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Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.4 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.4

Question 1.
Find the principle value of
(i) sec^-1 (\(\frac {2}{√3}\))
(ii) cot^-1 (√3)
(iii) cosec^-1 (-√2)
Solution:
(i) Let sec^-1 (\(\frac{2}{\sqrt{3}}\)) = θ
⇒ sec θ = \(\frac{2}{\sqrt{3}}\)
⇒ cos θ = \(\frac{\sqrt{3}}{2}\) = cos \(\frac{\pi}{6}\)
⇒ θ = \(\frac{\pi}{6}\)

(ii) cot^-1 (√3)
cot^-1 (√3) = θ
√3 = cot θ
cot \(\frac {π}{6}\) = cot θ
θ = \(\frac {π}{6}\)

(iii) cosec^-1 (-√2)
cosec^-1 (-√2) = θ
cosec θ = -√2 = -cosec(\(\frac {π}{4}\))
= cosec (-\(\frac {π}{4}\))
θ = –\(\frac {π}{4}\)

Question 2.
Find the value
(i) tan^-1 (√3) – sec^-1(-2)
(ii) sin^-1(-1) + cos^-1(\(\frac {1}{2}\)) + cot^-1(2)
(iii) cot^-1(1) + sin^-1(-\(\frac {√3}{2}\)) – sec^-1(-√2)
Solution:
x = tan^-1(√3)
tan x = √3 = tan \(\frac {π}{3}\)
x = \(\frac {π}{3}\)
y = sec^-1(-2)
sec y = -2 = -sec \(\frac {π}{3}\)
sec y = sec(π – \(\frac {π}{3}\))
sec y = sec(2\(\frac {π}{3}\))
y = (2\(\frac {π}{3}\))
tan^-1(√3) – sec^-1(-2) = \(\frac {π}{3}\) – \(\frac {2π}{3}\)
= \(\frac {π – 2π}{3}\) = –\(\frac {π}{3}\)

(ii) sin^-1(-1) + cos^-1(\(\frac {1}{2}\)) + cot^-1(2)
x = sin^-1(1)
sin x = -1 = sin(-\(\frac {π}{2}\))
x = –\(\frac {π}{2}\)
y = cos^-1(\(\frac {1}{2}\))
cos y = \(\frac {1}{2}\) = cos \(\frac {π}{3}\)
y = \(\frac {π}{3}\)
z = cot^-1(2)
cot z = 2
z = cot^-1(2) is constant.
sin^-1(-1) + cos^-1(\(\frac {1}{3}\)) + cot^-1(2)
= –\(\frac {π}{2}\) + \(\frac {π}{3}\) + cot^-1(2)
= –\(\frac {3π+2π}{6}\) + cot^-1(2)
= cot^-1(2) – \(\frac {π}{6}\)

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Poem 5 A Father To His Son Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Poem 5 A Father To His Son

12th English Guide A Father To His Son Text Book Back Questions and Answers

1. Fill in the blanks choosing the words from the box given and complete the summary of the poem:
(Text Book Page No. 64)

Lines 1-25:

The poet Carl Sandburg gives a vivid description of a father’s worldly (1) ______ in directing a son who is at the threshold of his (2) ______. Here the father motivates his son to be like a hard (3) ______ and withstand life’s (4) ______ and sudden betrayals. (5) ______ is like fertile soil. We can make our life fruitful if we are gentle, and take life as it comes. At times (6) _________ overtakes harshness. The growth of a (7) ______ can split a rock. One should have an (8) ________and strong will to achieve. Greed for (9) _________ has left men dead before they really die. Good men also have fallen prey in the quest for (10) ______ money. Time for (11) ______ is not a waste. When you seek knowledge never feel ashamed to be called a (12) ______ for not knowing, at the same time learn from your (13) _________and never (14) ______ it.
Answers:

1. wisdom
2. manhood
3. rock
4. challenges
5. life
6. gentleness
7. tender
8. deep
9. money
10. carry
11. leisure
12. fool
13. mistake
14. repeat

Lines 26-44:

Do (15) ______ often, and do not hesitate to accept your shortcomings, avoid (16) _________to protect self against other people. Solitude helps to be (17) and (18) ________ are taken in silent rooms. Instead of being one among many, be (19) ______. if that is your nature. The son may need lazy days to find his (20) ______abilities, to seek what he is born for. He will then know how free imaginations bring (21) ______ to the world, which (22) ______ change. During such resentment, let him know that it is time for him to be on his own, and (23) ______to achieve like Shakespeare, the Wright brothers, Pasteur, Pavlov, and Michael Faraday.
Answers:
(15) introspect
(16) white
(17) creative
18) final decision
(19) different
(20) inherent
(21) changes
(22) resents
(23) work

2. Based on your understanding of the poem answer the following questions in one or two sentences:
(Text Book Page No. 165)

Question a.
How would the poet’s advice help his son who is at the threshold of manhood?
Answer:
The poet’s advice would help the son at the threshold of manhood, to grow as a positive individual and succeed in life like great scientists and dramatists.

Question b.
‘A tough will counts.’ Explain.
Answer:
In life, everybody may face a tough situation which is surrounded by obstacles. But we should not give up our try to achieve our goal or success. One should have a deep desire and strong will power to achieve it.

Question c.
What happened to the people who wanted too much money?
Answer:
People who wanted too much money fell prey to greed. They lost their reputation also.

Question d.
What has twisted good men into thwarted worms?
Answer:
Questing for easy money in a dishonourable way has twisted goodmen into thwarted (frustrated) worms.

Question e.
How would his being alone help the boy?
Answer:
Solitude would help the boy to be creative.

Question f.
Where are the final decisions taken?
Answer:
The final decisions are taken in a silent room.

Question g.
What are the poet’s thoughts on ‘being different’?
Answer:
Instead of being one among many, one can be different if it is one’s nature to be so. One need not take conscious efforts to be different.

Question h.
Why does the poet advise his son to have lazy days?
Answer:
The poet advises his son to have lazy days because that helps him to seek his strong motives and find his own real inherent abilities.

Question i.
The poet says ‘Without rich wanting nothing arrives’ but he condemns ‘the quest of lucre beyond a few easy needs. Analyze the difference and write.
Answer:
Appreciating the rich wanting and condemning ‘the quest for lucre beyond a few easy’ needs seems like a conundrum. One needs to take both the statements with a pinch of salt. One needs strong will power to succeed. One can earn a lot too. Jack Ma has had a strong will and earned beyond lucre but invested a major part in community development and charitable works retaining some for his basic needs. Warren Buffet, Bill Gates, and Ratan Tata are other such examples. The wealth earned should benefit a large number of people and not the individual who initiated the wealth.

4. Read the lines given below and answer the questions that follow: (Text Book Page No. 166)

a) “Life is hard; be steel; be a rock.”

i) How should one face life?
Answer:
One should face life daringly like steel and hard rock.

ii) Identify the figure of speech in the above line.
Answer:
Metaphor.

b) “ Life is a soft loam; be gentle; go easy.”
And this too might serve him.

i) Why does the poet suggest to take life easy?
Answer:
Life is like fertile soil. If one is gentle and easy, he too can succeed.

ii) Identify the figure of speech in the above line.
Answer:
Metaphor.

c) Tell him solitude is creative if he is strong
and the final decisions are made in silent rooms.

i) Can be in solitude help a strong human being? How?
Answer:
Yes, being in solitude helps a strong human being. He becomes creative and strong in solitude.

ii) Identify the figure of speech in the above line.
Answer:
Transferred Epithet.

d) Tell him time as a stuff can be wasted.
Tell him to be a fool every so often

i) Why does the poet suggest that time can be wasted?
Answer:
Time can be wasted in learning new things and learning from one’s mistakes.

ii) Identify the figure of speech in the above line.
Answer:
Repetition.

e) Tell him to be a fool ever so often
and to have no shame over having been a fool
yet learning something out of every folly
hoping to repeat none of the cheap follies.

i) Is it a shame to be a fool at times?
Answer:
No, it is not a shame to be a fool at times and at the same time learn from your mistake and that should not be repeated.

ii) What does one learn from every folly?
Answer:
One does learn something from every failure.

f) ……………..Free imaginations
Bringing changes into a world resenting change.

i) How does free imagination help the world?
Answer:
Free imagination helps to bring changes into the world.

ii) Identify the figure of speech.
Answer:
Transferred epithet.

e) Pick out the alliterated words from the poem and write.
And this might stand him for the storms.
Answer:
Stands-Storms

Additional Questions:

a) “and serve him for humdrum monotony?

i) Who does ‘him’ refer to?
Answer:
‘Him’ refers to son.

ii) What does ‘humdrum monotony’ mean?
Answer:
Humdrum monotony means boring routine.

b) “Tell him too much money has killed men and left them dead years before burial”

i) What would kill the men?
Answer:
Too much money earning in a dishonest way would kill the men.

ii) What would bring if men greed for money?
Answer:
Greed for money has left men to die before they really die.

“Whatever the white lies and protective fronts”

i) Pick out the alliterated words from the above line.
Answer:
Whatever – Whitelies.

ii) What does ‘white lies’ mean?
Answer:
‘Whitelies’ means lies told to avoid hurting one’s feelings.

d) “has twisted good enough men sometimes into dry thwarted worms”.

i) What makes good men into thwarted worms?
Answer:
Questing for easy money makes good men into thwarted worms.

ii) What does ‘thwarted’ mean?
Answer:
‘Thwarted’ means frustrated.

5. Explain the following lines with reference to the context: (Text Book Page No. 167)

a) and guide him among sudden betrayals and tighten him for slack moments:

Reference:
These lines are taken from Poem – “A father to his son”, Poet – “Carl August Sandburg”.
Context:
The poet brings out his advice to his son.
Explanation:
The poet advises his son who is standing at the threshold of manhood. It’s a time when nearly each and every father becomes protective and cautious. So the poet motivates his son to be like a hard rock (daring) and bold enough to face challenges and sudden betrayals. ‘Slack moments’ refers to a state of depression also, he should know how to overcome that.

b. Brutes have been gentled where lashes failed.

Reference:
These lines are taken from Poem – “A father to his son”, Poet – “Carl August Sandburg”.
Context:
The poet tells his son how the brute will become gentle.
Explanation:
The poet motivates his son to reach manhood to be gentle. This will make him face the challenges of life and sudden betrayals. At times gentleness overtakes harshness. Thrashing may fail to change a man. But a gentle approach will make a brute good-natured.

c. Gentleness makes our life fruitful.
Yet learning something out of every folly hoping to repeat none of the cheap follies

Reference:
These lines are taken from Poem – “A father to his son”, Poet – “Carl August Sandburg”.
Context:
The poet tells his son not to repeat his mistakes.
Explanation:
The poet advises his son that making mistakes is common. He should not get discouraged. When he seeks knowledge never feel ashamed to make mistake. But at the same time, he could learn from his mistakes. Doing the same mistakes makes the man less effective. So we should be careful not to repeat the mistake.

d. ‘He will be lonely enough
to have time for the work.

Reference:
These lines are taken from the Poem – “A father to his son”, Poet – “Carl August Sandburg”.
Context:
The poet says how his son’s loneliness makes him work effectively.
Explanation:
The poet wants his son to know how free imagination brings changes to the world which resents change. During such resentment, let him know that it is time for him to be his own and try to achieve like great people.

6. Answer the following questions in about 100-150 words each: (Text Book Page No. 167)

Question a)
Explain how the poet guides his son who is at the threshold of manhood, to face the challenges of life.
Question b)
How according to the poet is it possible for his son-to bring changes into a world that resents change?

Introduction:
The poet Carl Sandburg gives a vivid description of a father’s worldly wisdom in directing a son who is at the threshold of “manhood”. The caring father wants him to be like a rock and face the storms of life and betrayals.

What is Life:
Life is like fertile soil, so he directs him to go easy with gentleness. “Life is a soft loam; be gentle; go easy.” We can make our life fruitful if we are gentle and take life as it comes. The poet tells his son how the brute will become gentle. This will make him face the challenges of life and sudden betrayals. At times gentleness overtakes harshness. Thrashing may fail to change a man. But a gentle approach will make a brute good-natured. Gentleness makes our life fruitful. The growth of a tender flower (gentleness) can split a rock (harshness).

Father’s advice:
One should have a deep and strong “will” to achieve his good. While achieving his goal, he would face discouragement but he should not get vexed. He should not give up his task. Greed for money has left men to die before they really also. Goodman also has fallen prey in the quest for easy money. But that should not be encouraged. He should earn money in the right way. When you seek knowledge never feel ashamed to be called a fool for not knowing, at the same time learn from his mistake and never repeat it. Do introspect often, and do not hesitate to accept your shortcomings and avoid white lies to protect yourself against other people. He wants his son to avoid white lies and tells him that solitude is creative.

Father’s belief:
The son may have his lazy days to seek his inner motives and find his talent. Free imaginations bring him to know that it is time for him to be on his own and work to achieve like Shakespeare, the Wright Brothers, Michael Faraday.

Conclusion:
The poet wants his son to know how free imagination brings changes to the world. During such resentment, let him know that it is time for him to be his own and try to achieve his goal.

கவிஞரைப் பற்றி:

சான்பர்க் (Sandburg) Swedish ancestry பெற்றேரருத்த இல்லினஸ்ஸின் (Illinois) a Giron கேல்ஸ்ஸ ர்க்கில் (Galesburg) பிறந்தவர். கார்ல் ஆகஸ்ட் சான்பர்க் (ஜனவரி 6, 1878 –ஜீலை 22, 1967) அமெரிக்காவை சார்ந்த கவிஞர், எழுத்தாளர் மற்றும் பதிப்பாளர் ஆவார். இவரின் இரு கவிதைகளுக்காகவும், ஆபிரகாம் லிங்கனின் (Abraham Lincoln) வாழ்க்கை வரலாற்றை எழுதியதற்காகவும் மும்முறை புலிட்சர் பரிசு (Pulitzer Prizes) வழங்கப்பட்டார்.

இவரின் வாழ்க்கையில் சான் பர்க் இலக்கியத்தில் சிறந்தவராக கருதப்பட்டார். முக்கியமாக இவரின் Chicago poems (1916) Corn huskers (1918) மற்றும் Smoke and steal (1920) ஆகியவற்றிக்காவும் சிறந்தவராக கருதப்பட்டார். இவர் 1967ல் இவரின் மரணத்தின் போது Lyndon B. Johnson ஆகியவர்களாலும் அமெரிக்காவில் சிறந்த கவிஞராக கருதப்பட்டார்.

கவிதையைப் பற்றி:
ஒவ்வொரு பெற்றோரும் தன் குழந்தையின் நலனையே விரும்புவர். அதை அவர்களுக்கு அறிவுரை வழங்கி வெளிப்படுத்துவர். இந்த கவிதையிலும் தந்தை தன் மகனுக்கு குழந்தை பருவம் முதல் இளமை வரை செய்ய வேண்டிய செயல்களை கற்று கொடுப்பதாக அமைத்திருக்கிறார். வாழ்க்கையின் இன்ப துன்பங்களை கற்று கொடுக்கிறார். அவன் புயலை தாங்கும் பாறையைப் போல் வாழ்க்கையை எதிர் கொள்ள வேண்டும்.

அவன் மென்மையான இதயம் கொள்ள வேண்டும். பேராசையுடன் இருக்க கூடாது. தன் தவறுகளிலிருந்து பாடம் கற்றுக் கொள்ள வேண்டும். தனிமையில் ஆக்கப்பூர்வமான சிந்தனைகளை சிந்திக்க வேண்டும். தன்னை சிறப்புமிக்கவனாக மாற்றிக் கொள்ளவேண்டும். தன்னைத்தானே முழுமையாக புரிந்து கொள்ள வேண்டும். இதனைப் பற்றி முழுமையாக இக்கவிதை வாசித்து புரிந்து கொள்வோம்.

A Father To His Son Summary in Tamil

வளரும் பருவத்தில் (manhood) தன் மகனிடம் தந்தை
என்ன செய்தியைக் கூறுவார்? “வாழ்க்கை கடினமானது, இரும்பென (steel) இரு. பாறையாய் (rock) இரு”.
அது அவனைப் புயலை (storm) எதிர்த்து நிற்கச் செய்யும்
தனிமையிலும் சோர்விலும் (humdrum monotony) அவனுக்கு உதவி செய்யும்.

எதிர்பாரா ஏமாற்றங்களில் (betrayals) அவனை வழி நடத்தும் (guide)
வலுவற்ற தருணங்களில் (slack moments) அவனுக்கு வலுவூட்டும்
“வாழ்க்கை எளிமையானது. நேர்மையாயிரு (gentle), எளிதாய் செல்”.
இதுவும் அவனுக்கு பயன்படும்.
சாட்டைகளின் (ashes) சரிவில் மிருகங்கள் (brutes) கூட மிருதுவாகிவிட்டது.

பாதையில் பூக்கும் (frail flower) பஞ்சுபோன்ற பூ கூட
பாறைகளை பிளந்து சிதறடிக்கிறது (shattered) சிலநேரங்களில்
கடினமானவையும் (tough) விருப்பங்களும் (desire) மிக முக்கியமானவை.
அதுபோன்றே பணம்படைத்தோரின் எளிய எதிர்பார்ப்புகளும்
சிறந்த எதிர்பார்ப்புகளின்றி ஏதும் வருவதில்லை.

அவனிடம் கூறுங்கள் அதிக பணம் மனிதரைக் கொன்றிருக்கிறது.
புதைப்பதற்கு (burial) பல வருடங்களுக்கு முன்பே என்று
தேவைகளைத் தூண்டிய பணம் குவிக்கும் ஆவல் (guest)
நல்ல மனிதர்களைக் கூட சிலநேரம்
வெறுக்கத்தக்க காய்ந்த (thwarted) புழுக்களாக (worms) மாற்றிவிடும் (twisted).

அவனிடம் கூறுங்கள் நேரம் வீணாக்குவதற்கே.
கூறுங்கள் அவனிடம் அடிக்கடி முட்டாளாக (fool)
முட்டாளாவதற்கு அவமானப்பட (shame) வேண்டாமென்று
அந்த முட்டாள்தனத்திலிருந்து (folly) ஏதேனும் கற்றுக்கொள்வதற்கு கூறுங்கள்
அதில் எதையும் திரும்ப (repeat) செய்யக் கூடாதென்று.

இவ்வாறாக உலகின் முட்டாள்களைப் (fool) பற்றிய
ஆழ்ந்த புரிதலை (intimate understanding) அடைய வேண்டுமென்று.
அடிக்கடி தனித்திருந்து சுயத்தை அடையக் கூறுங்கள்.
அனைத்துக்கும் மேலாக தன்னைப் பற்றி பொய் (lies) கூறக் கூடாதென்று
பிறரைக் காயப்படுத்தா பொய்களையும் (white lies), பாதுகாப்பு (protective) உரைகளையும்

பிறருக்கெதிராய் (against) அவன் பயன்படுத்திய போதிலும்
கூறுங்கள் அவனிடம் தனிமையே (solitude) புதுமை அவன் வலிமையாயிருந்தால்
மற்றும் இறுதி முடிவுகள் (decisions) உருவாவது அமைதியான அறையிலே (silent rooms).
அவனிடம் கூறுங்கள் பிறரிடமிருந்து வேறுபட்டிருக்க
இயற்கையாகவும் (natural) எளிதாகவும் (easy) வேறுபாடு வருமென்றால்

அவன் ஓய்வு நாட்கள் (lazy days) பெறட்டும் ஆழ்ந்த நோக்கங்களைத் தேட (deeper motive)
அவன் ஆழமாய் தேடட்டும் அவன் எங்கு பிறந்தான் என்பதை
பின் அவன் புரிந்துகொள்வான் ஷேக்ஸ்பியரையும் (shakespeare), ரைட் சகோதரர்களையும் (wright brothers), பாஸ்டரையும் (Pasteur), பாவ்லோவையும் (Pavlov) மைக்கேல் பாரடே (Michael Faraday) மற்றும் சுதந்திர
சிந்தனைகளை (free imaginations)

மாற்றங்களை விரும்பா உலகிற்கு மாற்றம் (resenting change) கொண்டு வருவனவற்றை
தேவையான அளவு தனிமையில் இருப்பான் அவனறிந்த
அவனுடைய வேலைகளைச் (work) செய்ய
சரியான நேரம் (time) பெற.

Tamilnadu State Board New Syllabus Samacheer Kalvi 4th English Guide Pdf Term 3 Supplementary Chapter 3 The Magic Pencil Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 4th English Solutions Term 3 Supplementary Chapter 3 The Magic Pencil

4th English Guide The Magic Pencil Book Back Questions and Answers

A. Choose the best answer.

Question 1.
Chris enjoyed doing all sorts of things except, writing and _____________
(a) Singing
(b) Art
(c) Acting
Answer:
(b) Art

Question 2.
One day Chris tried to draw a _____________.
(a) Rectangular
(b) Circle
(c) Triangle
Answer:
(b) Circle

Question 3.
Pencil asked him to draw _____________
(a) Pair of eyes
(b) Pair of ears
(c) Face
Answer:
(a) pair of eyes

Question 4.
Draw me some hair, quickly, I look like a ____________
(a) Princess
(b) Lollipop
(c) Prince
Answer:
(b) Lollipop

Question 5.
Before going to bed that night, Chris gave his new teacher a ___________
(a) Hearty thanks
(b) Costly pen
(c) A ring
Answer:
(a) Hearty thanks

B. Answer the following questions.

Question 1.
What was the truth finally learned by Chris?
Answer:
Chris learned that to learn to do things, you only needed to keep trying and to enjoy while doing so.

Question 2.
How can we do our work better?
Answer:
We can do our work better by practising a lot and enjoying what we do.

Question 3.
Why did he rub the circle again and again?
Answer:
He rubbed the circle again again because it did not look nice and the circle went on asking him to do it better.

Question 4.
Why was Chris worried?
Answer:
Chris was worried because he did not know if he had spent the previous afternoon talking with the little man or whether he was dreaming all of it.

Question 5.
What is the one thing you will try and improve after reading the story? How?
Answer:
Whatever one does, one has to imagine before doing and try to do it a bit better and better to improve the work.

I. Write True or False.

Question 1.
One day Chris found a pen of such lovely colours.
Answer:
False

Question 2.
Chris managed to draw two little spots outside the circle.
Answer:
False

Question 3.
Chris erased the circle and drew another one.
Answer:
True

Question 4.
Chris had never practiced more than two hours at a time.
Answer:
False

Question 5.
It made no difference whether you had the magic pencil or not.
Answer:
True

II. Identify the Character/Speaker.

Question 1.
“At least draw me a pair of eyes.”
Answer:
The drawing

Question 2.
“I don’t draw very well.”
Answer:
Chris

Question 3.
“I’m going to have to teach you how to draw until you can do me well.”
Answer:
The circle

Question 4.
“But I didn’t do anything!”
Answer:
The little drawing

Question 5.
“You are correct, but, thank you.”
Answer:
Chris

Question 6.
“OK. No problem.”
Answer:
The drawing

III. Choose the best answer.

Question 1.
He carefully kept the pencil in his ____________.
(a) Pocket
(b) School bag
(c) Cupboard
Answer:
(b) School bag

Question 2.
“Hey! You forgot my __________ again!”
(a)Ears
(b) Head
(c) Eyes
Answer:
(c) Eyes

Question 3.
Using ___________ and pencils was not easy for him.
(a) Pens
(b) Brushes
(c) Notebooks
Answer:
(b) Brushes

Question 4.
Just then, his drawing began to __________ to him.
(a) Listen
(b) Read
(c) Speak
Answer:
(c) Speak

Question 5.
Chris managed to draw ___________ little spots inside the circle.
(a) Two
(b) Three
(c) Four
Ans:
(a) Two

Let us read aloud

A. Read the passage 3 times and colour the medal for each time.

The school was decorated for the Annual Sports Day. The children came to the running track to cheer the runners. The next event was 800 meters running. Megala was in the race. She wanted to win the race, but the other runners were district and divisional winners. The race started. All had to finish two laps. At the end of the first lap, Megala was in the fifth place. Suddenly, she fell on the ground. Everyone ran to help her. But before that she got up and started to run. All children and teachers cheered her. She had come last, but the headmaster gave her a special prize.

Answer the following questions.

Question 1.
What was the event Megala participated?
Answer:
Megala participated in 800 meters running.

Question 2.
Why did everyone support Megala?
Answer:
Megala fell down. Everyone ran to help her.

Question 3.
What is the main idea of the story?
Answer:
The main idea is to encourage people who don’t stop trying.

Question 4.
Why did the head master give Megala a special prize?
Answer:
The headmaster gave Megala a special prize because she continued to run even after a fall.

Complete the following picture board.

Question 1.

Answer:
Once there was a wicked crane lived near But the crane took the fish one a pond. It told the fish and crab that by one to the woods and ate them the pond would be dried up soon due to a up. Only the bones of fish were severe drought. It offered to help them left. to take them to another pond which had plenty of water. All the fish and the crab agreed.

Question 2.

Answer:
One day, the crane took the crab on its Then the crab immediately back. The crane was about to eat the clawed the crane so hard that its crab also. The crab saw the bones of fish head broke and the wicked crane and understood the situation.
died.

Question 3.

Answer:
But the crane took the fish one by one to the woods and ate them up. Only the bones of fish were left.

Question 4.

Answer:
Then the crab immediately clawed the crane so hard that its head broke and the wicked crane died.

I can do

A. Choose the correct option.

Question 1.
The child got an _________ for winning the race.
(a) Award
(b) Magic
(c) Shock
Answer:
(a) Award

Question 2.
I got ___________ to see his favourite heroine.
(a) Fend
(b) Chance
(c) Deaf
Answer:
(b) Chance

B. Match with the opposite gender.

Question 1.
Prince – bridegroom
Answer:
prince – princess

Question 2.
hero – princess
Answer:
hero – heroine

Question 3.
bride – heroine
Answer:
bride – bridegroom

C. Write the correct word.

Question 1.

Answer:
Rooster

Question 2.

Answer:
Hen

Question 3.

Answer:
King

Question 4.

Answer:
Queen

Question 5.

Answer:
Tiger

Question 6.

Answer:
Tigress

D. Recite the poem Never give up with correct intonation.

E. Match the rhyming words.

Question 1.
Earn – day
Answer:
Earn – learn

Question 2.
Fend – learn
Answer:
Fend – end

Question 3.
Glow – end
Answer:
Glow – slow

Question 4.
play – slow
Answer:
play – day

F. Fill in the blanks with present continuous tense of the given word.

Question 1.
They __________ (eat) their breakfast.
Answer:
They are eating their breakfast.

Question 2.
He __________ (read) a news paper.
Answer:
He is reading a news paper.

Question 3.
Bharathi _________ (write) his home work.
Answer:
Bharathi is writing his home work.

The Magic Pencil Summary in English and Tamil

Chris was a little boy who enjoyed going to school and doing all sorts of things except art and writing. Using brushes and pencils was not easy for him. So, his artwork was never a happy ending, and he would give up quickly.

க்ரிஸ் என்ற சிறுவன் பள்ளிக்குச் செல்வதில் சந்தோஷப்படுபவன் அவனுக்கு படம் வரைவதுமற்றும் எழுதுவது ஆகியவற்றை தவிர, மற்ற அனைத்தையும் செய்வது பிடிக்கும். தூரிகைகளையும், பென்சில்களையும் உபயோகிப்பது அவனுக்கு எளிதாக இருக்கவில்லை . அதனால் படம் வரைவது அவனுக்கு எப்போதும் மகிழ்ச்சியைத் தருகிற செயலாக முடிந்ததில்லை , அதனால் அவன் விரைவில் (பாதியில்) விட்டுவிடுவான்.

But one day Chris found a pencil of such lovely colours that he could not resist and he tried to draw a circle. As always, it did not go well, he was about to throw the pencil away. Just then, his drawing began to speak to him.

ஆனால் ஒரு நாள் க்ரிஸ் பல அழகிய வண்ண ங்களைக் கொண்ட பென்சிலை கண்டவுடன், ஆசையை அடக்கஇயலாமல் ஒரு வட்டம் வரைய முயன்றான். வழக்கம் 4 போலவே அது சரியாக வராததால், அவன் பென்சிலை தூக்கி எறிய முற்பட்டான். அப்போது தான், அவனுடைய ஓவியம் அவனிடம் பேச ஆரம்பித்தது.

“Hey! Are you going to leave me like this? At least draw me a pair of eves ” said the drawing. Chris was shocked, but he managed to draw two little spots inside the circle.

“ஏய், என்னை இப்படியே விட்டுவிடப் போகிறாயா? எனக்கு குறைந்தபட்சம் கண்களையாவது வரைந்துவிடேன்” என்று அந்த ஓவியம் கூறியது. க்ரிஸ் அதிர்ந்து போனான், ஆனாலும் இரு சிறிய புள்ளிகளை அந்த வட்டத்திற்குள் வரைந்தான்.

“Much better, now I can see myself,” said the circle looking around at itself. “Ahh! What have you done to me?” “I don’t draw very well,” said Chris, trying to make excuses. “OK. No problem.” said the drawing. ” I am sure that if you try again, you’ll do better. Go on, rub me out!” So, Chris erased the circle and drew another one. Like the first one, it was not very round.

“பரவாயில்லை , இப்போது என்னையே என்னால் பார்க்க முடிகிறது” என்ற வட்டம், தன்னையே சுற்றிபார்த்துக் கொண்டு “ஆஹா… எனக்கு நீ என்னசெய்துவிட்டாய்?” என்றது. “எனக்கு நன்றாய் வரையத் தெரியாது” என்று கிரிஸ் மன்னிப்பு கோரினான். “பரவாயில்லை, ஒன்றும் பிரச்னையில்லை” என்ற வட்டம், “நீ மறுபடி முயன்றால், உன்னால் நன்றாகவரைய முடியும். என்னை தேய்த்து அழி” என்றது. 10 அதனால், க்ரிஸ் அந்த வட்டத்தை அழித்துவிட்டு வேறு ஒன்றை வரைந்தான். அது முன்னர் வரைந்து போல் முழு வட்டமாக இல்லை .

“Hey! You forgot my eyes again!” “Oh, yeah.”Hmm, I think I’m going to have to teach you how to draw until you can do me well;”. said the circle with its quick, squeaky little voice.

“ஹே! மறுபடியும் , என் கண்களை வரைய மறந்துவிட்டாய்!””ஆமாம்” என்றான் க்ரிஸ்.””ம்.. என்னை சரியாக நீ வரையும் வரையில் நான்தான் உனக்கு சொல்லித்தர வேண்டியிருக்கும் போல் உள்ளது,” என்று வட்டம் தன் விரைவான, மெல்லிய குரலில் கூறியது.

Chris, who was still shocked, thought that this was a good idea. He immediately found himself drawing and erasing circles.The circle would not stop saying “Rub this out, but carefully; it hurts,” or “Draw me some hair, quickly, I look like a lollipop!”and other funny remarks.

தன் அதிர்ச்சியிலிருந்து மீளாத க்ரிஸ், இது ஒரு நல்ல யோசனை என நினைத்தான். உடனே அவன் வட்டங்களை வரைதல், அழித்தல் என வேலையில்இறங்கினான். வட்டமும், “இதை அழி, கவனம்” “வலிக்கிறது” “எனக்கு கொஞ்சம் முடியை வரை, சீக்கிரம், நான் பார்ப்பதற்கு ஒரு லாலிபாப் மிட்டாய்) போல இருக்கிறேன்,” என்று விதவிதமாக குரல் கொடுத்துக் கொண்டிருந்தது.

After spending the whole afternoon together, Chris could now draw the little figure much better than most of his classmates. He was enjoying it so much that he did not want to stop drawing with this crazy new teacher of his. Before going to bed that night, Chris gave his teacher a hearty thank you for teaching him to draw.

மதியம் முழுவதும் செலவிட்டபின் க்ரிஸ் அந்த சிறிய உருவத்தை தன் மற்ற வகுப்பு தோழர்களைவிட சிறப்பாக வரைந்திருந்தான். அந்த கோமாளித்தனமானபுதிய ஆசிரியருடன் (ஓவியம்) வரைவது அவனுக்கு பிடித்திருந்ததால் அவன் வரைவதை நிறுத்தவில்லை. இரவு, படுக்கைக்கு செல்லுமுன் அவன் அந்த புதிய ஆசிரியருக்கு (ஓவியத்திற்கு), தனக்கு வரைய கற்றுத் new தந்ததற்கு மனதார நன்றி தெரிவித்தான்.

“But I didn’t do anything!” answered the little drawing.”Don’t you see that you’ve been practising a lot, and enjoying it all the while? I bet that’s the first time you’ve done that!”Chris stopped to think. The truth was that he had drawn so badly because he had never practised more than ten minutes at a time. He had always done it angrily. So, what the little drawing had said was correct. “You are correct, but, thank you,” he said.He carefully kept the pencil in his school bag before going to sleep.

“நான் எதுவும் செய்யவில்லையே!” என்றது அந்த சிறிய ஓவியம். அது மேலும், . .”நீ நன்றாக பயிற்சி செய்தாய், அதை மகிழ்ச்சியோடு செய்தாய் அல்லவா? இதுதான் முதல் முறை நீ அவ்வாறு செய்திருக்கிறாய் என்று நான் பந்தயமே கட்டுவேன்!” என்றது. க்ரிஸ் யோசிப்பதற்காக நின்றபொழுது, அந்த உண்மை புலப்பட்டது. அது யாதெனில், ஒரே சமயத்தில்அவன் பத்து நிமிடத்திற்கு மேல் தொடர்ந்து பயிற்சி செய்யாததால்தான் அவனால் சிறப்பாக வரைய இயலவில்லை. அவன் எப்போதும் ஒரு கோபத்துடனே அந்த பணியை செய்து வந்தான். எனவே, அந்த சிறிய ஓவியம் கூறியது சரிதான். “நீ கூறுவது சரியே. அதற்கு உனக்கு நன்றி”என அவன் கூறினான். தான் உறங்குமுன் அந்த பென்சிலை பத்திரமாக தன் பள்ளிக்கூட கையில் வைத்துக் கொண்டான்.

The next morning Chris jumped out of bed and went running to find his pencil, but it was not there. He searched everywhere, but there was no sign of it. The sheet of paper on which he had drawn The little figure, although still full of rubbing out marks, was completely blank. Chris was worried and he did not know if he had spent the previous afternoon talking with me the little man or whether he was dreaming all of it. So, to settle the matter, he took a pencil and paper and tried to draw a little man.

மறுநாள் காலை க்ரிஸ் துள்ளிக்கொண்டு தன் பென்சிலை தேடினான். ஆனால் அது இல்லை . எல்லா இடங்களிலும் அவன் தேடிப்பார்த்தான்ஆனால் அதற்கான தடயமே இல்லை. அவனுடைய அழித்தல்கள் நிறைந்த தடங்களை கொண்ட காகிதம் மட்டும். இருந்தது. ஆனால் அது அசிறியஓவியமின்றி, வெற்றுக் காகிதமாக இருந்தது. க்ரிஸ் மிகவும் வருத்தத்துடன், தான் நேற்று மதியம் பேசிக்கொண்டிருந்த சிறிய மனிதரஉண்மையில்வந்தவரா? அல்லது கனவா? என்று அவனுக்கு விளங்கவில்லை எனவே இந்த விஷயத்தை முடிப்பதற்காக, அவன் மறுபடி ஒரு பென்சிலையும், பேப்பரையும் எடுத்து அந்த சிறிய மனிதரை (ஓவியத்தை வரைய முயற்சித்தான்.

It turned out not bad at all, except for a couple of rough lines. He imagined his little teacher telling him to rub and fix them. Chris gladly rubbed out those bits and redrew them. He realised that the crazy little teacher had been right: it made no difference whether you had The magic pencil or not. To learn to do things,you only needed to keep trying and to enjoy while doing so.From that day on, whenever Chris tried to draw or paint, or do anything else, he always had fun imagining his drawing telling him “Come on my Friend do me bit better than that! I can’t go out looking like this!”

ஒரு சில கோடுகளைத் தவிர, ஓவியம் நன்றாகவே வந்தது. அவனுடைய சிறிய ஆசிரியர், அவனுக்குஅழித்து, வரைவது பற்றி சொல்லித் தருவது போல் கற்பனை செய்து கொண்டான். க்ரிஸ் அந்த சில கோடுகளை அழித்துவிட்டு, மீண்டும் வரைந்தான். அவனுடைய சிறிய ஆசிரியர் கூறியது சரியே! உங்களிடம் மாய பென்சில் இருக்கிறதோ இல்லையோ, வேண்டும், அதுவும் சந்தோஷத்துடன் செய்ய வேண்டும்ஒரு செயலை அறிவதற்கு நீங்கள் தொடர்ந்து முயல என்பதே அது! அன்றிலிருந்து,. எப்பொழுதெல்லாம் க்ரிஸ் வரைவதற்கோ, வண்ணம் பூசவோமுயலும்போதெல்லாம் அவனுடைய கற்பனையில் அந்த ஓவியம் அவனிடம் “வா, நண்பா என்னை முன்பு வரைந்ததைவிட சிறப்பாய் வரை. இது போன்ற தோற்றத்துடன்என்னால் வெளியில் செய்ய இயலாது” என கூறுவதுபோல்தோன்றும்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.3 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.3

Question 1.
Find the domain of the following functions
(i) tan^-1 (\(\sqrt {9-x^2}\))
(ii) \(\frac {1}{2}\) tan^-1 (1 – x²) – \(\frac {π}{4}\)
Solution:
(i) f(x) = \(\tan ^{-1}(\sqrt{9-x^{2}})\)
We know the domain of tan^-1 x is (-∞, ∞) and range is \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
So, the domain of f(x) = \(\tan ^{-1}(\sqrt{9-x^{2}})\) is the set of values of x satisfying the inequality
\(-\infty \leq \sqrt{9-x^{2}} \leq \infty\)
⇒ 9 – x² ≥ 0
⇒ x² ≤ 9
⇒ |x| ≤ 3

(ii) Range of tan^-1 x is R
-∞ < 1 – x² < ∞
-∞ < -x² < ∞
-∞ < x < ∞
x ∈ R
Domain = R

Question 2.
Find the value of
(i) tan^-1(tan\(\frac {5π}{4}\))
(ii) tan^-1(tan(-\(\frac {π}{6}\)))
Solution:

Question 3.
Find the value of
(i) tan(tan^-1(\(\frac {7π}{4}\)))
(ii) tan(tan^-1(1947))
(iii) tan(tan^-1(-0.2021))
solution:
We know that tan(tan^-1 x) = x
(i) \(\tan \left(\tan ^{-1} \frac{7 \pi}{4}\right)=\frac{7 \pi}{4}\)
(ii) tan(tan^-1(1947))= 1947
(iii) tan(tan^-1 (-0.2021)) = -0.2021

Question 4.
Find the value of
(i) tan(cos^-1(\(\frac {1}{2}\)) – sin^-1(-\(\frac {1}{2}\)))
(ii) sin(tan^-1(\(\frac {1}{2}\)) – cos^-1(\(\frac {4}{5}\)))
(iii) cos(sin^-1(\(\frac {4}{5}\)) – tan^-1(\(\frac {3}{4}\)))
solution:

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 3 Trigonometry Ex 3.8 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.8

Question 1.
Find the principal solution and general solutions of the following
(i) sin θ = – \(\frac{1}{\sqrt{2}}\)
(ii) cot θ = √3
(iii) tan θ = –\(\frac{1}{\sqrt{3}}\)
Answer:
(i) sin θ = – \(\frac{1}{\sqrt{2}}\)
We know that principal of sin θ lies in \(\left[-\frac{\pi}{2}, \frac{\pi}{2}\right]\)
sin θ = – \(\frac{1}{\sqrt{2}}\) < 0
∴ The principal value of sin θ lies in the IV quadrant.
sin θ = – \(\frac{1}{\sqrt{2}}\)
= – sin \(\left(\frac{\pi}{4}\right)\)
sin o = sin \(\left(-\frac{\pi}{4}\right)\)
Hence θ = \(-\frac{\pi}{4}\) is the principal solution.
The general solution is
θ = nπ + (- 1)ⁿ . \(\left(-\frac{\pi}{4}\right)\) , n ∈ Z
θ = nπ + (- 1)^{n + 1} . \(\frac{\pi}{4}\) , n ∈ Z

(ii) cot θ = √3

The principal value of tan θ lies in \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Since tan θ = \(\frac{1}{\sqrt{3}}\) > 0
The principal value of tan θ lies in the I quadrant.

The general solution of tan θ is
θ = nπ + \(\frac{\pi}{6}\) , n ∈ Z

(iii) tan θ = –\(\frac{1}{\sqrt{3}}\)
The principal value of tan θ lies in \(\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\)
Since tan θ = – \(\frac{1}{\sqrt{3}}\) > 0
The principal value of tan θ lies in the IV quadrant.

The general solution of tan θ is
θ = nπ – \(\frac{\pi}{6}\) , n ∈ Z

Question 2.
Solve the following equations for which solutions lies in the interval 0° ≤ 9 < 360°
(i) sin⁴x = sin²x
Answer:
sin⁴x – sin²x = 0
sin² x (sin² x – 1) = 0
sin² x [ – (1 – sin² x)] = 0
sin²x × – cos²x = 0
– sin²x cos²x = 0
(sin x cos x)² = 0
(\(\frac { 1 }{ 2 }\) × 2 sin cos x)² = 0
\(\frac { 1 }{ 4 }\) sin 2x = 0
sin 2x = 0
The general solution is
2x = nπ, n ∈ Z
x = \(\frac{\mathrm{n} \pi}{2}\), n ∈ Z

(ii) 2 cos²x + 1 = – 3 cos x
Answer:
2 cos²x + 1 = – 3 cos x
2 cos²x + 3 cos x + 1 = 0
2 cos²x + 2 cos x + cos x + 1 = 0
2 cos x (cos x + 1) + 1 (cos x + 1) = 0
(2 cos x + 1) (cos x + 1) = 0
2 cos x + 1 = 0 or cos x + 1 = 0
cos x = \(-\frac{1}{2}\) or cos x = – 1
To find the solution of cos x = \(-\frac{1}{2}\)
cos x = \(-\frac{1}{2}\)


To find the solution of cos x = – 1
cos x = – 1
cos x = cos π
The general solution is
x = 2nπ ± π, n ∈ Z
x = 2nπ + π or x = 2nπ – π, n ∈ Z

Consider x = 2nπ + π
when n = 0 , x = 0 + π = π ∈ (0°, 360°)
when n = 1 , x = 2π + π = 3π ∉ (0°, 360°)

Consider x = 2nπ – π
when n = 0, x = 0 – π ∉ (0°, 360°)
when n = 1, x = 2π – π = π ∈ (0°, 360°)
when n = 2, x = 4π – π = 3π ∉ (0°, 360°)
∴ The required solution are x = \(\frac{2 \pi}{3}\), \(\frac{4 \pi}{3}\), π

(iii) 2 sin²x + 1 = 3 sin x
Answer:
2 sin²x – 3 sin x + 1 = 0
2 sin²x – 2 sin x – sin x + 1 = 0
2 sin x (sin x – 1) – 1 (sin x – 1) = 0
(2 sin x – 1)(sin x – 1) = 0
2 sin x – 1 = 0 or sin x – 1 = 0
sin x = \(\frac { 1 }{ 2 }\) or sin x = 1
To find the solution of sin x = \(\frac { 1 }{ 2 }\)
sin x = \(\frac { 1 }{ 2 }\)
sin x = sin \(\left(\frac{\pi}{6}\right)\)
The general solution is x = nπ + (-1)ⁿ\(\frac{\pi}{6}\), n ∈ z

(iv) cos²x = 1 – 3 sin x
Answer:
1 – 2 sin²x = 1 – 3 sinx
2 sin² x – 3 sin x = 0
sin x(2 sin x – 3) = 0smx =
sin x = 0 or 2 sin x – 3 = 0
sin x = 0 or sin x = \(\frac{3}{2}\)
sin x = \(\frac{3}{2}\) is not possible since sin x ≤ 1
∴ sin x = 0 = sin 0
The general solution is x = nit ,
When n = 0, x = 0 ∉ (0°, 360°)
When n = 1, x = π ∈ (0°, 360°)
When n = 2, x = 2π ∉ (0°, 360°)
∴ The required solutions is x = π

Question 3.
Solve the following equations:
(i) sin 5x – sin x = cos 3x
Answer:

2 cos 3 x . sin 2x = cos 3 x
2 cos 3x . sin 2x – cos3x = 0
cos 3x (2 sin 2x – 1) = 0
cos 3x = 0 or 2 sin 2x – 1 = 0
cos 3x = 0 or sin 2x = \(\frac { 1 }{ 2 }\)
To find the general solution of cos 3x = 0
The general solution of cos 3x = 0 is
3x = (2n + 1)\(\frac{\pi}{2}\), n ∈ Z
x = (2n + 1)\(\frac{\pi}{6}\), n ∈ Z
To find the general solution of sin 2x = \(\frac{1}{2}\)
sin 2x = \(\frac{1}{2}\)
sin 2x = sin \(\left(\frac{\pi}{6}\right)\)
The general solution is

∴ The required solutions are

(ii) 2 cos²θ + 3 sin θ – 3 = θ
Answer:
2 cos²θ + 3 sin θ – 3 = θ
2(1 – sin²θ)+ 3 sin θ – 3 = θ
2 – 2 sin²θ + 3 sin θ – 3 = θ
– 2 sin²θ + 3 sin θ – 1 = θ
2 sin² θ – 3 sin θ + 1 = θ
2 sin²θ – 2 sin θ – sin θ + 1 = θ
2 sin θ (sin θ – 1) – (sin θ – 1) = θ
(2 sin θ – 1) (sin θ – 1) = 0
2 sin θ – 1 = 0 or sin θ – 1 = θ
sin θ = \(\frac { 1 }{ 2 }\) or sin θ = 1
To find the general solution of’ sin θ = \(\frac { 1 }{ 2 }\)
sin θ = \(\frac { 1 }{ 2 }\)
sin θ = sin \(\frac{\pi}{6}\)
The general solution is θ = nπ + (-1)ⁿ\(\frac{\pi}{6}\), n ∈ Z
To find the general solution of sin θ = 1
sin θ = 1
sin θ = \(\frac{\pi}{2}\)
The general solution is θ = nπ + (-1)ⁿ\(\frac{\pi}{2}\), n ∈ Z
∴ The required solutions are
θ = nπ + (-1)ⁿ\(\frac{\pi}{6}\), n ∈ Z (or)
θ = nπ + (-1)ⁿ\(\frac{\pi}{6}\), n ∈ Z

(iii) cos θ + cos 3θ = 2 cos 2θ
Answer:
cos 3θ + cos θ = 2 cos 2θ

2 cos 2θ . cos θ = 2 cos 2θ
cos 2θ . cos θ – cos 2θ = θ
cos 2θ (cos θ – 1) = θ
cos 2θ = θ or cos θ – 1 = θ
cos 2θ = θ or cos θ = 1
To find the general solution of cos 2θ = θ
The general solution is
2θ = (2n + 1)\(\frac{\pi}{2}\), n ∈ Z
θ = (2n + 1)\(\frac{\pi}{4}\), n ∈ Z
To find the general solution of cos θ = 1
cos θ = 1
cos θ = cos 0
The general solution is θ = 2nπ , n ∈ Z
∴ The required solutions are
θ = (2n + 1)\(\frac{\pi}{4}\), n ∈ Z (or)
θ = 2nπ, n ∈ Z

(iv) sin θ + sin 3θ + sin 5θ = 0
Answer:
sin 5θ + sin 3θ + sin θ = 0

2 sin 3θ . cos 2θ + sin 3θ = 0
sin 3θ (2 cos 2θ + 1) = θ
sin 3θ = 0 or 2 cos 2θ + 1 = θ
sin 3θ = 0 or cos 2θ = –\(\frac { 1 }{ 2 }\)
To find the general solution of sin 3θ = 0
The general solution is
3θ = nπ, n ∈ Z
θ = \(\frac{\mathbf{n} \pi}{3}\), n ∈ Z
To find the general solution of cos 2θ = –\(\frac { 1 }{ 2 }\)

The general solution is

∴ The required solutions are

(v) sin 2θ – cos 2θ – sin θ + cos θ = θ
Answer:

(vi) sin θ + cos θ = √2
Answer:

The general solution is

(vii) sin θ + √3 cos θ = 1
Answer:
Divide each term by 2

(viii) cot θ + cosec θ = √3
Answer:

(ix) tan θ + tan \(\left(\theta+\frac{\pi}{3}\right)\) + tan \(\left(\theta+\frac{2 \pi}{3}\right)\) = √3
Answer:

(x) cos 2θ = \(\frac{\sqrt{5}+1}{4}\)
Answer:
we know cos 36° = \(\frac{\sqrt{5}+1}{4}\), 36° = \(\frac{\pi}{5}\)
cos 2θ = cos 36° = cos \(\left(\frac{\pi}{5}\right)\)
The general solution is
2θ = 2nπ ± \(\frac{\pi}{5}\), n ∈ Z
θ = nπ ± \(\frac{\pi}{10}\), n ∈ Z

(xi) 2cos ²x – 7 cos x + 3 = 0
Answer:
2 cos²x – 7 cos x + 3 = 0
2 cos²x – 6 cos x – cos x + 3 = 0
2 cos x (cos x – 3) – 1 (cos x – 3) = 0
(2 cos x – 1) (cos x – 3) = 0
2 cos x – 1 = 0 or cos x – 3 = 0
cos x = \(\frac { 1 }{ 2 }\) or cos x = 3
Since – 1 ≤ cos x ≤ 1 , we have
cos x = 3 is not possible.
∴ cos x = \(\frac { 1 }{ 2 }\)
cos x = cos \(\frac{\pi}{3}\)
The general solution is x = 2nπ ± \(\frac{\pi}{3}\), n ∈ Z

Tamilnadu State Board New Syllabus Samacheer Kalvi 9th Science Guide Pdf Chapter 6 Light Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 9th Science Solutions Chapter 6 Light

9th Science Guide Light Text Book Back Questions and Answers

I. Choose the correct answer :

Question 1.
A ray of light passes from one medium to another medium. Refraction takes place when angle of incidence is
(a) 0°
(b) 45°
(c) 90°
Answer:
(c) 90°

Question 2.
is used as reflectors in torchlight.
(a) Concave mirror
(b) Plane mirror
(c) Convex mirror
Answer:
(a) Concave mirror

Question 3.
We can create enlarged, virtual images with
(a) concave mirror
(b) plane mirror
(c) convex mirror
Answer:
(a) concave mirror

Question 4.
When the reflecting surface is curved outwards the mirror formed will be
(a) concave mirror
(b) convex mirror
(c) plane mirror
Answer:
(b) convex mirror

Question 5.
When a beam of white light passes through a prism it gets
(a) reflected
(b) only deviated
(c) deviated and dispersedAnswer:
(c) deviated and dispersed

Question 6.
The speed of light is maximum in
(a) vacuum
(b) glass
(c) diamond
Answer:
(a) vacuum

II. State whether true or false. If false, correct the statement :

1. The angle of deviation depends on the refractive index of the glass.
Answer:
True

2. If a ray of light passes obliquely from one medium to another, it does not suffer any deviation.
Answer:
False.
Correct statement: If a ray of light passes obliquely from one medium to another, it bends and from the normal.

3. The convex mirror always produces a virtual, diminished and erect image of the object.
Answer:
True.

4. When an object is at the centre of curvature of concave mirror the image formed will be virtual and erect.
Answer:
False.
Correct statement: When an object is at the centre of curvature of concave mirror the image formed will be real and inverted.

5. The reason for brilliance of diamonds is total internal reflection of light.
Answer:
True.

III. Fill in the blanks :

1. In going from a rarer to denser medium, the ray of light bends ……………………….
Answer:
towards the normal

2. The mirror used in search light is ……………………….
Answer:
concave

3. The angle of deviation of light ray in a prism depends on the angle of . ……………………….
Answer:
incidence

4. The radius of curvature of a concave mirror whose focal length is 5cm is ………………………..
Answer:
10 cm

5. Large ……………………….mirrors are used to concentrate sunlight to produce heat in solar furnaces.
Answer:
concave

IV. Match- the following :

Answer:

V. Assertion & Reason :

Mark the correct choice as:
(a) If both assertion and reason are true and reason is the correct explanation.
(b) If both assertion and reason are true and reason is not the correct explanation.
(c) If assertion is true but reason is false.
(d) If assertion is false but reason is true

Question 1.
Assertion: For observing the traffic at a hairpin bend in mountain paths a plane mirror is preferred over the convex mirror and concave mirror.
Reason: A convex mirror has a much larger field of view than a plane mirror or a . concave mirror.
Answer:
(d) Assertion is false but reason is true

Question 2.
Assertion: The incident ray is directed towards the centre of curvature of spherical mirror. After reflection it retraces its path.
Reason : Angle of incidence (i) = Angle of reflection (r) = 0°.
Answer:
(a) Both assertion and reason are true and reason is the correct explanation

VI. Answer very briefly:

Question 1.
According to cartesian sign convention, which mirror and which lens has negative focal length?
Answer:
Concave mirror is having a negative focal length.

Question 2.
Name the mirror(s) that can give (i) an erect and enlarged image, (ii) same sized, inverted image.
Answer:
Concave mirror.

Question 3.
If an object is placed at the focus of a concave mirror, where is the image formed?
Answer:
The image will be formed at infinity as real and inverted.

Question 4.
Why does a ray of light bend when it travels from one medium to another?
Answer:
A ray of light bend when it travels from one medium to another due to the change in velocity of light in two different medium.

Question 5.
What is the speed of light in vacuum?
Answer:
The speed of light in vacuum is known to be almost exactly 300,000 km per second. In 1665 the Danish astronomer Ole Roemer first estimated the speed of light by observing one of the twelve moons of the planet Jupiter.

Question 6.
Concave mirrors are used by dentists to examine teeth. Why?
Answer:
As concave mirror produces virtual, erect and magnified images when an object is placed in

VII. Answer briefly :

Question 1.
a) Complete the diagram to show how a concave mirror forms the image of the object.
b) What is the nature of the image?

Answer:
a)

b) Real, inverted and magnified.

Question 2.
Pick out the concave and convex mirrors from the following and tabulate them. Rear-view mirror, Dentist’s mirror, Torch-light mirror, Mirrors in shopping malls, Make-up mirror.
Answer:

Question 3.
State the direction of the incident ray which after reflection from a spherical mirror retraces its path. Give a reason for your answer.
Answer:
When an incident ray is directed towards the centre of curvature, at all the points of the spherical mirror, the ray is always normal. Therefore, angle of incidence i = Angle of reflection r = 0°.

Question 4.
What is meant by magnification? Write its expression. What is its sign for real image and virtual image?
Answer:
Magnification is the increase in size of an image compared to true size.

(a) Negative sign – real image
(b) Positive sign – virtual image

Question 5.
Write the spherical mirror formula and explain the meaning of each symbol used in it.
Answer:
The expression relating the distance of the object u, distance of image v and focal length/of a spherical mirror is called the mirror equation. It is given as:
Mirror formula: \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)
Here, f – focal length of spherical mirror; u – distance of the objective; v – distance of the image.

VIII. Answer in detail :

Question 1.
a) Draw ray diagrams to show how the image is formed using a concave mirror, when the position of objeict is (i) at C (ii) between C and F (iii) between F and P of the mirror.
b) Mention the position and nature of image in each case.
Answer:
a) object At C
i)

(b) Position of an object: At C
Position of the image: At C

Nature of the image:
(i) Real
(ii) Inverted
(iii) Same size as the object

(ii) object At C and F

Position of the object: Between C and F
Position of the image: Beyond C

Nature of the image :
(i) Real
(ii) Inverted
(iii) Magnified

(iii) Object between F and P of the Mirror

Position of object : Between F and P
Position of the image : Behind the Mirror

Nature of the image :
(i) Virtual
(ii) Erect
(iii) Magnified

Question 2.
Explain with diagrams how refraction of incident light takes place from a) rarer to denser medium b) denser to rarer medium c) normal to the surface separating the two media.
Answer:
a) rarer to denser medium
When a ray of light travels from optically rarer medium to optically denser medium, it bends towards the normal.

b) denser to rarer medium
When a ray of light from an optically denser medium to an optically rarer medium it bends away from the normal.

c) normal to the surface separating the two media.
A ray of light incident normally on a denser medium it goes without any deviation.

IX. Numerical Problems:

Question 1.
A concave mirror produces three times magnified real image of an object placed at 7 cm in front of it. Where is the image located?
Answer:
Here given magnification m = 3
Object distance u = -7 cm
Magnification m = \(-\frac{v}{u}\) Real image
-3 = \(-\frac{v}{u}\)
3u = -v
v = 3u = 3 x 7 = 21 cm
The image will be formed at a distance of 21 cm in front of concave mirror from its pole.

Question 2.
Light enters from air into a glass plate having a refractive index of 1.5. What is the speed of light in glass?
Answer:
Refractive index of a glass plate μ = 1.5
Speed of light in vacuum is C = 3 x 10⁸ms^-1
Speed of light in glass V =?

speed of light in glass = 2 × 10⁸ms^-1

Question 3.
The speed of light in water is 2.25 × 10⁸ms^-1. If the speed of light in a vacuum is 3 × 10⁸ms^-1, calculate the refractive index of water.
Answer:
Speed of light in water V = 2.25 × 10⁸ms^-1
Speed of light in vacuum C = 3 × 10⁸ms^-1
Refractive index of water μ =?

X. Higher Order Thinking Skills.

Question 1.
Lightray emerges from water into the air. Draw a ray diagram indicating the change in its path in the water.
Answer:

Question 2.
When a ray of light passes from air into glass, is the angle of refraction greater than or less than the angle of incidence?
Answer:
Light bends towards the normal because glass is denser than air.
It bends towards normal since light has to travel with the lesser speed in the glass but within a short time.
r < i. The angle of refraction is less than the angle of incidence.

Question 3.
What do you conclude about the speed of light in diamond, if the refractive index of diamond is 2.41?
Answer:
Refractive index of diamond μ = 2.41

∴ Speed of light in a diamond (1.24 × 10⁸ms^-1) is less than the speed of light in air (3 × 10⁸ms^-1).
The refractive index of diamond is 2.42, it means that speed of light in air (vacuum) is 2.42 times the speed of light in a diamond.

Intext Activities

ACTIVITY – 1

Stand before the mirror in your dressing table or the mirror fixed in a steel almirah. Do you see your whole body? To see your entire body in a mirror, the mirror should be atleast half of your height. Height of the mirror= Your height/2.
Solution :
(i) If the height of a person is 5 feet, then he should use a plane mirror of 2Vi feet height and fix in a steal almirah.
(ii) Now if he stand before it his full body will be seen on the mirror because hight of the mirror = \(\frac{\text { Our hieight }}{2}\)

ACTIVITY – 2

Hold a concave mirror in your hand (or place it in a stand). Direct its reflecting surface towards the sun. Direct the light reflected by the mirror onto a sheet of paper held not very far from the mirror. Move the sheet of paper back and forth gradually until you find a bright, sharp spot of light on the paper. Position the mirror and the paper at the same location for few moments. What do you observe? Why does the paper catch fire?
Solution :
A concave mirror converges all the light rays coming from the Sun. All these light rays converge and meet at the focus of the mirror.
So, all the heat and light is focused on the principal focus (F). When a paper is kept at the focus (F), it starts burning, as this point is very hot.

ACTIVITY – 3

Take a convex mirror. Hold it in one hand. Hold a pencil close to the mirror in the upright position in the other hand. Observe the image of the pencil in the mirror. Is the image erect or inverted? Is it diminished or enlarged? Move the pencil slowly away from the mirror. Does the image become smaller or larger? What do you observe?

Solution :

1. When a pencil is held in the upright position in front of a convex mirror, its diminished, erect image is formed which is virtual and therefore seen in the convex mirror.
2. When the pencil is moved away from the convex mirror size of image becomes smaller and smaller but image remains erect.
3. As we move away, the object from the convex mirror, image shifts towards the focus.

ACTIVITY – 4

Refraction of light at air-water interface
Put a straight pencil into a tank of water or beaker of water at an angle of 45° and look at it from one side and above. How does the pencil look now?
The pencil appears to be bent at the surface of water.
Solution :

Both the above activities are the result of refraction of light. The bending of light rays when they pass obliquely from one medium to another medium is called refraction of light.

9th Science Guide Light Additional Important Questions and Answers

I. Choose the correct answer :

Question 1.
A ray of light is incident towards a plane mirror at an angle of 30° with the mirror surface. What will be the angle of reflection?
(a) 45°
(b) 30°
(c) 90°
(d) 60°
Answer:
(d) 60°

Question 2.
A 10 mm long bin is placed vertically in front of a concave mirror. A 5 mm long image of the bin is formed at 30 cm in front of the mirror. The focal length of this mirror is
(a) -20cm
(b) -30cm
(c) -60cm
(d) -40cm
Answer:
(a) – 20cm

Question 3.
A ray of light as it travels from medium A to medium B refractive index of the medium B relative to medium A is (μB/ μA)
(a) \(\frac{\sqrt{3}}{\sqrt{2}}\)
(b) \(\frac{\sqrt{2}}{\sqrt{3}}\)
(c) \(\frac{{1}}{\sqrt{2}}\)
(d) \(\sqrt{2}\)
Answer:
(b) \(\frac{\sqrt{2}}{\sqrt{3}}\)

Question 4.
Under which of the following conditions a concave mirror can form an image larger than the actual object?
(a) when the object is kept at a distance equal to its radius of curvature.
(b) when object is kept at a distance less than its focal length.
(c) when object is placed between the focus and centre of curvature
(d) when object is kept at a distance greater than its radius of curvature.
Answer:
(c) when object is placed between the focus and centre of curvature

Question 5.
In torches, searchlights and head lights of vehicles the bulb is placed …………………………… of the concave mirror.
(a) between and F of the reflector
(b) Very near to F
(c) between F & C
(d) at C
Answer:
(b) Very near to F

Question 6.
A boy is standing at a distance of 3m in front of a plane mirror. The distance between the boy and his image is ………………….. m
(a) 4
(b) 2
(c) 3
(d) 6
Answer:
(c) 3

Question 7.
The image formed by a concave mirror is real, inverted and of the same size as that of the object the position of the object should be
(a) beyond C
(b) between C & F
(c) at C
(d) at F
Answer:
(c) at C

Question 8.
Which of the following has the highest refractive index
(a) air
(b) water
(c) diamond
(d) glass
Answer:
(c) diamond

Question 9.
The image formed by a plane mirror is
(a) real
(b) diminished
(c) enlarged
(d) laterally inverted
Answer:
(d) laterally inverted

Question 10.
The incident ray passing through ‘F of a mirror ………………….. after reflection
(a) passes through C
(b) passes through F
(c) passes parallel to the principal axis
(d) passes through the pole
Answer:
(c) passes parallel to the principal axis

Question 11.
The incident ray passing through C of a mirror ………………….. after reflection.
(a) passes through C
(b) passes through F
(c) passes through P
(d) parallel to the principal axis
Answer:
(a) passes through C

Question 12.
The incident ray parallel to the principal axis of a mirror ………………….. after reflection.
(a) passes through C
(b) passes through F
(c) passes through P
(d) reverts back in the opposite direction
Answer:
(b) passes through F

Question 13.
According to sign convention the distance of the object.
(a) is always positive
(b) is always negative
(c) maybe positive or negative
(d) is equal to object height.
Answer:
(b) is always negative

Question 14.
According to sign convention the distance of the image.
(a) is always positive
(b) is always negative
(c) maybe positive or negative
(d) is equal to image height
Answer:
(c) maybe positive or negative

Question 15.
Total internal reflection will occur if the angle of reflection is
(a) 45°
(b) 60°
(c) 90°
(d) 99°
Answer:
(d) 99°

Question 16.
Magnification for the………………….. image is always …………………..
(a) real, positive
(b) real, negative
(c) virtual, negative
(d) virtual, positive
Answer:
(b) real, negative

Question 17.
If magnification is +1.5. The image is …………………..
(a) erect
(b) diminished
(c) real
(d) invected
Answer:
(a) erect

Question 18.
The refractive index of a denser medium with respect to rarer medium is
(a) 1
(b) greater than 1
(c) less than 1
(d) negative
Answer:
(b) greater than 1

Question 19.
We can see objects because of
(a) reflection
(b) refraction
(c) transmission
(d) diffraction
Answer:
(a) reflection

Question 20.
The image formed by a convex mirror is always
(a) real (b) enlarged
(c) virtual & enlarged
(d) diminished
Answer:
(d) diminished

Question 21.
As you move an object always from a convex mirror, its image becomes…………………..
and moves towards
(a) smaller, infinity
(b) smaller, focus
(c) enlarged, infinity
(d) enlarged, focus
Answer:
(b) smaller, focus

Question 22.
For a spherical mirror ………………….. is true.
(a) f = 2R
(b) R = 2f
(c) fR = 2
(d) fR = \(\frac { 1 }{ 2 }\)
Answer:
(b) R = 2f

Question 23.
The mirror formula is…………………..

Answer:
(c) \(\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

Question 24.
For a plane mirror, magnification m =
(a) 0
(b) 1
(c) ± 1
(d) ≤0
Answer:
(b) 1

Question 25.
Magnification for convex mirror is
(a) always positive
(b) always negative
(c) some times positive
(d) 1
Answer::
(a) always positive

Question 26.
If the angle of incidence i = 0, the angle of reflection r =
(a) 0°
(b) 90°
(c) 180°
(d) 45°
Answer:
(a) 0°

Question 27.
Refractive index of a medium is …………………..
(a) speed of light in air to speed of light in vacuum
(b) speed of light in vacuum to speed of light in air
(c) focal length to object distance
(d) speed of light in the medium × speed of light in the air
Answer:
(a) speed of light in air to speed of light in vacuum

Question 28.
Bending of light as it passes from one medium to another is called
(a) reflection
(b) diffraction
(c) refraction
(d) deviation
Answer:
(c) refraction

Question 29.
Ratio of sine of angle of incidence to sine of angle of refraction is ………………….
(a) gravitational law
(b) law of reflection
(c) law of refraction
(d) snell’s law.
Answer:
(d) snell’s law

Question 30.
Entire light is reflected back into denser medium is called
(a) total internal reflection
(b) refraction
(c) reflection
(d) total external refraction.
Answer:
(a) total internal reflection

Question 31.
Outer concentric shell in optic fiber is called
(a) cladding
(b) core
(c) mantel
(d) coat
Answer:
(a) cladding

Question 32.
When light is going from a denser to a less dense medium, the critical angle is the angle of incidence for which the angle of refraction is
(a) 48°
(b) 90°
(c) 42°
(d) 51°
Answer:
(b) 90°

Question 33.
A bundle of glass threads, each of which is capable of transmitting messages using light waves is called
(a) microscope
(b) convex
(c) periscope
(d) optic fibre
Answer:
(d) optic fibre

Question 34.
A ray of light travelling in medium 1 strikes and travels into another transparent medium 2. If the speed of light is greater in medium 1, the ray will
(a) refract towards the normal
(b) have an angle of incidence smaller than be angle of refraction
(c) refract away from the normal
(d) undergo total internal reflection
Answer:
(a) refract towards the normal

Question 35.
A ray of light travels from air into a glass block as shown. It makes an angle of 30° with the surface of the block. If the refractive index of the glass is 1.5, what will be the angle of refraction?

(a) 35.26°
(b) 1.30°
(c) 48.59°
(d) 19.47°
Answer:
(d) 19.47°

Question 36.
The field of view is maximum for …………………
(* FOV is the extent of the observable area that is seen at any given instant)
(a) plane mirror
(b) concave mirror
(c) convex mirror
Answer:
(c) convex mirror

Question 37.
A real and enlarged image can be obtained by using a
(a) convex mirror
(b) plane mirror
(c) concave mirror
Answer:
(c) concave mirror

Question 38.
Which of the following statements about total internal reflection is true?
(a) angle of incidence should be greater than the critical angle
(b) light must travel from a medium of higher refractive index to a medium of lower refractive index
(c) both (a) and (b)
Answer:
(c) both (a) and (b)

Question 39.
The focal length of a concave mirror is 5cm. Its radius of curvature is
(a) 5 cm
(b) 10 cm
(c) 2.5 cm
Answer:
(b) 10 cm

II. Fill in the blanks :

1. The ratio of the sine of the angle of incidence to the sine of …………………is constant.
Answer:
angle of refraction

2. A spherical mirror whose reflecting surface is curved outwards is called ………………… mirror.
Answer:
convex

3. All distances parallel to the principal axis are measured from the ………………… of the
mirror.
Answer:
pole

4. A negative sign in the value of magnification indicates that the image is …………………
Answer:
real

5. Light is refracted or bent while going from one medium to another because of its ………………… changes.
Answer:
speed

III. State whether true or false. If false, correct the statement:

1. The critical angle is defined as the angle of incidence at which the total internal reflection starts to occur.
Answer:
True.

2. The angle of incidence is equal to the angle of reflection for perfect reflection.
Answer:
True.

3. The image formed in a plane mirror is always inverted.
Answer:
False.
Correct statement: The image formed in a plane mirror is always erect.

4. A star appears twinkling into the sky because of the reflection of light by the atmosphere
Answer:
False.
Correct statement: A star appears twinkling into the sky because of the refraction of light by the atmosphere.

5. Mirage is an example of refraction and total internal reflection of light.
Answer:
True.

6. Optical Fibres are based on the phenomenon of dispersion
Answer:
False.
Correct statement: Optical Fibres are based on total internal reflection.

7. A water tank appears shallower when it is viewed from the top due to refraction.
Answer:
True.

8. Twinkling of stars and Mirage are the two phenomena occurring due to refraction.
Answer:
True.
Twinkling of stars and Mirage.

9. Angle of incidence is zero if a ray of light is incident normal to be surface separating the low media.
Answer:
True.

10. A real image is inverted and can be caught on the screen.
Answer:
True.

11. The minimum length of the mirror required to see the full image of the person is half ‘ of his height.
Answer:
true.

12. The pencil appears to be bent at the surface of the water is due to refraction.
Answer:
True.

13. The speed of light decreases in a denser medium, light bends towards the normal.
Answer:
True.

14. If the object is at infinity in front of a convex mirror the image is formed at infinity.
Answer:
False.
Correct statement: The image is formed at F, behind the mirror

15. An object is placed at a distance of 3cm from a plane mirror. The distance of the object and image is 3cm.
Answer:
False.
Correct statement: The distance of the object and image is 6 cm.

16. The distance from centre of curvature of the mirror to the pole is called the focal length of the mirror.
Answer:
False.
Correct statement: The distance between the centre of the mirror and the focal point of the mirror is called the focal length of a mirror.

17. Light is one of the slowest travelling energy with a speed of 3 × 10^-8ms^-1
Answer:
False.
Correct statement : (Light is one of the fastest travelling energy with a speed of 3 × 10^-8ms^-1

18. The angle of incidence at which the angle of refraction is Q£ is called the critical angle.
Answer:
False.
Correct statement: The angle of incidence at which the angle of refraction is 90° is called the critical angle.

IV. Match the following :

Question 1.

Answer:

Question 2.

Answer:

Question 3.

Answer:

Question 4.

Answer:

V. Assertion & Reason Type :

(a) If both assertion & reason are true and the reason is the correct explanation of the assertion.
(b) If both assertion & reason are true but the reason is not correct explanation of the assertion.
(c) If assertion is true but reason is false.
(d) If assertion & reason both are false.
(e) If assertion is false but reason is true.

Question 1.
Assertion : The air bubble shines in water.
Reason : Air bubble shines due to refraction of light.
Answer:
(c) If assertion is true but reason is false

Question 2.
Assertion : The focal length of the mirror is /and distance of the object from the
focus is V then the magnification of the mirror will be \(\left(\frac{f}{f-u}\right)\)

Answer:
(a) Both assertion & reason are true and the reason is the correct explanation of the assertion

Question 3.
Assertion : When an object is placed between two plane mirrors, then all the images found are of equal brightness.
Reason : Only two images are obtained in case of plane-parallel mirrors.
Answer:
(d) Assertion & reason both are false

Question 4.
Assertion: The mirrors used in torch lights are parabolic not concave.
Reason: The image formed by concave mirror is always virtual.
Answer:
(c) Assertion is true but reason is false

Question 5.
Assertion : The nature of the image depends on the size of the mirror.
Reason : Small mirrors always form a virtual image.
Answer:
(d) Assertion & reason both are false

Question 6.
Assertion : A real image cannot be produced by plane or convex mirror.
Reason : The focal length of a convex mirror is always taken as possitive.
Answer:
(e) Assertion is false but reason is true

VI. Answer very briefly :

Question 1.
Which is optically denser out of the two medium M₁& M₂ having the refractive indices = 1.71 and 1.36 respectively?
Answer:
M₁
Reason: Optical density increases as the value of the refractive index increases.

Question 2.
Two medium with refractive index 1.31 & 1.50 is given. In which case (i) Bending of light is more and (ii) speed of light is more.
Answer:
(i) 1.50 – Bending is more
(ii) 1.31 – Speed is more

Question 3.
Under what circumstances there won’t be any refraction of light when it enters from one medium to another?
Answer:

• When light incident at 90°, it will not bend.
• When light passes from denser medium to rarer medium and if it is incident at an angle greater than the critical angle, it will reflect but will not refract.

Question 4.
A ray of light traveling in air enters obliquely into water. Does the light ray bend towards the normal or away from the normal? Why?
Answer:

• When a ray of light travels from air into water obliquely, it bends towards the normal.
• This is because water is optically denser than air.
• On entering water, speed of light decreases and the light bends towards normal.

Question 5.
List down the uses of concave mirror.
Answer:
Concave mirrors are used :

• As Shaving mirror.
• As Reflectors in automobile headlights & torches.
• By dentists to see large images of the teeth of patients.
• To produce heat in solar furnaces.

Question 6.
What are the characteristics of the image formed on a plane mirror?
Answer:

• Image is upright.
• Size of the image is the same as the size of the object.

Question 7.
State the laws of reflection of light.
Answer:

• The incident ray, the normal at the point of incidence and the reflected ray, all lie in the same plane.
• Angle of incidence is equal to the angle of reflection.

Question 8.
Describe the nature of images formed by plane mirrors.
Answer:

• It is always virtual and erect.
• Its size is equal to that of the object
• It is formed at the same distance behind the mirror as the object is in front of the mirror.
• It is laterally inverted.

Question 9.
What is lateral inversion in a plane mirror?
Answer:
It means the apparent reversal of left and right in the mirror image compared with the object.

Question 10.
Explain why a ray of light passing through the centre of curvature of a concave mirror, gets reflected along with the same pattern.
Answer:
The ray passing through the centre of curvature incident to the mirror along its normal so < i = < r = 0
∴ The ray retraces its pattern

Question 11.
How tall does a mirror have to be to fit an entire person’s body?
Answer:
The height of the mirror should behalf of the person’s height regardless of the distance of the person from the mirror.

Question 12.
What is concave and convex mirror?
Answer:

• If the reflecting surface is curved inwards that is called concave mirror.
• The reflecting surface is curved outwards, then it is called convex mirror.

Question 13.
Define principal focus of concave mirror.
Answer:
Principal focus (F): The point on the principal axis of the spherical mirror where the rays of light parallel to the principal axis meet or appear to meet after reflection from the spherical mirror.

Question 14.
What is focal length (f) of a mirror?
Answer:
The distance between the pole (P) and the principal focus (F) of the spherical mirror is called the focal length.
f = \(\frac { R }{ 2 }\) , where R is the radius of curvature of the mirror.

Question 15.
Define Radius of curvature.
Answer:
The radius of the hollow sphere of which the spherical mirror forms a part is called the radius of curvature (R)
R = 2 × focal length

Question 16.
What is “aperture”?
Answer:
The diameter of the circular rim of the mirror is called the aperture of the mirror. It is the entire area of the reflecting surface of the mirror.

Question 17.
Distinguish between real & virtual image.
Answer:
Real :

1. Light rays that come from an object actually meet after reflection.
2. It can be obtained on a screen
3. Image is inverted

Virtual :

1. Light comes from an object does not actually meet but appears to meet.
2. It cannot be obtained on the screen.
3. The image is erect.

Question 18.
What do you mean by linear magnification?
Answer:
It is defined as the ratio of the height of the image (h_i) to the height of the object (h_o).
\(m=\frac{h_{i}}{h_{o}}(\text { or }) \quad m=-\frac{v}{u}\)

Question 19.
Which kind of mirrors are used in the shaving mirror? Why?
Answer:
Cancave mirror, to get magnified image. When a cancave mirror is held near the face (between the pole and focus of the mirror) then an upright and magnified image is seen.

Question 20.
Which mirror is used as a reflector? Why?
Answer:

• Concave mirrors are used as reflectors in torches, vehicle headlights and searchlights.
• To get a powerful parallel beam of light.

Question 21.
Write the uses of cancave mirror
Answer:

1. As a shaving mirror: Magnified face will be seen
2. As a dentist head mirror: Focuses the lights on to see a small area of the body (teeth, throat, etc.)
3. As reflectors: To get a powerful beam of light
4. In solar heaters: To focus sun light for heaters

Question 22.
What do you observe when an object is placed anywhere between P and infinity in front of a convex mirror?
Answer:

• The image is formed behind the mirror between the pole (P) and focus (F).
• Virtual and erect image.
• Diminished image.

Question 23.
What is the nature of the image formed by a concave mirror if the magnification produced by the mirror is +4?
Answer:
Positive sign of magnification indicates that image is virtual, erect and enlarged.

Question 24.
Between which two points of a concave mirror should an object be placed to obtain a magnification of -2?
Answer:
Negative sign of magnification indicates that image is real and inverted. Sign of image is magnified (enlarge)
∴ Object is placed between F and C.

Question 25.
To obtain an image twice the size of the object, between which two points related to a concave mirror should an object be placed?
Answer:
Between F (principal focus) and C centre of curvature.
Real Image.

Question 26.
Draw a ray diagram and also state the position the relative size and nature of image formed by a concave mirror, when an object is placed at C.
Answer:
Image Position: At C, itself
Size: Same size
Nature : (i) Real
(ii) Inverted

Question 27.
Why a pencil partly immersed in water appears to be bent at the water surface.
Answer:
The pencil dipped in water appears bent due to the refraction of light.
The angle of refraction depends on the refractive index of the medium.

Question 28.
How should a ray of light be incident on a rectangular glass slab so that it comes out from the opposite side of the slab without being displaced?
Answer:
Along the normal to the surface or at an angle of incidence of i = 0.

Question 29.
Why a convex mirror is preferred for rearview mirrors in cars?
Answer:

• It always forms virtual, erect, and diminished images.
• The field of view increases.

Question 30.
List four properties of the image formed by a convex mirror.
Answer:

• Always formed behind the mirror between P & F.
• Virtual & erect
• Size is always smaller than the object.
• Magnification is always positive.

Question 31.
List four properties of the image formed by the concave mirror when the object is placed between F & P
Answer:

• The image formed behind the mirror
• Enlarged
• Virtual
• Erect

Question 32.
What is meant by the refraction of light?
Answer:
Light does not travel in the same direction in all media. It changes its direction, the bending of a light ray when it passes from one medium to another is called refraction of light.

Question 33.
State the laws of refraction of light.
Answer:
(i) The incident ray, the refracted ray, and the normal to the interface of two transparent media at the point of incidence, all lie in the same plane.

(ii) The ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for a light of a given colour and for the given pair of media. This law is also known as Snell’s law of refraction.
If i is the angle of incidence and r is the angle of refraction, then \(\frac{\sin i}{\sin r}[latex] = constant
This constant is called the refractive index of the second medium with respect to the first medium. T

Question 34.
Define refractive index & write its unit.
Answer:
The refractive index of the second medium with respect to the first medium is defined as the ratio of the sine of the angle of incidence in the first medium to the sine of the angle of refraction in the second medium.
Unit: The refractive index has no unit as it is the ratio of two similar quantities

Question 35.
Define refractive index in terms of speed of light.
Answer:
The refractive index of a medium is also defined in terms of speed of light in different media

Question 36.
What is total internal reflection?
Answer:
Total internal reflection: When the angle of incidence exceeds the value of the critical angle, the refracted ray is not possible, since r > 90°, the ray is totally reflected back to the same medium (denser medium). This is called as total internal reflection.

Question 37.
Define the critical angle.
Answer:
The angle of incidence at which the angle of refraction is 90° is called the critical angle.

Question 38.
What are the conditions to achieve total internal reflection?
Answer:

• Light must travel from denser medium (Water) to rarer medium (Air).
• The angle of incidence inside the denser medium must be greater than that of the critical angle.

Question 39.
What is mirage? How it occurs?
Answer:

• Mirage is an optical illusion caused by the refraction of light from the sky by heated air.
• The air near the ground becomes hotter than the air at higher levels.
• The refractive index of air increases with its density. Hotter air is less dense, and has smaller refractive index than cooler air.
• If the air currents are small, that is, the air is still, the optical density of different layers of air increases with height.
• As a result, light from an object such as a car passes through a medium whose refractive index decreases towards the ground.
• Thus, a ray of light from such an object successively bends away from the normal and undergoes total internal reflection, if the angle of incidence for the air near the ground exceeds the critical angle.

Question 40.
How do twinkling stars occur? (or) what is the cause of the twinkling of stars?
Answer:
Refraction of light:

• Light from a star is refracted as it passes through our atmosphere because the light
  passes rapidly through moving cells of air with different densities, temperatures, etc.
• These cells bend light by different amounts and make the apparent position of the star move around. This movement is seen as twinkling.

Question 41.
What is the phenomenon used in optical fibre? Explain.
Answer:

• Optical fibres are extensively used for transmitting audio and video signals through long distances.
• Optical fibres too make use of the phenomenon of total internal reflection.
• Optical fibers are fabricated with high-quality composite glass/quartz fibres.
  Each fibres consists of a core and cladding. The refractive index of the material of the core is higher than that of the cladding.

When a signal in the form of light is directed at one end of the fibre at a suitable angle, it undergoes repeated total internal reflection along the length of the fibre and finally comes out at the other end. Optical fibres are extensively used for transmitting and receiving electrical signals which are converted to light between the ends of the fibre, over long distances.

Question 42.
Write any two uses of total internal reflection.
Answer:

1. Spectacular brilliance of diamonds.
2. Transmission of audio and video signals to long-distance through optical fibres.

Question 43.
What are the examples of total internal reflection in nature?
Answer:

1. Mirage
2. Twinkling of stars

Question 44.
Give two examples of the transparent medium that are denser than air.
Answer:
Water, glass.

Question 45.
A coin in a glass beaker appears to rise as the beaker is slowly filled with water why?
Answer:
Refraction of light at the air-water interface.

Question 46.
Name the spherical mirror(s) that has/have
(i) Virtual principal focus
(ii) Real principal focus
Answer:
(i) Convex
(ii) Concave.

VII. Long Answers

Question 1.
List the sign conventions for reflection of light by spherical mirrors.
(i) Write the formula for the spherical mirror.
(ii) Mirror Equation
Answer:

(i)

• The object is always placed on the left side of the mirror.
• All distances are measured from the pole of the mirror.
• Distances measured in the direction of light are taken as positive (along + X-axis) and those measured in the opposite direction are taken as negative (along – X-axis).
• All distances measured perpendicular to and above the principal axis (along + Y-axis) are considered to be positive.
• All distances measured perpendicular to and below the principal axis (along – Y-axis) are considered to be negative. Cartesian sign conventions are used to derive mirror formula and do simple calculations.

(ii) Mirror Equation
The expression relating the distance of the object u, a distance of image v, and focal length f of a spherical mirror is called the mirror equation.
[latex]\frac{1}{f}=\frac{1}{u}+\frac{1}{v}\)

f – focal length of a spherical mirror
u – Distance of the object
v – Distance of the image

Linear Magnification:

It can be defined as the ratio of the height of the image (h_i) to the height of the object (h_o)
m = \(\frac{h_{i}}{h_{o}}(\text { or }) \frac{-v}{u}\)
h_i = height of the image
h_o = height of the object

Question 2.
State the type of mirror used as
(i) Convex mirror
(ii) Concave mirror
Answer:
(i) Convex mirror :

• It gives a wide field of view
• It produces erect and small size image of the object. [As the vehicles approach the driver from behind, the size of the image increases. When vehicles are moving away from the driver, the image size decreases]

(ii) Concave mirror:
To see a large size image of the face.
When the object lies in between pole and principal focus, it forms a virtual, erect and enlarged image.

Question 3.
Write the rules for the construction of image by Concave mirrors, along with ray diagram. .
Answer:
(i) Rule 1 : A ray passing through the centre of curvature is reflected back along its own path.

(ii) Rule 2 : A ray parallel to the principal axis passes through the focus after reflection.

(iii) Rule 3 :A ray passing through the focus gets reflected and travels parallel to the principal axis.

(iv) Rule 4 : A ray AP incident at the pole of the mirror gets reflected along a path PB
such that the angle of incidence APC is equal to the angle of reflection BPC.

Question 4.
Describe the nature and location of the images for the different positions of object which is placed in front of the concave mirror.
Answer:

VIII. Higher-Order Thinking Skills :

Question 1.
M = 2.42 for diamond. What is the meaning of this statement in relation to the speed of light?
Answer:
It means that light travels 2.42 times faster in a vacuum than in a diamond.

Question 2.
A convex mirror is in water. What should be the change in its focal length?
Answer:
No change. The focal length of a convex mirror does not depend on the nature of the medium.

Question 3.
Are the laws of reflection true in the case of irregular reflection?
Answer:
Yes, at the point of incidence both laws of reflection will hold good.

Tamilnadu State Board New Syllabus Samacheer Kalvi 4th English Guide Pdf Term 3 Supplementary Chapter 2 The Wooden Toy Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 4th English Solutions Term 3 Supplementary Chapter 2 The Wooden Toy

4th English Guide The Wooden Toy Book Back Questions and Answers

A. Choose the best answer.

Question 1.
Mugund made ___________ using the dry woods.
(a) Pots
(b) Dolls
(c) Cups
(d) Deer
Answer:
(b) Dolls

Question 2.
In memory of his mother, he carved ___________ statue.
(a) Golden
(b) Sliver
(c) Wooden
(d) Brass
Answer:
(c) Wooden

Question 3.
____________ is a great risk to the environment.
(a) Paper
(b) Cotton cloth
(c) Plastic
(d) Wood
Answer:
(c) Plastic

Question 4.
Mugund learnt the art from his ___________
(a) Father
(b) Mother
(c) Grandfather
(d) Uncle
Answer:
(c) Grandfather

Question 5.
___________ was helpful for his father to drive out the wild animals.
(a) Drum
(b) Wooden tiger
(c) Wooden doll
(d) Clay doll
Answer:
(a) Drum

B. Write True or false.

Question 1.
Mugund loved wild animals.
Answer:
False

Question 2.
Mugund did not cut the raw wood.
Answer:
True

Question 3.
He started selling wooden toys at a high price.
Answer:
False

C. Answer the following questions.

Question 1.
How did Mugund’s mother die?
Answer:
Mugund’s mother died as the wild animals hunted her.

Question 2.
What did his mother say in his dream?
Answer:
Mugund’s mother said in his dream that he should do his part in eradicating the use of plastics through his art as plastics are a great risk to the environment.

Question 3.
What incident made Mugund make a wooden drum?
Answer:
Mugund made a wooden drum to drive out the wild animals because the losses of his father’s cattle kept min creasing and he had to do something.

Question 4.
Why was his father unable to sleep?
Answer:
His father was unable to sleep because the losses of the animals, he was rearing, kept increasing.

Question 5.
Which problem do you think you can solve with art? How?
Answer:
We can solve the problem of using plastic, which is a great risk to the environment. By replacing plastic toys with wooden dolls we can save the world.

I. Fill in the blanks.

Question 1.
Long ago, the wild animals hunted Mugund’s ___________
Answer:
Mother

Question 2.
Mugund started selling wooden toys at a ___________ rate.
Answer:
Cheap

Question 3.
Mugund’s father owned nothing but a flock of sheep and a piece of ____________.
Answer:
Land

Question 4.
The massive ___________ from the wooden drum helped his father, to drive out the wild animals.
Answer:
Noise

II. Write True or False.

Question 1.
Children used to play with his dolls known as marapachi bommai.
Answer:
True

Question 2.
The restlessness and worry made Mugund’s father healthy.
Answer:
False

Question 3.
Mugund started selling wooden toys in all corners of the land.
Answer:
True

Question 4.
Mugund was the son of a plumber.
Answer:
False

III. Name the character / speaker.

Question 1.
“Do your part in eradicating the use of plastics”.
Answer:
Mugund’s mother

Question 2.
“Mugund, cut the raw wood”.
Answer:
Mugund’s friend

IV. Answer the following questions.

Question 1.
Where did the wild dogs live? What did they do?
Answer:
The wild dogs lived in the mountains around the village. They hunted the animals in the forest and domestic animals in the village.

Question 2.
What did Mugund do every day?
Answer:
Mugund went to the forest everyday. He collected dry wood and made dolls with it for the children to play.

Question 3.
What did Mugund do in memory of his mother?
Answer:
Mugund carved a wooden statue in memory of his mother and prayed every day.

Question 4.
What did Mugund learn from his grandfather?
Answer:
Mugund learnt the art of making handicrafts from his grandfather. He made dolls using dry wood and statues of any photo that was shown to him.

Question 5.
How did Mugund’s father make a living?
Answer:
Mugund’s father was running a farm and rearing some animals like goat, cow and hen. He worked hard on the farm and took all the cattle to pasture every day.

Question 6.
Why did Mugund make a wooden drum?
Answer:
Mugund made a wooden drum so that the massive noise from the drum would help his father to drive out the wild animals.

Question 7.
What was the problem in using the drum?
Answer:
When the drum was used, the wild animals would not come to the village due to the massive noise. But, the animals came to the village as soon as someone stopped drumming. So, the problem in using the drum was that one should continuously drum without any break and that was not possible.

Question 8.
Why did Mugund refuse to cut the raw wood?
Answer:
Mugund wanted to follow his mother’s advice. He did not want to cut the raw wood and destroy the living trees in the forest.

Question 9.
How did Mugund save the animals in his village from the wild animals?
Answer:
Mugund designed some wooden tigers and wooden people and placed on the farm. The wild animals thought the wooden images were real and were. afraid thinking the people were awake.

Let us read aloud

A. Read the passage 3 times and colour the trees for each time.

Trees help us in many ways. The colour green is calming and heals your worries. By planting and caring for trees, we help improve our surroundings, as they give fresh air. When air is dirty the people of Delhi suffered a lot. But people of Madhubani district in Bihar have shown how art can be used to make our air clean. So that people made paintings on trees to stop people from cutting the trees.

Question 1.
Bihar people saved trees by ____________ painting.
Answer:
Bihar people save trees by painting on trees.

Question 2.
What is the main idea of the story?
Answer:
The main idea of the story is to stop cutting the trees and save the trees.

Do you want to try to write your own paragraph now?

Question 1.
Write a paragraph on cow.

Answer:

1. Cow is a domestic animal.
2. Cow gives us milk, butter and cheese.
3. The young one of a cow is calf.
4. Cows are decorated during ‘mattu pongal’.
5. We must not be rude but kind and loving.

Question 2.
Write a paragraph on monkey.

Answer:

1. Monkeys jump from tree to tree.
2. They eat fruits and nuts.
3. Monkeys carry their little ones on them.
4. Big monkeys are called chimpanzees.
5. We must not throw stones or drop plastic around them.

Question 3.
Write a paragraph on palm tree.

Answer:

1. Palm trees grow tall.
2. All the parts of a palm tree are useful.
3. Men climb to the top to take the palmyra.
4. Palm tree leaves are used to make hut roofs.
5. We must grow more palm trees around us.

Additional Questions and Answers.

Question 1.
Write a paragraph on Diwali.
Answer:

1. Diwali is the festival of light.
2. We burst crackers during Diwali.
3. People distribute sweets to their friends.
4. We decorate our houses with lights.
5. Diwali chases the darkness in our life and brings in light.

I can do

I. Choose the correct option.

Question 1.
We ___________ yarn to make sarees.
(a) Weave
(b) Water
(c) Knead
Answer:
(a) Weave

Question 2.
The plants because of the wind.
(a) Grow
(b) Bend
(c) Chokes
Answer:
(b) Bend

II. Match the words with similar meaning.

Question 1.
Truck – subway
Answer:
Truck – lorry

Question 2.
Under ground – lorry
Answer:
Under ground – subway

Question 3.
Tap – wallet
Answer:
Tap – faucet

Question 4.
Purse – faucet
Answer:
Purse – wallet

III. Write the words with same meaning,

Question 1.

Touch ______
Answer:
Flash light

Question 2.

Sink ______
Answer:
Wash basin

Question 3.

Flat ______
Answer:
Apartment

IV. Recite the poem The Painter with correct intonation.

V. Match the rhyming words.

Question 1.
Strokes – floor
Answer:
strokes – chokes

Question 2.
Shore – rush
Answer:
shore – floor

Question 3.
Brush – chokes
Answer:
Brush – rush

VI. Describe the picture with adjectives.

(sweet, red, round)

Question 1.
The apple is ____________
Answer:
Red

Question 2.
The apple tastes __________
Answer:
Sweet

Question 3.
It is ___________ in shape.
Answer:
Round

The Wooden Toy Summary in English and Tamil

Once there was a village circled by mountains and many big trees. It was the home to many wild animals, especially wild dogs. They used to hunt not only the animals in the forest but, also the domestic animals in the village. This affected the farmer who lived near the edge of the forest with his son the most.

ஒரு காலத்தில் மலைகளாலும், மரங்களாலும் சூழப்பட்ட ஒரு கிராமம் இருந்தது. அது பல காட்டு விலங்குகளின் குறிப்பாக காட்டுநாய்களின்-இல்லமாக திகழ்ந்த து. அந்த காட்டு நாய்கள் வனவிலங்குகளை மட்டுமல்லாது கிராமத்தில் வளர்க்கப்பட்டுவந்த வீட்டு விலங்குகளையும் வேட்டையாடும். காட்டோரம் தன் மகனுடன் வாழ்ந்து வந்த ஒரு விவசாயியை இது வெகுவாக பாதித்தது.

Mugund was the son of the farmer. He was good at creating many things. Every day he went into the forest to collect dry wood. He used to make dolls using the dry wood. Mugund’s art was very famous in the town. Children used to play with his dolls, mostly known as marapachi bommai.

முகுந்த் என்பது அந்த விவசாயியின் மகனின் பெயராகும். அவன் பல பொருட்களை உருவாக்குவதில் சிறந்து விளங்கினான். தினமும் காட்டிற்கு சென்று காய்ந்த விறகுகளை அவன் கொண்டு வருவான். அவற்றை உபயோகப்படுத்தி பொம்மைகளை தயாரிப்பான். அவனுடைய கலை அந்த நகரத்தில் மிகவும் பிரபலமானது. அவன் தயாரிக்கும் பொம்மைகளுக்கு “மரப்பாச்சி பொம்மை” என்றுபெயராகும். அவற்றுடன் குழந்தைகள் விளையாடுவர்.

Long ago, the wild animals hunted Mugund’s mother. That incident made Mugund hate wild animals. In memory of his mother, he carved a wooden statue of his mother and prayed every day. One night, he woke to hear his mother’s words, “Do your part in eradicating the use of plastics through your art because plastic is a great risk to the environment.”

வெகு காலத்திற்கு முன், முகுந்தின் – தாயார் வனவிலங்குகளால் வேட்டையாடப்பட்டார். அந்தசம்பவம், வனவிலங்குகளை முகுந்த் வெறுப்பதற்கு
காரணமாய் அமைந்தது. தன் தாயாரின் நினைவாக, அவன் மரத்தினால் தனது தாயின் சிலையைச் செய்து அதை தினமும் வணங்கி வந்தான். ஒரு நாள் இரவு, தன் தாயாரின் குரல் ஒலித்ததை கேட்டு உறக்கத்திலிருந்துஎழுந்தான். அந்தக் குரல் “உன் பங்களிப்பாக, பிளாஸ்டிக் பொருட்களின் உபயோகத்தை, உன் கலையின் மூலம் ஒழித்து விடு, ஏனெனில் பிளாஸ்டிக் சுற்றுச்சூழலுக்கு ஆபத்து விளைவிப்பதாகும்” எனஒலித்தது.

So, he started selling wooden toys at a cheap rate He was also clever at making handicrafts. He learnt the art from his grandfather. In the beginning, he made dolls for children, using dry wood. Then, he was making statues of any photo that was show to him.

அதனால், அவன் குறைந்த விலையில் மரப்பொம்மைகளை விற்கத் துவங்கினான். அவன் கைவினை பொருட்களை தயாரிப்பதிலும் நிபுணனாக இருந்தான், இதை அவன் தன் பாட்டனாரிடமிருந்து கற்று இருந்தான். முதலில், காய்ந்த மரத்துண்டுகளில் விறகுகளில் குழந்தைகளுக்கான பொம்மைகள் செய்யத் தொடங்கினான் அவன். பிறகு அவன் | தன்னிடம் காண்பிக்கப்படும் எந்த ஒரு புகைப்படத்திலும் உள்ள ஓர் உருவம் போல சிலைகள் செய்யத் துவங்கினான்.

His father owned nothing but a flock of sheep and a piece of land. Also, he worked hard to keep the farm running. He was rearing some animals like goat, cow and hen. His father took all the cattle to pasture every day. When he returned home, he would always count all the animals. One day, when his father returned, he saw that some animals were missing. His father was unable to sleep because the losses of the animals kept increasing. Mohan was worried about his father.He had to do something.

அவனது தந்தையாரிடம் சிறு ஆட்டு மந்தையும், சிறிது நிலமும் இருந்தது. அவர் கடுமையாய் உழைத்து தன் பண்ணையை நடத்தி வந்தார். அவர் ஆடு, பசு மற்றும் கோழி போன்றவற்றை வளர்த்து வந்தார். தினமும் அவற்றை மேய்ச்சலுக்கு அழைத்து செல்லும்அவர், வீடு திரும்பியதும் அவற்றை கணக்கெடுப்பார். ஒருநாள், அவர் இல்லம் திரும்பியதும் அவற்றில் சில குறைந்திருப்பதை கண்டார். விலங்குகளின் இழப்பு அதிகரிக்க, அதிகரிக்க, அவரால் உறங்க முடியாமல் போனது. தன் தந்தையை நினைத்து கவலைப்பட்ட முகுந்த், ஏதாவது செய்ய வேண்டுமென முடிவெடுத்தான்.

He had an idea. He made a wooden drum because the massive noise from the drum would help his father to drive out the wild animals. Mugund’s father was happy because the drum threatened the animals. But, the animals came as soon as someone stopped drumming. His father could not be awake all night. Soon, the wild animals started attacking only at night. The restlessness and worry made the father ill.

அவனுக்கு ஒரு யோசனை வந்தது. மரத்தாலான ஒரு முரசு அவனால் தயாரிக்கப்பட்டது. ஏனெனில் முரசிலிருந்து வரும்பெரும் சப்தம், காட்டு விலங்குகளை விரட்டிவிரட்டி அடிக்க, அவன் தந்தைக்கு உதவும் என நினைத்தான். அந்த முரசு, காட்டு விலங்குகளை பயமுறுத்துவதைக் கண்டு அவன் தந்தை மகிழ்ந்தார்.ஆயினும், முரசின் ஓசை நின்றவுடன் மறுபடியும் அவை வர ஆரம்பித்துவிட்டன. இரவு நேரம் அவரால் விழித்திருக்க முடியாதபொழுது அவை தாக்க ஆரம்பித்துவிட்டன. இதனால் அந்த உளைச்சலாலும், கவலையாலும் அவன் தந்தை நோய்வாய்பட்டார்.

The next day, Mugund went into the forest to find a hollow log of cedar. But, w too of cedar he could not find it. His friend told him to cut the raw wood. But, he refused. Mugund felt that his mother was still living in each tree. At last, they found some wood and brought it home. Mugund went to bed a little early. His father was beating the drums to drive all the animals

மறுநாள் காட்டிற்கு சென்ற முகுந்த் அங்கு ஏதாவது உட்புறம் காலியான தேவதாரு மரத்துண்டுகிடைக்குமா? என தேடினான். ஆனால், அது போல ஒரு மரத்துண்டு அவனுக்கு கிடைக்கவில்லை. ஒரு மரத்தையே வெட்டி தனக்கு வேண்டிய உட்குழிவான பகுதியை செய்து கொள்ளலாம் என அவனது நண்பன் சொன்னான். ஆனால் முகுந்த் மறுத்துவிட்டான். தன்தாயார் இன்னும் ஒவ்வொரு மரத்திலும் வாழ்வதாக முகுந்த் எண்ணினான். கடைசியில் அவர்களுக்கு ஏதோ ஒரு மரத்துண்டு கிடைத்தது. அதை வீட்டிற்கு அவர்கள் கொண்டு வந்தனர். away.முகுந்த் சீக்கிரம் உறங்கச் சென்றுவிட்டான். அவன் தந்தை விலங்குகளை விரட்டுவதற்கு முரசை ஒலித்துக் கொண்டே இருந்தார்.

Suddenly the sounds of the drum stopped. Mugund’s father was tired, and he slept. Nearly twenty-five animals got attacked that night. Then, Mugund thought of designing some wooden tigers and some wooden people to place on the farm. So, the animals would be afraid as the people were still awake.

முகுந்தின் தந்தை களைப்பில் உறங்கிவிட்டதால் திடீரென முரசின் ஓசை நின்றது. அன்றிரவு 25 விலங்குகள் வேட்டையாடப்பட்டன. அதனால், மரத்தினால் சில புலிகளையும், மனிதர்களையும் 9″ செய்து பண்ணையில் வைப்பதற்கு முகுந்த் திட்டமிட்டான். ஏனெனில், மனிதர்கள்விழித்திருப்பதை கண்டால் மிருகங்கள் அஞ்சும் அல்லவா?

From that day on wards, the farmer and his son had a good sleep. Most of the landowners ordered wooden animals from Mugund. They wanted to save their crops and farms. Soon, Mugund started selling toys to all 10 d selling toys to all corners of the land. This led to a demand for wooden dolls over plastic ones. He was happy that he was able to take part in saving the world through his art.

நிம்மதியாக உறங்கினர். தங்கள் பயிர்களையும்,பண்ணையையும் காக்க, பல நில உரிமையாளர்கள் மரத்தால் செய்யப்பட்ட மிருகங்களை செய்து தருமாறு முகுந்திடம் கேட்டனர். வெகு விரைவில், எல்லா பகுதிகளுக்கும் தன் தொடங்கினான். இதனால் பிளாஸ்டிக்கை விட மரப்பொம்மைகளுக்கு தேவை கூடியது. இந்த பங்கெடுத்ததில், முகுந்த் மிகவும் மகிழ்ச்சி அடைந்தான்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th English Guide Pdf Poem 4 Ulysses Text Book Back Questions and Answers, Summary, Notes.

Tamilnadu Samacheer Kalvi 12th English Solutions Poem 4 Ulysses

12th English Guide Ulysses Text Book Back Questions and Answers

Textual Questions:

1. Complete the summary of the poem, choosing words from the list given below:

Lines 1 to 32:

Ulysses is (1) _________ to discharge his duties as a (2) ______, as he longs for (3) ________. He is filled with an (4) ___________ thirst for (5) __________ and wishes to live life to the (6) ________. He has travelled far and wide gaining (7) _________ of various places, cultures, men and (8). He recalls with delight his experience at the battle of Troy. Enriched by his (9) ________ he longs for more and his quest seems endless. Like metal which would (10) ________ if unused, life without adventure is meaningless. According to him living is not merely (11) ___________ to stay alive. Though old but zestful, Ulysses looks at every hour as a bringer of new things and yearns to follow knowledge even if it is (12) ________.
Answers:

1. unwilling
2. king,
3. travel
4. unguenchable
5. adventure
6. fullest
7. experience
8. matters
9. knowledge
10.  rust
11. breathing
12. unattainable

Lines 33 to 42:

Ulysses desires to hand over his (1) ______ to his son Telemachus, who would fulfil his duties towards his subjects with care and (2) ______. Telemachus possesses patience and has the will to civilise the citizens of Ithaca in a (3) _______ way. Ulysses is happy that his son would do his work blamelessly and he would pursue his (4) ________ for travel and knowledge.
Answers:

1. kingdom
2. tender
3. prudence
4. guest

Lines 44 to 70:

Ulysses beckons his sailors to (1) ________ at the port where the ship is ready to sail. His companions who have faced both (2) ______and sunshine with a smile, are united by their undying spirit of adventure. Though death would end everything, Ulysses urges his companions to join him and sail beyond the sunset and seek a newer (3) _____, regardless of consequences. These brave hearts who had once moved (4) ______ and earth, may have grown old and weak physically but their spirit is young and (5) ______. His call is an inspiration for all those who seek true knowledge and strive to lead (6) _____ lives.
Answers:

1. gather
2. thunder
3. world
4. heaven
5. undaunted

2. Answer the following questions in one or two sentences each: (Text Book Page No. 131)

Question a.
‘Ulysses is not happy to perform his duties as a king’ Why?
Answer:
Ulysses is not happy to perform the ordinary duties of a king mainly because his heart is in voyages beyond horizon. He is bored with the task of enforcing law and order and giving reward and punishment to a savage race.

Question b.
What does he think of the people of his kingdom?
Answer:
Ulysses views the people of Ithaca as uncultured and uncivilized. They are like country bumpkins with a little bit of an attitude.

Question c.
What has Ulysses gained from his travel experiences?
Answer:
Ulysses has met people hailing from different cultural backgrounds. He has learned much from their manners, climates, councils, and governments. He learned strategies of warfare in battles.

Question d.
Pick out the lines which convey that his quest for travel is unending.
Answer:
“I cannot rest from travel: I will drink life to the lees;

Question e.
‘As tho’ to breathe were life!’ – From the given line what do you understand of Ulysses’ attitude to life?
Answer:
Ulysses strongly believes that just breathing is not life. Life has to be adventurous and full of action.

Question f.
What does Ulysses yearn for?
Answer:
Ulysses yearns for travel and adventure. He has a passion to travel to unknown lands.

Question g.
Who does the speaker address in the second part?
Answer:
The speaker addresses the readers in the second part explaining the difference between his roles and that of Telemachus.

Question h.
Why did Ulysses want to hand over the kingdom to his son?
Answer:
Ulysses wanted to hand over the kingdom to his son Telemachus who would fulfill his duties towards his subjects and his son would pursue his quest for travel and knowledge.

Question i.
How would Telemachus transform the subjects?
Answer:
Ulysses believes that his son Telemachus is wise and kind enough to transform rugged citizens into mild and civilized subjects by his tenderness and love.

Question j.
‘He works his work, I mine’ – How is the work distinguished?
Answer:
Here Ulysses’ work and his son’s work are distinguished. At the end of his parting with Ithaca, Ulysses has his duty to hand over his kingdom to his son Telemachus and his son has the duty of ruling the kingdom in a fair manner.

Question k.
In what ways were Ulysses and his mariners alike?
Answer:
Both Ulysses and his fellow sailors are now old. They no more have the strength they possessed in olden days moving earth and heaven. They are made weak by time and fate but strong in will “to strive, to seek, to find and not to yield.” They share the heroic temper and undying quest for knowledge and adventure.

Question l.
What could be the possible outcomes of their travel?
Answer:
The possible outcomes of their travel could be gaining true knowledge and leading meaningful lives.

3. Identify the figures of speech employed in the following lines:

4. Read the sets of lines from the poem and answer the questions that follow: (Text Book Page No. 132)

a) ……..I mete and dole ”
Unequal laws unto a savage race,
That hoard, and sleep, and feed, and know not me.

i. What does Ulysses do?
Answer:
Ulysses awards rewards and punishments to his people.

ii. Did he enjoy what he was doing? Give reasons.
Answer:
No, he didn’t enjoy what he was doing. He thought this life a waste when compared with the previous life (adventurous life). He also complained that the people were savage and they were only eating and sleeping.

b) Yet all experience is an arch wherethrough
Gleams that untravelled world, whose margin
fades
Forever and forever when I move.

i. What is experience compared to?
Answer:
Experience is compared to an ‘arch’.

ii. How do the fines convey that the experience is endless?
Answer:
His desire is to keep travelling and living a life of adventure.

c) Little remains: but every hour is saved
From that eternal silence, something more,
A bringer of new things; and vile it were

i. How is every hour important to Ulysses?
Answer:
As every hour passes, Ulysses gains experience.

ii. What does the term Little remains to convey?
Answer:
He is old and is left with a few more days of life.

d) This is my son, mine own Telemachus,
To whom I leave the sceptre and the isle Well-loved of me,

i. Who does Ulysses entrust his kingdom to, in his absence?
Answer:
Ulysses desires to hand over his kingdom to his son Telemachus.

ii. Bring out the significance of the ‘sceptre’.
Answer:
A ‘Sceptre’ is a ceremonial staff that symbolizes authority. Here, Ulysses gave the sceptre to his son. Who would do his work blamelessly and fulfill his duties towards his subjects with care?

e) That ever with a frolic welcome look
The thunder and the sunshine, and opposed

i. What do ‘thunder’ and ‘sunshine’ refer to?
Answer:
‘Thunder’ and ‘Sunshine’ refer to bad times and good times.

ii. What do we infer about the attitude of the sailors?
Answer:
We infer that the sailors have brave hearts. They had once moved heaven and earth, may have grown old and weak physically but their spirit is young and undaunted. Thus the sailor’s attitude is young and energetic.

f) Death closes all: but something ere the end,
Some work of noble note may yet be done,
Not unbecoming men that strove with Gods.

i. The above lines convey the undying spirit of Ulysses. Explain.
Answer:
Ulysses wants to do something great which can outweigh his previous achievements. He wants to achieve before his death.

ii. Pick out the words in alliteration in the above lines.
Answer:
ere, end
noble, note.

g) ……………for my purpose holds
To sail beyond the sunset and the baths
Of all the western stars, until I die.

i. What was Ulysses’ purpose in life?
Answer:
Ulysses purpose in life was to travel to unknown lands.

ii. How long would his venture last?
Answer:
His venture would last till his death.

h) One equal temper of heroic hearts,
Made weak by time and fate, but strong in will
To strive, to seek, to find, and not to yield.

i. Though made weak by time and fate, the hearts are heroic. Explain.
Answer:
Ulysses and his companions have brave hearts who had once moved heaven and earth, may have grown old and weak physically but their spirit is young and undaunted.

ii. Pick out the words in alliteration in the above lines.
Answer:
heroic hearts strive to seek.

Additional Questions:

a) “Match’d with an aged wife, I mete and dole”

i) Whom does ‘I’ refer to?
Answer:
‘I’ refer to king Ulysses.

ii) What does the word ‘mete’ mean?
Answer:
The word ‘mete’ means ‘to allot’ or ‘measure out’.

b) ‘Thro’ scudding drifts the rainy Hyades’

i) Explain ‘Scudding drifts’
Answer:
‘Scudding drifts’ are pounding showers of rain that one might encounter at sea during a storm.

ii) What do you mean by ‘Hyades’?
Answer:
‘Hyades’ means a group of stars in the constellation.

c) “Myself not least, but honour’d of them all
And drunk delight of battle with my peers”

i) Explain the phrase ‘Myself not least’.
Answer:
‘Myself not least’ means, Ulysses wasn’t treated like the least little thing but was honoured by everybody he met.

ii) Name the battle mentioned in the above lines.
Answer:
‘The battle of Troy’ is mentioned.

d) “Well-loved of me, discerning to fulfill
This labour, by slow prudence, to make mild”

i) Whose labour is mentioned as ‘this labour’?
Answer:
Son of Ulysses ‘Telemachus’ labour is mentioned here.

ii) How does Telemachus do his duties?
Answer:
Telemachus does his duties with care and mild. He will civilise the citizen of Ithaca ina prudence way.

e) “A rugged people and through soft degrees
Subdue them to the useful and the good

i) Who are rugged people?
Answer:
The people of Ithaca are rugged people.

ii) What does ‘rugged’ mean here?
Answer:
‘Rugged’ means that the people are a little uncivilized and uncultured.

f) “Death closes all but something ere the end,
Some work of noble note may yet be done”

i) What does ‘ere’ mean?
Answer:
‘ere’ means an old poetic word that means ‘before’.

ii) Is the poet ready to stop his work (travel)?
Answer:
No, the poet is not ready to stop his work (travel).

g) “I may be we shall touch the Happy Isles And see
the great Achilles, whom we knew”

i) What is referred to as ‘happy isles’?
Answer:
‘Happy Isles’ is referred to as the islands of the blessed.

ii) Who can be seen in the happy isles?
Answer:
Greek heroes like Achilles can be seen in the happy isles.

5. Explain with reference to the context the following lines: (Text Book Page No. 133)

a) I cannot rest from travel: I will drink
Lie to the lees:

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out Ulysses’s passion for travelling.
Explanation:
Ulysses decides that he cannot rest and wants to travel beyond. He is a restless spirit who doesn’t want to take a break from roaming the ocean in search of adventure.

b) I become a name;
For always roaming with a hungry heart

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out Ulysses’s fame.
Explanation:
Ulysses has become famous because he travelled to so many places. He has travelled far and wide gaining experience of various places, cultures, men, and matters.

c) How dull it is to pause, to make an end,
To rust unburnished, not to shine in use!

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out Ulysses’ boredom.
Explanation:
Ulysses gets boredom by just sitting around when he could be out exploring the world. Ulysses thinks himself to some kind of metallic instrument that is still perfectly useful and shiny but just rusts if nobody uses it. So he likes to travel far away, instead of being king in Ithaca.

d) To follow knowledge like a sinking star,
Beyond the utmost bound of human thought.

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet compares Ulysses to a ‘Sinking Star’.
Explanation:
On the one hand, Ulysses wants to chase after knowledge and try to catch it as it sinks like a star. On the other hand, Ulysses himself could be the ‘sinking star that makes sense too he is a great personality who is moving closer to death.

e) ‘He works his work, I mine

Reference:
This line is taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet talks about Ulysses’ work and his son’s work.
Explanation:
At the end of his parting with Ithaca, Ulysses has his duty to hand over his kingdom to his son Telemachus and his son has the duty of ruling the kingdom in a manner.

f) “You and I are old:
Old age hath yet his honour and his toil;”

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet talks about the spirit and power of Ulysses mental strength
Explanation:
Ulysses and his companions have brave hearts who had once moved heaven and çarth, may have grown old and weak physically but their spirit is young and undaunted.

g) The long day wanes the slow moon climbs: the deep
Means round with many voices”

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out the time of the journey of Ulysses and his companions.
Explanation:
He starts his journey to gain indented success. He says to his mariners not to forget that they have fought with the gods and they are the same persons who are now going for an adventure. He says that it is getting night and stars are coming out, the moon is appearing. It is the time they started their journey to get fresh knowledge and adventure.

h) It may be we shall touch the Happy Isles
And see the great Achilles, whom we knew”

Reference:
These lines are taken from Poem – “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out the confidence of Ulysses to reach Happy Isles.
Explanation:
Ulysses and his companion may reach Happy isles which can be assumed as heaven. There he has the ambition to meet his co- warrior in the war of Trojan. The Warrior wants to meet Achilles. All the warriors who are presently sailing knew Achilles very well.

i) “We are not that strength which in old days
moved earth and heaven;
Reference:
These lines are taken from “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out the daring performance of Ulysses and his companion.
Explanation:
Ulysses and his companions have brave hearts who had once moved heaven and earth, may have grown old and weak physically. But they still have the will to seek out and faœ challenges without giving up.

j) “To strive, to seek to find and not yield”.

Reference:
These lines are taken from “Ulysses”, Poet – “Alfred Tennyson”.
Context:
The poet brings out Ulysses’ determination in his work (travel).
Explanations:
Ulysses urges his companion to join him and sail beyond the sunset and seek a newer world. Ulysses is an inspiration for all those who seek true knowledge and strive to lead meaningful lives.

6. Answer the following questions in a paragraph of about 100 words each: (Text Book Page No. 133)

a) What makes Ulysses seek a newer adventure?
Answer:
Ulysses once a great hero of Ithaca is very aware that he is now old. Ulysses is unwilling to discharge his duties as a king as he longs for travel.

“I cannot take rest from travel; I will drink
Life to the lees: All time I have enjoyed”.

Ulysses is filled with an unquenchable thirst for adventure and wishes to live to the fullest. He has travelled far and wide gaining experience of various places, cultures, men, and matters. Ulysses wants to chase after knowledge and try to catch it as it sinks Ijke a star. Every hour is important to Ulysses because he has already wasted the time to be in Ithaca. Ulysses wants every hour as a bringer of new things and to yearn for more knowledge by travelling.

b) List the roles and responsibilities Ulysses assigns to his son Telemachus, while He is away:
Answer:
Ulysses obviously loves his son Telemachus. He assumes that Telemachus will be able to effectively rule the subjects and citizens of Ithaca with wisdom.

“This is my son, mine own Telemachus,
To whom I have the sceptre and the Isle,-”

Ulysses desires to hand over his kingdom to his son Telemachus, who would fulfill his duties towards his subjects with care and tenderness. His son is the right person to rule the people of Ithaca and He will surely civilise them in a prudence way. The people of Ithaca are rugged people which means they are a little uncivilized and uncultured but his son will rule them in a fine way. Ulysses is happy that his son would do his work blamelessly and he would pursue his quest for travel and knowledge.

c) What is Ulysses clarion’s call to his sailors? How does he inspire them?
Answer:
Ulysses was the king of Ithaca. He was very brave and courageous. He went on many adventures on the sea with his companions and fought many battles bravely. Ulysses beckons his sailors to gather at the port where the ship is ready to sail. His Companions who have faced both thunder and sunshine with a smile are united by their undying spirit of adventure.

His companions have brave hearts who had once moved heaven and earth, which means good times and bad times they may have grown old and weak physically but their spirit is young and undaunted. To start another great and long voyage. They will not surrender themself and try to discover a new world. His call is an inspiration for all those who seek true knowledge and strive to lead meaningful lives.
“To Strive to seek to find and not to yield”.

Paragraph:

a) What makes Ulysses seek a newer adventure?
b) List the roles and responsibilities Ulysses assigns to his son Telemachus, while He is away.
c) What is Ulysses clarion’s call to his sailors? How does he inspire them?

Introduction:
Ulysses was the king of Ithaca. He does not want to end his life as an idle king, but seek true knowledge and strive to lead meaningful lives.

Thirst for travel:
Ulysses is filled with an unquenchable thirst for travel and wishes to live life to the fullest. He has travelled far and wide gaining knowledge of various places, cultures men, and matters. Enriched by the experience he longs for more and his quest seems endless. Like metal that would rust if unused, life without adventure is meaningless. Ulysses looks at every hour as a bringer of new things and yearns to follow knowledge even if it is unattainable.

Son of Ulysses:
Ulysses desires to hand over his kingdom to his son Telemachus who would fulfill his duties towards his subjects with care and prudence. He would ‘civilise the citizens of Ithaca in a tender way.

Ulysses companions:
Ulysses beckons his sailors to gather at the port where the ship is ready to sail. His companions who have faced both thunder and sunshine with a smile are united by their undying spirit of adventure. Ulysses urges his companions to join him and sail beyond the sunset and seek a newer world regardless of the consequences. His call is an inspiration for all those who seek true knowledge and strive to lead meaningful lives.

Conclusion:
Thus Ulysses’ unquenchable thirst for travel is clearly dealt in this poem.

Listening:

Listen to the poem and fill in the blanks with appropriate words and phrases. If required listen to the poem again.
Choose the best option and complete the sentences.

Question 1.
________ works like madness ¡n the poet.
a) Wander—Thirst
b) Bidding Farewell
c) Eastern Sunrise
d) Western Seas
Answer:
a) Wander—Thirst

Question 2.
A man could choose ________ as his guide.
a) the sun
b) the hills
C) a star
d) a bird
Answer:
c) a star

Question 3.
There is no end of________ once the voice is heard.
a) walking
b) roaming
c) talking
d) voyaging
Answer:
d) voyaging

Question 4.
The old ships return, while the young ships ______.
a) drift
b) move
C) sail
d) wander
Answer:
c) sail

Question 5.
The blame is on the sun, stars, the road, and the _____.
a) hills
b) trees
c) seas
d) sky
Answer:
d) sky

கவிஞரைப் பற்றி:

ஆல்பிரர் லாட் டென்னிசன் (Alfred Lord Tennyson) (6 August 1809 – 6 October 1892) பிரிட்டிஸ் (British) கவிஞர். இவர் விக்டோரியா ராணியின் காலத்தைச் சார்ந்த ஒரு கவிச்சக்கரவர்த்தி (Poet Laureate). பிரிட்டிஸ் அரசாட்சியைச் சார்ந்த புகழ்பெற்ற புலவர்களில் இவரும் ஒருவர். “Break Break Break”, “The charge of the light Brigade”, “Tears, Idle Tears” மற்றும் “Crossing the bar” போன்ற சிறிய கவிதைகளை எழுதியுள்ளார். கிரேக்க இதிகாசங்களையும் இவர் கவிதை வடிவில் தந்துள்ளார். “Ulysses” மற்றும் “Idylls of the king and Tithonus” ஆகியவை அதற்கு சான்று. இசையோடு வார்த்தைகளை படைப்பது டென்னிசனின் தனித் திறமையே.

கவிதையைப் பற்றி:

கல்ஃப்ரட் லார்ட் டெனிசனின் “Ulysses” ஆங்கில இலக்கியத்தின் புகழ்பெற்ற நாடகத்தனி மொழிப் பாடல்களில் ஒன்று. “Ulysses” கிரேக்க நாட்டின் மாபெரும் வீரன். 20 ஆண்டுகள் கழித்து தன் நாடான இத்தாலிக்கு வருகிறான். பல நாடுகள் சென்று வெற்றி கொண்டு அங்குள்ள கலாச்சாரங்களை அறிகிறான்.

அதன் மூலம் பரந்து விரிந்த அறிவை பெறுகிறான் அந்த அறிவு தான் சாகும் வரை நீடிக்க வேண்டும் என்று எண்ணி தன் மகன் டெலமாகஸ்னிடம் நாட்டை ஒப்படைக்கிறது. அவனை மக்களை ஆட்சி செய்ய பணிக்கிறான். அவனைக் கொண்டு தன் நாட்டை நாகரீக பூமியாக மாற்றுகிறான்.

யுலிசஸ் என்பது ஒரு நாடக தனியுரை. இது வரிகளைக் கொண்ட முறையற்ற கவிதை. இதாகாவின் அரசனான யுலிசஸ் போருக்கு தன் படையைத் தயார் செய்கிறான். அவன் அவர்களுக்கு நேரத்தை வீணடிக்க கூடாது என அறிவுறுத்துகிறான். ட்ராய் போர் மற்றும் பல சமுத்திர சாதனைகளை கண்ட யுலிசஸ் வயது முதிர்ந்தவராகிறார். இதற்காக திரும்பி வந்த உடனே அடுத்த சாதனை படைக்க யுலிசஸ் தயாராகிறார். இன்னும் அதிகமான சாதனை படைப்பதே அவரது இலட்சியம்.

இந்த கவிதை மூன்று பாகங்களாக பிரிக்கப்படுகிறது. (அ) தனது நாட்டில் தன்னை இருக்கவிடாமல தொடர்ந்து சாதனை படைக்க எண்ணும் அவனது ஆர்வம், (ஆ) டெலிமேகஸ்க்கு செய்ய வேண்டிய கடமைகள் மற்றும் மகன் மீது அவன் கொண்ட நம்பிக்கை, (இ மாலுமிகளுக்கு புதிய தெரியாத நாடுகளைக் கண்டறிய உரத்தக் குரலில் யுலிசஸ் விடுக்கும் அழைப்பு.

Ulysses Summary in Tamil

உயர் மன்னருக்கு எந்த பயனுமில்லை – மனைவியுடன்
உலையருகில் அமர்ந்து பாறைகள் நடுவில் குளிர்காய்வதால்
உண்மை வேந்தன் யாரென்றே அறியா மக்களுக்கு
உட்கார்ந்து சட்டதிட்டங்களை வகுத்துக் கொண்டிருப்பதால்,

உருத்தலின்றி ஓயாமல் உண்டு ஓய்வெடுக்கும் இந்த மக்களால்
பயணத்திலிருந்து ஓய்ந்திருக்க முடியாது – வாழ்க்கையின்
அடியாழம் வரை சென்று (life to the lees) அனுபவிக்கப் போகிறேன்.
உச்ச இன்பமும் கண்டிருக்கிறேன் உச்ச வலியும் பெற்றிருக்கிறேன்.

என் அன்புக்குரியவர்களுடனும், தனிமையிலும், கடற்கரைகளிலும் (shore)
மழைதரும் நட்சத்திர குழுமங்களின் விரைவு சறுக்கலில்,
சமுத்திரமே சிக்கல்களுக்குள்ளானது. நான் பிரபலமாகிறேன்,
ஓயாமல் ஓடிக் கொண்டிருக்கும் என் தீராத் தாகம் கொண்ட இதயத்தால்.

பல நகரத்து மனிதர்களை நான் நன்கு அறிந்திருக்கிறேன்.
வேறுபட்ட பண்புகள், காலநிலை மற்ற அரசாங்கங்களுடன்,
அங்கு அனைவராலும் நான் கௌரவிக்கப்பட்டேன், (honour’d)
போர்களின் வெற்றியை நண்பர்களுடன் பகிர்ந்து பருகியிருக்கிறேன்.

ட்ராய் (Troy) போரில் சமவெளிகள் கூட சத்தமிட்டுக் கொண்டிருந்தன
நான் சந்தித்த அனைத்திலும் எனக்கும் பங்குண்டு
இருந்தும் இந்த அனுபவங்கள் வெறும் நுழைவாயிலே
எல்லைகள் மங்கும் பயணிக்கா உலகின் பிராகசத்திற்கு

எப்போதும் எல்லாநேரமும் நான் பயணிக்கும் போது
அதை முடிக்க நிறுத்துவது எவ்வளவு சோகமானது
உபயோகிக்காமல் அந்த அனுபவத்தை வீணாக்குவது
மூச்சுவிடுவது மட்டுமல்ல வாழ்க்கை, வாழ்க்கை மேல் வாழ்க்கை

ஒன்று என்பது மிகச் சொற்பம் எனக்கு
நான் வாழும் ஒவ்வொரு மணிநேரமும்
சாவின் கையிலிருந்து நான் காப்பாற்றிய கணம் ஒவ்வொன்றும்
புதுப்புது அனுபவம் தருவது, மற்றும் வெறுக்கத்தக்கது

வெறும் மூன்று வருடங்களுக்குள் என்னைத் தொலைப்பது,
ஏக்கத்தோடு விரும்புகிறது என் மனது
மூழ்கும் நட்சத்திரமாய் அறிவை பின்பற்றுவதற்கு
மனித சிந்தனையின் எல்லைகளையும் தாண்டி,

இது என் மகன், என் சொந்த மகன் டெலிமேக்ஸ்,
இவனுக்காகவே நான் விட்டுச்செல்கிறேன் இத்தீவையும் என் செங்கோலையும்
என் அன்புக்குரியவன், இப்பணியைச் செய்யவே வந்தவன்
எளிய ஞானத்தால் கடினமானவர்களை கனியச் செய்பவன்.

மற்றும் இலகுவான முறையில் இளைத்திடுவான்
அவர்களை உபயோகமானவர்களாகவும் நல்லவர்களாகவும்
கள்ளம் கூறவே முடியாதவன், பொது வாழ்வின்
மையமானவன், தோற்பதற்காக பிறவாதவன்

இளமையான அலுவல்களிலும் எம் இல்ல
இறைவனுக்கும் ஆராதனை செலுத்துவான்,
நான் சென்றபின் அவன் தன் வேலையைச் செய்கிறான். நான் என்னுடையதாக
அங்கிருக்கிறது துறைமுகம், கப்பல்கள் கிழம்பிய நிலையில்,

அங்குள்ளது அந்த கடிய, கரிய, பரந்த கடல் என் மாலுமிகள்
என்னோடு உழைத்து, உருவாக்கி, நினைத்த ஆத்மாக்கள்
இடியையும் சூரிய ஒளியையும் எப்போதும்
இன்முகத்துடன் எதிர்த்து நின்று வரவேற்பவர்கள்.

சுதந்திர இதயத்தோடும் நெற்றியோடும் நீயும் நானும் வயதானோர்,
முதிய வயதுடன் இன்னுமுண்டு பெருமையும் கடின உழைப்பும்,
இறப்பு அனைத்தையும் முடிக்கிறது. ஆனால் அதற்குமுன்
சில நல்ல செயல்கள் செய்யப்பட உள்ளது,

அது கடவுளோடு நடப்பவருக்கு பொருந்தாது.
பாறையினின்று வெளிச்சம் மிளிரத் துவங்குகிறது,
நீண்ட பகல் மறைகிறது. நிலவு துளிர்கிறது, ஆழ்ந்த
முணக்கங்கள் பல குரல்களால் சூழப்படுகிறது வாருங்கள் நண்பரே,

இன்னும் தாமதமில்லை புதிய உலகை தேடுவதற்கு
தள்ளுங்கள், ஒழுங்காய் அமர்ந்து ஒலியெழுப்பும்
கடல் எல்லைக் கோடுகளை அடிப்பதற்கு, ஏனெனில் என் இலக்கு
சூரிய அஸ்தமனத்தைத் தாண்டிய நிலப்பகுதிக்கு பயணிப்பது

அனைத்து மேற்கத்திய நட்சத்திரங்களுக்கு, இறக்கும் வரை
அந்த வளைகுடாக்குள் நம்மை அழித்து விடலாம்
மகிழ்ச்சித் தீவை நாம் அடைந்து நாமறிந்த
ஆகிலஸின் முகத்தையும் நாம் பார்க்கலாம்.

பலவற்றை நாம் பெற்றிருந்தும், பலவற்றை பொருத்திருந்தும்
பழைய பலத்தை நாம் இப்போது பெற்றிறாவிடினும் –
முன்பு பூமியையும் வானத்தையும் நகர்த்திய நாம், நாம் தான்,
ஒரு சிறந்த இதயத்தின் சமநிலை காலத்தாலும் விதியாலும் வலுவிழக்கிறது,
ஆனால் வலுப்பெறுகிறது. போராடி, தேடி அடைய வேண்டும்,
விடக் கூடாது என்ற மன உறுதியில்.

Tamilnadu State Board New Syllabus Samacheer Kalvi 12th Maths Guide Pdf Chapter 4 Inverse Trigonometric Functions Ex 4.2 Textbook Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 4 Inverse Trigonometric Functions Ex 4.2

Question 1.
Find all values of x such that
(j) -6π ≤ x ≤ 6π and cos x = 0
(ii) -5π ≤ x ≤ 5π and cos x = 1
Solution:
(i) cos x = 0
cos x = cos \(\frac {π}{2}\)
x = (2n + 1) \(\frac {π}{2}\), n = 0, ±1, ±2, ±3, ±4, ±5, -6

(ii) cos x = -1
cos x = cos π
x = (2n + 1) π, n = 0, ±1, ±2, -3

Question 2.
state the reason for cos ^-1 [cos(\(\frac {-π}{6}\))] ≠ –\(\frac {π}{6}\)
Solution:
cos ^-1 [cos(-\(\frac {π}{6}\))] = cos ^-1[ \(\frac {π}{6}\) ] = \(\frac {π}{6}\) ≠ \(\frac {-π}{6}\) ∉ [0, π]
Which is the principle domain of cosine function [∵ cos(-θ) = cos θ]

Question 3.
Is cos^-1 (-x) = π – cos^-1 true? justify your answer.
solution:

Question 4.
Find the principle value of cos^-1(\(\frac {1}{2}\))
solution:
y = cos^-1(\(\frac {1}{2}\))
cos^-1x range is [0, π]
cos y = \(\frac {1}{2}\) = cos = \(\frac {π}{3}\)
y = \(\frac {π}{3}\) ∈ [0, π]
principle value is \(\frac {π}{3}\)

Question 5.
find the value of
(i) 2 cos^-1 (\(\frac {1}{2}\)) + sin^-1 (\(\frac {1}{2}\))
(ii) cos^-1 (\(\frac {1}{2}\)) + sin^-1(-1)
(iii) cos^-1 (cos\(\frac {π}{2}\)cos\(\frac {π}{17}\) – sin\(\frac {π}{7}\)sin\(\frac {π}{17}\))
Solution:
(i) 2 cos^-1 \(\frac {1}{2}\) + sin^-1 \(\frac {1}{2}\)

(ii) cos^-1 \(\frac {1}{2}\) + sin^-1(-1)

Question 6.
Find the domain of
(i) f(x) = sin^-1 (\(\frac {|x|-2}{3}\)) + cos^-1 (\(\frac {1-|x|}{4}\))
(ii) g(x) = sin^-1 x + cos^-1 x
Solution:
(i) -1 ≤ sin^-1 (x) ≤ 1
-1 ≤ \(\frac {|x|-2}{3}\) ≤ 1
-3 ≤ |x| – 2 ≤ 3
-3 + 2 ≤ |x| ≤ 3 + 2
-1 ≤ |x| ≤ 5
|x| ≤ 5
since -1 ≤ |x| is not possible
-5 ≤ x ≤ 5 ………. (1)
By the definitions
-1 ≤ cos^-1 (x) ≤ 1
-1 ≤ \(\frac {1-|x|}{4}\) ≤ 1
-4 ≤ 1 – |x| ≤ 4
-5 ≤ -|x| ≤ 3
-3 ≤ |x| ≤ 5
-3 ≤ |x| is not possible
-5 ≤ x ≤ 5 ………. (2)
From 1 and 2 we get
domain is x ∈ [-5, 5]

(ii) g(x) = sin^-1 x + cos^-1 x
range of sin x and cos x is [-1, 1]
-1 ≤ x ≤ 1
∴ x ∈ [-1, 1]
The domain of g(x) = [-1, 1]

Question 7.
For what value of x, the inequality
\(\frac {π}{2}\) < cos^-1 (3x – 1) < π holds?
Solution:
\(\frac {π}{2}\) < cos^-1 (3x – 1) < π
cos \(\frac {π}{2}\) < (3x – 1) < cos π
0 < 3x < 1 < -1
0 + 1 < 3x < -1 + 1
1 < 3x < 0
The inequality is true, only when
0 < x < \(\frac {1}{3}\)

Question 8.
Find the value of
(i) cos[cos^-1(\(\frac {4}{5}\)) + sin^-1(\(\frac {4}{5}\))]
(ii) (cos^-1(cos \(\frac {4π}{3}\))) + cos^-1(cos(\(\frac {5π}{4}\)))
Solution:

Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 3 Trigonometry Ex 3.7 Text Book Back Questions and Answers, Notes.

Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 3 Trigonometry Ex 3.7

Question 1.
If A + B + C = 180° prove that
(i) sin 2A + sin 2B + sin 2C = 4 sin A sin B sin C
Answer:
sin 2A + sin 2 B + sin 2 C = 2 sin \(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) . cos \(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + 2 sin C cos C
= 2 sin (A + B) . cos (A – B) + 2 sin C cos C
= 2 sin( 180° – C) cos (A – B) + 2 sin C cos C (∴ A + B + C = 180°)
= 2 sin C cos (A – B) + 2 sin C cos C
= 2 sin C (cos(A – B) + cos C)
= 2 sin C [(cos (A – B) + cos (180° – (A + B))]
= 2 sin C [cos (A – B) – cos (A + B)]

= 2 sin C . 2 sin A . sin B
= 4 sin A sin B sin C

(ii) cos A + cos B – cos C = -1 + 4 cos \(\frac{\mathbf{A}}{2}\) cos \(\frac{B}{2}\) sin \(\frac{\mathbf{c}}{2}\)
Answer:

(iii) sin 2A + sin 2B + sin 2C = 2 + 2 cos A cos B cos C
Answer:

(iv) sin 2A + sin 2B – sin 2C = 2 sin A sin B cos C
Answer:
Given A + B + C = 180° ⇒ c = 180° – (A + B)

(v)
Answer:
Given A + B + C = 180° ⇒ A + B = 180° – C

(vi) sin A + sin B + sin C = 4 cos \(\frac{\mathbf{A}}{2}\) cos \(\frac{\mathbf{B}}{2}\) cos \(\frac{\mathbf{c}}{2}\)
Answer:

(vii) sin(B + C – A) + sin(C + A – B) + sin(A + B – C) = 4 sin A sin B sin C
Answer:
Given A + B + C = 180°
sin ( B + C – A) = sin (180° – A – A) = sin (180° – 2A) = sin 2A
sin ( C + A – B) = sin (180° – B – B) = sin ( 180° – 2B) = sin 2B
sin (A + B – C) = sin (180° – C – C) = sin ( 180° – 2C) = sin 2C
∴ sin ( B + C – A) + sin ( C + A – B) + sin (A + B – C) = sin 2A + sin 2B + sin 2C
= 2 sin \(\left(\frac{2 \mathrm{~A}+2 \mathrm{~B}}{2}\right)\) . cos \(\left(\frac{2 \mathrm{~A}-2 \mathrm{~B}}{2}\right)\) + 2 sin C . cos C
= 2 sin(A + B) . cos(A – B) + 2 sin C cos C
= 2 sin(180° – C) cos(A – B) + 2 sin C cos C
= 2 sin C cos(A – B) + 2 sin C cos C
= 2sin C(cos(A – B) + cos C)
= 2 sin C [cos(A – B) + cos (180° -(A + B))]
= 2 sin C [cos(A – B) – cos(A + B)]

Question 2.
If A + B + C = 2s, then prove that sin (s – A) sin (s- B )+ sin s . sin(s – C) = sin A sin B
Answer:
Given A + B + C = 2s , we have sin A sin B = \(\frac { 1 }{ 2 }\) [cos ( A – B) – cos ( A + B)]
sin(s – A) sin(s – B) + sins . sin(s – C) = \(\frac { 1 }{ 2 }\) [cos((s – A) – (s – B)) – cos(s – A + s – B)] + \(\frac { 1 }{ 2 }\) [cos (s – (s – C)) – cos (s + s – C)]
= \(\frac { 1 }{ 2 }\) [cos (s – A – s + B) – cos(2s – A – B)] + \(\frac { 1 }{ 2 }\) [cos(s – s + C) – cos(2s – C)]
= \(\frac { 1 }{ 2 }\) [cos (B – A) – cos(2s – A – B)] + \(\frac { 1 }{ 2 }\) [cos C – cos(2s – C)]
= \(\frac { 1 }{ 2 }\) [cos(A – B) – cos(A + B + C – A – B)] + \(\frac { 1 }{ 2 }\) [cos C – cos (A + B + C – C)]
= \(\frac { 1 }{ 2 }\) [cos (A – B) – cos C] + \(\frac { 1 }{ 2 }\) [cos C – cos(A + B)]
= \(\frac { 1 }{ 2 }\) [cos (A – B) – cos C + cos C – cos (A + B)] = \(\frac { 1 }{ 2 }\) [cos(A – B) – cos(A + B)]

Question 3.
If x + y + z = xyz prove that

Answer:
Given x + y + z = x y z ,
Let x = tan A,
y = tan B,
z = tan C
x + y + z = xyz ⇒ tan A + tan B + tan C = tan A tan B tan C
tan A + tan B + tan C – tan A tan B tan C = 0 ——– (1)

tan A + tan B + tan C – tan A tan B tan C = 0 ——– (2)
A + B + C = 180° ⇒ tan A + tan B + tan C – tan A tan B tan C = 0
⇒ tan (A + B + C) = 0
⇒ tan A + tan B + tan C – tan A tan B tan C = 0
⇒ tan (A + B + C) = 0
∴ tan 2(A + B + C) = o
⇒ tan (2A + 2B + 2C) = 0
⇒ tan 2A + tan 2B + tan 2C – tan 2A tan 2B tan 2C = 0 By eqn (1)
tan 2 A + tan 2B + tan 2C = tan 2A tan 2B tan 2C

Question 4.
If A + B + C = prove the following
(i) sin 2A + sin 2B + sin 2C = 4 cos A cos B cos C
Answer:

(ii) cos 2A + cos 2B + cos 2C = 1 + 4 sin A sin B sin C
Answer:

Question 5.
If ∆ABC is a right triangle and if ∠A = \(\frac{\pi}{2}\) then prove that
(i) cos² B + cos² C = 1
Answer:

∆ ABC is a right triangle. Given ∠A = 90°
we know A + B + C = 180°
∴ B + C = 180° – A
B + C = 180° – 90° = 90°

(ii) sin² B + sin² C = 1
Answer:

(iii) cos B – cos C = -1 + 2√2 cos \(\frac{\mathbf{B}}{2}\) . sin \(\frac{\mathbf{C}}{2}\)
Answer: