Class 12

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Ex 12(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Exercise 12(a)

Question 1.
Each question given below has four possible answers out of which only one is correct. Choose the correct one.
(i) \(\vec{a}\) = î + 2ĵ + k̂, \(\vec{b}\) = 2î – 2ĵ + 2k̂ and \(\vec{c}\) = -î + 2 ĵ + k̂ then
(a) \(\vec{a}\) and \(\vec{b}\) have the same direction
(b) \(\vec{a}\) and \(\vec{c}\) have opposite directions.
(c) \(\vec{b}\) and \(\vec{c}\) have opposite directions
(d) no pair of vectors have same direction
Solution:
(d) no pair of vectors have same direction

(ii) If the vectors \(\vec{a}\) = 2î + 3ĵ – 6k̂ and \(\vec{b}\) = -α î – ĵ + 2k̂ are parallel, then α = ______.
(a) 2
(b) \(\frac{2}{3}\)
(c) –\(\frac{2}{3}\)
(d) \(\frac{1}{3}\)
Solution:
(c) –\(\frac{2}{3}\)

(iii) If the position vectors of two points A and B are 3î + k̂, and 2î + ĵ – k̂, then the vector \(\overrightarrow{BA}\) is
(a) -î + ĵ – 2k̂
(b) î + ĵ
(c) î – ĵ + 2k̂
(d) î – ĵ – 2k̂
Solution:
(c) î – ĵ + 2k̂

(iv) If \(|k \vec{a}|\) = 1, then
(a) \(\vec{a}=\frac{1}{k}\)
(b) \(\vec{a}=\frac{1}{|k|}\)
(c) \(k=\frac{1}{|\vec{a}|}\)
(d) \(k=\frac{+1}{|\vec{a}|}\)
Solution:
(d) \(k=\frac{+1}{|\vec{a}|}\)

(v) The direction cosines of the vectors \(\overrightarrow{PQ}\) where \(\overrightarrow{OP}\) = (1, 0, -2) and \(\overrightarrow{OQ}\) = (3, -2, 0) are
(a) 2, -2, 2
(b) 4, -2, -2
(c) \(\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)
(d) \(\frac{2}{\sqrt{6}},-\frac{1}{\sqrt{6}},-\frac{1}{\sqrt{6}}\)
Solution:
(c) \(\frac{1}{\sqrt{3}},-\frac{1}{\sqrt{3}}, \frac{1}{\sqrt{3}}\)

Question 2.
Rectify the mistakes, if any
(i) \(\vec{a}-\vec{a}\) = 0
Solution:
\(\overrightarrow{0}\)

(ii) The vector \(\overrightarrow{0}\) has unique direction.
Solution:
indefinite direction

(iii) All unit vectors are equal.
Solution:
equal magnitude

(iv) \(|\vec{a}|=|\vec{b}| \Rightarrow \vec{a}=\vec{b}\)
Solution:
\(\vec{a}=\vec{b} \Rightarrow|\vec{a}|=|\vec{b}|\)

(v) Subtraction of vectors is not commutative.
Solution:
true

Question 3.
(i) If \(\vec{a}\) = (2, 1), \(\vec{b}\) = (-1, 0), find \(3 \vec{a}+2 \vec{b}\).
Solution:
\(3 \vec{a}+2 \vec{b}\) = 3 (2, 1) + 2 (-1, 0)
= (6 – 2, 3 + 0)
= (4, 3 )

(ii) If \(\vec{a}\) = (1, 1, 1) , \(\vec{b}\) = (-1, 3, 0) and \(\vec{c}\) =(2, 0, 2), find \(\vec{a}+2 \vec{b}-\frac{1}{2} \vec{c}\).
Solution:
\(\vec{a}+2 \vec{b}-\frac{1}{2} \vec{c}\)
= (1, 1, 1) + 2 (-1, 3, 0) – \(\frac{1}{2}\)(2, 0, 2)
= (1 – 2 – 1, 1 + 6 – 0, 1 + 0 – 1)
= (-2, 7, 0)

Question 4.
If A, B, C and D are the vertices of a square, find \(\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{DA}\).
Solution:
Let ABCD be a square.

Question 5.
The given points A, B, C are the vertices of a triangle. Determine the vectors \(\overrightarrow{A B}, \overrightarrow{B C} \text { and } \overrightarrow{C A}\) and the lengths of these vectors in the following cases.
(i) A (4, 5, 5), B (3, 3, 3), C (1, 2, 5)
Solution:

(ii) A (8, 6, 1), B (2, 0, 1), C (-4, 0, -5)
Solution:

Question 6.
Find the vector from origin to the midpoint of the vector \(\overrightarrow{{P}_1 {P}_2}\) joining the points P₁(4, 3) and P₂(8, -5).
Solution:
P₁ = (4, 3) and P₂ = (8, -5)
If P is the mid-point of P₁P₂ then P = (6, -1).
Position vector of P = \(\overrightarrow{{OP}}\) = 6î – ĵ

Question 7.
Find the vectors from the origin to the points of trisection the vector \(\overrightarrow{{P}_1 {P}_2}\) joining P₁ (-4, 3) and P₂ (5, -12).
Solution:

Question 8.
Find the vector from the origin to the intersection of the medians of the triangle whose vertices are A (5, 2, 1), B(-4, 7, 0) and C (5, -3, 5).
Solution:

Question 9.
Prove that the sum of all the vectors drawn from the centre of a regular octagon to its vertices is the null vector.
Solution:

Question 10.
Prove that the sum of the vectors represented by the sides of a closed polygon taken in order is a zero vector.
Solution:
Consider a closed polygon ABCDEFA.

Question 11.
(a) Prove that:
(i) \(|\overrightarrow{a}+\overrightarrow{{b}}| \leq|\overrightarrow{a}|+|\overrightarrow{b}|\)
State when the equality will hold;
Solution:

(ii) \(|\overrightarrow{a}-\overrightarrow{b}| \geq|\overrightarrow{a}|-|\overrightarrow{b}|\)
Solution:

(b) What is the geometrical significance of the relation \(|\overrightarrow{a}+\overrightarrow{b}|=|\overrightarrow{a}-\overrightarrow{b}|\)?
Solution:

Question 12.
Find the magnitude of the vector \(\overrightarrow{PQ}\), its scalar components and the component vectors along the coordinate axes, if P and Q have the coordinates.
(i) P (-1, 3), Q (1, 2)
Solution:

(ii) P (-1, -2), Q (-5, -6)
Solution:

(iii) P (1, 4, -3), Q (2, -2, -1).
Solution:

Question 13.
In each of the following find the vector \(\overrightarrow{PQ}\), its magnitude and direction cosines, if P and Q have co-ordinates.
(i) P (2, -1, -1), Q (-1, -3, 2);
Solution:

(ii) P (3, -1, 7), Q (4, -3, -1).
Solution:

Question 14.
If \(\vec{a}\) = (2, -2, 1), \(\vec{b}\) = (2, 3, 6) and \(\vec{c}\) = (-1, 0, 2), find the magnitude and direction of
\(\vec{a}-\vec{b}+2 \vec{c}\).
Solution:

Question 15.
Determine the unit vector having the direction of the given vector in each of the following problems:
(i) 5î – 12ĵ
Solution:

(ii) 2î + ĵ
Solution:

(iii) 3î + 6ĵ – k̂
Solution:

(iv) 3î + ĵ – 2k̂
Solution:

Question 16.
Find the unit vector in the direction of the vector \(\overrightarrow{r_1}-\overrightarrow{r_2}\), where \(\vec{r}_1\) = î + 2ĵ + k̂ and \(\vec{r}_2\) = 3î + ĵ – 5k̂.
Solution:

Question 17.
Find the unit vector parallel to the sum of the vectors \(\vec{a}\) = 2î + 4ĵ – 5k̂ and \(\vec{b}\) = î + 2ĵ + 3k̂. Also find its direction cosines.
Solution:

Question 18.
If the sum of two unit vectors is a unit vector, show that the magnitude of their difference is √3.
Solution:

Question 19.
The position vectors of the points A, B, C and D are 4î + 3ĵ – k̂, 5î + 2ĵ + 2k̂, 2î – 2ĵ – 3k̂ and 4î – 4ĵ + 3k̂ respectively. Show that AB and CD are parallel.
Solution:
Given that the
position vector of A = 4î + 3ĵ – k̂
position vector of B = 5î + 2ĵ + 2k̂
position vector of C = 2î – 2ĵ – 3k̂
position vector of D = 4î – 4ĵ + 3k̂

Question 20.
In each of the following problems, show by vector method that the given points are collinear.
(i) A (2, 6, 3), B (1, 2, 7) and C (3, 10, -1)
Solution:
Given that A = (2, 6, 3), B = (1, 2, 7) and C = (3, 10, -1)
Then

(ii) P (2, -1, 3), Q (3, -5, 1) and R (-1, 11, 9).
Solution:
Given that P = (2, -1, 3) Q = (3, -5, 1) and R = (-1, 11, 9)

Hence the points P, Q, R are collinear. (Proved)

Question 21.
Prove that the vectors 2î – ĵ + k̂, î – 3ĵ – 5k̂, 3î – 4ĵ – 4k̂ are the sides of a right angled triangle.
Solution:
Let A, B and C be the points whose position vectors are 2î – ĵ – k̂, î – 3ĵ – 5k̂ and 3î – 4ĵ – 4k̂ respectively.

Question 22.
Prove by vector method that:
(a) the medians of a triangle are concurrent;
Solution:

The symmetry of the result shows that the point G also lies on the other two medians.
Hence the medians are concurrent. (Proved)

(b) the diagonals of a parallelogram bisect each other;
Solution:

(c) the line segment joining the midpoints of two sides of a triangle is parallel to the third and half of it;
Solution:

(d) the lines joining the midpoints of consecutive sides of a quadrilateral is a parallelogram;
Solution:

⇒ SR = PQ and SR || PQ
Hence PQRS is a parallelogram.
(Proved)

(e) in any triangle ABC, the point P being on the side \(\overrightarrow{B C} \text {; if } \overrightarrow{P Q}\) is the resultant of the vectors \(\overrightarrow{A P}, \overrightarrow{P B}\) and \(\overrightarrow{P C}\) then ABQC is a parallelogram;
Solution:

Hence ABQC is parallelogram. (Proved)

(f) In a parallelogram, the line joining a vertex to the midpoint of an opposite side trisects the other diagonal.
Solution:

⇒ P divides BD into the ratio 1 : 2.
Similarly we can show that Q divides BD into the ratio 2 : 1.
Hence P, Q are the points of trisection of the diagonal BD. (Proved)

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 2 Solutions Short Stories Chapter 1 The Happy Man Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Short Stories Chapter 1 The Happy Man

Section-I

Questions For Discussion

Question 1.
Why was the narrator always hesitant to give advice?
Answer:
The narrator has always hesitated to give advice because how can one advise another how to act unless one knows that other is as well as one knows oneself?

Question 2.
“Each of us is a prisoner in a solitary town How does this statement reflect on human life?
Answer:
Everybody is in shackles. Man is not free. All human beings are like creatures in bondage and he is unable to take any independent decisions.

Question 3.
Does the paragraph logically lead to the story? Where do you find the connection?
Answer:
Yes, the paragraph is logically connected which leads to the story, “Life in a difficult ‘ business…provides the clue.

Question 4.
Why did Stephens meet the narrator? What made him do so?
Answer:
Stephens had come to meet the narrator of the story to know whether any English doctor has worked in Spain. He did so because the narrator had written a book on that.

Question 5.
What impression do you form about Stephens from his account of life at Camberwell? Is he happy with it?
Answer:
Stephens was a doctor who had been brought up by two old aunts. He was poor and had been married six years ago. He had no children.

Question 6.
Why does he want to go to Spain?
Answer:
There was no English doctor in Spain and the present lifestyle which he did not relish made him want to go to Spain.

Question 7.
Would you call him a romantic? Give reasons for our Answers
Answer:
Themainwasromantic who gave more emphasis on emotion without thinking about the fixture.

Question 8.
What does the narrator suggest to Stephens finally?
Answer:
The narrator finally suggested Stephensifhe did not want money and was content to earn just enough to keep body and soul together, he should go. Because he would lead a wonderful life.

Vocabulary
Derive adjectives from the following:

wonder	Spain
habit	absence
hesitate	confidence
emotion	thought
occasion	book
difficulty	silence
satisfaction	apology
quickly	laugh
practice	preciously
feet	marriage
mind	force
knowledge	face
information	hair
	money

Answer:
Words – AdjectiveForms
wonder – wonderful
habit – habitual
hesitate – hesitant
emotion – emotional
occasion – occasional
difficulty – difficult
satisfaction – satisfactory
quickly – quick
practice – practical
feet – factual
mind – mental
knowledge – knowledgeable
information – informative
thought – thoughtful
book – bookish
Spain – Spanish
silence – silent
absence – absent
confidence – confident
apology – apologetic
laugh – laughable
preciously – precise
marriage – marital
force – forcible
face – facial
hair – hairy
money – monetary

Section -II

Questions For Discussion

Question 1.
What change in place and time do you find in this section of the story?
Answer:
There is a change in place and time in this section of the story. The doctor has shifted to Spain and the time gap is around fifteen years.

Question 2.
Why does Stephens refuse to accept fees from the narrator? Do his words acknowledge his gratitude for the right suggestion of the narrator given to him years ago?
Answer:
Stephens refused to accept fees from the narrator as a token gesture of gratitude for the right suggestion the narrator had given to him a year ago.

Question 3.
What impression would you get about Stephens from his changed appearance
Spain?
Answer:
The changed appearance of Stephen in Spain suggests that he has become fit and bold. There is a sea change in his physical body politics.

Question 4.
In which context does Stephens say, “life is full of compensation’? What light does it draw on his character?
Answer:
When the narrator asked that he was married Stephens expressed his sorrow to say about his wife who did not like Spain and went back to Camberwell where she felt homely. He said, ’’Life is full of comprehension. This makes clear that Stephens had accepted the gains and losses of life.

