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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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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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BSE Odisha 10th Class English All Things Bright and Beautiful Text Book Questions and Answers

F. Let’s Read And Understand:

Question 1.
What does the poet think of all things?
(ସମସ୍ତ ଜିନିଷ ସମ୍ପର୍କରେ କବି କ’ଣ ଭାବିଛନ୍ତି ?)
Answer:
The poet thinks that all things are bright and beautiful and wise and wonderful.

Question 2.
Who has made all these things?
(କିଏ ଏ ସମସ୍ତ ଜିନିଷକୁ ନିର୍ମାଣ କରିଛନ୍ତି ?)
Answer:
The Lord God has made all these things.

Question 3.
What are the little things mentioned in the poem?
(କବିତାରେ ଉଲ୍ଲିଖ୍ କ୍ଷୁଦ୍ର ଜିନିଷଗୁଡ଼ିକ କ’ଣ ?)
Answer:
The little things mentioned in the poem are little flowers and little birds.

Question 4.
How does the poet describe the beauty of flowers?
(କବି କିପରି ଫୁଲଗୁଡ଼ିକର ସୌନ୍ଦର୍ଯ୍ୟ ବର୍ଣ୍ଣନା କରିଛନ୍ତି ?)
Answer:
The poet describes that God has given bright colors to flowers. When a little flower blossoms, it looks beautiful and its brightness attracts others. The beauty of the flowers lies in their bright colors.

Question 5.
How does the poet describe the little birds?
(କବି କିପରି କ୍ଷୁଦ୍ର ପକ୍ଷୀଗୁଡ଼ିକୁ ବର୍ଣ୍ଣନା କରିଛନ୍ତି ?)
Answer:
The poet describes that the little birds that sing sweetly are made by God. God has made their tiny wings which help them to fly.

Question 6.
How is the mountain described in the poem?
(କବିତାରେ ପର୍ବତ କିପରି ବର୍ଣିତ ହୋଇଛି ?)
Answer:
In the poem, the mountain is described as purple-headed.

Question 7.
Why does it appear so?
(ଏହା କାହିଁକି ଏପରି ଦେଖାଯାଏ ?)
Answer:
The bluish-red rays of the setting sun make the mountaintop look purple.

Question 8.
What brightens up the sky?
(ଆକାଶକୁ କ’ଣ ଉଜ୍ଜଳିତ କରିଥାଏ ?)
Answer:
The sunrise and the sunset brightens up the sky.

Question 9.
How does the sky look during the sunset ?
(ସୂର୍ଯ୍ୟାସ୍ତ ସମୟରେ ଆକାଶ କିପରି ଦେଖାଯାଏ ?)
Answer:
The sky looks bright during the sunset.

Question 10.
Which are the two seasons mentioned in the poem?
(କେଉଁ ଋତୁ ଦୁଇଟି କବିତାରେ ଉଲ୍ଲିଖୁତ ହୋଇଛି ?)
Answer:
The two seasons mentioned in the poem are winter and summer.

Question 11.
Why does the poet consider the summer sun pleasant?
(ଗ୍ରୀଷ୍ମକାଳୀନ ସୂର୍ଯ୍ୟଙ୍କୁ କବି କାହିଁକି ଆନନ୍ଦଦାୟକ ବୋଲି ବିଚାରିଛନ୍ତି ?)
Answer:
The summer comes after the winter and it gives great relief to the winter-hit people. The summer sun is warm and comfortable in England. That is why the poet considers the summer sun pleasant.

Question 12.
What do we enjoy in greenwood?
(ଆମେ ସବୁଜ ଅରଣ୍ୟରେ କ’ଣ ଉପଭୋଗ କରୁ ?)
Answer:
We enjoy the beauty of the tall trees in the green wood.

Question 13.
How are the meadows useful for us?
(ଘନ ତୃଣଭୂମିଗୁଡ଼ିକ ଆମ ପାଇଁ କିପରି ଉପଯୋଗୀ ?)
Answer:
The meadows are open areas of grassland where people play different games.

Question 14.
Where do the rushes grow?
(ନଳତୃଣଗୁଡ଼ିକ କେଉଁଠାରେ ବଢ଼ିଥା’ନ୍ତି ?
Answer:
The rushes grow by the waterside.

Question 15.
Why do people gather rushes ?
(ଲୋକମାନେ ନଳତୃଣଗୁଡ଼ିକୁ କାହିଁକି ସଂଗ୍ରହ କରନ୍ତି ?)
Answer:
People gather rushes every day because they are used for making mats and baskets.

Question 16.
Why has God given us eyes?
(ଭଗବାନ୍ ଆମକୁ ଚକ୍ଷୁ ଦେଇଛନ୍ତି କାହିଁକି ?)
Answer:
God has given us eyes to see all the beautiful things created by Him.

Question 17.
What should our lips tell?
(ଆମର ଓଷ୍ଠ | ଅଧର କ’ଣ କହିବା ଉଚିତ ?)
Answer:
Our lips should tell about the greatness of God and all His creations.

Question 18.
How does the poet describe God?
(କବି ଭଗବାନ୍‌ଙ୍କୁ କିଭଳିଭାବେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି ?)
Answer:
The poet describes God as Almighty who has made everything.

G. Let’s Appreciate:

The poet describes many things in the poem. Make a list of the things described in the poem.
(କବିତାରେ କବି ଅନେକ ଜିନିଷର ବର୍ଣ୍ଣନା କରିଛନ୍ତି । କବିତାରେ ବର୍ଣିତ ଜିନିଷଗୁଡ଼ିକର ଏକ ତାଲିକା କର ।)
Answer:
List of things described in the poem:

Flowers, birds, cold wind, pleasant summer sun, ripe fruit, mountains, rivers, sunset, sunrise, sky, garden, tall trees, greenwood, meadows, rushes, eyes, and lips.

Question 1.
Which of the things are bright and which of the things are small?
(କେଉଁ ଜିନିଷଗୁଡ଼ିକ ଉଜ୍ଜଳ ଓ କେଉଁ ଜିନିଷଗୁଡ଼ିକ କ୍ଷୁଦ୍ର ?)
Answer:
Bright things are                                                              Small things are
(i) colors of the little bird and little flower                       the little flower
(ii) purple-headed mountain and river                            the little bird
(iii) sunrise and sunset                                                     tiny wings
(iv) the sky
(v) the summer sun
(vi) the greenwood
(vii) the meadows

Question 2.
Which are the lines in the poem where the poet expresses his gratitude to God?
(କବିତାର କେଉଁ ଧାଡ଼ିଗୁଡ଼ିକରେ କବି ଈଶ୍ବରଙ୍କୁ ନିଜର କୃତଜ୍ଞତା ଜଣାଇଛନ୍ତି ?)
Answer:
The lines in the poem where the poet expresses his gratitude to God are as follows.
The Lord God made them all (Line 4)
He made their flowing colors (Line 7)
He made their tiny wings (Line 8)
He gave us eyes to see them (Line 21)
And lips that we might tell (Line 22)
How great is God Almighty (Line 23)

Question 3.
Is this poem a description or a prayer?
(ଏହି କବିତାଟି ଏକ ବର୍ଣ୍ଣନା ଅଥବା ପ୍ରାର୍ଥନା ଅଟେ ?)
Answer:
This poem is a description that gives a beautiful description of various wonderful things of God.

Question 4.
Why do you think so?
(ତୁମେ କାହିଁକି ଏପରି ଭାବୁଛ ?)
Answer:
This poem All Things Bright and Beautiful is more of a description. The word ‘prayer’ means a solemn request for help or expression of thanks addressed to God for His help and blessings. In this poem, the poet expresses his deep gratitude to God as the maker of all things bright and beautiful, wise and wonderful, and all creatures great and small. That is why the poet feels obliged and says some words in praise of Him. Thus, it is the description.

• Each stanza of the poem is a unit. The last word of one line is similar in sound to the last word of another line. These are rhyming words.
  Rhyming words in the poem are as follows.

  beautiful        small     sings     open      by       play       tell wonderful      all          wings    colors     sky     day       well

Activity I:
Students are divided into groups of four or five. Each group is asked to find the last word in each line of a stanza and put together all the words which have similar sounds. Each group is asked to present its findings.
(ଛାତ୍ରଛାତ୍ରୀମାନଙ୍କ ମଧ୍ୟରୁ ୪ ବା ୫ ଜଣଙ୍କୁ ନେଇ ଗୋଟିଏ ଗୋଟିଏ ଦଳ ଗଠନ କରି ପ୍ରତ୍ୟେକ ଦଳକୁ (କବିତାର) ପ୍ରତ୍ୟେକ ଧାଡ଼ିର ଶେଷ ଶବ୍ଦ ସହିତ ସମଧ୍ୱନିଜନିତ ଅନ୍ୟ ଶବ୍ଦଗୁଡ଼ିକୁ ଏକତ୍ର କରିବାକୁ କୁହାଯାଇଛି ।)
(This activity shall be done by the teacher in the class.)

Activity II:
(a) Fill in the blanks choosing the appropriate words given in brackets and read the lines.
1. God has given it _________.
2. So it can _________.
3. And it beautifully _________.
4. While going up in the _________.
(fly, sings, sky, wings)

Answers:
1. God has given it wings.
2. So it can fly.
3. And it beautifully sings.
4. While going up in the sky.

(b)
1. The meadows look _________.
2. Where we run and _________.
3. And the river is _________.
4. Where we bathe _________.
(play, every day, clean, green)

Answers:
1. The meadows look green.
2. Where we run and play.
3. And the river is clean.
4. Where we bathe every day.

Activity III:
Fill in the blanks with appropriate words.
(ଉପଯୁକ୍ତ ଶବ୍ଦ ବସାଇ ଶୂନ୍ୟସ୍ଥାନ ପୂରଣ କର ।)
1. He gave us ears to _________.
2. He gave us to see _________.
3. He gave us to taste things _________.
4. He gave us skin to _________things.
5. He gave us nose to _________.
6. We enjoy God’s creation through the five _________.

Answers:
1. hear
2. eyes
3. tongue
4. feel
5. smell
6. senses

Activity IV:
Given below are some clues. Pick up the lines of the poem following the clues.
(ନିମ୍ନରେ କେତେକ ସୂଚନା ଦିଆଯାଇଛି । ସୂଚନାଗୁଡ଼ିକୁ ଅନୁସରଣ କରି କବିତାଟିରୁ ଧାଡ଼ିଗୁଡ଼ିକୁ ବାହାର କର ।)
flower  __________________________________
colour  __________________________________
bird      __________________________________
wings   __________________________________
Now compare these lines with the appropriate stanza of the poem. What change in the rhyming pattern do you mark?
(ଏବେ ଏହି ଧାଡ଼ିଗୁଡ଼ିକୁ କବିତାର ଯଥୋପଯୋଗୀ ପଦ ସହ ତୁଳନା କର । ତୁମେ ଯତିପାତ କ୍ରମରେ କ’ଣ ପରିବର୍ତ୍ତନ ଲକ୍ଷ୍ୟ କରୁଛ ।)

flower Each little flower that opens a color
color   He made their glowing colors bird
bird     Each little bird that sings wings
wings  He made their tiny wings

The rhyming pattern of the original stanza in the poem and the above stanza is different. In the original stanza, the last word of a line rhymes with the last word of the alternate line, but in the above stanza, the last word of a line rhymes with the last word of the next line.

H. Let’s Listen And Speak:
Students are divided into groups of four to five. Each group is given a word from the poem. The members of a group discuss the word among themselves for five minutes. Then one group has to answer the questions on the word asked by the other groups. The following words may be picked up from the text.

mountain, sunset, sunrise, winter, summer, sun, river, garden, greenwood, meadow, rushed

[This can be used as a competitive game among the groups. Credit can be given for the number of correct answers to the questions by the members of a group. A maximum of ten questions shall be asked by each group and be given credit. At the end of the game, the total score is calculated for the winners and runners-up or serial positions of the groups. The teacher is to provide an equal number of words to each group and decide the equal number of questions to be asked by each group as well as the credit points for each correct answer. Also, the teacher can devise any other competitive game with the purpose of facilitating listening and speaking.]
(This assignment is to be done in the classroom by the teacher dividing the students into four to five groups.)

I. Let Us Write:
Read the line: The tall trees in the greenwood.
Trees are useful for mankind in many ways. Given below are some clues. Write a few lines on each.
(ଗଛଗୁଡ଼ିକ ମଣିଷ ଜାତି ପାଇଁ ଅନେକ ଦରକାରୀ । ନିମ୍ନରେ କେତେକ ସୂଚନା ଦିଆଯାଇଛି । ପ୍ରତ୍ୟେକ ବିଷୟରେ କେତୋଟି ଧାଡ଼ି ଲେଖ ।)
Tree

• Construction of a house( ଏକ ଘର ନିର୍ମାଣ)
• Furniture (ଆସବାବପତ୍ର)
• Translation results (ଅନୁବାଦ ଫଳାଫଳ)
• Rainfall (ବର୍ଷା)
• Temperature control (ତାପମାତ୍ରା ନିୟନ୍ତ୍ରଣ |)
• Soil erosion (ମୃତ୍ତିକା କ୍ଷୟ |)
• Deforestation (ଜଙ୍ଗଲ ନଷ୍ଟ)
• Afforestation (ବୃକ୍ଷରୋପଣ |)

Answer:
Trees
Construction of a house (ଗୃହ ନିର୍ମାଣ ଉପରେ):
Wood is necessary for the construction of a house. Its use was more in making traditional houses in the recent past. It was used mainly as pillars and bars. Presently it is used mainly for making doors and windows. Its use has been reduced only because of its costliness and less availability. It is our duty to save trees.

Furniture (ଆସବାବପତ୍ର):
Wooden furniture has an all-time great demand. Even though they are expensive today people still go for it because their value is incomparable. We get wood from trees which are used in making sofa-set, cot, cupboard, almirah, wardrobe, chair and table, bench and desk, dining table, etc. Thus trees in the form of furniture give us comfort and luxury.

Rainfall (ବର୍ଷା):
Rainfall also depends on the trees. The leaves of the trees release huge quantities of water vapor into the atmosphere which helps in the formation of clouds. The areas, which have more trees, receive more rainfall. So we see heavy rainfall in forests. Deserts have scanty rainfall because there are no trees.

Temperature control (ତାପମାତ୍ରା ନିୟନ୍ତ୍ରଣ |):
Trees are our real friends. When we sit under a shady tree in the hot summer, we feel relaxed. When the temperature rises, it is the tree that comes to our rescue. Its branches and green leaves help to absorb the heat and do not allow it to reach us. The trees provide shade for the animals in the summer.

Soil erosion (ମୃତ୍ତିକା କ୍ଷୟ |):
Soil erosion has become a tough problem today. Recently soil erosion in coastal lines has created a panic. It happens largely due to the loss of trees. It is the tree roots that bind the soil tightly and does not allow the soil to erode away. Deforestation is a cause of soil erosion. Loss of soil has certain bad consequences which are to be avoided. Let us not cut trees to avoid an unpleasant situation ahead.

Deforestation (ଜଙ୍ଗଲ ନଷ୍ଟ):
Deforestation means cutting down trees in the forests. Presently we come across such activities all over the world. Mostly, deforestation is done for the establishment of factories and new colonies, towns, and offices. Due to this, we are losing large hectares of forest every year. It has certain evil effects like soil erosion, earthquake, flood, cyclone, scanty rainfall, and rise in temperature. The animals will be the worst sufferer of deforestation as they will lose their habitat and food. It is definitely a step toward destruction.

Afforestation (ବୃକ୍ଷରୋପଣ |):
Afforestation is the process of planting trees on bare land in order to create a forest. It has become a need today as we have lost most of our greenery. Deforestation has caused much damage to us. We are to continue afforestation to fill up the loss caused by deforestation. Afforestation can check soil erosion, flood, cyclone, earthquake, and many other disasters. Let’s join in this great work of afforestation to make the world a safe place for human habitation.

BSE Odisha 10th Class English All Things Bright and Beautiful Important Questions and Answers

Very Short A Objective Questions With Answers:
Answer The Following Questions In A Word Or A Phrase:

Question 1.
What does the poet think of all things?
Answer:
bright and beautiful, wise and wonderful

Question 2.
What has been described as great and small?
Answer:
all creatures

Question 3.
Who made all things and creatures?
Answer:
The Lord God

Question 4.
What has God given to the little flowers?
Answer:
glowing colors

Question 5.
What has God given to the little bird?
Answer:
tiny winds

Question 6.
What do you mean by ‘opens’?
Answer:
blooms

Question 7.
What do you mean by ‘glowing’?
Answer:
bright

Question 8.
What do you mean by ‘tiny’?
Answer:
very small

Question 9.
What do you mean by ‘purple’?
Answer:
bluish-red

Question 10.
What is described as purple-headed?
Answer:
the mountain

Question 11.
What is running by the mountain?
Answer:
the river

Question 12.
What do the sunset and morning make to the sky?
Answer:
brightened

Question 13.
In which season does the cold wind blow?
Answer:
in winter

Question 14.
How is the summer sun described?
Answer:
pleasant

Question 15.
Where according to the poet, do we find ripe fruits?
Answer:
in the garden

Question 16.
Where do we see tall trees?
Answer:
in the greenwood

Question 17.
What do people do in the meadows?
Answer:
play

Question 18.
What do we call an open area of grassland?
Answer:
meadow

Question 19.
What according to the poet, grow by the water?
Answer:
the rushes

Question 20.
What is used for making mats and baskets?
Answer:
the rushes

Fill In The Blanks With Right Words:

1. All Things Bright and Beautiful is a wonderful poem written by ____________.
Answer:
C.F. Alexander

2. C.F. Alexander belongs to ____________.
Answer:
Ireland

3. C.F. Alexander is a famous ____________.
Answer:
Hymn writer and poet

4. The poem ‘All Things Bright and Beautiful’ is included in ____________.
Answer:
Hymn for Children

5. C.F. Alexander says that all things are bright and ____________.
Answer:
beautiful

6. C.F. Alexander says that all things are wise and ____________.
Answer:
wonderful

7. C.F. Alexander says that all creatures are great and ____________.
Answer:
small

8. According to C.F. Alexander ____________ made all the things and creatures.
Answer:
the Lord God

9. The two little things mentioned in the poem are a little bird and little ____________.
Answer:
flower

10. Each little flower that ____________.
Answer:
opens

11. Each little bird that ____________.
Answer:
sings

12. God has given the ____________to the little flower.
Answer:
glowing color

13. Glowing colors means ____________ colors.
Answer:
bright

14. God has made the ____________ of the little bird.
Answer:
tiny wings

15. The poet says that the mountain is ____________.
Answer:
purple-headed

16. The rays of the setting sun make the mountain-top appear ____________.
Answer:
purple

17. The ____________ is running by the mountain.
Answer:
river

18. ‘The sunset and the morning that ____________ up the sky’.
Answer:
brightens

19. The ____________ blows in winter.
Answer:
cold wind

20. The two seasons mentioned in the poem are winter and ____________.
Answer:
summer

21. The poet says that the summer sun is ____________.
Answer:
pleasant

22. The poet says that the ripe fruit is in the ____________.
Answer:
garden

23. The tall trees are in the ____________.
Answer:
greenwood

24. We ____________ in the meadows.
Answer:
play

25. A meadow is an open area of ____________.
Answer:
grassland

26. The ____________ grows by the water.
Answer:
rushes

27. Varieties of waterside plants are called ____________.
Answer:
rushes

28. The rushes are used for making ____________.
Answer:
mats and basket

29. The poet says that we gather ____________ every day.
Answer:
rushes

30. The meadows look ____________.
Answer:
green

31. The rushes grow by the ____________.
Answer:
water

32. We see the ____________ in the greenwood.
Answer:
tall trees

33. God has given us ears to ____________.
Answer:
hear

34. God has given us ____________ to see.
Answer:
eyes

35. God has given us ____________ to taste things
Answer:
tongues

Multiple Choice Questions With Answers
Pick out the correct alternative.

Question 1.
In the poem ‘All Things Bright and Beautiful’ the poet says that God has made all the creatures ____________.
(A) great and small
(B) wise and wonderful
(C) bright and beautiful
(D) all the above
Answer:
(A) great and small

Question 2.
Who has created all these beautiful things?
(A) Lord Jagannath
(B) Lord Shiva
(C) Lord Vishnu
(D) Lord God
Answer:
(D) Lord God

Question 3.
The little flowers are attractive because of ____________.
(A) their glowing colors
(B) their little petals
(C) their timely appearance
(D) their beauty and smallness
Answer:
(A) their glowing colors

Question 4.
The mountain top looks purple because ____________.
(A) the flowers bloom aplenty there
(B) lots of colorful birds fly over it
(C) the rays of the setting sun fall on it
(D) None of the above
Answer:
(C) the rays of the setting sun fall on it

Question 5.
The little things described in the poem are ____________.
(A) beautiful flowers and the blue sky
(B) rushes and green forests
(C) the summer sun and the garden
(D) little flowers and little birds
Answer:
(D) little flowers and little birds

Question 6.
At sunset, the mountain top looks ____________.
(A) green
(B) purple
(C) brown
(D) yellow
Answer:
(B) purple

Question 7.
The little birds have tiny wings. Here, ‘tiny wings’ means _____________.
(A) very small wings
(B) very big wings
(C) very ugly wings
(D) very nice wings
Answer:
(A) very small wings

Question 8.
The poem ‘All Things Bright and Beautiful’ is written by ____________.
(A) Sarojini Naidu.
(B) William Wordsworth
(C) Lord Alfred Tennyson
(D) Cecil Frances Alexander
Answer:
(D) Cecil Frances Alexander

Question 9.
The mountain top looks bluish-red at ____________.
(A) sunset
(B) noon
(C) mid-day
(D) midnight
Answer:
(A) sunset

Question 10.
The poet says that all the things in this universe are ____________.
(A) small, little, and careful
(B) gloomy, ugly, and wonderful
(C) foolish, stupid, and harmful
(D) bright, beautiful, and wonderful
Answer:
(D) bright, beautiful, and wonderful

Question 11.
The cold wind that is created by God blows in ____________.
(A) summer
(B) autumn
(C) spring
(D) winter
Answer:
(D) winter

Question 12.
The poet considers the summer sun pleasant because ____________.
(A) the summer sun is pleasant in India
(B) the summer is pleasant in England
(C) the bright rays of the sun fall on the earth
(D) summer is a beautiful season
Answer:
(B) the summer is pleasant in England

Question 13.
According to the poet, we can get ripe fruit ____________.
(A) in the garden
(B) on the farm
(C) in the market
(D) in the orchards.
Answer:
(A) in the garden

Question 14.
The meadows are very useful for us because ____________.
(A) we grow different crops there
(B) we play different games there
(C) there are plenty of flowers in them
(D) they attract children
Answer:
(B) we play different games there

Question 15.
Rushes usually grow ____________.
(A) by the waterside
(B) in or near the deserts
(C) by the hillside
(D) in the fields
Answer:
(A) by the waterside

Question 16.
God has given us eyes to ____________.
(A) see the beauty of His creation
(B) read the books
(C) watch television
(D) gaze at the scenery
Answer:
(A) see the beauty of His creation

Question 17.
God has given us lips to ____________.
(A) praise his greatness
(B) quarrel with our friends
(C) talk with our parents
(D) apply cosmetics
Answer:
(A) praise his greatness

Question 18.
The two seasons described in the poem are ____________.
(A) spring and rain
(B) winter and summer
(C) Autumn and spring
(D) rain and autumn
Answer:
(B) winter and summer

Question 19.
The poem ‘All Things Bright and Beautiful’ is ____________.
(A) a description of birds and animals
(B) a prayer to God, the Almighty
(C) the description of animals
(D) a description of the beauties of Nature
Answer:
(B) a prayer to God, the Almighty

Question 20.
The garden described in the poem is full of ____________.
(A) beautiful flowers
(B) small birds
(C) ripe fruits
(D) green vegetables
Answer:
(C) ripe fruits

Question 21.
God has given us ____________ to enjoy his creation.
(A) hands
(B) legs
(C) ears
(D) eyes
Answer:
(D) eyes

Question 22.
God has given us ____________ to hear the music of Nature.
(A) eyes
(B) lips
(C) ears
(D) nose
Answer:
(C) ears

Question 23.
God has given us the tongue to ____________ the things.
(A) smell
(B) lick
(C) see
(D taste
Answer:
(D) taste

Question 24.
God has given us ____________ to smell the fragrance of things.
(A) lips
(B) tongue
(C) skin
(D) nose
Answer:
(D) nose

Question 25.
C.F. Alexander was an ____________ poet.
(A) American
(B) Irish
(C) Mexican
(D) Canadian
Answer:
(B) Irish

All Things Bright and Beautiful Summary in English

Lead-In:
The poem ‘All Things Bright and Beautiful ’ by C.F. Alexander is a song praising the God who is believed to have created the universe. God has created beautiful sunrises and sunsets, trees and flowers, rivers and mountains, birds and animals. He has given us eyes to see, mouths to speak, noses to smell, skin to feel, tongues to taste, and ears to hear. Every activity, such as the change of seasons, the fragrance of flowers, etc. is done at His will. Thus God Almighty, who has made everything well, is really great to whom we should obey and worship.

Stanzawise Explanation:
Stanza – 1 (Lines 1 to 4)
All things bright and beautiful,
All creatures great and small,
All things wise and wonderful,
The Lord God made them all.
Gist:
In the 1st stanza, the poet describes the things and creatures that we see around us are bright and beautiful, great and small, and wise and wonderful. It is the Lord God who has made them all.
ଅନୁବାଦ : ପ୍ରଥମ ପଦରେ କବି ବର୍ଣ୍ଣନା କରିଛନ୍ତି ଯେ ଆମେ ଆମ ଚତୁଃପାର୍ଶ୍ଵରେ ଦେଖୁଥ‌ିବା ସମସ୍ତ ଜିନିଷ ଉଜ୍ଜ୍ବଳ ଏବଂ ସୌନ୍ଦର୍ଯ୍ୟମୟ, ସମସ୍ତ ପ୍ରାଣୀ ବିଶାଳ ଏବଂ କ୍ଷୁଦ୍ର, ବିଜ୍ଞ ଅଟନ୍ତି ।

Stanza – 2 (Lines 5 to 8)
Each little flower that opens,
Each little bird that sings,
He made their glowing colors,
He made their tiny wings.
Gist:
In the second stanza, the poet describes about God’s blessings to flowers and birds. God has given bright colors to each little flower that blossoms. He has given very small wings to each little bird that sings.
ଅନୁବାଦ : ଦ୍ଵିତୀୟ ପଦରେ କବି ଫୁଲ ଏବଂ ପକ୍ଷୀମାନଙ୍କୁ ଈଶ୍ବରଙ୍କ ଆଶୀର୍ବାଦ ବିଷୟରେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ପ୍ରତିଟି ପ୍ରସ୍ଫୁଟିତ ପୁଷ୍ପକୁ ସେ ଦେଇଛନ୍ତି ଉଜ୍ଜଳ ରଙ୍ଗ । ସୁମଧୁର କଣ୍ଠରେ ରାବ କରୁଥିବା ପ୍ରତ୍ୟେକ କ୍ଷୁଦ୍ର ପକ୍ଷୀକୁ ସେ ଦେଇଛନ୍ତି କ୍ଷୁଦ୍ର ସୁନ୍ଦର ଡେଣା । ଈଶ୍ବର ଫୁଲର ଆକର୍ଷଣୀୟ ରଙ୍ଗ ଓ କ୍ଷୁଦ୍ର ପକ୍ଷୀର କ୍ଷୁଦ୍ର ଡେଣା ତିଆରି କରିଛନ୍ତି ।

Stanza – 3 (Lines 9 to 12)
The purple-headed mountain,
The river running by,
The sunset and the morning,
That brightens up the sky.
Gist:
In the third stanza, the poet describes the mountain during the sunset and the morning. He has made the bluish-red mountain top with the river flowing by it. He has made the glowing sunset and the bright sunrise in the morning. The sunset and the sunrise brighten the sky.
ଅନୁବାଦ : ତୃତୀୟ ପଦରେ କବି ସୂର୍ଯ୍ୟାସ୍ତ ଓ ପ୍ରାତଃକାଳୀନ ପର୍ବତକୁ ନୀଳାଭ-ରକ୍ତିମ ବର୍ଣ୍ଣରଞ୍ଜିତ ମସ୍ତକଧାରୀ ବୋଲି ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ସୂର୍ଯ୍ୟାସ୍ତ ସମୟରେ ଅସ୍ତଗାମୀ ସୂର୍ଯ୍ୟର ନୀଳ-ଲୋହିତ ରଶ୍ମି ପାହାଡ଼ ଉପରେ ପଡ଼ି ତାହାକୁ ଅତ୍ୟନ୍ତ ସୌନ୍ଦର୍ଯ୍ୟପୂର୍ଣ୍ଣ କରିଥାଏ । ପ୍ରାତଃକାଳରେ ମଧ୍ୟ ସେହି ଏକା କଥା ଘଟିଥାଏ । ପାହାଡ଼ର ପାଦଦେଶରେ ପ୍ରବହମାନ ନଦୀର ଜଳ ମଧ୍ୟ ଉଦିତ ଏବଂ ଅସ୍ତଗାମୀ ସୂର୍ଯ୍ୟରଶ୍ମିରେ ଉଜ୍ଜ୍ଵଳିତ ହୁଏ । ତାହା ମଧ୍ୟ ଆକାଶକୁ ଉଜ୍ଜ୍ବଳିତ କରିଥାଏ । ଏ ସମସ୍ତ ସୌନ୍ଦର୍ଯ୍ୟମୟ ଏବଂ ଉଜ୍ଜ୍ବଳ ବସ୍ତୁର ସୃଷ୍ଟିକର୍ତ୍ତା ହେଉଛନ୍ତି ଈଶ୍ଵର ।

Stanza – 4 (Lines 13 to 16)
The cold wind in the winter,
The pleasant summer sun,
The ripe fruit in the garden,
He made them every one.
Gist :
In the fourth stanza, the poet says that God is the creator of the cold wind that blows in the winter and he has made the pleasant summer sun. He is also the maker of the ripe fruit in the garden. He has made everyone.
ଅନୁବାଦ : ଚତୁର୍ଥ ପଦରେ କବି କହିଛନ୍ତି ଯେ ଈଶ୍ବର ଶୀତଦିନେ ପ୍ରବାହିତ ହେଉଥ‌ିବା ଥଣ୍ଡା ପବନ ଏବଂ ଆନନ୍ଦଦାୟୀ ଗ୍ରୀଷ୍ମକାଳୀନ ସୂର୍ଯ୍ୟଙ୍କୁ ସୃଷ୍ଟି କରିଛନ୍ତି । ସେ ମଧ୍ୟ ବଗିଚାରେ ଥ‌ିବା ପାଚିଲା ଫଳର ନିର୍ମାତା । ସେ ପ୍ରତ୍ୟେକ ଜିନିଷକୁ ତିଆରି କରିଛନ୍ତି ।

Stanza – 5 (Lines 17 to 20)
The tall trees in the greenwood,
The meadows where we play,
The rushes by the water,
We gather every day.
Gist:
In this stanza, the poet describes the greenwood and the meadows. In the greenwood, one can enjoy the beauty of the tall trees. The variety of tall trees with their green leaves in the green wood is in fact a beautiful scene to see. There are also meadows where we play. A meadow is an open area of grassland which is ideal for sports activity. Everyone also takes interest in collecting the rushes that have grown in the waterside.
ଅନୁବାଦ : ଏହି ପଦରେ କବି ସବୁଜ ବଣ ଏବଂ ଘନ ତୃଣଭୂମି ସମ୍ପର୍କରେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ସବୁଜ ବଣରେ ବିଶାଳକାୟ ଉଚ୍ଚା ଗଛଗୁଡ଼ିକୁ ଈଶ୍ବର ସୃଷ୍ଟି କରିଛନ୍ତି । ପ୍ରତିଦିନ ଆମେ ସଂଗ୍ରହ କରୁଥ‌ିବା ଜଳଜ ଉଭିଦଗୁଡ଼ିକ ଈଶ୍ଵରଙ୍କର ଅବଦାନ । ଘନ ତୃଣଭୂମିଗୁଡ଼ିକ ସବୁଜ ଘାସପୂର୍ଣ୍ଣ ଏକ ଖୋଲା ଅଞ୍ଚଳ ଯେଉଁଠାରେ ଆମେ ଖେଳାଖେଳି କରୁ ।

Stanza – 6 (Lines 21 to 24)
He gave us eyes to see them,
And lips that we might tell How great is God Almighty,
Who has made all things well?
Gist:
In the last stanza, the poet describes the importance of the eyes and lips that God has given us. He also describes the greatness of God who has made all things well. God has given us eyes to see all the bright and beautiful things that he has made. He has also given us the lips so that we can tell and discuss His creations. This Almighty God, who has made everything bright and beautiful, great and small, and wise and wonderful, is really great.
ଅନୁବାଦ : ଶେଷ ପଦରେ ଈଶ୍ବର ଆମକୁ ଦେଇଥ‌ିବା ଆଖୁ ଓ ଓଷ୍ଠର ଗୁରୁତ୍ଵ କଥା କବି ବର୍ଣନା କରିଛନ୍ତି । ଈଶ୍ଵର ଆମକୁ ଆଖ୍ ଦେଇଛନ୍ତି ତାଙ୍କଦ୍ୱାରା ନିର୍ମିତ ସମସ୍ତ ଉଜ୍ଜଳ ଓ ସୌନ୍ଦର୍ଯ୍ୟପୂର୍ଣ୍ଣ ବସ୍ତୁକୁ ଦେଖିବାପାଇଁ । ସେହିପରି ସେ ଆମକୁ ଓଷ୍ଠ ଦେଇଛନ୍ତି ଯେପରି ଆମେ ତାଙ୍କ ସୃଷ୍ଟି ବିଷୟରେ କହିବା ବା ଆଲୋଚନା କରିପାରିବା । ଯେଉଁ ସର୍ବଶକ୍ତିମାନ୍ ଈଶ୍ବର ସମସ୍ତ ଜିନିଷକୁ ତିଆରି କରିଛନ୍ତି ବାସ୍ତବରେ ସେ ମହାନ୍ ଅଟନ୍ତି ।

About The Poet:
The full name of the poet C.F. Alexander is Cecil Frances Alexander. She was born in Dublin, Ireland in 1818. She was a famous hymn (ଧାର୍ମିକ ଗୀତ)writer and poet. Her famous works are ‘Hymn for Children ’, ‘Christmas Carol’, ‘Once in Royal David’s City’, ‘Verses ( କ୍ଷୁଦ୍ର କବିତା)for Holy (ପବିତ୍ର) Season ’. This poem ‘All Things Bright and Beautiful’ is included ( ଅନ୍ତର୍ଭୁକ୍ତ କରାଯାଇଛି) in ‘Hymn for Children’.

Word Meaning / Glossary:

bright (Adj.) – shining strongly, glittering (ଉଜ୍ଜ୍ୱଳ)
He is wearing a bright yellow dress.
creatures (N) – living beings
We should be kind to all creatures.
great (Adj) – big, large
wise (Adj) – prudent
He is a wise man.
Lord (N) – Creator (Here God)
wonderful (Adj) – full of astonishment, amazing, marvelous, fantastic (93999)
We had a wonderful time last night.
The weather was absolutely wonderful today
opens(V) – blooms
glowing (Adj) – bright, shining
Flowers have glowing colors.
little (Adj) – pleasingly small
tiny (Adj) – very small (ବହୁତ ଛୋଟ)
Small birds have tiny wings.
wing (N) – a part of the body of birds used for flying (ଡେଣା)
A bird has two wings
summer (N) – ଗ୍ରୀଷ୍ମ
sun (N) – rays (କିରଣ)
garden (N) – ବଗିଚା
purple-headed mountain (Phrase)- bluish red mountain top (ଅସ୍ତଗାମୀ ସୂର୍ଯ୍ୟକିରଣ ଲୋହିତ ବର୍ଷ ରଞ୍ଜିତ କରେ ।)
running by (V) – flowing by (ପ୍ରବାହିତ)
ripe (Adj) – (ପାଚିଲା)
The old man eats ripe fruits.
brightens (V) – shines, illuminates
pleasant (Adj) – Something that pleases
meadow (N) – an open area of grassland
Children love to play in the meadows.
rush (N) – a tall plant like grass that grows near or in water
A part of the river is filled with rushes.
gather (V) – collect
Children like to gather small pebbles,
Almighty (N) – all-powerful
Great (Adj) – glorious
Give us eyes (Phrase) – has given eyes to the man
lips (N) – one of the two fleshy edges of the mouth

BSE Odisha 10th Class English Detailed Text

• Chapter 1 All Things Bright and Beautiful
• Chapter 2 A letter to God
• Chapter 3 The Solitary Reaper
• Chapter 4 At the High School
• Chapter 5 Village Song
• Chapter 6 Festivals of North-East India
• Chapter 7 The Flower-School
• Chapter 8 Air Pollution: A Hidden Menace
• Chapter 9 From the Formalin Jar
• Chapter 10 School’s Goodbye
• Gift Nifty Timing

Odisha State Board CHSE Odisha Class 12 Invitation to English 4 Solutions Grammar Modal Verbs Textbook Activity Questions and Answers.

CHSE Odisha 12th Class English Grammar Modal Verbs

SECTION -1

Making requests (using can, could; may, will, would)
Read the sentences below carefully.
1. Suresh: Can you lend me your bicycle?
Mahesh: Of course, I’m not using it today.
2. Student: Could I borrow your dictionary, sir?
Teacher: Certainly. But it’s meant only for very advanced learners.
3. Shyam: Will you open the door, please?
Stranger: Sure.
4. Jatin: Would you mind repeating the last sentence, sir?
Speaker: Not at all. I said that…
5. Jina: May I ask a question, please?
Speaker: By all means.
6. Landlady: Will you please clean the kitchen?
Maid. Yes, ma’am. Right away.

The modal auxiliaries can, could, may, will, and would are used to make requests.
But we can well mark a slightly different way from the others.
1. The use of ‘can’ is informal, while could is more formal and polite. It suggests a more tentative attitude on the part of the speaker.
2. ‘May’ is used rather in a formal way to express a request.
3. ‘Will’ is also used to make requests when we don’t need to be particularly formal or polite.
4. ‘Would’ or would you mind is used for more polite requests or formal (with the 2nd person).

Activity – 1
Make a request to suit each of the situations suggested below, using the word supplied in brackets. In case no word has been suggested, you are free to choose your own words to make the request.
(a) You need some money. Ask a friend to lend you some. (can)
_________________________________
(b) You want a speaker in a seminar to explain something. Ask him to do so. (could/ would)
_________________________________
(c) You want your room key from the receptionist in a hotel. Ask the receptionist to give you the key. (can/may)
_________________________________
(d) You want a visitor to wait a minute while you get ready. (would)
_________________________________
(e) You are carrying a heavy bag. Ask someone to open the door for you. (could)
_________________________________
(f) You are on the phone. You want to speak to the chairman. (may)
_________________________________
(g) You want someone to tell you how to reach the railway station.
_________________________________
(h) You are buying a pair of shoes and want a receipt.
_________________________________
(i) You are working and want everybody to be quiet for some time.
_________________________________
(j) You need something to eat. Ask your mother.
_________________________________
(k) You are on a train and you would like to borrow a newspaper from another passenger, who has just finished reading it.
_________________________________
Answer:
(a) Can you lend me some money?
(b) Could you please explain something?
Would you explain something, please?
(c) Can you please give me the room key?
May I get the room key, please?
(d) Would you wait for a minute, please?
(e) Could you please open the door for me?
(f) May I talk to the chairman, please?
(g) Could you please tell me how to reach the railway station?
(h) Would you give me the receipt, please?
(Or) Could you please give me the receipt?
(i) Could you be silent for some time, please?
Would you mind keeping silent for some time?
(j) Can you give me something to eat?
(k) Would you mind giving me the newspaper for some time?

Activity – 2
Monisha is ill in bed and has to request her friend to do things for her. Use can, will, could or would for the requests that she must make. (More than one answer may be possible.)
(a) Monisha wants some books to read. She would like her friend to get some.
_________________________________
(b) Monisha doesn’t want to be disturbed by visitors.
_________________________________
(c) Monisha wants her friend to write a letter for her.
_________________________________
(d) Monisha wants some vegetable soup for lunch.
_________________________________
(e) Monisha wants her friend to fetch the mobile phone, which is in the next room.
_________________________________
(f) Monisha wants her friend not to go out and leave her alone.
_________________________________
(g) Monisha wants her friend to wash her clothes.
_________________________________
Answer:
(a) Can you lend me some books, please?
(b) Would you mind stop talking?
(c) Can you please write a letter for me?
(d) Could you/Can you provide me some vegetable soup for lunch, please?
(e) Can you get me the mobile phone from the next room, please?
(f) Would you stay for some time here, please?
(g) Can you please wash my clothes?

Activity – 3
Seema is staying in Leena’s home as a guest, and Leena has to request Seema to do a few things for her, which she is not able to do herself, for some reason or the other. Here is an example.
Seema, could you please clean the dishes after dinner? I’ve got to go to the market to buy a few things.
Can you make a few more requests to Seema on behalf of Leena, using the clues below? You also have to provide a reason for each request. (You should be specially polite while making more unusual requests.)
(a) switch off the lights
_________________________________
(b) make some tea
_________________________________
(c) water the plants in the garden
_________________________________
(d) feed the dog
_________________________________
(e) take the rubbish out of the dustbin
_________________________________
(f) take care of the neighbor’s children
_________________________________
(g) cook dinner
_________________________________
Answer:
(a) Could you please switch off the lights? I have to sweep the room.
(b) Could you please make me some tea?
I have got to wash my dresses.
(c) Would you please water the plants in the garden? I’ve to nurse my grandfather.
(d) Would you mind feeding the dog? I have got to do shopping.
I have to wash the utensils.
(e) Could you take the rubbish out of the dustbin, please?
I have to wash the utensils.
(f) Could you take care of the neighbor’s children, please? I have to have my bath.
(g) Could you please cook dinner?
I’ve, some sums to work out.

SECTION – 2

Asking for and granting permission
(using can, could, may, would)
Look at the examples below.
(a) Tarun: Can I use your typewriter to type out an application?
Friend: Yes, of course, you can.
(b) Tapas: Could I use the telephone?
Receptionist: Yes, sir. But this one is only for local calls.
(c) Journalist: Mr. Prime Minister, may I ask what you plan to do for unemployed engineers?
Prime Minister: New jobs are being created for them.
(d) Shefali: Would you mind if I sat here?
Stranger: No, not at all.
Can is used for permission usually in an informal style. When we talk to our intimate/ private men and women, we use ‘can’ for permission, and ‘could is used for permission when we are not sure whether the permission will be granted. It is usually used in ‘formal’ situations (i.e., for unknown people). Do remember this ‘could’ modal verb’ is never used to give permission to someone.
‘May and Would you mind’ are usually used for permission in a formal style. The speaker is even less sure of getting permission or feels that permission is likely to be refused.

Activity – 4
Ask for permission using can, could, or may. (More than one answer is possible.)
(a) You are at a seminar where someone is speaking. You want to ask the speaker a question.
Excuse me: _________________________________
(b) You are late for your English class. You want the teacher’s permission to get in.
_________________________________
(c) You are interviewing an actor. You would like to ask him something about his personal life.
_________________________________
(d) Yon wants to stay in the hostel. Ask the hostel warden for permission.
_________________________________
(e) You want to join the cricket team of your college. Ask the teacher in charge of the games.
_________________________________
(f) You have been invited to dinner by someone you do not know very well. You would like to ask for another piece of chicken.
_________________________________
(g) Your friend has a book that you want to read. Ask him/her.
_________________________________
Answer:
(a) You are at a seminar where someone is speaking. You want to ask the speaker a question.
Excuse me, could I ask you a question?
(b) You are late for your English class. You want the teacher’s permission to get in. Could, I get into the class? Or, May I come in?
(c) You are interviewing an actor. You would like to ask him something about his personal life.
Would you mind telling me a few words on your personal life?
Or, May I ask a few questions on your personal life?
(d) You want to stay in the hostel. Ask the hostel warden for permission.
Could you allow/grant me to stay in the hostel?
(e) You want to join the cricket team of your college. Ask the teacher in charge of the games.
Could I join the cricket team this year?
(f) You have been invited to dinner by someone you do not know very well. You would like to ask for another piece of chicken.
Could you give me one more piece of chicken?
(g) Your friend has a book that you want to read. Ask him/her.
Can you lend me your book for a night?

Activity – 5
Imagine that you are a guest at the places mentioned below. Use can (informal), could (semi-formal) or may (formal) to ask for permission to do a different thing at each place. (One has been done for you.) At your grandparents home Can I use the phone, grandfather?
(a) At your teacher’s home.
_________________________________
(b) At your neighbor’s home.
_________________________________
(c) At the house of a favorite uncle.
_________________________________
(d) At the house of a close friend.
_________________________________
(e) At the house of someone you are visiting for the first time.
_________________________________
(f) At the house of a friend of your elder brother.
_________________________________
(g) At a distant relative’s home
_________________________________
Answer:
(a) Could I use your bicycle?
(b) Can I use your comb?
(c) Can I have your photograph?
(d) Can I ride your scooter?
(e) Could I use your dictionary?
(f) Could I use your pen?
(g) Could I / May I switch on the TV?

Activity – 6
Say whether the sentences below are used to ask for permission or to make a request or whether they are used in formal or informal situations.
(a) Mr. Mohanty, would you please tell all the teachers to come for a meeting in my office at 3 o’clock?
(b) Can you put this parcel on the table, please?
(c) May I ask you a question about this job, sir?
(d) Would you mind sitting on that chair?
(e) Could you pass the salt, please?
(f) Can my friend stay here too?
(g) May I wait in the corridor outside?
Answer:
(a) Formal request
(b) Informal request
(c) Formal request
(d) More formal request
(e) Formal request
(f) Informal permission
(g) Formal permission

SECTION – 3

Making an offer to help (using will, would, shall, can, could)
(a) Rina: I want to take this bag with me.
Chhabi: I will (can) carry it for you.
Rina: Oh, thanks.
(b) Tarak: 1 must leave now.
Puma: Shall (Can) I get a taxi for you?
Tarak: Yes, please.
(c) Host: Would you like some more chicken?
Guest: Yes, please. Thank you.
(d) Pinaki : (to his friend’s friend) Could I buy the tickets for you?
Friends friend: Thank you very much.

Will, shall, and can are used in informal English to offer help to someone. will and shall are commonly abbreviated to ‘il (ill, We’ll, etc.) Will is used only in statements (e.g., I’ll carry your bag) but shall and can are used in questions as well as statements (e.g., Shall I carry your bag ? Can I carry your bag ? or I shall carry your bag / I can carn your bag). Could and would are used in questions as well as statements to offer help, in more formal situations. (e.g., could j carry your bag? ¡ could carry your bag!
Would you like me to carry your bag? I would be happy to carry your bag, etc.).

Activity – 7
Make offers to suit the following situations.
(a) Your friend accidentally drops his pen on the floor.
_________________________________
(b) An old man wants you to make room for him to sit down.
_________________________________
(c) A patient is sweating profusely and the windows are closed.
_________________________________
(d) An old man is carrying a heavy suitcase and gasping for breath.
_________________________________
(e) Your principal wants to get some medicines from a pharmacy.
_________________________________
(f) A stranger wants to go to a particular place and you are on a motorbike.
_________________________________
(g) Your friend does not have enough money to buy a book he needs.
_________________________________
(h) Your mother is not able to cook as she is unwell.
_________________________________
(i) Your sister is not able to work out a sum.
_________________________________
(j) Your younger brother is trying to reach a book on the top shelf of a cupboard.
_________________________________
Answer:
(a) Shall I/Can I lift it from the floor?
(Or) I’ll lift it form the floor.
(b) Would/Could I give you a seat here?
(c) Could/Would I open the windows for you?
(d) Could I carry the suitcase for you?
(e) Would / Could I bring some medicines for you, sir?
(f) Could I give you a lift?
(g) Shall / Can I lend you some money?
(h) I’ll cook for you.
(Or) Shall / Can I cook for you?
(i) Shall/Can I work out the sum for you?
(j) I’ll (will) get the book for you.
(Or) Shall/Can I get the book for you?

Activity-8
Study the offers below and say which ones are made in a formal situation in which each one could have been made.
(a) Shall I call the doctor for you?
_________________________________
(b) Would you like me to call the police?
_________________________________
(c) Shall I switch off the light?
_________________________________
(d) I can lend you two hundred rupees if you like.
_________________________________
(e) I’ll help you make the bed.
_________________________________
(f) Could I wait for you at the gate?
_________________________________
Answer:
(a) Shall I call the doctor for you?
Yes, I’m unwell, (formal)
(b) Would you like me to call the police?
Yes, I have to see the man stabbed.
(c) Shall I switch off the light?
Yes, I am awful tired now. (formal)
(d) I can lend you two hundred rupees if you like.
I’m badly in need of some money now. Oh, thanks.
(e) I’ll help you make the bed.
It’s very kind of you. I’m running a temperature now. (formal)
(f) Could I wait for you at the gate?
Yes, you may come and receive my other friends. (formal)

SECTION – 4

Making a suggestion (using shall, can, could)
(a) Pramod: It’s a lovely day. Shall we go for a walk?
Prashant: Yes, let’s do that.
(b) Nilima: Sisir is becoming more and more difficult to handle.
Manisha: We can talk to him if you like.
Nilima : No, I’ll manage without him.
(c) Girija: We need Sima’s room for the guest.
But she has gone home.
Gauri: We could go to her village tomorrow and collect the key.
In the sentences above, different ways of making suggestions have been shown.
The commonly used words are: Shall we /Can we /Could we (in questions), or You can /We can / We could….. (in statements), used together with if you like/want.
Suggestions can also be made by using let us (let’s), why don’t you/ we…. ? or how / what about…. ? Let’s and why don’t you/we…. ? are followed by the infinitive without to (e.g. Let’s stop here; why don’t you ask him ?, while How/What about….. ? are followed by an ‘-ing’ form (e.g., How about stopping here and eating lunch ?)

Activity – 9
Make suggestions to suit the following situations. (More than one answer is possible.)
(a) You think, your friend and you should go for a walk.
_________________________________
(b) You would like to have dinner at a restaurant with your neighbor.
_________________________________
(c) You feel like going to the park with your mother.
_________________________________
(d) You would like your father to take you to an uncle’s house.
_________________________________
(e) You have met somebody for the first time at a friend’s house. He is watching a film on television, but you would like to watch a cricket match, on a different channel.
_________________________________
(f) You feel like going to the theatre with some friends.
_________________________________
(g) It is 11.00 p.m. Your roommate in the hostel is reading a book, but you would like to sleep.
_________________________________
Answer:
(a) Let’s go for a walk.
Or, Can/Shall we go for a walk?
(b) Shall/Can we have dinner at a restaurant?
(c) Why don’t we got to the park now?
(d) Why don’t you take me to my uncle’s house?
(e) Could you change this channel? Let us see the cricket match in D.D. Sports.
(f) Let’s go to the theatre now.
Or, Why don’t we got to the theatre as we have some free moments now?
(g) Could you switch off the light? Let’s go to bed.

Activity – 10
Your friends and you are putting up a cultural show in your college. Make suggestions about the arrangements for the show, using the hints below. Study the example below and write your sentences.
(i) the place where the show is to be put up
(ii) decorating the stage
(iii) fixing the lights
(iv) getting singers and musicians to perform
(v) setting up the sound system
(vi) the guests to be invited
(vii) the refreshments to be served
Answer:
Example: We can invite the Chief Minister to be the Chief Guest.
(i) Shall we select/choose the old auditorium for the show?
(ii) Why don’t we decorate the stage by ourselves?
(iii) We shall invite the electrician for fixing the lights.
(iv) Let’s invite Akshay Mohanty and party for the musical show.
(v) What about setting up the sound system?
(vi) Why don’t we invite the Chief Minister and the Minister for Mass Education to be the guests?
(vii) The volunteers shall serve refreshments for the guests.

Activity – 11
Which of the following offer and which are suggestions? Say whether they are formal or informal.
(a) I can pay for your ticket if you like.
(b) What shall I do in case I don’t find Ram at home?
(c) Would you like them to wait for you?
(d) We could leave it until later.
(e) I can lend you the book.
(f) Could we paint this wall for you?
Answer:
(a) offer informal
(b) offer informal
(c) offer formal
(d) suggestion informal
(e) offer informal
(f) offer informal

SECTION – 5

1. Expressing ability to do something (using can be able to)
Study the following dialogues.
(a) Interviewer: Can you type?
Candidate: Yes sir. I can also take dictation in shorthand.
Interviewer: Will you be able to talk to our foreign clients?
Candidate: Yes sir. I can speak German and Italian.
(b) Teacher: Who can solve this problem?
Student: I can.
‘Can’ the modal in the above conversation is used to mean ‘ability ’ in general. ‘Be + able to’ is also used to mean the same meaning ‘ability’ to do something. ‘Can’ is informal/usual and ‘be + able to’ is usually formal.

Activity – 12
Complete the sentences below using can or be able to. (In some of the sentences, it will not be possible to use can.)
(a) Ask Karim about your friend’s condition. He might — tell you something.
(b) Ravi was bom and educated in Hyderabad. He — speaks Telugu.
(c) My friend can’t understand my problem. She’s never — understand it.
(d) I can’t lend you money but I — get the book for you.
(e) Meera — read Tamil but she doesn’t have any Tamil books.
(f) I haven’t — buy any books lately.
(g) We — travel a lot but we can’t do it now.
(h) Meet your teacher tomorrow. He — explain the question to you.
Answer:
(a) Ask Karim about your friend’s condition. He might be able to tell you something.
(b) Ravi was born and educated in Hyderabad. He can speak Telugu.
(c) My friend can’t understand my problem. She has never been able to understand it.
(d) I can’t lend you money but I will be able to get the book for you.
(e) Meera can read Tamil but she doesn’t have any Tamil books.
(f) I haven’t been able to buy any books lately.
(g) We used to be able to travel a lot but we can’t do it now.
(h) Meet your teacher tomorrow. He will be able to explain the question to you.

Activity – 13
List five things that you can do.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
List five things that you can’t do.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
Answer:
List five things that you can do.
1. I can lift this heavy box.
2. I will be able to get the first division.
3. I can speak and write in three languages.
4. I can give the answer to that question.
5. I will be able to swim in the river.

List five things that you can’t do.
1. I can’t lift an elephant.
2. I won’t be able to swim in the river.
3. I can’t read Greek.
4. I won’t be able to run 5 km at a stretch.
5. I won’t be able to get a medal in swimming

Activity – 14
A new student has joined your class. As the Secretary of the College Union, you would like to know which activities your new classmate would be able to take part in. Frame at least five questions that you might want to ask him and provide the answers that might be given.
Q. Can you draw and paint?
A. Yes, I can / No, I can’t.
1. Q. _________________________________
A. _________________________________
2. Q. _________________________________
A. _________________________________
3. Q. _________________________________
A. _________________________________
4. Q. _________________________________
A. _________________________________
5. Q. _________________________________
A. _________________________________
Answer:
Question 1.
Will you be able to contact the guests?
Answer:
Yes, I can.

Question 2.
Can you speak Hindi fluently?
Answer:
Yes, I can.

Question 3.
Will you be able to do shopping?
Answer:
Yes, I can do the shopping.

Question 4.
Will you be able to take care of the guests?
Answer:
Yes, I can.

Question 5.
Will you be able to see the seat arrangements?
Answer:
Yes, I can.

2. General ability versus the ability to do something in a particular situation. Look at the following sentences.

• Mohan could speak Assamese when he was a boy.
• When I was in London I could visit the museum every day.
• I had only a brief meeting with the Principal, but I was able to explain my difficulties to him.

In Sentence 1, could is used to refer to the general ability to do something that somebody possessed (in the past), while in Sentence 2, could indicate that the opportunity to do something was available. In Sentence 3, was able to indicate the ability, or the opportunity, to perform an action in a particular situation. Could is not used in such a context. Sometimes could is the past of ‘can’. We use ‘could’ to say that someone had the general ability to do something. But ‘was/were able to’ is used to indicate the past ‘ability + performance’ (result) which means ‘managed to do something in one particular situation.

Activity – 15
Use could or was/were able to in the sentences below. Use a negative if necessary. More than one answer is possible.
(a) The author of the book learned to write very early in life. He — write short stories when he was at school.
(b) My scooter didn’t start. Luckily I — borrowed a bicycle and got there in time for the interview.
(c) It was dark. We — see a thing.
(d) The children were warned that a fire had started, and they — move their belongings in time.
(e) I — meet my friend as the bus had left.
(f) The people in the neighboring village were having a party last night and you — have joined them.
(g) My friend ran after the bus and — get on.
(h) The freedom fighters had to live in the jungles for months. They — survive without food for several days.
Answer:
(a) The author of this book learned to write very early in life. He was able to write short stories when he was at school.
(b) My scooter didn’t start. Luckily I was able to borrow a bicycle and got there in time for the interview.
(c) It was dark. We couldn’t see a thing.
(d) The children were warned that a fire had started, and they were able to move their belongings in time.
(e) I could not meet my friend as the bus had left.
(f) The people in the neighboring village were having a party last night and you could have joined them.
(g) My friend ran after the bus and was able to get on.
(h) The freedom fighters had to live in the jungles for months. They were able to survive without food for several days.

Activity – 16
Saurabh is 40. Sometimes he feels that he has wasted his life. Read about Saurabh and replace some of the words with could have …, as shown in the example below.
Example: When Saurabh was 15 he had a chance to go abroad, but he decided not to go.
Ans. When Saurabh was 15 he could have gone abroad.
(a) Saurabh got a scholarship to study in a reputed public school. But he didn’t go.
_________________________________
(b) He was a good speaker, but he decided not to participate in debates.
_________________________________
(c) He had the opportunity to learn music under a famous teacher, but he decided against it.
_________________________________
(d) He was intelligent enough to come out first in the examination, but he did not try.
_________________________________
(e) He had the opportunity to start a business, but he did not want to.
_________________________________
(f) Everyone thought he had the creativity to write novels, but he never tried.
_________________________________
Answer:
(a) Saurabh could have studied in a reputed public school when he was young.
(b) He could have participated in debates when he was in school.
(c) He could have learned music under a famous teacher when he was 20 years old.
(d) He could have come out first in the examination if he had studied sincerely.
(e) He could have started a business when he was 30 years old.
(f) When he was 25 years old, he could have written novels.

Activity – 17
Use can, can’t, could, couldn’t was/were able to, where required. (Alternative answers are possible.)
(a) She — even speak properly when she was a girl, but now she’s a famous singer.
(b) Did you see anybody in the park? No, I — find anybody.
(c) An eagle — fly for hours.
(d) When my sister was just 7, she — speak Hindi much more fluently than she — now.
(e) On the fifth day the rescuers saw the children and — reach them without too much trouble.
(f) After weeks of training, I — climb some of the coconut trees.
Answer:
(a) She could not even speak properly when she was a girl, but now she’s a famous singer.
(b) Did you see anybody in the park? No, I could not find anybody.
(c) An eagle can fly for hours.
(d) When my sister was just 7, she was able to speak Hindi much more fluently than she can now.
(e) On the fifth day the rescuers saw the children and were able to reach them without too much trouble.
(f) After weeks of training, I was able to climb some of the coconut trees.

SECTION – 6

Indicating possibility (using may, can)
(a) This house is too small. We may sell it and buy a bigger one.
(b) That box is too heavy for you. You may drop it.
(c) Camels can survive for weeks in the desert, without water.
(d) Smoking can cause cancer.
‘May’ is used to express a specific possibility in the present or future. It can refer to a single occasion. But ‘can ’ is used to express a general theoretical possibility.

Activity – 18
Use can or may, as required, in the following sentences.
(a) The government — hike the bus fares next month.
(b) The villagers — convert this building into a hospital if everyone agrees.
(c) This medicine — cure any disease.
(d) My friends — put on a play here again next year.
(e) We’re going to do something different this year. We — decide to hire a professional drama group.
(f) Your boss is impressed with your work. You — get a promotion soon.
(g) The presence of lead particles in the air — cause brain damage in children.
(h) The machine has broken down and — takes some time to repair.
Answer:
(a) The government may hike the bus fares next month.
(b) The villagers may convert this building into a hospital if everyone agrees.
(c) This medicine can cure any disease.
(d) My friends may put on a play here again next year.
(e) We’re going to do something different this year. We may decide to hire a professional drama group.
(f) Your boss is impressed with your work. You may get a promotion soon.
(g) The presence of lead particles in the air can cause brain damage in children.
(h) The machine has broken down and may take some time to repair.

Activity – 19
A group of engineers has come up with a number of unusual products, for use at home. These products are :
1. A battery-operated fan.
2. A portable water heater.
3. Writing paper that glows in the dark.
4. Shirts made of edible material.
5. Shoes with a built-in alarm clock.
6. A bicycle that can float.
Think of some situations in which these products could prove to be very useful and frame sentences suggesting (to prospective customers) some possible uses for the products. One example is given.
Example
1. You can use the battery-operated fan to cool yourself when you are sitting in your garden.
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
Answer:
2. You can use the portable water heater when you go outside during chilly winter.
3. You can use writing paper that glows in the dark when there is no light.
4. You can use shirts made of edible material if you need.
5. You can use shoes with a built-in alarm clock to make use of the time properly.
6. You can use a bicycle that can float when you want to cross a flooded river.

SECTION – 7

Indicating present or future possibility (using may, might or could)
Look at the following sentences.
(a) Where’s Madhuri? She may/might / could be in the garden.
(b) There’s someone at the gate. It may / might / could be the postman.
(c) They’re not cooking dinner. They may / might / could be planning to go out tonight.
May, might, and could are used here to talk about present or future possibilities. Might is normally a little less sure than may, and could is less sure than may or might. Note that we can’t use can in the above examples. Can you say why? (Hint: Refer to the difference between can and may.)
‘May, might could’ all three models are used in sentences for possibility. There is still a little difference between them. May is a bit stronger than might or could. ‘Might’ is a little less sure than ‘may’ and ‘could’ is less sure than ‘may or might’.

Activity – 20
Rewrite the following sentences using ‘might’ or ‘could’.
(a) It is possible that she is cheating you.
_________________________________
(b) It is possible that they’ll come in the evening.
_________________________________
(c) It is possible that he is planning to sell the car.
_________________________________
(d) It is possible that she is telling the truth.
_________________________________
(e) This statement possibly contradicts his earlier statement.
_________________________________
(f) It is possible that one of them is a spy.
_________________________________
Answer:
(a) She might cheat me.
(b) They could come in the evening.
(c) He might sell the car.
(d) She might tell the truth.
(e) He might contradict his earlier statement.
(f) He might be a spy.

Activity – 21
Use may, might or could, together with the appropriate forms of the verbs in brackets.
1. Who is the girl Madhu is talking to? I’m not sure. She — (be) her sister.
2. Why are the boys shouting? I don’t know. They — (play).
3. Where is Manisha? I have no idea. She — (study) in the library.
4. Who is that man with Vijay? I’m not sure. It — (be) his uncle.
5. Shall I tell the Minister about you? You’d better not. He — (think) I want to ask him for a favor.
Answer:
1. Who is the girl Madhu is talking to? I’m not sure. She might be her sister.
2. Why are the boys shouting? I don’t know. The might he plane.
3. Where is Manisha? I have no idea. She might be studying in the library.
4. Who is that man with Vijay? I’m not sure. It might be his uncle.
5. Shall I tell the Minister about you? You’d better not. He may think I want to ask him for a favor.

Activity – 22
You are going for a walk, and you suddenly see a mysterious flying object, high up in the sky. Make five guesses about what the object could be.
1. _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
Answers
1. It might be a skylark.
2. It may be a balloon.
3. It might be a parachute.
4. It could be the wing of a damaged airplane.
5. It might be a soldier falling from an aircraft.

SECTION – 8

Referring to possibility in the past (using may, might, or could)
Look at the examples below.
(a) She was not in the hostel yesterday. She might / could have gone home.
(b) A: Do you think he saw you?
B: No, he was too far away. He couldn’t have seen me.
(c) You were stupid to throw stones at the dog. It might have attacked you.
We use may/might/could, together with some verbs in the present perfect form, to talk about the possibility in the past.

Activity – 23
Complete the sentences below, expressing possibility in the past.
(a) The other teams weren’t good, so our team — (win). „
(b) You know where the library is, don’t you? You — (pass) it on your way here.
(c) Why didn’t your friend answer the phone? He — (not/ hear) it ringing.
(d) The light’s on. They — (forget) to switch it off.
(e) I did not hear the child’s voice, and I thought he — (fall asleep).
(f) Our teacher is not at home. He — (go) to meet a friend.
(g) How did you get that stain on your saree? I’m not sure. The baby — (drop) food on it.
(h) A: I can’t find my umbrella. Have you seen it?
B: No. You — (leave) in the restaurant.
Answer:
(a) The other teams weren’t good, so our team might have won.
(b) You know where the library is, don’t you? You might have passed it on your way here.
(c) Why didn’t your friend answer the phone? He could/might not have heard it ringing.
(d) The light’s on. They might have forgotten to switch it off.
(e) I did not hear the child’s voice, and I thought he could/might have fallen asleep.
(f) Our teacher is not at home. He could have gone to meet a friend.
(g) How did you get that stain on your saree? I’m not sure. The baby might/could have dropped food on it.
(h) A: I can’t find my umbrella. Have you seen it?
B: No. You might/could have left in the restaurant.

SECTION – 9

Making a deduction (using must have/can’t have)
Look at the following example.
The old man has not had anything to eat for the last two days. He must be starving.
The speaker is deducing something (starving). She / He takes the help of logical analysis or the basis of evidence that is available. She / He is very much sure that what he/she says is correct. So in the above example, ‘must’ is used for deduction. Can’t: In negative sentences for logical analysis/conclusion ‘can’t’ is used. The speaker is very sure about some negative conclusion that she/he has reached. The use of ‘must have ’ and ‘can’t have ’ shows that the speaker has made a deduction about something that happened in the past.
Example
1. Ramesh has done very well in the examination. He must have worked really hard.
2. The library was closed all day yesterday. You can’t have been there yesterday.

Activity – 24
Answer the questions in Column A, using must or can’t, and choosing a suitable reason from Column B. (One answer has been provided.)

Example: (She can’t be ill. She has gone swimming.)
Answer:
2. They must be sleeping. Their bedroom lights are off.
3. He must be happy. He has just got a job.
4. He can’t be a Bengali. He speaks Telugu.
5. The shopkeeper can’t be honest. He charged more than the price.
6. These boys must be naughty. They play tricks on everyone.
7. She can’t be married. She is too young.

Activity – 25
Consider the situations below and use the words in brackets to frame sentences with ‘/must have’ and ‘can’t have
(a) Satish got the first division in the exam. (He / works hard)
_________________________________
(b) Someone saw Sudha in the college library at 8.00 a.m. yesterday. (She / stays / in bed / all morning)
_________________________________
(c) The traffic lights were red and the car stopped, (the driver/see / the red light)
_________________________________
(d) He knows a lot about teaching. ( He / a teacher when he was young)
_________________________________
(e) Girish knew exactly what to do. (He / learns / the skills / very carefully)
_________________________________
(f) My friend knew everything about our plan. (He / listens / to our conversation)
_________________________________
(g) Janaki walked past me without speaking. (She / see / me)
_________________________________
(h) There are five stitches on her head. (She / have / an accident)
_________________________________
Answer:
(a) He must have worked hard.
(b) She can’t have stayed in bed all morning.
(c) The driver must have seen the red light.
(d) He must have been a teacher when he was young.
(e) He must have learnt the skills very carefully.
(f) He must have listened to our conversation.
(g) She can’t have seen me.
(h) She must have had an accident.

SECTION – 10

Offering advice (using should, ought to, had better, be supposed to)
(a) If your toothache is not getting better, you should see a dentist.
(b) They really looked after you well. You ought to write a letter of thanks.
(c) Your roommates are complaining. You had better turn the music down.
Should and ought to are used to ask for as well as give advice. Ought to is preferred when the advice is given by someone in authority.
‘Had better’ (generally abbreviated to better) indicates a strong recommendation, made for a particular situation.
Should have … and ought to have … are used to show that someone did not do something (in the past) which was advisable.
Look at the examples below.
1. I should have bought that book yesterday, but I didn’t have the money.
2. Haven’t you been to see your doctor? You ought to have seen him yesterday

Activity – 26
Complete the sentences in the “Advice” column, using ‘should’ or ‘ought to’.

Answer:
i. I should have bought a new pen yesterday, but I didn’t have money.
ii. I should have looked for other books, but I didn’t have free moments.
iii. I should have given some money to the poor, but I didn’t get the key of my drawer.
iv. They ought to have asked their teacher as they did not solve it themselves.
v. I should have gone and collected the glasses from the shop.
vi. I should have taken some days off.

Activity – 27
Produce sentences indicating what the speaker should (not) / ought to have done in given situations.
(a) I’m in trouble because I didn’t wish my boss “Good morning”!
(b) The pen he used to write the examination was not good enough.
(c) Nirmal did not meet Seeta until it was too late.
(d) I’m sorry that he didn’t take your advice.
(e) Smita had to go to the bank opposite the college, but she hired a taxi.
(f) I sent a messenger three days ago, but he has not arrived yet.
(g) She left her books in the canteen. She didn’t find them when she went back.
Answer:
(a) I’m in trouble because I didn’t wish my boss “Good morning”!
I should have wished my boss “Good morning.”
(b) The pen he used to write the examination was not good enough.
He ought to have used a good pen to write the examination.
(c) Nirmal did not meet Seeta until it was too late.
Nirmal should have met Seeta in time.
(d) I’m sorry that he didn’t take your advice. He ought to have taken your advice.
(e) Smita had to go to the bank opposite the college, but she hired a taxi. Smita should not have hired a taxi.
(I) I sent a messenger three days ago, but he has not arrived yet. He should have arrived by this time.
(g) She left her books in the canteen. She didn’t find them when she went back. She should have been very careful.

Activity – 28
What advice would you offer someone in a difficult or dangerous situation, such as an Are, flood, cyclone, a roof falling in, or a wild animal running loose in the city?
Think of at least 7 such situations and form sentences to offer advice, using either had better or had better not.
Example (a fire) You’d better phone the fire brigade.
1. (a burglary) You’d better not _________________________________
2. _________________________________
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
7. _________________________________
Answer:
1. You’d better not fight against them.
2. (a flood) You’d better take shelter on a hill.
3. (cyclone) You’d better leave that old house.
4. (a wild animal running loose) You’d better not open the door.
5. You’d better telephone the police about the wild animal.
6. (a roof falling in) You’d better leave the house with your family members.
7. (afire) You’d better make lose your cattle.

