂, a(t₁ + t₂)]

Question 8.
If the normal at the point ‘t₁‘ on the parabola y² = 4ax meets the parabola again at the point t₂ then prove that t₂ = -(t₁ + \(\frac {2}{t_1}\))
Solution:
Equation of normal to y² = 4at’ t’ is y + xt = 2at + at³.
So equation of normal at ‘t₁’ is y + xt₁ = 2at₁ + at₁³
The normal meets the parabola y² = 4ax at ‘t₂’ (ie.,) at (at₂², 2at₂)
⇒ 2at₂ + at₁t₂² = 2at₁ + at₁³
So 2a(t₂ – t₁) = at₁³ – at₁t₂²
⇒ 2a(t₂ – t₁) = at₁(t₁² – t₂²)
⇒ 2(t₂ – t₁) = t₁(t₁ + t₂)(t₁ – t₂)
⇒ 2= -t₁(t₁ + t₂)
⇒ t₁ + t₂ = \(\frac{-2}{t_{1}}\)
⇒ t₂ = \(-t_{1}-\frac{2}{t_{1}}=-\left(t_{1}+\frac{2}{t_{1}}\right)\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.3

Question 1.
Identify the type of conic section of each of the equations.
(1) 2x² – y² = 7
(2) 3x² + 3y² – 4x + 3y + 10 = 0
(3) 3x² + 2y² = 14
(4) x² + y² + x – y = 0
(5) 11x² – 25y² – 44x + 50y – 256 = 0
(6) y² + 4x + 3y + 4 = 0
Solution:
(1) 2x² – y² = 7
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = 2, C = – 1
Elere A ≠ C also A and C are of opposite signs.
So the conic is a hyperbola.

(2) 3x² + 3y² – 4x + 3y + 10 = 0
A = 3, B = 0, C = 3, D = -4, E = 3, F = 10
A = C and B = 0 (No xy term)
∴ It is a circle.

(3) 3x² + 2y² = 14
A = 3, B = 0, C = 2, F = -14
A ≠ C and A & C are the same signs.
∴ It is an ellipse.

(4) x² + y² + x – y = 0
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = C and B = 0
So the given conic is a circle.

(5) 11x² – 25y² – 44x + 50y – 256 = 0
A =11, B = 0, C = -25, D = -44, E = 50, F = -256
A ≠ C and A & C are the opposite signs.
∴ It is a hyperbola.

(6) y² + 4x + 3y + 4 = 0
Comparing this equation with the general equation of the conic
Ax² + Bxy + Cy² + Dx + Ey + F = 0
We get A = 0 and B = 0
So the conic is a parabola.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.2 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.2

Question 1.
Find the equation of the parabola in each of the cases given below:
(i) focus (4, 0) and directrix x = -4.
(ii) passes through (2, – 3) and symmetric about y axis.
(iii) vertex (1,-2) and focus (4, – 2).
(iv) end points of latus rectum (4, -8) and (4, 8).
Solution:
(i) focus (4, 0) and directrix x = -4
Parabola is open rightwards vertex (0, 0)

a = 4
(Distance AS = 4 unit)
f² = 4(4) x
Equation of parabola
y² = 16x.

(ii) passes through (2, – 3) and symmetric about y-axis

x² = 4ay
It passes through (2, -3)
⇒ 2² = 4a(-3)
4 = -12a ⇒ a = \(-\frac{1}{3}\) ⇒ 4a = \(-\frac{4}{3}\)
∴ Equation of parabola is x² = \(-\frac{4}{3}\) y
3x²= – 4y.

(iii) vertex (1,-2) and focus (4, – 2)

In given data the parabola is open rightwards and symmetric about the line parallel to x-axis.
Equation of parabola
(y – k)² = 4a(x – h)
Vertex (h, k) = (1, -2)
(y + 2)² = 4a(x – 1)
a = AS = 3
Equation of parabola
(y + 2)² = 4(3)(x – 1)
(y + 2)² = 12(x – 1)

(iv) end points of latus rectum (4, -8) and (4, 8)

Focus = (4, 0)
Equation of the parabola will be of the form y² = 4ax
Here a = 4
⇒ y² = 16x

Question 2.
Find the equation of the ellipse in each of the cases given below:
(i) foci (± 3, 0), e = \(\frac {1}{2}\)
(ii) foci (0, ±4) and end points of major axis are (0, ±5).
(iii) length of latus rectum 8, eccentricity = \(\frac {3}{5}\) and major axis on x-axis.
(iv) length of latus rectum 4, distance between foci and major axis as y axis.
Solution:
(i) foci (± 3, 0), e = \(\frac {1}{2}\)
foci (± c, 0) = (± 3, 0)

e = \(\frac {1}{2}\)
c = ae = 3
a(\(\frac {1}{2}\)) = 3
a = 6 ⇒ a² = 36
b² = a² – c²
b² = 36 – 9 = 27
b² = 27
Equation of the ellipse be \(\frac {x^2}{a^2}\) + \(\frac {y^2}{b^2}\) = 1
\(\frac {x^2}{36}\) + \(\frac {y^2}{27}\) = 1

(ii) foci (0, ±4) and end points of major axis are (0, ±5)

foci (0, ±c) = (0, +4)
vertex (0, ±a) = (0, ±5)
∴ c = 4, a = 5
ae = 4
5e = 4
e = \(\frac {4}{5}\)
b² = a² – c²
= 25 – 16
b² = 9
Equation of the ellipse be \(\frac {x^2}{b^2}\) + \(\frac {y^2}{a^2}\) = 1
\(\frac {x^2}{9}\) + \(\frac {y^2}{25}\) = 1

(iii) length of latus rectum 8, eccentricity = \(\frac {3}{5}\) and major axis on x-axis.
e = \(\frac {3}{5}\)
Latus rectum \(\frac {2b^2}{a}\) = 8

(iv) length of latus rectum 4, distance between foci 4√2 and major axis as y-axis

Given \(\frac{2 b^{2}}{a}\) = 4 and 2ae = \(4 \sqrt{2}\)
Now \(\frac{2 b^{2}}{a}\) = 4 2b² = 4a
⇒ b² = 2a
2ae = \(4 \sqrt{2}\) ae = \(2 \sqrt{2}\)
So a²e² = 4(2) = 8
We know b² = a²(1 – e²) = a² – a²e²
⇒ 2a = a² – 8 ⇒ a² – 2a -8 = 0
⇒ (a – 4) (a +2) = 0 ⇒a = 4 or -2
As a cannot be negative
a = 4 So a² = 16 and b² = 2(4) = 8
Also major axis is along j-axis
So equation of ellipse is \(\frac{x^{2}}{8}+\frac{y^{2}}{16}\) = 1

Question 3.
Find the equation of the hyperbola in each of the cases given below:
(i) foci (± 2, 0), eccentricity = \(\frac {3}{2}\)
(ii) centre (2, 1) one of the foci (8, 1) and corresponding directrix x = 4.
(iii) passing through (5, -2) and length of the transverse axis along x axis and length 8 units.
Solution:
(i) foci (± 2, 0), eccentricity = \(\frac {3}{2}\)

(ii) centre (2, 1) one of the foci (8, 1) and corresponding directrix x = 4.
Distance CS = ae = 6 …….. (1)
Directrix \(\frac {a}{e}\) = 4 ……… (2)
(1) × (2) ⇒ ae × \(\frac {a}{e}\) = 24
a² = 24

∴ c = ae = 6
b² = c² – a²
= 36 – 24 = 12
The transverse axis is parallel to x-axis
∴ \(\frac {(x-h)^2}{a^2}\) – \(\frac {(y – k)^2}{b^2}\) = 1 (h, k) = (2, 1)
\(\frac {(x-2)^2}{24}\) – \(\frac {(y – 1)^2}{12}\) = 1

(iii) passing through (5,-2) and length of the transverse axis along x axis and of length 8 units.
Transverse axis along x-axis
\(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1
Length of transverse axis 2a = 8
⇒ a = 4

Question 4.
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
(i) y² = 16x
(ii) x² = 24y
(iii) y² = -8x
(iv) x² – 2x + 8y + 17 = 0
(v) y² – 4y – 8x + 12 = 0
Solution:
(i) y² = 16x

4a = 16
a = 4
(a) Vertex V (0, 0)
(b) Focus S(a, 0) = S(4, 0)
(c) Equation of the directrix x = – a
x = -4 ⇒ x + 4 = 0
(d) Length of the latus rectum = 4a = 4(4)
= 16

(ii) x² = 24y

(a) Vertex V (0, 0),
(b) Focus S (0, a) = S(0, 6)
(c) Equation of the directrix y = -a = -6
⇒ y + 6 = 0
(d) Length of the latus rectum = 4a
= 4 (6) = 24

(iii) y² = -8x
4a = 8,
a = 2

(a) Vertex V(0, 0) = ( 0, 0)
(b) Focus S(-a, 0) = (-2, 0)
(c) Equation of the directrix x = a = 2
x – 2 = 0
(d) Length of the latus rectum 4a = 8
(iv) x² – 2x + 8y + 17 = 0
x² – 2x = -8y – 17
(x – 1)² = -8y – 17 + 1
(x – 1)² = -8y – 16
(x – 1)² = -8(y + 2)
It is form of (x – h)² = -4a(y – k)
4a = 8 ⇒ a = 2
(a) Vertex be (h, k) = (1, -2)

(b) Foeus = (0 +h, -a + k) = (0 + 1, -2 – 2) = (1, -4)
(c) Equation of the directrix is y + k + a = 0
y – 2 + 2= 0
y = 0
(d) Length of latus rectum is 4a = 4 × 2 = 8 units,

(v) y² – 4y – 8x + 12 = 0

y² – 4y = 8x – 12
(y – 2)² = 8x – 12 + 4
= 8x – 8
= 8 (x – 1)
(y – 2)² = 8 (x – 1)
It is form of (y – k)² = Aa(x – h)
4a = 8 ⇒ a = 2
(a) Vertex (h, k) = (1, 2)
(b) Focus = (a+h, 0 + k) = (2 + 1, 0 + 2) = (3, 2)
(c) Equation of the directrix x = -a + h
= -2 + 1
= -1
x + 1 = 0
(d) Length of latus rectum is
4a = 4 × 2 = 8 units.

Question 5.
Identify the type of conic and find centre, foci, vertices and directrices of each of the following:
(i) \(\frac {x^2}{25}\) + \(\frac {y^2}{9}\) = 1
(ii) \(\frac {x^2}{3}\) + \(\frac {y^2}{10}\) = 1
(iii) \(\frac {x^2}{25}\) – \(\frac {y^2}{144}\) = 1
(iv) \(\frac {y^2}{16}\) – \(\frac {x^2}{9}\) = 1
Solution:
(i) \(\frac{x^{2}}{25}+\frac{y^{2}}{9}\) = 1
It is of the form \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}\) = 1, which is an ellipse
Here a² = 25, b² = 9
a = 5, b = 3
e² = \(\frac{a^{2}-b^{2}}{a^{2}}=\frac{25-9}{25}=\frac{16}{25}\) ⇒ e = \(\frac{4}{5}\)
Now e = \(\frac{4}{5}\) and a = 5 ⇒ ae = 4 and \(\frac{a}{e}=\frac{5}{4 / 5}=\frac{25}{4}\)
Here the major axis is along x axis
∴ Centre = (0, 0)
Foci = (± ae, 0) = (± 4, 0)
Vertices = (± a, 0) = (±5, 0)
Equation of directrix x = ± \(\frac{a}{e}\) (ie.,) x = ± \(\frac{25}{4}\)

(ii) \(\frac {x^2}{3}\) + \(\frac {y^2}{10}\) = 1
It is an ellipse. The major axis is along y axis

a² = 10 b² = 3
a = \(\sqrt {10}\) b = √3
c² = a² – b²
= 10 – 3 = 7
c = √7
ae = √7 .
\(\sqrt {10}\) = √7
e = \(\sqrt {\frac{7}{10}}\)
(a) Centre (0, 0)
(b) Vertex (0, ±a) = (0, ±\(\sqrt {10}\))
(c) Foci (0, ±c) – (0, ±√7)
(d) Equation of the directrix a
y = ±\(\frac{a}{e}\)
= ±\(\frac{\sqrt {10}}{√7}\).\(\sqrt {10}\) = ±\(\frac {10}{√7}\)
y = ±\(\frac {10}{√7}\)

(iii) \(\frac {x^2}{25}\) – \(\frac {y^2}{144}\) = 1
It is Hyperbola. The transverse axis the x axis.

a² = 25; b² = 144
a = 5; b = 12
c² = a² + b²
= 25 + 144 = 169
c = 13
ae = 13
5e = 13
e = \(\frac {13}{5}\)
(a) Centre (0, 0)
(b) Vertex (± a, 0) = (± 5, 0)
(c) Foci (± c, 0) = (± 13, 0)
(d) Equation of the directrix
x = ±\(\frac {a}{e}\) = ±\(\frac {5}{\frac{13}{5}}\) = ±\(\frac {25}{13}\)
x = ±\(\frac {25}{13}\)

(iv) \(\frac {y^2}{16}\) – \(\frac {x^2}{9}\) = 1
It is Hyperbola. The transverse axis the y axis.

a² = 16; b² = 9
a = 4; b = 3
c² = a² + b²
= 16 + 6 = 25
c = 5
ae = 5
4e = 5
e = \(\frac {5}{4}\)
(a) Centre (0, 0)
(b) Vertex (0, ±a) = (0, ±4)
(c) Foci (0, ±ae) = (0, ±5)
(d) Equation of the directrix
y = ±\(\frac {a}{e}\) = ±\(\frac {4}{\frac{5}{4}}\) = ±\(\frac {16}{5}\)
y = ±\(\frac {16}{5}\)

Question 6.
Prove that the length of the latns rectum of the hyperbola \(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1 is \(\frac {2b^2}{a}\)
Solution:
The latus rectum LL’ of an hyperbola \(\frac {x^2}{a^2}\) – \(\frac {y^2}{b^2}\) = 1 passes through S(ae, 0)
Hence L is (ae, y₁)

Hence proved

Question 7.
Show that the absolute value of the difference of the focal distances of any point P on the hyperbola is the length of its transverse axis.
Solution:

Let P be a point on the hyperbola.
Definition of conic
\(\frac {SP}{PM}\) = e; \(\frac {S’P}{PM’}\) = e
SP = e(PM) ……..(1)
S’P = e (PM’) ……….(2)
(2) – (1) ⇒ S’P – SP = e PM’- e PM
= e(PM’ – PM)
= e MM’
= e ZZ’
[∵ MM’ = ZZ’ = \(\frac {2a}{e}\) ]
= e(\(\frac {2a}{e}\))
S’P – SP = 2a (constant)
= length of the transverse axis.

Question 8.
Identify the type of conic and find centre, foci, vertices and directrices of each of the following:

(v) 18x² + 12y² – 144x + 48y + 120 = 0
(vi) 9x² – y² – 36x – 6y + 18 = 0
Solution:
(i) \(\frac {(x-3)^2}{225}\) + \(\frac {(y-4)^2}{289}\) = 1

It is an ellipse. The major axis is parallel to y axis
a² = 289, b² = 225
a = 17, b = 15
c² = a² – b²
= 289 – 225 = 64
c = 8
ae = 8
17e = 8
e = \(\frac {8}{17}\)
Centre (h, k) = (3, 4)
Vertices (h, ±a + k) = (3, 17 + 4) & (3, -17 + 4)!
= (3, 21) and (3, -13)
Foci (h + 0, ± c + k) = (3, 8 + 4) & (3, -8 + 4)
= (3, 12) and (3, -4)

(ii) \(\frac {(x+1)^2}{100}\) + \(\frac {(y-2)^2}{64}\) = 1
It is an ellipse. The major axis is parallel to the x-axis.
a² = 100, b² = 64
a = 10, b = 8
c² = a² – b²
= 100 – 64 = 36
c = 6
ae = 6
10 e = 6
e = \(\frac {6}{10}\) = \(\frac {3}{5}\)
centre (h, k) = (-1, 2)
vertices (h±a, k) = (-1±10, 2)
= (-1+10, 2) & (-1-10, 2)
= (9, 2) & (-11, 2)
foci (h±c, k) = (-1±6, 2)
= (-1+6, 2) & (-1-6, 2)
= (5, 2) & (-7, 2)
directrix x = ±\(\frac {a}{e}\) + h

(iii) \(\frac {(x+3)^2}{225}\) + \(\frac {(y-4)^2}{64}\) = 1
It is an hyperbola. The transverse axis is parallell to x axis.
a² = 225, b² = 64
a = 15, b = 8
c² = a² – b²
= 225 + 64
c² = 289
c = 17
ae = 17
5e = 17
e = \(\frac {17}{15}\)
centre (h, k) = (-3, 4)
vertices (h±a, k) = (-3±15, 4)
= (-3+15, 4) & (-3-15, 4)
= (12, 4) & (-18, 4)
foci (h±c, k) = (-3±17, 4)
= (-3+17, 4) & (-3-17, 4)
= (14, 4) & (-20, 4)
directrix x = ±\(\frac {a}{e}\) + h

(iv) \(\frac {(y-2)^2}{25}\) + \(\frac {(x+1)^2}{16}\) = 1
It is an hyperbola. The transverse axis is parallell to y axis.
a² = 25, b² = 16
a = ±5, b = 4
c² = a² + b²
= 25 + 16
= 41
c = \(\sqrt {41}\)
ae = \(\sqrt {41}\)
5 e = \(\sqrt {41}\)
e = \(\frac {\sqrt {41}}{5}\)
centre (h, k) = (-1, 2)
vertices (h, ±a + k) = (-1, ±5 + 2)
= (-1, 5 + 2) & (-1, -5 + 2)
= (-1, 7) & (-1, -3)
foci (h, ±c + k) = (-1, ±\(\sqrt {41}\) + 2)
= (-1, \(\sqrt {41}\) + 2) & (-1, –\(\sqrt {41}\) + 2)
directrix x = ±\(\frac {a}{e}\) + k

(v) 18x² + 12y² – 144x + 48y + 120 = 0
18x² – 144x + 12y² + 48y = -120
18 (x² – 8x) + 12 (y² + 4y) = -120
18 (x – 4)² + 12 (y + 2)² = -120 + 288 + 48
18(x – 4)² + 12 (y + 2)² = 216
\(\frac {18(x-4)^2}{216}\) + \(\frac {12(y+2)^2}{216}\) = 1
\(\frac {(x-4)^2}{12}\) + \(\frac {(y+2)^2}{18}\) = 1
It is an ellipse. The major axis is parallell to y axis.
a² = 18, b² = 12
a = \(\sqrt {18}\), b = 2√3
= 3 √2
c² = a² + b²
= 18 – 12
= 6
c = √6
ae = √6
3√2 e = √6
e = \(\frac {√6}{3√2}\) = \(\frac {√3}{3}\) = \(\frac {1}{√3}\)
centre (h, k) = (4, -2)
vertices (h, ±a + k) = (4, ±3√2 – 2)
= (4, 3√2 – 2) & (4, -3√2 – 2)
foci (h, ±c + k) = (4, ±√6 – 2)
= (4, ±√6 – 2) & (4, -√6 – 2)
directrix y = ±\(\frac {a}{e}\) + k
= ±\(\frac {3√2}{1}\) – 2
= ±3√6 – 2
y = 3√6 – 2 & y = -3√6 – 2

(vi) 9x² – y² – 36x – 6y + 18 = 0
9x² – 36x – y² – 6y = – 18
9(x² – 4x) – (y² + 6y) = -18
9(x – 2)² – (y + 3)² = -18 + 36 – 9
9(x – 2)² – (y + 3)² = 9
\(\frac {(x-2)^2}{1}\) – \(\frac {(y+3)^2}{9}\) = 1
It is hyperbola. The transverse axis is parallel to x axis.
a² = 1; b² = 9
a = 1; b = 3
c² = a² + b²
= 1 + 9
= 10
c = \(\sqrt {10}\)
ae = \(\sqrt {10}\)
e = \(\sqrt {10}\)
centre (h, k) = (2, -3)
vertices (h ± a, k) = (2 ± 1, -3)
= (2 + 1, -3) & (2 – 1, -3)
= (3, -3) & (1, -3)
foci (h ± c, k) = (2 ±\(\sqrt {10}\), -3)
= (2 + \(\sqrt {10}\), -3) & (2 –\(\sqrt {10}\), -3)
directrix x = ±\(\frac {a}{e}\) + h
= ±\(\frac {1}{\sqrt {10}}\) + 2 & x = –\(\frac {1}{\sqrt {10}}\) + 2

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 2 A Nice Cup of Tea Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 2 A Nice Cup of Tea

12th English Guide A Nice Cup of Tea Text Book Back Questions and Answers

Textual Questions:

Based on your understanding of the text, answer each of the following questions in one or two sentences:
(Note: IQ → Important Questions)

Question a.
What seems ‘Curious’ to the author? (IQ)
Answer:
The absence of “Tea” in the recipes of the cookery book is curious to the author.