Question 5.
Does the concluding passage reveal an attitude toward life? What kind of attitude
would you call it?
Answer:
The concluding passage of the story reveals an attitude toward life. It tells the man to earn just enough money to keep body and soul together.

Question 6.
Where does happiness lie in the word of the protagonist?
Answer:
According to the protagonist, happiness lies in earning just enough money to keep the body and soul together, and in enjoying life being poor.

Question 7.
Does the narrator favor a life of emancipation from conventionalities and stereotypes?
Answer:
The narrator favors a life of emancipation from the conventionalities and stereotypes of life warranting man together self and riches. But the narrator tells that one can enjoy life being poor.

Question 8.
Which one of the following do you find in Stephens that most appropriately
characterize him?
(a) a cynical attitude
(b) a pleasure-loving temperament
(c) morbidity born of frustrations
(d) A quest for freedom from conventions
Answer:
(d)Aquest for freedom from conventions

Question 9.
Can you guess what could happen if his wife had not deserted him?
Answer:
He could not have been free to go to Spain.

Question 10.
Can you call him “TheHappyMan”? Give reasons for your answer.
Answer:
He is “The Happy Man” because he is quite free and he enjoys life even in being poor. He does not run after money.

Questions For Composition

Question 1.
…………………. but by heaven I’ve enjoyed myself. I could not exchange the life I have had with that of any kind in the world”. Make a critical estimate ofStephensin the light of the given statement.
Answer:
The short story’s happy man” is written by William Somerset Maugham, an eminent and outstanding storyteller. He has written more than 100 stories. However, his stories express a realistic portrait of the degenerated society given to selfish pleasure and hedonism with no respect for human values or scruples encompasses a large area of human experience. In this light, Maugham’s story is superb and fantastic. It is really, the most typical story fall is a collection. However, the present story reveals that Stephens may not embody the essentials and philosophy of a happy man in a metaphysical sense, but projects undoubtedly a new vision and perspective.

What we notice is intimist spiritual attainment, but an abandonment of took-for-granted life and relationship in favor of a life of sunshine, color, and mirth. In him is there a quest for freedom and the pursuit of bohemian life. Maugham seems to provide a new pattern and direction to life through his protagonist. Yet the undertone of irony is apparent to the discerning reader. However, Stephens, following the suggestions of the narrator decided to stay in Spain. He went there at last. His wife did not back to Camberwell where she was even more Homely. But he enjoyed his work in Spain. He was very fat and bold. But his eyes twinkled gaily and his fleshy, red face bore an expression of perfect good humor.

The clothes he wore were terribly shabby. He earned just enough money to keep his body and soul together, but he should lead a wonderful life. Poor has he been and poor shall he always be, but by heaven, he has enjoyed himself. He says emphatically that he would not exchange the life he had with that of any king of the world. As a matter of feet, Maugham’s treatment of life through Stephens is most fascinating and heart-touching Maugham is, in fact, a keen observer of human attitude, on the whole, he has tried his level best to depict a full-fledged manner. Therefore, the way he has portrayed Stephens is superb and fantastic.

Question 2.
Critically comment on the title of the story.
Answer:
The short story“The happy man” is undoubtedly the best typical masterpiece of William Somerset Maugham, a prominent and outstanding storyteller of the twentieth century. Maugham is a prolific writer writing novels, short stories, plays, etc. in one. Hismasteryto provides appropriate titles to his writings is really outstanding. He has written more than 100 short stories. All these are repleted with a realistic portrait of the selfish pleasure and hedonism of society. However, the title of the work of art must be apt and suggestive. It should be precise, concise, and condensed.

Its motto should be to communicate reality vehemently. It should be just like a gorgeous, colorful signboard. It also speaks out the contents, of the shop from its very appearance. The titles are expressive of the contents of the work of art. The story, here, tells us about the life of a man who happens to be the happiest. However, Stephens comes to the narrator to know whether it would be better to go to Spain as a doctor. His future was involved in it and the narrator suggested to him that he had to earn just enough money to keep his body and soul together. He, however, decided to go there. But he was married. His wife did not cooperate with him. She never likes Spain and went back to Camberwellwhere she felt homely.

Stephens went alone and lived there happily. He led a wonderful life there. Poorhehadbeen and enjoyed himself like anything. He would not exchange the life he had with that of any kind in the world. The last lines of the story are themselves expressive of the feet that the protagonist of the story “TheHappyMan” has. The title bears the justification for the right caption of the story. As a matter of fact, the title of the story is most appropriate and suggestive. The way Maugham justified Stephens as the happiest man is really superb, alluring, elevating, and excellent.

Vocabulary
Derive nouns forms the following:

excavate	crucial
lovely	cruel
monumental	casual
interesting	occasional
arrogant	perceptive
expect	deceive
ideological	receive
rigorous	credulous
logical	rival

Answer:

Words	Noun forms
excavate	excavation
expect	expectation
lovely	love
ideological	ideology
monumental	monument
rigorous	rigorousness
interesting	interest
logical	logic
arrogant	arrogance
crucial	independence
cruel	cruelty
casual	casualty
occasional	occasion
perceptive	perception
deceive	deceit/deception
receive	receipt
credulous	credulity
rival	rivalry

Grammar
Supply suitable articles:

1. He is_________ M.A
Answer:
He is an M.A

2. I drank________ cup red tea.
Answer:
I drank a cup of red tea

3. I have not seen such_______  temple.
Answer:
I have not seen such a temple

4. He is_____ eunuch.
Answer:
He is a eunuch.

5. The cow is_______useful animal.
Answer:
The cow is a useful animal.

6. I covered_____half a mile.
Answer:
I covered a half mile

7. He is ______washerman.
Answer:
He is a washerman.

8. He is_______honourable man.
Answer:
He is an honorable man.

9. She is__________M.L.A.
Answer:
She is an M.L.A.

10. He is_______M.P.
Answer:
He is an M.P

11. Gopalis________beggar.
Answer:
Gopal is a beggar.

12. I saw_________tiger.
Answer:
I saw a tiger

13. ________cow is auseful animal.
Answer:
A cow is a useful animal.

14. _______poor should be helped.
Answer:
The poor should be helped.

15. He is _______one-eyed man.
Answer:
He is a one-eyed man.

16. Hari is___farmer.
Answer:
Hari is a farmer.

17. Give me____umbrella.
Answer:
Give me an umbrella.

18. She saw_______tiger_______forest.
Answer:
She saw a tiger in a forest

19. ______brave should be rewarded.
Answer:
A brave should be rewarded

20. What__________big temple.
Answer:
What a big temple.

21. There was______little water in the glass.
Answer:
There was a little water in the glass.

22. Rambabu is______ readerin English.
Answer:
Rambabu is a reader of English

23. ______universities cricket team came to this place to play a friendly match.
Answer:
A university cricket team came to this place to play a friendly match.

24. Give me __________ half kilo potato.
Answer:
Give me a half kilo of potato.

25. ___________ few people were present in the meeting.
Answer:
A few people were present at the meeting.

26. I like _________ red wine with lunch.
Answer:
I like a red wine with lunch.

27. London is_________ city.
Answer:
London is a city.

28. We electedhim as__________ M.L.A.
Answer:
We elected him as an M.L.A.

29. __________Ramayan is_______ famous epic.
Answer:
The Ramadan is a famous epic.

30. I shall backin__________hour.
Answer:
I shall be back in an hour.

31. I read_________Prajatantra every day.
Answer:
I read the Prajatantra every day.

32. He is holding________umbrella.
Answer:
He is holding an umbrella

33. He is__________ one – eyed.
Answer:
He is a one-eyed.

34. I like thebeauty of__________ Himalayas.
Answer:
I like the beauty of the Himalayas

35. ___________elephant is a strong animal.
Answer:
An elephant is a strong animal.

36. I like to give_________ useful present.
Answer:
I like to give a useful present.

37. London is in _________ Thames.
Answer:
London is in the Thames.

38. Is there_______ school in this town?
Answer:
Is there a school in this town?

39. He is__________ principalofour college.
Answer:
He is the principal of our college.

40. He is________lecturer.
Answer:
He is a lecturer.

41. _________Mahanadi is the longest river of Odisha.
Answer:
The Mahanadi is the longest river in Odisha.

42. He is__________ lecturer.
Answer:
He is a lecturer.

43. I saw_______ snake and_______ snake rushed towards me.
Answer:
I saw a snake and the snake rushed towards me.

44. I went by_________ Konark Express.
Answer:
I went by the  Konark Express.

45. She is___________ actress.
Answer:
She is an actress.

46. I like________ mangoes you eat.
Answer:
I like the mangoes you eat.

47. He is speaking like __________ Kalidas.
Answer:
He is speaking like a Kalidas.

48. She is________ mostbeautiful womanofour village.
Answer:
She is the most beautiful woman in our village.

49. He is____________first person to come.
Answer:
He is the first person to come.

50. There was__________ temple.
Answer:
There was a temple.

51. Sitais swimmingin __________ pond.
Answer:
Sita is swimming in thepond.

52. He aremaking__________union.
Answer:
He is making a union.

53. _______ Gita is_________ sacred book.
Answer:
The Gita is a sacred book.

54. He is________ European.
Answer:
He is a European

55. It is _________ great honor to be invited to the ceremony.
Answer:
It is a great honor to be invited to the ceremony

56. _________ I have a glass of milk.
Answer:
Could I have a glass of milk?

57. I _________ be twenty on my next birthday.
Answer:
I will be twenty on my next birthday.

58. Why_________ women be paid less than men for doing the same?
Answer:
Why should women be paid less than men for doing the same?

59. I________wear a coat today it is quite warm.
Answer:
I need not wear a coat today it is quite warm.

60 __________ I close the door.
Answer:
Shall I close the door?

61. It mayrain you_________ carryan umbrella.
Answer:
It may rain you should carry an umbrella.

62. It is late. You __________ go to bed.
Answer:
It is late. You should go to bed.

63. You_______hurry, there is enough time.
Answer:
You need not hurry, there is enough time

64. __________ you lend me your pen, please.
Answer:
Could you lend me your pen, please

65. India_________ take active steps to reduce population growth.
Answer:
India should take active steps to reduce population growth.

66. _______ you open the window, please?
Answer:
Could you open the window, please?

67. I am afraid the weather____________not improve for another two or three days.
Answer:
I am afraid the weather might not improve for another two or three days

68. You________respect your teacher.
Answer:
You should respect your teacher.

69. ________you stand on your hands.
Answer:
Can you stand on your hands?

70. After four he______ write well.
Answer:
After four he could write well.

71. __________ you lend me Rs 50?
Answer:
Could you lend me Rs 50?

Section-I

Pre-reading activity:
You might have at times thought about who a happy man is. What do you think brings happiness to one’s life?
(i) It is something related to wealth and material comforts.
(ii) Or is it purely a state of mind, with nothing much to do with one’s financial status or social or social position?
(iii) Does it he in a life of adventure and romance, a life of freedom and carefree enjoyment away who is a happy man?

Notes On The Writer:
William SomersetMaugham(1874-1965) is a prolific writer of the twentieth century having to his credit about 17 novels, 32 plays, more than 100 short stories, two travelogues, and two treatises containing his views of life and literature. Amonghisnovels “OfHumanBondage”. “The Moon and Six Pence” “The Printed VeilCakes and” and ‘The Razor’s Edge” have earned him critical acclaim.

His novels, plays, and short stories give a realistic portrait of a degenerate society, a society given to selfish pleasures and hedonism with no respect for human values or scruples encompassing a larger area of human experience. Most of them depicted the crumbling of the institution of marriage, which has almost become a tightrope around the neck of the spouse’s affair, such indulgences often leading to promiscuity. With deft and dexterous use of irony and satire, his vision grows from a study of the wider spectrum of life to an affirmation of its meaning at the individual level.

The Story:
A careful reading of the story reveals that Stephens may not embody the essentials and philosophy happy man in a metaphysical sense, but projects undoubtedly a new vision and perspective. What we notice is intimist spiritual attainment but an abandonment of taken-for-granted life and relationship in favor of a life of sunshine, color, and mirth. Intimate there is a quest for freedom and the pursuit of bohemian life. Maugham seems to provide a new pattern and direction to life through his protagonist. You have the undertone of irony apparent to the discerning reader.

GIST:
Paragraph -1
It is a dangerous thing to order the lives of others and it has been often a wonder that the politicians, reforms, and such like who are prepared to force upon their fellow measures that must alter their manners, habits, and points of view making a strong confidence in this regard. The thoughts and emotions of the neighbors can only be guessed. Life is a difficult business and it is found hard enough to make a complete and rounded thing.

GIST:
Paragraphs (2-3)
The narrator was a young man who lived in a modem apartment in London near Victoria Station. Late one afternoon, when he was beginning to think he had worked enough for that day, he heard a ring at the bell. He opened the doorto atotal stranger. He asked the narrator’s name. He asked to come in and he did it instantly. He led the stranger to his sitting room and told him to sit down. He seemed a trifle embarrassed. He also offered him cigarettes.

Gist:
Paragraphs (4-10)
The stranger said that his name was Stephens and he was a doctor. He said that the has read a book by the narrator about Spain and he wanted to ask him about that. The book is not so good. The fact remains that he knows something about there’s no one else who knew it so well. He was silent for a movement. He reached out for his seat and held. It is one hand absentmindedly stroking it with the other. He surmised that it gave him confidence.

Gist:
Paragraphs – (11-12)
He was brought up by two old aunts. He has never been anywhere. He has been married for six years. He has no children. He is a medical officer at the Camberwell Infirmary. There was something very striking in the short, sharp sentences he used. They heard a force bring. He had ’ not given him more than a cursory glance, but then looked at him with curiosity. He was a little man. thick-set and stout of thirty perhaps, with around red face from which store small, dark, and very bright eyes. His black hair was cropped close to a bullet-shaped head. He was dressed in a blue suit a good deal the worse for wear.