SECTION – 11

Expressing obligation or necessity (using must have to / had to, got to)
(a) I’ve got terrible pain in my back. I must go and see the doctor.
(b) I have got an appointment. I have to go and see the doctor at 9.00 tomorrow morning.
(c) Our teacher had given us fifty sums to work out. So I had to work late yesterday.
(d) My friend must be waiting for me. I’ve got to hurry.
‘Must’ is used for an internal obligation or when authority comes from the speaker. ‘Have to ’ is normally used for outside direction/obligation or when the authority comes from someone other than the speaker.
We use ‘had to’ when talking about past obligations or necessity. ‘Have got’ is sometimes used instead or ‘have to’ to talk about obligation or necessity but it is more informal.

Activity – 29
Complete the sentences using must or some form of have to. (In some cases, more than one answer is possible.)
(a) I really — find something cheaper. This is too expensive.
(b) A. — you — get a visa to go to Nepal?
B. No, you don’t but you — get one for Pakistan.
(c) You — fill in this form first. You can’t do anything until it is completed.
(d) Sudhir: I’ll meet you at the airport at 9 o’clock then.
Kamal: What! We — check in by 7.30.
(e) Jiban: This medicine tastes horrible. I’m going to take it only once a day.
Jiten: Now, don’t be silly. The doctor says you — take it 3 times a day.
Jiban: All right, I’ll take the medicine after meals.
Jiten: No, you — take the medicine before meals.
(f) You — remember to brush your teeth. If you don’t, you’ll have to go to the dentist.
(g) I — stay in bed yesterday because I wasn’t very well.
(h) I couldn’t go to the party last night because I — look after my youngest sister, who was ill.
Answer:
(a) I really must find something cheaper. This is too expensive.
(b) A: Have you got to get a visa to go to Nepal?
B: No, you don’t, but you have to get one for Pakistan.
(c) You have to fill in this form first. You can’t do anything until it is completed.
(d) Sudhir: I’ll meet you at the airport at 9 o’clock then.
Kamal: What! We have to check in by 7.30.
(e) Jiban: I’ve never tasted such horrible medicine. I’m going to take it only once a day.
Jiten: Now, don’t be silly. The doctor says you have to take it 3 times a day.
Jiban: All right, I’ll take the medicine after meals.
Jiten: No, you have to take the medicine before meals.
(f) You must remember to brush your teeth. If you don’t, you’ll have to go to the dentist.
(g) I had to stay in bed yesterday because I wasn’t very well.
(h) I couldn’t go to the party last night because I had to look after my youngest sister.

SECTION – 12

Expressing prohibition (using mustn’t, needn’t, don’t have to)
(a) You mustn’t jump over that wall. You’ll break your legs.
(b) You mustn’t drive that car. The brakes don’t work.
(c) Tomorrow is a holiday. You needn’t get up early.
(d) They needn’t buy the book. They can get it in the library.
(e) We don’t have to / need to go to a hotel. My mother can cook for us. ‘Mustn’t’ is usually used for prohibition or it is forbidden to do something.
But needn ’t is used for absence or obligation/necessity. Doesn ’t/ don’t have to, doesn’t / don’t need to’ are used when it is not necessary to do something.

Activity – 30
Choose the correct modal.
(a) They’ve been late for class three times this week. They mustn ’t/ needn’t be late again.
(b He mustn’t / needn’t tell our teacher about the meeting. Sudha has already told him.
(c) You mustn’t / don’t have to make any noise going into the house.
It’s very late and everybody is asleep.
(d) I mustn’t / don’t have to hurry. I’ve got plenty of time.
(e) You mustn’t / needn’t open the door before the bus stops. You could fall out.
(f) You don’t have to / mustn’t wash that shirt. It isn’t dirty.
(g) Sima needn’t/ mustn’t finish her essay today. She’s got to hand it in by next Friday.
(h) You needn’t / mustn’t wear your best clothes. You can wear what you like.
Answer:
(a) The mustn’t be late again.
(b) He needn’t tell our teacher about the meeting. Sudha has already told him.
(c) You mustn’t make any noise going into the house. It’s very late and everybody is asleep.
(d) I don’t have to hurry. I’ve got plenty of time.
(e) You mustn’t open the door before the bus stops. You could fall out.
(f) You don’t have to wash that shirt. It isn’t dirty.
(g) Sima needn’t finish her essay today.
She’s got to hand it in by next Friday.
(h) You needn’t wear your best clothes. You can wear what you like.

Activity – 31
List five things which a visitor to a zoo must not do.
1. (A) Visitors to a zoo mustn’t…..
2. (S)he…
3. _________________________________
4. _________________________________
5. _________________________________
6. _________________________________
7. _________________________________
8. _________________________________
Answer:
1. He mustn’t tease the wild animals.
2. He mustn ’t row boats himself in the lake without a guide.
3. He mustn’t throw stones at the birds.
4. He mustn’t give food to any animals there.
5. He mustn’t put his fingers inside a cage.
6. He mustn’t disfigure the walls.
7. He mustn’t go near the crocodiles.
8. He mustn’t terrify the small animals.

Activity – 32
You went on a picnic to some far-away place with a group of friends. As you did not know what things would be available there, you made elaborate preparations. Now, after your return, you are narrating your experiences to another group of friends, who would also like to go on a picnic to the same spot.
Tell your friends which of the arrangements made by you were necessary, and which of them were either unnecessary or proved to be unnecessary. Use had to, needed to, didn’t need to, didn’t have to, and need not have to talk about the arrangements which were either necessary or unnecessary.
Here are some of the arrangements that were made.
1. hiring a bus
2. buying fire-wood for cooking
3. carrying water for drinking and cooking
4. carrying food materials: rice daal, vegetables, meat
5. finding a place to cook in
6. finding a place to serve the food
7. going to places of interest nearby
8. thinking of ways to keep yourself entertained
9. washing utensils after the meal
10. making arrangements for the return journey.
Answer:
1. We had to hire a bus for the picnic.
2. We needn’t have to / didn’t have to buy firewood for cooking as it as plentily available there.
3. We didn’t have to carry water for drinking and cooking.
4. We had to carry food materials: rice, daal, vegetables, and meat.
5. We needed to / had to find a place to cook in.
6. We needed to find a place to serve the food.
7. We needn’t have to go to places of interest nearby.
8. We had to think of ways to keep ourselves entertained.
9. We needed to wash the utensils after the meal.
10. We needn’t have to make arrangements for the return journey as we had already arranged before.

Multiple-Choice Questions (MCQs) with Answers

Question 1.
Rain has stopped; you ___________ carry an umbrella with you.
(A) mustn’t
(B) ought not
(C) needn’t
(D) won’t
Answer:
(C) needn’t

Question 2.
A judge ___________ be upright.
(A) shall
(B) will
(C) must
(D) could
Answer:
(C) must

Question 3.
He ___________be at least thirty years old.
(A) can
(B) should
(C) will
(D) must
Answer:
(D) must

Question 4.
Shut the window, ___________?
(A) will you
(B) would you
(C) could you
(D) none of these
Answer:
(B) would you

Question 5.
___________ you open the door, please?
(A) Shall
(B) Will
(C) Can
(D) May
Answer:
(B) Will

Question 6.
You do ___________as you are told.
(A) will
(B) can
(C) must
(D) shall
Answer:
(D) shall

Question 7.
I ___________ try if you wish.
(A) shall
(B) will
(C) should
(D) would
Answer:
(B) will

Question 8.
_____ you rather have tea or coffee?
(A) Should
(B) Will
(C) Would
(D) Can
Answer:
(C) Would

Question 9.
He _____ prefers to have coffee.
(A) will
(B) can
(C) would
(D) none of these
Answer:
(C) would

Question 10.
We _____ disobey our parents.
(A) needn’t
(B) mustn’t
(C) can’t
(D) wouldn’t
Answer:
(B) mustn’t

Question 11.
I ____ do it now.
(A) could
(B) should
(C) can
(D) might
Answer:
(C) can

Question 12.
They worked hard and they succeed.
(A) may
(B) could
(C) might
(D) should
Answer:
(C) might

Question 13.
Let’s go for cricket, _____ we?
(A) should
(B) could
(C) would
(D) shall
Answer:
(D) shall

Question 14.
It _____ rain tonight.
(A) can
(B) could
(C) should
(D) may
Answer:
(D) may

Question 15.
I ___________ do it long ago.
(A) could
(B) might
(C) should
(D) would
Answer:
(A) could

Question l6.
He is so weak that he _____ walks.
(A) will not
(B) would not
(C) cannot
(D) may not
Answer:
(C) cannot

Question 17.
You ____ go now.
(A) can
(B) could
(C) ought
(D) none of these
Answer:
(A) can

Question 18.
_____ I use your telephone directory?
(A) May
(B) Can
(C) Shall
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

Question 19.
If you do this, you _____ be punished.
(A) will
(B) would
(C) shall
(D) can
Answer:
(A) will

Question 20.
I ____ do as you did.
(A) could
(B) should
(C) can
(D) would
Answer:
(D) would

Question 21.
Take heed less you ____ fall.
(A) would
(B) should
(C) might
(D) could
Answer:
(B) should

Question 22.
I _____ have my work here.
(A) must
(B) may
(C) can
(D) none of these
Answer:
(A) must

Question 23.
You _____ if the Court had instructed you to do so.
(A) shall have attended
(B) would have to attend
(C) would have had to attend
(D) would attend
Answer:
(C) would have had to attend

Question 24.
Tell my mother that she _____ telephone me at work for I will be home by seven o’clock this evening.
(A) needs not to
(B) need not to
(C) has no need
(D) need not
Answer:
(D) need not

Question 25.
The fire spread through the building quickly but everybody ___________.
(A) was able to escape
(B) managed to escape
(C) could escape
(D) both (A) and (B)
Answer:
(D) both (A) and (B)

Question 26.
The phone is ringing. It ___________be Tim.
(A) might
(B) can
(C) could
(D) both (A) and (C)
Answer:
(D) both (A) and (C)

Question 27.
Why did you stay at a hotel when you went to New York? You _____ with Barbara.
(A) can stay
(B) could stay
(C) could have stayed
(D) none of these
Answer:
(C) could have stayed

Question 28.
I’ve lost one of my gloves. I ___________ it somewhere.
(A) must drop
(B) must have dropped
(C) must be dropping
(D) must have been dropping
Answer:
(B) must have dropped

Question 29.
Take an umbrella with you when you go out, It _____ rain later.
(A) may
(B) might
(C) can
(D) could
Answer:
(A) may

Question 30.
What was wrong with you? Why ___________ go to the hospital?
(A) had you to
(B) did you have to
(C) must you
(D) none of these
Answer:
(B) did you have to

Question 31.
There’s plenty of time. You ___________ hurry.
(A) don’t have to
(B) mustn’t
(C) needn’t
(D) none of these
Answer:
(A) don’t have to

Question 32.
It was a great party last night. You _____ come. Why didn’t you?
(A) must have
(B) should have
(C) ought to have
(D) had to
Answer:
(B) should have

Question 33.
Jane ______ a car.
(A) suggested that I buy
(B) suggested that I should buy
(C) suggested me to buy
(D) none of these
Answer:
(A) suggested that I buy

Question 34.
I think all drivers _____ seat belts.
(A) should wear
(B) had better wear
(C) had better to wear
(D) none of these
Answer:
(A) should wear

Question 35.
It’s late. It’s time ___________ home.
(A) we go
(B) we must go
(C) we should go
(D) we went
Answer:
(D) we went

Odisha State Board CHSE Odisha Class 12 Invitation to English 1 Solutions Chapter 3 The Portrait of a Lady Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class English Solutions Chapter 3 The Portrait of a Lady

CHSE Odisha Class 12 English The Portrait of a Lady Text Book Questions and Answers

Unit Wise Gist and Glossary:

UNIT – I:
Gist:
The writer speaks of his own grandmother. By the time, he wrote the story, she was quite old and all her hair had been white. Her wrinkled face and body gave him a kind of surprise. Twenty years have elapsed since the writer had been with his grandmother. People said that once the old lady was as beautiful as a fairy. Her husband – the writer’s grandfather was also very handsome. His photo was being hung in the drawing room of the writer.

He was clad in a big turban and loose-fitting clothes. The writer noticed his ripe old age. Grandmother had always been short and fat, and her back was slightly bent. Wrinkles were across her face. When the writer came to know her, she had been in such a condition. She was always clad in a spotless white saree. Her silver locks were spread messily over her pale, wrinkled face. She was always in a state of saying a prayer that could not be heard distinctly. She was beautiful. She was a picture of calmness. She had a divine beauty.
ସାରମର୍ମ :
ଲେଖକ ତାଙ୍କ ନିଜ ବୁଢ଼ୀମା’ଙ୍କ ବିଷୟରେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ଯେତେବେଳେ ସେ ଗଛଟି ଲେଖିଥିଲେ, ସେତେବେଳକୁ ତାଙ୍କ ବୁଢ଼ୀମା’ ସମ୍ପୂର୍ଣ୍ଣ ବୁଢ଼ୀ ହୋଇଯାଇଥିଲେ ଏବଂ ତାଙ୍କର ସମସ୍ତ କେଶ ଧଳା ହୋଇ ଯାଇଥିଲା । ତାଙ୍କର କୁଞ୍ଚ୍ ମୁଖମଣ୍ଡଳ ଓ ଶରୀର ତାଙ୍କୁ ଏକପ୍ରକାର ବିସ୍ମିତ କରୁଥିଲା । ଦୀର୍ଘ ୨୦ ବର୍ଷ ଧରି ସେ ତାଙ୍କ ବୁଢ଼ୀମା’ଙ୍କ ସହିତ ଥିଲେ । ଲୋକମାନେ କହୁଥିଲେ ଯେ ଏକଦା ଏହି ବୁଢ଼ୀ ସ୍ତ୍ରୀଲୋକଜଣକ ପରୀ ଭଳି ସୁନ୍ଦରୀ ଥିଲେ । ତାଙ୍କ ସ୍ଵାମୀ –ଲେଖକଙ୍କ ବୁଢ଼ାବାପା ଖୁବ୍ ସୁନ୍ଦର ଥିଲେ । ତାଙ୍କ ଫଟୋ ଲେଖକଙ୍କ ବୈଠକଘରେ ଟଙ୍ଗା ଯାଇଥିଲା । ବଡ଼ ପଗଡ଼ି ଓ ଢିଲା ପୋଷାକ ତାଙ୍କର ସମଗ୍ର ଶରୀରକୁ ଆବୃତ କରୁଥିଲା ।

ଲେଖକ ତାଙ୍କର ପରିପକ୍ଵ ବୃଦ୍ଧ ଅବସ୍ଥାକୁ ଦେଖୁ ପାରୁଥିଲେ । ବୁଢ଼ୀମା’ ଗେଡ଼ୀ ଓ ମୋଟୀ ଥିଲେ ଏବଂ ତାଙ୍କ ଅଣ୍ଟା ଅଳ୍ପ ନଇଁ ପଡ଼ିଥିଲା । ତାଙ୍କ ମୁଖମଣ୍ଡଳରେ କୁଞ୍ଚେତ ରେଖାର ଦାଗସବୁ ରହିଥିଲା । ଲେଖକ ତାଙ୍କୁ ଜାଣିବା ଦିନଠାରୁ ସେ ସେହି ଅବସ୍ଥାରେ ଥିଲେ । ସେ ସର୍ବଦା ଦାଗହୀନ ଧଳା ଶାଢ଼ି ପରିଧାନ କରୁଥିଲେ । ରୁପା ସଦୃଶ ଦେଖାଯାଉଥ‌ିବା ତାଙ୍କର ଆଲୁଳାୟିତ କେଶରାଶି ତାଙ୍କର ମଳିନ ଓ କୁଞ୍ଚ ମୁଖମଣ୍ଡଳ ଉପରେ ବିଛାଇ ହୋଇ ପଡ଼ୁଥିଲା । ସେ ସର୍ବଦା ପ୍ରାର୍ଥନା କରୁଥିବା ଅବସ୍ଥାରେ ରହୁଥିଲେ, ଯାହାକି ସ୍ପଷ୍ଟଭାବେ ଶୁଣି ହେଉ ନ ଥିଲା । ସେ ସୁନ୍ଦରୀ ଥିଲେ । ସେ ନୀରତବାର ପ୍ରତିଛବି ଥିଲେ । ତାଙ୍କଠାରେ ସ୍ୱର୍ଗୀୟ ସୁଷମା ଭରି ରହିଥିଲା ।

Glossary:
wrinkled : କୁଞ୍ଚିତ ହୋଇଯାଇଥିଲେ
pretty : attractive without being very beautiful (ଆକର୍ଷଣୀୟା)
that believe: ବିଶ୍ଵାସ କରିବା କଷ୍ଟକର ଥିଲା
portrait : photograph or painting of a person (ପ୍ରତିକୃତି)
hung : ଝୁଲୁଥି
mantlepiece : a shelf (ଏକ ଥାକ)
turban : ପଗଡ଼ି
loose-fitting clothes : ଢିଲା ପୋଷାକ
beard : ଦାଢ଼ି
at least : ଅନ୍ତତଃ
sort : kind (ପ୍ରକାର )
as if : ସତେ ଯେମିତି
lots and lots : ବହୁତ/ ଅନେକ
revolting : (here) unbelievable (ଅବିଶ୍ୱାସ୍ୟ)
quite : ସମ୍ପୂର୍ଣ୍ଣ ଭାବରେ
absurd : not logical and sensible (ଉଦ୍ଭଟ)
undignified : not respectable ( ସମ୍ମାନଯୋଗ୍ୟ ନୁହେଁ)
treated : (here) considered (ବିଚାର କରୁଥିଲେ )
the Prophets : the Saints (ସାଧୁସନ୍ଥମାନେ )
slightly : a little (ଟିକିଏ)
bent : ନଇଁ ଯାଇଥିଲେ
criss-cross : ଛକି ଚିହ୍ନ
terribly old : very old (ବହୁତ ବୁଢ଼ା)
hobbled : walked awkwardly (କଷ୍ଟରେ ଚାଲୁଥିଲେ)
spotless : a very clear (ଦାଗହୀନ)
stoop : bend (ନଇଁ ପଡ଼ିବା)
beads of rosary : ଜପାମାଳିର ମାଳି
silver : white (ଧଳା)
locks : କେଶରାଶି
scattered : spread (ବିଛାଇ ହୋଇ ପଡ଼ିଥିଲା)
untidily : ଅସଂଯତ ଭାବେ
puckered : କୁଞ୍ଚ
constantly : ଲଗାତରଭାବେ
inaudible : ଅସ୍ପଷ୍ଟ
expanse : ବିସ୍ତୀର୍ଣ୍ଣ
serenity : calmness (ସ୍ନିଗ୍ଧତା)
contentment : satisfaction (ସନ୍ତୋଷ)

Think about it:
Question 1.
Why was it hard for the author to believe that his grandmother was once young and pretty?
Answer:
It was hard for the author to believe that his grandmother was once young and pretty, because he, in spite of staying with her for the last twenty years, did not find any change in her beauty. She was as elegant as ever.

Question 2.
How did the grandfather appear in his portrait?
Answer:
His grandfather appeared at least to be a hundred-year-old person in his portrait.

Question 3.
What sort of a person did he look in his portrait?
Answer:
He looked in his portrait as a sort of person who couldn’t have a wife or children, but could only have many grandchildren.

Question 4.
How does the author portray his grandmother?
Answer:
The writer states that his grandmother, short and fat, was a little bent. Age didn’t have any impact on her age and she was pretty and very active.

Question 5.
Why does he say, “the thought was almost revolting”?
Answer:
He says “that the thought was almost revolting”, because it was quite difficult on his part to believe that his grandmother was once pretty and young.

Question 6.
The grandmother had a divine beauty. How does the author bring this out?
Answer:
The author states that the grandmother had a divine beauty because she was a picture of rare calmness, peace and contentment. Her beauty resembling ‘the winter landscape in the mountains’ is also a case in point.

UNIT – II

Gist:
The relationship between the writer and his grandmother was quite friendly. She was active to the core. Every day, she used to wake up the writer in the morning to be ready to go to school. She was uttering the monotonous song while bathing and dressing the writer. The writer liked her very much. His grandmother was going to school with him because there was a temple attached to the school. She would sit inside and read holy books. After school was over, they came back home followed by dogs growling and fighting with each other for the chapattis they flung at them.
ସାରମର୍ମ :
ଲେଖକ ଏବଂ ବୁଢ଼ୀମା’ଙ୍କ ସମ୍ପର୍କ ସମ୍ପୂର୍ଣ୍ଣରୂପେ ବନ୍ଧୁତ୍ଵପୂର୍ଣ୍ଣ ଥିଲା । ସେ ଖୁବ୍ ଚଳଚଞ୍ଚଳ ଥିଲେ । ବିଦ୍ୟାଳୟକୁ ଯିବାକୁ ପ୍ରସ୍ତୁତ ହେବା ପାଇଁ ସେ ପ୍ରତିଦିନ ସକାଳେ ଲେଖକଙ୍କୁ ଉଠାଉଥିଲେ । ଲେଖକଙ୍କୁ ଗାଧୋଇଦେବା ଓ ପୋଷାକ ପିନ୍ଧାଇବା ସମୟରେ ସେ ଗୁଣୁଗୁଣୁ ସ୍ଵରରେ ବିରକ୍ତିକର ଗୀତ ଗାଉଥିଲେ । ଲେଖକ ତାଙ୍କୁ ବହୁତ ଭଲ ପାଉଥିଲେ । ସେ ପ୍ରତିଦିନ ତାଙ୍କ ସହିତ ବିଦ୍ୟାଳୟକୁ ଯାଉଥିଲେ କାରଣ ବିଦ୍ୟାଳୟକୁ ଲାଗି ମନ୍ଦିରଟିଏ ଥିଲା । ସେ ମନ୍ଦିର ଭିତରେ ବସି ପବିତ୍ର ବହିସବୁ ପଢୁଥିଲେ । ବିଦ୍ୟାଳୟ ଛୁଟି ହେବା ପରେ ସେମାନେ ଘରକୁ ଫେରୁଥିଲେ । ସେମାନଙ୍କୁ ପଛେ ପଛେ କୁକୁରମାନେ ଆସୁଥିଲେ । ବୁଢ଼ୀମା’ ଏବଂ ଲେଖକ ସେମାନଙ୍କ ଆଡ଼କୁ ଫୋପାଡ଼ୁଥିବା ଚପାତିଗୁଡ଼ିକ ପାଇଁ ସେମାନେ ପରସ୍ପର ମଧ୍ୟରେ କଳି କରୁଥିଲେ ।

Glossary:
wake : ଉଠେଇ ଦେବା
monotonous : boring (ବିରକ୍ତିକର)
sing-song : singing in a repeated rising and falling rhythm (ବାରମ୍ବାର ଉତ୍‌- ପତିତ ସ୍ଵରରେ ଗୀତ ଗାଇବା)
get heart : ମୁଖସ୍ଥ କରିବା
ever bothered : never cared
fetch : ଆଣିବା
tiny : very small
earthen : ମାଟି ତିଆରି
tie : bind (ବାନ୍ଧିବା)
stale : ବାସି
attached : connected (ସଂଲଗ୍ନ ଥିଲା)
priest : ପୂଜକ
rows : ଧାଡ଼ି ଧାଡ଼ି
chorus : ମିଳିତ ସ୍ଵର
scriptures : holy books (ପବିତ୍ର ପୁସ୍ତକସବୁ )
growling : make a low guttural sound of hositility in throat (ନିମ୍ନ ସ୍ଵର ଅସନ୍ତୋଷ ପ୍ରକାଶ କରି ଶବ୍ଦ କରିବା)

Think it out:
Question 1.
What was the grandmother’s routine in the village?
Answer:
The grandmother’s routine in the village comprised waking the writer up in the morning and preparing him for school. She also went to school with him and came back home together after his school was over.