Question b.
Why does the author say that it is important to include a tea recipe in cookery books?
Answer:
The author says that it is important to include a tea recipe in cookery books as it is one of the mainstays of civilization in the country.

Question c.
Mention the countries in which tea is a part of civilization? (IQ)
Answer:
It is one of the mainstays of civilization in the UK, Australia, Eire, and New Zealand.

Question d.
Which tea does the author prefer – China tea or Indian tea?
Answer:
The author prefers Indian tea.

Question e.
According to the author, What does the phrase “a nice cup of tea” refer to?
Answer:
Nice cup of tea means Indian tea which makes one feel wiser, optimistic and wiser.

Question f.
What is the second golden rule in the preparation of tea?
Answer:
The second golden rule is that tea should be made in small quantities in a teapot which is made up of China or earthenware.

Question g.
How does army tea taste? (IQ)
Answer:
Army tea tastes of grease and whitewash.

Question h.
Do tea lovers generally like strong tea or weak tea?
Answer:
Tea lovers generally like strong tea.

Question i.
Why should tea be directly added to the pot?
Answer:
Tea should be added directly to the pot because imprisoning tea leaves in strainers, muslin bags or other devices can be really harmful.

Question j.
Why does the author prefer the cylindrical cup to a flat cup?
Answer:
The author prefers a cylindrical cup as it holds more and the hotness is well maintained.

Question k.
What should be poured into the cup first tea or milk? (IQ)
Answer:
One should pour tea first into the cup and then add milk to the desired level. Thus one can regulate the amount of milk added to tea.

Question l.
Why does the author advise removing cream from the milk?
Answer:
The author advises removing cream from the milk as it gives the tea a sickly taste.

Question m.
Does the author like drinking tea with sugar? Give reasons.
Answer:
Adding sugar to tea will deprive tea of its real taste. Misguided people who take tea do it because of the sweetness and not because of the taste of tea.

Question n.
Why does the author refer to himself as being in a ‘minority’?
Answer:
The author refers to himself as being in a ‘minority’ with his view of drinking tea without sugar.

Question o.
Whom does the author call “misguided people”? What is his advice to them?
Answer:
Some misguided people admit that they drink tea for stimulation and warmth. They are not interested in tea. So, they add sugar to take the taste away. He advises them to drink tea without adding sugar for a fortnight. They would never again ruin the real taste of tea by adding sugar.

2. Based on your understanding of the text, answer each of the following questions in four or five sentences:
(Text Book Page No. 38)

Question a.
What are the author’s views on China tea?
Answer:
China tea has virtues which are not to be despised, it is economic. One can drink it without milk, but there is not much stimulation in it. One does not feel wiser, braver or more optimistic after drinking it.

Question b.
How does adding sugar affect the taste of tea? (IQ)
Answer:
Adding sugar affects the taste of tea to a greater extend. If the tea is sweetened it means one is merely tasting the sugar and not the tea. It is just similar to that of dissolving sugar in plain hot water.

Question c.
Elucidate the author’s ideas about teapots.
Answer:
The teapot should be made of China or earthen ware. Silver or Britannia ware teapot produce inferior quality tea. Enamel pots are worse. Though curiously enough a pewter teapot, a rarity nowadays, is not so bad.

3. Answer each of the following questions in a paragraph of 100-150 words: (Text Book Page No. 38)

a. Summarise George Orwell’s distinctive ideas in “A nice cup of tea”.
b. Discuss how the essay reveals the factual points and the author’s personal opinions on the preparation of tea.

While saying about the preparation of tea in a strong manner, the author brings in his personal view that one strong cup of tea is better than twenty weak ones. The same is the case when he speaks about pouring the tea into the cup first. His view in this regard is by adding milk after pouring the tea, one can exactly regulate the amount of milk. Adding of sugar to tea is strongly objected by him.

By doing so one is just tasting the sugar and not the tea. Orwell’s advice for those people to drink tea without sugar at least a fortnight, So that they will never ruin the tea by sweetening it. Thus it is made clear that the essay reveals not only the factual points but also author’s personal opinions on the preparation of tea.

Paragraph:

Note: Qns. No. 3 a & b:

Introduction:
George Orwell brings forth eleven golden rules in the preparation of tea. According to him “A nice cup of tea” always means an Indian tea.

A nice cup of tea:
He compares Indian tea with China tea and feels that China tea does not have much stimulation in it. He is of the opinion that tea should be made in China or earthenware. The third step is that the pot should be warmed by placing it on the hob. Fourthly the tea should be strong. Six heaped teaspoons of tea are needed for making a tea strong which may hinder the rationing in a family.

Tea making:
The fifth golden rule is that one should not use any strainers to imprison the tea. It should be poured. straight into the pot. In fact the tea brews properly only when it is loose. The next rule is the tea should be boiling at the moment of impact. Seventhly the tea should be stirred well.

The best way of drinking tea:
Eightly the better way to drink tea is by making use of cylindrical cups rather than flat, shallow type. Ninthly the cream in milk is to be taken off before using it for tea as it gives the tea a sickly taste. The tenth rule is that of pouring the tea into the cup first and then adding milk to it so that one can exactly regulate the amount of milk. The last rule is the proper way to drink tea is to drink it without sugar. If sugar is added then it means that one is tasting the sugar not the tea.

4. Based on your understanding of the text, complete the chart given below by choosing the appropriate words or phrases given in brackets. (Text Book Page No. 38)

Golden Rules of Tea Preparation:
(add sugar, shaken, milk, infused properly, strainers, without cream, taken to the kettle, small quantities, China or earthenware, stirred, warmed)

Question 1.
Tea should be made in ________ in a teapot.
Answer:
small quantities

Question 2.
The teapot should be made of________.
Answer:
China or earthenware

Question 3.
The pot should be __________ beforehand.
Answer:
warmed

Question 4.
The pot should not have ______.
Answer:
strainers

Question 5.
While pouring water the teapot should be ________
Answer:
infused properly

Question 6.
The tea leaves should be ______.
Answer:
stirred

Question 7.
After making tea, it should be ________ or the pot should be ________.
Answer:
shaken, taken to the kettle

Question 8.
The milk for the tea should be ______.
Answer:
without cream

Question 9.
The author does not like to _________ to tea.
Answer:
add sugar

Vocabulary:

a) Find out the synonym of the underlined word in each of the following sentences:

Question 1.
But because the best manner of making it is the subject of violent disputes.
a) agreements
b) applauses
c) conflicts
d) discussions
Answer:
c) conflicts

Question 2.
______ tea is one of the mainstays of civilization in the country.
a) a society in an advanced state of social development
b) a society that has slow progress
c) a society that has no progress
d) a society in an average state of social development
Answer:
d) a society in an average state of social development

Question 3.
______ that they only drink it in order to be warmed and stimulated.
a) motivated
b) discouraged
c) passive
d) admired
Answer:
a) motivated

Question 4.
_________ under the spout to catch the stray leaves.
a) fresh
b) loose
c) gathered
d) harmful
Answer:
b) loose

Question 5.
One is ______ to put in too much milk.
a) likely
b) certain
c) eager
d) responsible
Answer:
a) likely

b) Find out the antonym of the underlined word ¡n each of the following sentences:

Question 1.
________ which are not to be despised.
a) hated
b) liked
c) respected
d) defeated
Answer:
b) liked

Question 2.
One does not feel wise, braver or more ________  optimistic.
a) opportunistic
b) cheerful
c) realistic
d) pessimistic
Answer:
d) pessimistic

Question 3.
Not the flat, shallow type _____.
a) narrow
b) wide
c) deep
d) direct
Answer:
c) deep

Question 4.
Predicting the arrival of visitors ______.
a) journey
b) departure
c) migration
d) perusal
Answer:
b) departure

Question 5.
_____ but they are sufficient to show how sub-utilized the whole business has become.
a) enough
b) suffocative
c) inadequate
d) submissive
Answer:
c) inadequate

c) Fill in the boxes with the correct answers. The first one has been done for you: (Text Book Page No. 39)

Answer:

Listening: (Text Book Page No. 40)

Listen to the passage about the ‘Significance of Tea’ and answer the questions:

Questions:

Question 1.
Which country is the largest tea producer in the world?
Answer:
China is the largest tea producer in my world.

Question 2.
______ percentage of the tea produced ¡n India is exported.
Answer:
30

Question 3.
What is the role of antioxidants in tea?
Answer:
Antioxidants in tea might prevent cancer.

Question 4.
Drinking tea strengthens one’s _____, _____ and _____.
Answer:
Teeth, bones, and immune system.

Question 5.
How does tea drinking help a diabetic?
Answer:
Regular tea drinking might lower blood sugar.

Reading (Non-Verbal Representations):

Look at the following non-verbal representation. Based on your understanding and inference, Write a paragraph on career trends in the next decade: (Text Book Page No. 41)

Answer:
The chart shows the 10 fastest-growing occupations from 2018 to 2028. The most popular profession will be is the wind and solar energy fields. The technician course in the field will grow by 106%. Next, come personal care and home health aides. It has 85% growth. Physician Assistants and nurses stand third with 70% growth. Next comes software developers with 55% growth, so the highest is wind and solar energy technology and the lowest is a chef and food Analyst.

Task 1:
Now read the following article on the emerging career option in the modern era and answer the question that follows: (Text Book Page No. 42,43)

The students at the higher secondary level in schools start thinking of suitable courses to take up at the university level based on their aptitude, ability, and interests. While considering the higher education options, they should also plan the career path they wish to take. In today’s complex job scenario, there is a mismatch between demand and supply on one hand we have qualified professionals desperately trying to find a job, while on the other hand, there are many professions that need suitable talented employees. But such skilled employees are unavailable. Therefore, the need of the hour is that students have an understanding of the
emerging career options.

Schools should take the initiative to organise career guidance and counselling sessions for students. However, students need to remember that to build a strong career, they must understand the perspective field and their primary interest. It is also important for students to focus on overall personality development and hone their communication skills as these are important for the success of their career.

Students are also advised that in order to build a solid career foundation, they need to qualify suitably by pursuing a degree course in the chosen area of interest and also consider post-graduate education. Diploma/Short—term courses may help one find a job in the short run but may not promise career progression. Rapid advancement in science and technology and globalization has widened the scope of career options in the twenty-first century.
Let us consider some popular careers.

Fashion Designing:
The current cosmopolitan and fashion-conscious wave that has taken over our country has opened up a huge
arena for careers in fashion. These careers encompass designing clothes, costumes, jewellery, footwear, wardrobe, costumes, accessories, and the like.

Culinary Arts:
With food and cookery shows being a major trend across the world, culinary arts, a sub-domain of the hospitality sector has now become the most sought after career.

Paramedical sciences:

In recent times, there has been a great demand in the health care industry. Paramedical professionals who support medical practitioners in areas such as optometry, pathology, nursing, physiotherapy, and dentistry are much sought after.

Media, Journalism, and Advertising:

In this information era, print and entertainment media have become a force to reckon with. This arena has become a huge career playground because youngsters are attracted to it as the exposure and reach is greater through such mass media. We notice that radio and TV channels, internet companies, and advertising agencies are increasingly recruiting qualified professionals.

Hotel Management:

The hotel industry is the fastest growing industry in India. The number of international travellers (both for business and leisure) is increasing. The hospitality and service industry offers career options such as housekeeping, front-desk executives, tourism management, etc.

Sports Management:

With multinational companies supporting sports, careers in sports offer enormous scope. One need not be a player or an athlete to shine in a sports career because the field of sports offers various career options such as technical trainers, commentators, sports journalists, dieticians, referees, etc. Conducting sports events successfully, organizing the event laudably, preparing the ground for the event are all part of sports management.

Question a.
When do students start thinking about their career path?
Answer:
The students at the higher secondary level in schools start thinking of suitable courses as their career path based on their ability, aptitude, and interests.

Question b.
How can students build a strong career?
Answer:
They build a strong career by understanding the prospective field and their primary interest.

Question c.
What are the integral aspects of a successful career?
Answer:
The integral aspects of a successful career are personality development and communication skills.

Question d.
What is meant by ‘culinary art’?
Answer:
Culinary art is the art of preparing and cooking food a subdomain of the hospitality sector.

Question e.
Why is media a popular career option?
Answer:
Media is a popular career option because many youngsters are attracted to it as exposure and reach is greater through mass media.

Question f.
Name some paramedical courses mentioned in the passage.
Answer:
Some paramedical courses mentioned in the passage are optometry, pathology, nursing, physiotherapy, and dentistry.

Question g.
Why is the hotel industry seen as the fastest growing in India?
Answer:
The hotel industry is seen as the fastest-growing in India because the number of travellers on an international level is increasing.

Question h.
Does one have to be a player to opt for a career in the field of sports? Answer giving reasons.
Answer:
One need not be a player or an athlete to shine in a sports career because the field of sports offers various career options.

Question i.
Pick one word from the passage which is the opposite of ‘modern’.
Answer:
‘Past’

Question j.
Which word in the passage means ‘composed of people from many parts of the country’?
Answer:
International travellers.

Grammar:

Prepositions:

Recall your learning of basic prepositions and complete the sentences using the prepositions given in brackets: (Text Book Page No. 45)
(over, under, on, between, among, into, with, since, in front of near / beside)

Question a.
The boy jumped _____ a narrow stream.
Answer:
into

Question b.
Afsar will meet me _____ Friday morning.
Answer:
on

Question c.
The temple is _____ the bank.
Answer:
near

Question d.
My friend _____ his brother will meet me tomorrow.
Answer:
with

Question e.
There is usually a garden _____ a bungalow.
Answer:
in front of

Question f.
Yuvan has been studying well _____ childhood.
Answer:
since

Question g.
A trekker climbed _____ a mountain meticulously.
Answer:
on

Question h.
There was a skirmish _____ my brother and sister.
Answer:
between

Question i.
The laudable thoughts were apparent _____ many scholars in a conference.
Answer:
among

Question j.
It is easy to work _____ the aegis of a visionary leader.
Answer:
under

Task 2:
Complete the following passages using the prepositions given in brackets:
(among, for, at, to, in)

Question i.
When Lakshmi was (1) _____ school, she practiced music from Monday (2) _____ Friday. She involved herself (3) _____ the school orchestra. She was responsible for (4) _____ conducting many programmes. She was very popular (5) _____ her schoolmates, as she was kind, friendly, and helpful.

Answer:

1. at
2. to
3. in
4. for
5. among

(after, with, on, before, of, in, for)

Question ii.
(1) _____ the interview, Solomon was confident (2) _____ getting the job. He knew that he was qualified (3) _____ the
job. He was interested (4) _____ discharging his duty perfectly. The interview panel was impressed (5) _____ his attitude and skills. So (6) _____ the interview, he was (7) _____ cloud nine.

Answer:

1. before
2. of
3. for
4. in
5. with
6. after
7. on

Prepositional Phrases:
A prepositional phrase is made up of a preposition and a noun phrase.

Task 1:
Underline the prepositional phrases. The first two examples have been done for you: (Text Book Page No. 45) 

1. With reference to your advertisement in a local newspaper, I am applying for the post of salesman.
2. The assignment will be completed in a few weeks.
3. Ravi was appreciated by his teachers.
4. We feel sorry for our mistakes.
5. The boy studied well in spite of many obstacles.
6. Our nation is famous for its glorious culture.
7. We are proud of our children.
8. My brother will return home in the evening.

Task 2:

Fill in the blanks with suitable prepositional phrase given in brackets: (Text Book Page No. 46)
(in favour of, in case of, according to, on the whole, on account of, on behalf of, in spite of, instead of)

Question a.
_____ Kiran, Rajesh may attend a programme.
Answer:
Instead of

Question b.
Many tourists visited Ooty _____ heavy rains.
Answer:
in spite of

Question c.
Expressing gratitude _____ others is common in a vote of thanks.
Answer:
on behalf of

Question d.
_____, I had a happy childhood.
Answer:
On the whole

Question e.
Our teacher always acts _____ her students.
Answer:
in favour of

Question f.
_____ his laziness, the boy remained passive for a long time.
Answer:
On account of

Question g.
_____ Gandhiji, ahimsa means infinite love.
Answer:
According to

Question h.
_____ rain, take an umbrella.
Answer:
In the case of

Conjunctions:

Coordinating Conjunctions:

Subordinating Conjunctions:

Connectives or Linkers:

Task 1:
Choose the appropriate linker from within the brackets and complete the sentences:

Question a.
I could not complete my paper in the examination __________ (because, but) I was slow in answering the questions.
Answer:
because

Question b.
It started raining, _________ (yet, so) we could not play.
Answer:
so

Question c.
___________ (As, If) I got up early, I managed to reach school on time.
Answer:
As

Question d.
______ (Though/Whereas) he committed a mistake, he apologised ___________ (and/since) promised that he would not repeat it.
Answer:
Though, and

Question e.
This is __________ (how/what) it must be done.
Answer:
how

Question f.
The vendor saw the train moving slowly from the platform, ______ (therefore/until) he got in.
Answer:
therefore

Question g.
I was not well, ___________ (but/so) I did not attend the class.
Answer:
so

Question h.
______ (If, Although) she can drive, she travels by bus.
Answer:
Although

Question i.
______ (If/Unless) you register your name, you cannot participate in the competitions.
Answer:
Unless

Question j.
________ (As soon as/beside) my father arrived home, I narrated the incident.
Answer:
As soon as

Question k.
Be quick to hear _________ (then /and) slow to speak.
Answer:
and

Question l.
I am ___________ (neither/either) an ascetic in theory ________ nor/or) in practice.
Answer:
neither, nor

Question m.
We fail to harness the rainwater, ________ (consequently, nevertheless) we suffer.
Answer:
consequently

Question n.
My brother will certainly clear GRE; ______ (yet/for) he works very hard.
Answer:
for

Task 2:
Combine the sentences and rewrite them using the words given in the brackets: (Text Book Page No. 48)

Question a.
The well was deep. Therefore, the fox could not get out of the well, (because)
Answer:
The fox could not get out of the well because the well was deep.

Question b.
The work was over. We went home, (when)
Answer:
When the work was over, we went home.

Question c.
A library is a public place. We see a number of books kept there for reading, (where)
Answer:
A library is a public place where we see a number of books kept there for the reading.

Question d.
The culprit was caught. Immediately, he was taken to the police station, (as soon as)
Answer:
As soon as the culprit was caught, he was taken to the police station.

Question e.
The boys were stealing mangoes from a grove. At that time, the owner of the grove came in. (while)
Answer:
The owner of the grove came in while the boys were stealing mangoes from a grove.

Question f.
Artificially flavoured juices are hazardous to health. Moreover, they lead to kidney problems, (and)
Answer:
Artificially flavoured juices are hazardous to health and lead to kidney problems.

Question g.
Adit has been promoted. Ranjan has been promoted, (as well as)
Answer:
Adit as well as Ranjan has been promoted.

Question h.
Caesar was declared emperor. The conspirators killed him. (After)
Answer:
After Caesar was declared emperor, the conspirators killed him.

Task 3:
Fill in the blanks with appropriate correlative conjunctions: (Text Book Page No. 48)

Question a.
She is ________ an understanding person _____ everybody likes to be with her.
Answer:
such, that

Question b.
Suraj owns ________ a typewriter _______ a computer.
Answer:
both, and

Question c.
Vani is _______ a good singer _____ a good dancer.
Answer:
not only, but also

Question d.
Amit did not know _______ his father met his class teacher _________ not.
Answer:
whether, or

Question e.
I would _______ starve _______ beg.
Answer:
rather, than.

Writing:

Article Writing: (Text Book Page No. 49)
Task 1:

Write an article of 150 words for your school magazine to create an awareness of the dangers posed by the indiscriminate use of plastics, Expand the ideas given below as notes: (P No. 50)

The Government of Tamil Nadu has imposed a ban on the use of plastic. Effective implementation of this ban depends on public awareness and individual responsibility.

Notes:
a. Introduction

• Plastic – synthetic material – doesn’t decompose in the soil
• inevitable role of plastic – man’s day-to-day life

b. Human Health Hazard:

• Leeching of plastic into food – microplastic entering the food chain
• Human body’s inability to deal with this unnatural substance
• The reaction of microplastic in the human body and ill- effects

c. Adverse effects on plants and animals:

• Plastic particles choking waterways – affect aquatic animals
• Ingestion by aquatic and terrestrial animals – blocking of intestines and respiratory passages

d. Environmental Degradation:

• Manufacturing process & burning of plastics – pollute atmosphere
• Plastic – non-biodegradable – interferes with soil microorganisms – affects soil fertility

e. Conclusion:

• suggestions for restricted use -alternatives for a one-time use of plastics
• segregation of plastic waste – for recycling

Introduction:
Plastic is a synthetic material. It does not decompose in the soil. Its presence in the soil spoils the soil and it becomes barren. It has an inevitable role to play in the life of man. It has become a part of man’s day-to-day life.

Human Health Hazard:
It poses a health hazard. The micro part of plastic enters our food. It becomes like a leech in our food. It produces indigestion problems for aquatic and terrestrial animals. Its presence inside our body blocks the intestines and respiratory passages.

Environmental Degradation:
The manufacturing process and burning of plastics pollute the atmosphere. It is non-biodegradable so it interferes with soil micro-organism and affects soil fertility.

Conclusion:
We can go for the restricted use of plastic. The plastic companies may be restricted to make one-time use plastics. All plastic waste should be segregated into different types and used for recycling.

Task 2:
Now write an article of about 150 words for a leading newspaper on the various ways of maintaining personal hygiene and sanitation in order to ensure a healthy living. Make use of the hints given below: (Text Book Page No. 50)

Urban living brings with it very dense co-habitation, This can often result in the transfer of various communicable diseases that could quickly develop into an outbreak.

Hints:
a) Introduction – ‘Cleanliness is next to Godliness’ – brief explanation

b) Personal Hygiene

• Frequent washing of hands & regular bathing
• Brushing of teeth, cutting of nails & hair
• Wearing dean clothes

c) Keeping diseases at bay:

• Avoid street food
• Keep food containers closed with lids
• Drink boiled water
• Wash fruits and vegetables in flowing water

d) Keeping living area, surroundings, and the environment clean:

• Disposal of domestic organic waste on a daily basis, and hazardous waste in designated places
• Regular sweeping, mopping, and dusting
• Disinfection of toilets and bathing areas
• Avoid littering of public places
• Avoid spitting, urinating, and defecating in public places

e) Conclusion:
– Hygiene – a collective exercise – everyone’s involvement and practice, a must -b ensure community – health and happiness – celebrate life.

Introduction:
‘Cleanliness is next to Godliness’. This adage shows the importance of cleanliness. Cleanliness is important for a healthy life. If we keep ourselves and our place dean, we can avoid many diseases.

Personal Hygiene:
Our personal hygiene is important. We should wash our hands frequently. Regular bathing is necessary to maintain our hygiene. Brushing of teeth should be done every day before we take our first food. Cutting of nails and hair is also essential. We should always wear clean clothes.

Keeping diseases at bay:
We should avoid street food. Our food should be kept in dosed containers. We should drink only boiled water. Fruits and vegetables should be washed in flowing water.

Keeping living areas, surroundings, and the environment clean:
Our living area and surroundings should be kept clean. Domestic organic waste should be disposed of on daily basis. Our area should be swept, mopped, and dusted regularly. Disinfection lotion should be used in the toilets and bathing area. Littering in public places should be avoided. We should avoid spitting, urinating, and defecating in public places.

Conclusion:
Hygiene is a collective exercise. Everyone’s involvement and practice is needed. If we must ensure a healthy and happy community we can celebrate our life.

Essay Writing:

Task 1:
Write an essay of about 200 words each: (P No. 51)

1. The Profession you would like to choose:
Introduction:
Everyone has his dreams and plans in life. Some people want to become doctors, engineers, or collectors. I want to uplift our country. So I want to become a teacher. The teachers are the real builders of the nation.

Teaching Profession:
The world of tomorrow will be born from the school of today. Teachers are the trustees of common welfare. A teacher should be a friend, philosopher, and guide. A teacher should love his students. Our country needs such good teachers.

Service in the Village:
I like teaching very much. My motto in life is simple living and high thinking. India lives in her villages. So I will serve in a village. I will be earnest and sincere to my students. I will not be proud of. Thus I will be a good citizen and serve mankind.

2. The Importance of a Balanced Diet:

A balanced diet is very important to a healthy lifestyle. A balanced diet should contain all the right foods in the right quantities like carbohydrates, high fiber content, water, proteins, fats, vitamins, and minerals. If you want to lead a healthy lifestyle, eating healthy food is important. Fluids are very essential for the human body to have a healthy lifestyle. Drink a lot of water every day.

Eat fresh fruits and vegetables which will help avoid many health disorders. Our balanced diet should contain all five elements which are bitter, pungent, sour, sweet, and salt. Most people do not recognize the importance of chewing as it is essential to digest many of components. We must avoid eating when we don’t have an appetite. Excess food may lead to overweight. We must avoid eating while working or watching TV. It may lead to heartburn and colitis. A balanced diet keeps our bodies healthy and brisk.

3. A memorable journey:
The most memorable journey I have enjoyed is the train journey towards Mumbai. It is a three-day journey from Tirunelveli. During last summer vacation, with my parents. I went by train, I was able to learn about the different cultures and languages of the people. A college student was seated across he engaged me in a lively conversation.
They were from Chennai and talked about their purpose of visit.

I had an occasion to have a chat with a few Hindi – speaking people. They were very polite and kind to me. I was extremely ’ happy when the train passed through Mumbai, where I bought delicious apples. Though I could not understand Hindi, I talked with them in Tamil. They gave me nice apples and I gave them some money that pleased him. At the end of the second day, we reached Mumbai. The journey broadened my knowledge about our country.

Suggested Topics: (Text Book Page No. 51)

1. Importance of Physical Exercises / Sports and Games:
Regular physical exercise will improve your muscle strength. Exercise gives oxygen and nutrients to your tissues. It helps your cardiovascular system work more efficiently. When your heart and lung health improve, you have more energy to do daily activities. Exercise acts on the digestive system. It helps in digestion and induces appetite. The free movement of the parts of the body especially arms and limbs help you to lead a tension-free life in old age.

2. Travel and its Benefits:
Travelling improves your health. It cuts down stress. The health benefits of traveling are huge. Travelling makes your body feel better. Traveling is a source of knowledge, education, and experience. There is scope for improving one’s social and communication skills. Creative thoughts and broadening the horizon, enhancing tolerance are all the benefits of travel. Travel gives confidence, and it is a real education in life. The memories of travel give us pleasure.

3. Water Conservation:
Our lives depend fully on water. It is our duty to conserve water. We have only 3% of the water on earth. The remaining is 97% of saltwater in the seas. It is our responsibility not to pollute and abuse it. We must know how to conserve water. We can contribute to the conservation of potable water by protecting from water pollution. Modern irrigation methods help to solve water shortages and avoid wastage. Water can be saved in industries. Industries can adopt water recycling. Digging lakes, ponds, wells will help save rainwater. Children can be educated to save water and avoid wastage during their chores like washing, bathing, and cleaning.

4. Child Labour:
Child labour means making the children in hard labour which affects their physical and mental development. Children in the school-going age are employed in all kinds of jobs. They work in a bad atmosphere. They are never paid or paid less. The poverty of the parents is exploited to employ the children than giving them education. The children must go to school and only adults should be employed. The government should make strict laws to eradicate child labour. We should give a bright future to our children.

5. Mobile Phone – Advantages and Disadvantages:
A mobile phone is a device, which is used only for communication. However technological developments in the field of communication have made the phone a smartphone with features like video calls, surfing the net, play games, and take high-resolution pictures.

Smartphones have become a great disadvantage to people, especially to students. They get addicted to it, thereby inviting various health problems and social problems. Mobile phones should be useful and necessary gadgets for our everyday life. Without cell phones, life would be harder. While enjoying the benefits of phones, we must be aware of their abuses too. Mobile phones could cause many dangers if not used properly.

6. Consumerism – Wants and Needs:
Consumerism means the protection of the interests of the consumers. The growth of consumerism has led to many organizations improving their service to the customer. It is a social and economic order that encourages the acquisition of goods and services. Various methods are used to create demand. It protects consumers against harmful products or business methods.

Wants and needs:
We have to consume to live. We need food, water, shelter, and clothing. People go behind electronics, enjoyment, luxury, etc. They forget that what they “need” is not a real “need”. Many people cannot draw a line between the two. While one part of the world food is wasted, in the other part people are starving. People should learn not to waste anything.

7. Value of Education:
Education is necessary for all. It develops confidence and builds the personality of a person. School education plays an important role in everyone’s life. The whole education has been divided into three divisions such as the Primary, Secondary, and Higher Secondary education. Primary education prepares the base which helps throughout life. Secondary education prepares the path for higher studies.

Higher Secondary education decides the final path to life and career. Our education decides what kind of person we would be in the future. In the competitive world, it is a must for all to have a good education. It makes us strong, mentally, socially, and intellectually by increasing our knowledge level, technical skills, and good position in the job. The only way to fulfill all dreams is only through education.

8. Value-based Education:
The purpose of value-based education is to build the social, moral, and spiritual behaviour of a person. It plays a big role in teaching the importance of being honest with others, being humble’ in all situations, and be able to face challenges. It helps in shaping the individual’s behaviour to fit into society. It will have an impact on the whole society, making the world, a better place to live in. Value-based education plays a big role in shaping the individual’s behaviour, so that they can display good morals, interact with others well, and become spiritual in all aspects of life.

(ஆசிரியரைப் பற்றி:

ஜார்ஜ் ஆர்வெல் (George Orwell) என்னும் புனைப்பெயரால் (Pen name) அறியப்பட்ட எரிக் ஆர்த்த ர் ப்ளையர் (Eric Arthur Blair) (25 ஜீன் 1903 – 21 ஜனவரி 1950) ஒரு ஆங்கில புதினவியளாளர், கட்டுரையாளர், பத்திரிக்கையாளர், மற்றும் விமர்சகர். இவரின் படைப்புகள் நல்ல படிப்பினைகளையும், சமூக விழிப்புணர்வையும் ஏற்படுத்துவதாகவும், சர்வதிகாரத்திற்கு எதிராகவும், ஜனனாயகத்திற்கு ஆதரவாகவும் அமைக்கப்பட்டு இருக்கும்.

ஆர்வெல் இலக்கிய விமர்சனங்கள், கவிதைகள், புதினங்கள், தர்க்க இதழியல் போன்றவற்றை எழுதியுள்ளார். இவர் எண்ணியல் புதினமான Animal Farm (1945) மற்றும் டைஸ்டோபியன் புதினமான Nineteen Eighty – four(1949) ஆகியவற்றால் மிகச் சிறந்தவராக அறியப்பட்டார். 2008ஆம் ஆண்டு Times இவரை 1945 வரை உள்ள 50 சிறந்த British எழுத்தாளர்களில் இரண்டாவதாக பட்டியலிட்டது.

பாடத்தைப் பற்றி:

கொடுக்கப்பட்ட இந்த பாடப்பகுதி ஜார்ஜ் ஆர்வெல் அவர்களின் கட்டுரைகள், பத்திரிக்கைகள் மற்றும் கடிதங்களிலிருந்து எடுக்கப்பட்டது. தேநீர் நகரத்தின் ஆதாரப் பொருட்களுள் ஒன்றாக இந்தியா, அயர்லாந்து, ஆஸ்திரேலியா முதலிய நாடுகள் கருதப்படுகிறது. இந்தியா, இலங்கை தேயிலைதான் மிகச்சிறந்தது.

இப்பாடத்தில் தேனீர் தயாரிக்கும் விதத்தைப் பற்றியும், பல நாடுகளில் அதன் பயன்பாடுகள் பற்றியும் அதை எவ்வாறு அருந்த வேண்டும் என்பதைப்பற்றியும் ஜார்ஜ் ஆர்வெல் 11 (கருத்துக்கள் மூலம் தெளிவாக எடுத்துரைக்கிறார். அதைப்பற்றி முழுமையாக படித்து தெரிந்து கொள்வோம்.

A Nice Cup of Tea Summary in Tamil

தமிழாக்கம் நீங்கள் உங்கள் கையில் கிடைக்கும் சமையல் புத்தகத்தை எடுத்து அதில் ‘டீ’ தயாரிப்பதை தேடினீர்கள் (look up) என்றால், அதனைப் பற்றிய குறிப்பு கிடைக்காமல் போகலாம் அல்லது அதிகபட்சமாக நீங்கள் பல முக்கியமான கருத்துக்கள் விடுபட்ட (unmentioned) மேலோட்டமான சில வரிகளை காணலாம்.

இந்திய நாடு, இதேப்போல் ஐர், ஆஸ்திரேலியா, நியூசிலாந்து போன்ற நாடுகளின் நாகரிகத்தில் முக்கியமானதாக டீ இருப்பதால் மட்டும் இது ஆர்வமானதாக இல்லை, டீ-ஐ எப்படி சிறந்த முறையில் தயாரிக்க வேண்டும் என்பதே ஒரு காரசாரமான விவாத தலைப்பாக (violent disputes) இருப்பதால் தான்.

நான் என்னுடைய “தேநீர் தயாரிப்பதற்கான சொந்த சமையல் குறிப்பை (recipe)” பார்த்த போது 11ற்கும் குறைவான மிக முக்கியமான குறிப்புகளைக் கண்டேன். அவற்றில் 2 குறிப்புகள் பொதுவானதாக இருந்தாலும், குறைந்தது 4 குறிப்புகளாவது கண்டிப்பாக சர்ச்சைக்குரியவை (controversial). இங்கே குறிபிடப்பட்டுள்ள என்னுடைய 11 விதிகளில், ஒவ்வொன்றையும் நான் பொன்னாகவே (goldens) கருதுகிறேன்.