Gist:
Paragraphs – (13-22)
He again said that I must know what the duties of a medical officer in an infirmary are! One day is much like another and that’s all he has got to look forward for the root of his life. The narrator said that it was a means of livelihood; the one is pretty good and interrogated whether he thought there would be any change for an English doctor in Spain.

He continued that it was not like caramels, but there was sunshine, good wine, and color and there is the air you can breathe. He said that he heard by accident that there was no English doctor in service. It could be foolish on his part to give a good safe job for an uncertainty. His wife was also willing to his leaving the house. The narrator said that the doctor would lead a wonderful life. He left him.

Analytical Outlines

• It is a dangerous thing to order the lives of others.
• It has been often a wonder.
• However, the politicians, reformers, and such people.
• They prepare to force upon their fellows.
• They may have a view about their manners, habits, etc.
• They make strong confidence in this regard.
• The thought and emotions of the neighbor can only be guessed.
•  Life is a difficult business.
•  It is found that it is very hard to make a complete and minded thing.
• The narrator was a young man.
• The narrator was a young man.
• He lived in a modest apartment.
• He was; thinking one afternoon.
• He had worked enough for that day.
• He heard a ring at the bell.
• He opened the door.
• He found a stranger.
• He asked the narrator his name.
• He asked him to come in.
• He did it instantly.
• He led the stranger to his sitting room.
• The narrator told him to sit down.
•  He seemed a trifle embarrassed.
• He also offered him cigarettes.
• The stranger’s name was Stephens.
• He was a doctor.
• He said that he had read a book.
• The book is written by the narrator.
• The book was written about Spain.
• He wanted to ask him about that.
• The book is not so good.
• The feet is that he knows something about that.
• No other one knew so well.
• He was silent for a moment.
• He reached out for his head.
• He reached out for his holding.
• He absentmindedly stroked it with the other.
• He surmised about it.
• It gave him confidence.
• He was brought up by two old aunts.
• He has never been anywhere.
• He has been married for six years.
• He has no children.
• He is a medical officer.
• He is an officer at CambrewellInfirmacy.
• There was something very striking.
• He used short, sharp sentences.
• They heard a force bring.
• He had not given him more than a cursory glance.
• He looked at it with curiosity.
• He was a little man.
• He was thick-set.
• He was stout of thirty.
• He was with a round face.
• He was dark and very bright eyes.
• His black hair was cropped.
• It cropped close to a bullet-shaped head.
• He was dressed in a blue suit.
• It was worse for wear.
• He knew the duty of a medical officer.
• One day is much like another.
• That’s all he has got to look forward to for the livelihood.
• Themoneyispretty is good.
• It is interrogated why he had gone to him.
• He replaced to this question.
• He wanted to know about the chance of an English doctor in Spain.
• He said that it was not like carmen.
• But, he found there sunshine and good wine.
• He accidentally heard about something.
• There was no English doctor in service.
• It could be foolish to get a good job there.
• I was not certain about it.
• His wife was also willing to his leaving the house.
• The narrator said that the doctor would lead a wonderful life.
• He left him.

Meaning Of Difficult Words

flounder – to stumble, to thinking or speaking
confidence – reliance, trust
modest – humble, bashful
embarrassed – immediately, on the spur of the moment
stroked – disheartened, distressed
instantly – blow, an attach, abeat of pulse
surmised – doubted
glance – look
curiosity – anxious to learn, inquisition
stout – strong, robust
cropped – produced
pretty – beautiful, pleasing
interrogate – to question, to examine
infirmary -a hospital or place for the treatment of the sick
carmen – an opera(1 875) by George Bizet.

Section -II

Gist:
Paragraphs – (23-25)
Fifteen years passed by. The narrator happened to be in service and having some trifling indication asked the hotel porter whether there wasinEnglishdoctorinthe town. He said positive and gave him the address. He took a cab and when he reached the house, a little fat man came out of it. He hesitated when he caught sight of the narrator explaining his purpose and the doctor asked him to go in.

He lived in an ordinary Spanish house, with a patio and his consulting room which led out of it was littered with papers, books, medical appliances, and lumber. They finished the business and he asked the doctor what his fee was. The doctor shook his head and smiled. He said that there was no fee. He asked the narrator whether he remembered why the doctor had been there. It was because of something he had once said to him. His life changed only for the narrator, the doctor admitted. He said he was Stephens.

Paragraphs (26 – 28)
The narrator had forgotten all about it. He had not the least notion of what he was talking about. He remembered him of their interview and the narrator after a lot of thinking recalled the matter. Stephens did not believe he could get a chance to have sight of the narrator to give thanks to him for what he had done for him. The narrator looked at him. He was very fat and bold, his eyes twinkled gaily and his fleshy, red face bore an expression of perfect good humor. The clothes he wore were terribly shabby.

Gist:
Paragraphs (29-33)
The narrator asked whether Stephens had gotten married. Stephens replied in negative. Hardly and Stephens replied when a Spanish woman, no longer in her first youth, but still boldly and voluptuously beautiful appeared at the door. She spoke to him in Spanish and the narrator believed that she might have been theirs. of the house.

As he stood at the door to let the narrator out he said that later told him when he saw him lost that the former would go to Spainhe should earn enough money just to keep body and soul together but he should live a wonderful life. And the narrator was perfectly right. He has been and will be poor but he has enjoyed life to the brim.

Analytical Outlines

• Fifteen years passed by.
• The narrator happened to be in service.
• He has some trifling indisposition.
• He asked the hotel porter something.
• He asked if there was an English doctor in the town.
• He answered positively
• Then he gave him the address.
• He looked cab.
• He reached the house.
• A little fat man came outfit.
• He hesitated when he caught the sigh of the narrator.
• The narrator explained his purpose.
• The doctor asked him to go in.
• He lived in an ordinary Spanish house.
• He was living with a patio.
• He has a consulting room
• It was uttered with papers.
• It was uttered with books.
•  It was also littered with medical appliances and lumber.
• They finished the business.
•  He asked the doctor about his fees.
• The doctor shook his head.
• The doctor also smiled.
• He said that there was no fee.
• He asked the narrator something
• Whether he remembered why the doctor had been there.
• It was because of something he had once said to him.
• His life changed only for the narrator.
• The doctor admitted this.
• He said he was Stephens.
• The narrator had forgotten all about it.
• He had not the least notion.
• He was not concerned about what he was talking about.
• He reminded him of their interview.
• After a lot of thinking, the writer recalled the matter.
• Stephens did not believe it.
• He would get a chance to meet the narrator again.
• So that he would thank him for that.
• He thanked him for what he had done for him.
• The narrator looked at him.
• He was very fat.
• He was also very bold.
• His eyes twinkled gaily.
• His fleshy red face bore on expression.
• It was with perfect good humor.
• He wore terribly shabby clothes.
• The narrator asked whether Stephens had gotten married.
• Stephensrepliedinnegative.
• A woman appeared all the door.
• She was a Spanish woman.
• She was no longer in her first youth.
• But still, she was bold.
• She was voluptuously beautiful.
• She spoke to him in Spanish.
• The narrator believed that she might have been the Mrs. of the house.
• He stood at the door to let the narrator out.
• He said that the latter told him when he saw him last.
• The former would go to Spain.
• He should earn enough money there.
• He has just to keep body and soul together.
• But he should live a wonderful life.
• And the narrator was perfectly right.
• He has been and will be poor.
• But he has enjoyed life to the brim

Meaning Ofdifficult Words

trifle – unimportant
indisposition – un arrangement, un distribution, unplanned
porter – doorkeeper, a coolie
cab – covered four or two-wheeled carriage cabriolet
hesitate – to stop making a decision
litter – to cover with strew, to bring forth
appliances – instruments used for some special-purpose
lumber – a useful article, furniture stored away.
errand – business, purpose
patio – courtyard
admit – allow to enter
twinkle – to blink, to glitter, to shine
shabby – mean, low, paltry
boldly – courageously, daringly
sombrero – Aman’s hat with every wide brim which sowed especially in Mexico.
dissipated – drunken
voluptuously – luxuriously sensual
silenus – any group of forest spirits similar to stars but having the legs of horses.

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 2 Solutions Poem 5 Toads Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Poem 5 Toads

Pre-Reading activity:
What ideas do you associate with Toads? List them here… The poem you are going to read now has the title “Toads”. See if the ideas you associate with Toads are reflected in the poem. Your focus, however, should be on finding answer to. Is it real Toads that the poem is about? If not, what does the poet mean by Toads?

Notes On The Poet:
Philip Larkin (1922-1995) is one of the outstanding poet of the post-war generation of poets. His volumes – include “The North Ship” (1 995) and “The Less Deceived” (1955). His poetry responds to all he tints and flavours of provinced life. His sensitivity to human “absurdity and pathos” is strongly marked in many of his poems. The poem “Toads” is expressed the poet’s disgust with a vice-like grip of a routined engagement.

Questions For Discussion:

Question 1.
What does the poet mean by toads?
Answer:
The poet means by toads that they sit heavy with their hunkers which are as cold as snow.

Question 2.
How do the two questions with which the poem begins set the tone of the poem?
Answer:
The poet is disgusted with the toad that squats on his life. He wishes to drive it off. The tone marks a reaction against the ill luck of life.

Question 3.
The thing that oppresses the poet is first called “the toad” then “the brute” then “it”. Does this convey the poet’s progressive indifference to the creature? What else could this convey?
Answer:
The use of “the toad”, “the brute” and “it” display the poet’s progressive indifference to the creature. It also conveys an irksome attitude of the poet to the creature.

Question 4.
Which stanza expresses the poet’s intense disgust? What is he disgusted with?
Answer:
The poet is disgusted with a vice-like grip of a routined engagement.

Question 5.
Identify the stanza where alliteration is most pronounced? What purpose does it serve?
Answer:
Alliteration is the repetition of consonant speech sounds in the sequence of nearby woods. This is prominent in “Lots” of folk five on their wits/lecturers, lispers/losels, loblolly men, louts …”

Question 6.
What is the poet’s attitude to the people ‘who live on their wits? Why does he cite their examples?
Answer:
The poet holds a positive view for the people who live on their wits. He cites examples of witty persons because they don’t end as paupers.

Question 7.
What can the poet mean by the expression “Their unspeakable wives”?
Answer:
The wives are unspeakable because they cannot be studied and spoken off. They are unscrutable and unspeakable. They are as skinny as whippets.

Question 8.
What is the poet’s wish in Stanza 6?
Answer:
The poet says this in Stanza 6 which reflects an unpleasant experience. When one does not want the pension that is offered and one get’s angry.

Question 9.
In the first stanza the poet says “why should I let the toad work/squat on my life; in Stanza 7 he says” “For something sufficiently toad-like / squats in me too.” Are they two different squatters? Is there a difference of mood between Stanza -1 and Stanza – 7?
Answer: The squatter in stanza- 1 and the one in Stanza- 7 are different squatters. There is a difference of mood between Stanza- 1 and Stanza – 7.

Question 10.
What does the poet require from life? Is he frustrated because he can’t get “All at one sitting”?
Answer:
The poet requires a free and enchanting life rather than the routined engagement. He is not frustrated as such in the lines indicated.

Question 11.
The poet is a deft manipulated of words but he envies those who make a living through unscrupulous manipulation of words, who “blarney” their way to success. What could he mean would you consider it mock modesty?
Answer:
The poet through his enjoy of those who make a living through unscrupulous manipulation of words is quite choosy and idealist in employing right words in the right situations. It can be termed as a mock modesty.

Question 12.
What do these lines mean? Attempt a simple and brief paraphrase.
“I don’t say, one bodies the other
One’s spiritual truth
But I do say it’s hard to lose either.
When you have both”.
Answer:
These lines have a bearing with the previous lines. Something to ad-like sits in him heavy with its hind legs which never allow to blarney his way to getting the feme, the girl and the money all at one sitting. He does not say that one bodies the other one’s spiritual truth. It is also difficult to lose either of the two in the event of having the both.

Composition:

Question 1.
Assess the significance of the little “Toads”?
Answer:
The poem ‘Toads” is composed by Philip Larking, an eminent and out-standing poet of the post-war generation. His poetry responds to all the tints and flavours of provinced life. He has indeed great mastery in proving apt and suggestive title to his poems. His quality in this sense is superb and fantastic. This is a typical poem demonstrating this quality.

However, the title of work of art must be pointed, precise, concise, sharp and suggestive. It should be lie a colourful and attractive signboard which attracts the attention of the customers instantly. It can also show the inside contents of the shop. Similarly an attractive and suggestive title makes the reader spell bound to go through the piece of writing with much interest and fascination. The discussing poem ‘Toads” is sucha poem which satisfies all the characteristics of a good title. Toads are very inactive, rough and ugly creatures that sit heavy hindering its and other progress simultaneously.

The little taken from these living makes it clear that the toads keeping hanging on the poet which hinder his progress. Moreover, the poet starts the poem with two questions at the outset of the poem. One, “Why should I let the toad work/squat on my life?” Second, can I use my wit as a pitchfork/And drive the brute off?” The second stanza of the poem says that the toad soils six days of the week with its sickening poison just for paying a few bills that is out of proportion. A lot of people live on their wits. Lecturers, lispers, losels, loblolly- men, louts don’t end as paupers. Yet many more people live up lanes with fires in a bucket that eat winds falls and tinned sardines and seem to like it.

In the fifth stanza, the poet says that their children here got bare feet, their unspeakable wives are skinny as small thin racing dogs and yet no one actually stores. Had he been courageous enough to shout “stuff your pension” but he knows, all too well, that is the stuff that dreams are made on. In the seventh, eighth and ninth stanzas, the poet continues his thoughts saying that for something sufficiently toad-like squats in him to blarney his way to getting the fame and the girl and the money all at one sitting. He does not say that one bodies the other one’s spiritual truth but he does say that it is hard to lose either when one has the both. As a matter of fact, it is very much clear from the above description that, the title of the poem is apt and suggestive. The poet’s explanation about the toads as really fantastic, outstanding, though-provoking and appropriate.

Question 2.
Write an appreciation of the poem. First state the theme and say briefly how this theme is related to “Toads”. Then discuss how the problem is introduced and elaborated in the poem and whether there is any suggestion of a resolution of the problem. Also examine how the introducing stanza and the concluding stanza are related to each other and so the stanza in between. Identify the unusual words in the poem, if you find any and point out their relevance in the poem. And conclude your appreciation with your personnel response to the theme and its treatment in the poem.
Answer:
In fact, Philip Larkin’s poem ‘Toads” is his superb and fantastic composition. Here he expresses his disgust with a vice like grip of routined engagement. It is such a poem which satisfies the characteristics of a good poem. Toads are very inactive, rough and ugly creatures,
that sit heavy hindering its and the other’s progress simultaneously. The title taken from these living beings makes it clear that the toads keep hanging on the poet which hinder his progress.

However, the poet starts the poem with two questions at the outset of the poem One is –
“why should I let the toad work/squat on my life”? The second one is – “can’t I use my wit as a pitch work /And drive the brute off?” The second stanza of the poem says that the toad soils six days of the week with its sickening poison just for paying a few bills that is out of preparation. A lot of people live on their wits. Lecturers, lispers, losels, loblolly-men, louts don’t end as paupers yet, many more people live up lanes with fires in a bucket that act windfalls and tinned sardines and seemed to like it.

Moreover, the poet delineates in the fifth stanza that their children have got bare feet; their unspeakable wives are skinny as small racing dogs and yet no one actually shores”, but he knows all two well, that is the stuff that dreams are made on. In the seventh, eighth and ninth stanza the poet continues his thought saying that for something sufficiently toad like squats in him too. Its hind legs are so heavy that they are as hard luck and cold as snow which will never allow him to blarney his way to getting the fame and the girl and the money all at one sitting.

He does not say that one bodies the other one’s spiritual truth but he does say that it is hard to lose either when one has the both.
The presence of alliteration which is a repetition of speech sounds in the sequence of nearby words makes the poem very effective. The initial’s sounds in the words ‘six’ ‘soils’ and the final ‘s’ sound in the words- ‘that’s, ‘proportion’; The I sounds in ‘tots’ ‘folk’, ‘live’, ‘lecturers’, ‘lispers’, ‘losels’, ‘loblolly-men’, Touts’ etc. are the alliterative sounds that enrich the poem As a matter of feet, the poem ‘Toads” of Philip Larkin is a typical masterpiece of suggestion which teaches and delights at one. The way he conveys the theme through toads is really superb
and outstanding. One the whole, the poem is inspiring, thought-provoking, elevating and heart-touching.

Toads Summary in English

Why should the speaker let the toad work and quat it on his life? Whether he can use his intelligence as a pitch form and drive the brute off. It soils six days out of seven with its sickening poison. A lot of people live on their wits. Lecturers, lispers, losels, loblolly-men, louts don’t end as paupers. Lots of people also live up lanes with files in a bucket and act windfalls and tinned surdines. Their children have got bare fact. Their unspeakable wives are skinny as whippets and no one actually stars. The speaker can’t have say to shut “stuff your pension”. But he knows everything very well that dreams are made on Because something sufficiently toad-like sits on him and its hunkers are heavy as hard luck and cold as snow and will never allow him to talk pleasant but untrue things in order to convince or persuade people. He wishes to get the fame and the girl and the money all at one sitting. He does not say that one bodies one other one’s spiritual truth but he says it is hard to lose either when both are heard.

Analytical Outlines:

• The poet begins the poem with a question.
• Why should the speaker let the toad work and quit it on his life?
• Whether he can use his intelligence.
• He can use it as a pitchfork.
• He can drive the brute off.
• It soils six days out of seven.
• It soils with its sickening poison.
• A lot of people live on their wits.
• Lecturers and whispers don’t end as paupers.
• G. Losels, loblolly-men, and louts don’t end as paupers.
• Lots of people also live up lanes.
• They live up with fires in a bucket.
• They act windfalls.
• They act tinned surdines.
• Their children have got bare feet.
• Their unspeakable wives are skinny.
• They are skinny as whippets.
• No one actually starves.
• The speaker shouts something.
• He shouts, “stuff your poison”.
• But he knows everything very well.
• He knows that dreams are made on.
• Because, something sufficiently toad-like sits on him.
• Its hunkers are heavy.
• These are like hard hick.
• These are as cold as now.
• They will never allow him to talk pleasant.
• They will never allow him untrue things in order to convince or persuade.
• He wishes to get the fame.
• He wishes to get the money all at one sitting.
• He does not say that one bodies the other one’s spiritual truth.
• But he says it is hard to lose.

Meaning Of Difficult Words:

squat – to sit on one’s heels.
pitchfork- a fork with a long handle.
wit- intelligence
lispers- those who speak with a speech fault
losels- loafers.
loblolly-men- those who trick others into giving them money.
louts- rude, violent men.
windfalls- fruits blowing offa tree
sardines- small young fish that are often pecked in flat metal boxes.
whippets- small thin racing dogs
nippers- children.
stuff your pension- you say this when you do not want the pension that is offered and you are angry
hunkers- bent knees while the toad is sitting.
blarney- talk pleasant but untrue things in order to convince or persuade people.

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 2 Solutions Poem 4 Mirror Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Poem 4 Mirror

Pre-Reading activity:
Every one of us looks into a mirror everyday. In which way(s) is a mirror useful to us. Can you list them here? You are about to read a poem named Mirror. Can you guess what this poem tells the reader? Now read the poem and find out.

Notes On The Poet:
Sylvia Plath (1932-1963) in her life, as in her poetry, tried to fuse the role of‘Muse, Mother and Poet”. Her poetry is intensely perporial and powerfully confessional. Notable among her works age. “The Cotossues” (1960) and “Ariel” (1965). In the poem“Mirror” Plath shows how the mirror reflects more than mere images.

Questions For Discussion:
Question 1.
Who is the speaker in the poem?
Answer:
The mirror is the speaker in the poem.

Question 2.
What are the two things that the mirror in the poem reflects?
Answer:
It reflects both love and dislike.

Question 3.
Why is the mirror called the “eye of little God”?
Answer:
The mirror is called the “eye ofa little God” because it accepts reflection whatever it sees.

Question 4.
Why could the poet mean when she says”
“Now I am a lake……….”
Answer:
The poet means that the mirror is a tiny lake which accepts anything that comes its way. It also reflects things exactly like a lake without prejudice.

Question 5.
Why are the candles and moon “liars”
Answer:
The candles and the moon are “liars” because the candles and the moon do not speak of exactly what a women is.

Question 6.
How does the woman react to her reflection in the lake?
Answer:
The woman bends over the mirror lake and searches for what she really is and then turns to the liars.

Question 7.
Would our views of the aging women different if she instead of the mirror had narrated the story?
Answer:
The view would have been different if the aging women instead of the mirror had narrated story. The aging woman would have been a liar.

Question 8.
Here the poet uses at least three of the poetic devices: personification, metaphor and simile. Identify the times where these figures of speech are used.
Answer:
Personification: – “……………… I have no preconceptions\ ……………..I see I swallow immediately………………”.
Metaphor: “I am silver …………….”.The eye of a little god”, “Now I am a lake”
Smile: “Rises towards her day after day.
Like a terrible fish.

Question 9.
“………………….. and in one an old woman rises towards her day after day, like a terrible fish”. What is the significance of the image of a “terrible fish” here?
Answer:
The image of a “terrible fish” stands for the slow movement of time and death which are quite immediate.

Question 10.
Do you agree that the mirror in this poem reflects more than mere images? How sow?
Answer:
The mirror in this poem reflects more than mere images. It speaks the truth; it makes women search for the exactness.

Question 11.
Notice that the first stanza of he poem begins with “I can silver and exact” and the second stanza begins with “Now I am a lake”. Do these two autobiographical statements of the mirror contradict each other? It so, how are they reconciled in the poem?
Answer:
These two autobiographical statements. “I am silver and exact” and “Now I am lake” are two contradictory statements of the mirror. But both these statements and their ideas have reconciled the poem. It indicates that the mirror has two personalities. It is exact and faithful and at the same time profound and deep like a lake. It sometimes deceives in depth and is hence dangerous.

Composition:

Question 1.
Write an appreciation of the poem “Mirror” beginning with a statement of he theme and then proceeding to analyse the poem by lines along with your views regarding their communicative value (= how effectively the lines with their images and other poetic devices. If any communicate an idea). The conclusion would sum up the salient features of the poem and end with your general assessment of the poem.
Answer:
The poem“Mirror” is composed by Sylvia Plath, and eminent and out standing poet of the twentieth century. In her unique approach in English poem, plath is really superb and fantastic. The poem deals with something spectacular about mirror. The mirror as a reflecting device does something more than mere reflection. However, the poem is written in first person narrative giving an auto biographical sketch of the inanimate objects. Of course, the poem reflects life in mirror.

The barrier of the non-living things and rises above the personified in the poem to which human qualities have been attributed. It says that it is silver and exact. It neither exaggerates nor condemns, neither magnifies nor belittles. It speaks of as is it. Treats love and hatred alike. It is unprejudiced and truthful. It is the eye of a little god “The eye of a little god” is a metaphorical expression which tells that it is bright and truthful. Moreover, the second stanza is a continuance of the first one.

The mirror says that it meditates on the opposite wall. It is pink with speckles. Faces and darkness separate them over and over and now it is a lake. It says “Now I am a lake. A woman bands over it searching its reaches for what she really is. Then she turns to those liars – the candles and the moon. It sees her back and reflects it faithfully. She awards it with tears and an agitation of hands. Each day, she has drowned a young girl and in it an old woman rises towards her day after day like a terrible fish.

As a matter of fact the poem is unique attempt at making an imaginative and a thoughtful approach to life. The poet attributes human qualities to the living and non-living things. The approach and technique of the poem are balanced and impressive. On the whole, the poem is most inspiring, elevating and heart-touching.

Question 2.
Basing on what you know of the relationship between the Mirror and the Wall in the poem. Write a dialogue between them on the subject of the world around them.
Answer:
The wall – Good Morning, Miss Mirror
The mirror – Good morning Mr. Wall. How are you?
The wall – Fine, thank you – How are you?
The mirror – Fine, thank you. Why do you look so pensive today? What’s the matter?
The wall – It’s because I didn’t see you yesterday where’d you been?
The mirror – I’s in the bathroom the whole day.
The wall – I haven’t seen himself the whole day.
The mirror – You haven’t seen yourself.
The wall You myself. I seen myself in you everyday. Don’t I?
The mirror – You see yourself in me ! What do you mean?
The wall – Very simple Don’t people see themselves in you?
The mirror – Yes they do. So what?
The wall –  I also see myself in you exactly like that. This is what I do every day.
The mirror – No only you, everything and every bring do the same, don’t they?
The wall – Yes, of course. But there’s a difference.
The mirror – What is it?
The wall – Aren’t you feeling me in the room?
The mirror – Yes, I am. There is a lot of things that face me in the room. Chairs, tables, lights and so on.
The wall – But you are vis-a-vis me, aren’t you?
The mirror – Yes, I’m. So also you.
The wall – I do admit it. Therefore, I see myself in you.
The mirror – You see yourself in me, but I don’t see myself in you!
The wall – No, you don’t, you reflect me and I see myself.
The mirror – Why don’t you reflect me in you?
The wall – No, I don’t reflect anything.
The mirror – Oh! you only take from others, you don’t give.
The wall – Not exactly, I neither take nor give. I’m quite unconcerned.
The mirror- Is it?
The wall – Yes it is.

Mirror Summary in English

The mirror lays that is silver and exact. It has no preconceptions. Whatever it sees it accepts into its delicate surface and produce just as it is. It is unmisted by Love or dislike. It accepts everything be it a thing of love or hatred. It is not cruel. It is truthful. Most of the time-it meditates on the opposite wall. It is pink with speckles. The person who wishes to get his reflection through it looks at it and thinks it as a past of his heart. Faces and darkness separate the on looker and the mirror over and over. The mirror is a lake. A woman bends over it searching her reaches for what she really is. Then she turns to these liars, the candles or the moon. She rewards it with tears and an agitation of hands. It is important to her, she comes and goes. Each morning her face replaces the darkness. She has drowned a young girl and an old woman rises from it towards her(the young girl).

Analytical Outlines:

• The mirror says that it is silver and exact.
• It has no preconceptions.
• It has delicate surface.
• It accepts what it sees.
• It produces just as it is.
• It is unmisted by love.
• It is also unmisted by dislike.
• It accepts everything.
• It may be love.
• It may be hatred.
• It is not cruel.
• It is truthfull.
• Most of the time, it meditates on the opposite wall.
• It is pink with speckles.
• A person wishes to get his reflection.
• He looks at it.
• He thinks it as a part of his heart.
• Faces and darkness separate the onlooker and mirror over and over.
• The mirror is a lake.
• A woman bends over it.
• She searches her reaches for.
• She searches in it what she really it.
• Then she turns to those liars.
• She turns to the candles.
• She turns to the moon.
• She rewards it with tears.
• She rewards it with an agitation of hands.
• It is important to her.
• She comes and goes.
• Each morning, her face replaces the domes.
• Each morning her face replaces the darkness
• She has drowned a young girl.
• An old woman rises from it towards her.

Meaning Of Difficult Words:
preconceptions- opinions formed before knowing actual facts.
accept – to receive, to agree to
delicate- pleasing, graceful, tender
unmisted- not prejudiced, unaffected
hatred- disliking
cruel- pitiless, savage, severe, painful
meditate- consider deeply
speckles- sports
agitation- disturbance
domes- a rounded vault
flickers- flashing on and off quickly, agitation of
hands- waving of hands.

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 11 Differential Equations Ex 11(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 11 Differential Equations Exercise 11(b)

Solve the following differential equations.
Question 1.
\(\frac{d y}{d x}\) + y = e^-x
Solution:
Given equation is \(\frac{d y}{d x}\) + y = e^-x … (1)
This is a linear differential equation.
Here P = 1, Q = e^-x
So the integrating factor
I.F. = e^{∫P dx} = e^∫dx = e^x
The solution of (1) is given by
ye^x = ∫e^-x . e^x dx = ∫dx = x + C
⇒ y – xe^-x + Ce^-x

Question 2.
(x² – 1)\(\frac{d y}{d x}\) + 2xy = 1
Solution:
Given equation is (x² – 1)\(\frac{d y}{d x}\) + 2xy = 1

Question 3.
(1 – x²)\(\frac{d y}{d x}\) + 2xy = x \(\sqrt{1-x^2}\)
Solution:
Given equation is

Question 4.
x log x \(\frac{d y}{d x}\) + y = 2 log x
Solution:
Given equation is

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

Question 6.
\(\frac{d y}{d x}\) + y sec x = tan x
Solution:
Given equation is
\(\frac{d y}{d x}\) + y sec x = tan x
This is a linear equation where
P = sec x, Q = tan x
I.F. = e^{∫sec dx}
= e^{(sec x + tan x)} = sec x + tan x
The solution is y . (sec x + tan x)
= ∫(sec x + tan x) tan x dx
= ∫(sec x tan x + tan² x) dx
= ∫(sec x . tan x + sec² x – 1) dx
= ∫(sec x + tan x) – x + C
⇒ (y – 1) (sec x + tan x) + x = C

Question 7.
(x + tan y) dy = sin 2y dx
Given equation can be written as
Solution:

Question 8.
(x + 2y³)\(\frac{d y}{d x}\) = y
Solution:
Given equation can be written as

Question 9.
sin x\(\frac{d y}{d x}\)+ 3y = cos x
Solution:

Question 10.
(x + y + 1)\(\frac{d y}{d x}\) = 1
Solution:

Question 11.
(1 + y²) dx + (x – \(e^{-\tan ^{-1} y}\)) dy = 0
Solution:
Given equation can be written as

Question 12.
x\(\frac{d y}{d x}\) + y = xy²
Solution:
Given equation can be written as

⇒ z = -x ln x + Cx
⇒ \(\frac{1}{y}\) = -x ln x + Cx
⇒ 1 = -xy ln x + Cxy
∴ The solution is (C – ln x) xy = 1

Question 13.
\(\frac{d y}{d x}\) + y = y² log x
Solution:

Question 14.
(1 + x²)\(\frac{d y}{d x}\) = xy – y²
Solution:
The given equation can be written as

Question 15.
\(\frac{d y}{d x}\) + \(\frac{y}{x-1}\) = \(x y^{\frac{1}{2}}\)
Solution:
The given equation can be written as

Question 16.
\(\frac{d y}{d x}\) + \(\frac{y}{x}\) = x², y(1) = 1
Solution:
The given equation can be written as
\(\frac{d y}{d x}\) + \(\frac{y}{x}\) = x², y(1) = 1 … (1)
This is a linear equation.

Question 17.
\(\frac{d y}{d x}\) + 2y tan x = sin x, y\(\left(\frac{\pi}{3}\right)\) = 0.
Solution:

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 11 Differential Equations Ex 11(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 11 Differential Equations Exercise 11(a)

Question 1.
Determine the order and degree of each of the following differential equations.
(i) y sec² x dx + tan x dy = 0
Solution:
Order: 1, Degree: 1

(ii) \(\left(\frac{d y}{d x}\right)^4\) + y⁵ = \(\frac{d^3 y}{d x^3}\)
Solution:
Order: 3, Degree: 1

(iii) a\(\frac{d^2 y}{d x^2}\) = \(\left\{1+\left(\frac{d y}{d x}\right)^2\right\}^{\frac{3}{2}}\)
Solution:
Order: 2, Degree: 2

(iv) tan^-1\(\sqrt{\frac{d y}{d x}}\) = x
Solution:
Order: 1, Degree: 1

(v) ln\(\left(\frac{d^2 y}{d x^2}\right)\) = y
Solution:
Order: 2, Degree: 1

(vi) \(\frac{\frac{d y}{d t}}{y+\frac{d y}{d t}}\) = \(\frac{y t}{d y}\)
Solution:
Order: 1, Degree: 2

(vii) \(\frac{d^2 y}{d u^2}\) = \(\frac{3 y+\frac{d y}{d u}}{\sqrt{\frac{d^2 y}{d u^2}}}\)
Solution:
Order: 2, Degree: 3

(viii) \(e^{\frac{d z}{d x}}\) = x²
Solution:
Order: 1, Degree: 1

Question 2.
Form the differential equation by eliminating the arbitrary constants in each of the following cases.
(i) y = A sec x
Solution:
y = A sec x
Then \(\frac{d y}{d x}\) = A sec x tan x = y tan x

(ii) y = C tan^-1 x
Solution:

(iii) y = Ae^t + Be^2t
Solution:

(iv) y = Ax² + Bx
Solution:

(v) y = -acos x + b sin x
Solution:

(vi) y = a sin^-1 x + b cos^-1 x
Solution:

(vii) y = at + be^t
Solution:

(viii) y = a sin t + be^t
Solution:

(ix) ax² + by = 1
Solution:

Question 3.
Find the general solution ofthe following differential equations.
(i) \(\frac{d y}{d x}\) = \(\frac{e^{2 x}+1}{e^x}\)
Solution:
\(\frac{d y}{d x}\) = \(\frac{e^{2 x}+1}{e^x}\)
⇒ y = ∫(e^x + e^-x) dx = e^x – e^-x + C

(ii) \(\frac{d y}{d x}\) = x cos x
Solution:
\(\frac{d y}{d x}\) = x cos x
⇒ y = ∫x cos x dx
= x . sin x – ∫sin x dx – x sin x + cos x + C

(iii) \(\frac{d y}{d x}\) = t⁵ log t
Solution:

(iv) \(\frac{d y}{d x}\) = 3t² + 4t + sec² t
Solution:
\(\frac{d y}{d x}\) = 3t² + 4t + sec² t
⇒ y = t³ + 2t² + tan t + C

(v) \(\frac{d y}{d x}\) = \(\frac{1}{x^2-7 x+12}\)
Solution:

(vi) \(\frac{d y}{d u}\) = \(\frac{u+1}{\sqrt{3 u^2+6 u+5}}\)
Solution:

(vii) (x² + 3x + 2) dy – dx = 0
Solution:

(viii) \(\frac{d y}{d t}\) = \(\frac{\sin ^{-1} t e^{\sin ^{-1} t}}{\sqrt{1-t^2}}\)
Solution:

Question 4.
Solve the following differential equations.
(i) \(\frac{d y}{d x}\) = y + 2
Solution:

(ii) \(\frac{d y}{d t}\) = \(\sqrt{1-y^2}\)
Solution:
\(\frac{d y}{d t}\) = \(\sqrt{1-y^2}\)
⇒ \(\frac{d y}{\sqrt{1-y^2}}\) = dt
⇒ sin^-1 y = t + C

(iii) \(\frac{d y}{d z}\) = sec y
Solution:
\(\frac{d y}{d z}\) = sec y
⇒ cos y dy = dz
⇒ sin y = z + C

(iv) \(\frac{d y}{d x}\) = e^y
Solution:

(v) \(\frac{d y}{d x}\) = y² + 2y
Solution:

(vi) dy + (y² + 1) dx = 0
Solution:

(vii) \(\frac{d y}{d x}\) + \(\frac{e^y}{y}\) = 0
Solution:

(viii) dx + cot x dt = 0
Solution:
dx + cot x dt = 0
⇒ tan x dx + dt = 0
⇒ ∫tan x dx + ∫dt = C₁
⇒ In sec x + t = C₁
⇒ In sec x = C₁ – t
⇒ sec x = \(e^{C_1}\) . e^-t
⇒ cos x = \(e^{-C_1}\) . e^t
⇒ cos x = Ce^t where C = \(e^{-C_1}\)

Question 5.
Obtain the general solution of the following differential equations.
(i) \(\frac{d y}{d x}\) = (x² + 1) (y² + 1)
Solution:

(ii) \(\frac{d y}{d t}\) = e^2t+3y
Solution:

⇒ 2e^-3y + 3e^2t + 6C₁ = 0
⇒ 2e^-3y + 3e^2t = C
where C = -6C₁

(iii) \(\frac{d y}{d z}\) = \(\frac{\sqrt{1-y^2}}{\sqrt{1-z^2}}\)
Solution:

(iv) \(\frac{d y}{d z}\) = \(\frac{x \log x}{3 y^2+4 y}\)
Solution:

(v) x²\(\sqrt{y^2+3}\) dx + y\(\sqrt{x^3+1}\) dy = 0
Solution:

(vi) tan y dx + cot x dy = 0
Solution:
tan y dx + cot x dy = 0
⇒ tan x . dx + cot y dy = 0
⇒ ∫tan x dx + ∫cot y dy = 0
⇒ -ln cos x + ln siny = ln C
⇒ ln\(\frac{\sin y}{\cos x}\) = ln C
⇒ \(\frac{\sin y}{\cos x}\) = C
⇒ sin y = C cos x

(vii) (x² + 7x + 12) dy + (y² – 6y + 5) dx = 0
Solution:

(viii) y dy + e^-y x sin x dx = 0
Solution:
y dy + e^-y x sin x dx = 0
⇒ ye^y dy + x sin x dx = 0
⇒ ∫ye^y dy + ∫x sin dx = C
[Integrating by parts.
⇒ ye^y – ∫e^y dy + x(-cos x) – ∫(-cos x) dx = C
⇒ ye^y – e^y – x cos x + sin x = C
⇒ (y – 1) e^y – x cos x + sin x = C

Question 6.
Solve the following second order equations.
(i) \(\frac{d^2 y}{d x^2}\) = 12x² + 2x
Solution:

(ii) \(\frac{d^2 y}{d t^2}\) =e^2t +e^-t
Solution:

(iii) \(\frac{d^2 y}{d \vartheta^2}\) = -sin υ + cos υ + sec² υ
Solution:
\(\frac{d^2 y}{d \vartheta^2}\) = -sin υ + cos υ + sec² υ
Integrating we get
\(\frac{d y}{d υ}\) = ∫sin υ dυ + ∫cos υ dυ + ∫sec² υ dυ
= cos υ + sin υ + tan υ + A
Again integratingwe get
y = ∫(cos υ + sin υ + tan υ + A)dυ + B
where A, B are arbritrary constants.
⇒ y = sin υ – cos υ + ln |sec υ| + A.υ. + B

(iv) cosec x \(\frac{d^2 y}{d x^2}\) = x
Solution:
cosec x \(\frac{d^2 y}{d x^2}\) = x
\(\frac{d^2 y}{d x^2}\) = x sin x
Integrating we get
\(\frac{d y}{d x}\) = ∫x sin x dx + A
= x . (-cos x) – ∫(-cos x) dx + A
= -x cos x + ∫cos x dx + A
= -x cos x + sin x + A
Again integrating we get
y = -∫x cos x dx + ∫sin x + ∫A dx + B
= -{x sin x -∫1 . sin x dx} – cos x + Ax + B
= -x sin x – 2cos x + Ax + B

(v) x²\(\frac{d^2 y}{d x^2}\) + 2 = 0
Solution:

(vi) sec x \(\frac{d^2 y}{d x^2}\) = sec 3x
Solution:

(vii) \(\frac{d^2 y}{d x^2}\) = sec² x + cos² x
Solution:

(viii) e^-x\(\frac{d^2 y}{d x^2}\) = x
Solution:
e^–x\(\frac{d^2 y}{d x^2}\) = x
⇒ \(\frac{d^2 y}{d x^2}\) = xe^x
Integrating we get
\(\frac{d y}{d x}\) = ∫xe^x dx = ∫e^x dx + Ax + B
= xe^x – e^x – e^x + Ax + B
= (x – 2)e^x + Ax + B

Question 7.
Find the particular solutions of the following equations subject to the given conditions.
(i) \(\frac{d y}{d x}\) = cos x, given that y = 2 when x = 0.
Solution:
\(\frac{d y}{d x}\) = cos x
Integrating we get
y = ∫cos x dx = sin x + C
Given that when x = 0, y = 2
So 2 = C
∴ The particular solution is y = sin x + 2

(ii) \(\frac{d y}{d t}\) = cos² y subject to y = \(\frac{\pi}{4}\) when t = 0.
Solution:
\(\frac{d y}{d t}\) = cos² y
⇒ sec² y dy = dt
∫sec² dy = ∫dt
⇒ tan y = t + C
When t = 0, y = \(\frac{\pi}{4}\)
So tan \(\frac{\pi}{4}\) = C ⇒ C = 1
∴ The particular solution is tan y = t + 1

(iii) \(\frac{d y}{d x}\) = \(\frac{1+y^2}{1+x^2}\) given that y = √3 when x = 1.
Solution:

(iv) \(\frac{d^2 y}{d x^2}\) = 6x given that y = 1 and \(\frac{d y}{d x}\) = 2 when x = 0.
Solution:
\(\frac{d^2 y}{d x^2}\) = 6x ⇒ \(\frac{d y}{d x}\) = 3x² + 2
When x = 0, \(\frac{d y}{d x}\) = 2
So 2 = A
∴ \(\frac{d y}{d x}\) = 3x² + 2
Again integrating we get
y = x³ + 2x + B
When x = 0, y = 1
So B = 1.
∴ The particular solution is y = x³ + 2x + 1

Question 8.
(i) Solve : \(\frac{d y}{d x}\) = sec (x + y)
Solution:

(ii) Solve : \(\frac{d y}{d x}\) = sin(x + y) + cos(x + y)
Solution:

(iii) Solve : \(\frac{d y}{d x}\) = cos (x + y)
Solution:

(iv) Solve : \(\frac{d y}{d x}\) + 1 = e^x+y
Solution:

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 1 Solutions Unit 3 Text A: How to Write a Winning ‘Resume’ Textbook Activity Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Unit 3 Text A: How to Write a Winning ‘Resume’

Activity-1
Comprehension
Answer the following questions as briefly as you can:

Question (a)
The writer talks of two kinds of resume in the first paragraph, which of them does he think more useful and why?
Answer:
The two resumes mentioned in the first paragraph are ‘tombstone’ and ‘functional’. The‘functional’happens to be more preferable to the tombstone.