Question 2.
How did the grandmother take care of the writer during his childhood? Was she a good companion of the writer in the village?
Answer:
The grandmother took minute care of the writer during his childhood beginning from walking him up, bathing and dressing him to accompanying him to school and coming back home. She did not forget to give him breakfast. Yes, she was certainly a good companion of the writer, as his parents lived in the city.

Question 3.
What lessons did the writer learn from the village priest?
Answer:
The writer learnt the alphabet and the morning prayer from the village priest.

Question 4.
How did the grandmother spend her time at the temple?
Answer:
The grandmother spent her time at the temple in reading holy books.

Question 5.
Was she a religious person? How?
Answer:
Yes, she was a religious lady. Her morning prayer, frequent visits to the temple and reading holy books inside it arid throwing chapattis to the village dogs who followed them to their home justify this fact.

UNIT – III

Gist:
The writer and his grandmother went to the city after his parents’ comfortable settlement there. That marked a turning point in their friendship. In spite of sharing the same room, she no longer accompanied him to school. There was no sign of dogs in the streets. She started feeding sparrows in the courtyard of their city house. Years flew by. Their meeting grew much less. She enquired of him about what the teacher taught him. The writer responded to her treat they were taught English words, western science and the law of gravity.

As she could not help him in his study, she felt unhappy. When the writer went to University, he was allotted a room for his stay. The common bond of friendship suffered a setback. His grandmother accepted her loneliness with quiet resignation. She spent time with her spinning wheel. From sunrise to sunset she sat by her wheel spinning and reciting prayers. In the afternoon, she relaxed for a while to feed the sparrows. She was always getting surrounded by sparrows that were perching on her legs and shoulders. She enjoyed being in the midst of their company.
ସାରମର୍ମ :
ତାହା ସେମାନଙ୍କର ସମ୍ପର୍କରେ ଏକ ମୋଡ଼ ସୃଷ୍ଟି କଲା । ଏକା କୋଠରିରେ ରହିବା ସତ୍ତ୍ବେ, ବୁଢ଼ୀମା’ ଆଉ ତାଙ୍କ ତାହା ସେମାନଙ୍କର ସମ୍ପର୍କରେ ଏକ ମୋଡ଼ ସୃଷ୍ଟି କଲା । ଏକା କୋଠରିରେ ରହିବା ସତ୍ତ୍ବେ, ବୁଢ଼ୀମା’ ଆଉ ତାଙ୍କ ସହିତ ବିଦ୍ୟାଳୟକୁ ଯାଇପାରିଲେ ନାହିଁ । ସେଠାକାର ରାସ୍ତାମାନଙ୍କର କୁକୁରମାନଙ୍କର ଚିହ୍ନବର୍ଣ୍ଣ ନ ଥିଲା । ବୁଢ଼ୀମା’ ତାଙ୍କ ସହରରେ ଥ‌ିବା ଘର ଅଗଣାରେ ଘରଚଟିଆମାନଙ୍କୁ ଖାଇବାକୁ ଦେବା ଆରମ୍ଭ କରିଦେଲେ । ସମୟ ଗଡ଼ି ଚାଲିଲା । ସେମାନଙ୍କର ସାକ୍ଷାତ୍ କମିଯିବାକୁ ଲାଗିଲା। ଶିକ୍ଷକ କ’ଣ ପଢ଼ାଉଥିଲେ ସେ ଲେଖକଙ୍କୁ ସେ ବିଷୟରେ ପଚାରୁଥିଲେ । ଲେଖକ କହୁଥିଲେ ଯେ ସେମାନଙ୍କୁ ଇଂରାଜୀ ଶବ୍ଦ, ପାଶ୍ଚାତ୍ୟ ବିଜ୍ଞାନ ଓ ମାଧ୍ୟାକର୍ଷଣ ନିୟମ ଆଦି ପଢ଼ାଯାଉଛି ।

ଯେହେତୁ ବୁଢ଼ୀମା’ ପାଠପଢ଼ାରେ ସାହାଯ୍ୟ କରିପାରୁ ନ ଥିଲେ, ତେଣୁ ସେ ଦୁଃଖୀ ହେଲେ । ଯେତେବେଳେ ଲେଖକ ବିଶ୍ଵବିଦ୍ୟାଳୟକୁ ଗଲେ, ତାଙ୍କୁ ରହିବା ପାଇଁ ଗୋଟିଏ କୋଠରି ଦିଆଗଲା । ଏହିଠାରୁ ବନ୍ଧୁତ୍ଵର ସାଧାରଣ ବନ୍ଧନ ଛିନ୍ନ ହେଲା । ତାଙ୍କ ବୁଢ଼ୀମା’ ନିଃସଙ୍ଗତାକୁ ନୀରବ ପ୍ରତିବାଦ ସହ ଗ୍ରହଣ କରିନେଲେ । ସେ ଚରଖା ସହିତ ନିଜର ସମୟ ବିତାଇଲେ । ସୂର୍ଯ୍ୟୋଦୟଠାରୁ ସୂର୍ଯ୍ୟାସ୍ତ ପର୍ଯ୍ୟନ୍ତ ସେ ଚରଖା ପାଖରେ ବସି ରହୁଥିଲେ ଏବଂ ପ୍ରାର୍ଥନା କରୁ ଥିଲେ । ଅପରାହ୍ନରେ କିଛି ସମୟ ସେ ଘରଚଟିଆମାନଙ୍କୁ ଖୁଆଇବାରେ ବିତାଉଥିଲେ । ସେ ସର୍ବଦା ଘରଚଟିଆମାନଙ୍କ ଗହଣରେ ରହୁଥିଲେ ଯେଉଁମାନେ ତାଙ୍କ ଗୋଡ଼ ଓ କାନ୍ଧ ଉପରେ ବସି ଯାଉଥିଲେ । ସେ ସେମାନଙ୍କ ଗହଣରେ ଆନନ୍ଦ ଉପଭୋଗ କରୁଥିଲେ ।

Glossary:
comfortably settled : ସ୍ବଚ୍ଛନ୍ଦରେ ବସବାସ କଲେ
sent for : ପାଇଁ ପଠାୟାଇଛି
turning-point : ମୋଡ଼
took to : began (ଆରମ୍ଭ କଲେ)
sparrow : ଘରଚଟିଆ
years rolled by : ବର୍ଷ ପରେ ବର୍ଷ ବିତିଗଲା
western science : ପାଶ୍ଚାତ୍ୟ ବିଜ୍ଞାନ
the law of gravity: ମାଧ୍ୟାକର୍ଷଣ ନିୟମ
Archimedes principle : ଆର୍କିମେଡେଙ୍କ ନୀତି |
distressed : felt extreme anxiety or suffering (ଅତିଶୟ ଦୁଃଖ ଅନୁଭବ କଲେ )
announced : (here) told (କହିଲେ)
disturbed : confused (ଦ୍ବନ୍ଦ୍ବ ରେ ପଡ଼ିଲେ)
lewd : vulgar (ଇତର/ନୀଚ)
It …. harlots : ଏହା ଉପରେ
gentlefolk : gentle people (ଭଦ୍ରଲୋକ)
link : bond (ବନ୍ଧନ)
snapped : broke (ଭାଙ୍ଗିଗଲା|ତୁଟିଗଲା)
seclusion : loneliness (ଏକାକୀତ୍ଵ)
resignation : (here) calmness (ନୀରବରେ|ଶାନ୍ତଭାବେ)
spinning wheel : ଚରଖା
bits : pieces (ଟୁକୁରା)
veritable bedlam of
chirrupings : a genuine scene of noise or confusions caused by the chirruping of the sparrows which scattered and perched around the author’s grandmother
chirruping : ପକ୍ଷୀମାନଙ୍କର କାକଳି
shooed : drove away (ହୁଡ଼େଇଲେ / ତଡ଼ିଦେଲେ)

Think it out:
Question 1.
Why didn’t the grandmother accompany the writer to school in the city?
Answer:
The grandmother did not accompany the writer to school, because the latter went there in a motor bus.

Question 2.
Why couldn’t the grandmother help the writer with his lessons at the city school?
Answer:
The grandmother couldn’t help the writer with his lessons at the city school, because she did not know the subjects such as English, western science, the law of gravity, etc. which he was taught there.

Question 3.
Why did the lessons at the English school distress the grandmother?
Answer:
The lessons at the English school distressed the grandmother because the school didn’t teach about God and holy books to the students.

Question 4.
Why was she disturbed about music lessons at the English school?
Answer:
She was disturbed by music lessons at the English school, because, in her view, music had vulgar associations. It was meant exclusively for prostitutes, but not for gentlefolk.

Question 5.
What were the three ways in which the grandmother spent her days when the author went to University?
Answer:
The three ways in which the grandmother spent her days when the author went to University were spinning, reciting prayers and feeding the sparrows.

Question 6.
What was the happiest time of the day for her?
Answer:
The happiest time of the day for her was to be in the midst of chirruping sparrows and feeding them. Though they sat comfortably on her legs and shoulder, she smiled instead of driving them away.

Question 7.
How did she accept her seclusion?
Answer:
She calmly accepted her seclusion.

UNIT – IV

Gist:
The writer made up his mind to go to a foreign country for further studies. She knew that his grandmother would be sad. But she came to see him off at the railway station. She maintained silence. She did not show any emotion. She was totally absorbed in prayer. Her fingers kept on telling the beads of her rosary. At last, the writer departed. The parting from his grandmother was indeed heart-touching. It possibly marked the last sign of their physical contact. But that proved wrong. Five years elapsed. The writer came back home and was received at the station by his grandmother. She was speechless.

That evening he noticed a great change in her behavior. She stopped praying. She seemed to be very happy spending time with the older women folk. The following morning, she suffered from mild fever. She could not recover from it. At last, she died peacefully. This concluding unit ends on a moving note. Thousands of sparrows sitting scattered on the floor sadly witnessed the grandmother’s dead body. They neither chirruped nor touched little crumbs of bread. They flew away silently when the writer and his family members carried his grandmother’s dead body. Here ends the portrait of a pious lady.

ସାରମର୍ମ :
ଉଚ୍ଚଶିକ୍ଷା ନିମନ୍ତେ ବିଦେଶକୁ ଯିବା ପାଇଁ ଲେଖକ ମନସ୍ଥ କଲେ । ସେ ଜାଣିଥିଲେ ତାଙ୍କର ବୁଢ଼ୀମା’ ଦୁଃଖୀ ହେବେ । କିନ୍ତୁ ସେ ଲେଖକଙ୍କୁ ବିଦାୟ ଦେବା ପାଇଁ ଷ୍ଟେସନକୁ ଆସିଥିଲେ । ସେ ନୀରବ ଥିଲେ ଏବଂ କୌଣସି ଭାବପ୍ରବଣତା ଦେଖାଇ ନ ଥିଲେ । ସେ ପ୍ରାର୍ଥନା ଭିତରେ ସମ୍ପୂର୍ଣ୍ଣରୂପେ ମଜ୍ଜି ଯାଇଥିଲେ । ତାଙ୍କର ଆଙ୍ଗୁଳିଗୁଡ଼ିକ ଜପାମାଳିର ମାଳି ଗଡ଼ାଇବାରେ ଲାଗିଥିଲେ । ଶେଷରେ ଲେଖକ ବିଦାୟ ନେଲେ । ବାସ୍ତବରେ ବୁଢ଼ୀମା’ଙ୍କଠାରୁ ବିଦାୟ ମର୍ମସ୍ପର୍ଶୀ ଥିଲା । ଏହା ବୋଧହୁଏ ସେମାନଙ୍କର ଶାରୀରିକ ସଂସ୍ପର୍ଗର ଶେଷ ଚିହ୍ନ ଥିଲା । କିନ୍ତୁ ତାହା ଭୁଲ୍ ପ୍ରମାଣିତ ହେଲା। ପାଞ୍ଚ ବର୍ଷ ବିତିଗଲା । ଲେଖକ ଘରକୁ ଫେରିଲେ ଏବଂ ବୁଢ଼ୀମା’ ତାଙ୍କୁ ଷ୍ଟେସନରେ ପାଛୋଟି ନେଲେ । ସେ ନୀରବ ଥିଲେ ।

ସେଦିନ ସନ୍ଧ୍ୟାରେ ସେ ବୁଢ଼ୀମା’ଙ୍କର ବ୍ୟହାରରେ ଅଦ୍ଭୁତ ପରିବର୍ତ୍ତନ ଦେଖ‌ିଲେ । ସେ ପ୍ରାର୍ଥନା ବନ୍ଦ କରି ଦେଇଥିଲେ । ପୁରୁଖା ସ୍ତ୍ରୀଲୋକମାନଙ୍କ ସହିତ ସମୟ କଟାଇ ଖୁସିଥ୍‌ର ଜଣା ପଡୁଥିଲେ । ପରଦିନ ସକାଳେ ତାଙ୍କୁ ସାମାନ୍ୟ ଜ୍ଵର ହେଲା । ସେ ଏଥୁରୁ ରକ୍ଷା ପାଇ ପାରିନଥିଲେ । ଶେଷରେ ସେ ଶାନ୍ତିରେ ଆଖି ବୁଜିଲେ । ସେତେବେଳେର ଦୃଶ୍ୟ ଖୁବ୍ କରୁଣ ଥିଲା। ହଜାର ହଜାର ଘରଚଟିଆ ଚଟାଣ ଉପରେ ବିକ୍ଷିପ୍ତ ଭାବରେ ବସି ବୁଢ଼ୀମା’ଙ୍କର ମୃତ ଦେହକୁ ଅନାଉଥିଲେ । ସେମାନେ କୋଳାହଳ କରୁନଥିଲେ କିମ୍ବା ରୁଟି ଟୁକୁଡ଼ାକୁ ଛୁଇଁନଥିଲେ । ଯେତେବେଳେ ଲେଖକ ଏବଂ ତାଙ୍କର ପରିବାର ବୁଢ଼ୀମା’ଙ୍କ ଶବକୁ ନେଇଗଲେ, ସେମାନେ ନୀରବରେ ଉଡ଼ି ପଳେଇଲେ ।

Glossary:
further studies : (here) higher studies (ଉଚ୍ଚଶିକ୍ଷା)
upset : disappointed or worried (ହତାଶ ହେବା/ବିବ୍ରତ ହେବା)
sentimental : easily moved by tender feelings (ଭାବପ୍ରବଣ )
lost : ହଜିଯାଇଥିଲା
cherished : ଆନନ୍ଦ ଅନୁଭବ କରିଥିଲେ
the moist imprint : ଲୁହର ଛାପ
She …… words : The writer’s grandmother was speechless.
clasped : grasped tightly one’s hand
frivolous rebukes : affectionate scolding (ସ୍ନେହବୋଳା ଗାଳି)
thumped : hit heavily with the fist (ମୁଠାରେ ଜୋର୍‌ରେ ଆଘାତ କଲେ)
sagging skins : ଓହଳି ପଡ଼ିଥ‌ିବା ଚମଡ଼ା
dilapidated : old and in very bad condition (ଜରାଜୀର୍ଣ୍ଣ ଅବସ୍ଥାରେ ଥ‌ିବା)
warrior : ଯୋଦ୍ଧା
persuade : ପ୍ରବର୍ତ୍ତେଇବା
mild : ସାମାନ୍ୟ
before …. life : before the grandmother’s death (ବୁଢ଼ୀମା’ଙ୍କ ମୃତ୍ୟୁ ପୂର୍ବରୁ)
waste time : ଅଧ‌ିକ ସମୟ ନଷ୍ଟ କରିବା
protested : ପ୍ରତିବାଦ କଲୁ
ignored : ଅବଜ୍ଞା କଲେ
suspect : doubt (ସନ୍ଦେହ କରିବା)
lifeless : ନିର୍ଜୀବ
pallor : unnatural paleness ( ଅସ୍ଵାଭାବିକ ମଳିନତା)
customary : ପ୍ରଥା ଅନୁସାରେ
shroud : a piece of cloth or a sheet wrapped round a dead body
crude : rude (ନିଷ୍ଠୁର)
cremated : ଶବ ସତ୍କାର ହେଲା
lit : lighted (ଆଲୋକିତ କରୁ)
blaze : bright flame (ଉଜ୍ଜ୍ଵଳ ଦୀପ୍ତି)
golden light : ସୁନେଲି କିରଣ
stiff : hard (କଠିନ)
wrapped : covered (ଆବୃତ କଲେ)
scattered : ଛିନ୍ନଭିନ୍ନ
took no notice of: ଅନାଇଲେ ନାହିଁ
corpse : dead body (ମୃତ ଦେହ)
quietly : silently (ଚୁପ୍‌ଚାପ୍ ଭାବରେ)
swept : ଓଳେଇଦେଲେ

Think it out:
Question 1.
How did the grandmother see the author off at the railway station?
Answer:
The grandmother saw the author off at the railway station without showing any emotion. Besides, she silently kissed his forehead.

Question 2.
How did she receive him when he came back home from abroad?
Answer:
When he came back home from abroad, she embraced him in her arms. She was speechless and saying her prayers.

Question 3.
What were her happiest moments on the first day of his arrival?
Answer:
Her happiest moments on the first day of his arrival were in the company of her sparrows whom she fed longer and with affectionate scolding.

Question 4.
How did she celebrate his return in the evening? Does her behavior appear odd to you?
Answer:
She celebrated his return in the evening, thumping the weak skins of the ruined old drum and singing of the homecoming warriors in the company of the women of the neighborhood. Yes, her behavior appears odd to me as she stopped her prayer for the first time on that evening.

Question 5.
How did she pass away?
Answer:
She passed away peacefully, while she was laying in bed praying and telling her beads.

Question 6.
How did sparrows react when the author’s grandmother died?
Answer:
When the author’s grandmother died, the sparrows plunged into grief. They neither chirruped nor took any notice of little crumbs of bread.

Question 7.
“Next morning the sweeper swept the bread crumbs into the dust bin.” What does this line imply?
Answer:
This line implies that the sparrows were beside themselves with grief.

Post-Reading Activities:

Write a paragraph on the following points to portray the character of the grandmother :
The writer’s grandmother is a widow
She is very old – wrinkled face – her grey hair usually remains scattered on her puckered face – fat, short, and has a stoop – cannot walk straight – hobbles with her hand on her waist to balance her stoop
She belongs to a Punjabi family and lives with her son, daughter-in-law, and her grandson
She is religious – goes to the temple daily – reads holy books – tells the beads of the rosary
She is very kind – feeds the dogs with chapattis – feeds the sparrows and enjoys their company
She is a good companion – helps her grandson to get ready for school – helps him in his lessons – accompanies him to the school
She is culture loving – loves Indian culture, is fond of singing and spinning – has a strong dislike for western and scientific education
She is peaceful by nature – calm and cool – does not show resentment – becomes quiet and private instead
Her death is mourned by the family and her pet sparrows.

Answer:
The pen picture of a grandmother
The writer’s grandmother who comes from a Punjabi family is a widow. She is in a state of ripe old age. She is a deeply pious lady. She takes pleasure in walking to the temple every day, reading sacred books and telling the beads of the rosary. The writer’s grandmother epitomizes kindness. This finds a great reflection in her act of feeding the dogs and sparrows. She gives constant company to her grandson. She is an avid lover of Indian culture. She is the picture of serenity. Grandmother’s death is a stunning loss to the family and her fond sparrows.

Doing with words :
(A) Make sentences with the following expressions :
(i) the thought was almost revolting
(ii) an expanse of pure white serenity
(iii) a veritable bedlam of chirruping
(iv) frivolous rebukes
(v) the sagging skins of the dilapidated drum
Answer:
(i) the thought was almost revolting – I greatly enjoyed my grandparents’ company. The thought contrary to it was almost revolting to him.
(ii) an expanse of pure white serenity – My grandmother’s look epitomizes an expanse of pure white serenity.
(iii) a veritable bedlam of chirruping – The birds produce a veritable bedlam of chirruping.
(iv) frivolous rebukes – I am averse to your frivolous rebukes.
(v) the sagging skins of the dilapidated drum – I wanted him to beat the sagging skins of the dilapidated drum.

(B) Notice the following uses of the word ‘tell’ in the text.
1. Her fingers were busy telling the beads of her rosary.
2. I would tell her English words and little things about Western science and learning.
3. At her age one could never tell.
4. She told us that her end was near.
Given below are four different meanings of the word ‘tell’. Match each meaning with its corresponding sentence given above.
1. make something known to someone in spoken or written words
2. count while reciting
3. be sure
4. give information to somebody
Answer:
1 – 2; 2 – 1; 3 – 3; 4 – 4

(C) A popular dictionary gives the following meanings for the word ‘drop’. Match each meaning with its corresponding sentence given below :
‘drop’ :
1. a small round mass of liquid
2. a reduction
3. to fall
4. to become weaker
5. to send a letter
Sentences :
(a) The bottle dropped and broke to pieces.
(b) Drop a postcard to me about your choice of career.
(c) A heavy shower of rain caused a drop in temperature.
(d) She shed a few drops of tears on the grave of her pet.
(e) His voice dropped to a whisper.
Answer:
1 – (d); 2 – (c); 3 – (a); 4 – (e); 5 – (b).

CHSE Odisha Class 12 English The Portrait of a Lady Important Questions and Answers

I. Multiple-Choice Questions (MCQs) with Answers:

Question 1.
The author of ‘The Portrait of a Lady’ is ______________.
(A) Khushwant Singh
(B) R.K. Narayan
(C) Manoj Das
(D) Steve Jobs
Answer:
(A) Khushwant Singh

Question 2.
The lady portrayed in the story is
(A) Grandmother
(B) Sister
(C) Mother
(D) Daughter
Answer:
(A) Grandmother

Question 3.
The grandfather in the portrait hung on the wall looked like
(A) old, thin and wrinkly
(B) young, handsome, well built
(C) old, long white beard worn a big turban
(D) None of the above
Answer:
(C) old, long white beard worn a big turban

Question 4.
Grandmother looked
(A) Fat, slightly bent
(B) Old, short, slightly bent, fat
(C) Long, fat, slightly bent
(D) Old, fat, long
Answer:
(B) Old, short, slightly bent, fat

Question 5.
The author’s parents left him with his grandmother when
(A) he was an infant
(B) he was a child
(C) he was a young man
(D) he was a teenager
Answer:
(B) he was a child

Question 6.
The animal grandmother used to feed in the village is
(A) cats
(B) dogs
(C) cows
(D) sparrows
Answer:
(B) dogs

Question 7.
The parents of the author were living in
(A) abroad
(B) other villages
(C) other states
(D) City
Answer:
(D) City

Question 8.
In the temple, grandmother was
(A) doing meditation
(B) reading scriptures
(C) singing religious prayers
(D) teaching other kids religious prayer
Answer:
(B) reading scriptures

Question 9.
The author went to study in the city in
(A) English school in motor bus
(B) by walking
(C) Hindu school
(D) None of these
Answer:
(A) English school in motor bus

Question 10.
The grandmother went to school with the author because
(A) the school was attached to the temple
(B) to guard him
(C) to see how he was reading
(D) None of the above
Answer:
(A) the school was attached to the temple

Question 11.
In the courtyard of the city house, grandmother used to feed
(A) dogs
(B) cats
(C) sparrows
(D) cows
Answer:
(C) sparrows

Question 12.
Grandmother after listening to the things taught in the English schools becomes unhappy because
(A) She could not help the writer with his lessons.
(B) She desired science.
(C) She did not want the writer should learn English
(D) None of the above
Answer:
(A) She could not help the writer with his lessons.