எல்லாவற்றிக்கும் முதலாவதாக ஒருவர் இந்திய அல்லது சிங்கள (இலங்கை) தேநீர் இலைகளைத் தான் உபயோகப்படுத்த வேண்டும். சீனத் தேநீரின் மதிப்பிடத்தக்க பண்புகளையும் (virtues) நாம் இக்காலத்தில் வெறுக்க கூடாது, இது சிக்கனமானது (economical), பாலுடன் கலக்காமலும் இதனை அருந்தலாம், ஆனால் போதுமான அளவு உற்சாகம் (stimulation) இருக்காது.

அதனைப் பருகிய பிறகு, ஒருவர் அறிவார்ந்ததாகவும் (wiser), தைரியமானவராகவும் (braver), அதிக நேர்மறையாளராகவும் (optimistic) உணர மாட்டார். எவரேனும் ஒருவர் “ இது ஒரு மிகச்சிறந்த குவளைத் தேநீர்” என்ற வரிகளை உபயோகப்படுத்தினால், அது நிச்சயமாக இந்தியத் தேநீரையே குறிக்கும்.

இரண்டாவதாக, தேநீரை மிகச்சிறிய அளவில் மட்டுமே தயாரிக்க வேண்டும், அதாவது சிறிய தேநீர் குடுவையில் தான் தயாரிக்க வேண்டும். பெரிய பாத்திரத்தில் தயாரிக்கும் தேநீர் சுவையற்று (tasteless) இருக்கும், இராணுவத்தில் பெரிய கலனில் (cauldron) தயாரிக்கும் தேநீர், எண்ணெய்ப்பசை மற்றும் சுண்ணாம்பு போன்ற சுவையுடன் இருக்கும். தேநீர் குடுவையானது களிமண்ணால் அல்லது பீங்கானால் செய்யப்பட வேண்டும்.

வெள்ளி அல்லது உலோக கலவையில் ஆன தேநீர் குடுவையில் தரக்குறைவான தேநீரையே தயாரிக்க முடியும், கண்ணாடியால் ஆன பாத்திரங்கள் மிக மோசம். போதுமான ஆர்வமுடையதாக இருந்தாலும் காரியத்தால் ஆன தேநீர் குடுவை மிகவும் மோசமானது அல்ல. மூன்றாவதாக, குடுவையானது முன்னதாகவே சூடுபடுத்தப்பட (warmed) வேண்டும். குடுவையினை அடுப்பில் வைத்து சூடுபடுத்துவதே, வழக்கமான வெந்நீரால் சூடுபடுத்தும் முறையே சிறந்தது.

நான்காவதாக, தேநீர் திடமாக இருக்க வேண்டும். 1 லிட்டருக்கு சற்று அதிகமான கொள்ளளவு உடைய கலனில், நீங்கள் கழுத்துவரை நிரப்புவதாக இருந்தால், 6 தேக்கரண்டி (teaspoons) போதுமானதாக இருக்கும். போர் நடவடிக்கை (rationing) காலங்களில் வாரத்தின் அனைத்து நாட்களிலும் இம்முறையை பின்பற்ற இயலாது. ஆனால் ஒரு குவளை திடமான தேநீரானது 20 குவளை திடமற்றது. “அனைத்து உண்மையான தேநீர் விரும்பிகளுக்கும், தங்களது தேநீர் திடமாக இருந்தால் மட்டும் போதாது. ஒவ்வொரு வருடம் கடந்து போகும் போதும் அவர்களது தேநீர் கூடுதல் திடமாக இருக்க வேண்டுமென விரும்புகிறார்கள். அது வயதான ஓய்வூதியதாரர்களுக்கு (pensioners) கூடுதல் உணவுப்படி வழங்கப்படும் போது கண்டறியப்பட்ட உண்மை.

ஐந்தாவதாக, தேநீரானது நேரடியாக குடுவையினுள் இடப்படவேண்டும். வடிகட்டியோ அல்லது மெல்லிய துணியோ தேநீரை வடிகட்ட உபயோகப்படுத்தக் கூடாது. சில நாடுகளில் தேநீர் குடுவைகள், நீர்க்குழாயின் (spout) கீழே தேவையில்லாத சிறிய தேநீர் இலைகளை சேகரிக்க சிறிய கூடைகளுடன் இணைக்கப்பட்டிருக்கும். அது தீங்கு விளைவிக்கும். உண்மையில் ஒருவர் குறிப்பிட்ட அளவு தேநீர் இலைகளை விழுங்கினாலும், அது தீங்கு விளைவிக்காது. தேநீரானது குடுவையில் தளர்வாக இல்லாவிட்டால், அது முறையாக கலக்காது.

ஆறாவதாக, தேநீர் குடுவையிலிருந்து நேரடியாக தேநீர் கொதி கெண்டிக்கு (kettle) மாற்ற வேண்டும். அப்பொழுது நீரானது கொதித்து கொண்டிருக்க வேண்டும். அதாவது ஒருவர் கொதி கெண்டிக்கு ஊற்றும் போது நீராவி தான் உபயோகிக்க வேண்டும் என்பார்கள் ஆனால் என்னைப் பொறுத்தவரையில் அது எவ்வித வித்தியாசத்தையும் உண்டு பண்ணாது.
ஏழாவதாக தேநீர் தயாரித்த பிறகு, நன்கு கலக்கி, தேநீர் குடுவையை நன்கு குலுக்கி அதன்பின் தேநீர் இலைகளை அமரச் செய்ய வேண்டும்.

எட்டாவதாக, ஒருவர் காலைகுவளையில் தான் குடிக்க வேண்டும், காலை உணவுக் (breakfastcup) குவளையானது, உருளை வடிவில் (cylindrical type), ஆழமற்றும் காணப்படும். காலை உணவுக் குவளையானது அதிகக் கொள்ளளவு உடையது, வேறு வகையான குவளையில் அருந்தினால், அருந்த தொடங்கும் முன்பே பாதி ஆறிவிடும்.

ஒன்பதாவதாக தேநீர் தயாரிக்கும் முன்பே உபயோகப்படுத்தப்படும் பாலின் பாலேட்டினை நீக்கி விட வேண்டும். அதிக பாலேட்டுடன் கூடிய பால், மங்கிய (sickly) சுவையுள்ள தேநீரைத் தரும்.

பத்தாவதாக, ஒருவர் முதலில் தேநீரை குவளையில் ஊற்ற வேண்டும் இதுவே ஒரு முறையான கருத்தாகும். உண்மையில் பிரிட்டனில் உள்ள அனைத்து வீடுகளிலும் இது குறித்து இரு கருத்துக்கள் நிலவுகின்றன. பாலை முதலில் ஊற்ற வேண்டும் என்ற கருத்து சற்று கடுமையான விவாதங்கள் கொண்டு வந்தாலும், என்னுடைய கருத்தினை பதிலளிக்க முடியாததாகவே நான் வைத்து வருகிறேன். அது என்னவென்றால் தேநீரை முதலில் ஊற்றுவதால். ஒருவரால் தனக்கு தேவையான அளவு பாலை ஊற்றிக்கொள்ளலாம்.

மாற்றுக்கருத்தில், ஒருவர் தேவைக்கு அதிகப்படியான பாலை ஊற்றும் நிலைமை வரலாம். கடைசியாக (lastly) ஒருவர், தேநீரை ரஷிய நாட்டு வழக்கத்தில் அருந்தவில்லை என்றால், அவர் கண்டிப்பாக சர்க்கரை இல்லாமல் தான் அருந்த வேண்டும் என கருத்து சிலரால் மட்டுமே ஏற்றுக்கொள்ளப்படும் என்று எனக்கு தெரியும், இருந்தாலும் தேநீரில் சர்க்கரையைச் சேர்த்து அதன் சுவையை குறைக்கும்.

நீங்கள் எவ்வாறு உங்களை தேநீர் விரும்பி என்று அழைத்து கொள்ள முடியும்? இது தேநீரில் மிளகுத்தூளையோ (pepper) அல்லது உப்பையோ (salt) சேர்ப்பதற்கு சமமானதாகும். தேநீரை நீங்கள் இனிப்பூட்டினால் நீங்கள் தேநீரை சுவைக்கவில்லை, சர்க்கரையைத் தான் சுவைக்கிறீர்கள். இதற்கு நீங்கள் வெறும் சுடு தண்ணீரில் சர்க்கரையை கரைத்து அருந்தலாம்.

சிலர் தாங்கள் தேநீரை விரும்புவதில்லை என்றும், உற்சாகத்திற்காகவும் (stimulated) வெப்பமாக இருப்பதற்காக மட்டுமே தேநீரை அருந்துவதாகவும் அதனால் தான் சர்க்கரையைச் சேர்த்து தேநீரின் சுவையை நீக்குவதாகவும் சொல்லுவார்கள். அவ்வாறு தவறாக வழிகாட்டப்பட்டவர்களுக்கு (misguided) நான் கூறுவதாவது, நீங்கள் தொடர்ந்து இரு வாரங்களுக்கு தேநீரை சர்க்கரை இல்லாமல் அருந்தினீர்கள் என்றால், நீங்கள் மறுபடியும் தேநீரில் சர்க்கரை சேர்த்து வீணாக்கமாட்டீர்கள்.

தேநீர் அருந்துவதை குறித்து எழும்பக்கூடிய முரணான (controversial) கருத்துக்கள் இவை மட்டுமல்ல. இந்த தொழில் எவ்வளவு நுட்பமானது என்பதை காட்ட பல கருத்துக்கள் உள்ளன. மேலும் தேநீர் குடுவையைச் சுற்றி புரிந்து கொள்ள (mysterious) முடியாத ஆசாரங்கள் பல உள்ளன. எடுத்துக்காட்டாக நாம் ஏன் தேநீர் கோப்பையில் அருந்துகிறோம்).

தேநீர் இலைகளின் கிளை துணை உபயோகங்களை, தீர்க்க தரிசனம் கூறுவது, விருந்தினர்களின் வருகையை கணிப்பது, முயல்களுக்கு உணவாவது, தீக்காயங்களுக்கு மருந்தாவது தரையை கூட்டிப் பெருக்குவது குறித்து கூட நிறைய எழுதலாம். 2 (28 கிராம்) எடையுள்ள முறையாக கையாளப்பட்ட தேநீர் இலைகளில் இருந்து 20 தேநீர்

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.1 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 5 Two Dimensional Analytical Geometry – II Ex 5.1

Question 1.
Obtain the equation of the circles with a radius of 5 cm and touching the x-axis at the origin in a general form.
Solution:

Given radius = 5 cm and the circle is touching x axis
So centre will be (0, ± 5) and radius = 5
The equation of the circle with centre (0, ± 5) and radius 5 units is
(x – 0)² + (y ± 5)² = 5²
(i.e) x² + y² ± 10 y + 25 – 25 = 0
(i.e) x² + y² ± 10y = 0

Question 2.
Find the equation of the circle with centre (2, – 1) and passing through the point (3, 6) in standard form.
Solution:
Centre = (2, -1) = (h, k)
Passing through the point (3, 6)
Equation of the circle (x – h)² + (y – k)² = r² ………. (1)
(3 – 2)² + (6 + 1)² = r²
1² + 7² = r²
1 + 49 = r²
r² = 50
(1) ⇒ (x – 2)² + (y + 1)² = 50

Question 3.
Find the equation of circles that touch both the axes and pass-through (-4, -2) in a general form.
Solution:

Since the circle touches both the axes, its centre will be (r, r) and the radius will be r.
Here centre = C = (r, r) and point on the circle is A = (-4, -2)
CA = r ⇒ CA² = r²
(i.e) (r + 4)² + (r + 2)² = r²
⇒ r² + 8r +16 + r² + 4r + 4 – r² = 0
(i.e) r² + 12r + 20 = 0
(r + 2) (r + 10) = 0
⇒ r = -2 or -10
When r = -2, the equation of the circle will be (x + 2)² + (y + 2)² = 2²
(i.e) x² + y² + 4x + 4y + 4 = 0
When r = -10, the equation of the circle will be (x + 10)² + (y + 10)² = 10²
(i.e) x² + y² + 20x + 20y + 100 = 0

Question 4.
Find the equation of the circles with centre (2, 3) and passing through the intersection of the lines 3x – 2y – 1 =0 and 4x + y – 27 = 0.
Solution:
centre (2, 3) = (h, k)
Point of intersection
Solve 3x – 2y – 1 = 0 ………. (1)
4x + y – 27 = 0 ……… (2)
(1) ⇒ 3x – 2y = 1
(2) × 2 ⇒ 8x + 2y = 54
11x = 55
x = 5
put in (1)
15 – 2y – 1 = 0
14 = 2y
y = 7
Passing-through point is (5, 7)
Equation of circle be (x – h)² + (y – k)² = r² ……….(3)
(5 – 2)² + (7 – 3)² = r²
3² + 4² = r²
r² = 25
∴ (3) ⇒ (x – 2)² + (y – 3)² = 25
x² – 4x + 4 + y² – 6y + 9 – 25 = 0
x² + y² – 4x – 6y – 12 = 0

Question 5.
Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.
Solution:
The equation of a circle with (x₁ , y₁) and (x₂ , y₂ ) as end points of a diameter is
(x – x₁ )(x – x₂) + (y – y₁ )(y – y₂) = 0
Here the end points of a diameter are (3, 4) and (2, -7)
So equation of the circle is (x – 3 )(x – 2 ) + (y – 4) (y + 7.) = 0
x² + y² – 5x + 37 – 22 = 0

Question 6.
Find the equation of the circle through the points (1, 0), (-1, 0) and (0, 1).
Solution:
Let the general equation of the circle be
x² + y² + 2gx + 2fy + c = 0
It passes through the points (1, 0), (-1, 0) and (0,1)
1 + 0 + 2g + c = 0
2g + c = -1 ………(1)
1 + 0 – 2g + c = 0
-2g + c = -1 …………(2)
0 + 1 + 0 + 2f + c = 0
2f + c = -1
(1) + (2) ⇒ 2c = -2
c = -1
substitute in eqn (1)
2g – 1 = -1
2g = 0
g = 0
substitute in eqn (3)
2f – 1 = -1
2f = -1 + 1
2f = 0
f = 0
Therefore, the required equation of the circle
x² + y² – 1 = 0

Question 7.
A circle of area 9π square units has two of its diameters along the lines x + y = 5 and: x – y = 1. Find the equation of the circle.
Solution:

Area of the circle = 9π
(i.e) πr² = 9π
⇒ r² = 9 ⇒ r = 3
(i.e) radius of the circle = r = 3
The two diameters are x + y = 5 and x – y = 1
The point of intersection of the diameter is the centre of the circle = C
To find C: Solving x + y = 5 ……… (1)
x – y = 1 ………. (2)
(1) + (2) ⇒ 2x = 6 ⇒ x = 3
Substituting x = 3 in (1) we get
3 + y = 5 ⇒ y = 5 – 3 = 2
∴ Centre = (3, 2) and radius = 3
So equation of the circle is (x – 3)² + (y – 2)² = 3²
(i.e) x² + y² – 6x – 4y + 4 = 0

Question 8.
If y = 2√2 x + c is a tangent to the circle x² + y² = 16, find the value of c.
Solution:
The condition of the line y = mx + c to be a tangent to the circle x² + y² = a² is
c² = a²( 1 + m²)
a² = 16; m = 2√2 ⇒ m² = 4 × 2 = 8
c² = 16(1+8)
c² = 16(9)
c = ±4 × 3 = ±12
∴ c = ± 12.

Question 9.
Find the equation of the tangent and normal to the circle x² + y² – 6x + 6y – 8 = 0 at (2, 2).
Solution:
The equation of the tangent to the circle x² + y² + 2 gx + 2fy + c = 0 at (x₁, y₁) is
xx₁ + yy₁ + g(x + x₁) + f(y + y₁) + c = 9
So the equation of the tangent to the circle
x² + y² – 6x + 6y – 8 = 0 at (x₁, y₁) is
xx₁ + yy₁ – \(\frac{6\left(x+x_{1}\right)}{2}+\frac{6\left(y+y_{1}\right)}{2}\) – 8 = 0
(i.e) xx₁ + yy₁ – 3(x + x₁) + 3(y + y₁) – 8 = 0
Here (x₁, y₁) = (2, 2)
So equation of the tangent is
x(2) + y(2) – 3(x + 2) + 3(y + 2) – 8 = 0
(.i.e) 2x + 2y – 3x – 6 + 3y + 6 – 8 = 0
(i.e) -x + 5y – 8 = 0 or x – 5y + 8=0
Normal is a line ⊥r to the tangent
So equation of normal circle be of the form 5x + y + k = 0
The normal is drawn at (2, 2)
⇒ 10 + 2 + k = 0 ⇒ k = -12
So equation of normal is 5x + y – 12 = 0

Question 10.
Determine whether the points (- 2, 1), (0, 0) and s (- 4, – 3) lie outside, on or inside the circle x² + y² – 5x + 2y – 5 = 0.
Solution:
x² + y² – 5x + 2y – 5 = 0
(i) At (-2, 1) ⇒ (-2)² + 1² – 5(-2) + 2(1) – 5
= 4 + 1 + 10 + 2 – 5 = 12 > 0
∴ (-2, 1) lies outside the circle.

(ii) At(0, 0) ⇒ 0 + 0 – 0 + 0 – 5 = -5 < 0
(0, 0) lies inside the circle.

(iii) At (-4, -3) ⇒ (-4)² + (- 3)² – 5(-4) + 2(-3) – 5 = 16 + 9 + 20 – 6 – 5 = 34 > 0
(-4, -3) lies outside the circle.