Question (b)
Why does the writer advise the job seekers never to be apologetic in a resume?
Answer:
The writer advises the job seekers never to apologize because it is the hardest job of all. It creates a negative impression.

Question (c)
Who are the intended audience for this article? How do you know this?
Answer:
The intended audience for this article are job seekers of any shade and variety. The personal pronoun ‘you’ makes it explicit.

Question (d)
What does the writer want to done between the preparation of the first draft of the } resume and its despatch to the prospective employer?
Answer:
Clustering accomplishments like leadership skills, budget management skills, child development skills, sending it a printer because a printed resume is superior to photocopies are to be done between the first draft of the resume and its despatch to the prospective employer.

Activity-2
(Guessing The Meaning Of)

Choose the best answer:

Question (a)
One type of resume is called a ‘tombstone’ (Para -1) because:
(i) It lists what you have done in the post rather than what you can do in the future.
(ii) It lists your achievements in chronological order.
(iii) It leads you to failure in the job market.
Answer:
(iii) It leads you to failure in the job market.

Question (b)
‘Quick’in para 2 means:
(i) fast
(ii) efficient
(iii) alive
Answer:
(iii) alive

Question (c)
Took your own horn! (para – 6) means:
(i) don’t be modest
(ii) boast about your achievements
(iii) tell the employer what you have done in the past.
Answer:
(ii) boast about your achievements

Question (d)
When people clutch when asked to…. ? (para – 6) means:
(i) many people underestimate themselves.
(ii) many people panic.
(iii) many people hold into their old jobs when asked to leave.
Answer:
(i) many people underestimate themselves.

Question (e)
‘How to psych yourself up ’ (para – 9) means:
(i) How to make a list of your abilities before you write your resume.
(ii) How to write your resume most enthusiastically.
(iii) How to prepare yourself mentally before writing your resume.
Answer:
(i) How to make a list of your abilities before you write your resume.

Activity-3
Cohesive Devices

Say what the italicized words refer to in the passage.
(a) “Everyone does” __________ (para 6)
(b) ‘Oneofyours’ ____________ (para 6)
(c) ____________ about what it all means (para 9)
(d) ‘It shows an employer’ ____________ (para 9) ‘
Answer:
(i) does – clutch
(ii) yours – abilities
(iii) it – accomplishment
(iv) it- listing of accomplishments in the final resume.

Activity-4

Look at the following note, made by someone to repairing a resume. Decide which points should be included in the final vision.

• A job as Manager (Research and Development)
• Joined M. A. (Economics) in Delhi University
• Left after the first year because of father’s death.
• Studied Business Adm. at Indira Gandhi National Open University.
• Specialised in business application of computers.
• Not sure that I’d be good at doing!
• Have been without a job for three months.
• Can play violin.
• Chairperson of the parents Association of my son’s school.
• Helped friends to learn computers.
• Worked for three years as a sales representative for a computer film.
• Hated the hardware selling job.
• Get boarded quickly.
• Look after the local club’s budget and save 20% of its yearly income.
• Like working in a team.
• Can inspire young people to complete a task on time.
• Teach Economics to a group of 20 poor students of the local colleges without fees.
• 36 years old and only 5 years of salaried employment.

Now group the points you have chosen under the following heading:

• Vocational objectives
• Man management skills.
• Competition and team skills.
• Management skills
• Summary of background and the others.

Answer:
Vocational objectives:
(a) Specialised in the business application of computers.
(b) Helped a friend to learn computers.
(c) A job is manager (Research and Development)

VLAN management skills:
(a) Chairperson of the Parents Association of my sons’ school
(b) Look after the local club’s budget and save 20% of its yearly income.
(c) Can inspire young people to complete a task in time.

Competition and team skills:
(i) Like working in a team

Management skills:
(a) Worked for 3 years as a sales representative for a computer firm

Summary of backgrounds and the others:
(a) Joined M.A (Economics) in Delhi University.
(b) Left after the first year because of father’s death.
(c) Not sure what I’d be good at doing!
(d) Have been without a job for three months.
(e) Can pay for violin.
(f) Hated the hardware selling job.
(g) Get bored quickly.
(h) 36 years old and only 5 years of salaried employment.

Extra Activity – 4(A)

Give the derivatives of the following words in the Text – A

purpose	characterize
convince	accomplishments
employer	Skill
interview	world
familiar	people
quick	specific
writing	brief
functional	new
resume	education
important	necessarily
translating

Answer:

Words	Derivatives
purpose	Purposeful, purposive, purposefully
convince	conviction, convincing, convincingly
employer	employee, employment, employed
interview	interviewer, interviewee
familiar	familiarity, familiarise, familiarly
quick	quicken, quickly
writing	write, written
functional	functionalised, function, defunct, malfunctioned
resume	resumption, resuniptive
important	importance, importantly
translating	translate, translation
characterize	character, characteristic
accomplishments	accomplish, accomplished
Skill	skillful, skilled, unskilled, skillfulness
world	worldly, world-wide
people	popular, popularise, population, populate
specific	specifically, specify, specification
brief	briefly, briefness, brevity
new	newly, a new, newness
education	educational, educated, educationally, educationist, educate
necessarily	necessary, necessity, necessitate
identity	Identification, identity

Extra Activity – 4(B)

(i) Use the following phrases in sentences of your own:
drop in,
as well as,
of all shades and variety,
in particular,
have a good look at
Answer:
drop in – My friend occasionally drops in at my residence,
as well as – I as well as any friend can attend the meeting.
of all shades and variety – Sachin Tendulkar tormented the bowlers of all shades and variety.
in particular – I relish tea, in particular Tata Tea.
have a good look at – A good batsman should have a good at the pitch, before batting.

(ii)Derive adjectives from the following nouns:

Legend	comfort
pride	modesty
explosiveness	temperament
critic	nightmare

Answer:

Legend	:	legendary
pride	:	proud
explosiveness	:	explosive
critic	:	critical
comfort	:	comfortable
modesty	:	modest
temperament	:	temperamental
nightmare	:	nightmarish

(iii)Derive nouns from the following verbs:

reverse	encourage
achieve	admit
behave	react
endorse	expect
reflect	succeed

Answer:

reverse	:	reverence
achieve	:	achievement
behave	:	behavior
endorse	:	endorsement
reflect	:	admission
react	:	reaction
expect	:	expectation
succeed	:	success

(iv) Derive adjectives form the following nouns:

quintessence	passion
regret	culture
example	benefit
privacy	importance
pride	modesty

Answer:

Noun		Adjectives
quintessence	:	quiertessential
regret	:	regretful
example	:	exemplary
privacy	:	private
pride	:	proud
passion	:	passionate
culture	:	cultural
benefit	:	beneficial
importance	:	important
modesty	:	modest

(v) Derive verbs from the following nouns:
proposal
operator
introduction
requirement
provision
emission
advice
suspension

Answer:

Nouns	Verb forms
proposal	propose
operator	operate
introduction	introduce
requirement	require
provision	provide
emission	emit
advice	advise
suspension	suspend

(E)(i) Give the antonyms of the following words:

opening	reject
earlier	significant
indoor	success
cause	present
foul	before

Answer:

Words	Antonyms
opening	closing
earlier	later
indoor	outdoor
cause	effect
foul	fair
significant	insignificant
reject	accept
success	Mure
present	absent
before	after

(ii) Substitute the following expressions with one word each.
1. the system by which something can be measured.
2 Any substance that causes pollution.
3. Make people angiy.
4. Public warning to make people careful.
5. A group of people joining together to influence someone in power:

Answer:
1. index
2. pollutant
3. gall
4. alert
5. lobby

(iii) Insert articles, wherever, necessary, in the following sentences:
1. After college career, I shall join university.
2. Mr. Ahuja is Indian, his wife is European.
3. Business of thinking new thoughts is sign of civilization.
4. Japanese are industrious nation.
5. Democracy consists in giving people, things they want.
6. Freedom is spiritual quality.
7. Going abroad is unique opportunity.
8. Ganges is holiest among Indian rivers.
9. We had better have new look at whole problem.
10. He has read Upanishads.

Answer
1. ___________ a university
2. _________ an Indian __________ a European.
3. The business ___________ a sing __________.
4. The Japanese are an industrious nation.
5. __________the things __________.
6. ___________ a spiritual quality.
7. _________ a unique opportunity
8. Ganges is the holiest _________.
9. _________ a new look at the __________.
10. ___________ the Upanishads.

(iv) Derive nouns from the following verbs:

die	solve
enforce	emit
regulate	appear
exist	reduce
maintain	pollute

Answer:

Verbs	Noun Forms
die	death
enforce	enforcement
regulate	regulation
exist	existence
maintain	maintenance
solve	solution
enforce	emission
appear	appearance
reduce	reduction
pollute	pollution

(v)Match the words in column ‘A’ with their antonyms in column ‘B’

‘A’	‘B’
rising	easy
increase	rural
warm	harmless
urban	falling
offenders	cool
difficult	decrease
reduce	irregular
major	enhance
regular	defenders
harmful	minor

Answer:

‘A’	‘B’
rising	falling
increase	decrease
warm	cool
urban	rural
offenders	defenders
difficult	easy
reduce	enhance
major	minor
regular	irregular
harmful	harmless

What Does This Unit Contain?
In this unit you will have further practice in skimming and scanning as reading subskills. You will also have practice in referring and is assessing the communicative value of a Text.
The unit comprises the following sections:
(A) How to write a wining resume-Dick Irish
(B) Advertisement samples (From newspapers and magazines)
(C) On the education ofa man of business – Sir Arthur helps

Section-(A)

Imagine that you are the owner of a small factory producing garments. You have to select and engage five employees in your factory. What are the most important qualities that you would like your employees to possess. Next, suppose you have received more than twenty applications in response to your advertisement for five jobs and you can interview .only ten candidates, how are you going to short-list the ten candidates on the basis of their job applications (also called resumes). While reading Text – A, your focus should be on getting tips on how to select these ten interviewees.

How to Write a Winning ‘Resume’ Summary in English

The main purpose of a resume is to convince an employer to grant you an interview. There are two kinds. One is the familiar ‘tombstone’ that lists where you went to school and where you have worked in the chronological order. The other is what is called the ‘functional’ resume – descriptive, fon to read, unique to you and much more likely to land you and interview. It is handy to have a ‘tombstone ’ for certain occasions. But prospective employers throw away most of those unrequested ‘tombstone’ lists, preferring to interview the quick rather than the dead.

Put Yourself First:
While writing a resume, you have to feel yourself important. ‘Sell what you can do, not who you are’ practice translating your personality traits, character accomplishment and achievements into still areas in the world of work.

Took Your Own Horn:
Many people clutch when asked to think about their abilities. Some think they have none at all

Be specific, be concrete and be brief:
Turn bad news into good:
If you to mention your disappointment in work look for the positive side.

Never Apologize:
If you are returning to the work force after fifteen years as a parents, simply write a short paragraph in place of a chronology of experience. Don’t apologize for working at a being a mother; it’s the hardest job of all. If you have not special training or higher education, just don’t mention education.

How to Psych yourself up:
The secret is to think about the self before you start writing about yourself. Take four or five hours off not necessarily consecutive and simply write down every accomplishment in your life, on or off the job, that made you feel effective. Study the list and try to spot patterns. While studying your list, you will come closer to the meaning: identifying your marketable skills. Once you discover patterns, give names to your cluster of accomplishments (leadership skills, budget management skills, child development skill etc.). Try to list atleast three accomplishments under the same skills heading. You may take your drafts or more and several weeks, before you are already to show it to a stranger for a reaction. When you are satisfied, send it to a printer, a printed resume is far superior to photocopies.

Analytical Outlines

• The main purpose of a resume is to convince an employer.
• He is convinced to grant you an interview.
• There are two kinds.
• One is the familiar‘tombstone’.
• It can list where you went to school.
• It can also list where you have worked in the chronological order.
• The other is ‘functional’ resume.
• It is descriptive.
• It is‘fun to read’.
• It is also unique to you.
• It is much more likely to land you in an interview.
• It is handy to have a ‘tombstone’
• This we find in certain occasions.
• But prospective employers throw away these.
• They throw away most of those unrequired ‘tombstone’ list.
• They prefer to do the interview quick.
• For this reason, they throw away these lists.
• You have to feel yourself important while writing a resume.
• Sell what you can do, not who you are.
• you should practise translating your personality traits.
• You should practise character accomplishments.
• You should practise achievements into skill areas in the world of work.
• Many people clutch thinking about their abilities.
• Some think they have none at all.
• In writing a resume, one should be specific.
• He also should be concrete.
• He should be brief too.
• One should turn bad news into good one.
• You should always look for the positive side.
• You should never apologize.
• You are returning to the work force after fifteen years.
• Simply write a short paragraph.
• You can write it in place of chronology of experience.
• Don’t apologize for working at being a mother.
• It is the hardest job of all.
• You have no special training.
• You have no higher education.
• Then, just don’t mention education.
• You are going to write about yourself.
• So, first you have to think about the self.
• Take four or five hours off
• It should not be necessarily consecutive.
• Simply write down every accomplishment of your life.
• It is about on or off the job.
• The job that make you feel affective.
• Then study the list.
• Try to sport patterns.
• You are studying the list now.
• You will come closer to the meaning.
• Identify your marketable skills.
• Give name to you cluster of accomplishments.
• It may be just like leadership skills.
• It may be budget management skills.
• It may be child development skills.
• Try to list of least three accomplishments.
• These three must be written under the same skill heading.
• You may take your draft.
• You may take it to several weeks.
• Then you can show this to a stranger.
• You have to do this to know others’ reactions for it.
• Then send it to a printer.
• A printed resume is far superior to photocopies.