Question 13.
The common link of friendship was suspended when the writer ______________.
(A) went up to the university
(B) went up in a foreign trip
(C) married
(D) None of these
Answer:
(A) went up to the university

Question 14.
The grandmother died
(A) peacefully telling beads laying on the bed
(B) in the hospital
(C) while sleeping
(D) None of the above
Answer:
(A) peacefully telling beads laying on the bed

Question 15.
Why did the grandmother keep one hand on her waist?
(A) to pick up things easily
(B) to balance her stoop
(C) to correct her posture
(D) to eat food
Answer:
(B) to balance her stoop

Question 16.
The narrator had known his grandmother to be old and wrinkled for ______________.
(A) ten years
(B) thirty years
(C) twenty years
(D) twenty-five years
Answer:
(C) twenty years

Question 17.
The portrait of grandfather was hanging in the ______________.
(A) drawing room
(B) store room
(C) bedroom
(D) kitchen
Answer:
(A) drawing room

Question 18.
What did the author eat for breakfast?
(A) rice and curd
(B) thick bread with butter
(C) apples and bread
(D) thick and stale chapatis with a little butter and sugar spread on it
Answer:
(D) thick and stale chapatis with a little butter and sugar spread on it

Question 19.
The author treated the stories of grandmother’s youth and beauty as ______________.
(A) poetry
(B) fables
(C) drama
(D) None of these
Answer:
(B) fables

Question 20.
How did the grandmother spend her afternoon every day?
(A) by feeding hundreds of sparrows
(B) by taking a nap
(C) by talking to the author’s mother
(D) by going to temple
Answer:
(A) by feeding hundreds of sparrows

Question 21.
What change came in the grandmother’s evening time?
(A) she would sleep easily
(B) she would go for a walk
(C) she collected the women of the neighborhood
(D) she would talk with the author’s parents
Answer:
(C) she collected the women of the neighborhood

Question 22.
How did the grandmother spend her time in the city?
(A) spinning the wheel
(B) reading scriptures
(C) feeding dogs
(D) taking to neighbors
Answer:
(A) spinning the wheel

Question 23.
What did the village priest teach the students?
(A) scriptures
(B) alphabet and morning prayer
(C) moral lessons
(D) science
Answer:
(B) alphabet and morning prayer

Question 24.
What is the meaning of the word ‘chorus’?
(A) individually
(B) in a group
(C) between two people
(D) working hard
Answer:
(B) in a group

Question 25.
What was the grandmother doing inside the temple when the author was studying in the temple veranda?
(A) Reading scriptures
(B) Listening to the prayers
(C) Singing prayers
(D) Performing puja
Answer:
(A) Reading scriptures

Question 26.
Who would meet the author and his grandmother at the temple door?
(A) Sparrows
(B) Village monkeys
(C) Village dogs
(D) Village beggars
Answer:
(C) Village dogs

Question 27.
What was the turning point in the relationship of the author and his grandmother?
(A) The grandmother’s death
(B) The marriage of the author
(C) The separation of the author from his grandmother
(D) Their shifting from the village to the city
Answer:
(D) Their shifting from the village to the city

Question 28.
What did the grandmother do in her leisure in the city?
(A) Sang prayers
(B) Read scriptures
(C) Fed sparrows
(D) Fed pigeons
Answer:
(C) Fed sparrows

Question 29.
What was/were not taught to the author at the English school?
(A) English words
(B) Western science
(C) Scriptures
(D) Music lessons
Answer:
(A) English words

Question 30.
Why was the grandmother distressed with the teachings in English school?
(A) There was much emphasis on the alphabet
(B) There were no lessons on god and the scriptures
(C) Due to teaching music
(D) Due to teaching science
Answer:
(B) There were no lessons on god and the scriptures

Question 31.
When was the common link of friendship between the author and his grandmother snapped?
(A) When the author went abroad
(B) When the author joined the army
(C) When the author went to university
(D) When the author got a job
Answer:
(C) When the author went to university

Question 32.
What was the opinion of the grandmother about music?
(A) She supported music classes
(B) Music had a soothing effect
(C) Music had lewd associations
(D) Music was essential for the overall development
Answer:
(C) Music had lewd associations

Question 33.
What did the grandmother accept with resignation?
(A) Separation from the author
(B) Her fate
(C) Her ill-health
(D) Her approach to death
Answer:
(A) Separation from the author

Question 34.
How did the grandmother relax in the afternoon?
(A) By singing songs
(B) By reciting prayers
(C) By spinning the wheel
(D) By feeding the sparrows
Answer:
(D) By feeding the sparrows

Question 35.
Which was the happiest half-hour of the day for the grandmother?
(A) The time spent in the temple
(B) The time spent with the neighbors
(C) The time spent with the sparrows
(D) The time spent with the author
Answer:
(C) The time spent with the sparrows

Question 36.
What is the meaning of the sentence, “at her age one could never tell”?
(A) She was very old
(B) She did not eat much
(C) She did not behave properly
(D) She was so old that she could die at any moment
Answer:
(D) She was so old that she could die at any moment

Question 37.
Choose an appropriate word for the word ‘sentimental’ from the following:
(A) happy
(B) joyful
(C) emotional
(D) mournful
Answer:
(C) emotional

Question 38.
While going abroad what did the author cherish the most?
(A) Love of his family
(B) Care of his mother
(C) Affection of his grandmother
(D) His grandmother’s kiss on his forehead
Answer:
(D) His grandmother’s kiss on his forehead

Question 39.
When did the author come back home?
(A) After four years
(B) After five years
(C) After six years
(D) After two years
Answer:
(B) After five years

Question 40.
What is the synonym of the word ‘frivolous’?
(A) carefree
(B) serious
(C) funny
(D) mysterious
Answer:
(A) carefree

Question 41.
What is the meaning of the word ‘rebuke’?
(A) to hang
(B) to scold lightly
(C) to pray for mercy
(D) to learn something
Answer:
(B) to scold lightly

Question 42.
What change came over the author’s grandmother in the evening?
(A) she did not pray
(B) she started dancing wildly
(C) she collected drums from the neighborhood
(D) all of the above
Answer:
(A) she did not pray

Question 43.
What did the grandmother sing collecting the women of the neighborhood?
(A) Her prayers
(B) Home-coming of warriors
(C) Reception song for the author
(D) Scriptures
Answer:
(B) Home-coming of warriors

Question 44.
What happened the next morning?
(A) The grandmother became unconscious
(B) The author talked to his grandmother
(C) The grandmother was taken ill
(D) The grandmother started to sing again
Answer:
(C) The grandmother was taken ill

Question 45.
What did the grandmother tell all the family members?
(A) to call the doctor
(B) to bring her holy books
(C) to bring her a new rosary
(D) that her end was near
Answer:
(D) that her end was near

Question 46.
Why did the grandmother say that she was not going to talk to anyone?
(A) because she cannot speak
(B) because she wanted to pray
(C) because she wanted to die peacefully
(D) because she wanted to talk with the angels
Answer:
(B) because she wanted to pray

Question 47.
How did they know that she was dead?
(A) she closed her eyes
(B) the rosary fell from her fingers
(C) the doctor declared her dead
(D) her last prayer was said loudly
Answer:
(B) the rosary fell from her fingers

Question 48.
What was the custom regarding dead people?
(A) to cover the dead body with a red shroud
(B) to cover the dead body with a white shroud
(C) to cover the dead body with a black shroud
(D) to keep the dead body uncovered
Answer:
(A) to cover the dead body with a red shroud

Question 49.
Why did the family members stop halfway in the courtyard?
(A) as there were hundreds of ants
(B) as there were thousands of sparrows
(C) as there were thousands of monkeys
(D) as there were hundreds of dogs
Answer:
(B) as there were thousands of sparrows

Question 50.
Why did the sparrows not take notice of the bread crumbs lying on the floor?
(A) they never ate bread crumbs
(B) the bread crumbs were stale
(C) they were also mourning the death of their grandmother
(D) they had come to eat chapattis
Answer:
(C) they were also mourning the death of their grandmother

Question 51.
The bottle dropped and broke to pieces. (Pick out the correct dictionary meaning of the underlined word from the following)
(A) To fall
(B) To go down
(C) To become weaker
(D) To slip away
Answer:
(A) To fall

Question 52.
Drop me a postcard when you get there. (Pick out the correct dictionary meaning of the underlined word from the following)
(A) To fall
(B) To go down
(C) To send a letter
(D) To send away
Answer:
(C) To send a letter

Question 53.
Heavy rain can cause a drop in temperature. (Pick out the correct dictionary meaning of the underlined word from the following)
(A) A reduction
(B) To fall
(C) To become weaker
(D) To slip away
Answer:
(A) A reduction

Question 54.
A few drops of tears don’t wash out sins. (Pick out the correct dictionary meaning of the underlined word from the following)
(A) Shedding tears
(B) A small round mass of liquid
(C) Repentance
(D) Liquid substance
Answer:
(B) A small round mass of liquid

Question 55.
His voice dropped to a whisper. (Pick out the correct dictionary meaning of the underlined Word from the following)
(A) To fall
(B) To go down
(C) To become weaker
(D) A reduction
Answer:
(C) To become weaker

II. Short Type Questions with Answers:

Question 1.
Why was it hard for the author to believe that his grandmother was once young and pretty?
Answer:
It was hard for the author to believe that his grandmother was once young and pretty, because he, in spite of staying with her for the last twenty years, did not find any change in her beauty. She was as elegant as ever.

Question 2.
How does the author portray his grandmother?
Answer:
The writer states that his grandmother, short and fat, was a little bent. Age didn’t have any impact on her age arid she was pretty and very active.

Question 3.
The grandmother had a divine beauty. How does the author bring this out?
Answer:
The author states that the grandmother had a divine beauty because she was a picture of rare calmness, peace and contentment. Her beauty resembling ‘the winter landscape in the mountains’ is also a case in point.

Question 4.
What was the grandmother’s routine in the village?
Answer:
The grandmother’s routine in the village comprised waking the writer up in the morning and preparing him for school. She also went to school with him and came back home together after school was over.

Question 5.
How did the grandmother take care of the writer during his childhood? Was she a good companion of the writer in the village?
Answer:
The grandmother took minute care of the writer during his childhood beginning from waking him up, bathing and dressing him to accompanying him to school and coming back home. She did not forget to give him breakfast. Yes, she was certainly a good companion of the writer, as his parents lived in the city.

Question 6.
Was she a religious person? How?
Answer:
Yes, she was a religious lady. Her morning prayer, frequent visits to the temple and reading holy books inside it and throwing chapters to the village dogs who followed them to their home justify this fact.

Question 7.
Why couldn’t the grandmother help the writer with his lessons at the city school?
Answer:
The grandmother couldn’t help the writer with his lessons at the city school, because she did not know the subjects such as English, western science, the law of gravity, etc. which he was taught there.

Question 8.
Why did the lessons at the English school distress the grandmother?
Answer:
The lessons at the English school distressed the grandmother because the school didn’t teach about God and holy books to the students.

Question 9.
Why was she disturbed about music lessons at the English school?
Answer:
She was disturbed by music lessons at the English school, because, in her view, music had vulgar associations. It was meant exclusively for prostitutes, but not for gentlefolk.

Question 10.
What were the three ways in which the grandmother spent her days when the author went to University?
Answer:
The three ways in which the grandmother spent her days when the author went to University were spinning, reciting prayers and feeding the sparrows.

Question 11.
What was the happiest time of the day for her?
Answer:
The happiest time of the day for her was to be in the midst of chirruping sparrows and feeding them. Though they sat comfortably on her legs and shoulder, she smiled instead of driving them away.

Question 12.
What were her happiest moments on the first day of his arrival?
Answer:
Her happiest moments on the first day of his arrival were in the company of her sparrows whom she fed longer and with affectionate scolding.

Question 13.
How did she celebrate his return in the evening? Does her behavior appear odd to you?
Answer:
She celebrated his return in the evening, thumping the weak skins of the ruined old drum and singing of the homecoming warriors in the company of the women of the neighborhood. Yes, her behavior appears odd to me as she stopped her prayer for the first time that evening.

Introducing the Author:
Khuswant Singh (1915) is one of the most versatile writers of our time. He has distinguished himself as an outstanding journalist, novelist, historian, and short-story writer. A writer of international repute, Singh is known for his inimitable style, biting irony, and firebrand candidness. He has a deep understanding of the life around him. His works include The Mask of Vishnu, Train to Pakistan, which won the Grove Press Indian Fiction prize, The Voice of God and Other Stories, I shall not hear the Nightingale, Many Moods and Many Faces, A History of the Sikhs, A Bride for the Sahib and Other Stories, Delhi, The Company of Women and several collections of works.

Aspects of Khuswant Singh as a short-story writer and essayist indicate his versatility. His short stories show the felicity of his expression, his capacity for clear and realistic portrayal, and his unique lightness of touch. He has the qualities of the ideal short-story writer: ingenuity, compression and originality, and also a touch of fantasy. His art is different from that of Raja Rao, Mulk Raj Anand, R. K. Narayan, and Pravas Jhabvala.

About the Topic:
‘The Portrait of a Lady’ gives a vivid account of the writer’s, grandmother. She was affectionate, protective, and caring. The writer throws light on the three phases of the relationship he had had with his grandmother. In the first phase, she took care of the writer in the village and he was close to her. The second phase deals with his estrangement from her during his study in a city school. The last one dwells upon the snapping of the common link of friendship between them when he went to a foreign country for further studies. The writer presents a moving picture of the sparrows when his grandmother’s life came to an end.

Summary:
The writer speaks of his own grandmother. By the time, he wrote the story, she was quite old and all her hair had been white. Her wrinkled face and body gave him a kind of surprise. For twenty years, the writer was with his grandmother. People said that once the old lady was as beautiful as a fairy. Her husband – the writer’s grandfather was also very handsome. His photo was being hung in the drawing room of the writer. He was clad in a big turban and loose-fitting clothes. The writer noticed his ripe old age.

Grandmother had always been short and fat, and her back was slightly bent. Wrinkles were across her face. When the writer came to know her, she had been in such a condition. She was always clad in a spotless white saree. Her silver locks. were spread messily over her pale, wrinkled face. She was always in a state of saying a prayer that could not be heard distinctly. She was beautiful. She was a picture of calmness. She had a divine beauty. Both the writer and his grandmother were good companions.

His parents had left him with his grandmother at the village. They were in the city. Every day, she used to wake up the writer in the morning to be ready to go to school. She was uttering the monotonous song while bathing and dressing the writer. He liked her very much. His grandmother was going to school with him because there was a temple attached to the school. She would sit inside the temple and read holy books. The grandmother was a pious lady. When the writer’s parents were settled in the city, they sent for them.

That marked a turning point in their friendship. Years flew by. Their meeting grew less. Both the writer and his grandmother started spending days separately and the writer became separated from the close relationship with his grandmother. When he reported to her about the music lesson he was being taught his grandma was confused because she knew that music had been associated with harlots. She said nothing but her silence was louder than words. When the writer went to University, he was allotted a room for his stay.

The common bond of friendship was snapped. His grandmother accepted her loneliness with quiet resignation. She spent time with her spinning wheel. From sunrise to sunset she sat by her wheel spinning and reciting prayers. In the afternoon, she relaxed for a while to feed the sparrows. She was always getting surrounded by sparrows that were perching on her legs and shoulders. She enjoyed being in their company. When the writer decided to go to a foreign country for further studies, he thought his grandmother would be disappointed.

But she came to leave him at the railway station but did not talk or show any emotion. She was totally absorbed in prayer and her fingers were busy telling the beads of her rosary. After five years, he came back home and was received at the station by his grandmother. It seemed as if time had left no impact on her age. The author could feel her pulse as usual and the sparrows were with her. That evening she was seen very happy spending time with the older women folk. The next day morning she was found ill. The doctor was called for and he told them that the fever was mild and she would be well within a short time.

But she told others that her last time had come. She lay peacefully in bed saying prayers and telling her beads. Next time she breathed her last. Then the funeral arrangements and proceedings went on. The dead body of the grandmother was covered with a red shroud. They brought a crude stretcher to take her to be cremated. By that time, thousands of sparrows sat scattered on the floor. There was no chirruping. The picture of the grief-stricken sparrows was really poignant. The writer’s mother threw broken little crumbs of bread to them, but in vain. They never took any notice of the bread. With the departure of grandmother’s dead body, the sparrows flew away in silence.

ସାରାଂଶ:
ଲେଖକ ତାଙ୍କ ନିଜ ବୁଢ଼ୀମା’ଙ୍କ ବିଷୟରେ ବର୍ଣ୍ଣନା କରିଛନ୍ତି । ଯେତେବେଳେ ସେ ଗଳ୍ପଟି ଲେଖିଥିଲେ, ସେତେବେଳକୁ ତାଙ୍କ ବୁଢ଼ୀମା’ ସମ୍ପୂର୍ଣ୍ଣ ବୁଢ଼ୀ ହୋଇଯାଇଥିଲେ ଏବଂ ତାଙ୍କର ସମସ୍ତ କେଶ ଧଳା ହୋଇଯାଇଥିଲା । ତାଙ୍କର କୁଞ୍ଚ୍ ମୁଖମଣ୍ଡଳ ଓ ଶରୀର ତାଙ୍କୁ ଏକପ୍ରକାର ବିସ୍ମିତ କରୁଥିଲା । ଦୀର୍ଘ ୨୦ ବର୍ଷ ଧରି ସେ ତାଙ୍କ ବୁଢ଼ୀମା’ଙ୍କ ସହିତ ଥିଲେ । ଲୋକମାନେ କହୁଥିଲେ ଯେ ଏକଦା ଏହି ବୁଢ଼ୀ ସ୍ତ୍ରୀଲୋକଜଣକ ପରୀ ଭଳି ସୁନ୍ଦରୀ ଥିଲେ । ତାଙ୍କ ସ୍ଵାମୀ –ଲେଖକଙ୍କ ବୁଢ଼ାବାପା ଖୁବ୍ ସୁନ୍ଦର ଥିଲେ । ତାଙ୍କ ଫଟୋ ଲେଖକଙ୍କ ବୈଠକଘରେ ଟଙ୍ଗା ଯାଇଥିଲା । ବଡ଼ ପଗଡ଼ି ଓ ଢିଲା ପୋଷାକ ତାଙ୍କର ସମଗ୍ର ଶରୀରକୁ ଆବୃତ କରୁଥିଲା । ଲେଖକ ତାଙ୍କର ପରିପକ୍ଵ ବୃଦ୍ଧ ଅବସ୍ଥାକୁ ଦେଖ୍ ପାରୁଥିଲେ । ବୁଢ଼ୀମା’ ଗେଡ଼ୀ ଓ ମୋଟୀ ଥିଲେ ଏବଂ ତାଙ୍କ ଅଣ୍ଟା ଅଳ୍ପ ନଇଁ ପଡ଼ିଥିଲା ।

ତାଙ୍କ ମୁଖମଣ୍ଡଳରେ କୁଞ୍ଚ ରେଖାର ଦାଗସବୁ ରହିଥିଲା । ଲେଖକ ତାଙ୍କୁ ଜାଣିବା ଦିନଠାରୁ ସେ ସେହି ଅବସ୍ଥାରେ ଥିଲେ । ସେ ସର୍ବଦା ଦାଗହୀନ ଧଳା ଶାଢ଼ି ପରିଧାନ କରୁଥିଲେ । ରୁପା ସଦୃଶ ଦେଖାଯାଉଥିବା ତାଙ୍କର ଆଲୁଳାୟିତ କେଶରାଶି ତାଙ୍କର ମଳିନ ଓ କୁଞ୍ଚ୍ ମୁଖମଣ୍ଡଳ ଉପରେ ବିଛାଇ ହୋଇ ପଡ଼ୁଥିଲା । ସେ ସର୍ବଦା ପ୍ରାର୍ଥନା କରୁଥିବା ଅବସ୍ଥାରେ ରହୁଥିଲେ, ଯାହାକି ସ୍ପଷ୍ଟଭାବେ ଶୁଣି ହେଉ ନ ଥିଲା । ସେ ସୁନ୍ଦରୀ ଥିଲେ । ସେ ନୀରତବାର ପ୍ରତିଛବି ଥିଲେ । ତାଙ୍କଠାରେ ସ୍ଵର୍ଗୀୟ ସୁଷମା ଭରି ରହିଥିଲା । ଲେଖକ ଏବଂ ତାଙ୍କ ବୁଢ଼ୀମା’ ଉତ୍ତମ ବନ୍ଧୁ ଥିଲେ । ତାଙ୍କୁ ତାଙ୍କ ବାପାମା’ ଗାଁରେ ତାଙ୍କ ବୁଢ଼ୀମା’ଙ୍କ ପାଖରେ ଛାଡ଼ି ଚାଲି ଯାଇଥିଲେ । ସେମାନେ ସହରରେ ରହୁଥିଲେ । ପ୍ରତ୍ୟେକ ଦିନ ସକାଳେ ଲେଖକଙ୍କୁ ତାଙ୍କ ବୁଢ଼ୀମା’ ଶେଯରୁ ଉଠାଇ ସ୍କୁଲ୍ ଯିବାପାଇଁ ପ୍ରସ୍ତୁତ କରାଉଥିଲେ ।

ଲେଖକଙ୍କୁ ଗାଧୋଇ ଦେବା ଓ ପୋଷାକ ପିନ୍ଧାଇବା ସମୟରେ ସେ ବିରକ୍ତିକର ଗୀତ ଗାଉଥିଲେ । ଲେଖକ ତାଙ୍କୁ ଖୁବ୍ ଭଲ ପାଆନ୍ତି । ତାଙ୍କ ବୁଢ଼ୀମା’ ତାଙ୍କ ସହିତ ସ୍କୁଲ୍ ଯାଉଥିଲେ କାରଣ ସ୍କୁଲ୍‌କୁ ଲାଗି ମନ୍ଦିରଟିଏ ଥିଲା । ସେ ମନ୍ଦିର ଭିତରେ ବସୁଥିଲେ ଏବଂ ଧର୍ମଗ୍ରନ୍ଥ ପଢ଼ୁଥିଲେ । ତାଙ୍କ ବୁଢ଼ୀମା’ ଜଣେ ଧାର୍ମିକ ମହିଳା ଥିଲେ । ଲେଖକଙ୍କ ପିତାମାତା ସହରରେ ପ୍ରତିଷ୍ଠିତ ହୋଇଗଲା ପରେ ସେମାନଙ୍କୁ ଡକାଇ ପଠାଇଲେ । ଏହିଠାରୁ ବନ୍ଧୁତ୍ଵରେ ଗୋଟିଏ ନୂତନ ମୋଡ଼ ସୃଷ୍ଟି ହେଲା । ସମୟ ଗଡ଼ି ଚାଲିଲା । ସେମାନଙ୍କ ଦେଖାସାକ୍ଷାତ୍ କମିଗଲା । ଲେଖକ ଏବଂ ତାଙ୍କ ବୁଢ଼ୀମା’ ଦୁହେଁ ନିଜର ସମୟ ଅଲଗା ଭାବେ ବିତାଇଲେ ଏବଂ ଲେଖକ ଓ ତାଙ୍କ ବୁଢ଼ୀମା’ଙ୍କ ମଧ୍ୟରେ ଥିବା ନିବିଡ଼ ସମ୍ପର୍କ ବିଛିନ୍ନ ହେଲା । ଯେତେବେଳେ ସେ ତାଙ୍କୁ ଗୀତ ଶିଖ୍ ବିଷୟରେ କହିଲେ, ତାଙ୍କ ବୁଢ଼ୀମା’ ଦ୍ବନ୍ଦ୍ବରେ ପଡ଼ିଲେ କାରଣ ବାରାଙ୍ଗନାମାନଙ୍କ ସହିତ ଗୀତର ସମ୍ପର୍କ ରହିଛି ବୋଲି ସେ ଜାଣିଥିଲେ ।

ସେ କିଛି କହି ନଥିଲେ କିନ୍ତୁ ତାଙ୍କର ନୀରବତା କଥାଠାରୁ ଅଧିକ ଥିଲା । ଯେତେବେଳେ ଲେଖକ ବିଶ୍ଵବିଦ୍ୟାଳୟକୁ ଗଲେ, ତାଙ୍କୁ ରହିବା ପାଇଁ ଗୋଟିଏ କୋଠରି ଦିଆଗଲା । ଏହିଠାରୁ ବନ୍ଧୁତ୍ଵର ସାଧାରଣ ବନ୍ଧନ ଛିନ୍ନ ହେଲା । ତାଙ୍କ ବୁଢ଼ୀମା’ ନିଃସଙ୍ଗତାକୁ ନୀରବ ପ୍ରତିବାଦ ସହ ଗ୍ରହଣ କରିନେଲେ । ସେ ଚରଖା ସହିତ ନିଜର ସମୟ ବିତାଇଲେ । ସୂର୍ଯ୍ୟୋଦୟଠାରୁ ସୂର୍ଯ୍ୟାସ୍ତ ପର୍ଯ୍ୟନ୍ତ ସେ ଚରଖା ପାଖରେ ବସି ରହୁଥିଲେ ଏବଂ ପ୍ରାର୍ଥନା କରୁଥିଲେ । ଅପରାହ୍ନରେ କିଛି ସମୟ ସେ ଘରଚଟିଆମାନଙ୍କୁ ଖୁଆଇବାରେ ବିତାଉଥିଲେ । ସେ ସର୍ବଦା ଘରଚଟିଆମାନଙ୍କ ଗହଣରେ ରହୁଥିଲେ ଯେଉଁମାନେ କି ତାଙ୍କ ଗୋଡ଼ ଓ କାନ୍ଧ ଉପରେ ବସି ଯାଉଥିଲେ । ସେ ସେମାନଙ୍କ ଗହଣରେ ଆନନ୍ଦ ଉପଭୋଗ କରୁଥିଲେ । ଯେତେବେଳେ ଲେଖକ ଅଧ‌ିକ ପଢ଼ିବାପାଇଁ ବିଦେଶ ଯିବାକୁ ସ୍ଥିର କଲେ, ସେ ଭାବିଲେ ତାଙ୍କ ବୁଢ଼ୀମା’ ଦୁଃଖପ୍ରକାଶ କରିବେ ।

କିନ୍ତୁ ସେ ତାଙ୍କୁ ରେଳ ଷ୍ଟେସନରେ ଛାଡ଼ିବା ପାଇଁ ଆସିଥିଲେ ମଧ୍ୟ କିଛି କହିଲେ ନାହିଁ କି ଭାବପ୍ରବଣତା ଦେଖାଇଲେ ନାହିଁ । ସେ ସମ୍ପୂର୍ଣ୍ଣଭାବେ ପ୍ରାର୍ଥନା ଭିତରେ ମଜ୍ଜି ଯାଇଥିଲେ ଏବଂ ତାଙ୍କ ଆଙ୍ଗୁଳିରେ ଜପାମାଳିର ମାଳା ଗଡ଼ାଉଥିଲେ । ପାଞ୍ଚ ବର୍ଷ ପରେ ସେ ଘରକୁ ଫେରି ଆସିଲେ ଏବଂ ବୁଢ଼ୀମା’ ତାଙ୍କୁ ଷ୍ଟେସନରୁ ପାଛୋଟି ଆଣିଥିଲେ । ସମୟ ତାଙ୍କ ବୟସ ଉପରେ କୌଣସି ପ୍ରଭାବ ପକାଇବା ଭଳି ଜଣାପଡୁନଥିଲା । ଲେଖକ ଅନୁଭବ କରିପାରୁଥିଲେ ତାଙ୍କ ନାଡ଼ି ଠିକ୍ ଥିଲା ଏବଂ ଘରଚଟିଆମାନେ ତାଙ୍କ ସହିତ ଥିଲେ । ସେହି ସନ୍ଧ୍ୟାରେ ସେ ବହୁତ ଖୁସି ଥିଲେ ଏବଂ ବୟସ୍କ ମହିଳାମାନଙ୍କ ସହ ସମୟ ବିତାଉଥିଲେ । ପରଦିନ ସକାଳେ ସେ ଅସୁସ୍ଥ ହୋଇଥ‌ିବାର ଜଣାପଡ଼ିଲା । ଡାକ୍ତର ଡକାଗଲା ଏବଂ ସେ କହିଲେ ଜ୍ଵର ସାମାନ୍ୟ ଅଛି ଓ ସେ ଅଳ୍ପ ସମୟ ମଧ୍ୟରେ ଭଲ ହୋଇଯିବେ ।

କିନ୍ତୁ ବୁଢ଼ୀମା’ କହିଲେ ତାଙ୍କର ଶେଷ ସମୟ ଆସିଗଲାଣି । ଶାନ୍ତିରେ ବିଛଣାରେ ପଡ଼ିରହି ସେ ପ୍ରାର୍ଥନା କରୁଥିଲେ ଏବଂ ମାଳାଜପ କରୁଥିଲେ । ପରେ ପରେ ସେ ଶେଷ ନିଃଶ୍ଵାସ ତ୍ୟାଗ କଲେ । ତା’ପରେ ବୁଢ଼ୀମାଙ୍କର ଅନ୍ତିମ ସଂସ୍କାର ପାଇଁ ବନ୍ଦୋବସ୍ତ କରାଗଲା । ତାଙ୍କ ମୃତ ଦେହକୁ ଲାଲ୍ ଲୁଗାରେ ଆବୃତ କରାଗଲା । ତାଙ୍କୁ ଦାହ କରିବାକୁ ନେବା ପାଇଁ ଏକ ପୁରୁଣା କୋକେଇ ଅଣାଗଲା । ସେତେବେଳେ ହଜାରହଜାର ଘରଚଟିଆ ଚଟାଣ ଉପରେ ଏଣେତେଣେ ବସିଥା’ନ୍ତି । ସେମାନେ କୌଣସି ଶବ୍ଦ କରୁ ନ ଥିଲେ । ଦୁଃଖ- କାତର ପକ୍ଷୀମାନଙ୍କର ଦୃଶ୍ୟ ଥିଲା ବାସ୍ତବିକ ମର୍ମସ୍ପର୍ଶୀ । ଲେଖକଙ୍କର ମା’ ସେମାନଙ୍କ ପାଖକୁ କେତେ ଖଣ୍ଡ ରୁଟି ଟୁକୁଡ଼ା ପକାଇ ଦେଲେ । କିନ୍ତୁ ସେମାନେ ରୁଟି ଟୁକୁଡ଼ାକୁ ଆଡ଼ ଆଖିରେ ଚାହିଁଲେ ନାହିଁ । ବୁଢ଼ୀମା’ର ମୃତ ଦେହ ନିଆଗଲାପରେ ଘରଚଟିଆମାନେ ନୀରବରେ ଉଡ଼ିଗଲେ ।

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 13 Introduction To Three-Dimensional Geometry Ex 13 Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 13 Introduction To Three-Dimensional Geometry Exercise 13

Question 1.

Fill in the blanks in each of the following questions by choosing the appropriate answer from the given ones.
(a) The distance of the point P(x₀, y₀, z₀) from z – axis is [\(\sqrt{x_0^2+y_0^2}, \sqrt{y_0^2+z_0^2}, \sqrt{x_0^2+z_0^2},\)\(\sqrt{\left(x-x_0\right)^2+\left(y-y_0\right)^2}\)]
Solution:
\(\sqrt{x^2+y^2}\)

(b) The length of the projection of the line segment joining (1, 3, -1) and (3, 2, 4) on z – axis is ___________. [1, 3, 4, 5]
Solution:
5

(c) the image of the point (6, 3, -4) with respect to yz – plane is _____________. [(6, 0, -4), (6, -3, 4), (-6, -3, -4), (-6, 3, -4)]
Solution:
(-6, 3, -4)

(d) If the distance between the points (-1, -1, z) and (1, -1, 1) is 2 then z = _______________. [1, √2, 2, 0]
Solution:
1

Question 2.
(a) identify the axis on which the given points lie : (1, 0, 0), (0, 1, 0), (0, 0, 1)
Solution:
x-axis, y-axis, z-axis

(b) Identify the planes containing the points! (7, 0, 4), (2, -5, 0), (0, √2, -3)
Solution:
xz-plane, xy-plane, yz-plane.

Question 3.
(a) Determine, which of the following points have the same projection on x-axis. (2, -5, 7), (2, √2, -3), (-2, 1, 1), (2, -1, 3)
Solution:
(2, -5, 7), (2, √2, -3) and (2, -1, 3) have the same projection on x-axis.

(b) Find the projection of the point (7, -5, 3) on:
(i) xy-plane
Solution:
(7, -5, 0)

(ii) yz-plane,
Solution:
(0, -5, 3)

(iii) zx-plane
Solution:
(7, 0, 3)

(iv) x-axis
Solution:
(7, 0, 0)

(v) y-axis,
Solution:
(0, -5, 0)

(vi) z-axis.
Solution:
(0, 0, 3)

Question 4.
When do you say two lines in space are skewed? Do they intersect?
Solution:
A pair of non-co-planar lines are called skew lines. Skew lines do not intersect.

Question 5.
From the three pairs of lines given below, identify those which uniquely determine a plane:
(i) intersecting pair,
(ii) parallel pair,
(iii) a pair of skew lines.
Solution:
Out of given three pairs
(i) Intersecting pair and
(ii) Parallel pair of lines determine a plane.

Question 6.
Determine the unknown coordinates of the following points if :
(i) P(a, 2, -1)∈ yz – plane
Solution:
a = 0

(ii) Q(-1, y, 3) ∈ zx-plane
Solution:
y = 0

(iii) R(√2, -3, c) ∈ xy-plane
Solution:
c = 0

(iv) S(7, y, z) ∈ x-axis
Solution:
y = 0, z = 0

(v) T(x, 0, z) ∈ y-axis
Solution:
x = 0 , z = 0

(vi) V(a, b, -3) ∈ z-axis
Solution:
a = b = 0

Question 7.
Which axis is determined by the intersection of:
(i) xy-plane and yz-plane
Solution:
y-axis

(ii) yz-plane and zx-plane
Solution:
z-axis

(iii) zx-plane and xy-plane
Solution:
x-axis

Question 8.
Which axis is represented by a line passing through origin and normal to:
(i) xy-plane
Solution:
z-axis

(ii) yz-plane
Solution:
x-axis

(iii) zx-plane.
Solution:
y-axis

Question 9.
What are the coordinates of a point which is common to all the coordinate planes?
Solution:
Origin 0(0, 0, 0) is common to all coordinate planes.

Question 10.
If A, B, and C are projections of P(3, 4, 5) on the coordinate planes, find PA, PB, and PC.
Solution:
PA = 5, PB = 3, PC = 4.

Question 11.
(a) Find the perimeter of the triangle whose vertices are (0, 1, 2) (2, 0, 4) and (-4, -2, 7).
Solution:

(b) Show that the points (a, b, c), (b, c, a), and (c, a, b) form an equilateral triangle.
Solution:

(c) Show that the points (3, -2, 4) (1, 1, 1) and (-1, 4, -1) are collinear.
Solution:
Let A = (3, -2, 4), B = (1, 1, 1) and C = (-1, 4, -2)
D. rs of AB are < -2, 3, -3 >
D. rs of BC are < -2, 3, -3 >
As D. rs of AB is the same as d.rs of
BC it follows that A, B, and C lie on the same straight line.
So the points are collinear. (Proved)

(d) Show that points (0, 1, 2), (2, 5, 8), (5, 6, 6), and (3, 2, 0) form a parallelogram.
Solution:

(e) Show that the line segment joining (7, -6, 1) (17, -18, -3) intersect the line segment joining (1, 4, -5), (3, -4, 11) at (2, 0, 3).
Solution:

D.rs of AP are < -5, 6, 2 >
D.rs of PB are < -15, 18, 6>
i.e., < -5, 6, 2 >
Thus d.r.s. of AP are the same as the d.r.s. of PB.
So A.P.B. are collinear.
Again d.rs. of CP are < 1, -4, 8 >
D. rs. of PD are < 1, -4, 8 >
Thus d.rs. of CP and d.rs. of PD are equal.
So the points C.P.D. are collinear.
Hence line AB intersects the line CD at P.        (Proved)

(f) Find the locus of points that are equidistant from points (1, 2, 3) and (3, 2, -1).
Solution:
Let A = (1, 2, 3), B = (3, 2, -1)
Let P (x, y, z) be equidistant from A and B.
Then PA = DB
(x – 1 )² + (y – 2)² + (z – 3)²
= (x – 3)² + (y – 2)² + (z + 1)²
⇒ (x – 1)² – (x – 3)² + (y – 2)² – (y – 2)² + (z – 3)² – (z + 1)² = 0
⇒ (x – 1 + x – 3) (x – 1 – x + 3) + (z – 3 + z + 1)(z – 3 – z – 1) = 0
⇒ (2x – 4) . 2 + (2z – 2) . (- 4) = 0
⇒ x – 2 – 2z + 2 = 0
⇒ x – 2z = 0 This is the required locus.

Question 12.
(a) Find the ratio in which the line segment through (1, 3, -1) and (2, 6, -2) is divided by zx-plane.
Solution:

(b) Find the ratio in which the lines segment through (2, 4, 5), (3, 5, -4) is divided by xy-plane.
Solution:

(c) Find the coordinates of the centroid of the triangle with its vertices at (a₁, b₁, c₁), (a₂, b₂, c₂), and (a₃, b₃, c₃)
Solution:

(d) If A (1, 0, -1), B (-2, 4, -2), and C (1, 5, 10) be the vertices of a triangle and the bisector of the angle BAC, meets BC at D, then find the coordinates of the point D.
Solution:

(e) Prove that the points P(3, 2, -4), Q(5, 4, -6) and R(9, 8, -10) are collinear. Find the ratio in which point Q divides the line segment PR.
Solution:
Given that P = (3, 2, -4)
Q = (5, 4, -6), R = (9, 8, -10)
D. rs. of PQ are < 2, 2, -2 >
D. rs. of QR are < 4, 4, -4 >
i.e., < 2, 2, -2 >
Thus D.rs. of PQ and QR are the same.
So P, Q, R lie on the same straight line.
Hence P, Q, and R are collinear.     (Proved)
Let Q divides the join of PR in ratio k: 1
∴ \(\frac{9 k+3}{k+1}\) = 5, \(\frac{8 k+2}{k+1}\) = 4, \(\frac{-10 k-4}{k+1}\) = -6
⇒ k = \(\frac{1}{2}\)
Thus the ratio is 1: 2

Odisha State Board BSE Odisha 10th Class Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a) Textbook Exercise Questions and Answers.

BSE Odisha Class 10 Maths Solutions Algebra Chapter 2 ଦ୍ବିଘାତ ସମୀକରଣ Ex 2(a)

Question 1.
ନିମ୍ନଲିଖ ଉକ୍ତିଗୁଡ଼ିକରେ ଥ‌ିବା ତ୍ରୁଟିକୁ ସଂଶୋଧନ କରି ଲେଖ ।
(i) x² – 4x + 4 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ବାସ୍ତବ ଓ ଭିନ୍ନ ।
(ii) x² – 5x + 6 = 0 ସମୀକରଣର ପ୍ରଭେଦକ 2 ଅଟେ ।
(iii) ax? + bx – c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{c}{a}\)।
(iv) ax’ + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ \(\frac{b}{a}\)।
(v) 1 ଓ -1 ମୂଳ ବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣଟି x² + 1 = 0 ।
(vi) x² = 0 ଦ୍ୱିଘାତ ସମୀକରଣର ମୂଳ ସମାନ ନୁହଁନ୍ତି ।
(vii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳ ଦ୍ଵୟର ସମଷ୍ଟି \(– \frac{3}{2}\)।
(viii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ \(\frac{1}{3}\)।
ଉ-
(i) x² – 4x + 4 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ବାସ୍ତବ ପରିମେୟ ଓ ସମାନ ।
(ii) x² – 5x + 6 = 0 ସମୀକରଣର ପ୍ରଭେଦକ 1 ଅଟେ ।
(iii) ax² + bx – c = 0 ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{-b}{a}\)।
(iv) ax² + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\)।
(v) 1 ଓ – 1 ମୂଳବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣଟି x² – 1 = 0।
(vi) x² = 0 ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ ଅଟନ୍ତି ।
(vii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ସମଷ୍ଟି \(\frac{2}{3}\)
(viii) 3x² – 2x – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{-1}{3}\)।

(i) ଏଠାରେ a = 1, b = -4, c = 4
ପ୍ରଭେଦକ (D) = b² – 4ac = (-4)² – 4 × 1 × 4 = 16 – 16 = 0
∴ ମୂଳଦ୍ବୟ ବାସ୍ତବ ଓ ସମାନ ।

(ii) ଏଠାରେ a = 1, b=-5, c = 6
ପ୍ରଭେଦକ (D) = b² – 4ac = (- 5)² – 4 (1) (6) = 25 – 24 = 1

(iii) ax² + bx – c = 0 ମୂଳଦ୍ଵୟର ସମଷ୍ଟି \(\frac{-b}{a}\)।
(iv) ax² + bx + c = 0 ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\)।
(v) ମୂଳବିଶିଷ୍ଟ ଦ୍ୱିଘାତ ସମୀକରଣ, x² – (α + ß) x + αß = 0
⇒ x² – { 1 + (- 1)} x + 1 (-1) = 0 ⇒ x² – 1 = 0
(vi) x = 0 ଦ୍ୱିଘାତ ସମୀକରଣ ମୂଳଦ୍ଵୟ ସମାନ ଅଟନ୍ତି । (କାରଣ ପ୍ରଭେଦକ (D) = 0)
(vii) ଏଠାରେ a = 3, b = -2, c = -1 ମୂଳଦ୍ଵୟ ସମାନ = \(\frac{-b}{a}\) = \(\frac{-(-2)}{a}\) = \(\frac{2}{3}\)
(viii) 3x² – 2x-1=0 ଏଠାରେ a = 3, b = -2, c = 1 ମୂଳଦ୍ବୟର ଗୁଣଫଳ \(\frac{c}{a}\) = \(\frac{-1}{3}\)

Question 2.
ନିମ୍ନଲିଖୂ ପ୍ରଶ୍ନମାନଙ୍କର ସଂକ୍ଷିପ୍ତ ଉତ୍ତର ଦିଅ ।
(i) ଗୋଟିଏ ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ 3 ଓ -5 ହେଲେ, ସମୀକରଣଟି ନିରୂପଣ କର ।
(ii) mx² – 2x + (2m – 1) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ 3 ହେଲେ, m ର ମାନ ନିରୂପଣ କର ।
(iii) x² – px + 2 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 2 ହେଲେ, p ର ମାନ ନିରୂପଣ କର ।
(iv) 4x² – 2x + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଓ ଅଭିନ୍ନ ହେଲେ, c ର ମାନ ନିରୂପଣ କର ।
(v) 5x² + 2x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ – 2 ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
(vi) x² – kx + 6 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3 ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
(vii) 2x² + kx + 3 = 0 ସମୀକରଣର ଦୁଇଟି ମୂଳ ବାସ୍ତବ ଓ ସମାନ ହେଲେ, k ର ମାନ ନିରୂପଣ କର ।
ସମାଧାନ :
(i) ଗୋଟିଏ ଦ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ 3 ଓ – 5 । ଅର୍ଥାତ୍ α = 3 ଓ ß = – 5
x² – (α + ß) x + αß = 0
⇒ x² – (3 – 5) x + (3)(-5) = 0 ⇒ x² + 2x – 15 = 0

(ii) mx² – 2x + (2m – 1) = 0 ମୂଳଦ୍ଵୟର ଗୁଣଫଳ = 3
ଏଠାରେ a = m, b = – 2, c = 2m – 1
ମୂଳଦ୍ବୟର ଗୁଣଫଳ = \(\frac{c}{a}\) ⇒ 3 \(\frac{2m-1}{m}\)
⇒ 3m = 2m – 1 ⇒ 3m – 2m = 1 ⇒ m = -1
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ଗୁଣଫଳ 3 ହେଲେ m = -1 ହେବ ।

(iii) x² – px + 2 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 2।
⇒ 2² – p(2) + 2 =0 ⇒ 4 – 2p + 2 = 0 ⇒ 6 = 2p ⇒ p = \(\frac{6}{2}\) = 3
∴ pର ମାନ = 3

(iv) 4x² – 2x + c = ଫିର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ । ଏଠାରେ a = 4, b = – 2, c = c
ପ୍ରଭେଦକ (D) = 0 ⇒ b² – 4ac = 0 ⇒ (-2)² – 4 (4) c = 0 ⇒ 4 – 16c = 0
⇒ -16c = -4 = c = – \(\frac{-4}{16}=\frac{1}{4}\)
∴ c = \(\frac{1}{4}\)
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଏବଂ ଅଭିନ୍ନ ହେଲେ c ର ମାନ \(\frac{1}{4}\) ହେବ।

(v) 5x² + 2x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ – 2 ।
⇒ 5(- 2)² + 2(- 2) + k = 0 ⇒ 20 – 4 + k = 0 ⇒ 16 + k = 0 ⇒ k = -16
∴ ‘k’ ର ମାନ -16 ପାଇଁ ଦତ୍ତ ସମୀକରଣର ଗୋଟିଏ ମୂଳ -2 ହେବ ।

(vi) x² – kx + 6 = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3।
⇒ 3² – 3k + 6 = 0 ⇒ 9 – 3k + 6 = 0 ⇒ -3k = -15 ⇒ \(\frac{-15}{-3}=5\)
∴ ଦତ୍ତ ସମୀକରଣର ଗୋଟିଏ ମୂଳ 3 ହେଲେ k ର ମାନ 5 ହେବ ।

(vii) 2x² + kx + 3 = 0, ଏଠାରେ a = 2, b = k, c = 3
ସମୀକରଣର ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଓ ସମାନ ହେଲେ b² – 4ac = 0
⇒ k² – 4 (2) (3) = 0 ⇒ k² – 24 = 0 ⇒ k² = 24 ⇒ k = ±√24 ⇒ k = ± 2√6
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟ ବାସ୍ତବ ଓ ସମାନ ହେଲେ k ର ମାନ ±2√6 ହେବ ।

Question 3.
ପ୍ରତ୍ୟେକ ପ୍ରଶ୍ନପାଇଁ ଥ‌ିବା ସମ୍ଭାବ୍ୟ ଉତ୍ତରଗୁଡ଼ିକ ମଧ୍ୟରୁ ଠିକ୍ ଉତ୍ତରଟି ବାଛି ଲେଖ ।
(i) ନିମ୍ନଲିଖ୍ ସମୀକରଣମାନଙ୍କ ମଧ୍ୟରୁ କେଉଁଟି x ରେ ଏକ ଦ୍ଵିଘାତ ସମୀକରଣ ?
(a) x² – x – 12 = 0
(b) x² + 12 = 3
(c) x + = x²
(d)x (x – 1 ) (x + 5) = 0

(ii) 7x² – 9x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ସ୍ବରୂପ କ’ଣ ?
(a) ବାସ୍ତବ ସଂଖ୍ୟା ଓ ପରସ୍ପରଠାରୁ ପୃଥକ୍
(b) ବାସ୍ତବ ସଂଖ୍ୟା ଏବଂ ଏକ ଓ ଅଭିନ୍ନ
(c) ବାସ୍ତବ ହେବେ ନାହିଁ
(d) ଏଥୁରୁ କେଉଁଟି ନୁହେଁ

(iii) ନିମ୍ନଲିଖ ମଧ୍ୟରୁ କେଉଁଟି – 6 ଓ 8 ମୂଳ ବିଶିଷ୍ଟ ଦ୍ବିଘାତ ସମୀକରଣ ?
(a) (x + 6) (x+8)= 0
(b) (x + 6) (x – 8) = 0
(c) (x – 6) (x + 8) = 0
(d) (x – 6) (x – 8) = 0

(iv) 3x² + 2√5 x – 5 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ଓ ହେଲେ αß ର ମୂଲ୍ୟ କେତେ ?
(a) 3
(b) 2√5
(c) \(\frac{2√5}{3}\)
(d) \(\frac{-5}{3}\)

(v) 4x – 2x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ α ଓ ß ହେଲେ α + ß ର ମୂଲ୍ୟ କେତେ ?
(a) \(\frac{1}{16}\)
(b) 4
(c) \(\frac{1}{2}\)
(d) -8

(vi) 4x + 3x + 7 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହେଲେ \(\frac{1}{α}+\frac{1}{ß}\) ର ହେଲେ କେତେ ?
(a) \(\frac{3}{7}\)
(b) \(– \frac{3}{7}\)
(c) \(\frac{7}{3}\)
(d) \(– \frac{7}{3}\)

(vii) ଗୋଟିଏ ଦ୍ବିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି ଓ ଗୁଣଫଳ ଯଥାକ୍ରମେ 4 ଓ \(\frac{5}{2}\) ହେଲେ ନିମ୍ନଲିଖ ମଧ୍ୟରୁ କେଉଁଟି ?
(a) 2x² + 8x + 5 = 0
(b) 2x² – 8x + 5 = 0
(c) 2x² + 8x – 5=0
(d) 2x² – 8x – 5 = 0
ଉ-
(i) x² – x – 12 = 0
(ii) ବାସ୍ତବ ସଂଖ୍ୟା ଓ ପରସ୍ପରଠାରୁ ପୃଥକ୍
(iii) (x +6) (x – 8) = 0
(iv) \(\frac{-5}{3}\)
(v) \(\frac{1}{2}\)
(vi) \(– \frac{3}{7}\)
(vii) 2x² – 8x + 5 = 0

Question 4.
ନିମ୍ନଲିଖୂତ ଦ୍ବିଘାତ ସମୀକରଣମାନଙ୍କୁ ପୂର୍ବ ବର୍ଗରେ ପରିଣତ କରି ସମାଧାନ କର ।
(i) x² + x – 6 = 0
(ii) 2x² – 9x + 4 = 0
(iii) 14x² + x – 3 = 0
(iv) 3x² – 32x + 12=0
(v) x² + 2px – 3qx – 6pq = 0
(vi) √3x² + 10x + 8√3 = 0
(vii) 25x² + 30x + 7 = 0
(viii) 3a²x² + 8abx + 4b² = 0 (a ≠ 0)
(ix) x² + ax + b = 0
(x) x² + bx = a² – ab
ସମାଧାନ :
(i)

(ii)

(iii)

(iv)

(v) x² + 2px – 3qx – 6pq = 0

(vi) √3x² + 10x + 8√3 = 0

(vii) 25x² + 30x + 7 = 0

(viii) 3a²x² + 8abx + 4b² = 0 (a ≠ 0)

(ix) x² + ax + b = 0


(x) x² + bx = a² – ab

Question 5.
ଦ୍ଵିଘାତ ସୂତ୍ର ପ୍ରୟୋଗ କରି ନିମ୍ନଲିଖ ସମୀକରଣମାନଙ୍କର ବୀଜ ବା ମୂଳ ନିରୂପଣ କରି ।
(i) 4x² – 11x + 6 = 0
(ii) (2x – 1)(x – 2) = 0
(iii) x² – (1+√2)x+ 2 = 0
(iv) a(x² + 1) = x(a2 + 1), a ≠ 0
(v) 6x² + 11x + 3 = 0
(vi) 2x² + 41x – 115 = 0
(vii) 12x² +x – 6 = 0
(viii) (6x + 5)(x – 2) = 0
(ix) 15x² – x – 8 = 0
(x) (x + 5)(x – 5) = 39
ସମାଧାନ :
(i) 4x² – 11x + 6 = 0

(ii) (2x – 1)(x – 2) = 0
⇒ 2x² – 4x -x + 2 = 0 ⇒ 2x² – 5x + 2 = 0
ଏଠାରେ a = 2, b = -5, c = 2

(iii) x² – (1+√2)x+ 2 = 0
ଏଠାରେ a = 1, b = – (1+√2), c = √2

(iv) a(x² + 1) = x(a² + 1) ⇒ a(x² + 1) – x(a² + 1) = 0
⇒ ax² + a – x(a² + 1) = 0 ⇒ ax² – x(a² + 1) + a = 0
ଏଠାରେ a = a, b = -(a² + 1), c = a

(v) 6x² + 11x + 3 = 0
ଏଠାରେ a = 6, b = 11, c = 3

(vi) 2x² + 41x – 115 = 0
ଏଠାରେ a = 2, b = 41, c = -115

(vii) 12x² +x – 6 = 0
ଏଠାରେ a = 12, b = 1, c = -6

(viii) (6x + 5)(x – 2) = 0 ⇒ 6x² -12x + 5x – 10 = 0 ⇒ 6x² -7x – 10 = 0
ଏଠାରେ a = 6, b = -7, c = -10

(ix) 15x² – x – 8 = 0
ଏଠାରେ a = 15, b = -1, c = -8

(x) (x + 5)(x – 5) = 39 ⇒ x² – 25 = 39 ⇒ x² – 25 – 39 = 0 ⇒ x² – 64 = 0
ଏଠାରେ a = 1, b = 0, c = -64
x = \(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}=\frac{0 \pm \sqrt{0^2-4(1) 64}}{2(1)}=\frac{0 \pm \sqrt{256}}{2}=\frac{\pm 16}{2}=\pm 8\)
⇒ x = 8 ବ। x = -8
∴ ସମୀକରଣର ମୂଳଦ୍ଵୟ 8 ଓ -8 ।

Question 6.
ଯଦି 4x² – 13x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 12 ଗୁଣ ହେଲେ kରେ ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର 4x² – 13x + k = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ । ଏବଂ ଅନ୍ୟଟି 12α ।
ଏଠାରେ a = 4, b = 13 6 c = k
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = \(\frac{-b}{a}\) ⇒ α + 12α = \(\frac{-(-13)}{4}\) ⇒ 13α = \(\frac{13}{4}\) ⇒ α = \(\frac{13}{4}\) × \(\frac{1}{13}\) = \(\frac{1}{4}\)
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = \(\frac{-c}{a}\) ⇒ α.12α = \(\frac{k}{4}\) ⇒ 12α² = \(\frac{k}{4}\) ⇒ 12 × (\(\frac{1}{4}\))² = \(\frac{k}{4}\) ⇒ \(\frac{12}{16}\) = \(\frac{k}{4}\) ⇒ 16k = 48 ⇒ k = 3
∴ kର ମାନ 3 ହେଲେ ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 12 ଗୁଣ ହେବ ।

Question 7.
x² – 5x + p = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟି ଅପେକ୍ଷା 3 ଅଧିକ ହେଲେ pର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର x² – 5x + p = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ α ଓ ଅନ୍ୟଟି α + 3
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + α + 3 = \(\frac{-(-5)}{1}\)
⇒ 2α + 3 = 5 ⇒ 2α = 5 – 3 = 2 ⇒ α = \(\frac{2}{2}\) = 1
α ର ମାନ ସମୀକରଣରେ ବସାଇଲେ 1² – 5 (1) + p = 0
⇒ 1 – 5 + p = 0 ⇒ p – 4= 0 ⇒ p = 4
∴ p ର ମାନ 4 ହେଲେ ଗୋଟିଏ ମୂଳ ଅପରୂଟି ଅପେକ୍ଷା 3 ଅଧିକ ହେବ ।

Question 8.
ଯଦି 2x² – 5x + 3 = 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß ହୁଏ ତେବେ α²ß + αß²ର ମୂଲ୍ୟ ନିରୂପଣ ‘କର ।
ସମାଧାନ :
2x² – 5x + 3= 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß।
ମୂଳଦ୍ଵୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-5)}{2}\) ⇒ α + ß = \(\frac{5}{2}\)
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{3}{2}\)
∴ α²ß + αß² = αß (α + ß)\(\frac{3}{2}\)(\(\frac{5}{2}\)) = \(\frac{15}{4}\)

Question 9.
ଯଦି 2x² – 6x + 3 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ (α + 1) (ß + 1) ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
2x² – 6x + 3= 0 ସମୀକରଣର ମୂଳଦ୍ୱୟ α ଓ ß।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-6)}{2}\) = \(\frac{6}{2}\) = 3
ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{3}{2}\)
∴ (α + 1) (ß + 1) = αß + α + ß + 1 = \(\frac{3}{2}\) + 3 + 1 = \(\frac{3+6+2}{2}\) = \(\frac{11}{2}\)
∴ (α + 1) (ß + 1) = \(\frac{11}{2}\)

Question 10.
ଯଦି 2x² – (p + 1) x + p – 1 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟର ଅନ୍ତର ଓ ଗୁଣଫଳ ସମାନ ହେଲେ pର ମାନ ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର 2x² – (p + 1) x + (p – 1) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
ବୀଜଦ୍ଵୟର ସମଷ୍ଟି α + ß = \(\frac{-{-(p+1)}}{2}\) = \(\frac{p+1}{2}\) ଏବଂ αß = \(\frac{p-1}{2}\)
ପ୍ରଶାନୁସାରେ ବୀଜଦ୍ଵୟର ଅନ୍ତର, ବୀଜଦ୍ୱୟର ଗୁଣଫଳ ସହ ସମାନ ।
∴ α – ß = aß ⇒ (α – ß)² = (aß)² ⇒ (α + B)² – 4aß = (αß)²
⇒ (\(\frac{p+1}{2}\))² – 4(\(\frac{p-1}{2}\)) ⇒ (\(\frac{p-1}{2}\))² = (\(\frac{p+1}{2}\))² – (\(\frac{p-1}{2}\))² = 4 (\(\frac{p-1}{2}\))
⇒ p . 1 = 2p – 2 ⇒ p = 2
∴ ଦତ୍ତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ଅନ୍ତର ଓ ଗୁଣଫଳ ସମାନ ହେଲେ p ର ମାନ 2 ହେବ ।

Question 11.
ଯଦି 5x² – 3x – 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ α³ + ß³ = \(\frac{117}{125}\)
ସମାଧାନ :
5x²-3x-2=0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-3)}{5}\) = \(\frac{3}{5}\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{-2}{5}\)
∴ α³ + ß³ = (α + ẞ)³ – 3αß (α + B)
= (\(\frac{3}{5}\))³ – 3(\(\frac{3}{5}\))(\(\frac{-2}{5}\)) = \(\frac{27}{125}+\frac{18}{25}\) = \(\frac{27+90}{125}\) = \(\frac{117}{125}\)
∴ α³ + ß³ = \(\frac{117}{125}\) (ପ୍ରମାଣିତ)

Question 12.
ଯଦି 5x² + 17x + 6 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ ତେବେ \(\frac{1}{α²}+\frac{1}{ß²}\) ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
5x² + 17x + 6 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß।
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-17}{5}\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{6}{5}\)
\(\frac{1}{α²}+\frac{1}{ß²}\) = \(\frac{ß²+α²}{α²ß²}\) = \(\frac{(α+ß)²-2αẞ}{(αß)²}\)
=\(\frac{\left(\frac{-17}{5}\right)^2-2\left(\frac{6}{5}\right)}{\left(\frac{6}{5}\right)^2}=\frac{\frac{289}{25}-\frac{12}{5}}{\frac{36}{25}}\) = \(\frac{289-60}{25}\) × \(\frac{25}{36}\) = \(\frac{229}{36}\)
∴ \(\frac{1}{α²}+\frac{1}{ß²}\) ର ମୂଲ୍ୟ \(\frac{229}{36}\) ।

Question 13.
x² – 8x + 16p = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହେଲେ \(\frac{αß}{α + ß}\) ପରିପ୍ରକାଶକୁ p ମାଧ୍ୟମରେ ପ୍ରକାଶ କର ।
ସମାଧାନ :
x² – 8x + 16p = 0 ମୂଳ ଦ୍ଵୟ α ଓ ß।
∴ ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = \(\frac{-(-8)}{1}=8\), ମୂଳଦ୍ବୟର ଗୁଣଫଲ = αß = \(\frac{16p}{1}=16p\)
∴ \(\frac{αß}{α + ß}\) = \(\frac{16p}{8}\) = 2p

Question 14.
ଯଦି x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ଏକ ଓ ଅଭିନ୍ନ ହୁଏ, m ର ମୂଲ୍ୟ ନିରୂପଣ କର ।
ସମାଧାନ :
x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ ।
ପ୍ରଭେଦକ (D) = 0
ଏଠାରେ a = 1, b = – 2 (5+ 2m), c = 3 (7 + 10m)
D = b² – 4ac = 0
⇒ {-2(5+ 2m)}² – 4 × 1 × 3 (7 + 10m) = 0
⇒ 4 (25 + 20m + 4m²) – 4 × 3 (7 + 10m) = 0
⇒ 100+ 80m + 16m² – 12 (7 + 10m) = 0
⇒ 16m² + 80m + 100 – 84 – 120m = 0 16m² – 40m + 16 = 0 ⇒ 2m² – 5m+2=0 2m² – 4m – m + 2=0
⇒ 2m (m – 2) – 1 (m – 2) = 0 ⇒ (m – 2) (2m – 1) = 0
m – 2 = 0 | 2m – 10 ⇒ m = 2 | m =
∴ m ର ମାନ 2 କିମ୍ବା \(\frac{1}{2}\) ହେଲେ x² – 2 (5 + 2m) x + 3 (7 + 10m) = 0 ସମୀକରଣର ମୂଳଦ୍ବୟ ଏକ ଓ ଅଭିନ୍ନ ହେବେ ।

Question 15.
(i) ଯଦି a = b = c ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ, ସମୀକରଣ
(x – a)(x – b) + (x – b)(x – c) + (x – c)(x – a) = 0 ର ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଏବଂ ଏକ ଓ ଅଭିନ୍ନ ।
(ii) ଯଦି a + b + c = 0 ଏବଂ a, b, c ∈ Q ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0 ସମୀକରଣର ପରିମେୟ ହେବେ ।
ସମାଧାନ :
(i) a = b = c ହେଲେ, (x – a) (x – b) + (x – b) (x – c) + (x – c) (x – a) = 0
⇒ (x – a)² + (x – a)² + (x – a)² = 0
⇒ 3 (x – a)² = 0 ⇒ (x – a)² = 0 ⇒ x² – 2ax + a² = 0
ଏଠାରେ ପ୍ରଭେଦକ (D) = b² – 4ac = (-2a)² – 4(1) a² = 4a² – 4a² = 0
∴ D = 0 ହେଲେ, ମୂଳଦ୍ୱୟ ବାସ୍ତବ ଏବଂ ଏକ ଓ ଅଭିନ୍ନ ।

(ii) ଯଦି a+b+c=0, a, b, c ∈ Q
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0
a + b + c = 0
⇒ b + c = a, c + a = – b, a + b = -c
(b + c – a) x² + (c + a – b) x + (a + b – c) = 0
⇒ -2ax² + (-2b) x + (- 2c) = 0 ⇒ 2 (ax² + bx + c) = 0
⇒ ax² + bx + c = 0
ପ୍ରଭେଦକ (D) = b² – 4ac = (-b)² – 4ac = (a + c)² – 4ac = (a – c)²

Question 16.
ଗୋଟିଏ ଦ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟର ସମଷ୍ଟି 3 ଓ ମୂଳଦ୍ବୟର ବର୍ଗର ସମଷ୍ଟି 29 ହେଲେ, ସମୀକରଣଟି ନିରୂପଣ କର ।
ସମାଧାନ :
ମନେକର ସ୍ଵିଘାତ ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ।
ମୂଳଦ୍ବୟର ସମଷ୍ଟି = α + ß = 3
ମୂଳଦ୍ଵୟର ବର୍ଗର ସମଷ୍ଟି = α² + ß² = 29
⇒ (α + ß)² – 2 aẞ = 29 ⇒ 3² – 2αß = 29
⇒9 – 2αẞ = 29 ⇒ – 2αß = 29 – 9 = 20
αß = \(\frac{-20}{2}\) = -10
ସମୀକରଣଟି x² – (a + ẞ) x + αß = 0
⇒ x² – 3x + (-10) = 0 ⇒ x² – 3x – 10 = 0

Question 17.
ଯଦି 2x² – 4x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ \(\frac{α}{ß}+\frac{ß}{α}\) + 4(\(\frac{1}{α}+\frac{1}{ß}\)) + 2αß = 12
ସମାଧାନ :
2x² – 4x + 2 = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଓ ß ।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + ß = \(\frac{-(-4)}{2}\) = -2 ଏବଂ ମୂଳଦ୍ଵୟର ଗୁଣଫଲ αβ = \(\frac{2}{2}\) = 1
L.H.S. = \(\frac{α}{ß}+\frac{ß}{α}\) + 63(\(\frac{1}{α}+\frac{1}{ß}\)) – 2αß
= \(\frac{ß²+α²}{αß}\) + 63\(\frac{(α+ß)}{(αß)}\) – 2αß
= \(\frac{(α+ß)²-2αß}{(αß)}\) + 4\(\frac{(α+ß)}{(αß)}\) + 2αß
= \(\frac{(2)²-2×1}{1}\) + \(\frac{4(2)}{1}\) + 2 × 1
= 2 + 8 + 2 = 12 = R.H.S.

Question 18.
(i) ଯଦି ax² + bx + c = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 4 ଗୁଣ ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ 4b² = 25ac।
(ii) ଯଦି x² – px + q = 0 ସମୀକରଣର ଗୋଟିଏ ମୂଳ ଅପରଟିର 2 ଗୁଣ ହୁଏ, ତେବେ ପ୍ରମାଣ କର ଯେ 2p² = 9q ।
ସମାଧାନ :
(i) ମନେକର ax² + bx + c = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଏବଂ 4α।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + 4α = \(\frac{-b}{a}\) ⇒ 5α = \(\frac{-b}{a}\) ⇒ α= \(\frac{-b}{5a}\) .. (i)
ମୂଳଦ୍ଵୟର ଗୁଣଫଲ α.4α = \(\frac{c}{2}\)
⇒ \(4 α^2=\frac{c}{a} \Rightarrow 4 \times (\frac{-b}{5a})^2=\frac{c}{a}\) [(i)]
⇒ \(\frac{4b²}{25a²}=\frac{c}{a} \Rightarrow 4ab²=25a²c \Rightarrow 4b²=25 ac\) (ପ୍ରମାଣିତ)

(ii) ମନେକର x² – px + q = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ α ଏବଂ 2α।
∴ ମୂଳଦ୍ଵୟର ସମଷ୍ଟି α + 2α = \(\frac{-(-p)}{1}\) ⇒ 3α = p ⇒ α= \(\frac{p}{3}\) .. (i)
ମୂଳଦ୍ଵୟର ଗୁଣଫଲ α.2α = \(\frac{q}{1}\) = 2α² = q
⇒ 2 × (\(\frac{p}{3}\))³ = q ⇒ \(\frac{2p²}{3}\) = q ⇒ 2p² = 9q (ପ୍ରମାଣିତ)

Question 19.
(i) ଯଦି 41x² – 2 (5a + 4b) x + (a² + b²) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ ହୁଅନ୍ତି, ତେବେ ପ୍ରମାଣ କର ଯେ, \(\frac{a}{b}=\frac{5}{4}\)।
(ii) ଯଦି x² + px + q = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟର ସମଷ୍ଟି ସେମାନଙ୍କର ବର୍ଗର ସମଷ୍ଟି ସହ ସମାନ ଯେ, 2q = p (p + 1)।
(ii) ଯଦି x² + px + q = 0 ସମୀକରଣର ଗୋଟିଏ ବୀଜ ଅନ୍ୟଟିର ବର୍ଗ ହୁଏ, ତେବେ ଦର୍ଶାଅ ଯେ p³ + q² + q = 3pq।
ସମାଧାନ :
(i) 41x² – 2 (5a + 4b) x + (a² + b²) = 0 ସମୀକରଣର ମୂଳଦ୍ଵୟ ସମାନ।
ଏଠାରେ a = 41, b = -2(5a + 4b), c = (a² + b²)
ପ୍ରଭେଦକ (D) = b² – 4ac = 0
⇒ {-2 (5a + 4b)}² – 4 (41) (a² + b²) = 0
⇒ 4 (25a² + 40ab + 16b²) – 4 (41a² + 41b²) = 0
⇒(25a² + 40ab + 16b² – 41a² – 41b²) = 0
⇒(-16a² + 40ab – 25b²) = 0
⇒(16a² – 40ab + 25b²) = 0
⇒(4a)² – 2.4a.5b + (5b)² = 0
⇒ (4a – 5b)² = 0
⇒4a – 5b = 0 [∴ a² – 2ab + b² = (a – b)²]
⇒ 4a = 5b ⇒ \(\frac{a}{b}=\frac{5}{4}\)।

(ii) x² + px + q = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟର ସମଷ୍ଟି ସେମାନଙ୍କର ବର୍ଗର ସମଷ୍ଟି ସହ ସମାନ ।
ମନେକର ସମୀକରଣର ବୀଜଦ୍ଵୟ α ଓ ß।
ବୀଜଦ୍ୱୟର ସମଷ୍ଟି α + ß = – p ଏବଂ ବୀଜଦ୍ବୟର ଗୁଣଫଳ αß = q
କିନ୍ତୁ ଦତ୍ତ ଅଛି α + ß = α² + ß²
⇒ α + ß = α² + ß² – 2αß ⇒ – p = (- p)² – 2q
⇒ 2q = p² + p ⇒ 2q = p (p + 1) (ପ୍ରମାଣିତ)

(iii) x + px + g = 0 ସମୀକରଣର ଗୋଟିଏ ବୀଜ ଅପରଟିର ବର୍ଗ ।
ମନେକର ସମୀକରଣର ବୀଜଦ୍ଵୟ α ଓ α²।
ବୀଜଦ୍ୱୟର ସମଷ୍ଟି α + α² = – p
ବୀଜଦ୍ବୟର ଗୁଣଫଳ α.α² = q ⇒ α³ = q
α + α² = – p = (α + α²)³ = -p³
⇒ a³ + α⁶ + 3α · a² (α + α²) = – p³ ⇒ q + q² + 3q (- p) = – p³
⇒ q² + q – 3pq = -p³ ⇒ p³ + q² + q = 3pq (ପ୍ରମାଣିତ)

Question 20.
ଯଦି a(b – c) x² + b(c – a) x + c (a – b) = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟ ସମାନ ହୁଏ, ତେବେ ଦର୍ଶାଅ ଯେ, \(\frac{2}{b}=\frac{1}{a}+\frac{1}{c}\)
ସମାଧାନ :
a(b – c) x² + b(c – a) x + c (a – b) = 0 ସମୀକରଣର ବୀଜଦ୍ଵୟ ସମାନ ।
ସମୀକରଣର ପ୍ରଭଦେକ (D) = 0
⇒ {b (c – a)}² – 4a (bc) c (a – b) = 0
⇒ b² (ca)² – 4a (b -c) c (a – b) = 0
⇒(bc – ab)² – 4 a(b – c) · c (a – b) = 0
⇒ (ab – ca + ca – bc)² – 4a (b- c) · c (a – b) = 0
⇒ {a (b-c) + c (a – b)}² – 4a (b – c) c (a – b) = 0
⇒ {a (bc) -c (a – b)}² = 0 ⇒ (ab – ac- ca + bc) = 0
⇒ ab + bc = 2 ca ⇒ \(\frac{ab}{abc}+\frac{bc}{abc}=\frac{2ca}{abc}\) (abc ଦ୍ବାରା ଉଭୟ ପାର୍ଶ୍ଵକୁ ଭାଗ କଲେ)
⇒ \(\frac{1}{c}+\frac{1}{a}=\frac{2}{b}\) (ପ୍ରମାଣିତ)