Question 11.
Find the centre and radius of the following circles.
(i) x² + (y + 2)² = 0
(ii) x² + y² + 6x – 4y + 4 = 0
(iii) x² + y² – x + 2y – 3 = 0
(iv) 2x² + 2y² – 6x + 4y + 2 = 0
Solution:
(i) x² + (y + 2)² = 0
(i.e) x² + y² + 4y + 4 = 0
Comparing this equation with the general form x² + y² + 2gx + 2fy + c = 0
we get 2g = 0 ⇒ g = 0
2f = 4 ⇒ f= 2 and c = 4
Now centre = (-g, -f) = (0, -2)
Radius = r = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{0+4-4}\)
∴ Centre = (0, -2) and radius = 0

(ii) x² + y² + 6x – 4y + 4 = 0
Comparing with the general form we get
2g = 6, 2f = -4
⇒ g = 3, /= -2 and c = 4
Centre = (-g, -f) = (-3, 2)
Radius = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{9+4-4}\)= 3
∴ Centre = (-3, 2) and radius = 3

(iii) x² + y² – x + 2y – 3 = 0
2g = -1; 2f = 2; c = -3
g = \(\frac{-1}{2}\) f = 1
Centre (-g, -f) = (\(\frac{1}{2}\), -1)
Radius = \(\sqrt{g^2+f^2-c}\) = \(\sqrt{\frac{1}{4}+1+3}\)
\(\sqrt{\frac{1+4+12}{4}}\)
\(\sqrt{\frac{17}{4}}\) = \(\frac{\sqrt{17}}{2}\)

(iv) 2x² + 2y² – 6x + 4y + 2 = 0
(÷ by 2) ⇒ x² + y² – 3x + 2y + 1 =0
Comparing this equation with the general form of the circle we get
2g = -3, 2f= 2
g = \(-\frac{3}{2}\), g= 1 and c = 1
So centre = (-g, -f) = (\(\frac{3}{2}\), -1)
and radius = \(\sqrt{g^{2}+f^{2}-c}=\sqrt{\frac{9}{4}+1-1}=\frac{3}{2}\)
∴ Centre = (\(\frac{3}{2}\), -1) and radius = \(\frac{3}{2}\)

Question 12.
If the equation 3x² + (3 – p) xy + qy² – 2px = 8pq represents a circle, find p and q. Also determine the centre and radius of the circle.
Solution:
3x² + (3 – p) xy + qy² – 2px = 8pq represent a circle means,
Co-efficient of x² = co-efficient of y²
3 = q ⇒ q = 3
Co-efficient of xy = 0
3 – p = 0 ⇒ p = 3
3x² + 3y² – 6x = 8 (3)(3)
3x² + 3y² – 6x – 72 = 0
(÷3) x² + y² – 2x – 24 = 0
2g = -2; 2f = 0; c = -24
g = -1 f = 0
Centre (-g, -f) = (1, 0)
Radius = \(\sqrt{g^2+f^2-c}\) = \(\sqrt{1+0+24}\)
= \(\sqrt{25}\) = 5

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Prose Chapter 1 Two Gentlemen of Verona Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Prose Chapter 1 Two Gentlemen of Verona

12th English Guide Two Gentlemen of Verona Text Book Back Questions and Answers

Textual Questions:

I. Answer the following questions in one or two sentences each based on your understanding of the story:
(Note: IQ Important Questions)

Question a.
Who did the narrator meet at the outskirts of Verona? (IQ)
Answer:
The Narrator met Nicola and Jacopo at the outskirts of Verona.

Question b.
Why did the driver not approve of the narrator buying fruits from the boys?
Answer:
The driver did not approve of the narrator buying fruits from the boys because of their shabby appearance.

Question c.
The boys did not spend much on clothes and food, why?
Answer:
The boys had to save every penny towards the weekly medical bill of their sister Lucia. So, they did not spend much on clothes and food.

Question d.
Were the boys saving money to go to the states? How do you know?
Answer:

1. The boys had the commitment to saving the life of their sister.
2. So they were not saving money to go to the states.

Question e.
Why did the author avoid going to Lucia’s room?
Answer:

1. The author did not like to disturb the happy family party.
2. So he avoided going to Lucia’s room.

Question f.
What was Lucia suffering from? (IQ)
Answer:
Lucia was suffering from tuberculosis of the spine.

Question g.
What made the boys join the resistance movement against the Germans?
Answer:

1. The Germans killed the boy’s father and made them homeless.
2. This made the boys join the resistance movement.

Question h.
What made the boys work so hard? (IQ)
Answer:
They did not want charity from the hospital. The determination to save the life of their sister made the boys work hard.

Question i.
Why didn’t the boys disclose their problem to the author?
Answer:

1. The boys didn’t like to gain sympathy.
2. So they did not disclose their problem to the author.

2. Answer the following questions in three or four sentences each: (Text Book Page No. 5)

Question a.
Describe the appearance of Nicola and Jacopo.
Answer:
One boy had worn Jersey and cut-off khaki pants. The other had a shortened army tunic gathered in loose folds about his skinny frame. They had tangled hair and dark earnest eyes.

Question b.
What were the various jobs undertaken by the little boys? (IQ)
Answer:
They shined shoes, sold fruits, hawked newspapers, conducted tourists round the town, and ran errands.

Question c.
How did the narrator help the boys on Sunday? (IQ)
Answer:
The author took the boys in his car to a tiny village called Poleta, set high upon a hill. He drove the car up to a large red-roofed villa. The boys asked the author to come thereafter for an hour and went inside.

Question d.
Who took the author to the cubicle? (IQ)
Answer:
The nurse who was taking care of the boy’s sister Lucia took the author to the cubicle.

Question e.
Describe the girl with whom the boys were talking to in the cubicle.
Answer:

1. The girl seemed to be about twenty.
2. She wore a pretty lace jacket.
3. Propping up on pillows, she was listening to the chatter of the boys.
4. Her eyes were soft and tender.

Question f.
Recount the untold sufferings undergone by the siblings after they were rendered homeless.
Answer:
The boys and their sister were thrown in the streets. Lucia had to give up her singing lessons. They had suffered horribly from near starvation and exposure to the cold winter. Lucia developed tuberculosis of the spine. The boys built a home from the rubbles. They had to admit Lucia to a nursing home. To pay the weekly medical bill, they worked from dawn to midnight doing odd jobs eating very little.

Question g.
The narrator did not utter a word and preferred to keep the secret to himself. Why? Substantiate the statement with reference to the story.
Answer:

1. The narrator kept the secret to himself because he knew that the boys did not like to reveal their secret to anyone.
2. When the narrator asked them what did they do with the money they earned, they were not ready to give a prompt reply for it.

3. Answer the following in a paragraph of 100-150 words each: (Text Book Page No. 5)

Question a.
What was the driving force that made the boys do various jobs?
Answer:
In the war-hit Verona, everything was difficult. Food had become scarce and dear. The hospital which offered to treat Lucia was forced to charge a weekly fee. Work was scarce. But the boys were determined to save the life of their beloved sister.

After the untimely death of the father in the war, the two little boys Nicola and Jacopo took the responsibility of earning money by doing all odd jobs for defraying the medical expenses for their sister on their tender shoulders. They spent very little on their food and clothes. The driving force behind their selfless sacrifice and hard work from dawn to midnight was the love they had for their elder sister. They wanted her to get well soon and become an accomplished singer in life. Once you set a goal far above your capacity but work hard ceaselessly, you are bound to achieve it.

Question b.
How was the family affected by the war?
Answer:
The family was terribly affected by the war. Their father, a well-known singer had been killed in the early part of the war. After some time a bomb had destroyed their home and so the three children Nicola, Jacopo, and Lucia were thrown out into the streets. Their comfortable and cultured life got destroyed by the war. In fact, they suffered horribly from near starvation and exposure to the cold winter.

For many months they lived in a shelter made of broken building walls and bricks. In the meantime, the two boys get separated from their sister. They were under German rule for nearly three years. The boys grew to hate the Germans just because they suffered a lot because of them. In fact, they were the first to join the resistance movement against the Germans.

Question c.
Write a character sketch of Nicola and Jacopo.
Answer:
Nicola was 13 and Jacopo only 12. They were brothers. They were tanned, had tangled hair and dark earnest eyes. Though they were just kids, they were serious about their work. They did hundreds of errands for the tourists. They were found doing brisk business shining shoes or selling wild berries. They had the skill to find seats in the theater for the tourists and also guide the tourists through many important sites of the city of Verona such as Juliet’s tomb. Jacopo was lively as a squirrel.

Nicola’s smile was steady and engaging yet in their innocent faces, one could find seriousness far beyond their years. What struck one was the extreme willingness of both the boys to work. Under the scorching Sun, they hawked newspapers. When the narrator enquired what they did with the money they earned as they were not spending it on clothes or food or saving it for emigrating to America, Nicola coloured but he did not reveal the secret family adversity. Both are gentlemen because they did not want anyone’s sympathy.

Question d.
What message is conveyed through the story “Two Gentlemen of Verona”
Answer:
The message conveyed through the story is one can overcome one’s adversities with strong will and determination. Nothing is impossible in this world. It is one’s hard work and dedication which can help one to achieve one’s goal. The boys in the story were badly affected by the war. In spite of it they were ready to do many odd jobs to save their sister.

This action of the boys throws light on the fact that family is the true demonstration of love, affection, and faith. Yet another message which gets conveyed is that it is the situation and circumstance which one faces in one’s life that makes one shoulder responsibilities with strong determination. In simple words, we can say that Nature is the best teacher who teaches us many lessons in our life.

Question e.
Justify the title of the story “Two Gentlemen of Verona”.
Answer:
In the story ‘Two Gentlemen of Verona’, the two orphan boys Jacopo and Nicola work immensely and exhaustively. They shine shoes, sell newspapers, run errands, and show tourists round the city. They take only figs and black tea as food. They save every penny for the medical treatment of their sister Lucia who is suffering from tuberculosis of the spine. The narrator himself admits that their willingness to work impressed him. They demonstrate an unusual devotion to their work.

The objective of their hard work and purpose behind their half-starved daily routine is not known to many in Verona. Anyone may polish shoes or hawk newspapers but it is the magnanimity of heart and nobleness of purpose that actually determines whether one is a real gentleman or a hypocrite. Hence the title ‘‘Two Gentlemen of Verona” is justified.

Question f.
Adversity brings out the best as well as the worst in people. Elucidate this statement with reference to the story.
Answer:
No human life is possible without adversities. In fact, it is these adversities that bring out the qualities of self-confidence and endeavor in a person. It depends upon the mentality of a man to make it the worst or brings out the best out of it. In this story, the two boys faced the great disaster of losing their father and their home because of the war. To add fuel to it their sister suffered from tuberculosis of the spine.

This was the worst adversity in their life as they lost almost everything at a young age. but they did not lose hope. They had a strong determination to work hard and earn money for the treatment of their sister. Many good qualities like love, devotion, sacrifice, sincerity, and maturity get revealed just because of the adversities they face in their life. Thus the statement “Adversity brings out the best as well as the worst in people” is justified.

Question g.
Which character do you like the most in the story and why?
Answer:
Of all the characters, I like Nicola who is a 13-year-old boy (i.e.) one of the two gentlemen of Verona. Though he is small, he is mature beyond his years. Like John Keets, he hated sympathy and self-pity. He does not want any favour except for the opportunity to work. He has an engaging smile. He and his brother Jacopo were hardworking and devoted to their sister Lucia. He has seriousness far beyond his years.

Even when kindly enquired by the narrator as to why he was spending little on clothes and food, he doesn’t open up. He colours deeply and grows pale. He even avoided the eyes of the narrator. When his squirrel-like brother requested the narrator to send them in his car to Poleta on Sunday, Nicola doesn’t like it. He glares at his brother in vexation and says, “we couldn’t think of troubling you, sir.” He wins the respect of all readers because of his maturity, willingness to work, and devotion to his sister.

Paragraph:

Introduction:
A.J. Cronin has explained the importance of dedication towards a relationship in the story, “Two Gentlemen of Verona”.

About the story:
The story is about the two boys named Nicola and Jacopo, who do numerous things to earn money only to pay for their sister’s treatment who suffers from tuberculosis of the spine. The narrator was driving down the foothills of the Alps along with his companion. At that time, two young boys who sold wild strawberries stopped their car.

Two gentlemen of Verona:
‘The small boys appeared to be quite shabby. The boys were brothers, The elder one Nicola was 13 and the younger Jacopo was 12 years old. The narrator and his companion bought the biggest basket of strawberries from the boys. They came to know that the boys did many kinds of jobs like selling fruits, polishing shoes, selling newspapers, etc., to earn money. During the time of their stay in the town, the young boys were very helpful.

Lucia’s Suffering:
The boys earned money but they spent only a little. The boys earned the money to cure their sister who was hospitalised for tuberculosis of spine. They had a decent life before the war and the war made them orphans. They tried their best to make the payments regularly to the hospital, The narrator drove them to the hospital one Sunday and knew everything about the boys and he did not reveal it to the boys. He drove them back in silence.

Conclusion:
Their selfless action brought nobility to human life, they were really two gentlemen of Verona.

Vocabulary:
a) Read the following words taken from the story. Give two synonyms and one antonym for each of these words. Use a dictionary, if required: O(Text Book Page No. 6)

Answer:

b) Homophones and Confusables: (Text Book Page No. 6, 72, 148)
Homophones are two or more words with the same sound but with different spellings and meanings. You have already learned that homophones are words that sound alike but are different in spelling and
meaning.
E.g. feet – feat / face – phase / sort – sought / hair – heir/

Question 1.
What are confusables?
Answer:
Confusables /confusables are words that are commonly confused with one another in meaning or usage
because of slight similarities in spelling, pronunciation, or meaning.
e.g. moment – movement / except – expect / human – humane / discover – invent.

(i) Given below is a list of common confusables. Distinguish the meaning of each pair of words by framing your own sentences: (Text Book Page No. 6)

a) emigrate – leave one’s country/move abroad (my friend wants to emigrate from Asia)
immigrate – come to live permanently in a foreign country (He wants to immigrate to India)

b) beside – near (He stands beside me)
besides – in addition to (Besides having a car, he also has a bike)

c) judicial – legal (The court ordered judicial custody of the convict)
judicious – wise (The lawyer argued in a judicious manner)

d) eligible – qualified (He ¡s an eligible hand)
illegible – not clear (Mostly doctor’s prescriptions are illegible)

e) conscience – moral sense (His conscience promoted him to know his mistakes)
conscious – awareness (He has consciously abused his teacher)

f) industrial – commercial (The industrial chemicals are polluting the river)
industrious – hard-working (Sathish is an industrious student)

g) eminent – famous (Ramesh is an eminent scientist)
imminent – about to happen (There is an imminent danger of corona virus)

h) illicit – illegal (Ten people were arrested for brewing illicit liquor)
elicit – bring out (The teacher elicited answers from the student)

i) prescribed – advised (The doctor prescribed powerful medicines to me)
proscribed – remove (The police proscribed the striking students)

j) affect – change (The place is affected by the flood)
effect – the result of a change (The effect of the flood in very heavy)

k) aural – related to hearing
oral – related to speaking

l) born – related to birth (Raji was born on 2nd January 2020)
borne – carry (The people near the border borne the brunt of the attack.)

(ii) Fill in the blanks using suitable homophones or confusables:

Answer:

c) Give the meanings of the following phrasal verbs and frame sentences using them: (Text Book Page No. 7)

Question 1.
cut off
Answer:

• to remove something by cutting
• The branch was cut off from the tree

Question 2.
come upon
Answer:

• meet someone by chance
• I came upon my Maths teacher in Chennai

Question 3.
put out
Answer:

• stop something burning
• The firefighters put out the fire

Question 4.
draw up
Answer:

• stop
• A taxi drew up outside the hotel

Question 5.
pass out
Answer:

• become unconscious/faint
• The politician passed out when the income tax officials quizzed him.

Question 6.
take off
Answer:

• Start flying/remove clothing
• The flight took off at the right time.

Question 7.
turn away
Answer:

• refuse permission
• The reporters who came to interview the Prime Minister were turned away.

Question 8.
stand by
Answer:

• help someone who ¡s in difficult to be ready.
• My friend stood by me all the time.

Question 9.
bank on
Answer:

• depend on
• The whole team is banking on him to win the match.

d) Read the list of words formed by adding suffixes: (Text Book Page No. 7)
frequently, satisfaction, willingness, inevitable, preparation, government, periodic, management,
population, department, announcement, comfortable, resemblance, nobility.

Form two derivatives from each of the following words by adding prefixes and suffixes: (Text Book Page No. 7)

Answer:

Listening:

Floods are an inevitable natural disaster which can occur in any part of the world. Floods can prove all the more
disastrous in localities, where population density is high. Preparation for Disaster Management has become imperative for any city, town, or village during monsoons. The Government Department entrusted with Disaster Management makes periodic announcements about the precautions to be taken whenever floods are anticipated.

Now, you are going to listen to the cautionary instructions that are given to the general public living in flood-prone areas. Listen carefully and complete the following sentences:

Question a.
The announcement was made by the Department of _______.
Answer:
Disaster Management.

Question b.
Widespread heavy rains are expected from the early hours of _______.
Answer:
Sunday.

Question c.
The public is asked to find out the locations of _______.
Answer:
the closest flood shelters available and routes to reach them

Question d.
An emergency kit should contain water bottles, biscuit packets, and a _______.
Answer:
whistle to signal for help

Question e.
A list of__________ should be displayed on the wall.
Answer:
emergency telephone numbers

Question f.
Important documents can be secured by keeping them in a ___________case.
Answer:
waterproof

Question g.
Damage to refrigerators can be avoided by _______.
Answer:
leaving their door open

Question h.
Mobile phones should be charged to enable the marooned to contact their friends, relatives, and _______.
Answer:
emergency services

Question i.
___________ should be placed in the toilet bowls to prevent sewage inflow.
Answer:
Sandbags

Question j.
Listen to the_________ and follow the instructions implicitly.
Answer:
periodic news updates

Speaking: (Text Book Page No. 8)

Drafting a Speech:

Task 1:
On the occasion of World Environment Day, you have been asked to deliver a speech during the morning assembly on the importance of tree planting. Write the speech in about 100 – 150 words:

1. Introduction
2. Suggested value points:
   Pollution control – Medicine – Necessary for wildlife – Cause rainfall
3. Conclusion

Respected Principal, the chief guest

Good evening. I am immensely delighted to speak to you on World Environment Day. All of you know that
we celebrate Environment Day on 5th June, every year. Let me explain why we celebrate World Environment
Day. The relationship between humanity and the environment is a delicate balance. Since the industrial revolution,
the world’s population has increased exponentially.

With the population growth, the environment has been profoundly affected Deforestation, pollution and global climatic changes are amongst the adverse effect the explosive population and technological expansion have introduced. The main objective of Environment Day is to gain a greater understanding of the environment.

This enhanced awareness, I believe, will help the country reduce its carbon footprint, increase the use of solar power, reduce and recycle non-biodegradable waste and evolve alternative technologies which would reduce our dependence on fossil fuels.

Moreover, tree planting will be done on a mission mode by school children and college students representing
NCC and NSS wings. This would spread the forest cover and give shelter to the wildlife and also ensure
plentiful rainfall sustaining life on this lovely planet. The student community shall disseminate the urgent need to
conserve water and other natural resources appeal to the younger generation, I mean my friends to be socially
responsive and do their part to preserve the environment.

Task 2:
Prepare a speech on “The importance of a reading habit” in about 100—150 words as using the hints given below together with your own ideas: (Text Book Page No. 9)

1. Introduction
2. Suggested value points
   Knowledge enrichment — Skill development — Meaningful usage of time — Overall development
3. Conclusion

The most distinguished chief guest, revered Principal, dignitaries on the Dias and off the dais, my beloved teachers and friends. This morning I wish to share my views on a man-making habit called ‘Reading’.

Books are the quietest and most constant of friends. They are the most accessible and wisest of counsellors and the most patient of teachers. Some schools do focus on developing a flair for reading by keeping a library period. Children are allowed to borrow books and also share their observations with their peers after the library hour is over. Such sharing introduces children to the wonderful world of books.

The art of reading is in great part that of acquiring a better understanding of life from one’s encounter with it in a book. Through reading, one exposes oneself to new things, new ways to solve a problem. Reading is a very useful hobby. Wiseman has lauded the importance of reading and the hobby of reading. Kofi Annan said, “Literacy is a bridge from misery to hope”.

William James said, “So it is with children who learn to read fluently and well. They begin to take flight into whole new worlds as effortlessly as young birds take to the sky”. Dear friends let us read books and conquer the world.

Reading – Note Making: (Text Book Page No. 9)

Read the passage given below and make notes:

To match the best cities across the world, the Government of India initiated ‘smart cities’ to drive economic growth and improve the quality of life of people. The agenda under smart city promises to resolve urban sustainability problems. Urban forests provide a range of important ecosystem services that are critical for the sustainability of cities. Urban forestry, which is defined more as ‘Management of Trees’ contributes to the physiological, sociological, and economic well-being of the society.

Mangroves, lakes, grasslands, and forests in and around our cities, act as sponges that absorb the air and noise pollution and they present themselves as our cultural and recreational hotspots. However, these spots are rapidly being reclaimed and replaced in the name of development. The presence of urban green has shown to increase the economic value of the place.

Urban forests contribute to reducing the cost of building stormwater drain systems for municipalities and neutralizing the urban heat island effect. Plants not only provide shade but also help in regulating the micro-climate. They help regulate energy budgets, improve air quality, and curtail noise pollution. Trees, herbs, shrubs, and grasses arrest sedimentation and prevent other pollutants from entering our water systems, This will give a chance for our urban lakes and rivers to recover and help improve aquatic ecosystems.

Biodiversity also gets a boost through the urban forests and helps create corridors connecting the forest areas, High biodiversity areas can also help to build resilient ecosystems. The availability of forests within our urban areas gives an opportunity for children to connect to the natural environment and learn about native species.
Answer:
Smart city:
1. Initiation by Indian Government

• Economic growth
• Urban sustainability.

2. Urban forestry

• management of trees
• Act as sponges to absorb pollution.

3. Benefits of urban forestry

• Regulated micro-climate
• Arrests sedimentation and pollutants.

Grammar:

Task 1:
Tick the correct options and complete the dialogue:

A: Hello. What do you watch/are you watching?

B: A programme about the Jillian Wala Bagh massacre, which I recorded last night. I study /I’m studying about it this term.

A: All that I know / I’ve known about it is that hundreds of people died /had died in it.

B: Yes, it was much, much worse than anyone has expected/had expected. It went on / has gone off for hours. Do you want / Have you wanted to watch the programme with me?

A: No, thanks. I’ve got to do some veena practice. I’ve just remembered / I just remembered that we’ve got a concert tomorrow, and I don’t have/haven’t had time to practice my new piece this week.

B: OK. I’ve already done / I already did my practice, so I’ve got time to watch TV. See you later.

Task 2:
Complete the sentences with the correct tense form of the verbs in brackets: (Text Book Page No. 11)

Question a.
(tell) me exactly what (happen) last night!
Answer:
Tell me exactly what happened last night.

Question b.
Mrs. Mageswari is my Maths teacher. She (teach) me for four years.
Answer:
Mrs. Mageswari is my maths teacher She has been teaching me for four years.

Question c.
I (never /think) of a career ¡n medicine before I spoke to my Biology teacher but now I (seriously! consider) it.
Answer:
I had never thought of a career in medicine before I spoke to my biology teacher but now I seriously consider it.

Question d.
Oh no! I (forget) to bring my assignment! What am I going to do? This is the second time I (do) this!
Answer:
Oh no I forgot to bring my assignment! what am I going to do? This is the second time I am doing this.

Question e.
I can’t remember what my teacher (say) yesterday about our homework. I (not listen) properly because Hussain (talk) to me at the same time.
Answer:
I can’t remember what my teacher said yesterday about our homework. I did not listen properly because Hussian was talking to me at the same time.

Question f.
Last year we (go) on a school trip to Kanyakumari. We (have) a very interesting time.
Answer:
Last year we went on a school trip to Kanyakumari. We had a very interesting time.

Question g.
At the moment I (think) about what course to pursue next year but I (not make) a final decision yet.
Answer:
At the moment I am thinking about what course to pursue next year but I have not made a final decision yet.

Question h.
I (get) up at 7 every morning but this morning I (sleep) for a long time and I (not get) up until 8.
Answer:
I get up at 7 every morning but this morning I slept for a long time and I did not get up until 8.

Task 3:
Fill in the blanks with the correct form of the verbs given in the brackets:

Question a.
Everyone _________ when the earthquake hit the small town. (sleep)
Answer:
was sleeping

Question b.
Evangeline _______ her job a couple of years ago. (quit)
Answer:
quit

Question c.
Where ___________ your last holidays? (you spend)
Answer:
did you spend

Question d.
I think Suresh _________ for Tiruvallur next morning. (leave)
Answer:
will leave

Question e.
I was angry that I _______ such a mistake (make).
Answer:
had made

Question f.
My mother was tired yesterday because she __________ well the night before (not sleep).
Answer:
did not sleep

Question g.
Her parents ___________ in Coimbatore for two weeks from today (be).
Answer:
havebeen

Question h.
Nothing much ________ when I got to the meeting (happen).
Answer:
had happened

Question i.
Scientists predict that by 2050, man ________ on Mars. (land)
Answer:
will land

Question j.
Sh! Someone ___________ to our conversation! (listen)
Answer:
is listening

Question k.
The plane ________ off in a few minutes. (take)
Answer:
will take

Question l.
They _________ about me when I interrupted their conversation. (talk)
Answer:
were talking

Question m.
Justin and his parents _________ in an apartment right now because they can’t find a cheap house. (live)
Answer:
are living

Question n.
Rajini Prem’s family _________ in Chengalpet now. (be)
Answer:
is
Question o.
Yusuf_________ to the movies once in a while. (go)
Answer:
goes

Question p.
This _________ an easy quiz so far (be).
Answer:
has been

Question q.
Our team _________ any games last year. (not win)
Answer:
did not win

Question r.
We _________ a wonderful film at the cinema last night. (see)
Answer:
saw

Question s.
Hurry up! The movie ________ (already begin)
Answer:
has already begun.

Modal Auxiliaries: (Text Book Page No. 12)

Modal Auxiliary is a special auxiliary that is used to denote a particular mood or expression of the subject.
There are 13 Modal Auxiliaries (four of which are quasi-modals/ margins).

Task 1:
Fill in the blanks with modal auxiliaries: (Text Book Page No. 14)

Question a.
The candidates _______ answer five out of ten questions.
Answer:
must

Question b.
How _______ you open my bag?
Answer:
dare/can

Question c.
Tajudeen ________ finish this work by Monday.
Answer:
will

Question d.
_______ I go to school today?
Answer:
Shall

Question e.
I wish you ________ tell me the truth.
Answer:
would

Question f.
Poonam __________ not catch the bus yesterday.
Answer:
could

Question g.
People who live in glass houses ______ not throw stones.
Answer:
should/must

Question h.
You ________ not go to the market as I have brought vegetables.
Answer:
need

Question i.
_______ you have taken all this trouble?
Answer:
Must

Question j.
You ______ be joking.
Answer:
must

Question k.
I tried to climb up the tree, but _____ not.
Answer:
could

Question l.
Hima Das ran so fast that she ______ win the medal.
Answer:
could

Question m.
You ________ lead a horse to water, but you _______ make it drink.
Answer:
can, cannot

Question n.
I ________ like to have a cup of coffee.
Answer:
would

Question o.
My grandfather _____ visit this temple when he was young.
Answer:
used to/would

Task 2:
Complete the following sentences with modals using the clues given:

Question a.
You _________ help the needy. (moral obligation)
Answer:
must/ought to

Question b.
If I were you, I ________ not behave like that. (conditional sentence)
Answer:
would

Question c.
I _______ never tell a lie. (determination)
Answer:
will

Question d.
My uncle _______ have reached by now. (possibility)
Answer:
may

Question e.
The patient is critical. He __________be taken to the hospital.(compulsion)
Answer:
must

Question f.
I ________ to play hockey when I was a student. (past habit)
Answer:
used to

Question g.
You _______ not attend my class. (order)
Answer:
must

Question h.
He ___________ come today. (remote possibility)
Answer:
might

Question i.
You ___________ follow the traffic rules. (regulation)
Answer:
must

Question j.
He play the match. (willingness)
Answer:
will

Question k.
You __________ not waste time on it. (necessity)
Answer:
need

Question l.
Had the doctor come in time, he _______ have saved the patient.(probability)
Answer:
would

Reported Speech:

Task 1:
Read what these people say and rewrite as sentences: (Text Book Page No. 15)underlines

Question 1.
I am very busy.
Answer:
Raja said that he was very busy.

Question 2.
I have completed my work.
Answer:
Satya said that he had completed his work.

Question 3.
I don’t like to go out.
Answer:
Johnson said that he didn’t like to go out.

Question 4.
I have just come back from Chennai.
Answer:
Akshita said that she had just come back from Chennai.

Question 5.
I am learning English.
Answer:
Jayan said that he was learning English.

Question 6.
I bought a pen yesterday.
Answer:
Madhu said that she had bought a pen the previous day.

Question 7.
We will go shopping tomorrow.
Answer:
Joseph and Mary said that they would go shopping the next day.

Question 8.
We can’t attend the party.
Answer:
Afsar and Ayesha said that they could not attend the party.

Question 9.
How are you?
Answer:
Satish asked how he was.

Question 10.
I am fine. Thank you
Answer:
Victor said that he was fine and thanked him.

Task 2:
Read the following dialogue and complete the report in the space provided:

Priya: Where are you going to?
Vijay: I am going to the railway station.
Priya: Why are you going there?
Vijay: I want to receive my uncle who is coming from Bangalore.

Question 1.
Priya asked Vijay ___________
Answer:
Priya asked Vijay where he was going.

Question 2.
Vijay replied __________
Answer:
Vijay replied that he was going to the railway station.

Question 3.
Priya further inquired ___________
Answer:
Priya further enquired why he was going there.

Question 4.
Vijay stated that ___________
Answer:
Vijay stated that he wanted to receive his uncle who was coming from Bangalore.

b) Teacher: Why are you late?
Divya: I missed the bus.
Teacher: You should have reached the bus stop on time.
Divya: My grandmother is ill. So, I had to take her to the doctor.
Teacher: I am sorry. What ails her?
Divya: She has a high fever.

Question 1.
The teacher asked Divya why she was late. Divya replied that (a) ________.The teacher told her that (b) _____. Divya said that her grandmother was ill so she had to take her to the doctor. The teacher felt sorry and further asked her (c) _____. Divya explained that she (c)_________ high fever.
Answers:
(a) She had missed the bus
(b) She should have reached the bus stop on time.
(c) what ailed her?
(d) had

Task 3:
Rewrite the following passage in indirect speech: (Text Book Page No. 16)

Question 1.
Pradeep got out of bed with much excitement. “It is going to be a lovely sunny day,” he remarked
to his sister Varshini. “Just let me sleep a bit longer, Pradeep,” Varshini begged, “and since you are feeling so
enthusiastic, “she suggested, “Why don’t you go and help a mother in cooking?” Sure, I will say Pradeep.
“Can I help you, mum?’ he said to his mother. “Yes, of course. There are idlis and vadas on the dining table.
Have your breakfast.” “Thank you, mum; I’ll surely help you by eating them.”
Answer:
Pradeep got out of bed with much excitement. He told his sister Varshini that it was going to be a lovely sunny day. Varshini begged him to let her sleep a bit longer and since he was feeling so enthusiastic she asked him why not go and help a mother in cooking. Pradeep said that he would. He asked his mother if he could help her. The mother replied positively and added that there were idlis and vadas on the dining table and told him to have his breakfast. Pradeep thanked his mother and said that he would surely help her by eating them.

Writing:
Read the following letter carefully, discuss with your partner, and answer the questions:

Sir,
I request you to publish the following letter in your daily to address an important issue which needs immediate redressal.

During weekends motorcyclists are seen racing on the East Coast Road and the Old Mahabalipuram road of Chennai. The amateur racers are risking their own lives and of the public as well. They are fearless and irresponsible, not knowing the price of human lives. Risking others and their lives for their pleasure is highly condemnable.

Even school students indulge in such activities and cause fatal accidents. The racers have started
occupying the lanes and streets of busy localities. As such, the violation of traffic rules often results in the loss of young lives. Such reckless riders who violate traffic rules should be punished severely. As a responsible citizen of society, I request the authorities concerned to take appropriate measures to put an end to this menace.
Yours truly,
xxxxx.

Questions:

Question a)
Who is the sender of the letter?
Answer:
Srivastava is the sender of the letter.

Question b)
Who is the receiver?
Answer:
The editor of a daily is the receiver.

Question c)
What is the issue?
Answer:
Motorcycle racing is the issue.

Question d)
What is the request of the sender?
Answer:
The request of the sender to the authorities concerned is to take appropriate measures to put an end to the motorcycle racing.

Question e)
Who will take steps after reading it?
Answer:
The traffic police will take steps after reading it.

b) You have chosen Computer Science in the Higher Secondary Course. Write a letter to your friend giving reasons for your choice. Read the clues given in brackets to complete the letter.

Dear Arjun (Greeting),

Hope you are well (enquire about his well-being). I would like to say that I have chosen computer science in Hr. Sec course. Firstly I want you to help me with my future (the reason for your choice of group). I wish to become an Engineer (state your ambition). We come to hear a lot of instances of misusing social media. (discuss recent unhealthy happenings in social media and society). These have made me select the course so that after knowing the system well. I will be able to find out something to stop such things (demand or need of this profession). I have plans to pursue M.S in the US (higher studies or specialization).

All the best for your CA preparation. Convey my regards to all at home.

Yours lovingly,
(your name)

Task: (Text Book Page No. 18)
a) You had been to your Grandma’s house during the summer holidays. You enjoyed your stay in her company. Write a letter to your Grandma stating how much you miss her after returning to your home.

My dear Grandma,

I hope, you are quite well. But I am not fine here, because I miss you a lot. I enjoyed your company during my summer holidays. I feel very sad after returning to my home. I am expecting my next vacation to come. I felt very happy when I stayed with you. Take care of your health. See you on your next vacation.

Yours lovingly,
Arjun S.

Address on the envelope
To

STAMP

Mrs. R.Vasantha,
No.75, West Street,
Trichy – 627032.

b) You are the head of the English department in a renowned institution. You are invited to preside over the inauguration of the English Literary club in your alma mater. Respond to the letter you have received either accepting the invitation or expressing your inability to attend the function.

From
M Ravi Kumar,
Head of the Department of English,
Joseph College of Arts and Science,
Madurai – 627035

To
The Principal,
ABC College of Arts and Science
Trichy – 620177

Sir,

Sub: Accepting your invitation – reg.

This is to kindly inform you that I have received your invitation to the inauguration of the English Literary club. I am really happy to preside over the function in my alma mater. I am sure that I will be at the function on time.
Thanking you,

Yours faithfully,
M Ravikumar.

Madurai,
10.04.2020.

Address on the envelope
To

STAMP

The Principal
ABC College of Arts and Science
Trichy-620177

c. Write a letter to the Headmaster of your school requesting him to help you obtain a duplicate mark sheet of class XII, which you lost while traveling.

From
S. Anand,
No. 12, West Street,
Virudhunagar.

To
The Headmaster,
TCS. Hr. Sec. School,
Virudhunagar.

Sir,
Sub: Requesting to obtain a duplicate mark sheet of class XH-reg.

I would like to bring to your kind notice that I had missed my mark sheet for class XII while traveling. Therefore, I kindly request you to help me to obtain a duplicate mark sheet.

Thanking you,

Yours faithfully,
B. Anand.

Virudhunagar,
15.04.2020.

Address on the envelope
To

STAMP

The Headmaster,
TCS. Hr. Sec. School,
Virudhunagar.

d) Write a letter to AZ Company requesting them to replace the defective juicer that you bought recently. Include the following details: the problem, date of purchase, receipt number, model, and warranty.

From
S. Rahul,
No.2, North Street,
Kovilpatti.

To
The manager,
AZ company,
Chennai-627201

Sir,

Sub: Requesting to replace the defective juicer-reg.

I would like to bring to your kind notice that I had bought a juicer in your company a week ago. Now it is not working but properly due to magnetic sensors. I have also mentioned the date of purchase and receipt number. So, kindly replace the defective juices as early as possible.
Thanking you,

Yours faithfully,
S. Raghul.

Kovilpatti,
20.05.2020.

Address on the envelope

To

Stamp

The manager,
AZ company,
Chennai-627201

e) You wish to become a pilot. Write a letter to a college enquiring about the details of the pilot training course offered by the college. Include the following details in your inquiry: duration of the course, fee structure, scholarships, hostel facilities, and placement details.

From
D.Kumar,
No.75, East street,
Tenkasi.

To
The principal,
ABC College of Technology,
Coimbatore.

Sir.

Sub: Enquiring about the details of the pilot training course offered-reg.
This is to inform you that I would like to know about the pilot training course offered at your college. Please let me know the duration of the course, fee structure, scholarships, hostel facilities, and placement details as soon as possible.

Thanking you,

Yours faithfully,
D. Kumar.

Tenkasi,
25.04.2020.

Address on the envelope

To

STAMP

The principal,
ABC College of Technology,
Coimbatore.

f) Write a letter to the manager of Waves Furniture Company ordering furniture for a coaching center. Include the following details: description of the furniture, number of pieces, mode of payment, time, and delivery options.

From
S. Ramesh,
No.72, Anbu Nagar, Palayamkottai.

To
The manager,
The waves furniture company,
Chennai.

Sir,

Sub: Ordering some furniture-reg.

We are in need of some furniture for our coaching center. Kindly send the goods by train to the above address.

Thanking you,

Yours faithfully,
S. Ramesh.

Palayamkottai,
20.06.2020.

Address on the envelope
To

STAMP

The manager,
The waves furniture company,
Chennai.

g. Write an application for the post of Personal Secretary to the Managing Director of a company. Include the following details: Educational qualification, experience, various other qualifications required for the post.

From
XXX
YYY
ZZZ.

To
The Managing Director,
Software solution,
Chennai-28

Sir,

Sub: Application for the post of personal secretary -reg.

Ref: Advertisement in The Hindu dated 8th June 2020.

I read your advertisement in “The Hindu” dated 8th June 2020.1 wish to apply for the post of personal secretary. I have given below my bio-data. If I am appointed, I assure you that I will discharge my duties to your entire satisfaction.

Bio – Data

1. Name of the applicant: xxx
2. Residential Address: yyy
3. Father’s name: A.Jeyaraj
4. Date of birth and age: 27th Dec 1990
5. Age: 28 years old
6. Sex: Male/Female
7. Educational Qualification: M.A. English
8. Experience: 3 years
9. Languages Known: Tamil, English, and Hindi
10. Special Talent: Fluency in English, good knowledge of computer, a good athlete
11. Salary expected: 15,000/- per month

Thanking you,

Declaration:

I, XXX hereby declare that the information which I have furnished is true to the best of my knowledge.

Yours faithfully,
Place: yyy, XXX
Date: 10.06.2020.

Address on the envelope

To

STAMP

The Managing Director,
Software solution,
Chennai-28

h) Write a letter to the editor of a newspaper about the nuisance created by the roadside vendors blocking the pavements and occupying the parking zone.

From
K. Ashok,
No.7, West Mambalam st,
Villupuram.

To
The Editor,
The Indian Express,
Villupuram-27.

Sir,

Sub: Publishing the nuisance created by the roadside vendors in your newspaper -reg.

This is to bring to your kind attention that the roadside vendors are blocking the pavements and occupying the parking zone and thereby creating a nuisance to the public. So, please bring the news to the government by publishing this in your newspaper.

Thanking you,

Yours faithfully,
K.Ashok.

Villupuram,
05.07.2020.

Address on the envelope

To

STAMP

The Editor,
The Indian Express,
Villupuram-27.

j) Write a letter to your relative or friend who is admitted in the hospital for treatment of jaundice. Advise him/her not to worry about the illness and be positive. Assure him/her of your psychological and financial help during the crisis.

My dear Friend,

I heard that you are admitted to the hospital for the treatment of jaundice. It is only a common disease, especially in summer days. So, you take rest and always think positive which will enable you to recover from it soon. If you need any financial help, please inform me at once, So that I will help and be with you.

Yours lovingly,
Arun S

Address on the envelope
To

STAMP

Mrs. M. Karthick,
No.45, North street,
Tirunelveli

ஆசிரியரைப் பற்றி:

ஆர்ச்சிபால்டு ஜோசப் க்ரோனின் (Archibald Joseph Cronin) (1896-1981) ஸ்காட்டிஷை சார்ந்த நாவலாசிரியர், நாடக ஆசிரியர் மற்றும் இயற்பியலாளர் ஆவார். மருத்துவப் பயிற்சிப் பெற்ற க்ரோனின் இருபதாம் நூற்றாண்டின் புகழ் பெற்ற கதை சொல்லுபவரில் ஒருவர், அவரின் பல கதைகள் இவரின் மருத்துவ பணியிலிருந்து வெளிப்பட்டதாகவும் (emerged) அவைகளின் கதைப்பாணி, சமூக அக்கறையுடையதாகவும், அமைக்கப்பட்டிருக்கும்.

க்ரோனின் புத்தகங்கள் அதிகமாக விற்பனையாவது மட்டுமல்லாமல் சில படைப்புகள் (The Citadel and The Keys of the Kingdom) வெற்றிகரமான படங்களாகவும், வானொலி மற்றும் தொலைகாட்சிகளிலும் ஒளிபரப்பப்பட்டன. இவரின் “Novella country doctor” என்னும் படைப்பு தேர்ந்தெடுக்கப்பட்டு BBC வானொலியிலும், தொலைக்காட்சி தொடரிலும் அதிக நாட்களாக ஒளிபரப்பப்பட்டது.

பாடத்தைப் பற்றி:

கொடுக்கப்பட்டுள்ள இந்த பாடத்தின் ஆசிரியர் A.J.Cronin இரு சிறுவர்களின் வாழ்க்கைப்பற்றியும், அவர்கள் தங்களின் சிறுவயதிலேயே அனுபவிக்கின்ற துன்பங்களைப் பற்றியும் விவரிக்கிறார். பெற்றோரை தங்களின் சிறு வயதிலேயே இழந்த முதுகெலும்பு காசநோயால் பாதிக்கப்பட்ட (Tuberculosis of the spine) சகோதரியைக் காப்பாற்ற போராடும் இரு சகோதரர்களின் செயல்களில் வெளிப்படும் அன்பு, அர்ப்பணிப்பு, தியாகம், நேர்மை மற்றும் முதிர்ச்சி ஆகியவை குறித்த ஒரு கதை கொடுக்கப்பட்டுள்ளது. அவர்களுடைய செயல்கள் எவ்வாறு மனிதநேயத்திற்கு ஒரு புதிய நம்பிக்கையை ஊட்டுகிறது என்பதை அறிய தொடர்ந்து வாசிப்போம்.

Two Gentlemen Of Verona Summary in Tamil

நாங்கள் மகிழுந்தில் (Car) வெரோனா புறநகர்பகுதியில் ஆல்ப்ஸ் (Alps) மலையின் அடிவாரம் வழியாக பயணித்த போது இரு சிறுவர்கள் எங்களை நிறுத்தினர். அவர்கள் காட்டு ஸ்ட்ராபெரி (strawberry) பழங்களை விற்றுக் கொண்டிருந்தனர். ”வாங்காதீர்கள்” என்று, எங்களின் எச்சரிக்கையான (Cautious) வாகன ஓட்டுநர் லூகி (Luigi) கூறினான். “வெரோனா நகரின் உட்பகுதியில் இதை விட சிறந்த பழங்களை நீங்கள் பெறலாம். மேலும் இந்தப் பையன்கள்….” என்று அவர்களின் அழுக்குத் தோற்றத்தை ஏற்றுக்கொள்ளாத வகையில் அவரது தோளை அழுத்தினார். ஒரு சிறுவன் மேலாடையையும், வெட்டப்பட்ட காக்கி காற்சட்டையையும் அணிந்திருந்தான்.

மற்றொருவன் சிறியதாக்கப்பட்ட, முழங்கால் வரை அணியக்கூடிய உடையை அவனது மெல்லிய உடம்பில் தொளதொளவென் அணிந்திருந்தான். பழுப்பு நிறத்தையும், கலைந்த முடியையும், ஊக்கமான கண்களையும் உடைய அந்த இரு சிறிய உருவங்களை இன்னும் கூர்ந்து நோக்கியபடியே, நாங்கள் அவர்களால் கவரப்பட்டதை உணர்ந்தோம். என்னுடன் வந்தவர் (companion), அச்சிறுவர்களிடம் பேச்சுக்கொடுத்து அவர்களிருவரும் சகோதரர்கள் என்று அறிந்தார். மூத்தவன் பெயர் நிக்கோலா (Nicola), வயது 13; எங்கள் காரின் கதவின் அருகே வந்து நின்றவன் பெயர் ஜாகோபா (Jacopo), வயது 12-யை நெருங்கும். நாங்கள் அவர்களின் பெரிய கூடை முழுவதையும் வாங்கிக்கொண்டு (bought) நகரத்தை நோக்கிப் புறப்பட்டோம்.

அடுத்த நாள் காலையில் நாங்கள் எங்கள் விடுதியில் இருந்து வெளியே வந்தபோது, எங்களின் அந்த நண்பர்கள் காலணிகளை பளபளப்பாக்கும் பெட்டியில் (shoe shine box) குணிந்தவாறு, நகரின் பொது சதுக்கத்தின் (public square) நீர்வீழ்ச்சி அருகில் சுறுசுறுப்பாக வேலை செய்வதைக் கண்டோம்.

சிறிது நேரம் அவர்களைக் கவனித்தோம் (watched). அவர்களின் தொழில் மந்தமான (slackened) போது நாங்கள் அவர்களிடம் சென்றோம். அவர்கள் எங்களை இன்முகத்தோடுவரவேற்றார்கள் “நீங்கள் வாழ்வாதாரத்திற்கு தான் பழங்களை விற்றீர்கள் என்று நினைத்தேன்” என்றேன்.

“நாங்கள் நிறைய வேலைகள் பார்ப்போம்” ஐயா என்றான் நிக்கோலா. அவன் நம்பிக்கையுடன் (hopefully) எங்களை நோக்கினான். “நாங்கள் இங்கு வரும் பார்வையாளர்களுக்கு இந்த நகரத்தையும், ஜீலியட்டின் கல்லறையையும் மற்றும் அவர்கள் விரும்பும் இடங்களையும் சுற்றிக்காண்பிப்போம்’, என்றான்.

நான் புன்னகையுடன் “சரி எங்களுக்கும் சுற்றிக் காண்பி” என்றேன். நாங்கள் சுற்றிப்பார்த்து கொண்டிருந்த போது, அவர்களின் குறிப்பிடத்தக்க நடத்தை (demeanour) என் ஆர்வத்தை மேலும் தூண்டியது. அவர்கள் குழந்தைத்தனத்துடன் பல செயல்களில் கள்ளக்கபடமில்லாமல் (artless) இருந்தார்கள். ஜாகோபா அணிற்பிள்ளைப் (squirrel) போன்று மிகவும் சுறுசுறுப்புடன் இருந்தான். நிக்கோலா எப்பொழுதும் சிரித்த முகத்தோடு இருந்தான். இருந்தாலும் அச்சிறுவர்களின் குழந்தை முகங்களில், அவர்களின் வயதுக்கு அப்பாற்பட்ட தீவிரம் (seriousness) காணப்பட்டது.

அதற்கு அடுத்த வாரத்தில் அவர்களை நாங்கள் அடிக்கடி (frequently) பார்த்தோம். அவர்கள் எங்களுக்கு மிகவும் உபயோகமாக (useful) இருந்தார்கள். எங்களுக்கு அமெரிக்க சிகரெட்டுகள் வேண்டுமென்றாலும், இசை நிகழ்ச்சிக்கு சீட்டு வேண்டுமென்றாலும், நல்ல உணவகத்திற்கு செல்ல வேண்டுமென்றாலும் எங்களின் தேவைகளை நிறைவேற்ற நாங்கள் நிக்கோலா மற்றும் ஜாகோபாவை நம்பினோம். அவர்களின் வேலை செய்யும் ஆர்வம் எங்களை வெகுவாக ஈர்த்தது. இந்த கடுமையான வெயிலிலும் அவர்கள், காலணிகளை பளபளப்பாக்குதல், பழங்கள் விற்றல், ஓர் இடத்திலிருந்து இன்னொரு இடத்திற்கு எடுத்துச் சென்று செய்தித்தாள்களை விற்றல், பார்வையாளர்களை சுற்றிக் காண்பித்தல் என அனைத்து வேலைகளையும் ஒரே நேரத்தில் செய்தனர்.

ஒரு நாள் இரவு அவர்களை காற்றோட்டமான, ஆள் நடமாட்டமில்லாத (deserted), சதுக்கத்தின், விளக்குகளுக்கு கீழே, கல் நடைபாதையில் (pavement) ஓய்வெடுப்பதை கண்டோம். நிக்கோலா கலைப்புடன் அமர்ந்திருந்தான். விற்காத ஒரு கட்டு செய்தித்தாள்கள் அவன் காலடியில் கிடந்தன. ஜாகோபா, அவனது சகோதரரின் தோளின் மேல் தலைவைத்து தூங்கி கொண்டிருந்தான். நேரம் நள்ளிரவை நெருங்கியது.

“ஏன் இவ்வளவு நேரம் இங்கே இருக்கிறீர்கள், நிக்கோலா?”

“பதுவாவிலிருந்து (Padua) வரும் கடைசி பேருந்துக்காக காத்துக் கொண்டிருக்கிறோம். அது வந்தவுடன் எங்களின் அனைத்து செய்தித்தாள்களையும் விற்று விடுவோம்”. என்றான்.

“நீங்கள் இவ்வளவு கடினமாக உழைக்க வேண்டுமா? பார்பதற்கு மிகவும் களைப்பாக (tired) இருக்கிறீர்கள்”. என்று நான் கேட்டேன்.

“நாங்கள் அதனை குறையாக தெரிவிக்கவில்லை ஐயா”, என்றான்.

மறுநாள் காலை நான் காலணிகளை பளபளப்பாக்க சதுக்கத்தின் நீர்வீழ்ச்சி அருகே சென்றபோது, “நிக்கோலா, நீங்கள் உழைப்பதைப் பார்த்தால் நீங்கள் நிறைய சம்பாதிக்க வேண்டும். நீங்கள் ஆடைகளில் செலவலிப்பதில்லை. மிகக் குறைவாகவே சாப்பிடுகிறீர்கள், வழக்கமாக நீ கருத்த ரொட்டித்துண்டு (blackbread) மற்றும் அத்திப்பழங்களை (figs) மட்டுமே சாப்பிடுவதை நான் கண்டிருக்கிறேன். உங்கள் பணத்தை வைத்து நீங்கள் என்ன செய்கிறீர்கள்? என்று என்னிடம் சொல்”.

அவன் உடனே குழம்பிப்போய் மிகுந்த வருத்தமுற்றான். பின்பு தரையைப் பார்த்துக் குணிந்தான்.
”அமெரிக்காவிற்கு புலம் பெயர்வதற்காகவா (emigrate) பணத்தை சேமிக்கிறீர்கள்?” என்று கேட்டேன். அவன் என்னை பக்கவாட்டில் பார்த்து பேசினான். “எங்களுக்கும் அமெரிக்கா போக வேண்டும் என்று பெரிய ஆசை உண்டு” ஆனால், இங்கே, இப்போது நாங்கள் வேறு திட்டங்கள் வைத்திருக்கிறோம்”.

“என்ன திட்டங்கள்?” (plans)
அவன் சங்கடத்துடன் (uncomfortably) புன்னகைத்தான். “சாதரணமான திட்டங்கள் தான்”, என்றான் மெதுவான குரலில்.

“நல்லது,” “நாங்கள் வரும் திங்கட்கிழமை புறப்படுகிறோம். நாங்கள் புறப்படுவதற்குள் உனக்கு ஏதாவது செய்ய வேண்டுமா?” என்றேன். வேண்டாமென் நிக்கோலா தலையை அசைத்தான். ஆனால் திடிரென ஜாகோபா, ஐயா நாங்கள் ஒவ்வொரு ஞாயிற்றுகிழமையும் முப்பது கிலோமீட்டர் அப்பால் இருக்கக்கூடிய ‘பொலேடா (Poleta) என்ற இடத்திற்கு வாடகை மிதிவண்டியில் (hire bicycles) செல்வோம். நீங்கள் எங்களிடம் மிக கனிவுடன் நடந்து கொள்வதால், நாளை எங்களை உங்கள் காரில் அங்கு அழைத்து செல்லலாம் என்றான். நான் லூகியிடம் ஞாயிற்றுகிழமை ஓய்வு. இருந்தபோதும் உங்களுக்காக கார் ஓட்டுகிறேன்” என்று பதிலளித்தேன்.

சிறிய இடைவெளிக்குப்பின், நிக்கோலா அவனது சகோதரனை எரிச்சலுடன் (Vexation) முறைத்தான். “உங்களுக்கு தொந்தரவு வேண்டாம் என்று நினைத்தோம் ஐயா”
“இது ஒன்றும் தொந்தரவு இல்லை”.

தனது உதட்டை கடித்தபடியே மெல்லிய குரலில் சரி நல்லது’ என்றான். அடுத்த கிராமத்திற்கு காரில் பயணமானோம். நாங்கள் அங்கு வசிக்கக் கூடிய இடம் மிகச்சாதரணமாகத்தான் இருக்கும் என கற்பனை செய்திருந்தேன். ஆனால், ஜாகாபாவோ எங்களை பெரிய சிவப்புக் கூரையிட்ட, பெரிய கல் சுவரால் சூழப்பட்ட கிராமப்புற வீட்டுக்கு அழைத்துச் சென்றான். என்னால் என் கண்களையே நம்பமுடியாமல் திகைத்திருந்த வேளையில், என்னுடன் வந்த இரு பயணிகளும் காரில் இருந்து குதித்து இறங்கினர்.

“நாங்கள் அதிக நேரம் எடுத்துக்கொள்ள மாட்டோம் ஐயா, ஒரு மணி நேரம் மட்டுமே. நீங்கள் இங்கே உள்ள தேநீர் கடையில் ஏதேனும் அருந்த விரும்புகிறீர்களா?”. அவர்கள் இருவரும் சுவரின் பின்னால் மறைய (disappear) ஆரம்பித்தனர்.

சில நிமிடங்களுக்கு பிறகு, நானும் அவர்களை பின்தொடர்ந்தேன். நான் கம்பியினால் ஆன ஒரு வாசலைக் கண்டேன். தீர்மானமாக (determinedly) அழைப்பு மணியை அடித்தேன்.

இரும்பு வளையத்தினால் (steel-rimmed) ஆன கண்ணாடியை அணிந்த ஒரு கனிவான பெண்மணி வந்தாள். அந்த பெண்மணி வெள்ளை நிற செவிலியர் உடையுடன் வந்தாள். நான் வியந்து பார்த்தேன்.

“நான் இங்கே இரு சிறுவர்களை அழைத்து வந்தேன்”. ஓ! அப்படியா! என்று அவர் முகம் பிரகாசமானது. அவள் கதவை திறந்து என்னை உள்ளே அனுமதித்தாள். நிக்கோலா, ஜாகோபாவிடம், நான் உங்களை அழைத்துச் செல்கிறேன்” என்றேன்.

அவள் என்னை குளிர்ந்த, பளிங்கினால் ஆன தாழ்வாரம் (vestibule) வழியே ஒரு மருத்துவமனைக்கு அழைத்துச்சென்றாள். (அந்த கிராமத்து வீடே இப்போது மருத்துவமனையாகி இருந்தது. ஒரு சிறிய படுக்கை அறையின் வாசலில் அவள் நின்று, தன் வாயில் அவள் கையை வைத்து புன்னகைத்தப்படி, கண்ணாடி பிளவின் (glass partition) வழியே என்னைப் பார்க்கச் சொன்னாள்.

அந்த இரு பையன்களும், 20 வயது மதிக்கத்தக்க அழகான பின்னலாடை அணிந்திருந்த தலையணைகளால் தாங்கப்பட்டு படுக்கையிலிருந்த பெண்ணின் அருகில் கட்டிலில் அமர்ந்திருந்தனர். அந்த பெண் அவர்கள் பேசுவதைக் (chatter) கேட்டுக் கொண்டிருந்தாள். அவளது கண்கள் இளமையாகவும், மென்மையாகவும் இருந்தது. பார்த்தவுடன் அவளது தோற்றம் அவளுடைய சகோதரர்களை ஒத்திருப்பதை யாராலும் சொல்ல முடியும். அவளது மேசையில் ஒரு ஜாடி நிறைய காட்டு மலர்களும், கூடவே பழங்களும், நிறைய புத்தகங்களும் இருந்தன.

“நீங்கள் உள்ளே போகவில்லையா?” என்று முனுமுனுத்தாள் அந்த செவிலியப் பெண். “உங்களைப் பார்த்தால் ‘லூசியா (Lucia) மகிழ்வாள்” என்றாள் செவிலி.

நான் தலையை அசைத்து மறுத்த படியே அங்கிருந்து நகர்ந்தேன். அவர்களின் மகிழ்ச்சியான குடும்ப சந்திப்பின் போது உள்ளே நுழைய வேண்டாம் என்று நான் நினைத்தேன். ஆனால் படிகட்டுகளின் கீழே நின்று அவளிடம் அந்த இரு சிறுவர்களைப் பற்றி நீ அறிந்ததை கூறு என்று கெஞ்சி (begged) கேட்டேன். அவளும் சம்மதித்தாள்.

“அவர்கள் இருவருக்கும் அவர்களின் அக்கா லூசியாவைத் தவிர இவ்வுலகில் யாரும் கிடையாது” என்று விவரித்தாள் (explained). மனைவியை இழந்த அவர்களின் தந்தை ஒரு நல்ல பாடகர் (singer), அவர் போர்காலத்தில் கொல்லப்பட்டார்.

பின் சிறிது காலத்தில் அவர்கள் வீட்டின் மீது ஒரு குண்டு விழுந்து, இம்மூன்று சிறுவர்களையும் வீதிக்கு தூக்கி எறிந்தது. அவர்கள் எப்போதும் சுகமான (comfortable) வாழ்வை வாழ்ந்து வந்தார்கள். லூசியாவோ ஒரு பாடகராக பயிற்சி செய்து கொண்டிருந்தாள். மேலும் அவர்கள் கடுங்குளிரினாலும், பசியினாலும் கடுமையாகப் பாதிக்கப்பட்டார்கள்.

பல மாதங்கள், அவர்கள் பழைய செங்கல் மற்றும் சிறந்த பொருள்களினால், அவர்களே செய்த கூடாரத்தில் வாழ்ந்து வந்தார்கள். அதன்பின் 3 வருடங்கள் ஜெர்மனியர்கள் இந்த நகரை ஆண்டார்கள் ஜெர்மானியர்களை (Germans) வெறுத்தபடியே (hate) இச்சிறுவர்கள் வளர்ந்த னர்.

“ஜெர்மானியர்களை எதிர்த்து எதிர்ப்பு இயக்கம் (resistance movement) தோன்றிய போது இவர்கள் முதலில் போய் அதில் இணைந்தனர். போர் முடிவடைந்து அமைதி திரும்பியபோது, அவர்கள் தங்கள் அன்பிற்குரிய சகோதரியிடம் திரும்பி வந்தார்கள். மேலும் தங்களது சகோதரி முதுகெலும்பு காசநோயால் (tuberculosis) பாதிக்கப்பட்டிருப்பதை கண்டறிந்தார்கள்”, என்று அவள் ஒரு கணம் நிறுத்தி மூச்சை உள்ளிளுத்தாள்.

“அவர்கள் அவளை கை விட்டு (give up) விட்டார்களா? என்ற கேள்விக்கு நான் பதில் கூற வேண்டியதில்லை. அவர்களே அவளை இங்கு கொண்டு வந்து எங்களிடம் அவளை இந்த மருத்துவமனையில் சேர்த்துக் கொள்ளும் படி வேண்டி கேட்டுக் கொண்டார்கள், இந்த 12 மாதங்கள் அவள் எங்கள் நோயாளியாகவே (patient) இருக்கிறாள், மேலும் அவளது நிலையில் முன்னேற்றம் இருக்கிறது. அவள் மீண்டும் எழுந்து வந்து பாடுவாள் என்ற நம்பிக்கை எங்களுக்கு உள்ளது”.

“இங்கு எல்லாமே இப்போது மிக கடினமாக (difficult) உள்ளது. எனவே உணவு, தங்குமிடம் என அனைத்திற்கும் நாங்கள் பணம் வசூலிக்கவில்லையென்றால் எங்களால் மருத்துவமனையை நடத்த இயலாது. ஆனால் ஒவ்வொரு வாரமும் லூசியாவின் சகோதரர்கள் அவளுக்கான கட்டணத்தை (payment) செலுத்திவிடுவார்கள்.

அவர்கள் என்ன வேலை செய்கிறார்கள் என்று தெரியவில்லை, நானும் கேட்பதில்லை. வெரோனா நகரில் வேலைக் கிடைப்பது மிகக் கடினம். என்னவாக இருந்தாலும் சரி, அவர்கள் நன்றாக செய்கிறார்கள் என்று எனக்குத் தெரியும்”.

“ஆமாம், இதைவிடச் சிறப்பாக அவர்களால் செய்ய இயலாது” என்று நானும் சம்மதித்தேன் (agreed). அவர்கள் என்னிடம் வரும் வரையில் நான் வெளியே காத்திருந்தேன். வந்ததும் மீண்டும் நகருக்கு திரும்பினோம். அவர்கள் என்னிடம் எதுவும் பேசாமல் அமர்ந்திருந்தார்கள். நானும் அவர்களிடம் ஒரு வார்த்தைக்கூட கேட்கவில்லை. அவர்கள் தங்கள் சகோதரி குறித்த இரகசியத்தை (secret) தங்களுடன் மட்டுமே வைத்துக் கொள்ள விரும்புவார்கள் என்று எனக்குத் தெரியும்.

போர் (war) அவர்களது மனநிலையை உடைக்கமுடியவில்லை . அவர்களின் தன்னலமற்ற செயல், மனித வாழ்க்கைக்கு ஒரு புதிய பெருந்தன்மையையும் (nobility), மனித சமுதாயத்திற்கு ஒரு பெரிய நம்பிக்கையைத் (hope) தரக்கூடிய உறுதியையும் அளித்துள்ளன.

Glossary:

Additional:

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.6 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.6

Choose the most suitable answer from the given four alternatives:

Question 1.
The value of sin^-1(cos x), 0 ≤ x ≤ π is
(a) π – x
(b) x – \(\frac {π}{2}\)
(c) \(\frac {π}{2}\) – x
(d) x – π
Solution:
(c) \(\frac {π}{2}\) – x
Hint:
sin^-1(cos x) = sin^-1(sin(\(\frac {π}{2}\) – x)) = \(\frac {π}{2}\) – x

Question 2.
If sin^-1 x + sin^-1 y = \(\frac {2π}{3}\); then cos^-1 x + cos^-1 y is equal to
(a) \(\frac {2π}{3}\)
(b) \(\frac {π}{3}\)
(c) \(\frac {π}{6}\)
(d) π
Solution:
(b) \(\frac {π}{3}\)
Hint:
sin^-1x + cos^-1x + cos^-1y + sin^-1y = \(\frac {π}{2}\) + \(\frac {π}{2}\) = π
\(\frac {2π}{3}\) + cos^-1x + cos^-1y = π
cos^-1x + cos^-1y = π – \(\frac {2π}{3}\) = \(\frac {3π-2π}{3}\) = \(\frac {π}{3}\)

Question 3.
sin^-1\(\frac {3}{5}\) – cos^-1\(\frac {12}{13}\) + sec^-1\(\frac {5}{3}\) – cosec^-1\(\frac {13}{12}\) is equal to
(a) 2π
(b) π
(c) 0
(d) tan^-1\(\frac {12}{65}\)
Solution:
(c) 0
Hint:

Question 4.
If sin^-1 x = 2sin^-1 α has a solution, then
(a) |α| ≤ \(\frac {1}{√2}\)
(b) |α| ≥ \(\frac {1}{√2}\)
(c) |α| < \(\frac {1}{√2}\)
(d) |α| > \(\frac {1}{√2}\)
Solution:
(a) |α| ≤ \(\frac {1}{√2}\)
Hint:
If sin^-1 x = 2sin^-1 α has a solution then
–\(\frac {π}{2}\) ≤ 2sin^-1α ≤ \(\frac {π}{2}\)
–\(\frac {π}{4}\) ≤ sin^-1α ≤ \(\frac {π}{4}\)
sin(\(\frac {-π}{4}\)) ≤ α ≤ sin\(\frac {π}{4}\)
–\(\frac {1}{√2}\) ≤ α ≤ \(\frac {1}{√2}\)
-|α| ≤ \(\frac {1}{√2}\)

Question 5.
sin^-1(cos x) = \(\frac {π}{2}\) – x is valid for
(a) -π ≤ x ≤ 0
(b) 0 ≤ x ≤ π
(c) –\(\frac {π}{2}\) ≤ x ≤ \(\frac {π}{2}\)
(d) –\(\frac {π}{4}\) ≤ x ≤ \(\frac {3π}{4}\)
Solution:
(b) 0 ≤ x ≤ π
Hint:
sin^-1 (cosx) = \(\frac {π}{2}\) – x is valid for
cos x = sin (\(\frac {π}{2}\) – x)
cos x ∈ [0, π]
∴ 0 ≤ x ≤ π

Question 6.
If sin^-1 x + sin^-1 y + sin^-1 z = \(\frac {3π}{2}\), the value of show that x²⁰¹⁷ + y²⁰¹⁸ + z²⁰¹⁹ – \(\frac {9}{x^{101}+y^{101}+z^{101}}\) is
(a) 0
(b) 1
(c) 2
(d) 3
Solution:
(a) 0
Hint:

Question 7.
If cot^-1 x = \(\frac {2π}{5}\) for some x ∈ R, the value of tan^-1 x is
(a) –\(\frac {π}{10}\)
(b) \(\frac {π}{5}\)
(c) \(\frac {π}{10}\)
(d) –\(\frac {π}{5}\)
Solution:
(c) \(\frac {π}{10}\)
Hint:
tan^-1 x + cos^-1 \(\frac {π}{2}\)
tan^-1x = \(\frac {π}{2}\) – cot^-1 x = \(\frac {π}{2}\) – \(\frac {2π}{5}\)
= \(\frac {5π-4π}{10}\) = \(\frac {π}{10}\)

Question 8.
The domain of the function defined by f(x) = sin^-1 \(\sqrt {x-1}\) is
(a) [1, 2]
(b) [-1, 1]
(c) [0, 1]
(d) [-1, 0]
Solution:
(a) [1, 2]
Hint:
f(x) = sin^-1 \(\sqrt {x-1}\)
\(\sqrt {x-1}\) ≥ 0
-1 ≤ \(\sqrt {x-1}\) ≤ 1
∴ 0 ≤ \(\sqrt {x-1}\) ≤ 1
0 ≤ x – 1 ≤ 1
1 ≤ x ≤ 2
x ∈ [1, 2]

Question 9.
If x = \(\frac {1}{5}\) the value of cos(cos^-1x + 2sin^-1x) is
(a) –\(\sqrt{\frac {24}{25}}\)
(b) \(\sqrt{\frac {24}{25}}\)
(c) \(\frac {1}{5}\)
(d) –\(\frac {1}{5}\)
Solution:
(d) –\(\frac {1}{5}\)
Hint:
cos[cos^-1x + sin^-1x + sin^-1x] = cos(\(\frac {π}{2}\) + sin^-1x)
= -sin(sin^-1x)
[∵ cos(90+θ) = -sin θ]
= -x = –\(\frac {1}{5}\)

Question 10.
tan^-1(\(\frac {1}{4}\)) + tan^-1(\(\frac {2}{9}\)) is equal to
(a) \(\frac {1}{2}\)cos^-1(\(\frac {3}{5}\))
(b) \(\frac {1}{2}\)sins^-1(\(\frac {3}{5}\))
(c) \(\frac {1}{2}\)tan^-1(\(\frac {3}{5}\))
(d) tan^-1(\(\frac {1}{2}\))
Solution:
(d) tan^-1(\(\frac {1}{2}\))
Hint:

Question 11.
If the function f(x) = sin^-1(x² – 3), then x belongs to
(a) [-1, 1]
(b) [√2, 2]
(c) [-2, -√2]∪[√2, 2]
(d) [-2, -√2]
Solution:
(c) [-2, -√2]∪[√2, 2]
Hint:
-1 ≤ x² – 3 ≤ 1
-1 + 3 ≤ x² ≤ 1 + 3
⇒ 2 ≤ x² ≤ 4
±√2 ≤ x ≤ ± 2
[-2, -√2]∪[√2, 2]

Question 12.
If cot^-1 2 and cot^-1 3 are two angles of a triangle, then the third angle is
(a) \(\frac {π}{4}\)
(b) \(\frac {3π}{4}\)
(c) \(\frac {π}{6}\)
(d) \(\frac {π}{3}\)
Solution:
(b) \(\frac {3π}{4}\)
Hint:
A + B + C = π (triangle)
cot^-1 2 + cot^-1 3 + C = π

Question 13.
sin^-1(tan\(\frac {π}{4}\)) – sin^-1(\(\sqrt{\frac {3}{x}}\)) = \(\frac {π}{6}\). Then x is root of the equation
(a) x² – x – 6 = 0
(b) x² – x – 12 = 0
(c) x² + x – 12 = 0
(d) x² + x – 6 = 0
Solution:
(b) x² – x – 12 = 0
Hint:

Question 14.
sin^-1(2 cos²x – 1) + cos^-1(1 – 2 sin²x) =
(a) \(\frac {π}{2}\)
(b) \(\frac {π}{3}\)
(c) \(\frac {π}{4}\)
(d) \(\frac {π}{6}\)
Solution:
(a) \(\frac {π}{2}\)
Hint:
sin^-1(2 cos² x – 1) + cos^-1(1 – 2 sin²x)
= sin^-1 (2 cos² x – 1) + cos^-1 (1 – sin² x – sin² x)
= sin^-1(2 cos² x – 1) + cos^-1(cos² x – (1 – cos²x))
= sin^-1(2 cos² x – 1) + cos^-1(cos² x – 1 + cos²x)
= sin^-1(2 cos² x – 1) + cos^-1(2 cos² x – 1)
= \(\frac {π}{2}\) [∵ sin^-1 x + cos^-1 x = \(\frac {π}{2}\)]

Question 15.
If cot^-1(\(\sqrt {sinα}\)) + tan^-1(\(\sqrt {sinα}\)) = u, then cos 2u is equal to
(a) tan²α
(b) 0
(c) -1
(d) tan 2α
Solution:
(c) -1
Hint:
cot^-1 x + tan^-1 x = \(\frac {π}{2}\)
∴ u = \(\frac {π}{2}\)
cos 2u = cos 2(\(\frac {π}{2}\)) = cos π = -1

Question 16.
If |x| ≤ 1, then 2 tan^-1 x – sin^-1\(\frac {2x}{1+x²}\) is equal to
(a) tan^-1x
(b) sin^-1x
(c) 0
(d) π
Solution:
(c) 0
Hint:
sin^-1\(\frac {2x}{1+x²}\) = 2 tan^-1x
∴ 2 tan^-1 x – 2 tan^-1 x = 0

Question 17.
The equation tan^-1 x – cot^-1 x = tan^-1(\(\frac {1}{√3}\)) has
(a) no solution
(b) unique solution
(c) two solutions
(d) infinite number of solutions
Solution:
(b) unique solution
Hint:
tan^-1 x – cot^-1 x = tan^-1(\(\frac {1}{√3}\)) …….. (1)
tan^-1 x – cot^-1 x = \(\frac {π}{2}\) ……… (2)
Add 1 and 2
2 tan^-1 x = \(\frac {π}{6}\) + \(\frac {π}{2}\) = \(\frac {2π}{3}\)
tan^-1 x = \(\frac {π}{3}\)
x = √3 which is uniqe solution.

Question 18.
If sin^-1 x + cot^-1(\(\frac {1}{2}\)) = \(\frac {π}{2}\), then x is equal to
(a) \(\frac {1}{2}\)
(b) \(\frac {1}{√5}\)
(c) \(\frac {2}{√5}\)
(d) \(\frac {√3}{2}\)
Solution:
(b) \(\frac {1}{√5}\)
Hint:

Question 19.
If sin^-1 \(\frac {x}{5}\) + cosec^-1\(\frac {5}{4}\) = \(\frac {π}{2}\), then the value of x is
(a) 4
(b) 5
(c) 2
(d) 3
Solution:
(d) 3
Hint:

Question 20.
sin(tan^-1 x), |x| < 1 is equal to
(a) \(\frac {x}{\sqrt{1-x^2}}\)
(b) \(\frac {1}{\sqrt{1-x^2}}\)
(c) \(\frac {1}{\sqrt{1+x^2}}\)
(d) \(\frac {x}{\sqrt{1+x^2}}\)
Solution:
(d) \(\frac {x}{\sqrt{1+x^2}}\)
Hint:
tan a = x
W.K.T 1 + tan² a = sec² a
1 + x² = sec² a
sec a = \(\sqrt{1+x^2}\)
\(\frac {1}{cosa}\) = \(\sqrt{1+x^2}\)
cos a= \(\frac {1}{\sqrt{1+x^2}}\)
sin a = \(\sqrt{1-cos^2a}\) = \(\sqrt{1-\frac {1}{1+x^2}}\)
\(\sqrt{\frac{1+x^2 -1}{1+x^2}}\) = \(\frac {x}{\sqrt{1+x^2}}\)