Meaning Of difficult Words
Resume – summary
convince – to persuade fully, to cause to believe
grant – to permit, to allow
familiar – well – known, general, well-acquainted
chronology – the science of computing time, a scheme of the table of time, order of time.
functional – active, professional
descriptive – narrative, explaining in detail
unique – stole, special
handy – convenient, dexterous
prospective – expecting for future
accomplishments – completeness, happenings, fulfillment
achievement – performance, gain.
clutch – to grasp, tightly, to hatch, to snatch
concrete – material, not abstract, real
positive side – bright side, good side
mention – to refer to, to speak about
disappoint, – to be hopeless
apologize – make frank acknowledgment
consecutive – following in regular order, or one after another
pattern – type, order
effective – fruitful, necessary
identify – to find out, recognize
cluster – a bunch, swarm, crowd

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 2 Solutions Poem 3 Of a Questionable Conviction Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Poem 3 Of a Questionable Conviction

Pre-Reading activity:
Have you ever written poems? If so, what was your purpose in writing them? Why does a poet write poems?To persuade the readers into his own beliefs? Is it always possible to know if the poet is sincerely expressing his conviction in his poems? The poem you are going to read has
the title of a questionable conviction. Can you guess what the poem is about? Now read the poem and find out.

Notes On The Poet:
Jayanta Mahapatra from(1928) is foremost among the Indian English poets. His poetry expresses an ‘unhealable rift” a profound sense of loss. A tireless experimenter, Mahapatra’s poetic idiom is subtle and suggestive. His well known poetry collection are “Close the Sky”, Ten by Ten (1971), ‘A Rain Rated (1976). ‘A Father’s Hours’ (1976) and Relationship (1980) and ‘Burden of waves and Fruit’ (1986). ‘Ofa Questionable Conviction’ addresses the issue of how important convictions are to the writing of a poem.

Questions For Discussion:

Question 1.
Why does the poet think the man who talks of pain invented it himself?
Answer:
The poet thinks that he man who talks of pain invented it himself because he has made virtue out of it.

Question 2.
What is the main idea in Stanza 1?
Answer:
The main idea in Stanza 1 is that it is perhaps he who has invented pain himself because he has made virtue out of it.

Question 3.
What, according to the poet ‘his excuse to live’?
Answer:
Waiting for hours in the night towards another night is, according to the poet, his excuse.

Question 4.
Can the walls be lonely? Why does the poet use this expression?
Answer:
Walls, in poetry, can be lonely. The poet makes use of this expression to bring about a kind of personification in the poem.

Question 5.
“For months together the window has been deceiving him”. What could the poet mean by these lines?
Answer:
The window has been deceiving him for months together, because light has been simply coming in and going out. He has not been able to polish and heart by means of the light.

Question 6.
The poet described in he poem ‘has been trying to polish the light on his heart? How?
Answer:
The light on his heart is poor and the poet is not able to polish his heart by means of the light that enters and exits through the window.

Question 7.
You can easily see that in the first three stanza only the present tense forms are used. In the final stanza, however, past tense forms are used. Why is this shift in the concluding stanza?
Answer:
The use of present perfect progressive in the third stanza makes it rather explicit that the action started some times in the past and it continues into the present. Hence, it has a past reference. The past tense from in the concluding stanza tell that the poet has been doing that from the past till the present.

Question 8.
Would you consider the ending of the poem satisfactory? Explain your point of view.
Answer:
The ending of the poem is satisfactory because writing poem beside a lonely wall does not harm anybody.

Question 9.
What can you say about the tone of the poem?
Answer:
The tone of the poem is pain and simple.

Question 10.
What do you mean by –
(i) “The empty window in his lonely wall” (stanza 2)
(ii) “The eyes saw the pain in the mirror” (stanza 4)
(iii) “They did not grudge him that.” (stanza 4)
Answer:
(i) The only well without window doors.
(ii) The poet’s eyes saw the pain in the mirror.
(in) The people did not give or allow anything unwillingly.

Of a Questionable Conviction Summary in English

This is a man who talks of pain as though it belonged to him alone. Perhaps he has invented it himself and made virtue of it. And this man may be a poet. He waits in the night for hours. He keeps waiting for another night because, that is his excuse to live. The empty window in his lonely wall belongs to him alone. The window has been deceiving him for months together. Light comes in and goes out of its own without any hindrance. He has been trying to polish the light on his heart. Everybody says that he is a poet. His eyes witnessed the pain in the mirror which reflected his image. They did not grudge him that such a harmless pastime never ruined anybody’s sleep.

Analytical Outlines:

• The poet talks about a man.
• That man talks of pain.
• The pain belongs to him along.
• Perhaps, he has invented it himself.
• He makes virtue of it.
• That man may be a poet.
• He waits in the night for hours.
• He keeps waiting for another night.
• Because that is his excuse to live.
• It is the empty window in his lonely wall.
• It belongs to him alone.
• The window has been deceiving him.
• It has been deceiving him for months together.
• Light comes in.
• Light goes out of its own.
• It is without any hindrance.
• He has been trying to polish the light.
• He will polish it in his heart.
• Everybody says that he is a poet.
• His eyes witnessed the pain.
• It witnessed it in the mirror.
• The mirror reflected his image.
• They did not grudge him.
• It is a harmless pastime.
• It never ruined anybody’s sleep

Meaning Of Difficult Words:

conviction – a strong belief or opinion.
virtue – good quality
deceiving – misleading, cheating, betraying
hindrance- obstacle, impediment, obstruction
polish- to refine, to make or become smooth and shining.
witness- to see, to give evidence
image- a statue, an idol, an idea, a reflection
reflect- to express, to throw or come back
grudge- give or allow something very unwillingly
pastime- an enjoyable or interesting activity

Odisha State Board CHSE Odisha Class 12 Approaches to English Book 2 Solutions Poem 2 The Goat Paths Textbook Exercise Questions and Answers.

CHSE Odisha 12th Class Alternative English Solutions Poem 2 The Goat Paths

Pre-Reading activity:
The goat is a very common animal in our part of the country. What qualities do you associate with goats? Think up five words that come to your mind when you think of goats. The poem you are about to read has the title. “The Goat-Paths”. Can you guess what the poem is about? Write your guess here. Now read the poem is see what it is really about.

Notes On The Poet:
James Stephens (1882-1950), a British poet and novelist, is known for such work as Insurrections (1909). The Crack of gold (1912). The Hill of Vision (1912). Green Branches (1912) and Collected Poems (1936). His ‘delicates inspired’ poetry makes effective use of imagery, the familiar scene is often ‘translated into an image for a human meaning’. In this poem, the poet likes the goats, seeks harmony with Nature.

Questions For Discussion:

Question 1.
Where are the straying goats found?
Answer:
The goats prefer to go to the heather and not to a grassy field because there was nothing stir.

Question 2.
Why do the goats go to the heather and not to a grassy field?
Answer:
The goats prefer to go to the heather and not to a grassy field because there was nothing stir.

Question 3.
Are these goats different from the others of their kind?
Answer:
These goats are different from the others of their kind because they behave in different way from the others.

Question 4.
How many times para the words relating to ‘quiet’ used in this poem?
Answer:
Five times.

Question 5.
How does the poet related ‘quietly in quietness’ (line 13 to ‘the moving sky’?
(Line 16). If you were to make two sections of the poem how would you divided it?
Answer:
“Quietly in quietness’ means being alone in a lonely place. The moving sky implies the limitless sky.

Question 6.
How would you read of someone called the first section ‘observation’ and the second ‘reflection’?
Answer:
It would be right to say that the first section of the poem is based on ‘observation’ and the second section on ‘reflection’.

Question 7.
What do you notice in the voice of the poet? urgency, defiance, arrogance, envy, frustration, expectation or a sense of oneness with God’s creation?
Answer:
Urgency, defiance, expectation, a sense of oneness with God’s creation.

Question 8.
What does the poet say he would do when his ‘sunny solitude’ is distributed?
Answer:
He would stray apart and brood, he would beat a hidden way through the quiet heather spray in the sunny solitude.

Question 9.
Why does the poet call the goats ‘wise’?
Answer:
The poet calls the goats wise because they brood and beat the hidden way through the quiet heather spray in the sunny solitude.

Question 10.
The expression ‘IfI were’ conveys a wish. What is the poet’s wish?
Answer:
The poet’s wish is to be wise enough to brood and beat the hidden way through the quiet heather spray to a sunny solitude. He would run away and make an angry sound and would stare and turn and bound to the deeper silence where nothing disturbs.

Question 11.
I would think until I found/something I can never find’. How would you comment on the complexity of thought implicit in these lines?
Answer:
It is just like attaining the unattainable. The first lines is in simple past tense while the second line occurs in simple present form. The use of simple past in the present delineates are unfulfilled of he poet who would never find it. Hence, it is unfulfilled wish.

Question 12.
Can you write a simple paraphrase of the last stanza?
Answer:
The last stanza speaks of attaining of the unattainable. The poet makes use of the simple past tense form of verb, that is ‘found’ in the present context. The grammatical usage of such expression explains the unfulfilled wish of the poet. The poet is of the view that he will go on thinking until he has found what he can never find.

Question 13.
Point out same of the striking images in the poem?
Answer:
There are some striking images in the poem. They are-crooked paths, sunny quietness, crouching, beaten way etc.

Question 14.
What purpose do the words ‘quiet sunniness’. Sunny quietness’ ‘deeper sunniness’, ‘Quietly in quietness’. ‘Sunny quietude’. ‘Sunny solitude’ serve?
(i) They cast a spell on the reader.
(ii) They add to the musically of the poem
(iii) They are meant to create ambiguity for the reader.
Answer:
(iii) They are meant to create ambiguity for the reader.

Question 15.
Can you think of possible revisions of the following lines of the poem?
Line 17: “If you approach they run away.”
Line 30: “And should you come I’d run away”
Answer:
“If you approach they run away”
“If you come I’d run away”

Composition

Question 1.
Would you agree that the poem suggest the possibility of a harmony within the self and within the natural process of life and world”? Justify your answer.
Answer:
The poem‘ The Goat – Paths” is undoubtedly the master piece of James Stephens, an eminent and out-standing British poet and novelist. In this discussing poem, he expresses the possibility of a harmony within the selfand with the natural process of life and the world. The goats and goat paths are natural elements. The process of life is best reflected by means of these things. Life and life’s process are a part of nature. The outer reflections cost a deep spell on human life. It is because the external nature has a tremendous influence on the internal nature of man. Man internalises the outer nature which is at times didactic and delightful. The nature says words worth, ‘is the friend, philosopher and guide’, for man. In this discussing poem ‘The Goat – Paths,’ the poet James Stephens reflects the human self and natural processes. The poem ultimately leads the poet to identify himself with the goats! He says, “IfI were as wise as they I would stray apart and brood ….”. If a man appears on the scene, he would run away, he would like goats make an angry sound. He would is to a place where nothing stirs in the silence ofthe furze. He would also like to think in the airy quietness through the quiet sunniness, he would stray away to brood by hidden, beaten way in the sunny solitude. He would think until he found something he can never and something lying on the ground. As a matter offact, Stephens has tried his best to establish a harmony within the self and with the natural process of life and the world. The way Stephens explains it is superb and fantastic. On the whole. Stephens’s expression is most during, evaluating, inspiring and heart-touching.

Question 2.
Comment on the appropriateness of the title “The Goat-Paths”.
Answer:
The poem “The Goat-Paths” is, indeed, the best typical master-piece of James Stephens, a prominent and outstanding British poet and novelist of the twentieth century. His ‘delicately inspired’ poetry tinged with apt and suggestive titles is undoubtedly superband excellent. However, the title of any piece of art must be thoroughly exact, appropriate and suggestive. It should be like a colourful and attractive signboard of a shop. An attractive signboard automatically arrests the attention of the customers and makes them spell bound to have a visit to the shop. It also explains what a shop contains similarly, and apt and suggestive title arrests the attention of the reader instantly and makes them spell bound to go through it completely. It is like ‘the face is the index of heart.’ The discussing poem ‘The Goat-Paths”| bears the same ideas to prove the authenticity and appropriateness of the title of the poem. Moreover, the goat-paths are usually crooked and they lead uphill. They also wind about through the heather in and out of the quiet sunniness. The goats keep cropping here and there, they pause and turn and pass. When approaches they run away, leap and stare and they go away to the sunny quietude with a sudden angry sound. The poet brings oneness between the goats and his life. In feet, appropriateness of the title applies to the poem. The poem bears all qualities of being an apt and suggestive one. The external natural things like the goats, goat-paths have been identified with human life. The poet wishes to internalise these values and learn a lot from the goats. As a matter of feet, the title of the poem‘ The Goat-Paths” is apt and suggestive. The way the poet has expressed the central idea of the poem through the appropriate title is superb and outstanding. One the whole, the title of the poem is thought-provoking, inspiring and heart enduring.

