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Odisha State Board CHSE Odisha Class 11 Invitation to English 1 Solutions Chapter 2 The Legend behind a Legend Textbook Exercise Questions and Answers.

CHSE Odisha 11th Class English Solutions Chapter 2 The Legend behind a Legend

CHSE Odisha Class 11 English The Legend behind a Legend Text Book Questions and Answers

UNIT – I
Gist with Glossary

Gist:
The writer walks down memory lane. Exactly 25 years ago, he had spent two days and two nights with Khairi, the tigress of Jashipur, and a collection of wild animals of Saroj and Nihar. A news item on the latest exploits of Khairi evoked his interest to visit the place. He came to know that Saroj Raj Chaudhury was taking care of Khairi. He wrote a letter to him and met with a prompt response. He was filled with great joy. Mr. Chaudhury invited him to Khairi-Jashipur, giving him particular directions on how to reach there. The writer apprised him of when and how he would visit him.

Glossary:
bandit queen : queen of the robbers (ଦସ୍ୟୁରାଣୀ)
menagerie : a collection of wild animals (ବଣ୍ୟଜନ୍ତୁ ମାନ ଙ୍କ ସଂଗ୍ରହାଳୟ)
exploits : some unusual thing that someone does that you think is brave, exciting or entertaining
domesticated : an animal trained to live with or work for humans (ଗୃହପାଳିତ)
struck : occurred (ମନେପଡ଼ିଲା)
gruff : unfriendly and cruel (ନିଷ୍ଠୁର ସ୍ବଭାବସମ୍ପନ୍ନ)
tough : strict and severe (ଶୃଙ୍ଖଳିତ)
brooked no nonsense : tolerated only important and necessary things (ବାଜେ କଥା ସହ୍ୟ କରିପାରନ୍ତି ନାହିଁ)
suffered no feels : did not tolerate stupidity in others (ନିର୍ବୋଧତାକୁ ପ୍ରଶ୍ରୟ ଦିଅନ୍ତି ନାହିଁ)
itnerant articles : articles published in different magazines (ବିଭିନ୍ନ ପତ୍ରିକାରେ ପ୍ରକାଶିତ ଅନେକ ଲେଖା )
shot in the dark : a hopeful attempt (ଏକ ଆଶାପୂର୍ଣ୍ଣ ଉଦ୍ୟମ )
utter : great (ମାତ୍ରାତ୍ଵିକ)
delight : pleasure (ଆନନ୍ଦ)
precise : exact (ନିର୍ଦ୍ଦିଷ୍ଟ)
instructions : directions (ନିର୍ଦ୍ଦେଶ )

Think it out:
Question 1.
Who is Khairi?
Answer:
Khairi is a legendary tigress of Jashipur.

Question 2.
How did the writer come to know about Khairi?
Answer:
The writer came to know about Khairi when he had read a small news item in The Statesman that threw light on the latest exploits of the tigress in the Similipal forests of Odisha.

Question 3.
Who was the foster father of Khairi?
Answer:
Saroj Raj Chaudhury was the foster father of Khairi.

Question 4.
Which State does the writer belong to?
Answer:
The writer belongs to Odisha.

Question 5.
What did he learn about Saroj Raj Chaudhury as a person?
Answer:
He learnt that Saroj Raj Chaudhury tolerated only important and necessary things, but not stupidity in others.

Question 6.
How did he contact Mr. Chaudhury?
Answer:
He contacted Mr. Chaudhury by writing a letter to him after getting his address.

Question 7.
Why did he refer some of his articles to Mr. Chaudhury?
Answer:
He referred some of his articles to Mr. Chaudhury in the hope of getting his response.

Question 8.
Did Mr. Chaudhury reply to the author’s letter? What did he write?
Ans.
Yes, Mr. Chaudhury replied to the author’s letter. The former wanted the latter to inform him in advance of the manner and the time of his arrival.

UNIT-II
Gist with Glossary

Gist:
The writer reached Khairi-Jashipur by an overcrowded bus. It was 4 a.m. He was soon provided with food and shelter. In other words, he was accorded fabulous hospitality, thanks to Saroj Chaudhury. Terror seized him when he heard the clear voice of the Tiger just outside the door. It did not last long before the bearer met him to serve hot tea and biscuit and assured him of the presence of Khairi who was making loving inquiries about the new guest in the house. He met Saroj Chaudhury, ‘a frail man in his fifties, slightly balding on the top; the latter greeted the former in a polite manner after asking Jambu, the bear, to get down because the animal holding on to Chaudhury’s waist. They conversed with each other. In Mr. Chaudhury, the writer found a humble and careful man. One of the most caring persons he had ever met in his life was Mr.

Glossary:
semidarkness: half-darkness (ଅର୍ଥ ଅନ୍ଧକାର)
click : sound (ଶବ୍ଦ)
detailed : was given minute instructions (ସମ୍ପୂର୍ଣ୍ଣ ସୂଚନା ପାଇଥିଲେ )
escort : guide (ପଥ ପ୍ରଦର୍ଶନକାରୀ)
with a start : in fear (ଭୟଚକିତ ହୋଇ)
terror struck : the writer was seized with fear (ଭୟ ବିହ୍ବଳିତ)
sloth : lazy behaviour (ଆଳସ୍ୟ ସ୍ବଭାବସମ୍ପନ୍ନ )
frail : weak (ଦୁର୍ବଳ)
slightly : a little (ଅତି ଅଳ୍ପ)
gruff : rude, unfriendly
no-nonsense : doing things quickly and effectively without worring too much about people’s fear (ଲୋକଙ୍କ ମନ୍ତବ୍ୟ ପ୍ରତି ଉଦାସୀନ)
humane : caring people and animals ( ମାନବ ପ୍ରତି ସମ୍ବେଦନଶୀଳ)

Think it out:
Question 1.
How did the writer come to Bhubaneswar?
Answer:
The writer came to Bhubaneswar by train.

Question 2.
How did he go to Jashipur from Bhubaneswar?
Answer:
He went to Jashipur from Bhubaneswar in an over-packed bus.

Question 3.
How did the forest guard receive him?
Answer:
The forest guard received him in a very cordial manner. He guided the writer, took him to the guest house, and made him stay in the guest house, assuring him that the water was in the jug.

Question 4.
Why was he terror-struck?
Answer:
He was terror-struck because he heard the clear voice of the Tiger just outside his door.

Question 5.
What did the bearer tell him about Khairi?
Answer:
The bearer told him that Khairi was trying to know about the new guest in the house. There was a ring of friendliness about Khairi.

Question 6.
What was Mr. Chaudhury doing when the writer met him?
Answer:
When the writer met Mr. Chaudhury, he was sitting on a large chair.

Question 7.
How did Mr. Chaudhury greet the author?
Answer:
Mr. Chaudhury warmly greeted the author.

Question 8.
What was the name of the bear?
Answer:
The name of the bear was Jambu.

Question 9.
What was the physical appearance of Mr. Chaudhury?
Answer:
Mr. Chaudhury was a weak man in his fifties with a little baldness on the top.

Question 10.
What kind of man did the author find Mr. Chaudhury to be?
Answer:
In the author’s estimation, Mr. Chaudhury was friendly and responsive. Besides, he was caring to the core.

UNIT – III
Gist with Glossary

Gist:
This part begins with Mr. Chaudhury narrating a wonderful story to the writer. His house turned into a habitat for different species of wild animals. He conducted an experiment to exaggerate that the animals could exist with each other if they were together from childhood. He brought Khairi and one of the most dangerous snakes, krait close to her. The writer marked Khairi’s reaction – it was one of fondness for the strange creature. Whenever the krait got too close to Khairi, he would pull it by its back.

Once he became inattentive and was bitten by a krait. Some of its poison entered his blood and therefore, he was now a permanent patient of low blood pressure. As soon as Mr. Chaudhury finished this wonderful story Jambu tried to give the writer his bear hug, but the former’s stem warning prevented him from doing so. Mr. Chaudhury has a well-knit joint family that was living inside the compound. It comprised a mongoose, a pangolin, wild cat twins, a country dog, and a blind Hyena, each having a name.

Glossary:
emerged : became known (ଜଣାପଡ଼ିଲା)
sips : drink (something) by taking small mouthfuls (ଅଳ୍ପ ଅଳ୍ପ ପିଇବା)
debunked : exaggerated
co-exist : live together (ଏକତ୍ର ବାସ କରିବା)
infancy : childhood (ପିଲାଦିନ)
unmindful : inattentive (ଅମନୋଯୋଗୀ)
tied : bound (ବାନ୍ଧିଥିଲେ )
tourniquet : a piece of cloth bound tightly on an arm or leg to stop bleeding
hypo-glycaemia : condition of having a very low blood pressure (ନିମ୍ନ ରକ୍ତଚାପ)
astonishing : wonderful (ଆଶ୍ଚର୍ଯ୍ୟଜନକ)
take a fancy : to start liking someone (ଜଣକୁ ଭଲ ପାଇବାକୁ ଆରମ୍ଭ କରିବା)
hug : to put ones arms around someone to show love (ଆଲିଙ୍ଗନ)
dissuade : prevent (ବାଧା ଦେବା)
fondness : affection (ସ୍ନେହ, ଶ୍ରଦ୍ଧା)
progressed : advanced (ଆଗେଇ ଚାଲିଲା)
intennittent : occurring occasionally (ସାମୟିକଭାବେ ଘଟୁଥିବା)
crackle : making shout sharp sounds (ସ୍ଵଚ୍ଛ ଅବଶିଷ୍ଟ ଉଚ୍ଚ ଶବ୍ଦ)
veritable : real (ବାସ୍ତବ)

Think it out:
Question 1.
What theory did Mr. Chaudhury prove wrong?
Answer:
The theory that Mr. Chaudhury proved wrong was that the different species of wild animals cannot co-exist unless they are together from childhood.

Question 2.
What was his first story about?
Answer:
The first story was about how his house became the habitat of different species of wild animals who all come at different stages of their lives. It also dealt with their coexistence and the close relationship between Khairi and krait, a dangerous snake.

Question 3.
Why is it so unique and amazing?
Answer:
It is so unique and amazing because, during this experiment, Khairi showed her reaction to the presence of krait, the most poisonous snake. Khairi was curious to know more about the krait as it was a stranger to her.

Question 4.
Why did Mr. Chaudhury allow Khairi to come near the krait?
Answer:
Mr. Chaudhury allowed Khairi to come near a krait to know how they dealt with each other.

Question 5.
What was Khairi’s reaction to the presence of the krait?
Ans.
Khairi’s reaction to the presence of a krait was one of curiosity to know more about the latter.

Question 6.
How did the experiment affect him?
Answer:
The experiment made him a permanent patient of low blood pressure.

Question 7.
What did the bear try to do with the writer?
Answer:
The bear tried to put his arms around the writer to show his love.

Question 8.
What prevented the bear from doing so?
Answer:
Mr. Chaudhury’s strict ‘no’ prevented the bear from doing so.

Question 9.
What kind of family did Mr. Chaudhury have?
Answer:
Mr. Chaudhury had a genuine joint family that comprised a mongoose, a pangolin, wild cat twins, a country dog, and a blind Hyena, each having a name.

Question 10.
What was his relationship with different animals?
Answer:
His relationship with different animals was quite familiar. His act of naming each of them is a case in point.

UNIT – IV

Gist:
Khairi was brought to Saroj Raj Chaudhury as a two-month cub who was hungry and confused. Veteran forester and instinctive lover of wildlife as he was, Saroj imitated the sounds of a mother tigress. It worked wonderfully. The tiger cub’s confidence was restored. Saroj became nostalgic. He recollected his birthday when his mother had presented him with a gun, with which he, as a young man, shot wildlife in a carefree manner. But, soon he realized that it was a mistake and happiness lies in the conservation of these harmless beautiful animals. As the Director of Project Tiger, Saroj was the first to introduce the Tiger Tracing Method of tiger census. For the night, both camped at a guest house deep in the jungle. Never before had the writer experienced one night in a magnificent wooden structure with rooms and a bath that stood 15 feet high from the ground.

Glossary:
cub : (here) a young tigress (ବାଘଛୁଆ, ଛୁଆ ବାଘୁଣୀ)
famished : very hungry (କ୍ଷୁଧାଉଁ)
confused : disturbed (ବିବ୍ରତ ହେଲା)
snarls: making angry sounds in one’s throat and showing teeth
veteran : experienced (ଅଭିଜ୍ଞ, ଦକ୍ଷ)
handle : deal with (ଆୟତ୍ତ କରିବା)
firmly : determindedly (ଦୃଢ଼ ଭାବରେ )
anchored : restored (ଶାନ୍ତ ହେଲା)
the legends : (here) Saroj Raj Chaudhury and Khairi (କିମ୍ବଦନ୍ତୀ )
tag along : accompanied someone (ବ୍ୟକ୍ତିବିଶେଷଙ୍କ ସହ ଯାତ୍ରା
snaked (v) : moved in or had a senes of long curves (ଅଙ୍କାବଙ୍କା ରାସ୍ତାରେ ଗଲା)
amidst: in the midst of (ମଝିରେ)
lush foliage: leaves of trees growing luxuriously
abandon : in an uncontrolled way (ଅବିଚାରିତ ଭାବେ)
conserving: preventing land, water, etc. from being damaged (ସଂରକ୍ଷଣ କରିବା)
wanton harm: reckless harm
authority : (here) Saroj Choudhury (କର୍ତ୍ତୃପକ୍ଷ )
pugmarks: the mark of the footprint of an animal (ପଶୁର ପାଦଚିହ୍ନ)
distinctive: very clear
meticulously: carefully attending to every detail
functional: practical and simple
build on stilts: build on one of a set of posts
a top: at the top of (ଉପରିଭାଗରେ )
magnificent : very beautiful (ଖୁବ୍‌ ସୁନ୍ଦର)

Think it out:
Question 1.
How and when did Mr. Chaudhury come across Khairi?
Answer:
Mr. Chaudhury came across Khairi when 12 Kharia tribals of Similipal brought her to him when she was a two-month cub. It was on October 5, 1974.

Question 2.
In what condition did he And it?
Answer:
He found it in a state of hunger and confusion.

Question 3.
How did he manage the hungry and confused cub?
Answer:
He managed the hungry and confused cub by copying the sounds of the mother tigress. Within minutes, she became firmly confident.

Question 4.
How did he treat wildlife in a young age?
Answer:
He treated wildlife uncontrollably in a young age.

Question 5.
What did he say about his change of attitude towards wildlife to the author?
Answer:
He said to the author that his change of attitude towards wildlife took place because of his realization that there was greater happiness in safeguarding the beautiful wild animals that do not cause reckless harm to man.

Question 6.
What was his contribution to the Tiger Project?
Answer:
His contribution to the Tiger Project was the introduction of the Tiger Tracing Method of tiger census. As a result, one can measure the pugmarks of each animal distinctly and record their characteristics very carefully.

Question 7.
What was the guest house like?
Answer:
The guest house was a wooden structure with simple rooms and a bath. It was built on one of the set of posts and was at a height of 15 feet.

Question 8.
What new experience did the author have in the Tiger Reserve area?
Answer:
The author experienced for the first time, one night stay in the Tiger Reserve area that was unique, especially on a very beautiful ‘machan’.

UNIT – V
Gist with Glossary

Gist :
The writer revisited Khairi-Jashipur after three months. His interest to know more about Khairi gained momentum. Besides Mr. Chaudhury’s old acquaintances, he caught sight of a young python. He focused on Mr. Chaudhury whose quest and passion was amazing. Meanwhile, Mr. Chaudhury got a message from the World Wildlife Fund. He went to New Delhi by air for an urgent meeting. The writer saw him off at the Dum Dum Airport, Calcutta. It was his last meeting with Mr. Chaudhury, a legend behind a legend. Khairi and Mr. Chaudhury are no more.

Glossary:
gracious: kind
in addition to besides
python: a very large snake that kills animals for food by wrapping itself around them and crushing them (ଅଜଗର ସାପ )
quest : search (ଅନ୍ଵେଷଣ)
legend: someone who very many people know about and admire (କିମ୍ବଦନ୍ତୀ ପୁରୁଷ)
unique : extraordinary (ଅସାଧାରଣ)
due: worth (ଯୋଗ୍ୟ)

Think it out:
Question 1.
After what interval of time did the writer visit Mr. Chaudhury for the second time?
Answer:
After three months, the writer visited Mr. Chaudhury for the second time.

Question 2.
What new addition to the Chaudhury family did he find there?
Answer:
The new addition to Chaudhury’s family he found there was an eight-foot-long young python.

Question 3.
Why did he get less time to interact with Mr. Chaudhury this time?
Answer:
He got less time to interact with Mr. Chaudhury because at that moment Mr. Chaudhury got a wireless message from the World Wildlife Fund to attend an important meeting at New Delhi.

Question 4.
Who died first, Khairi or Mr. Chaudhury?
Answer:
Khairi died first.

Question 5.
Who are the two legends the writer talks about?
Answer:
The two legends the writer talks about are Khairi and Mr. Saroj Raj Chaudhury.

Question 6.
Is the text more about Mr. Chaudhury or Khairi?
Answer:
The text throws much light on Mr. Chaudhury, yet Khairi does not lag far behind.

Question 7.
Can you guess now why the title of the text is “The Legend behind the Legend”?
Answer:
The title is aptly justified because the legendary passionate and instinctive lover of wildlife has been instrumental in transforming a two-month-old tiger baby into a legend. She is Khairi.

Post-Reading Activities:

I. Arranging in Order
Provided below are some events from the lesson. These are not in order. Arrange them in order as they occur in the lesson by putting numbers within the brackets provided against the items. One is done for you.
(a) Khairi played with the krait. ( )
(b) Khairi was brought to Mr. Chaudhury. ( )
(c) The writer sees Mr. Chaudhury off at Dum Dum Airport. (8)
(d) The writer reads a news item about Khairi. ( )
(e) Chaudhury writes a letter to the writer. ( )
(f) The writer reaches Jashipur by bus. ( )
(g) He stays with Chaudhury in a camp guest house in the forest. ( )
(h) The writer saw a python as a pet of Chaudhury. ( )
Answer:
(a) Khairi played with the krait. (6)
(b) Khairi was brought to Mr. Chaudhury. (5)
(c) The writer sees Mr. Chaudhury off at Dum Dum Airport. (8)
(d) The writer reads a news item about Khairi. (1)
(e) Chaudhury writes a letter to the writer. (2)
(f) The writer reaches Jashipur by bus. (3)
(g) He stays with Chaudhury in a camp guest house in the forest. (4)
(h) The writer saw a python as a pet of Chaudhury. (7)

II. Note-making
Notes-making helps you to develop your reading and writing skills. This lesson has, you know, two major themes – Khairi and Mr. Chaudhury. You have to read the lesson, make notes (in words and phrases) on these two, and then use these points to write about them. One has been done below on Khairi as a model. Make notes on Mr. Chaudhury.

Notes on Khairi
Para 1
→ Tigress of Jashipur
→ Made the forest famously
→ Domesticated tigress in the Similipal forest of Odisha
→ Writer reads a news item about Khairi
Para 5
→ Khairi roared to welcome the writer
→ He was terror struck
Para 9
→ On October 5, 1974, Khairi was brought as a cub, hungry, confused
Para 15
→ Chaudhury manages her imitating the sounds of a mother tigress.
The death of Khairi was followed by the death of Chaudhury.
With the help of these notes, write a paragraph on Khairi.
Khairi:
Khairi was a domesticated tigress. She made the Simmilipal forest and Jashipur famous. The writer read about her from a news item. Then he visited Jashipur to see Khairi and Chaudhury who had kept Khairi as a pet. He came to know from Mr. Chaudhury that Khairi was brought to Chaudhury on October 5, \91A by twelve Kharia tribals. It was then a small cub, hungry and confused. Chaudhury handled the cub well by imitating the sounds of a tigress. She grew up as a domesticated tigress under the loving care of Chaudhury. But she did not live long. Chaudhury also died soon after the death of Khairi.

Now write notes (from the lesson) and develop the notes into a write-up on Mr. Chaudhury.

Notes on Mr. Chaudhury
Para 3
→ Mr. Chaudhury was a very responsible person.
Para 4
→ Hospitable to the core
Para 6
→ A weak man in his fifties, slightly balding on the top
→ Nice and down-to-earth
→ One of the most humane beings
Para 7
→ His experiment concerning the co-existence of wild animals in the presence of Khairi and the krait
→ The latter is a dangerous snake
→ Noticed Khairi’s reaction of fondness
→ A permanent patient with low blood pressure
Para 8
→ Strict
→ Possessed a joint family of animals in his house
Para 9
→ An officer of the Indian Forest Service
→ Veteran forester and instinctive lover of wildlife
→ Showed skill in handling hungry and confused two-month-old tiger cub
→ Imitated the sounds of a mother tigress
Para 11
→ An authority on the tiger and Director of Project Tiger in India
→ Introduced the Tiger Tracing Method of tiger census
Para 13
→ Gracious
Para 14
→ Journey to New Delhi for an important meeting
Para 15
→ The writer’s last meeting with him in the Dum Dum Airport, Calcutta
→ A legend behind a legend
→ He is no more.
Mr. Chaudhury
Mr. Chaudhury, responsible, hospitable, and down-to-earth, was a weak person in his fifties. He was one of the most humane beings. He made an experiment by effecting contact between Khairi and the krait, one of the most dangerous snakes, to know about the co-existence of different wild animals. Khairi’s reaction, he noticed, was one of great love. Mr. Chaudhury, a veteran forester and an instinctive lover of wildlife possessed a joint family of different animals in his house. He was strict. He showed his skill in handling the hungry and confused two-month-old tiger cub by imitating the sounds of a mother tigress. Mr. Chaudhury, an authority on the tiger and Director of Project Tiger in India, was the first to introduce the Tiger Tracing Method of tiger census. The writer saw such a graceful legend off in Dum Dum Airport on his way to New Delhi, for the last time. Mr. Chaudhury is no more.

III. Doing with words Collocation
(a) Collocation in expressions means which words go with which other words. Collocations are fixed expressions. For example sweet dreams, daydreams, bad dreams, pipe dreams, hard-earned money, public money, extra money, and tax-payers money.

Answer:

(b) Find out five collocations from the test. (Example: to take a fancy).
Answer:
brooked no nonsense
suffered no fools
terror-struck
no-nonsense
hypo-glycaemia

(c) Which word in each line does not collocate with the headword?
(i) a theory: come up with, do, debunk, build
(ii) a debate: open, listen to, join in, find
(iii) legend: fresh, famous, well-known, sports
(iv) veteran: soldier, idealist, activist, man
(v) gracious: welcome, hospitality, building, smile
Answer:
(i) do
(ii) find
(iii) fresh
(iv) man
(v) building

CHSE Odisha Class 11 English The Legend behind a Legend Important Questions and Answers

I. Short Answer Type Questions with Answers

1. Read through the extract and answer the questions that follow.
Khairi made the entire forest where she lived famously. She was not a bandit queen but Khairi, the tigress of Jashipur. It was exactly 25 years ago when I spent two days and two nights with Khairi and the menagerie of Saroj and Nihar, I had read a small news item in The Statesman about the latest exploits of a domesticated tigress in the Similipal forests of Odisha. Suddenly, it struck me that this was happening in my own State. I thought, “why not attempt to experience it myself ?” I spoke to N.S. Ayyangar, a senior journalist in Berhampur, and a few other elders.

I was told that Khairi was under the care of a rather gruff and tough man called Saroj Raj Chaudhury who brooked no nonsense and suffered no fools. I got his address and wrote asking if I could visit him. For good measure, I referred to a few itinerant articles I had written for Indian magazines. It was a shot in the dark and I did not really expect to hear from him. But, to my utter delight, I got a letter within a week inviting me to Khairi-Jashipur, giving precise instructions about how to reach there. Mr. Chaudhury also asked me to let him know in advance how and when I was reaching. I gave him a date and said I would be taking a bus from Bhubaneswar on a particular night.

Questions :
(i) Why was the forest made famous?
(ii) “Why not attempt to experience it myself ?” What does ‘It’ refer to?
(iii) Why did the writer contact N.S. Ayyanger and a few others? What was the result?
(iv) Explain the expression “It was a shot in the dark.”.
(v) Suggest a suitable title to the extract.

Answers :
(i) The forest was made famous by Khairi, the tigress of Jashipur because it was her abode.
(ii) ‘It’ refers to the writer’s curiosity to be aware of the latest exciting things carried by a tigress in the Similipal forests of Odisha. She had been to live with and work for humans.
(iii) The writer contacted N.S. Ayyanger and a few other seniors to know about Khairi. He learned that Saroj Raj Chaudhury, who was rather an unfriendly and severe man, took care of the tigress.
(iv) The writer’s reference to a few articles he had written for Indian magazines was a sort of hopeful attempt to see Khairi and Saroj Raj Chaudhury’s positive response to his letter.
(v) The Writer’s Quest of Khairi

2. Read through the extract and answer the questions that follow.
I packed my bag, took the train, and boarded the overcrowded bus from Bhubaneswar. I arrived sometime before 4.00 a.m. wondering where to go in that semidarkness. To my utter surprise, within a minute there was the click of boots and a voice welcoming me to Khairi-Jashipur. The Forest Guard, detailed to escort me, took me to the guest house, put me in my room, and assured me that water was in the jug; I could sleep as long as I wanted and Saab would see me as soon as I was ready.

I think I had an hour of blissful sleep. I woke up with a start when I heard the unmistakable voice of the Tiger just outside my door. I was terror-struck. Within minutes, a bearer came to the room with hot tea and biscuits. He smiled at the expression on my face and assured me that it was only Khairi outside the door, making friendly inquiries about the new guest in the house. I finished my tea, had a quick shower and went to the main house.

Saroj Raj Chaudhury was sitting on a large chair. There was a sloth bear behind him, holding on to his waist and making gurgling sounds. He said, “Get down, Jambu, get down’’ and rose to greet me – a frail man in his fifties, slightly balding on the top. We got talking. I didn’t find a gruff and rough no-nonsense man. What I found was one of the most humane human beings I had ever met in my life.

Questions :
(i) Describe the bus the writer had boarded.
(ii) When did he reach Jashipur?
(iii) Describe the treatment according to the writer in Jashipur.
(iv) How did a bearer react to the writer’s terror-stricken face?
(v) Throw light on Jambu.

Answers :
(i) The bus the writer had boarded was packed with passengers beyond its capacity.
(ii) The writer reached Jashipur sometime before 4 a.m. It was half-dark.
(iii) As soon as the writer reached Jashipur, the Forest Guard led him to the guest house, and showed him his room. He assured the writer of the presence of a jug filled with water. Later a bearer provided him with hot tea and biscuits in his room.
(iv) A bearer reacted smilingly to the writer’s terror-stricken face.
(v) The bear Jambu was seen in a lazy mood, behind Saroj Raj Chaudhury, and holding on to his waist making gurgling sounds.

3. Read through the extract and answer the questions that follow.
Here is the first story that emerged from this very unusual man between sips of coffee: “As you will see, I have different species of wild animals in this house. They all came in at different stages of their lives. I have debunked the theory that they cannot co-exist unless they are together from infancy. One thing I wanted to experiment with was the reaction of a young tiger to a snake. One day, when Khairi was much younger, we found a baby krait in the house. As you know, the krait is one of the most poisonous snakes.

I was noting Khairi’s reaction to its presence. Khairi was curious to know more about this strange new creature. Every time the krait got too close to Khairi, I would pull it back by its tail. This went on for some time. At some point, I must have been a little unmindful. It turned around and bit me. I immediately tied a tourniquet above that and got the poison out. I saw the doctor as soon as possible. Luckily it was a baby. Still, some of the poison got into my bloodstream and as a result, I am now a permanent patient of hypo-glycemia.”

By the time he finished this astonishing story, Jambu took a fancy to me and climbed behind to give me his bear hug. A stern ‘no’ from Saroj was enough to dissuade him from this expression of fondness. As the day progressed, between our conversations and the intermittent crackle on the VHF wireless set by which he was giving instructions to his men in the forests, I got to know a veritable joint family that was living inside the compound – a mongoose, a pangolin, wild cat twins, a country dog, and a blind Hyena. Each had a name.

Questions :
(i) When did Saroj narrate the first story to the writer?
(ii) What is the theory that Mr. Chaudhury has exaggerated?
(iii) ‘It turned round and bit me.’ What does ‘It’ refer to?
(iv) How was Mr. Saroj Chaudhury’s story?
(v) Throw light on Jambu.

Answers :
(i) Between sipping coffee, Saroj narrated the first story to the writer.
(ii) The theory that Mr. Chaudhury has exaggerated is that different species of wild animals cannot co-exist unless they are together from childhood.
(iii) ‘It’ refers to a krait, one of the most poisonous snakes.
(iv) Mr. Chaudhury’s story was wonderful.
(v) The bear Jambu was a picture of fondness. He started liking the writer climbing behind. The creature was interested to give a bear hug, but in vain, because of Mr. Chaudhury’s strict ‘no’.

4. Read through the extract and answer the questions that follow.
Khairi’s story started on October 5, 1974, when 12 Kharia tribals of Similipal brought a two-month-old tiger cub to Saroj Raj Chaudhury, an officer of the Indian Forest Service. Saroj noticed that it was a female – famished and confused. His first experience of what was to become his passion in life was angry snarls and scratching claws. But, the veteran forester and instinctive lover of wildlife knew how to handle a hungry, angry cub. He imitated the sounds of a mother tigress.

“Within minutes, her confidence was firmly anchored in the fostering human,” is how he recalled those first few minutes between the legends. Early the next morning, Saroj started his inspection of the Tiger Reserve area. I tagged along in the jeep that snaked through a narrow road in the woods amidst lush foliage. “My mother gave me a gun for my eighth birthday. As a young man, I shot wildlife with abandon. But soon, I realized that there is greater happiness in conserving these beautiful animals that do no wanton harm to man” is one of the things he told me about his life during that long travel.

At that time, he was an authority on the tiger and Director of Project Tiger in India. Saroj introduced the Tiger Tracing Method of tiger census where the pugmarks of each animal with distinctive measurements and characteristics are meticulously recorded. For the night, we camped at a guest house deep in the jungle. It was a wooden structure with functional rooms and a bath. It was built on stilts and stood a good 15 feet above the ground. I experienced for the first time, one night atop a magnificent machan.

Questions :
(i) What picture of Saroj Chaudhury do you get in the 1st para of the extract?
(ii) When did he go to inspect the Tiger Reserve area?
(iii) Describe his journey to this place.
(iv) When did Mr. Chaudury’s realization concerning the conservation of wildlife come?
(v) What was the writer’s experience of staying one night at the guest house a top?

Answers :
(i) In the first para of the extract, we learn that Saroj Chaudhury, an officer of the Indian Forest Service, was a veteran forester and instinctive lover of wildlife. The way he handled the two-year-old tiger cub is a case in point.
(ii) Early the next morning of his arrival, he went to visit the Tiger Reserve area.
(iii) In the course of his journey, Saroj Chaudhury in the jeep went through a narrow road in the woods amidst leaves of trees growing luxuriantly.
(iv) Mr. Chaudhury’s realization concerning the conservation of wildlife came when he, as a young man, had shot wildlife in a carefree life.
(v) The writer’s experience of staying one night at the guest house atop was very beautiful.

II. Multiple Choice Questions (MCQs) with Answers
Choose the correct option.

Unit – I
The text
Khairi made ………………. night.

Question 1.
Who was the tigress of Jashipur?
(a) Nhairi
(b) Khairi
(c) Bhairi
(d) Shairi
Answer:
(b) Khairi

Question 2.
Where did Khairi live?
(a) Bhitarkanika
(b) Similipal forests
(c) Kanchanjanga
(d) National Zoo, Kolkata
Answer:
(b) Similipal forests

Question 3.
Who was N. S. Ayyangar ?
(a) a politician
(b) a senior journalist
(c) a zoologist
(d) a veterinary doctor
Answer:
(b) a senior journalist

Question 4.
Khairi was under the care of:
(a) N. S. Ayyangar
(b) Hariharan
(c) Saroj Raj Chaudhury
(d) Nihar Raj Chaudhury
Answer:
(c) Saroj Raj Chaudhury

Question 5.
Khairi was a :
(a) domesticated tigress
(b) wild tigress
(c) zoo tigress
(d) tigress of a circus
Answer:
(a) domesticated tigress

Question 6.
Who had invited the author to Khairi- Jashipur?
(a) Nihar Raj Chaudhury
(b) Saroj Raj Chaudhury
(c) N. S. Ayyangar
(d) Forest ranger
Answer:
(b) Saroj Raj Chaudhury

Unit – II
The text
I packed my bag, ……………… met in my life.

Question 7.
Who escorted the author to the guest house from the bus stop at Khairi- Jashipur?
(a) Forest Ranger
(b) Forest Guard
(c) Forest Guide
(d) none of the above
Answer:
(b) Forest Guard

Question 8.
What was Khairi doing outside the guest house when the author was inside the room?
(a) making friendly enquiries
(b) making fun
(c) searching for enemies if any
(d) none of the above
Answer:
(a) making friendly enquiries

Question 9.
Who was Jambu?
(a) a monkey
(b) a bear
(c) a sloth bear
(d) a donkey
Answer:
(c) a sloth bear

Unit – III
The text
Here is the first story……………..had a name.

Question 10.
The name of the snake living in Mr. Chaudhury’s house was :
(a) cobra
(b) Python
(c) krait
(d) rattlesnake
Answer:
(c) krait

Question 11.
Mr. Chaudhury was bitten by a snake and as a result, he became a permanent patient of
(a) diabetics
(b) hypo-glycaemia
(c) leukaemica
(d) high blood pressure
Answer:
(b) hypo-glycaemia

Question 12.
How did Mr. Chaudhury instruct his men in the forests?
(a) on the computer internet
(b) on the VHF wireless
(c) on the T.V.
(d) by the mobile phone
Answer:
(b) on the VHF wireless

Question 13.
What did Mr. Saroj Chaudhury do when he was bitten by a krait, the poisonous snake?
(a) immediately cut the biting place
(b) immediately applied for medicine
(c) immediately tied a tourniquet
(d) met a doctor
Answer:
(c) immediately tied a tourniquet

Unit – IV
The text
Khairi’s story…….. magnificent machan.

Question 14.
When did Khairi come to Mr. Chaudhury’s hands?
(a) Nov. 5, 1974
(b) Dec. 5, 1974
(c) Oct. 5, 1974
(d) Sept. 5, 1974
Answer:
(c) Oct. 5, 1974

Question 15.
Who got the baby tiger and handed it over to Mr. Chaudhury?
(a) 12 Kharia tribals
(b) 12 Gonda tribals
(c) 12 Santhal tribals
(d) none of them
Answer:
(a) 12 Kharia tribals

Question 16.
Who was Saroj Raj Chaudhury?
(a) Indian Police Service officer
(b) Indian Foreign Service officer
(c) Indian Forest Service officer
(d) a low cadre forest official
Answer:
(c) Indian Forest Service officer

Question 17.
What do you mean by the word ‘famished’?
(a) very tired
(b) very smart
(c) very careful
(d) very hungry
Answer:
(d) very hungry

Question 18.
How did Mr. Choudhury handle and consoled the hungry and angry cub?
(a) by giving it milk to drink
(b) by showing her the picture of a mother tigress
(c) by making the sounds of a mother tigress
(d) by leaving it all alone
Answer:
(c) by making the sounds of a mother tigress

Question 19.
Where does lie the greater happiness of Mr. Chaudhury?
(a) in killing animals
(b) in conserving animals
(c) in destroying animals’ habitat
(d) none of the above
Answer:
(b) in conserving animals

Question 20.
What do you mean by the word ‘wanton harm’?
(a) no harm
(b) less harm
(c) reckless harm
(d) secret harm
Answer:
(c) reckless harm

Question 21.
Who was then an authority on the tiger and Director of Project Tiger in India?
(a) Nihar Raj Chaudhury
(b) Bhasker Raj Chrudhury
(c) Saroj Raj Chaudhury
(d) N. S. Ayyangar
Answer:
(c) Saroj Raj Chaudhury

Question 22.
Which parts of speech is the word ‘meticulously’?
(a) noun
(b) verb
(c) adverb
(d) adjective
Answer:
(c) adverb

Question 23.
Which according to the author was a magnificent machan?
(a) a guest house deep in the jungle
(b) the building where Saroj Chaudhury lived
(c) the house where Khairi and other animals lived
(d) none of the above
Answer:
(a) a guest house deep in the jungle

Unit – V
The text
I went to ……………… 25 years hence.

Question 24.
When did the author come to Khairi- Jashipur again?
(a) after six months
(b) after four months
(c) after three months
(d) after seven months
Answer:
(c) after three months

Question 25.
What was the purpose of the second visit of the author to Khairi-Jashipur?
(a) to know more about Mr. Chaudhury
(b) to know more about Khairi
(c) to see the place again
(d) to enjoy the nature
Answer:
(b) to know more about Khairi

Question 26.
Which new animal do he saw in his second visit?
(a) a pangolin
(b) a blind hyena
(c) a rattlesnake
(d) a young python
Answer:
(d) a young python

Question 27.
What did the author search about in his second visit?
(a) about Saroj Chaudhury and his passion
(b) about World Wildlife Fund
(c) about the animals
(d) none of the above
Answer:
(a) about Saroj Chaudhury and his passion

Question 28.
Where came a wireless message to the Chaudhury?
(a) Department of Forest
(b) World Wildlife Fund
(c) Central Government
(d) none of the above
Answer:
(b) World Wildlife Fund

Question 29.
To whom the author has described a legend behind a legend?
(a) Khairi
(b) Mr. Saroj Chaudhury.
(c) Nihar Raj Chaudhury
(d) none of the above
Answer:
(b) Mr. Saroj Chaudhury.

Question 30.
Where did the author meet Mr. Chaudhury last time?
(a) at New Delhi
(b) in Dum Dum Airport
(c) at Mumbai
(d) at Jashipur
Answer:
(b) in Dum Dum Airport

Question 31.
Who made the forest famous?
(a) Mr. Chaudhury
(b) Khairi
(c) author
(d) tourist
Answer:
(b) Khairi

Introducing the Author:
Hariharan Balakrishnan excels in the art of writing articles on wildlife. He is also a columnist.

About the Topic:
‘The Legend Behind A Legend’, as the title suggests, deals with two legends: Mr. Saroj Raj Chaudhury and Khairi; the former was an authority on tiger and Director of Project Tiger, and the latter a magnificent famous tigress. Mr. Chaudhury was a foster father of Khairi. The writer showers accolade on both legends.

Summary:
The writer takes us back to the Similipal forests of Odisha, which served as the habitat of Khairi, the tigress of Jashipur. The place carved out a name for itself, thanks to this tigress. She was not a queen of the robbers. She was the queen of Jashipur. The writer goes down memory lane. 25 years have elapsed since he had spent two days and two nights with Khairi and other wild animals of Saroj and Nihar. A news item on the latest exploits of Khairi evoked his interest to visit the place. He came to know that Saroj Raj Chaudhury was taking care of Khairi.

He wrote a letter to him and met with a prompt response. He was filled with great joy. Mr. Chaudhury invited him to Khairi – Jashipur, giving him particular directions on how to reach there. The writer apprised him of when and how he would visit him. This was his meeting. The writer left Berhampur by train. He reached in Jashipur before 4 a.m. by an overpacked bus. The Forest Guard was present there to cordially welcome him. He made all comfortable arrangements for the writer. He spent an hour of sound sleep.

Terror gripped him when he heard the clear voice of the Tiger just outside the door. Within minutes, the bearer came to his room and served him with hot tea and biscuits. He smiled at the panic-stricken expression of his face. He assured the writer of the presence of Khairi who was making loving enquiries about the new guest in the house. He met Saroj Chaudhury, a frail man in his fifties, slightly balding on the top; the latter greeted the former in a polite manner after asking Jambu, the bear, to get down, because the animal holding on to Chaudhury’s waist.

They conversed with each other. In Mr. Chaudhury, the writer found a humble and careful man. One of the most caring persons he had ever met in his life was Mr. Chaudhury. While sipping tea, Mr. Chaudhury narrated a story to the writer. He drew the latter’s attention to the presence of different species of wild animals in his house. They all had not come at the same time. He exaggerated the theory that they could not exist with each other unless they were together from childhood. He conducted an experiment to ascertain the truth.

He brought Khairi and one of the most dangerous snakes, krait. The writer marked Khairi’s reaction – it was one of fondness for the strange creature. Whenever the krait goes too close to Khairi, Mr. Chaudhury would pull it by back by its tail. Once he became inattentive and was bitten by the krait. Some of its poison entered his blood and therefore, he was now a permanent patient with low blood pressure. As soon as Mr. Chaudhury finished this wonderful story, Jambu tried to give the writer his bear hug, but the former’s stern warning prevented him from doing so.

Mr. Chaudhury has a well-knit joint family that was living inside the compound. It comprised a mongoose, a pangolin, wild cat twins, a country dog, and a blind Hyena, each having a name. Khairi’s story dates back to October 5, 1974, when twelve Khaira tribals of Similipal brought a two-month-old tiger cub to Saroj Raj Chaudhury who was an IFS officer. He found the female cub in a state of hunger and confusion. He managed it by imitating the sounds of a mother tigress. Her anger and disturbance vanished at once.

She was in her element. Saroj became nostalgic. He recollected his birthday when his mother had presented him with a gun, with which he, as a young man, shot wildlife in a carefree manner. But, soon he realized that it was a mistake and happiness lies in the conservation of these harmless beautiful animals. As the Director of Project Tiger, Saroj was the first to introduce the Tiger Tracing Method of tiger census. For the night, both camped at a guest house deep in the jungle. Never before had the writer experienced spending one night in a magnificent Wooden structure with rooms and baths that stood 15 feet high from the ground.

It is three months since the writer last visited Khairi-Jashipur. Then he went there again for the second time to know more about Khairi. Saroj welcomed him in his characteristic gracious manner. This time the writer saw a python as a pet of Chaudhury. His passion for wildlife knew no end. In a response to a message from the World Wildlife Fund, he went to New Delhi by plane with a view to attending an important meeting. In just over three months, Khairi passed away. Saroj Raj Chaudhury did not survive for long. The topic comes to a close with the writer saluting Saroj Chaudhury. He is worthy of it.

ସାରାଂଶ:
“The Legend Behind A Legend’ ବିଷୟଟି ଦୁଇଟି କିମ୍ବଦନ୍ତୀକୁ ଆଧାର କରି ରଚିତ । ବାଘମାନଙ୍କ ଉପରେ ନିଜର ଦକ୍ଷତା ହାସଲ କରିପାରିଥିବା Project Tigerର ନିର୍ଦ୍ଦେଶକ Mr. Saroj Raj Chaudhury ଏବଂ ପ୍ରସିଦ୍ଧ ମହାବଳ ବାଘୁଣୀ ‘ଖଇରୀ’ର ଜୀବନୀ ଉପରେ ଏହା ପର୍ଯ୍ୟବସିତ । ସରୋଜ ରାଜ ଚୌଧୁରୀ ଖଇରୀର ପାଳିତ ପିତା ଭଳି ଥିଲେ । ଶିମିଳିପାଳ ଜଙ୍ଗଲର ପ୍ରସିଦ୍ଧ ବାଘୁଣୀ ଥିଲା ଖଇରୀ । ସେ ଥୁଲା ଯଶିପୁରର ମହାବଳ ବାଘୁଣୀ । ଲେଖକ ସ୍ମୃତିଚାରଣ କରି କହନ୍ତି ଯେ ୨୫ ବର୍ଷ ପୂର୍ବେ ସେ ଦୁଇ ଦିନ ଓ ଦୁଇ ରାତି ଖଇରୀ ସହିତ ସରୋଜ ଓ ନିହାରଙ୍କ ବନ୍ୟଜନ୍ତୁ ସଂଗ୍ରହାଳୟରେ ସମୟ ଅତିବାହିତ କରିଥିଲେ । ଲେଖକ ଖଇରୀର ଅଦ୍ଭୁତ କାର୍ଯ୍ୟକଳାପ ବିଷୟରେ ‘The Statesman’ର ଏକ ଖବରରୁ ଜାଣିପାରିଥିଲେ ଏବଂ ସେଇ ସ୍ଥାନକୁ ବୁଲିଯିବା ପାଇଁ ଆଗ୍ରହ ପ୍ରକାଶ କରିଥିଲେ ।

ସେ ଜାଣିବାକୁ ପାଇଲେ ଯେ, ଖଇରୀ ସରୋଜ ରାଜ ଚୌଧୁରୀଙ୍କ ତତ୍ତ୍ଵାବଧାନରେ ପାଳିତ ହେଉଛି । ସେଥ‌ିପାଇଁ ଲେଖକ ସେଠାକୁ ଯିବାର ଅନୁମତି ମାଗି ସରୋଜଙ୍କ ପାଖକୁ ପତ୍ର ଲେଖିଲେ । ସରୋଜ ଅତି ଖୁସିରେ ଲେଖକଙ୍କୁ ନିମନ୍ତ୍ରଣ ପତ୍ର ଲେଖୁଲେ ଏବଂ ଯିବାପାଇଁ ସମସ୍ତ ତଥ୍ୟ ସହିତ ତାରିଖ ମଧ୍ୟ ଜଣାଇଲେ । ଭୋର ୪ଟା ସମୟରେ ଲେଖକ ଏକ ଜନଗହଳିପୂର୍ଣ୍ଣ ବସ୍‌ରେ ବସି ଖଇରୀ-ଯଶିପୁରରେ ପହଞ୍ଚିଲେ । ତାଙ୍କୁ ଉତ୍ତମ ଆତିଥ୍ୟ ସତ୍କାର କରାଗଲା । ଖାଦ୍ୟ ଓ ବିଶ୍ରାମ ପାଇଁ ସବୁପ୍ରକାରର ବ୍ୟବସ୍ଥା କରାଯାଇଥିଲା । ଲେଖକ ବିଶ୍ରାମ ନେଉଥ‌ିବାବେଳେ ଦ୍ଵାରଦେଶର ବାହାରେ ବାଘୁଣୀର ଗର୍ଜନ ଶୁଣି ଭୟଭୀତ ହୋଇଯାଆନ୍ତି । ଏହାର ଅଳ୍ପ ସମୟ ପରେ ଜଣେ ବ୍ୟକ୍ତି ଚା’ ଓ ବିସ୍କୁଟ ଧରି ଆସିଲେ ଏବଂ କହିଲେ ଖଇରୀ ବାଘୁଣୀ ବାହାରେ ଥାଇ ଆନନ୍ଦରେ ଗର୍ଜନ କରି ନୂତନ ଅତିଥିଙ୍କୁ ସ୍ଵାଗତ କରୁଛି ।

ତା’ପରେ ଲେଖକ ସରୋଜଙ୍କୁ ସାକ୍ଷାତ କଲେ । ଦୁର୍ବଳ ଶରୀରଧାରୀ ପଚାଶ ବର୍ଷୀୟ ଏହି ବ୍ୟକ୍ତିଜଣକ ଟିକେ ଚନ୍ଦା ଥିଲେ । ସେ ଲେଖକଙ୍କୁ ଅତି ଭାବରେ ସ୍ଵାଗତ କଲେ ଏବଂ ତାଙ୍କ ଅଣ୍ଟାକୁ ଧରି ଠିଆ ହୋଇଥିବା ଭାଲୁକୁ ବସିବାକୁ କହିଲେ । ପରସ୍ପର କଥାବାର୍ତ୍ତା ହେଲେ । ଲେଖକ ସରୋଜ ରାଜ ଚୌଧୁରୀଙ୍କଠାରେ ଭଦ୍ର ଯେଉଁ ବିନମ୍ର ସ୍ଵଭାବ ଦେଖିଥିଲେ, ସେ ତାଙ୍କ ଜୀବନରେ ଅନ୍ୟ କାହାଠାରେ ଦେଖିନଥିଲେ । କଥାବାର୍ଭା ସମୟରେ ଶ୍ରୀଯୁକ୍ତ ଚୌଧୁରୀ ମହାଶୟେ କହିଲେ ତାଙ୍କ ଘର କିଭଳି ଭାବେ ବିଭିନ୍ନ ଜୀବଜନ୍ତୁମାନଙ୍କର ଏକ ଆଶ୍ରୟସ୍ଥଳୀ ହୋଇଯାଇଛି । ଜୀବଜନ୍ତୁମାନଙ୍କୁ ଯଦି ଶୈଶବାବସ୍ଥାରୁ ଏକାଠି ରଖାଯାଏ, ସେମାନେ ପରସ୍ପର ସହିତ ମିଳିମିଶି ରହିପାରିବେ ବୋଲି ସେ କହିଥିଲେ । ଏହାର ପରୀକ୍ଷଣ ନିମନ୍ତେ ସେ ଖଇରୀ ନିକଟରୁ ତାଙ୍କ ଅଗଣାରୁ ଧରା ଯାଇଥିବା

ଏକ ବିଷଧର ନାଗସାପକୁ ଆଣିଥିଲେ । ସେତେବେଳେ ଖଇରୀ ଖୁବ୍ ଛୋଟ ଥିଲା । ଖଇରୀର ସେହି ସାପ ପ୍ରତି ପ୍ରତିକ୍ରିୟାକୁ ଲେଖକ ଲକ୍ଷ୍ୟ କରିଥିଲେ । ଏଇ ବିଷଧର ସାପ ପ୍ରତି ଖଇରୀର ଆଗ୍ରହ ପ୍ରକାଶ ପାଇଥିଲା । ଯେତେବେଳେ ଏହି ସାପଟି ଖଇରୀ ଆଡ଼କୁ ଆଗ୍ରସର ହେବାକୁ ଚାହୁଁଥିଲା, ଲେଖକ ତାକୁ ଲାଞ୍ଜ ଧରି ପଛକୁ ଟାଣି ଦେଉଥିଲେ । ଥରେ ସେ ଅନ୍ୟମନସ୍କ ହୋଇ ଏହି ବିଷଧର ନାଗସାପକୁ ଟାଣିଦେବା ସମୟରେ, ସେ ଲେଖକଙ୍କୁ କାମୁଡ଼ି ଦେଇଥିଲା । ତାଙ୍କ ରକ୍ତରେ କିଛି ବିଷ ପ୍ରବାହିତ ହୋଇଯାଇଥିଲା । ତା’ପରଠାରୁ ସେ ନିମ୍ନ ରକ୍ତଚାପ ରୋଗରେ ପୀଡ଼ିତ ହୋଇଥିଲେ । ଏହି ସମୟରେ ଭାଲୁ ଲେଖକଙ୍କୁ କୁଣ୍ଢାଇବାକୁ ଆସୁଥିଲା । କିନ୍ତୁ ସରୋଜଙ୍କ କଡ଼ା ନିର୍ଦ୍ଦେଶ ହେତୁ ସେ ସେଥୁରୁ ନିବୃତ୍ତ ରହିଲା ।

ସରୋଜଙ୍କର ଏହି ଯୌଥ ପରିବାରରେ ସମସ୍ତେ ଯଥା ନେଉଳ, ଗୋଧ, ପକ୍ଷୀ, ସାପ, ଦେଶୀ କୁକୁର, ବାଘ, ଭାଲୁ ସମସ୍ତେ ଉତ୍ତମ ବୁଝାମଣାରେ ଏକ ଶୃଙ୍ଖଳିତ ଜୀବନଯାପନ କରୁଥିଲେ । ଖଇରୀ ଯେତେବେଳ ଏକ ୨ ମାସର ବାଘଛୁଆ ଥିଲା, ସେତେବେଳେ ଶିମିଳିପାଳର ୧୨ ଜଣ ଖରିଆ ଆଦିବାସୀ ତାକୁ ସରୋଜଙ୍କ ନିକଟକୁ ଆଣିଥିଲେ । ସେ ଥିଲେ ଜଙ୍ଗଲ ବିଭାଗର ଜଣେ ଅଧିକାରୀ ଥିଲେ । ଏହି ବାଘଛୁଆଟି ଥୁଲା ଭୋକିଲା ଓ ବିବ୍ରତ । ସେ ରାଗି ଗର୍ଜନ କରୁଥିଲା ଓ ତା’ର ପଞ୍ଝାକୁ ଘୋଷାରୁଥିଲା । ସରୋଜ ଏକ ମା’ ବାଘର ସ୍ଵରକୁ ଅନୁକରଣ କରିଥିଲେ ଯାହାକି ଖଇରୀକୁ ପୋଷା ମନେଇବା ପାଇଁ ଚମତ୍କାର ଭାବେ କାର୍ଯ୍ୟ କରିଥିଲା । ସେଥ‌ିରେ ସେ ସଫଳ ହୋଇଥିଲେ ଏବଂ ଖୁସିରେ ବିଭୋର ହୋଇଯାଇଥିଲେ । ତା’ ପରଦିନ ସକାଳୁ ସରୋଜ ଲେଖକଙ୍କୁ ନେଇ ଏକ ଜିପ୍‌ରେ ବ୍ୟାଘ୍ର ସଂରକ୍ଷଣ ଅଞ୍ଚଳ ବୁଲିବାକୁ ଗଲେ ।

ତାହା ଥିଲା ଏକ ସରୁ ଅଣଓସାରିଆ ରାସ୍ତା । ବାଟରେ ସରୋଜ ଅତୀତର ସ୍ମୃତିଚାରଣ କରି କହିଲେ, ତାଙ୍କୁ ଜନ୍ମଦିନରେ ତାଙ୍କ ମା’ ଏକ ବନ୍ଧୁକ ଉପହାର ଦେଇଥିଲେ ଯାହାଦ୍ଵାରା ଜଣେ ଯୁବକଭାବେ ସେ ବନ୍ୟଜନ୍ତୁମାନଙ୍କୁ ମୁକ୍ତଭାବେ ଶିକାର କରିଥିଲେ । ତା’ପରେ ସେ ଅନୁଭବ କଲେ ଯେ ପଶୁମାନଙ୍କୁ ମାରିବା ଏକ ଅପରାଧ। ଆନନ୍ଦ ଥାଏ ଏହି ନିରୀହ ସୁନ୍ଦର ଜୀବଜନ୍ତୁମାନଙ୍କୁ ସଂରକ୍ଷଣ କରିବାରେ । ବ୍ୟାଘ୍ର ପ୍ରକଳ୍ପର ନିର୍ଦ୍ଦେଶକ ଭାବେ ସେ ପ୍ରଥମେ ବ୍ୟାଘ୍ର ଗଣନା ପ୍ରଣାଳୀ ପ୍ରଚଳନ କରିଥିଲେ । ସେହି ରାତ୍ରିରେ ଉଭୟେ ଘଞ୍ଚ ଜଙ୍ଗଲ ମଧ୍ୟରେ ଥିବା ଏକ ଅତିଥୁ ଗୃହରେ ରାତ୍ରିଯାପନ କରିଥିଲେ । ଏହା ପୂର୍ବରୁ ଲେଖକ ଭୂମିଠାରୁ ୧୫ ଫୁଟ ଉଚ୍ଚରେ କାଠରେ ନିର୍ମିତ ଏକ ଘରେ ରହିବାର ଆନନ୍ଦ କେବେ ଅନୁଭବ କରିନଥିଲେ । ସେହିଘରେ କେତେଗୁଡ଼ିଏ କୋଠରୀ ସହ ଏକ ଗାଧୁଆଘର ଥିଲା। ତିନିମାସ ପରେ ଲେଖକ ପୁନର୍ବାର ସେହି ଖଇରୀ ଓ ଯଶିପୁରକୁ ବୁଲିବାକୁ ଗଲେ ।

ଖଇରୀ ବିଷୟରେ ଅଧିକ ଜାଣିବାର ଇଚ୍ଛା ତାଙ୍କୁ ସେଠାକୁ ପୁନର୍ବାର ଟାଣି ନେଇଥିଲା । ଶ୍ରୀ ଚୌଧୁରୀ ତାଙ୍କୁ ସ୍ଵାଗତ କଲେ ଏବଂ ଭାରି ଖୁସି ହେଲେ । ସେ ସେଠାରେ ଅନ୍ୟ ଜୀବମାନଙ୍କ ସହିତ ଏକ ଆଠ ଫୁଟ ଲମ୍ବର ଏକ ଅଜଗର ସାପ ଦେଖିଲେ । ତା’ପରେ ସେ ଚୌଧୁରୀ ଜୀବଜନ୍ତୁମାନଙ୍କୁ ସଂରକ୍ଷଣ କରିବାର ନିଶା ବିଷୟରେ ଜାଣିବାକୁ ଆଗ୍ରହ ପ୍ରକାଶ କଲେ । ଏହି ସମୟରେ ଏକ ଜରୁରୀ ସଭାରେ ଯୋଗ ଦେବାପାଇଁ ବିଶ୍ବ ବନ୍ୟଜନ୍ତୁ ପାଣ୍ଠି ତରଫରୁ ଏକ ତାରବାର୍ତ୍ତା ଆସି ପହଞ୍ଚିଲା। ସେ କଲିକତାର ଦମ୍ଦମ୍ ଉଡ଼ାଜାହାଜ ପଡ଼ିଆରୁ ବିମାନ ଯୋଗେ ଦିଲ୍ଲୀ ଯାତ୍ରା କଲେ । ଏହା ଥିଲା ଚୌଧୁରୀଙ୍କ ସହିତ ଲେଖକଙ୍କର ଶେଷ ସାକ୍ଷାତ । ଏହାର ତିନି ମାସ ପରେ ଖଇରୀର ମୃତ୍ୟୁ ଘଟିଥିଲା । ତା’ପରେ ଖଇରୀ ବିନା ଚୌଧୁରୀ ମଧ୍ୟ ବେଶି ଦିନ ବଞ୍ଚୁରି ନ ଥିଲେ ।

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 14 Limit and Differentiation Ex 14(e) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 14 Limit and Differentiation Exercise 14(e)

Question 1.

Find derivatives of the following functions from the definition :
(i) 3x² – \(\frac{4}{x}\)
Solution:

(ii) (4x – 1)²
Solution:

(iii) 2 + x + √x³
Solution:

(iv) x – \(\sqrt{x^2-1}\)
Solution:

(v) \(\frac{1}{x^{2 / 5}}\) + 1
Solution:

Question 2.
(i) cos (ax + b)
Solution:
Let y = cos (ax + b)
Then \(\frac{d y}{d x}\) = -sin (ax + b) × \(\frac{d}{d x}\) (ax + b) by chain rule.
= -sin(ax + b). a = -a sin (ax + b)

(ii) x² sin x
Solution:
Let y = x² sin x
Then \(\frac{d y}{d x}=\frac{d}{d x}\) (x²). sin x + x² \(\frac{d}{d x}\)
[ ∴ \(\frac{\mathrm{d}}{\mathrm{dx}}(u \cdot v)=\frac{d u}{d x} \cdot v+u \cdot \frac{d v}{d x}\)
= 2x sin x + x² cos x

(iii) \(\sqrt{\tan x}\)
Solution:
Ley y = \(\sqrt{\tan x}\) = \((\tan x)^{\frac{1}{2}}\)
Then \(\frac{d y}{d x}=\frac{1}{2}(\tan x)^{-\frac{1}{2}} \times \frac{d}{d x}\)(tan x)
= \(\frac{1}{2 \sqrt{\tan x}}\) sec² x.

(iv) cot x²
Solution:
Let y = cot x²
Then \(\frac{d y}{d x}=-{cosec}^2 x^2 \times \frac{d}{d x}\left(x^2\right)\)
= – cosec² x². 2x
= -2x. cosec² x²

(v) cosec 3x
Solution:
Let y = cosec 3x
Then \(\frac{d y}{d x}\) = -3 cosec 3x . cot 3x

Question 3.
(i) √x sin x
Solution:
Let y = √x sin x
Then \(\frac{d y}{d x}=\frac{d}{d x}\)(√x) sin x + √x. \(\frac{d}{d x}\)(sin x)
= \(\frac{1}{2 \sqrt{x}}\) sin x + √x. cos x

(ii) \(\sqrt{x^2+1}\)cos x
Solution:

(iii) tan x – x² – 2x
Solution:
Let y = tan x – x² – 2x
\(\frac{d y}{d x}\) = sec² x – 2x – 2

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 14 Limit and Differentiation Ex 14(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 14 Limit and Differentiation Exercise 14(d)

Question 1.

Find the derivative of the following functions ‘an initio’, that is, using the definition.
(i) 2x³
Solution:

(ii) x⁴
Solution:

(iii) x² + 1
Solution:

(iv) \(\frac{1}{x}\)
Solution:

(v) \(\frac{1}{3 x+2}\)
Solution:

(vi) \(\frac{1}{x^2}\)
Solution:

(vii) \(\frac{x}{x+1}\)
Solution:

(viii) t(t – 1)
Solution:

(ix) s² – bs + 5
Solution:

(x) √x
Solution:

\(\frac{1}{\sqrt{z}+\sqrt{z}}=\frac{1}{2 \sqrt{z}}\)

(xi) tan θ
Solution:

(xii) cos 2θ
Solution:

(xiii) x sin x
Solution:

Question 2.
Find the derivative of the following function from the definition at the indicated points. Test whether the following functions are differentiable at the indicated points. If so find the derivative.
(i) x⁴ at x = 2
Solution:

(ii) 2x² + x + 1 at x = 1
Solution:

(iii) x³ + 2x² – 1 at x = 0
Solution:
Let x³ + 2x² – 1
Then \(\left.\frac{d y}{d x}\right]_{x=0}\) = \(\lim _{h \rightarrow 0}\left[\frac{\left(h^3+2 h^2-1\right)-(-1)}{h}\right]\)
= \(\lim _{h \rightarrow 0}\) (h² + 2h) = 0

(iv) tan x at x = \(\frac{\pi}{3}\)
Solution:

(v) \(\sqrt{3 x+2}\) at x = 0
Solution:

(vi) In x at x = 2
Solution:

(vii) \(e^x\) at x = 1
Solution:

(viii) sin² θ at θ = \(\frac{\pi}{4}\)
Solution:

Question 3.
\(\frac{x+1}{x-1}\) at x = -1
Solution:
We know that a function f(x) is differentiable at a point
x = c if (i) L.H.D. exists
(ii) R.H.D. exists
(iii) L.H.D. = R.H.D
Let f(x) = \(\frac{x+1}{x-1}\)

Thus L.H.D. and R.H.D. both exist and L.H.D. = R.H.D.
Hence f(x) is differentiable at x = -1 and the derivative is –\(\frac{1}{2}\)

Question 4.
√x at x = 0
Solution:
Let f(x) = √x
Then f(0) = 0

Question 5.
f(x) = \(\left\{\begin{array}{r}
1-x, x \leq \frac{1}{2} \\
x, x>\frac{1}{2}
\end{array} \text { at } x=\frac{1}{2}\right.\)
Solution:

Question 6.
f(x) = \(\left\{\begin{array}{r}
\sin \frac{1}{x}, x \neq 0 \\
0, x=0
\end{array}\right.\) at x = 0
Solution:
f(0) = 0

Question 7.
f(x) = \(\left\{\begin{array}{r}
x^2 \sin \frac{1}{x^{\prime}}, x \neq 0 \\
0, x=0
\end{array}\right.\) at x = 0
Solution:
f(0) = 0

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 14 Limit and Differentiation Ex 14(f) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 14 Limit and Differentiation Exercise 14(f)

Differentiate.

Question 1.
x⁸ + x⁷
Solution:
Let  y = x⁸ + x⁷
Then \(\frac{d y}{d x}\) = 8x⁷ + 7x⁶

Question 2.
x^5/3 – x^1/2
Solution:
Let y = x^5/3 – x^1/2
\(\frac{d y}{d x}=\frac{5}{3} x^{\frac{2}{3}}-\frac{1}{2} x^{-\frac{1}{2}}\)

Question 3.
x³ – 5x
Solution:
Let y = x³ – 5x
Then \(\frac{d y}{d x}\) = 3x² – 5

Question 4.
√x + \(\frac{1}{\sqrt{x}}-\sqrt[3]{x^2}\)
Solution:
Let y = √x + \(\frac{1}{\sqrt{x}}-\sqrt[3]{x^2}\)
= \(x^{\frac{1}{2}}+x^{-\frac{1}{2}}-x^{\frac{2}{3}}\)
⇒ \(\frac{d y}{d x}=\frac{1}{2} x^{\frac{-1}{2}}-\frac{1}{2} x^{\frac{-3}{2}}-\frac{2}{3} x^{\frac{-1}{3}}\)

Question 5.
x² + 2x – sin x + 5
Solution:
x² + 2x – sin x + 5
\(\frac{d y}{d x}\) = 2x + 2 – cos x

Question 6.
\(\frac{1}{2} x^{\frac{1}{2}}+\frac{1}{3} x^{\frac{1}{3}}\)
Solution:
\(\frac{1}{2} x^{\frac{1}{2}}+\frac{1}{3} x^{\frac{1}{3}}\)
\(\frac{d y}{d x}=\frac{1}{4} x^{\frac{-1}{2}}+\frac{1}{9} x^{\frac{-2}{3}}\)

Question 7.
ax² + b tan x + ln x³
Solution:
ax² + b tan x + ln x³
\(\frac{d y}{d x}\) = 2ax + b sec² x + \(\frac{3}{x}\)

Question 8.
√x(√x + 1)
Solution:
Let y = √x(√x + 1) = \(x+x^{\frac{1}{2}}\)
\(\frac{d y}{d x}=1+\frac{1}{2} x^{\frac{-1}{2}}\)

Question 9.
(x – 1)²
Solution:
Let y = (x – 1)²
Then \(\frac{d y}{d x}\) = 2(x – 1)

Question 10.
(x² – x + 2)²
Solution:
Let y = (x² – x + 2)²
\(\frac{d y}{d x}\) = 2(x² – x + 2) × \(\frac{d}{d x}\)(x² – x + 2)
= 2(x² – x + 2)(2x – 1)

Question 11.
x sin x – \(\frac{e^x}{1+x^2}\)
Solution:

Question 12.
tan 2x + sec 2x
Solution:

Question 13.
\(\frac{x^2}{x+1}-\frac{x}{1-x}\)
Solution:

Question 14.
\(\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
Solution:

Question 15.
\(\frac{\tan x-\cos x}{\sin x \cos x}\)
Solution:

Question 16.
\(\left(\frac{x-1}{x+1}\right)^2\)
Solution:

Question 17.
x³ (1 + x)(2 – x)
Solution:

Question 18.
x₃ (sin x) e^{4 ln x}
Solution:

Question 19.
\(\frac{1}{\sqrt{x}}\) + x ln x³
Solution:

Question 20.
x² log₂ x + sec x
Solution:

Question 21.
\(\frac{x^2-1}{x^3+1}\)
Solution:

Question 22.
(x³ + 1)(3x² + 2x – 7)
Solution:

Question 23.
cot x – sec x – log₁₀ x
Solution:
\(\frac{d y}{d x}\) = -cosec ² x – sec x. tan x – \(\frac{1}{x} \log _{10} e\)

Question 24.
\(\frac{1-\cos x}{1+\cos x}\)
Solution:

Question 25.
\(\frac{1-\tan x}{1+\tan x}\)
Solution:

Question 26.
\(\frac{\left[x^{\frac{3}{5}}-2 e^2 \ln x+\ln ^{\frac{2}{3}}\right]}{(1+x)}\)
Solution:

Question 27.
cosec x + cot x
Solution:
Let y = cosec x + cot x
\(\frac{d y}{d x}\) = -cosec x. cot x – cosec ² x

Question 28.
tan² x + sec² x
Solution:
Let y = tan² x + sec² x
\(\frac{d y}{d x}\) = 2 tan x. \(\frac{d}{d x}\)(tan x) + 2 sec x \(\frac{d}{d x}\)(sec x)
= 2 tan x. sec² x + 2 sec² x. tan x
= 4 sec² x tan x

Question 29.
tan² x + a^x
Solution:
tan² x + a^x
\(\frac{d y}{d x}\) = 2 tan x. sec² x + a^x. ln a

Question 30.
sin² x + x ln x
Solution:
sin² x – x ln x

Question 31.
cos² x + e^x cos x
Solution:

Question 32.
\(\frac{a^x-b^x}{x}\)
Solution:

Question 33.
\(\frac{e^x+e^{-x}}{x^2+1}\)
Solution:

Question 34.
\(\frac{\ln x}{x^2}\)
Solution:

Question 35.
Show that f(x) = \(\left\{\begin{array}{l}
x \sin \frac{1}{x}, x \neq 0 \\
0, x=0
\end{array}\right.\) is not differentiable x = 0
Solution:
Differentiability

BSE Odisha Class 7 Science Important Questions

• Chapter 1 ପଦାର୍ଥ Important Questions
• Chapter 2 ଭୌତିକ ଓ ରାସାୟନିକ ପରିବର୍ତ୍ତନ Important Questions
• Chapter 3 ଅମ୍ଳ, କ୍ଷାରକ ଓ ଲବଣ Important Questions
• Chapter 4 ତନ୍ତୁରୁ ବସ୍ତ୍ର Important Questions
• Chapter 5 ପୋଷଣ Important Questions
• Chapter 6 ତାପ ଓ ତାପ ସଂଚରଣ Important Questions
• Chapter 7 ପାଣିପାଗ, ଜଳବାୟୁ, ପ୍ରାଣୀମାନଙ୍କ ଉପଯୋଜନ Important Questions
• Chapter 8 ମାଟି (ମୃତ୍ତିକା) Important Questions
• Chapter 9 ଜୀବନ ପାଇଁ ଶ୍ଵାସକ୍ରିୟା – ପ୍ରାଣୀ ଓ ଉଭିଦର ଶ୍ୱସନ Important Questions
• Chapter 10 ଉଦ୍ଭିଦରେ ବଂଶ ବିସ୍ତାର Important Questions
• Chapter 11 ଗତି ଓ ସମୟ Important Questions
• Chapter 12 ବିଦ୍ୟୁତ୍ ସ୍ରୋତ ଓ ଏହାର ପ୍ରଭାବ Important Questions
• Chapter 13 କେତୋଟି ପ୍ରାକୃତିକ ଘଟଣା Important Questions
• Chapter 14 ଆଲୋକ Important Questions
• Chapter 15 ଜଳ – ଅମୂଲ୍ୟ ପ୍ରାକୃତିକ ସମ୍ପଦ Important Questions
• Chapter 16 ଜଙ୍ଗଲ ସମ୍ପଦ Important Questions
• Chapter 17 ଆବର୍ଜନାର ପରିଚାଳନା Important Questions

BSE Odisha 7th Class Text Book Solutions

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 1 Solutions Unit 4 Text A: The Year 2050-Reflections of a Futurist Textbook Activity Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Unit 4 Text A: The Year 2050-Reflections of a Futurist

Activity-1

Vocabulary:
Choose the word from the passage, which more or less mean the following. The paragraph numbers have been given in brackets.
(i) One who studies changes in population in an area (5).
(ii) long existence (5)
(iii) to be flooded with something (6)
(iv) the things that develop from a particular thing (9)
(v) natural potency to behave in a particular way (17)
(vi) the act of controlling or influencing somebody or something by clever or unfair mean (20)

Answer:
(i) One who studies changes in population in an area – demographer.
(ii) long existence – longevity
(iii) to be flooded with something – inundating
(iv) the things that develop from a particular thing-evolve
(v) natural potency to behave in a particular way-genetics
(vi) the act of controlling or influencing somebody or something by clever or unfair mean – manipulation

Activity-2

Facts And Opinions:
Some facts as well as some opinions to the writer have been presented in the essay. Put the facts and opinions in different columns below:

Facts	Opinion
New 18% of Americans reach the age of 90.	More than 50% of people who were born in 1960 will be alive by 2050

Answer:

Facts	Opinion
New 18% of Americans reach the age of 90	(i) more than 50% of people who were born
Stroke deaths and rheumatic heart disease will reduce by 20% and 50%	(ii) Deaths from cardiovascular diseases, hypertension heart diseases will reduce by hypertension, and heart stroke will reduce considerably.

Activity – 3

Remedial Grammar:
Fill in each with the appropriate verb phrase from the following list.
must have          let might have been      wouldn’t be
won’t be             would happen               mustn’t have rung

(a) Sunita: Do you know a girl of Standard V was knocked down by a town bus in front of our school gate this afternoon?
Binita: Oh no! I always said this _________ sooner or later.
Sunita: She is badly injured but she _________ they say. But she _________ out of hospital of a few weeks.
(b) Gopi: There is a letter on the floor outside the door. The postman _________ it.
Moti: Well, he _________ it outside. Someone _________ it. Why didn’t he ring the bell?
Gopi: he always rings the bell. You _________ out when he came.
Moti: I haven’t been out. So he _________ the bell.

Answer:
(a) Sunita: Do you know a girl of Standard V was knocked down by a town bus in front of our school gate this afternoon?
Binita: Oh no! I always said this would happen sooner or later.
Sunita: She is badly injured but she will live they say. But she won’t be out of the hospital of a few weeks.
(b) Gopi: There is a letter on the floor outside the door. The postman must have left it.
Moti: Well, he shouldn’t have left it outside. Someone might have taken it. Why didn’t he ring the bell?
Gopi: he always rings the bell. You might have been out when he came.
Moti: I haven’t been out. So he mustn’t have run the bell.

Extra Activity – 3(A)
Make sentences with the following expression from Text A (in sentences of your own). Don’t copy out exact sentences from the text.

Remarkable	Inexhaustible
Survive	Unending
Spectacular	Solar
Availability	Progeny
Antibiotics	Argument
Span	Measure
Longevity	Orbit
Varieties	Contamination
Non-depletable	Cosmos, Spawn

Answer:
Remarkable — Invention of the computer is a remarkable achievement of modern science.
Survive — We cannot survive without oxygen.
Spectacular — Your performance is really spectacular.
Availability — You will be given arrears only in the availability of funds.
Antibiotics — Antibiotics are administered in the treatment of many kinds of diseases.
Span — He lived a long span of 120 years
Longevity — Man doesn’t live only by longevity of years.
Varieties — This dish is made from varieties of ingredients.
Non-depletable — The ozone layer is not non-depletable
Inexhaustible — He continues working still as if his energy were inexhaustible.
Unending — Money is not an unending flow.
Solar — Today many types of work are conducted by using solar power.
Progeny — On need not give birth to numerous progeny in the days of population explosion.
Argument — He argues his income by earning from myriads of sources.
Measure — Can you measure his temperature?
Orbit — Every planet has its own orbit.
Contamination — Contamination of water is a great offense.
Cosmos — One should keep the cosmos pure at any cost.
Spawn — Reptiles usually spawn eggs.

Extra Activity – 3(B)
1. (i) Derive Adjectives from the following nouns.

Bride	charity
electricity	episode
bureaucrat	friend
Minister	authenticity
inclusion	legend

Answer:

Nouns	Adjectives
Bride	brides
episode	episodic
bureaucrat	bureaucratic
inclusion	inclusive
authenticity	authentic
charity	chaste
electricity	electric
Minister	ministerial
friend	friendly
legend	legendary

(ii) Give antonyms of the following:

right	short
seriously	lull
auspicious	above
special	down
senior	strong
alive	transparent
nearness	resistible
include	logical
ascend	legal
persuade	personal

Answer:

Words	Antonyms
right	Wrong
seriously	lightly
auspicious	inauspicious
special	ordinary
senior	Junior
alive	dead
nearness	remoteness /distance
include	exclude
ascend	descend
persuade	dissuade
short	long
full	empty
above	below
down	up
strong	weak
transparent	opaque
resistible	irresistible
logical	illogical
legal	illegal
personal	impersonal

(iii) Substitute the following expressions with one word each:
(a) strong dislike
(b) sympathy for someone who has experienced great sorrow.
(c) to say that something is very bad.
(d) to show pity.
(e) likely to bring good luck.

Answer:
(a) strong dislike – disgust
(b) sympathy for someone who has experienced great sorrow – condolence
(c) to say that something is very bad – rubbish
(d) to show pity-relent
(e) likely to bring good luck – auspicious

(iv) The following words are wrongly spelled. Rewrite them correctly.

burocrat	protected
condolence	sholder
cooperative	dinastic
Goodby	vegetarian
gimiks	colloqual

Answer:

Word	Correct Form
burocrat condolence cooperative good by gimiks protected sholder dynastic vegetarian colloquial	Bureaucracts condolence co-operative good bye gimmicks protracted shoulders dynastic vegetarian cotloquial

Section-A

How will you look after 50 years?
What will be the major changes in the world by that time?
Think of the possible changes in the fields of agriculture medicine and transport. List out three of the possible changes.
(i) _____________________________
(ii) ____________________________
(iii) ___________________________

The Year 2050-Reflection Of A Futurist Summary in English

Summary:

A remarkable feature of 2050 will be that most of the 1960 babies will still be alive because of a biomedical revolution that is underway. Death rules of different life-killing diseases have dropped considerably. This has become possible due to the availability of antibiotics, better health care, attention to diet, jogging, and exercise the effects in the United States are clear-cut and lasting. But increased longevity and improve health are like to have several drawbacks:

• world population will be larger than it might have been
• low birth rate and increased longevity combine to raise the average age of the population
• A period of difficult social adjustment will be likely.

However, there is a really good chance that a huge increase in food production can come from such development as:

• new plant varieties, obtained through genetic engineering which are photosynthetically efficient use less water and tend to be self-fertilizing,
• improved uses of the ocean, including the domestication of seeing animals aquaculture and
• tropical agriculture which will open to the world many billions of acres of land currently unusable.

Before nondepletable alternatives and commercially developed, new synthetic fuel industries for the conversion of coal into gaseous and liquid fuels and the extraction of petroleum of liquids from oil shale are likely to arise. Solar, geothermal, wind power, and fusion are electric-producing items. By the year 2050, we should be well along toward utilizing two virtually inexhaustible energy resources; solar electric power and nuclear power resources between now and 2050. They are (i) electronics, genetics, and psychology.

By the early in century machines will be available that perform better than human beings. In fact, genetics is a science about to become a technology. This technology will lead to the ability to ‘design’ plants and animals to perform human functions. In agriculture, scientists will be able to produce plants that have improved photosynthetic efficiency, minimum water requirements, self-fertilizing characteristics, and a desired spectrum of nutrient qualities. In mining, organisms will metabolize desired ones tells and thus concertable them for later ‘harvesting’.

In the production of pharmaceuticals, microorganisms will be used as factory workers to produce chemicals normally found only in natural body and plant processes. Finally, in medicine, scientists will intervene in the process by which genetic diseases such as sickle cell anemia. Tay Sachs disease and mongolism are passed from parents to their progeny to cure these diseases before conception. They will also address other diseases such as cancer or heart disease and even aging itself.  Of course, Psychology by 2050 will be ready to take off. The ‘trigger’ discovery will help us know how memory is recorded and retrieved.

It is not clear till now whether memory is chemical, electrical, or physical knowledge of sharing and retrieving of memory will improve education, persuasion, rehabilitation, personality development, and knowledge itself and open the huge and exciting possibility of expanding mental capacity closer to the limits of human potential. Perhaps by 2050, observers in the orbital city cloud follow the world food supply and predict harvest size and crop diseases. Many things can be controlled from the orbit. The boom – babies will face significant challenges in the years ahead.

Analytical Outlines:

• Most of the 1960 babies will still be alive in 2050.
• 2050 will be remarkable for a biomedical revolution.
• Death rates of different life-killing diseases have dropped considerably.
• This has become possible due to the availability of antibiotics.
• It will be possible to better health care.
• It will be possible to taking attention to diet.
• It will be possible due to jogging.
• It will be possible due to exercise.
• It will entirely affect the United States.
• But increased longevity has several dements.
• Improved health has also some demerits.
• The world population will be much longer.

• Low – birth rate will raise the average age ofthe population.
• Increased longevity will also help to raise it.
• A period of difficult social adjustment will be likely.
• This increase in population will develop something.
• It will develop a huge increase in food production.
• It will increase new plant varieties.
• These varieties will be obtained through genetic engineering.
• They are photosynthetically efficient.
• They will use less water.
• They will tend to be self-fertilizing.
• Improved uses of the ocean will take place.
• It will include the domestication of seeing animals in aquaculture.
• It will be possible for tropical agriculture.
• It will utilize billions of acres of unused land in agriculture.
• It will commercially develop non-depletable alternatives.
• New synthetic fuel industries will be there.
• It will convert coal to gases.
• It will also convert coal to liquid fuel.
• The extraction of petroleum of liquids from oil shale is likely to rise.
• There will be various electric-producing items.
• The use of solar power will be there.
• Geothermal use will be there.
• The use of wind power will be there.
• The use of fusion will also be there.
• By 2050 are will be using two virtually exhaustible energy resources.
• One is solar electric power.
• Another is nuclear fusion.
• These are, actually, highly expensive.
• The author also predicts three more power resources.
• One is electronics.
• The other is genetics.
• The other one is psychology.
• There will be the use of machines.
• They will perform better than human beings.
• In feet, genetics is a science about technology.
• This technology will lead to the ability to ‘design’ plants.
• It will also design animals to perform human functions.
• In agriculture, scientists will be able to produce plants.
• It has improved photosynthetic efficiency.
• It has improved minimum water requirements.
• It has improved self-fertilizing characteristics.
• It has developed a desired spectrum of nutrient qualities.
• In mining, organisms will metabolize desired metals.
• It will convertible them for later ‘harvesting’

• We can find changes in the production of pharmaceuticals.
• Here, microorganisms will be used as natural bodies.
• It will be also used in plant processes.
• Finally, scientists will intervene in medicine.
• They will try to cure some genetic diseases.
• One such disease is sickle cell anemia.
• Another is Tay Sachs disease.
• Other such one is mongolism.
• These diseases are passed from parents to their progeny.
• They will try to cure these diseases before conception.
• They will also address other diseases.
• One such disease is cancer.
• Other one is heart disease.
• Of course, Psychology by 2050 will be ready to take off.
• We will have the‘trigger’discovery.
• It will help us to know how memory is recorded and retrieved.
• It is not clear still now whether memory is chemical.
• Or it is electrical.
• The physical knowledge of storing and retrieving of memory will improve education.
• It will improve persuasion.
• It will improve rehabilitation.
• It will improve personality development.
• It will improve knowledge itself

• It will open the huge exciting possibility of expanding mental capacity.
• It will be closer to the limits of human potential.
• Perhaps by 2050, observers in the orbital city cloud follow the world food supply.
• It will predict harvest size.
• It will predict crop disease.
• Many things can be controlled from the orbit.
• The boom-babies will free significant changes in the years ahead.

Meanings Of Difficult Words:

nascent – just beginning and expected to become stronger and bigger.
arable – land suitable for growing crops.
augment – to grow longer, to increase the value or effectiveness of something.
Luddites – those who are strongly opposed to using modem machines and methods.
spawned – laid eggs (fish, frog, salmon, etc).
spectacular – very important, showy, eye-catching.
cardiovascular diseases – diseases of the heart.
hypertensive rheumatic – disease relating to tension and blood pressure.
heart disease – heart disease giving too much pain.
antibodies – medicine administered against micro-bacteria and other living organisms causing disease in human bodies.
optimistic – a hopeful inclination.
drawbacks – demerits, weaknesses, faults, etc.
longevity – living a very long span of life.
computed – calculated, reckoned, estimated.

aquaculture – water culture, treatment of water.
non-depletabIe – that which cannot be depleted or exhausted
solar – of the sun, the power coming from the sun.
geothermal – ‘geo’ means earth and thermal means heat. Hence, the energy emanates from the heat emitted from the earth.
progeny – the successor of a kind of parentage.
human potential – energy of human beings.
contamination – defiling or pocketing something.
accomplish – to attain, to gain, to have
perspective – a bright and hopeful future
cosmos – universe
decade – a period of ten years
exploration – discovery, finding something from a search.
illustrate – to explain, exemplify
utility – vainness, something without results.
infuse – mix, bind, amalgamate
stagger – move unsteadily due to heavy load overhead.

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Odisha State Board BSE Odisha 10th Class Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b) Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Maths Solutions Geometry Chapter 1 ଜ୍ୟାମିତିରେ ସାଦୃଶ୍ୟ Ex 1(b)

Question 1.
ଚିତ୍ରରେ △ABC ର \(\overline{\mathbf{BC}}\) ବାହୁ ଉପରିସ୍ଥ D ଏକ ବିନ୍ଦୁ, ଯେପରିକି \(\overline{\mathbf{AD}}\), ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ । ତଳେ ଥ‌ିବା ଅନୁପାତ ମାନଙ୍କ ମଧ୍ୟରୁ ଠିକ୍ ଅନୁପାତଟି ବାଛି ନିମ୍ନରେ ଥ‌ିବା ଶୂନ୍ୟସ୍ଥାନ ପୂରଣ କର ।
△ABD ଓ △ADC ର କ୍ଷେତ୍ରଫଳର ଅନୁପାତ …………………….
(AB: DC, BD: AC, AB : AC, AD : BC)

Question 2.
△ABC ର ∠ABC ର ପମଦୁଖପୃକ \(\overline{\mathbf{AC}}\) ବାକୁକ୍ଲି D ଦିନ୍ଦୁ6ର ଛେଦ ଦ6ର | AB = 4 ସେ.ମି. BC = 6 ସେ.ମି. ଏବଂ AC = 5 ସେ.ମି. ହେଲେ, AD ଓ CD ନିର୍ଣ୍ଣୟ କର ।
Solution:
△ABCର ∠ABCର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AC}}\) ।

⇒ \(\frac { AB }{ BC }\) = \(\frac { AD }{ DC }\)
⇒ \(\frac { AD }{ DC }\) = \(\frac { AB }{ BC }\) = \(\frac { 4 }{ 6 }\)
⇒ \(\frac { AD }{ DC }\) = \(\frac { 2 }{ 3 }\)
∴ AD = 2x ପେ.ମି. 6ହଲ, DC = 3x ପେ.ମି. |
AC AD + DC = 2x 6ପେ.ମି. + 3x ପେ.ମି. = 5 × ପେ.ମି.
ପ୍ରଶ୍ନନୁସାରେ 5x = 5 ⇒ x = 1
∴ AD = 2x ପେ.ମି. = 2 ପେ.ମି. ଓ DC = 3x ପେ.ମି. = 3 ପେ.ମି. |

Question 3.
△ABC ର \(\overline{\mathbf{AB}}\), \(\overline{\mathbf{BC}}\) ଓ \(\overline{\mathbf{CA}}\) ବାହୁ ତ୍ରୟର ଦୈର୍ଘ୍ୟକୁ ଯଥାକ୍ରମେ c, a ଓ b ଏକକ ରୂପେ ସୂଚିତ କରାଯାଏ । ∠ACB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AB}}\) କୁ M ବିନ୍ଦୁରେ ଛେଦକଲେ, ପ୍ରମାଣ କର ଯେ
(i) AM = \(\frac{b c}{a+b}\)
(ii) BM = \(\frac{c a}{a+b}\)
Solution:
△ABC 6ର ∠ACB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{CM}}\) |

⇒ \(\frac { AC }{ BC }\) = \(\frac { AM }{ BM }\)
⇒ \(\frac { b }{ a }\) = \(\frac { AM }{ BM }\)
∴ AM = bx ଏକକ 6ଦୃ6କ, BM = ax ଏକକ
∴ c = AB = AM + BM = bx + ax = x (a + b) ⇒ x = \(\frac{c}{a+b}\)
∴ AM = bx = \(\frac{bc}{a+b}\) ଓ BM = ax = \(\frac{ac}{a+b}\) (ପ୍ରମାଣିତ)

Question 4.
(i) ଟିଦୃ6ର, △ABC ର \(\overline{\mathbf{AC}}\) ଦାକ୍ ପ୍ରତି ମଧ୍ୟମା \(\overline{\mathbf{BP}}\) | ∠BPC ଏର୍ବ ∠BPA ର ଅସ୍ତ୍ର୫ପମହି ଖଣ୍ଡକ ଯଥାକ୍ସେ \(\overline{\mathbf{BC}}\) ଓ \(\overline{\mathbf{AB}}\) କ୍ମ X ଓ y ବ୍ବ୍ର6ର 6ଚ୍ଛଦ କରତି | ପ୍ରମାଣ କର 6ସ \(\overleftrightarrow{\mathbf{X} \mathbf{Y}}\) || \(\overline{\mathbf{AC}}\) |

Solution:

Question 5.
ଚିତ୍ର ରେ △ABC ଉ \(\overline{\mathbf{BP}}\) ମଧ୍ୟମା | ∠ABC ର ସମଦୃଖଣ୍ଡକ \(\overleftrightarrow{\mathbf{P Y}}\) , \(\overline{\mathbf{AB}}\) କୁ Y ଦିନ୍ଦରେ 6ଚ୍ଛଦ କରେ | \(\overline{\mathbf{AC}}\) ସହି ସମାବର କରି Y ଦିନ୍ଦୁରେ \(\overleftrightarrow{\mathbf{YX}}\) ଅଙବ କରାଯାଇଚ୍ଚି , ଯେପରି ର।ତ୍ରା \(\overline{\mathbf{BC}}\) କୁ X ଦିନ୍ଦୁରେ ଛେଦ କଦୁଚ୍ଛ | ପ୍ରମାଣ କର ଯେ \(\overrightarrow{\mathbf{P X}}\) , ∠BPC ର ସମଦ୍ରିଖଣ୍ଡକ |

Solution:
ଦତ୍ତ : △ABC ର \(\overline{\mathbf{BP}}\) ଏକ ମଧ୍ୟମା | ∠APB ର ପ୍ରସଦ୍ଵିଖଶ୍ରକ \(\overleftrightarrow{\mathbf{P Y}}\) , \(\overline{\mathbf{AB}}\) କ Y ଦିନ୍ଦରେ ଛେଦକ6ର | \(\overline{\mathbf{AC}}\)ସହ ସମାନ୍ତର କରି Y ଦିନ୍ଦୁରେ \(\overleftrightarrow{\mathbf{YX}}\) ରଥନ କରାଯାଇଗ୍ଲି 6ଯପରି ତାହା \(\overline{\mathbf{BC}}\) କ୍ମି X ବିନ୍ଦୁଦକରୁଛି |
ପ୍ରାମାଣ୍ୟ : \(\overleftrightarrow{\mathbf{P X}}\) , ∠BPC ର ସମଦ୍ବିଖଣ୍ଡକ |
ପ୍ରମାଣ : △ABP ରେ ∠APB ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AB}}\) କୁ Y ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { BP }{ AP }\) = \(\frac { BY }{ AY }\)
△ABC 6ର \(\overline{\mathrm{XY}}\) || \(\overline{\mathrm{AC}}\) ⇒ \(\frac { BY }{ AY }\) = \(\frac { BX }{ CX }\)
∴ \(\frac { BP }{ AP }\) = \(\frac { BX }{ CX }\)
⇒ \(\frac { BP }{ CP }\) = \(\frac { BX }{ CX }\) (∵ AP = CP (ଦର))
⇒ \(\overrightarrow{\mathrm{PX}}\) , ∠BPC ର ପ୍ରସଦ୍ଵିଖଶ୍ରକ |

Question 6.
△ABC ରେ ∠BAC ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ ଏବଂ ∠ABC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ ( ବିନ୍ଦୁରେ ଛେଦ କରେ । ପ୍ରମାଣ କର ଯେ \(\frac { AQ }{ QP }\) = \(\frac{\mathbf{A B}+\mathbf{A C}}{\mathbf{B C}}\) |
Solution:
ଦତ୍ତ : △ABC ରେ ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ । ∠ABC ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ Q ବିନ୍ଦୁରେ ଛେଦକରେ ।
ପ୍ରାମାଣ୍ୟ : \(\frac { AQ }{ QP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\)
ପ୍ରମାଣ : △BAC ରେ ∠BAC ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{BC}}\) କୁ P ବିନ୍ଦୁରେ ଛେଦକରେ ।

⇒ \(\frac { AB }{ AC }\) = \(\frac { BP }{ CP }\) ⇒ \(\frac { AB }{ BP }\) = \(\frac { AC }{ CP }\) (ଏକାନ୍ତର ପ୍ରକ୍ରିୟା ଦ୍ବାରା )
⇒ \(\frac { AB }{ BP }\) = \(\frac { AC }{ CP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BP}+\mathrm{CP}}\) (କ୍ରମିକଯୋଗ ପ୍ରକ୍ରିୟା ଦ୍ଵାରା)
⇒ \(\frac { AB }{ BP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\) …(i)
ପୁନଶ୍ଚ △ABP ରେ ∠ABP ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathbf{AP}}\) କୁ Q ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { AB }{ BP }\) = \(\frac { AQ }{ QP }\) …(ii)
(i) ଓ (ii) କୁ \(\frac { AQ }{ QP }\) = \(\frac{\mathrm{AB}+\mathrm{AC}}{\mathrm{BC}}\) (ପ୍ରମାଣିତ)

Question 7.
ABCD ସାମାନ୍ତରିକ ଚିତ୍ରର ∠BAD ର ସମଦ୍ବିଖଣ୍ଡକ, \(\overline{\mathbf{BD}}\) କଣ୍ଠକୁ K ବିନ୍ଦୁରେ ଛେଦକରେ ଏବଂ ∠ABC ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathbf{AC}}\) କଣ୍ଠକୁ L ବିନ୍ଦୁରେ ଛେଦ କରେ ।
ସମାଧାନ :\(\overrightarrow{\mathrm{LK}}\) || \(\overline{\mathbf{AB}}\) ।
ପ୍ରାମାଣ୍ୟ : \(\overrightarrow{\mathrm{LK}}\) || \(\overline{\mathbf{AB}}\)
ଅଙ୍କନ : \(\overrightarrow{\mathrm{AK}}\), \(\overline{\mathbf{DC}}\) କୁ M ବିନ୍ଦୁରେ ଛେଦକରୁ । K ବିନ୍ଦୁରେ \(\overline{\mathbf{AB}}\) ସହ ସମାନ୍ତର ଭାବେ ଅଙ୍କିତ ରେଖା \(\overline{\mathbf{AD}}\) କୁ N ବିନ୍ଦୁରେ ଛେଦକରୁ ।
ପ୍ରମାଣ : △BAD ରେ ∠DAB ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathbf{DB}}\) କୁ K ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { AD }{ AB }\) = \(\frac { DK }{ KB }\)
△DAB ରେ \(\overline{\mathbf{NK}}\) || \(\overline{\mathbf{AB}}\) |

⇒ \(\frac { DK }{ KB }\) = \(\frac { DN }{ AN }\)
△ ADM ରେ \(\overline{\mathbf{NK}}\) || \(\overline{\mathbf{DM}}\) ⇒ \(\frac { DN }{ AN }\) = \(\frac { KM }{ AK }\)
∴ \(\frac { AD }{ AB }\) = \(\frac { BC }{ AB }\) (∵ AD = BC)
△ ABC ରେ \(\overrightarrow{\mathrm{BL}}\) , ∠ABC ବିନ୍ଦୁରେ ଛେଦକରେ ।
⇒ \(\frac { BC }{ AB }\) = \(\frac { CL }{ AL }\)
⇒ \(\frac { KM }{ AK }\) = \(\frac { CL }{ AL }\) (∵\(\frac { BC }{ AB }\) = \(\frac { AD }{ AB }\) = \(\frac { DK }{ KB }\) = \(\frac { DN }{ AN }\) = \(\frac { KM }{ AK }\) )
⇒ \(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{MC}}\)
⇒ \(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{AB}}\) (∵\(\overline{\mathbf{KL}}\) || \(\overline{\mathbf{AB}}\) ) (ପ୍ରମାଣିତ)

Question 8.
ABCD ଚହୁକୁଳର ∠DAB ଓ ∠DCB 6କାଣଦ୍ୱଯଉ ପମଦଖଣ୍ଡକ ପରପକ \(\overline{\mathbf{BD}}\) କଣ୍ଡ ରପରେ ଛେଦକରଚି | ପ୍ରାମାଣ କର ଯେ ∠ABC ଓ ∠ADC ର ପମ ଦିଖଣ୍ଡକଦୁଯ ପରସ୍ତକ୍ \(\overline{\mathbf{AC}}\) କଣ୍ଡ ରପ6ଭ 6ଚ୍ଚଦ କରି6ବା
Solution:
ଦର :ABCD ଚହୁକୁଳର ∠DAB ଓ ∠DCB 6କାଣଦ୍ୱଯଉ ପମଦଖଣ୍ଡକ \(\overline{\mathbf{AC}}\) କଣ୍ଡ ରପ6ଭ 6ଚ୍ଚଦ କରି6ବା
ପ୍ତମାତା : △BAD ରେ ∠DAB ର ସମଦିଖଣ୍ଡକ \(\overrightarrow{\mathrm{AE}}\) |

⇒ \(\frac { AB }{ AD }\) = \(\frac { BE }{ ED }\) …..(i)
ଚହୁକୁଳର △BAD ରେ ∠BCD ର ଛେଦକରଚି \(\overrightarrow{\mathrm{CE}}\) |
⇒ \(\frac { BC }{ CD }\) = \(\frac { BE }{ ED }\) ….(ii)
(i) ଓ (ii) ଦ୍ଦ \(\frac { AB }{ AD }\) = \(\frac { BC }{ CD }\)
⇒ \(\frac { AB }{ BC }\) = \(\frac { AD }{ CD }\) (ଏକାନ୍ତର ପ୍ରତଯାଦ୍ଧାରା)
ମରେକର ABC ର ସପଦଖଣୃକ AC କୁ F ଦିନ୍ଦୁରେ 6ଛଦକରେ |
⇒ \(\frac { AB }{ BC }\) = \(\frac { AF }{ FC }\) ⇒ \(\frac { AD }{ DC }\) = \(\frac { AF }{ FC }\) (∵\(\frac { AB }{ BC }\) = \(\frac { AD }{ DC }\))
⇒ \(\overline{\mathrm{DF}}\) , ADC ର ସପଦିଖଣ୍ଡଦ (ପ୍ରମାଣିତ)

Question 9.
△ABC ରେ ∠B ର ସମଦ୍ଵିଖଣ୍ଡକ, \(\overline{\mathrm{AC}}\) କୁ E ବିନ୍ଦୁରେ ଏବଂ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ବିନ୍ଦୁରେ ଛେଦକରେ । \(\overline{\mathrm{FE}}\) || \(\overline{\mathrm{BC}}\) ହେଲେ ପ୍ରମାଣ କର ଯେ, △ABC ସମଦ୍ବିବାହୁ ।
ସମାଧାନ :
ଦତ୍ତ : △ABC ରେ ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ବିନ୍ଦୁରେ ଓ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ବିନ୍ଦୁରେ ଛେଦକରେ ଓ \(\overline{\mathrm{FE}}\) ||\(\overline{\mathrm{BC}}\) |
ପ୍ରାମାଣ୍ୟ : △ABC ସମଦ୍ବିବାହୁ |
ପ୍ରମାଣ : △ABC ରେ ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ରେ ଛେଦକରେ ।

⇒ \(\frac { AC }{ BC }\) = \(\frac { AF }{ FB }\)
ସେହିପରି ∠Cର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ F ରେ ଛେଦ କରେ ।
⇒ \(\frac { AC }{ BC }\) = \(\frac { AF }{ FB }\)
\(\overline{\mathrm{FE}}\) || \(\overline{\mathrm{BC}}\) (ଦତ୍ତ)
⇒ \(\frac { AF }{ FB }\) = \(\frac { AE }{ EC }\) ⇒ \(\frac { AC }{ BC }\) = \(\frac { AB }{ BC }\)
⇒ AB = AC
⇒ △ABC ସପଦିଖଣ୍ଡଦ (ପ୍ରମାଣିତ)

Question 10.
△ABC ରେ ∠A, ∠B ଓ ∠C ର ସମଦ୍ବିଖଣ୍ଡକ, \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CA}}\) ଓ \(\overline{\mathrm{AB}}\) କୁ ଯଥାକ୍ରମେ D, E ଓ F ବିନ୍ଦୁରେ ଛେଦକଲେ ପ୍ରମାଣ କର ଯେ \(\frac { BD }{ DC }\) . \(\frac { CE }{ EA }\) . \(\frac { AF }{ FB }\) = 1
Solution:
ଦତ୍ତ : △ABC ରେ ∠A, ∠B ଓ ∠C ର ସମଦ୍ଵିଖଣ୍ଡକ \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CA}}\) ଓ \(\overline{\mathrm{AB}}\) କୁ ଯଥାକ୍ରମେ D, E ଓ F ବିନ୍ଦୁରେ ଛେଦକଲେ |
ପ୍ରାମାଣ୍ୟ : \(\frac { BD }{ DC }\) . \(\frac { CE }{ EA }\) . \(\frac { AF }{ FB }\) = 1
ପ୍ରମାଣ : △ABC ରେ ∠A ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{BC}}\) କୁ D ରେ ଛେଦକରେ ।

⇒ \(\frac { BD }{ DC }\) = \(\frac { AB }{ AC }\)
ସେହିପରି ∠B ର ସମଦ୍ବିଖଣ୍ଡକ \(\overline{\mathrm{AC}}\) କୁ E ରେ ଛେଦକରେ ।
⇒ \(\frac { CE }{ EA }\) = \(\frac { BC }{ AB }\)
∠Cର ସମଦ୍ୱିଖଣ୍ଡକ \(\overline{\mathrm{AB}}\) କୁ Fରେ ଛେଦକରେ ।
⇒ \(\frac { AF }{ FB }\) = \(\frac { AC }{ BC }\)
∴ \(\frac { BD }{ DC }\) × \(\frac { CE }{ EA }\) × \(\frac { AF }{ FB }\) = \(\frac { AB }{ AC }\) × \(\frac { BC }{ AB }\) × \(\frac { AC }{ BC }\) = 1 (ପ୍ରମାଣିତ)

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Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 12 Conic Sections Ex 12(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 12 Conic Sections Exercise 12(b)

Question 1.

Fill in the blanks by choosing the correct answer from the given ones :
(a) The equation of the directrix to the parabola x² = -6y is _____________. [y + 6 = 0, 2y – 3 = 0, y – 6 = 0, 2y + 3 = 0]
Solution:
2y – 3 = 0

(b) The eccentricity of the parabola y² = 8x is ____________. (2, 8, 0, 1)
Solution:
1

(c) The line y + x = k is tangent to the parabola y² + 12x = 0 if k = ______________. (-3, 3, 6, -6)
Solution:
3

(d) The latus rectum of the parabola (y – 2)² = 8(x + 3) is ______________. (2, 4, 8, 16)
Solution:
8

(e) The equation of tangent to the parabola x² = 6y at vertex is _______________. (x = 0, y = 0, x = \(\frac{-3}{2}\), y = \(\frac{-3}{2}\))
Solution:
y = 0

(f) The equation of axis of the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}\) = 1 is ___________. (x = 4, y = 3, x = 0, y = 0)
Solution:
y = 0

(g) The equation of the major axis of the ellipse \(\frac{(x+1)^2}{16}+\frac{(y-2)^2}{25}\) = 1 is __________. (x = 4, x = -1, y = 5, y = 2)
Solution:
x = -1

(h) The distance between the focii of the ellipse 3x² + 4y² = 1 is _____________. (1, \(\frac{1}{\sqrt{3}}\), \(\frac{2}{\sqrt{3}}\), \(\frac{1}{2 \sqrt{3}}\)
Solution:
\(\frac{1}{\sqrt{3}}\)

(i) The eccentricity of the ellipse \(\frac{x^2}{16}+\frac{y^2}{25}\) = 1 is _______________. (\(\frac{4}{5}, \frac{5}{4}, \frac{3}{5}, \frac{16}{25}\))
Solution:
\(\frac{3}{5}\)

(j) The line y = 2x + K is a tangent to the ellipse 5x² + y² = 5 if K = ______________. (2, 5, √3, √21)
Solution:
3

(k) The length of the latus rectum of the ellipse \(\frac{(x-2)^2}{4}+\frac{(y+3)^2}{25}\) = 1 is _______________. (\(\frac{4}{25}, \frac{2}{5}, \frac{5}{2}, \frac{8}{5}\))
Solution:
\(\frac{8}{5}\)

(l) The equation of the conjugate axis of the hyperbola \(\frac{x^2}{9}-\frac{(y+2)^2}{16}\) = 1 is ____________. (x = 0, x = 3, y = -3, y = 4)
Solution:
x = 0

(m) the hyperbola \(\frac{y^2}{16}-\frac{x^2}{12}\) = 1 intersects x – axis at ___________. [(0, ±4), (±2√3, 0), (2, 0), no where]
Solution:
no where

(n) The eccentricity of the hyperbola 4x² – 3y² = 1 is ____________. (\(\frac{4}{3}, \frac{3}{4}, \frac{\sqrt{21}}{3}, \frac{\sqrt{7}}{2 \sqrt{3}}\))
Solution:
\(\frac{\sqrt{21}}{3}\)

(o) The latus rectum of the hyperbola \(\frac{x^2}{9}-\frac{y^2}{16}\) = 1 is ___________. (\(\frac{16}{9}, \frac{9}{16}, \frac{1}{9}, \frac{32}{9}\))
Solution:
\(\frac{32}{9}\)

(p) The line y = 3x – k is a tangent to the hyperbola 6x² – 9y² = 1 if k ____________. (1, \(\frac{5}{3 \sqrt{2}}, \frac{1}{\sqrt{6}}, \frac{2}{3}\))
Solution:
\(\frac{5}{3 \sqrt{2}}\)

Question 2.
Mention which of the following statements are true (T) and false (F) :
(a) The equation y = x² + 2x + 3 represents a parabola with its axis parallel to y – axis.
Solution:
True

(b) The latus rectum of the parabola y² = -8x is 2.
Solution:
False

(c) The eccentricity of the parabola (y – 1)² = 2(x + 3)² is \(\frac{1}{3}\).
Solution:
False

(d) The line y = 3 is a tangent to the parabola (x + 2)² = 6(y – 3).
Solution:
True

(e) The equation Ax² + By² = 1 represents an ellipse with its axis parallel to x – axis, if A > B > 0.
Solution:
False

(f) The focii of the ellipse \(\frac{x^2}{3}+\frac{y^2}{2}\) = 1 are the points (±1, 0).
Solution:
True

(g) The equation of the ellipse with focii at (0, ±4) and vertices (0, ±7) is \(\frac{x^2}{16}+\frac{y^2}{49}\) = 1.
Solution:
False

(h) The length of the latera recta of the ellipse \(\frac{x^2}{9}+\frac{y^2}{4}\) = 1 and \(\frac{(x+2)^2}{4}+\frac{(y-1)^2}{9}\) = 1 are equal.
Solution:
True

(i) The equation of the latera recta of the ellipse \(\frac{(x-4)^2}{16}+\frac{(y-1)^2}{9}\) = 1 are x = 4 ± √7.
Solution:
True

(j) The line y = x + 2 is a tangent to the ellipse \(\frac{x^2}{2}+\frac{y^2}{1}\) = 1.
Solution:
False

(k) The conjugate axis of the hyperbola, \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1 meets the hyperbola at two points which are at distance 2b from each other.
Solution:
False

(l) The conjugate axis of the hyperbola, \(\frac{(y-3)^2}{9}+\frac{(x+2)^2}{3}\) = 1 is parallel to the line x = 4.
Solution:
False

(m) The length of the transverse axis of the hyperbola with focii at (±5, 0) and vertices at (±2, 0) is 10.
Solution:
False

(n) The latera recta of the ellipse \(\frac{x^2}{25}-\frac{y^2}{16}\) = 1 are same.
Solution:
True

(o) The y – axis is tangent to the hyperbola ay² – bx² = 1
Solution:
False

Question 3.
Find the equation of the parabola in each of the following cases :
(a) the vertex at (0, 0) and focus at (0, 3).
Solution:

(b) the vertex at (0, 0) and directrix x – 2 = 0.
Solution:

(c) the vertex at (6, -2) and focus at (-3, -2).
Solution:

and the parabola facing towards left.
Eqn. of the parabola is (y – k)² = -4a(x – h)
or, (y + 2)² = -4 × 9(x – 6)
= -36(x + 6)
or, (y + 2)² + 36(x – 6) = 0

(d) the vertex at (-2, 1) and focus at (-2, 4).
Solution:

(e) the length of the latus rectum is 6. and the vertex is at (0, 0), the parabola opening to the right.
Solution:
The length of the latus rectum is 6
∴ 4a = 6
The parabola opens to right and vertex at (0, 0).
∴ Eqn. of the parabola is y² = 4ax = 6x.

(f) the vertex is at (0, 0) the parabola opening to the left and passing through (-1, 2).
Solution:
Vertex at (0, 0), parabola opening to left, passing through (-1, 2).
∴ Let the eqn. of the parabola be y² = -4ax
As it passes through (-1, 2),
we have 4 = -4a (-1) or, a = 1
∴ Eqn. of the parabola is y² = 4x.

(g) the vertex at (0, 0) the parabola opens downwards, and the latus rectum of length 10.
Solution:
Vertex at (0, 0), the parabola opens downward, length of the latus rectum is 10.
∴ 4a = 10
∴ Eqn. of the parabola is
x² = -4ay or, x²  = -10y.

(h) the axis is vertical and the parabola passes through the points (0, 2), (-1, 1), (2, 10).
Solution:
Axis is vertical, parabola passes through the points (0, 2), (-1, 1), and (2, 10).
Let the eqn. of the parabola be
x² + 2gx + 2fy + c = 0. As it passes through the above points,
we have 0 + 0 + 2f . 2 + c = 0
⇒ c = -4f, 1 – 2g + 2f . 1 + c = 0
⇒ c = 2g – 2f – 1 and
4 + 2g . 2 + 2f . 10 + c = 0
⇒ c = -4g – 20f – 4
∴ -4f = 2g – 2g – 1

∴ Equation of the parabola is
x² + 2gx + 2fy + c = 0
or, x² + 2x – y + 2 = 0
or, y = x² + 2x + 2

(i) the axis is horizontal and the parabola passes through the points (2, -1), (-2, -4), and (-1, 3).
Solution:
Le the eqn. of the parabola be
y² + 2gx + 2fy + c = 0
As it passes through the points (2, -1), (-2, -4), and (-1, 3)
we have 1 + 2g . 2 +2f (-1) + c = 0    …(1)
16 + 2g (-2) + 2f (-4) + c = 0     …(2)
and 9 + 2g (-1) + 2f . 3 + c = 0    …(3)
∴ From eqn. (1) → 1 + 4g – 2f + c = 0
⇒ c = 2f – Ag – 1
Eqn. (2) → 16 – 4g – 8f + c = 0
⇒ c = 8f + 4g – 16
and eqn. (3) → 9 – 2g + 6f + c = 0
⇒ c = 2g – 6f – 9
∴ – 1 + 2f – 4g = 8f + 4g – 16
or, -6f = 8g – 15 or, f = \(\frac{8 g-15}{-6}\)
Again -1 + 2f – 4g = 2g – 6f – 9
or, 8f = 6g – 8 or, f = \(\frac{6 g-8}{8}\)
∴ \(\frac{8 g-15}{-6}=\frac{6 g-8}{8}\)
or, 32g – 60 = -18g + 24
or, 50g = 84

(j) Vertex at (1, 3) and the directrix, x + 3 = 0.
Solution:
Vertex at (1, 3), directrix x + 3 = 0
∴ h = 1, k = 3
We have the directrix is x = h – a
∴ h – a = -3
or, a = h + 3 = 4
∴ Eqn. of the parabola is
(y – k)² = 4a(x – h)
or, (y – 3)² = 16(x – 1)

(k) Vertex at (1, -1) and the directrix y – 2 = 0
Solution:
Vertex at (2, -1), directrix y – 2 = 0
∴ h = 1, k = -1
We have the directrix is y = k – a
∴ k – a = 2
or, a = k – 2 = -1 – 2 = – 3
∴ Eqn. of the parabola is
(x – h)² = 4a(y – k)
⇒ (x – 1)² = 4 (-3) (y + 1)
⇒ (x – 1)² = -12 (y + 1)
⇒ (x – 1)² + 12 (y + 1) = 0

(l) the focus at(-2, 3) and the directrix 3x + 4y – 2 = 0.
Solution:
Focus at (-2, 3),
directrix 3x + 4y – 2 = 0.

Question 4.
Find the equation of the ellipse in each of the following cases :
(a) center at (0, 0), one vertex at (0, -5) and one end of minor axis is (3, 0).
Solution:

(d) centre at (0, 0), one vertex at (7, 0) and one end of the minor axis is (0, -5).
Solution:

(c) foci at (±5, 0), and the length of the major axis is 12.
Solution:
Foci at (±5, 0),
length of the major axis is 12
∴ c = 5, 2a = 12
∴ a = 6
∴ b² = a² – c² = 36 – 25 = 11
Equ. of the ellipse is \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{25}+\frac{y^2}{4}\) = 1

(e) center at (5, 4) and the major axis, is of length 16 and the minor axis is of length 10.
Solution:
Centre at (5, 4), major axis 16, minor axis 10.
∴ h = 5, k = 4, 2a = 16, 2b = 10
∴ a = 8, b = 5
Eqn. of the ellipse is \(\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}\) = 1
or, \(\frac{(x-5)^2}{64}+\frac{(y-4)^2}{25}\) = 1

(f) Centre at (-3, 3), vertex at (-3, 6), and one end of minor axis at (0, 3).
Solution:
Centre at (-3, 3), vertex at (-3, 6),
one end of minor axis (0, 3).

(g) Centre at (0, 0), axes parallel to coordinate axes, eccentricity is \(\frac{1}{\sqrt{2}}\) and the minor axis is of length 5.
Solution:
(0, 0), axes parallel to coordinate axes, eccentricity is \(\frac{1}{\sqrt{2}}\), and the minor axis is 5.

(h) centre at (0, 0) axes parallel to coordinate axes, eccentricity is \(\frac{\sqrt{3}}{2}\) and the ellipse passing through the point (√3, \(\frac{1}{2}\))
Solution:

we have 3 + 4 × \(\frac{1}{4}\) = a² or, a² = 4
∴ Eqn of the ellipse is x² + 4y² = 4

(i) centre at (0, 0), one end of the major axis is (-5, 0) and eccentricity \(\frac{3}{5}\)
Solution:
centre at (0, 0), one end of the major axis is (-5, 0), eccentricity \(\frac{3}{5}\)
∴ a = 5, \(\frac{c}{a}\) = \(\frac{3}{5}\) or, c = 3
∴ b² = a² – c² = 25 – 9 = 16
∴ Eqn. of the ellipse is \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{25}+\frac{y^2}{16}\) = 1

(j) axis parallel to coordinate axes, the centre at (0, 0) and the ellipse passing through (3, -2) and (-1, 3).
Solution:
Axis parallel to coordinate axes, centre at (0, 0), ellipse passing through (3, -2) and (-1, 3).
Let the eqn. of the ellipse be

(k) centre at (3, 4), axis parallel to x – axis and passing through (6, 4) and (3, 6).
Solution:
Centre at (3, 4), axis parallel to x – axis, ellipse passing through (6, 4) and (3, 6).
Let the eqn. of the ellipse be

(l) Centre at (-2, 1) axis parallel to y – axis, eccentricity is \(\frac{\sqrt{7}}{4}\) and the ellipse passing through (-2, 5).
Solution:
Centre at (-2, 1), axis parallel to y – axis, eccentricity is \(\frac{\sqrt{7}}{4}\) passing through (-2, 5)

Question 5.
Obtain the equation of a hyperbola in each of the following cases :
(a) foci at (±4, 0) and vertices (±2, 0).
Solution:
Here c = 4, a = 2
∴ b² = c² – a² = 16 – 4 = 12
∴ Eqn. of the hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{4}-\frac{y^2}{12}\) = 1

(b) foci at (0, ±72) and vertices (0, ±1).
Solution:

(c) centre at (0, 0) transverse axis along x – axis of length 4, and focus at (2√5,0).
Solution:
Here 2a = 4, c = 2√5
∴ a =2
∴ b² = c² – a² = 20 – 4 = 16
∴ Eqn. of the hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{4}-\frac{y^2}{16}\) = 1

(d) centre at (0, 0), the conjugate axis along x – axis of length 6 and eccentricity 2.
Solution:
Here 2b = 6 ⇒ b = 3, \(\frac{c}{a}\) = 2
or, c = 2a
We have a² + b² = c²
or, a² + 9 = 4a²
or, 3a² = 9 or, a² = 3
∴ Eqn. of the hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{3}-\frac{y^2}{9}\) = 1

(e) foci at (±2√3, 0) and eccentricity √3.
Solution:
Here c = 2√3, \(\frac{c}{a}\) = √3
or, a = \(\frac{c}{\sqrt{3}}\) = 2
∴ b² = c² – a² = 12 – 4 = 8
∴ Eqn. of the hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{4}-\frac{y^2}{8}\) = 1

(f) centre at (0, 0) transverse axis is along y – axis, the distance between the foci is 14 and the distance between the vertices is 12.
Solution:
Here 2c = 14, 2a = 12
∴ c = 7, a = 6
∴ b² = c² – a² = 49 – 36 = 13
∴ Eqn. of the hyperbola is \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1 or, \(\frac{x^2}{36}-\frac{y^2}{13}\) = 1

(g) centre (1, -2), transverse axis parallel to the x-axis of length 6 and conjugate axis of length 10.
Solution:
Centre (1, -2), transverse axis parallel to x – axis of length 6, the conjugate axis of length 10.
∴ 2a = 6, 2b= 10
∴ a = 3, b = 5, h = 1, k = -2
∴ Eqn. of the hyperbola \(\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}\) = 1 or, \(\frac{(x-1)^2}{9}-\frac{(y-2)^2}{25}\) = 1

(h) Centre (2, -3), eccentricity \(\frac{5}{3}\) and hyperbola passing through (5, -3).
Solution:
Here h = 2, k = -3, \(\frac{c}{a}=\frac{5}{3}\) or, c = \(\frac{5 a}{3}\) we have c² = a² + b²

(i) centre at origin, axis perpendicular to y-axis and the hyperbola passes through the points (3, -2) and (5, -7).
Solution:
Let the eqn. of the hyperbola be \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1
As the hyperbola passes through the points (3, -2) and (5, -7)
we have \(\frac{9}{a^2}-\frac{4}{b^2}\) = 1     …..(1)

or, 45x² – 16y² = 341.

(j) The transverse axis parallel to the y-axis, the hyperbola passes through the points (\(\frac{11}{3}\), 0), (1, 2) and its centre is the intersection of the lines. x + y – 6 = 0, 4x – y + 1 = 0.
Solution:
Solving x + y – 6 = 0
\(\frac{4 x-y+1=0}{5 x=5 \quad \text { or, } x=0}\)
∴ y = 6 – x = 6 – 1 = 5
∴ Centre of the hyperbola is at (1, 5).

Question 6.
Reducing to standard form, obtain the coordinates of the vertex, focus, endpoints of the latus rectum, the length of latus return, the equation of axis and directrix of the following parabolas:
(a) y² – 4x + 4y – 1 = 0
Solution:
y² – 4x + 4y – 1 = 0
or, y² + 4y = 4x + 1
or, y² + 4y + 4 = 4x + 5
or, (y + 2)² = 4(x + \(\frac{5}{4}\))
or, (y + 2)² = 4 × 1 × (x + \(\frac{5}{4}\)) standard from

Length of the latus rectum
= 4a = 4 × 1 = 4
Eqn. of the axis is y = k or, y = -2
Eqn. of the directrix is x = h – a
or, \(\frac{-5}{4}\) – 1 \(\frac{-9}{4}\)
or, 4x + 9 = 0

(b) 2x² – 4y + 6x – 3 = 0
Solution:
2x² – 4y + 6x – 3 = 0
or, 2x² + 6x = 4y + 3
or, 2(x² + 3x) = 4(y + \(\frac{3}{4}\))

(c) x² + x + y + 1 = 0
Solution:
x² + x + y + 1 = 0

and (0, -1)
Length of the latus rectum = 4a = 1.
Eqn. of the axis x = h or x = –\(\frac{1}{2}\)
or, 2x + 1 = 0
Eqn. of the directrix is y = k – a or, y = \(\frac{-3}{4}+\frac{1}{4}\)
or, y = –\(\frac{1}{2}\) or, 2y + 1 = 0

(d) y² + 14y – 3x + 1 = 0
Solution:
y² + 14y – 3x + 1 = 0
or, y² + 14y = 3x – 1
or, y² + 2.y.1 + 49 = 3x – 1 + 49
or, (y + 7)² = 3x + 48 = 3 (x + 16)
or, (y + 7)² = 4 × \(\frac{3}{4}\) (x + 16)
This is the standard form

y = k or, y = -7
or, y + 7 = 0
Eqn of the directrix is x = h – a
or, x = -16 = \(\frac{3}{4}\) = \(\frac{-67}{4}\)
or, 4x + 67 = 0

Question 7.
Reducing to standard form, obtain the coordinates of the centre, the foci, the vertices, the endpoints of the minor axis, the endpoints of latera recta, the equation of the directrices and the eccentricity of the following ellipses :
(a) 3x² + 4y² + 6x + 8y – 5 = 0
Solution:
3x² + 4y² + 6x + 8y – 5 = 0
or, 3(x² + 2y) + 4(y² + 2y) = 5
or, 3(x² + 2x + 1 – 1) + 4(y² + 2y + 1 – 1) = 5
or, 3(x + 1)² – 3 + 4(y + 1)² – 4 = 5
or, 3(x + 1)² + 4(y + 1)² = 12
or, \(\frac{(x+1)^2}{4}+\frac{(y+1)^2}{3}\) = 1 is the standard form.
∴ h = -1, k = -1, a² = 4, b² = 3
∴ a = 2, b = √2, c = \(\sqrt{a^2-b^2}\) = 1
Centre at (h, k) = (-1, -1), the vertices of (h±a, k)
= (-1±2, -1) = (1, -1)
and (-3, -1) foci at (h±c, k)
= (-1±1, -1) = (-2, -1) and (0, -1)
The endpoints of minor axis are (h, k±b) = (-1, -1±√3)
Endpoints of latera recta are (h + c, k±\(\frac{b^2}{a}\)) and (h – c, k±\(\frac{b^2}{a}\))

(b) 4x² + 8y² + 4x + 24y – 13 = 0
Solution:
4x² + 8y² + 4x + 24y – 13 = 0
or, 4(x² + x) + 8(y² + 3y) = 13

(c) 2x² + 3y² – 12x + 24y + 60 = 0
Solution:
2x² + 3y² – 12x + 24y + 60 = 0
or, 2(x² – 6x) + 3(y² + 8y) = -60
or, 2(x² – 2.x.3 + 9 – 9) + 3(y² + 2.y.4 + 16 – 16 = -60
or, 2(x – 3)² – 18 + 3 (y + 4)² – 48 = -60
or, 2 (x – 3)² + 3 (y + 4)² = 6
or, \(\frac{(x-3)^2}{3}+\frac{(y+4)^2}{2}\) = 1 is the standard form.
∴ h = 3, k = -4, a² = 3, b² = 2
∴ a = √3, b = √2, c = \(\sqrt{a^2-b^2}\) = 1
Centre at (h, k) = (3, -4),
Foci at (h±c, k)
= (3±1, -4) = (4, -4) and (2, -4)
Vertices at (h±a, k) = (3±√3, -4)
The endpoints of the minor axis are (h, k±b) = (3, -4±√2)

(d) 9x² + 4y² + 36x – 8y + 4 = 0
Solution:
9x² + 4y² + 36x – 8y + 4 = 0
or, 9(x² + 4x) + 4(y² – 2y) = -4
or, 9(x² + 4x + 4 – 4) + 4(y² – 2y + 1 – 1) = -4
or, 9(x + 2)² – 36 + 4(y – 1)² – 4 = -4
or, 9(x + 2)² + 4(y – 1)² = 36
or, \(\frac{(x+2)^2}{4}+\frac{(y-1)^2}{9}\) = 1, This is the standard form
∴ h = -2, k = 1, a² = 9, b² = 4
∴ a = 3, b = 2, c = \(\sqrt{a^2-b^2}\) = √5
∴ Centre at (h, k) = (-2, 1)
Foci at (h, k±c) = (-2, 1±√5)
Vertices at (h, k±a)
= (-2, 1±3)
Endpoints of minor axis are (h±b, k) = (-2±2, 1)
The endpoints of latera recta are (h ± \(\frac{b^2}{a}\), k ± c) = (-2 ± \(\frac{4}{3}\), 1 ± √5)
End of directrices arty = k ± \(\frac{a^2}{c}\)
or y = 1 ± \(\frac{9}{\sqrt{5}}\)
Eccentricity is \(\frac{c}{a}\) = \(\frac{\sqrt{5}}{3}\).

Question 8.
Reducing to standard form, obtain the coordinates of the centre, the vertices, the foci, the endpoints of the conjugate axis, the endpoints of latera recta, the equation of directrices and the eccentricity of the following hyperbola :
(a) x² – 2y² – 6x – 4y + 5 = 0
Solution:
x² – 2y² – 6x – 4y + 5 = 0
or, x² – 6x – 2(y² + 2y) =-5
or, x² – 2.x.3 + 9 – 9 – 2(y² + 2y + 1 – 1) = -5
or, (x – 3)² – 2(y + 1)² + 2 = 4
or, (x – 3)² – 2(y + 1)² = 2
or, \(\frac{(x-3)^2}{2}-\frac{(y+1)^2}{1}\) = 1 the standard form
∴ h = 3, k = -1, a² = 2, b² = 1
∴ a = √2 , b = 1, c \(\sqrt{a^2+b^2}\) = √3
∴Centre at (h, k) = (3, -1)
Vertices (h±a,  k) = (3±√2, -1)
Foci at (h±c, k) = (3±√3 , -1)
The endpoints of a conjugate axis are (h, k±b) = (3, -1±1)
Endpoints of latera recta are (h ± c, k ± \(\frac{b^2}{a}\)) and (3±√3, -1 ± \(\frac{1}{\sqrt{2}}\))
Eqn. of directrices are x = h ± \(\frac{a^2}{c}\) = 3 ± \(\frac{2}{\sqrt{3}}\) or, x = 3 ± \(\frac{2}{\sqrt{3}}\)
Eccentricity = \(\frac{c}{a}=\frac{\sqrt{3}}{\sqrt{2}}\)

(b) 9y² – 4x² – 90y + 189 = 0
Solution:
9y² – 4x² – 90y + 189 = 0
or, 9(y² – 10y) – 4x² = -189 .
or, 9(y² – 2.y.5 + 25 – 25) – 4x² = -189
or, 9(y – 5)² – 225 – 4x² = -189
or, 9(y – 5)² – 4x² = 225 – 189 = 36
or, \(\frac{(y-5)^2}{4}-\frac{(x)^2}{9}\) = 1 the standard form
h = 0, k = 5, a² = 4, b² = 9
a = 2 , b = 3, c \(\sqrt{a^2+b^2}\) = √13
Centre at (h, k) = (0, 5)
Vertices (h, k±a) = (0, 5±2)
Foci at (h , k±c) = (0, 5±√13)
The endpoints of a conjugate axis are (h±a, k) = (0±2, 5) = (±2, 5)
Endpoints of latera recta are (h ± \(\frac{b^2}{a}\), k ± c) = (0 ± \(\frac{9}{2}\), 5 ± √13)
Eqn. of directrices are y = k ± \(\frac{a^2}{c}\) = 5 ± \(\frac{4}{\sqrt{13}}\)
Eccentricity = \(\frac{c}{a}\) = \(\frac{\sqrt{13}}{2}\)

(c) 49x² – 4y² – 98x + 48y – 291 = 0
Solution:
49x² – 4y² – 98x + 48y – 291 = 0
or, 49(x² – 2x) – 4(y² – 12y)= 291
or, 49(x² – 2x + 1 – 1) – 4(y² – 2.y.6 + 36 – 36) = 291
or, 49(x – 1 )² – 49 – 4(y – 6)² + 144 = 291
or, 49(x – 1)² – 4(y – 6)²
= 291 – 144 + 49 = 196
or, \(\frac{(x-1)^2}{4}\) – \(\frac{(y-6)^2}{49}\) = 1
h= 1, k = 6, a² = 4, b² = 49
a = 2, b = 7, c = \(\sqrt{a^2+b^2}\) = √53
Centre at (h, k) = (1, 6)
Vertices at (h±a, k) = (1±2, 6)
Foci at (h±c, k) = (1±√53, 6)
Endpoints of latera recta are (h ± c, k ± \(\frac{b^2}{a}\)) = (1 ±√53, 6 ± \(\frac{49}{2}\))
Eccentricity = \(\frac{c}{a}=\frac{\sqrt{53}}{2}\)
Endpoints of conjugate axis are (h, k±b) = (1, 6±7) = (1, -1) and (1, 13)

(d) 3x² – 2y² – 4y – 26 = 0
Solution:
3x² – 2y² – 4y – 26 = 0
or, 3x² – 2(y² + 2y) = 26
or, 3x² – 2(y² + 2y + 1 – 1) = 26
or, 3x² – 2(y + 1)² + 2 = 26
or, 3x² – 2(y + 1)² = 24
or, \(\frac{x^2}{8}-\frac{(y+1)^2}{12}\) = 1 Standard form
h= 0, k = -1, a² = 8, b² = 12
a = 2√2, b = 2√3, c = \(\sqrt{a^2+b^2}\) = √20 = 2√3
Centre at (h, k) = (0, -1)
Vertices at (h±a, k) = (±2√2, -1)
Foci at (h±c, k) = (±2√5, -1)

Question 9.
Prove that the equation of the parabola whose vertex and focus are at distances α and β from the origin on the x-axis respectively is y² = 4(β – α)(x – α)
Solution:

Question 10.
Find the locus of the point of trisection of a double ordinate of the parabola y² = 4ax.

Question 11.
(a) Prove that a double ordinate of the parabola y² = 4ax of length 8a subtends a right angle at its vertex.
Solution:

(b) Find the angle which a double ordinate of length 2a subtends at its vertex and focus.
Solution:

Question 12.
(a) Obtain the equations of the tangent and normal of the parabola y² = 4ax at a point where the ordinate is equal to three times the abscissa.
Solution:
Putting y = 3x in the parabola equation.
we have y² = 4ax
or, 9x² = 4ax
or, x = \(\frac{4 a}{9}\)
∴ y = 3x = \(\frac{4 a}{3}\)
∴ The point of contact is (\(\frac{4 a}{9}\), \(\frac{4 a}{3}\))

(b) Find the equation of tangents and normals to the parabola y² = 4ax at the ends of its latus rectum.
Solution:
The endpoints of the latus rectum of the parabola y² = 4ax are (a, 2a) and (a, -2a).
∴ Eqn. of the tangent at (a, 2a) is yy₁ = 2a (x + x₁)
or, 2ay = 2a (x + a)
or, y = x + a
or, x – y + a = 0
Eqn. of the tangent at (a, -2a) is -2ay = 2a(x + a).
or, -y = x + a
or, x + y + a = 0
Eqn. of the normal at (a, 2a) is y – y₁ = \(\frac{-y_1}{2 a}\) (x – x₁)
or, y + 2a = \(\frac{+2 a}{2 a}\) (x – a)
or, y – 2a = -x + a
or, x – y – 3a = 0

(c) Find the equations of tangents and normals to the parabola y² = 4ax at the points, where it is cut by the line y = 3x – a.
Solution:
Solving y = 3x – a, y² = 4ax
∴ (3x – a)² = 4ax
or, 9x² + a² – 6ax – 4ax = 0
or, 9x² – 10ax + a² = 0
or, 9x² – 9ax – ax + a² = 0
or, 9x(x – a) – a(x – a) = 0
or, (x – a) (9x – a) = 0
∴ x = a, x = \(\frac{a}{9}\)
∴ y = 3x – a = 3a – a = 2a

(d) Show that the tangent to the parabola y² = 4ax at the point (a’, b’) is perpendicular to the tangent at the point (\(\frac{a^2}{a^{\prime}}, \frac{-4 a^2}{b^{\prime}}\)).
Solution:

∴ The product of their slopes = -1
∴ The two tangents are perpendicular to each other.

(e) A tangent to the parabola y² = 8x makes an angle of 45° with the line 3x – y + 5 = 0. Find the equation and the point of contact.
Solution:

or, 4a + 2y + 2 = 0 or, 2x + y + 1 = 0

(f) Prove that, for all values of k, the line y = k(x + a) + \(\frac{a}{k}\) is a tangent to the parabola y² = 4a(x + a).
Solution:

(g) Obtain the condition that the line lx + my + n = 0 will touch the parabola y² = 4ax
Solution:
We have lx + my + n = 0
or, y = \(\frac{-l x-n}{m}\)
Now putting the value of y in the parabola Eqn., we have y² = 4ax.
or, \(\frac{-l x-n}{m}\)2 = 4ax
or, l²x² + n² + 2lnx = 4am²x
or, l²x² + x(2ln – 4am²) + n² = 0
a’ = l², b’ = 2ln – 4am², c’ = n²
As the line is a tangent to the parabola,
we have b^’2 – 4a’c’ = 0.
or, (2ln – 4am²)² – 4l²x² = 0
or, 4l²n² + 16a²m⁴ – 16alnm² – 4l²n² = 0
or, 16am²(am² – ln) = 0
or, am² – ln = 0
or, am² = ln

(h) Prove that the line 4x – 2y – 1 = 0 touches the parabola whose focus is at (0, 0) and the directrix is the line y = 2x – 1.
Solution:
According to the definition,

Question 13.
(a) If (-2, 0) and (2, 0) are the two vertices of a triangle with a perimeter of 16, then obtain the locus of the third vertex.
Solution:

or, 8x² + 9y² – 288 = 0
∴ This is the locus of the 3rd vertex of the triangle.

(b) A point in a plane is such that the sum of its distances from point (2, 2) and (6, 2) is 12. Find the locus of the point.
Solution:

or, x² + 484 – 44x
= 9x² + 9y² – 108x – 36y + 360
or, 8x² + 9y² – 64x – 36y – 124 – 0 which is the locus of the point P.

(c) Obtain the equation of the ellipse which has its centre at the origin, a focus at (2, 0) and the corresponding directrix is the line 2x = 7. Calculate the length of the latus rectum.
Solution:
Centre at (0, 0), focus at (2, 0),
directrix is 2x = 7

(d) Find the equation of the ellipse which has its centre at (-1, 4), eccentricity \(\frac{1}{\sqrt{3}}\) and the ellipse passes through the point (3, 2).
Solution:

Question 14.
(a) Find the equation of the tangent and normal to the ellipse \(\frac{x^2}{16}+\frac{y^2}{9}\) = 1 at the point (\(\frac{8}{3}\), √5)
Solution:

(b) Find the equation of the tangent and normals to the ellipse 2x² + 3y² = 6 at the endpoints of the latera recta.
Solution:
2x² + 3y² = 6

(c) Prove that the line y = 2x + 5 is a tangent to the ellipse 9x² + 4y² = 36 and find the point of contact.
Solution:
Putting y = 2x + 5 in the ellipse eqn.
we have 9x² + 4y² = 36
or, 9x² + 4(2x + 5)² = 36
or, 9x² + 4(4x² + 25 + 20x) = 36
or, 9x² + 16x² + 100 + 80x – 36 = 0
or, 25x² + 80x + 64 = 0     …..(1)
∴ b² – 4ac = (80)² – 4 × 25 × 64
= 6400 – 6400 = 0
∴ The line y = 2x + 5
touches the ellipse 9x² + 4y² = 36.
Now from eqn. (1),
we have (5x + 8)² = 0

(d) Find the equation of the tangent to the ellipse 4x² + 5y² = 20 which are parallel to the line x – y = 2
Solution:
4x² + 5y² = 20

(e) Find the equation of the tangent to the ellipse 4x² + 9y² = 1, which are perpendicular to 2ax + y – 1 = 0.
Solution:
4x² + 9y² = 1

(f) Prove that the line x cos α + y sin α = p touches the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1, if p² = a² cos² α + b² sin² α.
Solution:

(g) Prove that the product of the distances of the foci from any tangent to the ellipse \(\frac{x^2}{a^2}+\frac{y^2}{b^2}\) = 1 is equal to b²
Solution:
The tangent at (x₁, y₁) to the ellipse
\(\frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \text { is } \frac{x x_1}{a^2}+\frac{y y_1}{b^2}=1\)

Question 15.
(a) Find the equation of the hyperbola which has it foci at (0, 0) and (0, 4) and which passes through the point (12, 9).
Solution:
Foci at (0, 0) and (0, 4)
∴ Centre at (0, 2)

(b) Find the equation of the hyperbola with foci at (±3, 0) and directrices x = ± 2.
Solution:
Foci at (±3, 0) and directrices x = ±2.
∴ c = 3, \(\frac{a^2}{c}\) = 2, a² = 2c = 6
∴ b² = c² – a² = 9 – 6 = 3
∴ Eqn. of the ellipse \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1
or, \(\frac{x^2}{6}-\frac{y^2}{3}\) = 1 or, x² – 2y² = 6

(c) Find the foci and latus rectum of the hyperbola whose transverse and conjugate axes are 6 and 4 and whose centre is at (0, 0).
Solution:
The transverse axis is 6, the conjugate axis is 4, the centre is at (0, 0).
∴ 2a = 6, 2b = 4
∴ a = 3, b = 2
∴ c = \(\sqrt{a^2+b^2}=\sqrt{9+4}=\sqrt{13}\)
The foci are (±c, 0) = (±√13 , 0)
∴ Length of the latus rectum = \(\frac{2 b^2}{a}=\frac{2 \times 4}{3}=\frac{8}{3}\)

Question 16.
(a) Find the equation of tangent and normal to the hyperbola x² – 6y² = 3 at the point (-3, -1).
Solution:

(b) Find the equation of the tangent to the hyperbola 4x² – 11y² = 1 which is parallel to the straight line 20x – 33y = 13.
Solution:

(c) Find the equation of tangent to hyperbola 9x² – 16y² = 144 which are perpendicular to the line 2x + 3y = 4.
Solution:
9x² – 16y² = 144
or, 18x – 32y\(\frac{d y}{d x}\) = 0

(d) Prove that the line x + y + 2 = 0 touches the hyperbola 3x² – 5y² = 30 and find the point of contact . Find also the equation of normal at the point.
Solution:
x + y + 2 = 0
or, y = -x – 2
putting y = -x – 2 in the hyperbola equation we have 3x² – 5y² = 30
or, 3x² – 5 (-x – 2)² = 30
or, 3x² – 5 (x² + 4 + 4x) = 30
or, 3x² – 5x² – 20 – 20x = 30
or, 2x² + 20x + 50 = 30
or, x² + 10x + 25 = 0
b² – 4ac = 100 – 4 × 25 = 0
The line x + y + 2 = 0 touches the hyperbola 3x² – 5y² = 30
Now solving x² + 10x + 25 = 0
we have x = – 5.
y = – x – 2 = 5 – 2 = 3
The point of contact is (-5, 3).
Eqn. of the normal is
y – y₁ = m (x – x₁)
or, y – 3 = 1 (x + 5)
or, x – y + 8 = 0

(e) Prove that the line x cos α + y sin α = p touches the hyperbola \(\frac{x^2}{a^2}-\frac{y^2}{b^2}\) = 1, if p² = a² cos² α – b² sin² α.
Solution:

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Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 15 Statistics Ex 15 Textbook Exercise Questions and Answers.

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CHSE Odisha Class 11 Math Solutions Chapter 15 Statistics Exercise 15

Question 1.
If the values observed are 1, 2, …..,n each with frequency 1, find
(i) the mean value
Solution:
Mean of 1, 2, 3, ….. n
= \(\frac{1+2+3 \ldots . . .+n}{n}=\frac{n(n+1)}{2 n}=\frac{n+1}{2}\)

(ii) the mean deviation from the mean separately for two cases when n is odd and when n is even.
Solution:
If n is even, let n = 2m.

Question 2.
For the same set of values as in (1) above, find the variance and standard deviation.
Solution:
x: 1, 2, 3, ….., n

Question 3.
From the table below, find the mean value and the variance.
(a) Values: 1  2  3 ….. n
Frequency: 1  2  3 …. n
Solution:
x: 1  2  3 ….. n
y: 1  2  3 …. n

Question 4.
From the table below, find the mean and the variance.
Solution:
(a) Values: 1  2  5 ….. (2n – 1)
Frequency: 1  1  1        1

(b) Values: 2  4  6 …..2n
Frequency: 1  1  1      1

Question 5.
From the table below, calculate the mean and the variance
\(\text { Values } \quad \mathbf{0} \quad 1 \quad 2 \ldots \quad r \ldots n\)
\(\text { Frequency: } \quad{ }^n \mathbf{C}_0{ }^n \mathbf{C}_1{ }^n \mathbf{C}_2{ }^n \mathbf{C}_r \ldots . .{ }^n \mathbf{C}_n\)
Solution:

Question 6.
From the following table calculate the mean, mean deviation from the mean, and variance.

Marks	Number of students
30-35	5
35-40	7
40-45	8
45-50	20
50-55	16
55-60	12
60-65	7
65-70	5

Solution:

C. I	f	Mid value (x)	d = x – A
30-35	5	32.5	-15
35-40	7	37.5	-10
40-45	8	42.5	-5
45-50	20	47.5	0
50-55	16	52.5	5
55-60	12	57.5	10
60-65	7	62.5	15
65-70	5	67.5	20
	∑f = 80

Let A (working mean) = 47.5, i = 5

u = d/i	fu	u2	fu2
-3	-15	9	45
-2	-14	4	28
-1	-8	1	8
0	0	0	0
1	16	1	16
2	24	4	48
3	21	9	63
4	20	16	80
	∑fu = 44		∑fu2 = 44

Question 7.
In a soccer league, two teams A and B have the following records
A: Goals scored: 0  1  2  3  4
Number of matches: 11 18 8 6 2
B: Goals scored: 0  1  2  3  4  5
Number of matches: 5 20 10 6 3 1
Which team is more consistent? Which is a better team.
Solution:

∴ The mean of B is more than that of A, so B is the better team. A is more consistent as its variance is less than that of B.

Question 8.
The coefficient of variation is defined as \(\sigma / \bar{x}\), that is the standard deviation divided by the mean value. Find the coefficient of variation c.v. for each of the following sets of observations.
(i) 2, 3, 4, 2, 5, 7, 8, 9
Solution:

(ii) 5, 7, 9, 10, 7, 5, 8, 9, 3
Solution:

(iii) 3, 3, 3, 4, 4, 4, 5, 5, 5
Solution:

Question 9.
Suppose the values x₁, x₂, …. x_n having frequency f₁, f₂, …. f_n respectively having mean value x̄ and variance σ². Let a be a fixed real number
x₁ + a, x₂ + a, ….. , x_n + a with frequency f₁, f₂, ….. f_n respectively will have mean value x̄ + a and variance σ.
Solution:

Question 10.
Find the mean and deviation from the mean and the standard deviation of a, a + d, a + 2d, …. , a + 2nd assume that d > 0.
Solution:

Question 11.
Let x₁, x₂, …. x_n be a set of observations with mean value 0 and variance σ²_x and y₁, y₂, …. y_m be another set of observations with mean value 0 and variance σ²_y. Find the mean value and variance of the set of observations x₁, x₂, …. x_n , y₁, y₂, …. y_m combined.
Solution:
x₁, x₂, …. x_n be a set of observations with mean value 0 and variance σ²_x and y₁, y₂, …. y_m be another set of observations with mean value 0 and variance σ²_y

Question 12.
Find which group of the following data is more dispersed :

Range	10-20	20-30	30-40	40-50	50-60
(Group A) Frequency	5	1	3	2	1
(Group A) Frequency	1	3	2	3	1

Solution:
Let us find the mean and standard deviation for the given two distributions.
(i) Mean deviation about mean
M. D = \(\frac{1}{N} \sum_{i=1}^n f_i\left|x_i-\bar{x}\right|\)

(ii) Mean deviation about median
M. D = \(\frac{1}{N} \sum_{i=1}^n f_i\left|x_i-M\right|\)

(iii) variance
Variance is the mean of squared deviations from the mean.

(iv) Standard deviation
Standard deviation is the square root of the mean of squared deviations from the mean.
∴ Standard deviation

Question 13.
The price of land per square meter and that of gold per ten grams over five consecutive years is given below. Decide, which price maintains better stability. [Hint: Stability ⇔ Consistency]

Price of land/Sq.meter(₹)	1500	2500	2600	3000	4000
Price of gold/10 gms(₹)	2500	2600	2750	2900	2850

Solution:

Odisha State Board CHSE Odisha Class 12 Foundations of Education Solutions Unit 1 Contribution of Educators Long Answer Questions.

CHSE Odisha 12th Class Foundations of Education Unit 1 Contribution of Educators Long Answer Questions

Long Answer Questions With Answers

Question 1:
Discuss the life philosophy of Gandhi.
Answer:
Gandhi enunciated integral philosophy of fife. He was a naturalist, an idealist,
individualist in one. His ‘Experiment on Truth’ was the outcome of his experience and prominent philosophical activities are his concept of God, truth, doctrines of morality, non¬violence, satyagraha, labor, equality, citizenship, brotherhood of man His life was concerned with:

• His concept of truth.
• His concept of karma.
• His concept of non-violence.
• His concept of satyagraha.
• His idea of centralization.
• His idea of machine.
• His concept of the village.
• His news of morality.

1) His concept of truth – Gandhiji believed in truth to be the ultimate reality and God can be realized through truth. God is truth, and truth is God. He said truth is manifested both externally and it is expressed through the voice of God. He was the pioneer of truth and non¬violence and conquered the brutal force. One can realise god through truth.

2) His concept of Karma – In Gita, there is view on life and karma. Gandhiji was deeply influenced by Gita for a religious dedication to the service of man. Service of humanity is God. Religion is not a part from human activity. Action takes its origin from Brahma and Brahma is present in all kinds of sacrifice of service. To Gandhi, society and social service are an integral part of life and they are sacred activities.

3) His concept of non-violence – Non-violence of Gandhi was equivalent to love. His concept of non-violence retained deeply in Indian spirituality. The concept ofAhimsa or non-violence of Gandhi was a means and that an end. Man is the end of his material, mental and moral well-being and growth.

4) His concept of Satyagraha – Gandhiji’s concept of Satyagraha was dynamic aspect of non-violence and a tool that created a human context for social conflict. Truth is the end and non-violence is the means to human activities.The term ‘ Satyagraha’ is derived from the Gujarati word ‘agrapha’ which means firmness. For Gandhiji satyagraha is dynamic quality of non-violence. Satyagraha for Gandhiji’s way a truth force for acting socially and humanely.

5) His idea of decentralization – Gandhiji was against concentration of power and individualism of capitalism. He wished a kind of society where economic and social structure of decentralization on the basis of industry and agriculture. This is the productivity aim of education.

6) His idea of machine – Gandhiji was not against the machine, but he did not want it to become the master of machine. He opposed strongly machines because it created unemployment and exploitation of the poor workers by capitalists and too much dependence on man on machine. So he suggested to limit the manufacture of machine and emphasized on cottage industry and handicrafts.

7) His concept of the village – To Gandhiji, village is a small group of people, consisting a unit of society. So the village should be self-governing. He considered that it should be self¬sufficient in the matter of its vital necessities of life like food, clothing and shelter. Secondly his village was not an agricultural community, there should be a balance between agriculture and the village industries. He desired to create agro-industrial community.

8) Gandhiji’s gramraj – Village self government was the opinion of Gandhi. His idea of Gram raj or village self government means it is a complete republic independent or its neighbours are independent with other necessaries. Thus, for every villages the first concern will be no caste and hopes to abandon untouchability and create a class less society.

9) His views on morality – To Gandhiji, the end of all knowledge is the development of morality. The society and individual progress through morality, purity in thought, speech and deeds. So a social foundation of truth and purity should be established through education. To him moral education is to be imparted in schools. Morality is the best virtue of humanity. By participation in games and sports discipline in thought and action is maintained.

Question 2:
Write a note on the Educational Philosophy of Gandhi.
Answer:
As a socio-political, reformer, educationist, idealist, naturalist, social leader and practical philosopher, Gandhiji father of the Nation, the apostle ofpeace and non-violence, the champion of Freedom movement led a scheme of education of India known as ‘Basic Education’. In another way it is known as “Nayee Talim”. His educational philosophy is the potent force for social reconstruction. To him true education is “An all round drawing out of the best in child and man” – body, mind and spirit. The chieftenents ofhis educational philosophy are as follows:

• Education should be free and compulsory.
• Craft centred education.
• Self supporting education
• Emphasis on mother tongue.
• Child centredness.
• Emphasis of education on non-violence.

1) Education should be free and compulsory : Gandhi advocated free and compulsory education for 7 to 14 years and wanted to combine primary education with secondary education called it English Less Matriculation Courses. To him democracy will become successful when education will be free and compulsory. It will develop love for creative work. As India is a poor land and 60 % of population are below the poverty line so education should be free and compulsory for them.

2) Craft centred education : He believed in the principle of learning by doing’ of John Dewey. The basic education aimed at providing education on crafts. He introduced basic crafts like spinning and weaving, carpentry and agriculture. Introduction of crafts evoke the spirit of love for work and teach them the dignity of labour. To him the whole educative process be imparted through handicraft. They will leam the motto “work is worship”. It will develop the dignity of labour.

3) Self-supporting education: Gandhiji knew that India is a poor state and it cannot afford to educate the millions. So Gandhi suggested education to be self supporting. The concept of “Karma Yoga” and dignity of labour will help in the intellectual development. So the child should pay labour partly by binding a gap between education and life drawing upon the cultural, social and vocational potentialities. It is a measure of social reconstruction.

4) Emphasis on mother tongue: Gandhi emphasized mother tongue as the medium of instruction. To him the English system of education hinders understanding and clarity of ideas. By mother tongue, the children can express their views clearly and understand others and this would build sound foundation of education.

5) Child centredness: Child-centredness is an important feature of Basic Education which means the children should be taught to the needs, interests, and capacities of children. So the curriculum and the method of teaching are to be developed to the capacities of learners. Different crafts and subjects to be included in the curriculum to meet individual differences.

6) Education based on non-violence: A unique feature of Gandhiji’s education philosophy was the application of the law of non-violence. He wanted to build a classless society and elimination of exploitation. By the scheme of non-violence and peace, he conquered the heart of brutal forces. So his education of philosophy is based on non-violence. He wanted to create a generation that should believe in non-violence.

Question 3:
What should be the aims, curriculum and methods of teaching of Basic
Education?
Answer:
M. K. Gandhi is called an idealist, a realist, a spiritual person in one. He advocated his philosophy of education and put stress on religious education. The main aims of this philosophy are as follows :

• The utilitarian aim.
• The cultural aim.
• Harmonious development aim.
• Complete living aim.
• Character building aim.

1. The utilitarian aims : To fulfill this aim, the basic needs of human life like food, clothing and shelter and self-supporting to be imparted. The self-supporting aspects aimed at self-sufficient and education to meet one’s expenses. It is otherwise known as ‘Bread and Butter Aims ’ of education.

2. The cultural aims: Culture is essential to refine one’s personality.One should have the qualities of mind which should be reflected in one’s own conduct. Such aims helps in the transmission of culture.

3. Harmonious development aim: To Gandhi, education means “An all round draw ing out of the best in child and man, with body, mind and spirit”. To Gandhi, harmonious development means – innate and acquired powers development from social to intellectual. Basic education helps with all round development of personality of the individuals.

4. Complete living aims: To Gandhi, life is very complex. So he formulated a scheme of education which would fit the children to later life and a child to be prepared for complete living. He should learn how to support his living, social adjustment, occupation and self¬reliance.

5. Character building aims: Character building was the chief aim of basic education. To him character is the expression ofthe w’hole personality including the ethical and spiritual aspects. One should subordinate his own interest to the greater interest ofthe society, cooperate his fellow being about a new social order. Such a person is really a man of character. In his aims of education, Gandhi emphasis the building of character.

The individual character will influence the national character.
i)Curriculum: Gandhi emphasized on child centred curriculum. Education should be related to the environment of the child. He opposed English as the medium of instruction and mother tongue as the medium of instruction up to the level of matriculation. To him English hinders the clarity of thought and put a check on self-expression.My mother tongue, one can express his view correctly and understand others. It also helps in the development of nationalism and patriotism
He introduced craft as a part of curriculum and the whole process of education should be imparted through some handicrafts.
ii) Craft: Education should be given through the medium of some craft on productive work. So different handicrafts like weaving, spinning, carpentry, earthen pot building etc.
iii) Activity centred: The teaching of various subjects should be emphasized. Teaching of craft will be the center point and the teaching of all subjects should be related to craft.The co-related teaching methods are to be employed.
iv) Mother tongue: Mother tongue should be medium of instruction. It will help the children for clear expression and clear understanding, develop patriotism and nationalism.
v) Religious and moral education: For the development of personality, character religions and moral education is to be given. All should respect to all religions. Ethics of all religions is to be taught as a part of education. To Gandhi there is need of moral leaders in free India and building modem India.

Question 4:
Discuss the essential features of Basic Education. Explain the gift of Basic education to education.
Answer:
The essential features of Basic education include:

• Free and compulsory education.
• Purposeful activity-centred education.
• Emphasis on mother tongue.
• Self-supporting education.
• Primary importance for village.
• New cooperative regime.
• Dignity of labor.
• Co-operative work.
• Integrated teaching.
• Educates body, mind, and spirit.

1. Free and compulsory education: Basic Education implies a free and compulsory education for all children between the age of 7 to 14 years. It will reduce the disparity among the children.

2. Purposeful activity centred education: Basic Education centers round some purposeful activity or useful and productive craft training which supports self supporting aims of education.

3. Mother tongue: The medium of instruction should be mother tongue of the child. By this the child can express his views fluently and understand others’ views. It also inculcates the spirit of nationalism and patriotism.

4. Self-supporting: Basic Education is aimed at self-supporting. It followed the principles of learning by doing. They earn from their craft work as well, so as to cover their expenses. Thus craft has both educational and economic value.

5. Primary importance for the village: Basic education was primarily devised for the village. Gandhiji say, “In discussing the question of primary education, I have neither to deliberately confirmed myself to the village, as it is to villages that the bulk of Indians population resides’. To tackle successfully the question of village is to solve the problem for the cities also.

6. New cooperative regime: Basic education aims at bringing about a new cooperative regime in place of the present in-human regime based on exploitation and violent forces.

7. Dignity of labor: Basic education curriculum inculcates the virtue of dignity of labor, a keen sense of discipline, and a great sense of responsibility. Labour-centred education reduces disparity among pupils. It helps with self-employment.

8. Cooperative work: In the scheme of Basic education both the teachers and pupils work for community development and social progress.

9. Integrated teaching: In Basic education, all the subjects are taught in an integrated way. All the instructions are co-related. It seeks to develop the child as a whole. The child is taught with co-related teaching methods of all subjects like math, general science, social sciences, language, drawing and paintings etc. It helps the harmonious development of the child.

10. Educates body, mind, and spirit: Basic education is meant to educate the body, mind and spirit with an unique relation among them. It seeks to develop the child as a whole.

Question 5:
Discuss the causes of downfall of Basic education.
Answer:
Inspite of the merits of Basic education, the scheme was criticised by the richer classes, educationists and suffer from a number of limitations. After the death of Gandhiji the scheme was given a death-blow. The most important reasons of the failure of Basic Education are as follows :

• The Unclear Concept.
• Emphasis on Idealistic view.
• Emphasis on Economic aspects.
• Compact Area approach. ‘
• Absence of Text Books.
• Lack of Trained Skilled Teachers and Textbooks.
• Faculty timetable.
• Costliness of Basic Education.
• Opposition of Traditionalists.
• Matriculation of Minus English.
• Lack of Research.

1) The Unclear Concept: In that period most of the educationists the common people, education administrators as well were not clear about the concept of Basic Education. They were confused of craft education and mechanical education. The common people could understand nothing. In that period, there was no provision of propagation and no mass media system to highlight the program. So the concept of the scheme could not touch the common people and got failure.

2. Emphasis on Idealistic Approach: The scheme laid stress on some idealistic practices like manual work. Such scheme of education was not accepted by the British and the intellectuals because they educated people do not appreciate that their children could do any manual labour. They sent their children to public schools and English medium schools. So the confusion is created.

3. Emphasis on Economic Aspects: In Basic Education, too much emphasis was given on economic aspect. The craft centredness was not accepted by the intellectuals as well as educationists. The productivity activity of self supporting aspect exploits the child labour and craft work puts emphasis on economic aspect. The students become money minded. The guardians felt that their children were turned into laborers, so they opposed the basic ideals of craft.

4. Compact Area Approach: Basic schools were opened in some specific areas, especially in rural areas but not in town areas. The scheme was worked out in a limited area on an experimental basis. So compact area approach was a major cause of the failure of such education system.

5. Absence of Text Books: Basic scheme of education emphasized on craft education. It was a mechanical education. Text books were riot emphasized and no text book was prepared as there were no writers to prepare textbooks on craft training. It was another major causes of the downfall of Basic Education.

6. Lack of Qualified teachers: It was a new type of education like craft. The traditional teachers failed to understand the new pattern of education and the curriculum prepared by Dr. Jakir Hussain. Qualified trained teachers were not available as it was mechanical teaching. There was no provision of teachers’ training. So lack of qualified trained teachers, the Basic Scheme of Education led its downfall.

7. Faculty Time Table: In Basic Education much more was invested or devoted for craft work and other subjects were neglected. In a Basic School 2/3rd. of the time was utilized in craft work. On the timetable, academic subjects were taught after craft work. So academic subjects were neglected. Agricultural students become tired to their academic work. So the faulty timetable was an obstacle of spreading Basic Education.

8. Costliness of Basic Education: As Basic Education needed equipment, so more initial cost was required to purchase craft equipment. There were no funds to meet such expenses and the Govt, could not afford it so it led its downfall.

9. Opposition of Traditionalists: The dream of Gandhi to build a classless society was strongly opposed by the higher class people. So the traditionalists and conservatives were afraid that the new social order would upset their position and so they strongly opposed the system of education.

10. Matriculation Minus English Course: Gandhiji emphasized that English should not be taught to the students in matriculation stages. But the richer classes opposed this and did not prefer to admit their children in such a school. So the strength of the school reduced day by day.

11. Lack of Research: No research activities were encouraged and no research centers were set up. So lack of research, newer methods of teaching, and techniques the Basic Scheme of Education led its downfall.

Question 6:
Discuss the aims of education of Satyabadi School.
Or Explain Gopabandhu’s Educational thoughts.
Or Discuss the contribution of Gopabandhu to the present education.
Answer:
Gopabandhu believed in universal education. The organizers of national Education League opined that everyone has the right of being educated, just as the rays of sun and moon. One shared equally by the people. Pandit Nilakantha Das emphasized classless society education. The people of Odisha are poor and they cannot afford for the education of their children. So Gopabandhu proposed an education that should be ideal, forced, and inexpensive. In 1909 he set up a School at Satyabadi named as Open Air Schooling based on the ideals of Gopabandhu.

The aims, main tenents and educational thoughts of Gopabandhu are discussed below.
1. In-expensive Education: Gopbandhu was hilly aware of that India being a poor country and Odisha a poor province it cannot pay for education of the entire population. So the cost of education to be reduced. He experimented with the groove school on the lines of ancient Gurukul System with no school building and tuition fee payable by the students should be minimum. They should lead a simple and austre life in the school hostel.

2. Idealistic Education – Gopabandhu believed that it is not a costly school building but the idealistic and dedicated teachers who can make a good school were appointed. It is remarked that a school does not consist of only buildings, chairs, and tables, there must be well-educated, sincere and idealistic teachers. No education worthwhile can be imparted without good and efficient teachers.

3. Practical Education – Gopabandhu was cirtical about the prevailing system of education which does not equip the individual to meet the requirement of life. He wanted education to be practical which should make the students economically independent.
To him the present system of education failed to prepare our students for the struggle of life. So they should be taught crafts to maintain their livelihood and they should be taught physical exercise, industry and agriculture etc.

4. Religious and Moral Education: Gopabandhu believed in the all round development of the personality of an individual through education. The students must be taught craft skills in order to capable them to earn their living. There is need of civilized and cultured individuals. So there is need of religious and moral instructions for morality.

5. Social Service and National Integration: Gopabandhu did not stress on individuality. To him, individual is a part of society. So education would enable the individuate to perform the social functions as efficiently as successfully as possible. For him education is a preparation for a life of dedicated social service in the society or nation.Through this education, he wanted to bring about emotional and national integration. In the community dinner in his hostel, every day, high or low sit together and take meals.

6. Women’s Education – Gopabandhu was revolutionary in nature. He knew that in the backward and traditional society of Odisha,a great deal of courage is essential to advocate women’s education. To him, women are the wealth of the family as well as the wealth of the nation. They are the Goddess of family life. If women are educated, they will take care of their children.

7. Mother tongue as the Medium of Instruction – Gopabandhu emphasized on the importance of the mother tongue in the education of a child. It is essential to develop his mental powers. It is also essential to realize the intellectual cultural and spiritual aims of education So education should be imparted through the mother tongue. By mother tongue, the creative powers is to be developed.

Question 7:
Discuss the main features of Groove School ?
Answer:
The main basic principles in which the groove school grew up includes the following:

• Open Air School.
• Free Education.
• Ideal Teachers.
• All round development of Personality.
• Teaching Craft Skills.
• New Methods of Teaching.
• Community dinner and Cultural programmes.
• Emphasis on co-curricular activities.

Importance on Mother’s tongue.

1. Open Air School: Gopabandhu knew well that Indians cannot afford and spend the amount of money in constructing school building and to reduce the expenditure in education without reducing the educational standards the attempts been made opening a groove school on the lines of old Gurukul system Thus, it is an Open Air School similar to Shantiniketan.

2. Free Education: Education was free and minimum fee was charged. The attempts to set up school, an old Gurukul system and the students will lead a simple austere life.

3. Ideal Teachers: Gopabandhu put high premium on the quality of teachers. Gopabandhu aimed at ideal education and teachers should be ideal sacrificing in nature. The teachers of Satyabadi school had voluntarily given up the pleasures of life for the purpose of rendering service to the community.

4. All round development of Personality: Satyabadi system of education aimed at the development of all the aspects of the personality. He emphasized character building inculcation of social values, virtues qualities of good citizenship, patriotism, brotherhood and spirituality. For the development of good qualities various co-curricular activities, debates, excursions, physical exercises, games and prayer assemblies are essential.

5. Teaching Craft Skills: The system of education strongly opposed the system of education bookish and aimed at imparting education of art and craft skills. Then the children will be able to prepare for the future, learn the struggle for life. Craft education may enable to earn their livelihood.

6. New Method of Teaching: Satyabadi Vana Vidyalaya was a residential school and the teachers and students stay together, in the hostels. The Headmaster, asks the teachers to submit their class notes to him for supervision. The teachers and the Headmasters, sit together and discuss mutually the course. The programs like debate, excursion etc. are continued.

7. Community dinner and Cultural program: The elected Secretary (from the boarders) manage the hostel The school and hostel for self-discipline democratic management and ideal student life. The students and teachers take dinner together. It teaches them community living.

8. Emphasis on co-curricular activities: To bring an all around development of personalities of the students various types of co-curricular activities were arranged in the Satyabadi School, such as (i) Literary activities (ii) Debates and games (iii) Prayer assembly (iv) Physical exercises (v) Literary magazines etc. Debates are aimed at oratoral abilities of the students. Physical exercises brings about the development of character, discipline and virtues. Prayer assembly develops the discipline and moral instructions.

9. Importance of Mother tongue: Mother tongue emphasized on the medium of instruction. It helps in understanding and developing nationalism, and patriotism and the child can express his views clearly and understand others.

Question 8:
Explain, the causes of downfall of Open Air Schooling or Satyabadi Vana Vidyalaya.
Answer:
Like the downfall of Basic Education of Gandhi, for some reasons Satyabadi Vana Vidyalaya led its downfall. The chief causes are:

• Lack of local support and unclear concept.
• Economic condition.
• Lack of help of the Govt.
• Participation of Gopabandhu in Indian National Movement.
• The death of Utkalmani.

1. Lack of local support and unclear concept – Satyabadi Vana Vidyalaya was surrounded by conservative villages. Conservative people and Brahmin society. Such conservatives did not appreciate the idealistic education system of Gopabandhu. Pandit Nilakantha Das wanted to build a classless society education which was a stroke to the conservatives.

The conservatives opposed this and they do not like to read their children with other backward-class children. They wanted to continue the superstitions.Lack of local support the enrolment of children is reduced.To oppose Gopabandhu’s system of education in 1912 on March 22, the conservatives fired the school and the main property of school library was destroyed. Such an incident shook the strength of the school.

2. Non-cooperation of the Govt.: It was not a traditional education system nor followed the British system of education and opposed the older beliefs, superstitions and conservatism. It is filled with idealism, patriotism, nationalism and social service programs.It aimed at creating leader for the state. So the British opposed it. No Govt, grant lias come and the application for Govt. Recognition was canceled. The school was transferred under Calcutta University in 1916 and then to Patna University in 1917, but it could not get the Govt. help.

3. Economic Condition : The third cause of the downfall of Open Air Schooling was the economic condition of the school. In 1921 Vana Vidyalaya was transferred into a National School. But the Govt, grant only two hundred rupees per year was refused and cut off very relationship from Patna University. In 1923, it turned to a National College and become autonomous. But it did not exist long. It suffered from the financial crisis. The teachers demanded to merge the college with the University. For this Gopabandhu remained away from the college. But the colleagues failed to continue the college for which it led its downfall.

4. Participation in Non-cooperation Movement: In 1920, Utkalamani joined in the Non-cooperation movement. He invested all his time and resources in the Freedom struggle. He found no time and resources to invest in groove school. Thus, the school led its downfall

5. The Death of Utkalamani: The day before the World famous Car Festival on June 17, 1928, Gopabandhu died in an immature death. The glorious chapter of Odia’s history’ came to an end. The next generation did not give any importance to the institution and just five years after the death of Utkalamani, the other Satyabadi Panchasakhas died one after another, the school was neglected and led its downfall.

Question 9:
Discuss the educational philosophy of Sri Aurobindo.
Answer:
Sri Aurobindo dedicated his whole life for society and education to provide contribution to travel towards divine perfection and to express the power, harmony, beauty and joy of self-realization.By education, he means that which will offer the tools whereby one can live for the divine for the country for oneself and for others. His principle of the philosophy of education, the awareness of man as a spiritual being.

Integral Education – Aurovindo’s integral education means integral growth of the individual’s personality. The function of education is to study the mind of individuals, people, nature, the universe. He put more emphasis to study the mind.

The human mind consists of four layers. They are :
1. Chitta – the storehouse of memory.
2. Manas – the sixth sense like – sight, sound, taste, smell, touch.
3. Budhi – thought or intellect.
4. Truth – Satya
Integral education, attempts to the integral development of physical being, vital beings, psychic being and mental being about a transformation of man into a spiritual being.

Aurobindo’s philosophy of Education are:
1. Education of the Physical being: To Aurovindo beauty is the ideal of physical life such as (i) To discipline and control the physical function (ii) For harmonious development of the body and physical movements (iii) Rectification of defects (iv) To awaken the body consciousness one has to undertake physical exercises. The factors of spiritual discipline, service, bhakti, and yoga are essential physical education. Restlessness is the important aspect to control the body and to achieve. Concentration physical education also controls sex drives or impulses. Emphasis is given on games and sports which an renew physical and higher forms of energy, develop tolerance, self control, friendliness etc.

2. Education of the Vital Being : It helps in the development of character. Vital education emphasizes on the vital being of man by which the man be able to understand the inner and outer world. It develops self observation. Vital being means utilization of the sense organs which help us to receive knowledge. The senses like a sight hearing, small, touch, taste and mind should be trained. Vital education also aimed at the aesthetic personality development.

3. Education of the Mental Being: Mental being education emphasizes on mental science and concentration. The mother says to silence the mind, one has to take the help of classical yoga. By yoga, one can acquire mastery of the mind. So knowledge of the education of mental being which helps is the gradual liberation from ignorance.
Mental education has three-fold functions:
i)To gather old knowledge.
ii) To discover new knowledge.
iii) To develop the capacity use and apply the knowledge acquired.
Through the application of knowledge, the pupil develops cognition, ideas, intelligence and mental perception. For this man becomes the source of knowledge.

4. Education for Psyche Being: Psyche being is the psychological centre of mind. The function of education is to enable man to become conscious of the psychological centre which is key to an integral personality. Psyche education is to enable an individual to see his soul grow in freedom. It supports the vital, physical, and mental being. When an individual develops psyche consciousness, he understands life and himself.

To him the psyche being is a spiritual personality put forward by the soul in its evaluation. The business of education is to develop the capacity of psychological being towards a realization of potentialities. Psyche being is possible through yoga or tapasya of love. As a result of this yoga one can attain liberation from suffering.As a result four-fold approval like the physical, the mental, the psyche and love in the ii idi v ideal student, the man gets liberation from the material world, desires, ignorance and suffering.
A tota 1 spiritual education is the goal of education and spiritual transformation of man is the goal o f integral education.

Question 10:
Discuss the philosophical thoughts of Rousseau.
Answer:
Rousseau’s philosophical thoughts are related to Naturalism and Negative Education.

1) His Naturalism
a) God has made all humans good but when they come in contact with society they become spoiled. In order to change them again into good, we should bring them back to nature.
b) In the beginning of human civilization, man was happy and good, but now he is unhappy. If he goes back to nature, he will again be happy and good. Thus, a child be educated and developed according to his natural tendencies. Society and school has no role to play in the process.
c) He did not like old values and traditions of the society. According to him, social relations can be brought about by destroying these values.
d) There are three main forms of naturalism such as Social, Psychological and Physical. In his social naturalism, he devises education as a method to mold the society. He opined that we could not become a man and citizens at the same time. Out of two options, we should become a man only. Thus, the individuality of man is honored by him. Psychological naturalism meant that the child should be given chance to develop on the basis of his inner feeling and natural tendencies and experiences gained from contact with others are harmful and unnatural.By physical naturalism, Rousseau means that child should be given chance to come in contact with birds, animals, and other physical objects of nature and learn in the process. This learning will make him free from evils.
e) He opposes the organization of education in social foundations. Thus he opposed school/education in the formal sense and advocated an individual basis of education.
f) He opposed too all sorts of habit formation in the child. It is because this can make a child traditional.
Thus, Rousseau’s Naturalism is fully of many unnatural and impracticable ideas and he himself realized it but he put three ideas with such a force that is influenced not only the society of Europe but also the educational system of the period.

2) Negative Education
In the 17th. century, Europe, man was considered bad by nature. So efforts were made to change the nature of man by imparting religious education.
Rousseau went contrary to this believing infallibility of man and proposed the idea of Negative Education. By this education he means not teaching truth or virtues to a child but shielding his heart from evils and mind from errors. The feature of his negative education are given below:
a) Nothing against the interest, attitude on age of the child should be taught. He should be given full freedom to choose his own curriculum.
b) The education of a child should be based on his natural tendencies and stages of development by using different organs and senses of the child. Mind should be less taxed for the purpose. Mind should be inactive toll the child develops discretion power in him thus he emphasized, the training of senses by keeping the mind idle.
c) Child should be protected from outside environment to keep him alien to vices. In this way, there will not be any need to impart knowledge of virtues to the child. Virtues may be taught of the later stage of life.
d) The child should not be taught anything at all, especially from books. Small children should learn from nature itself.
e) Thus by Negative Education, Rousseau opposed not only the mental development of the individuals/child but he also opposed moral and spiritual development.

Question 11:
Discuss the different phases of education of Emile as supported by Rousseau. Curriculum, methods of teaching and discipline.
Answer:
Rousseau’s programme of education for Emile is devised into different phases and Rousseau had divided the whole programme of education curriculum on the basis of the development stages of human child.
(i) Infancy (from 00 to 5 years): At this stage instead of giving the child controlled information of various subjects it is better to pay attention to the development of child’s body and his sense organs. He should be allowed to play with whatever things he likes. The dresses should be made for free movement. His toys should be cheap ordinary and natural like leaves, plants flowers, stems etc. According to Rousseau Emile should be given a negative Education druing infancy.

(ii) Childhood (5 to 12 years): Rousseau opposed the use of textbooks during this period. The child should be given chance to leam everything through observation and experiences. These experiences develop sense organs, which will lead to the development of mind and power of reasoning. He should be allowed full freedom to use his sense, the sense organs, the eyes to be trained to measure height, weight, and distance.

(iii) Adolescence (12-15 years): During this period natural curiosity of the adult develops. So he should be taught natural science and languages, mathematics, music, painting and social services. He should use maps in learning geography.

(iv) Adulthood (15 – 20 years): The organs become active with a maturity of mind and intellect he should leam social and moral education like objects of social services.
His Discipline: Rousseau advocated complete freedom, left free to the environment.
Self discipline is learnt in the process of experiences. There is no scope ofgiving any punishment to the child but natural process of feed back in stills discipline in him.

Question 12:
Dsicuss the life philosophy of Rousseau. Give his educational aims and ‘Self Education’ and curriculum.
Answer:
Life Philosophy of Rousseau: Jean Jacques Rousseau (1712 -1778) lost his mother just after his birth and his father brought him up but he could not look after him. Rousseau fell to prey to all sorts of bad habits. He originally belonged to Geneva and the beauty of that place lured him to use it and it made him a careless man.
Rousseau got matured. He hated the society for its evils. Evil customs and artificial traditions and tried to retun it on the line of nationalism and wished everybody shun the evil society and live with nature.

Out of five books, “The progress of arts and science”, “New Heloise”, Confessions, ‘Social Contract’ and ‘Emile’ are unique and the last two books ‘Social Contract’ and ‘Emile’ brought great name and fame to him.His ideas of education can be seen in Emile. It is a novel whose hero is Emile and the heroine is Sofia. In his book, Rousseau keeps Emile away from society and culture and leaves him under the guidance of an ideal teacher in the natural environment and Emile is educated in an atmosphere of natural beauty. There are five chapters in the book. The first chapter describes education of Emile is in fancy, childhood, adolescence and adulthood and the last chapter deals with the education of Emile’s wife Sofia.

People reacted against his book “Emile very sharply. France and Switzerland banned it end it was put into the fire at many place in Europe consequently. Rousseau had to leave France for England in 1766.After 11 years of exile, he returned to France and wrote his last book “Confession”. Rousseau’s philosophical thoughts are related to Naturalism and Negative Education.

Educational Aims: Rousseau emphasized on the following aims of education, l) We are bom weak and we want strength. We are poor and we want help. Whatever we do, not have is to be given by education is the ultimate aim of education.

• To establish harmony between man, object and nature.
• Child attains pleasure by using his organs and senses and by applying his strength. So the aims of education is to develop his various innate powers by helping him in his natural activities.
• Books are not end of education. They are only means and the child is the end. The aim of education is to develop the child to be fullest for a complete and happy life.

His Self-Education:
i) He opposes strongly the imposition of ideals and morals into the mind of the child from
outside. Children should learn these things through activities. It is because the children are more interested in activities rather than sitting idle and hearing lectures. At that stage, helps enough power of assimilate between construction and destruction. His only concern is to bring about change will form through any activity.
ii) Body can become strong through physical exericse and mind also become strong through self study. In self-education the child can proceed further according to his own physical and mental capacities.
iii) Only that knowledge gets retained for a longer period, which is learned from self-experiences. We should accept the experiences of others only after our own wisdom.
iv) Blind fellowship is not accepted at all. A child should not learn a thing because he has been asked to do so but he should learn oniyit in the process of his self study.
v) Special emphasis is to be given on the physical development of the child.
Curriculum
Rousseau was against the fixed curriculum, the child should be educated through activities and first-hand experiences.During infancy positive instructions to be imparted with good health training of senses and cultivation of natural habits. At the stage of childhood provision of in parting physical education through a set of gymnastics and the exercises training of senses.

At the stage of boyhood, the chief intellect is to be trained through teaching of good sense of physical senses, language, mathematics, manual works, social relations, music and drawing.At adolescence morality of the individual is to be trained through teaching of good education and by activity method and occupation. Moral education subjects are : history, religion, aesthetics, physical culture and sex education etc. are included in the curriculum at the adolescence stage.

Question 13:
Discuss John Dewey’s contribution to educational thought and practice.
Answer:
John Dewey is one of the greatest educationists of the modem age. He has revolutionized the exponent of pragmatism.
Meaning of Education to John Dewey: John Dewey considered individuality as the aim of education. According to him, all education proceeds by the participation of the individual in social consciousness of the race. The educative process, according to John Dewey has two aspects – Psychological and Sociological because every individual is a psychological as well as social being. So no aspect can be neglected in the process of education.

1.  Education as life: According to John Dewey education is a process of living. So the school experiences should have a resemblance with life outside the school and the school functions as a society in miniature form.
2.  Education as Growth: Education is a continuous process that adds to child’s experience resulting in the growth and development of the child. It helps the child to grow to its full extent.
3.  Education as Reconstruction of Experience: Every generation inherits certain experiences from its previous generation. These experiences are to be modified according to the changing situations through education.
4. Education as a Social Process: Man is a social being and education socializes to human child. Right education helps the child make suitable adjustments with his social environment.John Dewey and Aims of Education: John Dewey is of the opinion that education process no aim beyond itself, it is its own end. There are no fixed aim of education to John Dewey.

Because, human life changes with the changes in time, place and situations and education should cater to the changing nature of human life. Education should therefore aim at cultivating a dynamic and adaptable mind in the child so that he can suitably adjust with his changing environment. Education should also create new value for the child. Education should aim at inculcating democratic values and attitudes in the child.

John Dewey and Curriculum: Curriculum according to John Dewey should reflect the child’s social life and social activities. It should be flexible, and changeable and it should take into consideration the child’s interests and educative experiences. As per example the curriculum at the primary stages should be based on the fourfold interests of the small child, interests in conservation and communication interests in inquiry interests in making change or construction and interest in artistic expression. Hence subjects like reading, writing, counting, handwork and drawing etc. are to be included at this stage.

The curriculum at higher students of education must have provisions for the environment and reorganization of past experiences. It just stimulates the learner to acquire new experiences and new ideas to they learned ones. John Dewey has also put emphasis on curriculum. This means each subject should be linked with the other and each should also related to the day life of the child.

John Dewey and Method of Teaching: John Dewey put emphasis on learning by doing. He stressed project method and this method is meant for the child. Earning was to be emphasized on teaching. The students should be free to carry on their whole planning and activity. Learning should be incidental and an outcome of the purposeful activity.

John Dewey and Discipline: John Dewey believed in the theory of free discipline and self-discipline. Discipline imposed from outside is directive with eyes of the John Dewey. Discipline should be social in character. The natural impulses of the child should be channelized in a socially desirable way. The main function of school discipline is to cultivate in the children’s social attitude, habits and ideal conduct through cooperative activity.

John Dewey and Role of the Teacher: In John Dewey’s system of education the child occupies the central position. The teacher is the friend, philosopher and guide of students. The teacher has to observe the pupil’s planning, encourage their activity and provide them the necessary opportunity and environment. John Dewey’s teacher is free to frame his own curriculum and carry on the administration ofhis own school.

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Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Tense Patterns Unit 2 The Present Perfect Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Tense Patterns Unit 2 The Present Perfect

SECTION- 1:
Examine the use of the Present Perfect in the following sentences.
(a) A: Where’s your T.V. set? I don’t see it.
B: I have sold it.
(b) A: Why are you looking so happy?
B: I have just got a job.
In the above examples, the speaker ‘B’ talks about some events beginning in the past and lasting up to the present moment (or still continuing). Though the event started in the past, it is connected to the present moment of speaking. In this sense, we used the Present Perfect Tense.

Activity — 9
Complete the sentences marked B. Use the verb in brackets, together with ‘just/already/yet’.
A: What does your wife think of your plan?
B : I __________(not tell) her yet.
A: Would you like something to eat?
B : No, thanks I __________(just/eat).
A: Is your brother here yet?
B : Yes, he __________(just/arrive).
A: What’s on TV today?
B: I don’t know. I __________(not see) the programme yet.
A: Do you know where Bidhu lives?
B : Yes, he __________(just/move) to Satyanagar.
A: Are your friends coming to the circus with us?
B : No, they __________(already/see) it.
A: When is Prakash leaving?
B : He __________(already/leave).
Answer:
1. A: What does your wife think of your plan?
B: I have not told her yet.
A: Would you like something to eat?
B: No, thanks I have just eaten.
A: Is your brother here yet?
B: Yes, he has just arrived.
A: What’s on TV today?
B: I don’t know. I have not seen the program yet.
A: Do you know where Bidhu lives?
B: Yes, he has just moved to Satyanagar.
A: Are your friends coming to the circus with us?
B: No, they have already seen it.
A: When is Prakash leaving?
B: He has already left.

Activity – 10
Study the situations suggested below and makeup sentences with “yet”, “already” or “just”.
1. You are going to Koraput next Sunday. You phone your travel agent to buy a ticket for you.
Later your father says. ‘Shall I get the ticket for you ?”
You: No, (buy) ___________________________________.
2. Alok goes to the Post Office but returns after a while. His friend asks you if he is still at the Post Office.
You: No, (come back) ___________________________________.
3. You know that one of your classmates is looking for a house. When you meet him, you want to know if he has been successful.
You: ___________________________________.
4. You visit a friend’s house after lunch. He asks if you would like something to eat.
You: ___________________________________.
5. You are doing your homework. Your brother thinks that you have finished and turns the light off. What would you tell him?
You: ___________________________________.
6. Amar goes out. Ten minutes later his friend comes and asks you if he can meet Amar.
You: ___________________________________.
Answer:
1. No, I have already bought it from a travel agent.
2. No, he has already come back.
3. Have you got a house yet?
4. Have you had your lunch yet?
5. I have not finished my homework yet.
6. Amar has iust gone out

Activity – 11
Below is a list of things that your parents have asked you to do today. You have checked the things you’ve done so far. Talk about the things you’ve already done and the things you haven’t done yet. (Two have been done for you as examples.)
1. do the washing up
2. do your homework ✓
3. wash the scooter
4. write to the brother
5. read today’s newspapers ✓
6. defrost the fridge
7. buy some fruits ✓
8. watch the news on TV
9. clean the windows ✓
10. water the plants
11. empty the dustbins ✓
12. phone uncle
Answer:
1. I haven’t done the washing up yet.
2. I have already done my homework.
3. I have not washed the scooter yet.
4. I have not written to my brother yet.
5. I have already read today’s newspaper.
6. I have not de-frosted the fridge yet.
7. I have already bought some fruit.
8. I have not watched the news on TV.
9. I have already cleaned the windows.
10. I haven’t watered the plants yet.
11. I have not emptied the dustbin yet.
12. I have not phoned my uncle yet.

Activity – 12
Anil, Anima, Mohan and Anand are talking about the places they have visited. Fill in the spaces using the information in the chart below.

	Kolkata	Koraput	Puri	Sambalpur	Shillong
Anil	Yes	No	No	Yes	No
Anima	Yes	No	Yes	Yes	No
Mohan	No	No	Yes	No	No
Anand	Yes	No	Yes	Yes	No

1. Anil __________been to Kolkata, but Mohan ___________.
2. Three people __________ been to Puri.
3. Only one person __________been to Sambalpur.
4. Mohan is the only one who __________ visited only one place.
5. Nobody __________ been to Shillong.
6. Two people __________ been to three places.
7. Anima and Mohan __________ both been to Puri, but neither __________ been to Koraput.
Answer:
1. Anil has been to Calcutta, but Mohan hasn ’t.
2. Three people have been to Puri.
3. Only one person hasn’t been to Sambalpur.
4. Mohan is the only one who has visited only one place.
5. Nobody has been to Shillong.
6. Two people have been to three places.
7. Anima and Mohan have both been to Puri, but neither haven’t been to Koraput.

Note:
Look at the difference between ‘have /has been ’ and ‘have/has gone ‘Has /have been’ means went and returned. But ‘has gone/have gone means went and not returned. The Present Perfect form of ‘go’ (has/have gone) is not used when the subject of the sentence is 7, we or you.’ The Present Perfect is used to refer to some happening in the past, for which the time of action is not given.

SECTION – 2
Look at the sentences below.
1. Hari didn’t have a beard six months ago. He has a beard now. He has grown a beard.
2. Malati was very shy. She is smart now. She has become smart.
3. She was a little baby when I last saw her. She is a young girl now. She has grown up.
When a change has taken place between now and sometime before now, we use the Present Perfect Tense.

Activity – 13
Study the situations below and make up appropriate sentences using the verbs suggested.
1. Yesterday my sister bought a pen. She can’t find it now. (lose)
______________________________________________.
2. The children were playing here some time ago. Now they are not seen, (leave)
______________________________________________.
3. My friend weighed 50 kilograms. Now he weighs 70. (gain weight)
______________________________________________.
4. The man met with an accident. Now he is not able to speak, (loses voice)
______________________________________________.
5. It was raining in the morning. Now the sky is clear. (stop)
______________________________________________.
6. The tiger attacked the man. He is dead now. (kill)
______________________________________________.
7. He had some paper with him. Now he does not have any to write on. (run out)
______________________________________________.
8. My teacher got a job in a bank. He is not coming to school anymore, (resign)
______________________________________________.
Answer:
1. She has lost it somewhere.
2. They have already left.
3. He has gained weight.
4. He has lost voice in the accident.
5. The rain has already stopped.
6. The tiger has already killed the man.
7. He has already run out of paper.
8. He has already resigned from school.

SECTION – 3
Present Perfect is often used with the following time expressions.

lately	until now	ever	for five years
not yet	never	always	over the last eight years
recently	just	so far	in the past Iwo years
in recent years	already	since 1990

Do remember that the expressions like “last year, ago, yesterday” etc. cannot be used in the Present Perfect.

Activity – 14
Rewrite the following sentences putting the words in brackets in the right place. The first one has been done for you.
1. My teacher has wanted to be a writer. (never)
Ans. My teacher has never wanted to be a writer.
2. I’ve found him helpful, (always)
______________________________________________.
3. People have misunderstood him. (often)
______________________________________________.
4. I’ve had lunch. (just)
______________________________________________.
5. Has he been to Puri? (ever)
______________________________________________.
6. Don’t panic. The police have arrested the culprit, (already)
______________________________________________.
Answer:
2. I’ve always found him helpful.
3. People have often misunderstood him.
4. I’ve Just had lunch.
5. Has he ever been to Puri?
6. Don’t panic. The police have already arrested the culprit.

Activity – 15
Imagine that you suddenly run into an old friend whom you have not met for the last five years. But he has changed so much that you can hardly recognize him. Describe the changes that have taken place in your friend.

a) _______________________________
b) _______________________________
c) _______________________________
d) _______________________________
e) _______________________________
Answer:
1. He has grown into a young man.
2. He has become strong and healthy.
3. He has grown fair and tall.
4. He has made himself smart and confident.
5. He has grown a thick beard.

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