The Goat Paths Summary in English

The crooked paths go every way upon the hill. They wind about though the heather in and out of the quiet sunniness. The goats there, day after day, stray in sunny quietness, cropping here and there as they halt and turn and pass. There is a bit of Heather spray, a mouthful of the grass in the deep sunniness in the place where nothing stirs quietly in the quietness. In quiet of the furze, they come and lie staring on the roving sky. When somebody approaches they run away. They leap and stare, they bound away with a sudden angry sound of the sunny quietude. Crouching down where nothing stirs in the silence of these furze, crouching down again to brood in the sunny solitude. If we were as wide as they were, he would stray apart and brood, he would beat a hidden way through the quiet heather spray to a sunny solitude. If someone came he would run away, he would make an angry sound and would stare and turn and bound to the deeper quietude to the place where nothing stirs in the silence of the furze. He would think as long as they in that airy quietness through the quiet sunniness he would stray away to brood by a hidden beaten way in the sunny solitude.

Analytical Outlines:

• The crooked paths go every way.
• It goes every way upon the hill.
• They wind about through the heather.
• They wind about in and out of the quiet sunniness.
• There, the goats stray in sunny quietness.
• The goats stray day after day.
• They halt here and there.
• They turn here and there
• They pass here and there
• They crop here and there
• There is a bit of heather spray.
• It is mouthful of the grass.
• It is in the deep sunniness in the place.
• There nothing stirs quietly.
• Actually, there is an entire quietness.
• They come in the quiet of the furze.
• They lie staring on the roving sky.
• They run away when somebody approaches.
• They leap.
• They stare
• They bound away with a sudden angry sound.
• They do it with the sound of the sunny quietude.
• They crouch down.
• Nothing stirs in the silence of the furze.
• They crouch down again.
• They brood in the sunny solitude.
• If he were as wise as they.
• He would stray apart.
• He would brood.
• He would beat a hidden way through the quiet heather.
• He would spray to a sunny solitude
• If someone came.
• He would run away.
• He would make an angry sound.
• He would stare.
• He would turn.
• He would bound to the deeper quietude.
• There nothing stirs in the silence of the furze.
• He would think as long as they were in that airy quietness.
• He would think this through the quiet sunniness.
• He would stray away to brood.
• He would brood by a hidden beaten way.
• He would do this in the sunny solitude.

Meaning Of difficult Words:

croocked- bent, not straight
heather- wasteland covered with strubs
cropping- grazing
furze- shrub with spikes
roving (sky) – moving (here, appearing to move)
quietude – calmness, serenity, solitude
crouching – lying close to the ground
beat- make a path
stare- to look fixedly, to glance
solitude- loneliness, calmness, pin drop silence
brood- act ofbreeding
stray- to wander
spray- to sprinkle

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Ex 12(d) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 12 Vectors Exercise 12(d)

Question 1.
Each question given below has four possible answers out of which only one is correct. Choose the correct one.
(i) \(\vec{a} \cdot \vec{b} \times \vec{a}\) = _______.
(a) \(\overrightarrow{0}\)
(b) 0
(c) 1
(d) \(\vec{a}^2 \vec{b}\)
Solution:
\(\vec{a} \cdot(\vec{b} \times \vec{a})\) = \((\vec{b} \times \vec{a}) \cdot \vec{a}\)
= \(\vec{b} \cdot(\vec{a} \times \vec{a})\) = \(\vec{b} \cdot \overrightarrow{0}\)
= 0 [∴ Dot product is commutative and in the scalar triple product the dot and cross can be interchanged.]

(ii) \((-\vec{a}) \cdot \vec{b} \times(-\vec{c}))\) = _______.
(a) \(\vec{a} \times \vec{b} \cdot \vec{c}\)
(b) \(-\vec{a} \cdot(\vec{b} \times \vec{c})\)
(c) \(\vec{a} \times \vec{c} \cdot \vec{b}\)
(d) \(\vec{a} \cdot(\vec{c} \times \vec{b})\)
Solution:
\((-\vec{a}) \cdot \vec{b} \times(-\vec{c})\) = \(\vec{a} \cdot(\vec{b} \times \vec{c})\)

(iii) For the non-zero vectors \(\vec{a}, \vec{b}\) and \(\vec{c}, \vec{a} \cdot(\vec{b} \times \vec{c})\) = 0 if
(a) \(\vec{b} \perp \vec{c}\)
(b) \(\vec{a} \perp \vec{b}\)
(c) \(\vec{a} \| \vec{c}\)
(d) \(\vec{a} \perp \vec{c}\)
Solution:
\(\vec{a} \cdot(\vec{b} \times \vec{c})\) = \((\vec{a} \times \vec{b}) \cdot \vec{c}\)
\(\vec{c} \perp(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})\)
but \(\vec{a} \times \vec{b}\) is perpendicular to \(\vec{a}\) and \(\vec{b}\)
∴ \(\vec{a} \| \vec{b}\)

Question 2.
Find the scalar triple product \(\vec{b} \cdot(\vec{c} \times \vec{a})\) where \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) are respectively.
(i) î + ĵ, î – ĵ, 5î + 2ĵ + 3k̂
Solution:

= 1 (0 – 3) + 1 (0 – 3) + 0 (5 – 2)
= 3 – 3 = -6

(ii) 5î – ĵ + 4k̂, 2î + 3ĵ + 5k̂, 5î – 2ĵ
Solution:

= 5 (18 + 10) + 1 (12 – 25) + 4 (- 4 – 15)
= 140 – 13 – 76 = 140 – 89 = 51

Question 3.
Find the volume of the parallelopiped whose sides are given by the vectors.
(i) î + ĵ + k̂, k̂, 3î – ĵ + 2k̂
Solution:

= 1 (0 + 1) – 1 (0 – 3) + 1 (0 – 0)
= 1 + 3 = 4 cube units.

(ii) (1, 0, 0), (0, 1, 0), (0, 0, 1).
Solution:

Question 4.
Show that the following vector are co-planar
(i) î – 2ĵ + 2k̂, 3î + 4ĵ + 5k̂, -2î + 4ĵ – 4k̂
Solution:

(ii) î + 2ĵ + 3k̂, -2î – 4ĵ + 5k̂, 3î + 6
Solution:

Question 5.
Find the value of λ so that the three vectors are co-planar.
(i) î + 2ĵ + 3k̂, 4î + ĵ + λk̂ and λî – 4ĵ + k̂
Solution:

(ii) (2, -1, 1), (1, 2, -3) and (3, λ, 5)
Solution:

⇒ 2 (10 + 3λ) + 1 (5 + 9) + 1 (λ – 6) = 0
⇒ 20 + 6λ +14 + λ – 6 = 0
⇒ 7λ + 28 = 0 ⇒ λ = -4

Question 6.
If \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) mutually perpendiculars, show that \([\vec{a} .(\vec{b} \times \vec{c})]^2\) = a²b²c²
Solution:

Question 7.
Show that \([\vec{a}+\vec{b} \vec{b}+\vec{c} \vec{c}+\vec{a}]\) = 2\([\vec{a} \vec{b} \vec{c}]\)
Solution:

Question 8.
Prove that \([\vec{a} \times \vec{b} \vec{b} \times \vec{c} \vec{c} \times \vec{a}]\) = \([\vec{a} \vec{b} \vec{c}]^2\)
Solution:

Question 9.
For \(\vec{a}\) = î + ĵ, \(\vec{b}\) = -î + 2k̂, \(\vec{c}\) = ĵ + k̂ obtain \(\vec{a} \times(\vec{b} \times \vec{c})\) and also verify the formula \(\vec{a} \times(\vec{b} \times \vec{c})\) = \((\vec{a} \cdot \vec{c}) \vec{b}-(\vec{a} \cdot \vec{b}) \vec{c}\).
Solution:

Question 10.
Prove that \(\vec{a} \times(\vec{b} \times \vec{c})+\vec{b} \times(\vec{c} \times \vec{a})+\vec{c} \times(\vec{a} \times \vec{b})\) and hence prove that \(\vec{a} \times(\vec{b} \times \vec{c}), \vec{b} \times(\vec{c} \times \vec{a}), \vec{c} \times(\vec{a} \times \vec{b})\) are coplanar.
Solution:

Question 11.
If \(\vec{a}\), \(\vec{b}\) and \(\vec{c}\) unit vectors and \(\hat{a} \times(\hat{b} \times \hat{c})=\frac{1}{2} \hat{b}\) find the angles that â makes with b̂ and ĉ, where b̂, ĉ are not parallel.
Solution:

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 9 Integration Additional Exercise Textbook Exercise questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 9 Integration Additional Exercise

Question 1.
∫\(\sqrt{1-\sin 2 x}\) dx
Solution:
I = ∫\(\sqrt{1-\sin 2 x}\) dx
= ∫\(\sqrt{(\cos x-\sin x)^2}\) dx
= ∫(cos x – sin x) dx
= sin x + cos x + c

Question 2.
∫\(\frac{d x}{1+\sin x}\)
Solution:
I = ∫\(\frac{d x}{1+\sin x}\)
= ∫\(\frac{1-\sin x}{\cos ^2 x}\)
= ∫sec² x – sec x tan x dx
= tan x – sec x + c

Question 3.
∫\(\frac{\sin x}{1+\sin x}\) dx
Solution:

Question 4.
∫\(\frac{\sec x}{\sec x+\tan x}\) dx
Solution:
I = ∫\(\frac{\sec x}{\sec x+\tan x}\) dx
= ∫\(\frac{\sec x(\sec x-\tan x)}{\sec ^2 x-\tan ^2 x}\) dx
= ∫sec² x – sec x tan x dx
= tan x – sec x + c

Question 5.
∫\(\frac{1+\sin x}{1-\sin x}\) dx
Solution:
I = ∫\(\frac{1+\sin x}{1-\sin x}\) dx
= ∫\(\frac{(1+\sin x)^2}{\cos ^2 x}\) dx
= ∫[sec² x+ tan² x+ 2sec x tan x) dx
= ∫[2sec² x – 1 + 2sec x tan x) dx
= 2tan x – x + 2sec x + c

Question 6.
∫tan^-1 (sec x + tan x) dx
Solution:

Question 7.
∫\(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\) dx
Solution:
I = ∫\(\frac{\cos 2 x-\cos 2 \alpha}{\cos x-\cos \alpha}\) dx
= ∫\(\frac{\left(2 \cos ^2 x-1\right)-\left(2 \cos ^2 \alpha-1\right)}{\cos x-\cos \alpha}\) dx
= 2 ∫(cos x + cos α) dx
= 2 sin x + 2x cos α + c

Question 8.
∫tan-1\(\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\) dx
Solution:

Question 9.
∫\(\frac{d x}{\sqrt{x+1+} \sqrt{x+2}}\)
Solution:

Question 10.
∫\(\frac{2+3 x}{3-2 x}\) dx
Solution:

Question 11.
∫\(\frac{d x}{\sqrt{x}+x}\)
Solution:

Question 12.
∫\(\frac{d x}{1+\tan x}\)
Solution:

Question 13.
∫\(\frac{x+\sqrt{x+1}}{x+2}\) dx (Hints put : \(\sqrt{x+1}\) = t)
Solution:

Question 14.
∫sin^-1\(\sqrt{\frac{x}{a+x}}\) dx (Hints put : x = a tan² t)
Solution:

Question 15.
∫e^x\(\left(\frac{2+\sin 2 x}{1+\cos 2 x}\right)\) dx
Solution:

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

Question 17.
∫\(\frac{x^2-1}{x^4+x^2+1}\) dx
Solution:

Question 18.
∫\(\frac{x^2 d x}{x^4+x^2+1}\)
Solution:

Question 19.
∫\(\sqrt{\cot x}\) dx
Solution:

Question 20.
∫\((\sqrt{\tan x}+\sqrt{\cot x})\) dx
Solution:

Question 21.
∫\(\frac{\mathrm{dx}}{x\left(x^4+1\right)}\)
Solution:

Question 22.
∫\(\frac{\mathrm{dx}}{e^x-1}\)
Solution:

Question 23.
∫\(\frac{(x-1)(x-2)(x-3)}{(x+4)(x-5)(x-6)}\) dx
Solution:

Question 24.
∫\(\frac{d x}{\left(e^x-1\right)^2}\)
Solution:

Question 25.
∫\(\frac{d x}{\sin x \cos ^2 x}\)
Solution:

Question 26.
\(\int_2^4 \frac{\left(x^2+x\right) d x}{\sqrt{2 x+1}}\)
Solution:

Question 27.
\(\int_{-a}^a \sqrt{\frac{a-x}{a+x}}\) dx
Solution:

Let a² – x² = t²
-2x dx = 2t dt
x = -a ⇒ 0 t = 0
x = a ⇒ t = 0
= 0
I = aI₁ – I₂ = aπ

Question 28.
\(\int_0^{\pi / 2}(\sqrt{\tan x}+\sqrt{\cot x})\) dx
Solution:

Question 29.
\(\int_0^{\pi / 2} \frac{\cos x d x}{1+\cos x+\sin x}\)
Solution:

Question 30.
\(\int_0^1\)x (1 – x)ⁿ dx
Solution:

Question 31.
\(\int_0^{\pi / 2}\)sin 2x log (tan x) dx
Solution:

Question 32.
\(\int_0^{\pi / 2} \frac{\sin ^2 x d x}{\sin x+\cos x}\)
Solution:

Question 33.
\(\int_0^{\pi / 2} \frac{\sin ^2 x d x}{1+\sin x \cos x}\)
Solution:

Question 34.
\(\int_0^{\pi / 2} \frac{x d x}{\sin x+\cos x}\)
Solution:

Question 35.
Prove that \(\int_0^\pi\) x sin³ x dx = \(\frac{2 \pi}{3}\)
Solution:

Question 36.
\(\int_{\pi / 5}^{3 \pi / 10} \frac{\sin x d x}{\sin x+\cos x}\)
Solution:

Question 37.
\(\int_0^\pi\)|cos x| dx
Solution:

Question 38.
\(\int_1^4\)(|x – 1| + |x – 2| + |x – 3|) dx
Solution:

Question 39.
\(\int_{-\pi / 2}^{\pi / 2}\)(sin |x| + cos |x|) dx
Solution:

Question 40.
\(\int_0^\pi\)log (1 + cos x) dx
Solution: