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Panorama English Book Class 9 Solutions Chapter 7 Kathmandu

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Bihar Board Class 9 English Kathmandu Text Book Questions and Answers

A. Answer the following questions orally:

Write any eight-digit number with 6 in ten lakhs place and 9 in ten-thousandth place.

Question 1.
Have you ever visited a sacred place? Share your experiences with your friends.
Answer:
Yes, I have visited a sacred place. It is Deoghar or Baba Dham in Jharkhand. It is a very fine place. The whole place was charmed. One can get, people worshipping Lord Shiva there, I also entered the temple and worshipped the Lord. It is a worth visiting place. It was the month of Shrawan (July) in this month Lakhs of people come here bringing the Ganga water in Karwar. The whole city turns in Kawarias colour. That is ochrous (Gerua). The whole environment looks beautiful.

Question 2.
Name some of the holy places of your state.
Answer:
Some holy places of our state are Bodh Gaya, Rajgir, Pawapuri, many places in Darbhanga, Pumiya and Patna.

Question 3.
Describe the surroundings of a holy place you have visited.
Answer:
Once I got a chance to visit Gurudawara the temple of Patna Saheb. It is famous all over India and abroad. It is a place of pilgrimage for the Sikhs. It is the holy place of Guru Gobind Singhji. Thousands of devotees and worshippers visit it daily. Recitations from Holy Granth go on in the temple at all times. It is very ennobling and to sit in the temple for an hour. Surroundings of the holy place are full of shops. Only Sikhs are seen here as shopkeepers. A visit to this religious place is not without merit.

B.1.1. Write ‘T’ for true and ‘F’ for false statements:

1. At Pashupatinath, there is an atmosphere of ‘febrile confusion’.
2. By the main gate an Indian struggles for permission to enter.
3. I consider what route should take back home.
4. From a balcony a basket of flowers and leaves, old offerings now wilted, is dropped into the lake.
5. I enter a Nepal Airport office and buy a ticket for the day after tomorrow flight.

Answer:

1. — T
2. — F
3. — T
4. — T
5. — F

B.1.2. Answer the following questions very briefly:

Question 1.
With whom does Mr Vikram Seth visit the two temples in Kathmandu?
Answer:
Mr Vikram Seth visited the two temples in Kathmandu with his son and nephew.

Question 2.
Why does a party of saffron-clad Westerner struggle?
Answer:
A party of saffron-clad Westerner struggles for permission to enter the temple.

Question 3.
Briefly describe Baudhnath Stupa?
Answer:
At the Boudhanath Stupa there is a sense of stillness. It has a white dome small shops are there. That is a heaven of quietness in the busy streets around.

Question 4.
What does the author buy at Nepal Airlines?
Answer:
At Nepal Airlines, the author buys a ticket for the next day’s flight.

Question 5.
When will the Kaliyug end on earth?
Answer:
The Kaliyug will end on earth when the small shrine half protruding from the stone platform on the river bank at the Pashupatinath emerges fully. The goddess inside will escape, and the evil period of the Kaliyug will end on earth.

B.2. Answer the following questions very briefly:

Question 1.
Where does the anther look at the flute seller?
Answer:
The author looks at the flute seller standing in a comer of the square near the hotel.

Question 2.
Name three kinds of the flute.
Answer:
The three kinds of the flute are the reed neh, the recorders and the deep baosuri of Hindustani classical music.

Question 3.
What does the flute seller have in his hand?
Answer:
In the flute seller’s hand, there is a pole with an attachment at the top from which fifty or sixty bansuri protrude.

Question 4.
Why does the author find it difficult to go away from the square?
Answer:
Tire author attracted by the flute music so he finds it difficult to go away from the square.

C. 1. Long Answer Type Questions

Question 1.
Why is Kathmandu famous? Describe briefly.
Answer:
Kathmandu is the capital of Nepal. It is famous for its two temples that are most sacred to Hindu and Buddhists. The first is die Pashupatinath temple. The second is the Baudhnath stupa that is a heaven of the compass in the busy streets around. Besides these, Kathmandu is a very lovely wealthy and religious place.

Question 2.
Describe Baudhnath Stupa and its surroundings.
Answer:
At Baudhnath stupa there is calm and quiet just outside and in the shrine. There are no crowds. Outside the shrine there are small shops of Tibetan immigrants selling felt bags. Tibetan prints and silver jewellery. The Buddhist shrine is a haven of quietness. It is a complete contrast of the Pashupatinath shrine.

Question 3.
Describe daily happenings at Pashupatinath.
Answer:
At Pashupatinath, there is an atmosphere of utter confusion mixed with excitement in and outside the shrine. Priests, hawkers, devotees, tourists, cows, monkeys, dogs and pigeons – all roam through the grounds. The crowd of worshippers push each other to go to the front to get “darshan”. There is noise confusion and disorder. There is a fight of monkeys inside the temple and quarrel for permission to enter by the saffron-clad foreigners.

Question 4.
What, according to the author, has been the pattern of the flute seller’s life?
Answer:
According to the author die flute seller stands in a comer of the square near. In his hand is a pole with an attachment at the top from which fifty or sixty bansuris protrude in all directions like die quills of a porcupine. From time to time he stands the pole on the ground selects a flute and plays for a few minutes. The sound rises clearly above the noise of the traffic and the hawker’ cries. He plays slowly meditatively, without excessive display. He makes sale also. Sometimes he breaks off playing to talk to the fruit seller. This has been the pattern of his life for years.

Question 5.
The author was moved by the music of the flute. Describe a similar experience of your own.
Answer:
Once there was a cultural programme at Ravindra Kala Bhawan in Patna. I had been there. I was watching it. A man appeared at the stage, at first sight, he looked like an ordinary man. He played the guitar and it was so good that I listened patiently. I was so charmed that I felt to be in a world of pleasure.

C. 2. Group Discussion

Discuss the following in groups or pairs

Question 1.
Religious tolerance is inbuilt in Indian society.
Answer:
India is a secularism country. Here people of all religions, irrespective of caste or creed enjoy equal rights. There is no religion of the state. This thought is nothing new for us, as it is embedded in the cultural ethos that makes us tolerant, magnanimous and receptive to ail religions like Sikhism, Jainism and Buddhism and of course Hinduism. People over the centuries lived in peace, except for the last two centuries when foreign rules visited this harmony by their much-maligned policy of divide and rule. Yet we are tolerant Benjamin Franklin said, “We must indeed hang together or, most assuredly we shall all hang separately” The true success of this belief will be when we regard ourselves first as Indians and then as Hindu. Sikhs and Muslims.

Question 2.
Music has overwhelming power.
Answer:
It is true to say that music haš overwhelming power. Music is such an art that can soothe and relax our heart. It is an art of making pleasing. It is combinations of sounds in rhythm and harmony. It finds people with a còmmon bond. It is also a source of living to hear music it is to be drawn into the commonality of all mankind to be moved by music. Its motive force too is living breath, It clearly differs from noise.

Comprehension Based Questions with Answers

1. I get a cheap room in the centre of town and sleep for hours. The next morning, with Mr Shah’s son and nephew, I visit the two temples in Kathmandu that are most sacred to Hindus and Buddhists.
At Pashupatinath (outside which a sign proclaims ‘Entrance for the Hindus only’) there is an atmosphere of ‘febrile confusion’. Priests, hawkers, devotees, tourists, cows, monkeys, pigeons and dogs roam through the grounds. We offer a few flowers. There are so many worshippers that some people trying to get the priest’s attention are elbowed aside by others pushing their way to the front. A princess of
the Nepalese royal house appears; everyone bows and makes way. By the main gate, a party of saffron-clad Westerners J struggle for permission to enter. The policeman is not convinced that they are ‘The Hindus’ (only Hindus are allowed to enter the temple). A light breaks out between two monkeys. One chases the other, who jumps onto a shiva linga, then runs screaming around the temples and down, to the river, the holy Bagmati, which flows below. A corpse is being cremated on its banks; washerwomen are at their work and children bathe. From a balcony a basket of flowers and leaves, old offerings now wilted, is dropped into the river. A small shrine half protrudes from the stone platform on the river bank. When it emerges fully, the goddess inside will escape, and the evil period of the Kaliyug will end on earth.

Questions:

1. Name the lesson and the author of the above passage.
2. What does ‘febrile confusion’ apply here?
3. What made the ‘febrile confusion’?
4. Why can some people not get the priest’s attention?
5. Which actions show that the members of the royal of Nepal are respected by common people?
6. Which word/words in the passage mean the following:
   (a) pushed to one side
   (b) bends with respect.

Answers:

1. The name of the lesson is ‘Kathmandu’. The author is Vikram Seth.
2. ‘Febrile confusion’ here implies excited, disorderly nervous movements and noises.
3. The febrile confusion was created by a crowd of devotees, hawkers, priests tourists, cows, monkeys, pigeons and dogs roaming through the ground.
4. because they are pushed by others who want to come to the front.
5. When a Nepalese princess came for worshipping in the temple every one bowed and made way for her.
6. (a) elbowed
   (b) bows

2. At the Boudhanath stupa, the Buddhist shrine of Kathmandu, there is, in contrast, a sense of stillness. Its immense white dome is ringed by a road. Small shops stand on its outer edge: many of these are owned by Tibetan immigrants; felt bags, Tibetan prints and silver jewellery can be bought here. There are no crowds: this is a haven of quietness in the busy streets around.
Kathmandu is vivid, mercenary, religious, with small shrines to flower-adorned deities along with the narrowest and busiest streets; with fruit sellers, flute sellers, hawkers of postcards; shops selling Western cosmetics, film rolls and chocolate; or copper utensils and Nepalese antiques. Film songs blare out from the radios, 6ar horns sound, bicycle bells ring, stray cows low questioningly at motorcycles, vendors shout out their wares. I indulge myself mindlessly: buy a bar of ’ marzipan, a com-on-the-cob roasted in a charcoal brazier on the pavement rubbed with salt, chilli powder and lemon); a couple of love story comics, and even a Reader’s Digest. All this I wash down with Coca Cola and a nauseating orange drink and feel much the better for it.

Questions:

1. What does the author want to contrast the Buddhist shrine with?
2. What does ring with a road imply?
3. Whose shops are there outside the Buddhist Shrine? What do they sell?
4. What contrast is there between the inside of the Buddhist shrine and its surroundings?
5. What type of city is Kathmandu?
6. What does the writer do to pass his time?
7. What does ‘wash down’ imply here?
8. Which words in the passage mean the following.
   (a) to satisfy one’s desire
   (b) safe place.

Answers:

1. It is contrasted with the Pashupatinath temple in Kathmandu.
2. It implies that there is a road all around the dome.
3. There are shops of Tibetan immigrants. They sell felt bags, Tibetan prints and silver jewellery is located in the busy streets of Kathmandu.
4. Inside the shrine, there is peace and quiet whereas the surroundings are noisy as the temple in located in the busy streets of Kathmandu.
5. Kathmandu is a religious city with narrow streets. These have shrines dedicated to different gods. There is noise and disorder but Kathmandu is full of life.
6. He buys some light reading and eating materials.
7. It implies that he reads and eats while sipping a Coca Cola and orange drink.
8. (a) Indulge
   (b) haven

3. I consider what route I should take back home. If I were -propelled by enthusiasm for travel purse, I would go by bus and train to Patna, then sail up the Ganges past Benaras to Allahabad, then up the Yamuna, past Agra to Delhi. But I am too exhausted and homesick; today is the last day of August. Go home, I tell myself: move directly towards home. I enter a Nepal Airlines office and buy a ticket for tomorrow’s flight.
I look at the flute seller standing in a comer of the square near the hotel. In his hand is a pole with an attachment at the top from which fifty or sixty bansuris protrude in all directions, like the quills of a porcupine. They are of bamboo: there are cross-flutes and recorders. From time to time he stands the pole on the ground, selects a flute and plays for a few minutes. The sound rises clearly above the noise of the traffic and the hawkers’ cries. He plays slowly, meditatively without excessive display. He does not shout out his wares. Occasionally he makes a sale, but in a curiously offhanded way as if this were incidental to his enterprise. Sometimes he breaks off playing to talk to the fruit seller. I imagine that this has been the pattern of his life for years.

Questions:

1. Why does the speaker not travel by bus or train?
2. How does the author describe the flute seller in such a manner?
3. Why does the flute seller play on the flute for just a few minutes?
4. While other’s shout out their, wares how does the flute seller attracts the attention of the customers?
5. How does he play the flute?
6. Which words in the passage mean the following:
   (a) without any preparation
   (b) not much show off.

Answers:

1. The speaker is feeling homesick. So to reach his home early he decides to go by air instead of by bus or train.
2. The author is attracted by the flutes and also by the flute seller. The flute reminds him of the commonality of all mankind.
3. The flute seller does not seem to bother much about the sale of his flutes.
4. He attracts the attention of his customers by playing on different flutes.
5. He plays the flute slowly, meditatively and without much show-off.
6. (a) offhanded way
   (b) excessive display.

4. I find it difficult to tear myself away from the square. Flute music always does this to me: it is at once the most universal and most particular of sounds. There is no culture that does not have its flute the reed neh, the recorder, the Japanese shakuhachi, the deep bansuri of Hindustani classical music, the clear or breathy flutes of South America, the high-pitched Chinese flutes. Each has its specific fingering and compass. It weaves its own associations. Yet to hear any flute is,, it seems to me, to be drawn into the commonality of all mankind, to be moved by music closest in its phrases and sentences to the human voice. Its motive force too is living breath: it too needs to pause and breathe before it can go on. That I can be so affected by a few familiar phrases on the bansuri, surprises me at first, for on the previous occasions that I have returned home after a long absence abroad, ! have hardly noticed such details, and certainly have not invested them with the significance I now do.

Questions:

1. What does ‘tear me away’ imply?
2. What fact shows that the writer is very fond of the flute?
3. How is flute music universal?
4. What does it mean to hear any flute?
5. How can the author be affected by the flute?
6. Which words in the passage mean the following
   (a) used by all
   (b) special.

Answers:

1. It implies that the author could not leave the place.
2. The fact that is difficult for him to move away from it shows that he likes it.
3. There is no culture in the world which does not have its own flute. This shows that the flute is universal.
4. To hear any flute means to be drawn into the commonality of all mankind.
5. The author can be so affected by a few familiar phrases on the bansuri, surprises him that he had hardly noticed such details.
6. (a) universal
   (b) particular.

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Bihar Board Class 10 Maths Solutions Chapter 2 बहुपद Ex 2.2 Text Book Questions and Answers.

BSEB Bihar Board Class 10 Maths Solutions Chapter 2 बहुपद Ex 2.2

Bihar Board Class 10 Maths बहुपद Ex 2.2

Bihar Board Class 10 Math Book Solution In Hindi प्रश्न 1.
निम्न द्विघात बहुपदों के शून्यक ज्ञात कीजिए और शून्यकों तथा गुणांकों के बीच के सम्बन्ध की सत्यता की जाँच कीजिए-
(i) x² – 2x – 8
(ii) 4s² – 4s + 1
(iii) 6x² – 3 – 7x
(iv) 4u² + 8u
(v) t² – 15
(vi) 3x² – x – 4
हल
(i) दिया गया बहुपद = x² – 2x – 8
= x² – (4 – 2)x – 8
= x² – 4x + 2x – 8
= (x² – 4x) + (2x – 8)
= x(x – 4) + 2 (x – 4)
= (x – 4) (x + 2)
x² – 2x – 8 = (x – 4) (x + 2)
जब बहुपद x² – 2x – 8 = 0 हो तो (x – 4) (x + 2) भी शून्य होगा जिसका अर्थ है कि या तो x – 4 = 0 या फिर x + 2 = 0
यदि हो x – 4 = 0 हो तो x = 4 और यदि x + 2 = 0 हो तो x = -2
अत: बहुपद x² – 2x – 8 के शून्यक = 4 व -2
बहुपद x² – 2x – 8 की तुलना बहुपद ax² + bx + c से करने पर,
a = 1, b = -2 तथा c = -8
तब, बहुपद के गुणांकों और शून्यकों में सम्बन्ध
शून्यकों का योगफल = \(-\frac{b}{a}=-\left(\frac{-2}{1}\right)=2\)
तथा शून्यकों का गुणनफल: = \(\frac{c}{a}=\frac{-8}{1}=-8\)
और जो शून्यक हमने ज्ञात किए थे उनका योगफल भी 2 तथा गुणनफल (-8) है।
अत: बहुपद के गुणांकों और शून्यकों के बीच के उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

(ii) दिया गया बहुपद = 4s² – 4s + 1
= (2s)² – 2(2s) . 1 + (1)² [∵ (a – b)² = a² – 2ab + b²]
= (2s – 1)²
4s² – 4s + 1 = (2s – 1)²
जब बहुपद 4s² – 4s + 1 = 0 हो तो (2s – 1)² भी शून्य होगा जिसका अर्थ है कि
(2s – 1)² = 0
⇒ (2s – 1) = 0
⇒ 2s = 1
⇒ s = \(\frac{1}{2}\)
यहाँ बहुपद के दोनों शून्यक समान हैं,
अत: बहुपद 4s² – 4s + 1 के शून्यक = \(\frac{1}{2}\) व \(\frac{1}{2}\),
बहुपद 4s² – 4s + 1 की तुलना बहुपद as² + bs + c से करने पर,
a = 4, b = -4 तथा c = 1
तब, बहुपद के शून्यकों और गुणांकों में सम्बन्ध
शून्यकों का योगफल = \(-\frac{b}{a}=-\left(\frac{-4}{4}\right)=1\)
तथा शून्यकों का गुणनफल = \(\frac{c}{a}=\frac{1}{4}\)
और जो शून्यक हमने ज्ञात किए हैं उनका भी योगफल (\(\frac{1}{2}+\frac{1}{2}\) = 1) तथा गुणनफल (\(\frac{1}{2} \times \frac{1}{2}=\) \(\frac{1}{4}\)) है।
अत: बहुपद के शून्यकों और गुणांकों के बीच उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

(iii) दिया गया बहुपद = 6x² – 3 – 7x
= 6x² – 7x – 3
= 6x² – (9 – 2)x – 3
= 6x² – 9x + 2x – 3
= (6x² – 9x) + (2x – 3)
= 3x(2x – 3) + 1(2x – 3)
= (2x – 3) (3x + 1)
बहुपद 6x² – 3 – 7x = (2x – 3) (3x + 1)
जब बहुपद 6x² – 3 – 7x = 0 हो तो (2x – 3) (3x + 1) भी शून्य होगा जिसका अर्थ है कि या तो 2x – 3 = 0 या फिर 3x + 1 = 0
यदि 2x – 3 = 0 हो तो 2x = 3 ⇒ x = \(\frac{3}{2}\)
और यदि 3x + 1 = 0 हो तो 3x = -1 ⇒ x = \(-\frac{1}{3}\)
अत: बहुपद 6x² – 3 – 7x के शून्यक \(\frac{3}{2}\) व \(-\frac{1}{3}\)
अब, बहुपद 6x² – 3 – 7x की तुलना मानक द्विघात बहुपद ax² + bx + c से करने पर,
a = 6, b = -7 तथा c = -3
तब, बहुपद के शून्यकों और गुणांकों में सम्बन्ध

अत: बहुपद के गुणांकों और शून्यकों के बीच के उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

(iv) दिया गया बहुपद = 4u² + 8u = 4u(u + 2)
यदि उक्त बहुपद 4u² + 8u = 0 हो तो 4u(u + 2) = 0 जिसका अर्थ है कि
4u = 0 ⇒ u = 0 या फिर u + 2 = 0 ⇒ u = -2
अत: बहुपद 4u² + 8u के शून्यक = 0 व -2
अब, बहुपद 4u² + 8u की तुलना बहुपद au² + bu + c से करने पर,
a = 4, b = 8 तथा c = 0
तब, बहुपद के गुणांकों और शून्यकों में सम्बन्ध
शून्यकों का योगफल = \(-\frac{b}{a}=-\frac{8}{4}=-2\)
और शून्यकों का गुणनफल \(\frac{c}{a}=\frac{0}{4}=0\)
और हमने जो शून्यक ज्ञात किए हैं, उनका योगफल (-2 + 0) = -2 तथा गुणनफल {(-2) × 0} = 0 है
अत: बहुपद के गुणांकों और शून्यकों के बीच के उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

(v) दिया गया बहुपद = t² – 15
जब बहुपद t² – 15 = 0 हो तो t² = 15 या t = ±√15
अत: बहुपद t² – 15 के शून्यक = +√15 व -√15
यहाँ शून्यकों का योगफल (+√15 – √15) = 0 तथा गुणनफल {√15 × (-√15)} = -15 है।
दिए गए बहुपद t² – 15 = 0 की तुलना मानक द्विघात बहुपद at² + bt + c से करने पर,
a = 1, b = 0 तथा c = -15
तब, बहुपद के गुणांकों और शून्यकों के मध्य सम्बन्ध
शून्यकों का योगफल = \(-\frac{b}{a}=-\frac{0}{1}=0\)
और शून्यकों का गुणनफल = \(\frac{c}{a}=\frac{-15}{1}=-15\)
जो कि उपर्युक्त फलन से मेल खाता है।
अत: बहुपद के गुणांकों और शून्यकों के मध्य उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

(vi) दिया गया बहुपद = 3x² – x – 4
= 3x² – (4 – 3)x – 4
= 3x² – 4x + 3x – 4
= (3x² – 4x) + (2x – 4)
= x(3x – 4) + 1(3x – 4)
= (3x – 4) (x + 1)
= (3x – 4) (x + 1)
जब बहुपद 3x² – x – 4 = 0 हो तो (3x – 4) (x + 1) = 0
जिसका अर्थ है कि या तो 3x – 4 = 0 या फिर x + 1 = 0 है।
यदि 3x – 4 = 0 हो तो 3x = 4 ⇒ x = \(\frac {4}{3}\)
और यदि x + 1 = 0 हो तो x = -1
अत: बहुपद के शून्यक = \(\frac {4}{3}\) व -1
अब दिए हुए बहुपद 3x² – x – 4 की तुलना मानक द्विघात बहुपद ax² + bx + c से करने पर,
a = 3, b = -1 तथा c = -4
तब, बहुपद के गुणांकों a, b, c और बहुपद के शून्यकों के बीच सम्बन्ध
शून्यकों का योगफल = \(-\frac{b}{a}=-\frac{(-1)}{3}=\frac{1}{3}\)
और शून्यकों का गुणनफल = \(\frac{c}{a}=\frac{-4}{3}\)
और जो शून्यक हमने ज्ञात किए हैं उनका भी योगफल = \(\left(-1+\frac{4}{3}\right)=\frac{1}{3}\) और गुणनफल \(\left(\frac{4}{3} \times-1\right)=-\frac{4}{3}\) है।
अत: बहुपद के गुणांकों और शून्यकों के बीच उपर्युक्त सम्बन्ध सत्य हैं।
इति सिद्धम्

Bihar Board Class 10 Math Book Solution In Hindi Pdf Download प्रश्न 2.
एक द्विघात बहुपद ज्ञात कीजिए, जिसके शून्यकों के योगफल तथा गुणनफल क्रमशः दी गई संख्याएँ हैं
(i) \(\frac{1}{4}\), -1
(ii) √2, \(\frac{1}{3}\)
(iii) 0, √5
(iv) 1, 1
(v) \(\frac{-1}{4}\), \(\frac{1}{4}\)
(vi) 4, 1
हल
(i) माना द्विघात बहुपद के शून्यक α तथा β हैं।
तब, शून्यकों का योगफल = α + β तथा शून्यकों का गुणनफल = αβ
दिया गया है कि शून्यकों का योगफल \(\frac{1}{4}\) तथा गुणनफल -1 है।
α + β = \(\frac{1}{4}\) और αβ = -1
तब, द्विघात बहुपद = (x – α) (x – β)
= x² – (α + β) x + αβ
= x² – \(\frac{1}{4}\) x + (-1)
= \(\frac{4 x^{2}-x-4}{4}\)
= k(4x² – x – 4)
अत: अभीष्ट बहुपद 4x² – x – 4 या k(4x² – x – 4) है, जहाँ k = \(\frac{1}{4}\) एक वास्तविक संख्या है।

(ii) माना द्विघात बहुपद के शून्यक α तथा β हैं।
तब, शून्यकों का योगफल = α + β तथा गुणनफल = αβ
दिया गया है कि बहुपद के शून्यकों का योगफल √2 तथा गुणनफल \(\frac{1}{3}\) है।
α + β = √2 तथा αβ = \(\frac{1}{3}\)
तब, द्विघात बहुपद = (x – α) (x – β)
= x² – (α + β) + αβ
= x² – √2x + \(\frac{1}{3}\)
= \(\frac{1}{3}\)(3x² – 3√2x + 1)
= k(3x² – 3√2x + 1)
अत: अभीष्ट बहुपद k(3x² – 3√2x + 1) है, जहाँ k = \(\frac{1}{3}\) एक वास्तविक संख्या है।

(iii) माना द्विघात बहुपद के शून्यक α तथा β हैं।
तब, शून्यकों का योगफल = (α + β) और शून्यकों का गुणनफल = αβ
दिया गया है कि शून्यकों का योगफल 0 तथा गुणनफल √5 है।
तब, α + β = 0 तथा αβ = 15
द्विघात बहुपद = (x – α)(x – β)
= x² – (α + β)x + αβ
= x² – 0 . x + √5
= x² + √5
अतः अभीष्ट बहुपद = x² + √5

(iv) माना द्विघात बहुपद के शून्यक α तथा β हैं।
तब, शून्यकों का योगफल = α + β तथा शून्यकों का गुणनफल = αβ
दिया गया है कि शून्यकों का योगफल 1 तथा गुणनफल 1 है।
तब, α + β = 1 तथा αβ = 1
द्विघात बहुपद = (x – α) (x – β)
= x² – (α + β)x + αβ
= x² – (1) . x + 1
= x² – x + 1
अतः अभीष्ट बहुपद = x² – x + 1

(v) माना द्विघात बहुपद के शून्यक α व β हैं।
तब, शून्यकों का योगफल = α + β तथा शून्यकों का गुणनफल = αβ
दिया गया है कि शून्यकों का योगफल \(-\frac{1}{4}\) तथा गुणनफल \(\frac{1}{4}\) है।

(जहाँ k एक वास्तविक संख्या है)
अत: अभीष्ट बहुपद = 4x² + x + 1 अथवा k(4x² + x + 1) जहाँ k = \(\frac{1}{4}\) एक वास्तविक संख्या है।

(vi) माना द्विघात बहुपद के शून्यक α व β हैं।
तब, शून्यकों का योगफल = (α + β) तथा गुणनफल = αβ
दिया गया है कि शून्यकों का योगफल 4 तथा गुणनफल 1 है।
α + β = 4 तथा αβ = 1
द्विघात बहुपद = (x – α) (x – β)
= x² – (α + β)x + αβ
= x² – 4x + 1
अत: अभीष्ट बहुपद = x² – 4x + 1

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Bihar Board Class 9 English The Gift of The Magi Text Book Questions and Answers

A. Form small groups and discuss the following:

The Gift Of The Magi Questions And Answers Bihar Board Class 9 Question 1.
The importance of gifts on great occasions.
Answer:
The gift is presented on great occasions. It is a token of love and affection. It should be kept with the utmost care. It is just like a treasure of love which is given by his/her affectionate persons. It gives one happiness. Sharing a gift adorn the day. It makes one feel important and adds to one’s happiness and pleasure.

Question Answer Of The Gift Of Magi Bihar Board Class 9 Question 2.
Importance of Christmas, Eid, Diwali and New Year presents.
Answer:
India is a land of fairs and festivals. These speak of the past glory and prosperity of our country. Christmas, Eid, Diwali and New year all are very important festivals. We celebrate these with great pomp and show. We present gifts on these occasions. This adds joy, happiness and deep love for one another. We also hope to celebrate it next year with our near and dear.

B.1.1. Complete the following sentences on the basis of the unit you have studied:

1. Della counted her money ________ times.
2. Expenses had been greater than Della had ________
3. The two precious possessions that Jim and Della had were _______
4. The Queen of Sheba might have been envious of Della’s __________
5. “Will you buy my hair?” said __________
6. Della bought _________ for her husband.

Answer:

1. three
2. calculated
3. Jim’s gold watch and Della’s golden hair
4. beautiful hair
5. Della
6. a platinum fob chain for Jim’s watch.

B.1. 2. Answer the following questions very briefly:

Gift Of The Magi Questions And Answers Bihar Board Class 9 Question 1.
Who are Jim and Della?
Answer:
Jim and Della are husband and wife. They love each other very much.

The Gift Of The Magi Question Answer Bihar Board Class 9 Question 2.
Who is the mistress of the home?
Answer:
Della is the mistress of the home.

Bihar Board English Book Class 9 Pdf Download Question 3.
What is the possession of Della in she took pride?
Answer:
Della had beautiful possession in the form of her long golden hair.

Bihar Board Class 9 English Book Solution Question 4.
What was the precious possession of Jim?
Answer:
Jim’s precious possession watch his gold was which had inherited from his father and grandfather.

The Gift Of Magi Question Answers Bihar Board Class 9 Question 5.
Why did Della sale her hair?
Answer:
Della sold her hair to by Christmas’ gift for her husband.

The Gift Of The Magi Solution Bihar Board Class 9 Question 6.
What was worthy of the watch?
Answer:
The platinum fob chain that she bought was worthy of the watch.

Question 7.
Why did Della buy a platinum fob chain?
Answer:
Della bought a platinum fob chain for Jim’s gold watch, it was a true match for it. It was to be presented on Christmas Eve.

B.2.1. Write ‘T’ for true and ‘F’ for false statements:

1. Jim will say that Della looks like a Coney Island chorus girl.
2. Della had a habit of saying noisy prayers.
3. Jim scolded Della for selling her hair.
4. Jim bought a set of combs for Della.
5. The Magi presented a gift to infant Christ.

Answer:

1. — T
2. — F
3. — F
4. — T
5. — T

B.2.2. Answer the following questions briefly:

Question 1.
Why does Della say, “Please God, make him think I am still pretty”?
Answer:
Della says, “Please God, make him think I am still pretty.” She says because she had got her hair cut. She is afraid that Jim may not like her. looks after her beautiful hair is cut. Her beautiful hair made her beautiful.

Question 2.
“He simply stared at her fixedly with that peculiar expression on his face”. Why did Jim stare at her fixedly?
Answer:
Jim stared at her fixedly he had brought costly combs for her golden hair. Which she had lost. He was bewildered to see Della with hair on her head.

Question 3.
“Maybe the hairs of my head were numbered but nobody could ever count my love for you.” Why did Della say so?
Answer:
When Jim stared at Della fixedly, she thought that Jim did not appreciate him without her hair. So in order to convince Jim of her love she said so.

Question 4.
Why did Jim say about their gifts that “they’re too nice to use at present?”
Answer:
Both the husband-wife sold their precious possession for gifts, for each other so the gifts were useless presently. So Jim said so.

Question 5.
Who is Magi? Why are Jim and Della called the Magi?
Answer:
The Magi were wise men, who invented the art of giving Christmas presents. Jim and Della are called the Magi because of the selfless love they showed for each other.

C. 1. Long Answer Type Questions

Question 1.
What is the significance of the title “The Gift of the Magi”?
Answer:
The title the Gift of the Magi depicts how the process of sharing gifts began. It was started by the Magi who were too wise men-wonderfully wise men, who brought a gift to the Babe Christ. This shows that sharing gift adds to the happiness and pleasure of the particular day. In fact, the value of gifts comes from its feelings and emotion, but not from its materialistic value.

Question 2.
How can you say that Jim and Della loved each other very much?
Answer:
Jim and Della were husband and wife. According to tradition on Christmas day they had to present the gift. They were poor so they could not buy a costly gift. It has so happened that both had to sell each of their possession Della sold her golden hair for which she longed for a beautiful set of combs. She got cut’ her hair and sold it and bought platinum chain for Jim’s gold watch. On the other side, Jim sold his gold watch for Della. Thus both lost their possessions. They sacrificed for their lover and beloved.

Question 3.
Describe the family status as well as the family life of Jim and Della.
Answer:
Jim and Della were not very sound economically. The family earning was $20 a week only. They were hand to mouth. They had no money left to save. Della saved some money by bulldozing the shopkeepers. Which instigates the moral reflection that life was made up of sobs, sniffles and smiles with sniffles predominating.

Question 4.
Who invented the art of giving Christmas gifts and why are Jim and Della called the Magi?
Answer:
The Magi invented the art of giving Christmas gifts by giving gift to Babe Christ. Jim and Della sacrificed their most precious possessions to buy a suitable gift for each other. So they are called the Magi. They were not selfish rather the giver of the greatest treasure of their house. They emotionally presented each other and with their true heart.

Question 5.
The essence of love is sacrifice. Justify this statement with reference to ‘The Gift of the Magi; Jim and Della were right in their decision.
Answer:
The essence of love is sacrifice. No doubt it is true to say. A true lover always thinks only of the well and happiness of his lover or beloved. Lover love will remain forever. He thinks that it is possible that the sea goes dry but there is, no possibility of the feeling of love for his beloved deserting his heart. Lover feels that his beloved is always as fresh as a rose of June. Jim and Della were like the same. Both sold their costly possessions for their lover and beloved. So, their decision to sacrifice their possessions for the other was in fact the dissolution of age which so important for love.

Question 6.
Do you think that to sell their possessions for Christmas gifts was wise? Give your own opinion.
Answer:
Yes, I think that to sell their possessions for Christmas gifts was a wise to step. Because if a lover or beloved can sacrifice their lives than.what is the value of material things. Jim and Della sold them the greatest treasures of their possessions it was done in emotion. So, in my opinion, the gifts were no doubt wise ones.

C.2. Group Discussion

Discuss the following in groups or pairs:

Question 1.
Christmas and its importance.
Answer:
Christmas and its importance because every festival has its own importance.The&e speak of the past glory and prosperity of the concerning religion. They are traditionally Christians celebrate Christmas on 25th December every year. It is a celebration of the birth of Jesus Christ. Every Christ and makes merry and a happy new year. Small Christmas tree is set up at and decorated with tinsel, candles and presents etc. Every person gives a present to each other and wishes good.

Question 2.
Love overrides helplessness.
Answer:
It is said that everything is fair in love and war. It is true in the sense of Jim and Della, both sacrificed for each other with their home treasures. It was love which over rode on them. For the sake of love, one does any kind of deed so that he or she loves remaind happy. The same is seen in this story. Jim and Della sacrificed their gifts to each other, the greatest possessions for each other’s happiness.

Comprehension Based Questions with Answers

1. One dollar and eighty-seven cents. That was all. And sixty cents of it was in pennies. Pennies saved one and two at a time, by bulldozing the grocer and the vegetable man and the butcher until one’s cheek burned with the silent imputation of parsimony that such close dealing implied. Three times Della counted it. One dollar and eighty-seven cents. And the next day would be Christmas.
There was clearly nothing left to do but flop down on the shabby, little couch and howl. So Della did it. Which instigates the moral reflection that life is made up of sobs, sniffles, and smiles, with sniffles predominating. While the mistress of the home is gradually subsiding from the first stage to the second, take a look at the home. A furnished flat at $8 per week. It did not exactly beggar description, but it certainly had that word on the look-out the mendicancy squad.
In the vestibule below was a letter-box into which no letter would go, and an electric button from which no mortal finger could coax a ring. Also appertaining thereunto was a card bearing the name “Mr. James Dillingham Young”. The “Dillingham” had been flung to the breeze during a former period of prosperity when its possessor was being paid $30 per week. Now, when the income was shrunk to $20. the letters of “Dillingham” looked blurred, as though they were thinking seriously of contracting to a modest and unassuming D.-But whenever Mr. James Dillingham Young came home and reached his flat above he was called “Jim” and greatly hugged by Mrs. James Dillingham Young already introduced to you as Della. Which is all very good.

Questions:

1. Name the story and its author.
2. How did Della save money?
3. How much money did Della have?
4. What was the cause of Della’s weeping?
5. Find the word from the passage which mean’s – ‘meant’.

Answers:

1. The name of the story is ‘The Gift of the Magi’ and its the author is O. Henry.
2. Della saved money at a time by bulldozing the grocer and the vegetable man and the butcher until one’s cheek burned with silent imputation.
3. Della had one dollar and eighty-seven cents in all. Sixty cents of it was in pennies.
4. The cause of Della’s weeping is that life is made up of sobs sniffles and smiles with sniffles predominating.
5. Implied.

2. Della finished her cry and attended to her cheeks with the pow der rug. She stood by the window and looked out dully at a grey cat walking a grey fence in a grey backyard. Tomorrow would be Christmas Day, and she had only $1.87 with which to buy Jim a present. She had been saving every penny she could for months, with this result. Twenty dollars a week doesn’t go far. Expenses had been greater than she had calculated. They always are. Only $1.87 to buy a present for Jim: Her Jim. Many a happy hour she had spent planning for something nice for him. Something fine and rare and sterling-something just a little bit near to being worthy of , the honour of being owned by Jim. There was a pier-glass between the windows of the room. Perhaps you have seen a pier-glass in an $8 flat. A very thin and very”agile person may, by observing his reflection in a rapid sequence of longitudinal strips, obtain a fairly accu-rate conception of his looks. Della, being slender, had mas-tered the art. Suddenly she whirled from the window and stood before the glass. Her eyes were shining brilliantly, but her face had lost its colour within twenty seconds Rapidly she pulled down her hair and let it fall to its full length.

Questions:

1. How many dollar had Della?
2. How had she been saving money?
3. Why did she suddenly whirled from the window?
4. Find the word from the passage which mean of standard value.

Answers:

1. Della had one dollar and eighty-seven cents.
2. She had been saving every penny she could, for month.
3. While thinking an idea came into her mind that she had beautiful golden hair which she could sell to get enough money for Jim’s presents. So suddenly shewhirled from the window.
4. Sterling.

3. Now, there were two possessions of the James Dillingham Young in which they both took a mighty pride. One was Jim’s gold watch that had been his father’s and his grandfather’s. The other was Della’s hair. Had the Queen of Sheba lived in the flat across the airshaft, Della would have let her hair hang out the window some day to dry just to depreciate Her Majesty’s jewels and gifts. Had King Solomon been the janitor, with all his treasures pile up in the base¬ment, Jim would have pulled out his watch every time he passed just to see him pluck at his beard from envy.
So now Della’s beautiful hair about her, rippling and shining like a cascade of brown waters. It reached below her knee and made itself almost a garment for her. And then she did it up again nervously and quickly. Once she faltered for a minute and stood still while a tear or two splashed on the worn red carpet.
On went her old brown jacket; on went her old brown hat. With a whirl of skirts and with the brilliant sparkle still in her eyes, she fluttered out of the door and down the stairs to the street.

Questions:

1. What were two possessions of the James Dillingham Young?
2. How was Della’s hair?
3. How did Della go to the street.
4. Find the word from the passage which mean ‘golden hair’.

Answers:

1. The two possessions James Dillingham Young were the Della’s hair and the gold watch of Jim.
2. Della’s hair was beautiful fell about her, rippling and shining like a cascade of brown waters.
3. On went her old brown jacket, on went her old brown hat. With a whirl of skirts and with the brilliant sparkle still in her eyes, the fluttered out of the door and down the stairs to the street.
4. Brown waters.

4. Where she stopped the sign read, “Mme So’fronie. Hair Goods of All Kinds.” One flight up Della ran, and collected herself, panting. Madame, large, too white, chilly, hardly looked the “Sofronie”.
“Will you buy my hair?” asked Della.
” I buy hair,” said Madame, “Take your hat off and let’s have sight at the looks of it.”
Down rippled the brown cascade.
“Twenty dollars,” said Madame, lifting the mass with a prac¬ticed hand.
“Give it to me quick,” said Della.
Oh, and the next two hours tripped by on rosy wings. Forget the hashed metaphor. She was ransacking the stores for Jim’s present.
She found it at last. It surely had been made for Jim, and no one else. There was no other like it in any of the stores, and , she had turned all of them inside out. It was a platinum fob chain simple and chaste in design, properly proclaiming its value by substance alone and not by meretricious omamen- tation-as all good things should do. It was even worthy of The Watch. As soon as she Saw it she knew that it must be Jim’s. It was like him. Quientness and value-the description applied to both. Twenty-one dollars they took from her for it, and she hurried home with the 87 cents. With that chain on his watch Jim might be properly anxious about the time in any company. Grand as the watch was, he sometimes looked at it on the sly on account of the old leather strap that he used in place of a chain.

Questions:

1. How did Della think when she got a chain in a shop?
2. What type of was the chain?
3. How much did she pay for the chain?
4. Find the words from the passage which means: ‘attractive but of little value’.

Answers:

1. Della thought that it surely had been made for Jim, and so no one else. There was no other like it in any of the stores.
2. The chain was a platinum fob chain simple and chaste in design, property proclaiming its value by substance done and not by meretricious ornamentation as all good things should do.
3. She paid twenty one dollars.
4. Meretricious.

5. Tradition of giving presents of gifts is very common on some occasions in every religion. For the Christiansit is Christmas, for the Hindus it is Diwali, for the Muslims it is Eid etc. When Della reached home her intoxication gave way a little to prudence and reason. She got out her curling irons and lighted the gas and went to work repairing the ravages made by generosity added to love. Which ii always a tremendous task, dear friends-a mammoth task.
Within forty minutes her head was covered with tiny, close- lying curls that made her look wonderfully like a truant school boy. She looked at her reflection in the mirror long, . carefully, and critically.
“If Jim doesn’t kill me,” she said to herself, “before he takes a second look at me, he’ll say I look like a Coney Island chorus girl. But what could I do-oh! What could I do with a dollar and eighty-seven cents?”
At seven o’clock the coffee was made and the frying-pan was on the back of the stove, hot and ready to cook the chops.

Questions:

1. What is the tradition? The author describes here?
2. What did Della do after reaching home?
3. Which task is tremendous?
4. What did Della think of her looking?

Answers:

1. Tradition of giving present or gifts is very common on some occasions in every religion. For the Christianist is Christmus, for the Hinduist is Diwali, for the Muslims it is Eid.
2. When Della reached home her intoxication gave away a little to prudence. She got out her curling irons and lighted gas and went to work repairing her hair.
3. The work which made by generosity added to love is always a tremendous task.
4. Della thought she would look like a Coney Island chorus girl.

6. Jim was never late. Della doubled the fob chain in her hand and sat on the comer of the table near the door that he always entered. Then she heard his step on the stairway down on the first flight, and she turned white for just a moment. She had a habit of saying little silent prayers about the simplest everyday things, and now she whispered: “Please God. make him think I am still pretty.”
The door pened and Jim stepped in and closed it. He looked thin and very serious. Poor fellow, he was only twenty-two and to be burdened with a family! He needed a new over¬coat and he was without gloves.
Jim Stepped inside the door, as immovable as a setter at the scent of quail. His eyes were fixed upon Della, and there was an expression in them that she could not read, and it terrified her. It was not anger, nor surprise, nor disapproval, nor-horror, nor any of the sentiments that she had been prepared for. He simply stared at her fixedly with that peculiar expression on his face.
Della wriggled and went for him.

Questions:

1. Was Jim ever late to reach his home?
2. Where did Della sit to wait for Jim?
3. Why did she turn white?
4. How did Jim enter the room?
5. Describe the situation when both him and Della met?

Answers:

1. No, Jim was never late to reach his home.
2. Della sat on the comer of the table near the door that Jim always entered and waited for him.
3. As soon as Della heard the sound of step turned white for a moment.
4. The door was opened and Jim stepped in.
5. As Jim entered the room. His eyes fixed upon Della’s hair there was an expression in them that she could not read and it terrified her, it was no anger, nor surprise, nor disapproval, nor horror, nor any sentiments that she had been prepared for. He simply stared at her fixedly.

7. “Jim, darling,” she cried, “don’t look at me that way. I had my hair cut off and sold it because I couldn’t have lived through Christmas without giving you a present. It’ II grow out again—you won’t mind, will you? I just had to do it. My hair grows awfully fast. Say ‘Merry Christmas!’ Jim, and let’s be happy. You don’t know what a nice—what a beautiful, nice gift I’ve got for you.”
“You’ve cut off your hair?” asked Jim laboriously, as if he had not arrived at that patent fact yet even after the hardest mental labour.
“Cut it off and sold it,” said Della. “Don’t you like me just as well, anyhow? I’m me without hair, ain’t I?”
Jim looked about the room curiously.
“You say your hair is gone?” he said with an air almost of idiocy.
“You needn’t look for it,” said Della. It’s sold, I tell you— sold and gone, too. It’s Christmas Eve, the boy. Be good to me, for it went for you. Maybe the hairs of my head were numbered”. She went with a sudden serious sweetness. Shall I put the chops on, Jim?”

Questions:

1. What did Della say to Jim?
2. What did Jim reply?
3. What did Della say in the last?
4. Find the word from the passage which means: ‘on the occasion’.

Answers:

1. Addressing as Jim, darling Della told that she had her hair cut off and sold because she could not live without giving Jim Christmas present. It would grow again.
2. Jim replied silently that she had cut off her hair as if he had not arrived at that patent fact yet.
3. At last, Della requested Jim to be good to her for it had gone for him.
4. Eve.

8. Out of his trance, Jim seemed quickly to wake. He enfolded his Della. For ten seconds let us regard with discreet scrutiny some inconsequential object in the other direction. Eight dollars a week or million a year—what is the difference? A mathematician or a wit would give you the wrong answer. The magi brought valuable gifts, but that was not among them. This dark assertion will be illuminated later on. Jim drew a package from his overcoat pocket and threw it upon the table.
“Don’t make any mistake, Dell?” he said, “about me”. I don’t’ think there’s’anything in the away of a haircut or a shave or a shampoo that could make me like my girl any less. But if you’ll unwrap that package you may see why you had me going a while at first.” White fingers and nimble tore at the string and paper. And then an ecstatic scream of joy; and then, alas! a quick feminine change to hysterical tears and wail, necessitating the immediate employment of all the comforting powers of the lord of the flat.
For there lay The Combs—the set of combs, side and back, that Della had worshipped for long in a Broadway window. Beautiful combs, pure tortoise-shell, with jewelled rims— just the shade to wear in the beautiful vanished hair. They were expensive combs, she knew, and her heart had simply craved and yearned over them without the least hope of possession. And now they were hers, but the tresses that should have adorned the coveted adornments were gone. But she hugged them to her bosom, and at length, she was able to look up with dim eyes and a smile and say: “My hair grows so fast, Jim” And then Della leapt up like a little singed cat and cried, “Oh, oh!”

Questions:

1. What will be illuminated later on?
2. What did Jim tell, having thrown the gift on the table?
3. What we’re in the packet of the gift bought by Jim?
4. What did they do at last?
5. Find the word from the passage which means ‘put the arms round tightly to show love’.

Answers:

1. The dark assertion will be illuminated later on.
2. Jim told that does not think there was anything in the way of a hair cut or a shave or a shampoo that could make him like his girl any less.
3. There were combs—the act of combs, side and back, that Della had worshipped for long.
4. At last, they were hers. But she hugged them to her bosom, and at length, she was able to look up with dim eyes and a smile.

9. Jim had not yet seen his beautiful present. She held it out to him eagerly upon her open palm. The dull precious metal seemed to flash with a reflection of her bright and ardent spirit.
“Isn’t it a dandy, Jim? I hunted all over town to find it.. You’ll have to look at the time a hundred times a day now. Give me your watch I want to see how it looks on it.”
Instead of obeying, Jim tumbled down on the couch and put his hands under the back of his head and smiled.
“Dell,” said he, “let’s put our Christmas presents away and keep ’em a while. They’re too nice to use just at present. I sold the watch to get the money to buy your combs. And now suppose you put the chops on.”
The Magi, as you know, were wise men-wonderfully wise when-who brought a gift to the Babe in the manger. They invented the art of giving Christmas presents. Being wise, their gifts were no doubt wise ones, possibly bearing the privilege of exchange in case of duplication. And here I have lamely related to you the uneventful chronicle of two foolish children in a flat who most unwisely sacrificed for each other the greatest treasures of their house. But in the last word to the wise of these days, let it be said that of all who give gifts these two were the wisest. Of all who give and receive gifts, such as they are the wisest. Everywhere they are the wisest. They are the Magi.

Questions:

1. How did Della show Jim’s presentation?
2. What did Jim say to Della about presents?
3. Who were Magi?
4. Find the word from the passage which means “excellent”.

Answers:

1. Della held the chain out to him eagerly upon her open palm and show the presentation.
2. Jim told Della that they should put their Christmas presents away and should keep them awhile. They were so nice to use just at present.
3. Magi were wise men-wonderful, wise men who brought a gift to the Babe in the manger. They invented the art of giving Christmas presents.
4. Dandy.

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Bihar Board Class 10 Maths Solutions Chapter 5 समांतर श्रेढ़ियाँ Ex 5.2 Text Book Questions and Answers.

BSEB Bihar Board Class 10 Maths Solutions Chapter 5 समांतर श्रेढ़ियाँ Ex 5.2

Bihar Board Class 10 Maths समांतर श्रेढ़ियाँ Ex 5.2

Bihar Board Class 10 Math प्रश्न 1.
निम्नलिखित सारणी में, रिक्त स्थानों को भरिए, जहाँ A.P. का प्रथम पद a, सार्वान्तर d और n वाँ पद a_n है:

हल
(i) दिया है, a = 7, d = 3, n = 8, a_n = ?
n वाँ पद (a_n) = a + (n – 1)d
= 7 + (8 – 1) × 3
= 7 + (7 × 3)
= 7 + 21
= 28
अत: an = 28

(ii) दिया है, a = -18, n = 10, a_n = 0, d = ?
n वाँ पद (a_n) = a + (n – 1)d
⇒ 0 = -18 + (10 – 1)d
⇒ -18 + 9d = 0
⇒ 9d = 18
⇒ d = 2
अतः d = 2

(iii) दिया है, d = -3, n = 18, a_n = -5, a = ?
n वाँ पद (a_n) = a + (n – 1)d
⇒ -5 = a + (18 – 1) × (-3)
⇒ -5 = a + (-51)
⇒ a = -5 + 51 = 46
अत: a = 46

(iv) दिया है, a = -18.9, d = 2.5, a_n = 3.6, n = ?
n वाँ पद (a_n) = a + (n – 1)d
⇒ 3.6 = -18.9 + (n – 1) (2.5)
⇒ 18.9 + 3.6 = (n – 1) (2.5)
⇒ (n – 1)(2.5) = 22.5
⇒ n – 1 = 9
⇒ n = 1 + 9 = 10
अतः n = 10

(v) दिया है, a = 3.5, d = 0, n = 10.5, a_n = ?
n वाँ पद (a_n) = a + (n – 1)d
= 3.5 + (10.5 – 1) (0)
= 3.5 + 0
= 3.5
अत: a_n = 3.5

Exercise 5.2 Class 10 Solutions In Hindi Bihar Board प्रश्न 2.
निम्नलिखित में सही उत्तर चुनिए और उसका औचित्य दीजिए :
(i) A.P.: 10, 7, 4,……, का 30 वाँ पद है :
(A) 97
(B) 77
(C) -77
(D) -87
(ii) A.P.: -3, \(-\frac{1}{2}\), 2,….. का 11 वाँ पद है :
(A) 28
(B) 22
(C) -38
(D) -48\(\frac{1}{2}\)
हल
(i) दी हुई A.P. : 10, 7, 4, …….
यहाँ a = 10 तथा d = 7 – 10 = -3
A.P. का 30 वाँ पद (a₃₀) = a + (n – 1)d
= 10 + (30 – 1) × (-3)
= 10 + (-87)
= -77
अत: विकल्प (C) सही है।

(ii) दी हुई A.P. : -3, \(-\frac{1}{2}\), 2,…….
यहाँ a = -3 तथा d = \(-\frac{1}{2}\) – (-3) = \(\frac{5}{2}\)
A.P.का 11वाँ पद (a₁₁) = a + (n – 1)d
= -3 + (11 – 1) × \(\frac{5}{2}\)
= -3 + 10 × 5
= -3 + 25
= 22
अतः विकल्प (B) सही है।

Bihar Board Class 10th Math Solution प्रश्न 3.
निम्नलिखित समान्तर श्रेढ़ियों में रिक्त खानों (boxes) के पदों को ज्ञात कीजिए :

हल
(i) पहला पद (a) = 2, तीसरा पद = 26, दूसरा पद = ?
माना सार्वान्तर (d) है,
तब, तीसरा पद (a₃) = a + 2d = 26
⇒ 2 + 2d = 26
⇒ 2d = 24
⇒ d = 12
दूसरा पद = a + d = 2 + 12 = 14
अत: रिक्त बॉक्स का पद (a₂) = 14

(ii) पहला पद = ?, दूसरा पद = 13, तीसरा पद = ?, चौथा पद = 3
माना पहला पद (a) तथा सार्वान्तर (d) है।
तब, दूसरा पद = a + d
प्रश्नानुसार, a + d = 13 …….(1)
और चौथा पद = a + 3d
प्रश्नानुसार, a + 3d = 3 ………(2)
समीकरण (2) में से समीकरण (1) को घटाने पर,
2d = -10 ⇒ d = -5
समीकरण (1) में d का मान रखने पर,
a + d = 13
⇒ a + (-5) = 13
⇒ a = 13 + 5 = 18
और तीसरा पद = a + 2d = 18 + 2(-5) =18 – 10 = 8
अत: रिक्त बॉक्सों के पद क्रमशः 18 व 8 हैं।

(iv) -4, a₂, a₃ , a₄, a₅, 6
पहला पद (a) = -4
माना सार्वान्तर d है।
तब, छठा पद = a + 5d
परन्तु छठा पद = 6
a + 5d = 6
⇒ -4 + 5d = 6
⇒ 5d = 10
⇒ d = 2
दूसरा पद (a₂) = a + d = -4 + 2 = -2
तीसरा पद (a₃) = a + 2d = -4 + 2 × 2 = -4 + 4 = 0
चौथा पद (a₄) = a + 3d = -4 + 3 × 2 = -4 + 6 = 2
पाँचवाँ पद (a₅) = a + 4d = -4 + 4 × 2 = -4 + 8 = 4
अत: बॉक्सों के रिक्त पद क्रमशः -2, 0, 2, 4 हैं।

(v) a, 38, a₃, a₄, a₅, -22
माना पहला पद (a) तथा सार्वान्तर (d) है।
तब, दूसरा पद = a + d
परन्तु a + d = 38 ……..(1)
और छठा पद = a + (6 – 1)d = a + 5d
परन्तु a + 5d = -22 ………(2)
समीकरण (2) में से समीकरण (1) को घटाने पर,
(a + 5d) – (a + d) = -22 – 38
⇒ 4d = -60
⇒ d = -15
समीकरण (1) में d का मान रखने पर,
a + (-15) = 38
⇒ a = 38 + 15
⇒ a = 53
तीसरा पद (a₃) = a + 2d = 53 + 2(-15) = 53 – 30 = 23
चौथा पद (a₄) = a + 3d = 53 + 3(-15) = 53 – 45 = 8
पाँचवाँ पद (a₅) = a + 4d = 53 + 4(-15) = 53 – 60 = -7
अत: बॉक्सों के रिक्त पद क्रमशः 53, 23, 8, -7 हैं।

Bihar Board Class 10 Math Book Solution In Hindi प्रश्न 4.
A.P.: 3, 8, 13, 18, …… का कौन-सा पद 78 है?
हल
दी गई A.P. : 3, 8, 13, 18, ……..
पहला पद (a) = 3 तथा सार्वान्तर (d) = 8 – 3 = 5
माना n वा पद (a_n) 78 है।
n वाँ पद (a_n) = 78
⇒ a + (n – 1)d = 78
⇒ 3 + (n – 1)5 = 78
⇒ 3 + 5n – 5 = 78
⇒ 5n = 78 + 5 – 3 = 80
⇒ n = 16
अत: 16 वाँ पद 78 है।

Bihar Board Class 10 Math Solution In Hindi प्रश्न 5.
निम्नलिखित समान्तर श्रेढ़ियों में से प्रत्येक श्रेढ़ी में कितने पद हैं?
(i) 7, 13, 19, ……, 205
(ii) 18, 15\(\frac{1}{2}\), 13, ….., -47
हल
(i) दी गई समान्तर श्रेढ़ी (A.P.) : 7, 13, 19, …… , 205
पहला पद (a) = 7 तथा सार्वान्तर (d) = 13 – 7 = 6
माना दी गई A.P. में n पद हैं जिसमें n वाँ पद (a_n) = 205
n वाँ पद (a_n) = 205
⇒ a + (n – 1)d = 205
⇒ 7 + (n – 1)6 = 205
⇒ 7 + 6n – 6 = 205
⇒ 6n = 205 + 6 – 7 = 204
⇒ n = 34
अतः दी गई श्रेढी (A.P.) में 34 पद हैं।

(ii) दी गई समान्तर श्रेढ़ी (A.P.) : 18, 15\(\frac{1}{2}\), 13, ….., -47
पहला पद (a) = 18
तथा सार्वान्तर (d) = 15\(\frac{1}{2}\) – 18
= \(\frac{31}{2}\) – 18
= \(\frac{31-36}{2}\)
= \(\frac{-5}{2}\)
माना दी गई श्रेढ़ी में n पद हैं।
n वाँ पद 4 (a_n) = -47
⇒ a + (n – 1)d = -47
⇒ 18 + (n – 1)(\(\frac{-5}{2}\)) = -47
⇒ \(-\frac{5(n-1)}{2}\) = -47 – 18 = -65
⇒ (n – 1) = \(\frac{65 \times 2}{5}\) = 26
⇒ n = +1 + 26 = 27
अतः दी गई श्रेढी (A.P.) में 27 पद हैं।

Bihar Board Class 10 Math Book Solution In Hindi Pdf Download प्रश्न 6.
क्या A.P. : 11, 8, 5, 2 का एक पद -150 है? क्यों?
हल
दी गई A.P. : 11, 8, 5, 2
पहला पद (a) = 11 तथा सार्वान्तर (d) = 8 – 11 = -3
माना n वाँ पद (a_n) = -150 है।
n वाँ पद (a_n) = -150
⇒ a + (n – 1)d = -150
⇒ 11 + (n – 1) × -3 = -150
⇒ -3(n – 1) = -150 – 11 = -161
⇒ (n – 1) = 53.6 (लगभग)
⇒ n = 53.6 + 1 = 54.6
n का मान एक पूर्ण संख्या नहीं है।
अतः दी गई A.P. का कोई पद -150 नहीं है।

Bihar Board 10th Class Math Solution प्रश्न 7.
उस A.P. का 31 वाँ पद ज्ञात कीजिए, जिसका 11 वाँ पद 38 है और 16 वाँ पद 73 है।
हल
माना A.P. का पहला पद (a) तथा सार्वान्तर (d) है।
दिया है, A.P. का 11 वाँ पद (a₁₁) = 38
⇒ a + (n – 1)d = 38
⇒ a + (11 – 1)d = 38
⇒ a + 10d = 38 ………(1)
पुनः दिया है, A.P. का 16 वाँ पद (a₁₆) = 73
⇒ a + (16 – 1)d = 73
⇒ a + 15d = 73 ……..(2)
समीकरण (2) में से समीकरण (1) को घटाने पर,
(a + 15d) – (a + 10d) = 73 – 38
⇒ 5d = 35
⇒ d = 7
समीकरण (1) में d का मान रखने पर,
a + 10 × 7 = 38
⇒ a + 70 = 38
⇒ a = 38 – 70 = -32
श्रेढ़ी का 31 वाँ पद (a₃₁) = a + (31 – 1)d
= -32 + 30 × 7
= -32 + 210
= 178
अतः A.P. का 31 वाँ पद = 178

10 Class Ka Math Bihar Board प्रश्न 8.
एक A.P. में 50 पद हैं, जिसका तीसरा पद 12 है और अन्तिम पद 106 है। इसका 29 वाँ पद ज्ञात कीजिए।
हल
माना A.P. का प्रथम पद (a) तथा सार्वान्तर (d) है।
तब, तीसरा पद = a + (3 – 1)d = a + 2d
और अन्तिम 50 वाँ पद = a + (50 – 1)d = a + 49d
तब प्रश्नानुसार,
a + 2d = 12 ………(1)
a + 49d = 106 ……(2)
समीकरण (2) में से समीकरण (1) को घटाने पर,
(a + 49d) – (a + 2d) = 106 – 12
⇒ 47d = 94
⇒ d = 2
तब समीकरण (1) में d का मान रखने पर,
a + 2 × 2 = 12
⇒ a + 4 = 12
⇒ a = 8
A.P. का 29 वाँ पद = a + (29 – 1)d
= 8 + 28 × 2
= 8 + 56
= 64
अतः दी गई A.P. का 29 वाँ पद 64 है।

Bihar Board Math Solution प्रश्न 9.
यदि किसी A.P. के तीसरे और नौवें पद क्रमशः 4 और -8 हैं तो इसका कौन-सा पद शून्य होगा?
हल
माना श्रेढ़ी का पहला पद (a) तथा सार्वान्तर (d) है।
A.P. का तीसरा पद (a₃) = a + 2d
तथा नौवाँ पद (a₉) = a + (9 – 1) d = a + 8d
तब प्रश्नानुसार,
a + 2d = 4 ……(1)
a + 8d = -8 ……(2)
समीकण (2) में से समीकरण (1) को घटाने पर,
(a + 8d) – (a + 2d) = -8 – 4
या 6d = -12
या d = -2
समीकरण (1) में d का मान रखने पर,
a + 2 x (-2) = 4
⇒ a – 4 = 4
⇒ a = 8
माना श्रेढ़ी का n वाँ पद शून्य होगा, अर्थात्
a_n = 0
n वाँ पद (a_n) = 0
⇒ a + (n – 1)d = 0
⇒ 8 + (n – 1) × (-2) = 0
⇒ -2(n – 1) = -8
⇒ (n – 1) = 4
⇒ n = 5
अतः दी गई A.P. का 5 वाँ पद शून्य होगा।

Bihar Board Class 5 Math Solution In Hindi प्रश्न 10.
किसी A.P. का 17 वाँ पद उसके 10 वें पद से 7 अधिक है। इसका सार्वान्तर ज्ञात कीजिए।
हल
माना A.P. का पहला पद (a) तथा सार्वान्तर (d) है।
तब, 17 वाँ पद (a₁₇) = a + (17 – 1)d = a + 16d
10 वा पद (a₁₀) = a + (10 – 1)d = a + 9d
प्रश्नानुसार, 17 वाँ पद, 10 वें पद से 7 अधिक है।
17 वाँ पद (a₁₇) – 10 वाँ पद (a₁₀) = 7
⇒ (a + 16d) – (a + 9d) = 7
⇒ 7d = 7
⇒ d = 1
अत: श्रेढ़ी का सार्वान्तर (d) = 1

Bihar Board Math Solution Class 10 प्रश्न 11.
A.P. : 3, 15, 27, 39, ….. का कौन-सा पद उसके 54 वें पद से 132 अधिक होगा?
हल
माना अभीष्ट पद n वाँ पद है।
दी गई A.P. : 3, 15, 27, 39, …..
प्रथम पद (a) = 3 तथा सार्वान्तर (d) = 15 – 3 = 12
तब, श्रेढ़ी का 54 वाँ पद (a₅₄) = a + (54 – 1)d
= 3 + (53 × 12)
= 3 + 636
= 639
n वॉ पद (a_n) = 54 वें पद से 132 अधिक
= 639 + 132
= 771
n वाँ पद (a_n) = 771
a + (n – 1)d = 771
3 + (n – 1) 12 = 771
(n – 1)12 = 771 – 3 = 768
n – 1 = 64
n = 64 + 1 = 65
अतः श्रेढ़ी का 65 वाँ पद 54 वें पद से 132 अधिक है।

Bihar Board Class 5 Math Solution प्रश्न 12.
दो समान्तर श्रेढ़ियों का सार्वान्तर समान है। यदि इनके 100 वें पदों का अन्तर 100 है, तो इनके 1000 वें पदों का अन्तर क्या होगा?
हल
माना पहली A.P. का पहला पद a तथा सार्वान्तर d है और दूसरी A.P. का पहला पद A तथा सार्वान्तर d है क्योंकि सार्वान्तर समान है।
तब, पहली श्रेढ़ी का 100 वाँ पद = a + (100 – 1)d = a + 99d
दूसरी श्रेढ़ी का 100 वा पद = A + (100 – 1) d = A + 99d
दोनों श्रेढ़ियों के 100 वें पदों का अन्तर = (A + 99d) – (a + 99d) = A – a
तब, प्रश्नानुसार, A – a = 100 ……(1)
अब, पहली श्रेढ़ी का 1000 वाँ पद = a + (1000 – 1)d = a + 999d
दूसरी श्रेढ़ी का 1000 वाँ पद = A + (1000 – 1)d = A + 999d
दोनों श्रेढ़ियों के 1000 वें पदों का अन्तर = (A + 999d) – (a + 999d) = A – a
दोनों श्रेढ़ियों के 1000 वें पदों का अन्तर = A – a = 100 [समीकरण (1) से]
अत: 1000 वें पदों का अन्तर = 100

Bihar Board Class 5 Math Book Solution प्रश्न 13.
तीन अंकों वाली कितनी संख्याएँ 7 से विभाज्य हैं?
हल
तीन अंकों की संख्याओं की सूची : 100, 101, 102, ……., 999
3 अंकों की 7 से विभाज्य पहली संख्या = 105
और अन्तिम संख्या = 994
तब, 7 से विभाज्य 3 अंकीय संख्याओं की सूची :
105, (105 + 7), (105 + 7 + 7), ……….., 994
= 105, 112, 119,…….,994
माना कुल संख्याएँ n हैं।
पहली संख्या (a) = 105, सार्वान्तर (d) = 7, n वाँ पद (a_n) = 994
n वा पद (a_n) = 994
a + (n – 1)d = 994
105 + (n – 1) × 7 = 994
(n – 1) × 7 = 994 – 105 = 889
(n – 1) = \(\frac{889}{7}\) = 127
n = 127 + 1 = 128
अतः 7 से विभाज्य तीन अंकीय संख्याएँ 128 हैं।

Bihar Board Class 5th Math Solution In Hindi प्रश्न 14.
10 और 250 के बीच में 4 के कितने गणज हैं?
हल
10 से बड़ा 4 का पहला गुणज = 12
250 से छोटा 4 का पहला गुणज = 248
10 और 250 के बीच 4 के गुणजों की सूची :
12, 12 + 4, (12 + 4 + 4),……., 248
12, 16, 20, 24, …….., 248.
माना गुणजों की संख्या n है।
यहाँ, पहला पद (a) = 12, सार्वान्तर (d) = 16 – 12 = 4
n वा पद (a_n) = 248
⇒ a + (n – 1)d = 248
⇒ 12 + (n -1) 4 = 248
⇒ 12 + 4n – 4 = 248
⇒ 4n = 248 + 4 – 12 = 240
⇒ n = 60
अत: 10 और 250 के बीच 4 के गुणजों की संख्या = 60

Bihar Board Class 10th Math Solution In Hindi प्रश्न 15.
n के किस मान के लिए, दोनों समान्तर श्रेढ़ियों 63, 65, 67, ….. और 3, 10, 17,…..के n वें पद बराबर होंगे?
हल
पहली समान्तर श्रेढ़ी : 63, 65, 67,……
पहला पद (a) = 63, सार्वान्तर (d) = 65 – 63 = 2
श्रेढ़ी का n वा पद = a + (n – 1)d
= 63 + (n – 1)2
= 63 + 2n – 2
= 61 + 2n
दूसरी समान्तर श्रेढ़ी : 3, 10, 17, ……
पहला पद (A) = 3 सार्वान्तर (D) = 10 – 3 = 7
श्रेढ़ी का n वाँ पद = A + (n – 1)D
= 3 + (n – 1)7
= 3 + 7 n – 7
= 7n – 4
दोनों श्रेढ़ियों के n वें पद बराबर हैं।
7n – 4 = 61 + 2n
⇒ 7n – 2n = 61 + 4
⇒ 5n = 65
⇒ n = 13
अतः दी गई दोनों श्रेढ़ियों के 13 वें पद समान हैं।

Bihar Board Class 10 Math Solution प्रश्न 16.
वह A.P. ज्ञात कीजिए जिसका तीसरा पद 16 है और 7 वाँ पद 5 वें पद से 12 अधिक है।
हल
माना पहला पद a है तथा सार्वान्तर d है।
दिया है, A.P. का तीसरा पद = 16
a + 2d = 16 ……(1)
श्रेढ़ी का 7 वाँ पद (a₇) = a + (7 – 1)d = a + 6d
तथा 5 वाँ पद (a₅) = a + (5 – 1)d = a + 4d
7 वाँ पद 5 वें पद से 12 अधिक है
(a + 6d) – (a + 4d) = 12
⇒ a + 6d – a – 4d = 12
⇒ 2d = 12
⇒ d = 6
d का मान समीकरण (1) में रखने पर,
a + 2 × 6 = 16
⇒ a = 4
श्रेढ़ी का पहला पद (a) = 4
दूसरा पद (a₂) = a + d = 4 + 6 = 10
तीसरा पद (a₃) = a + 2d = 4 + 2 × 6 = 4 + 12 = 16
चौथा पद (a₄) = a + 3d = 4 + 3 × 6 = 4 + 18 = 22
अत: अभीष्ट A.P. : 4, 10, 16, 22, …….. है।

Bihar Board 10th Math Solution प्रश्न 17.
A.P. : 3, 8, 13, ….., 253 में अन्तिम पद से 20 वाँ पद ज्ञात कीजिए।
हल
दी गई A.P. : 3, 8, 13, ………, 253
पहला पद (a) = 3, सार्वान्तर (d) = 8 – 3 = 5
यदि श्रेढ़ी को अवरोही क्रम में लिखें तो यह निम्नवत् होगी
253, (253 – 5), (253 – 10), (253 – 15), ……., 3
या 253, 248, 243, 238, ………, 3
पहला पद (a) = 253 तथा सार्वान्तर (d) = 248 – 253 = -5
श्रेढ़ी का 20 वाँ पद = a + (20 – 1)d
= 253 + 19 × (-5)
= 253 – 95
= 158
अतः दी गई A.P. के अन्तिम पद से 20 वाँ पद = 158
वैकल्पिक विधिः A.P. का अन्त से n वाँ पद = l – (n – 1)d
जहाँ, पर l = अन्तिम पद यहाँ, l = 253, d = 8 – 3 = 5, n = 20
A.P. का अन्त से 20वाँ पद = 253 – (20 – 1) (5)
= 253 – 19 × 5
= 253 – 95
= 158

Bihar Board Class 5th Math Solution प्रश्न 18.
किसी A.P. के चौथे और 8 वें पदों का योग 24 है तथा छठे और 10 वें पदों का योग 44 है। इस A.P. के प्रथम तीन पद ज्ञात कीजिए।
हल
माना A.P. का पहला पद a तथा सार्वान्तर d है।
प्रश्नानुसार, 4वाँ पद (a₄) + 8 वाँ पद (a₈) = 24
⇒ a + (4 – 1)d + a + (8 – 1)d = 24
⇒ a + 3d + a + 7d = 24
⇒ 2a + 10d = 24
⇒ a + 5d = 12 ……..(1)
तथा 6वाँ पद (a₆) + 10वाँ पद (a₁₀) = 44
⇒ a + (6 – 1)d + a + (10 – 1)d = 44
⇒ a + 5d + a + 9d = 44
⇒ 2a + 14d = 44
⇒ a + 7d = 22 ……..(2)
समीकरण (2) में से समीकरण (1) को घटाने पर,
(a +7d) – (a + 5d) = 22 – 12
⇒ 2d = 10
⇒ d = 5
d का यह मान समीकरण (1) में रखने पर,
a + 5 × 5 = 12
⇒ a + 25 = 12
⇒ a = -13
तब, श्रेढ़ी का पहला पद (a₁) = -13
दूसरा पद (a₂) = a + d = -13 + 5 = -8
तीसरा पद (a₃) = a + 2d = -13 + 2 × 5 = -13 + 10 = -3
अतः दी गई A.P. के प्रथम तीन पद = -13, -8, -3

प्रश्न 19.
सुब्बाराव ने 1995 में ₹ 5000 के मासिक वेतन पर कार्य आरम्भ किया और प्रत्येक वर्ष ₹ 200 की वेतन वृद्धि प्राप्त की। किस वर्ष में उसका वेतन ₹ 7000 हो गया?
हल
पहले वर्ष में प्रारम्भिक वेतन = ₹ 5000 प्रतिमास
दूसरे वर्ष में वेतन = ₹ (5000 + 200) = ₹ 5200
प्रतिमास तीसरे वर्ष में वेतन = ₹ (5200 + 200) = ₹ 5400 प्रतिमास
इस प्रकार प्रत्येक वर्ष के वेतन (₹)
5000, 5200, 5400, …….. एक समान्तर श्रेढ़ी बनाते हैं।
जिसका पहला पद (a) = 5000 तथा सार्वान्तर (d) = 200
माना n वर्ष बाद वेतन ₹ 7000 होगा।
तब, n वाँ पद = 7000
a + (n – 1)d = 7000
⇒ 5000 + (n – 1) 200 = 7000
⇒ (n – 1) × 200 = 7000 – 5000
⇒ (n – 1) × 200 = 2000
⇒ (n – 1) = 10
⇒ n = 10 + 1 = 11
अत: 11 वें वर्ष में सुब्बाराव का वेतन ₹ 7000 हो जायेगा।

प्रश्न 20.
रामकली ने किसी वर्ष के प्रथम सप्ताह में ₹ 5 की बचत की और फिर अपनी साप्ताहिक बचत ₹ 1.75 बढ़ाती गई। यदि n वें सप्ताह में उसकी साप्ताहिक बचत ₹ 20.75 हो जाती है, तो n ज्ञात कीजिए।
हल
प्रथम सप्ताह की बचत = ₹ 5
प्रत्येक सप्ताह की बचत में उत्तरोत्तर ₹ 1.75 की वृद्धि होती है।
प्रत्येक सप्ताह की बचतें एक A.P. का निर्माण करती हैं जिसका पहला पद (a) = 5 तथा सार्वान्तर (d) = ₹ 1.75
n वें सप्ताह में बचत = 20.75
a + (n – 1)d = 20.75
⇒ 5 + (n – 1) 1.75 = 20.75
⇒ (n – 1) × 1.75 = 20.75 – 5
⇒ (n – 1) × 1.75 = 15.75
⇒ n – 1 = 9
⇒ n = 9 + 1 = 10
अत: n = 10

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Bihar Board Class 9 English Abraham Lincoln’s Letter to His Son’s Teacher Text Book Questions and Answers

A. Answer the following questions orally:

Abraham Lincoln’s Letter To His Son’s Teacher Solutions Bihar Board Question 1.
What do you know about Abraham Lincoln, the famous President of America?
Answer:
Abraham Lincoln was the sixteenth President of the United States of America. He was the man who abolished slavery by Proclamation in 1863. He was shot-dead in 1865.

Abraham Lincoln’s Letter To His Son’s Teacher Questions Answers Pdf Bihar Board Question 2.
Has your father ever written any letter to your teacher?
Answer:
No, he has never written any letter to my teacher.

Abraham Lincoln Letter To His Son’s Teacher Question Answer Bihar Board Question 3.
Can you imagine how much your father is worried about your future?
Answer:
Yes, like every father he is very much worried about my future. He wants it to be good at every step. So he gives proper care of my studies.

B.1. Write ‘T’ for true and ‘F’ for false statement:

1. It is a letter written by a father to his son.
2. All men are not just and true.
3. A dollar earned is of far more value than five pounds.
4. One should be taught to mourn over losing.
5. One should be taught to fail rather than to cheat.

Answer:

1. — F
2. — T
3. — T
4. — F
5. — T

B.2. Complete the sentences on the basis of your reading of the poem:

1. Teach him to sell his ________ and brain to the highest _________
2. Teach him to be _________ with gentle people.
3. Teach him to ________ at cynics.
4. Teach him it is far _________ to fail than to ________
5. Let him learn early that the bullies are the easiest to _________
6. Teach him the _______ of books.
7. He should be given quiet time to ponder the _________ mystery of birds in the sky.
8. One should have sublime _________ in himself to have faith in mankind.

Answer:

1. brawn, bidder
2. gentle
3. scoff
4. honourable, cheat
5. lick
6. wonder
7. eternal
8. faith.

C.1. Long Answer Type Questions

Abraham Lincoln Letter To His Son’s Teacher Poem Questions And Answers Bihar Board Question 1.
Why did Abrahafti Lincoln write a letter to his son’s teacher?
Answer:
Abraham Lincoln wrote a letter to his son’s teacher suggesting to give such an education which can make him strong with body, mind and spirit.

Abraham Lincoln’s Letter To His Son’s Teacher Poem Bihar Board Question 2.
What does Lincoln mean by saying that “for every scoundrel, there is a hero; that for every selfish Politician, there is a dedicated leader…”
Answer:
The saying is true. He means to say that there is always every scoundrel there is a hero and for every selfish Politician, there is a dedicated leader. It depends upon thinker as what he .thinks. We should consider it within our heart about the concerning man.

Letter To A Teacher Prose Questions And Answers Bihar Board Question 3.
A child should be treated gently but not cuddled. Do you agree? Give your opinion.
Answer:
Too much of love spoil the child. A child definitely needs well discipline and manner. Emersion says, “Secret of Education lies in respecting pupils.” At the time of giving education, he should be treated kindly but at his fault he must be punished. He.should be treated kindly but a not at his fault.

Abraham Lincoln Letter To His Son’s Teacher Question And Answer Bihar Board Question 4.
“All men are not just, all men are not true.” Comment on this statement.
Answer:
The poet is right to say that all men are not just and are not true. It’s human nature differs individually. Some are kind and some are rude. So Lincoln advises the teacher to teach the boy about human nature. So that he may beware of the people in Future.

Lincoln’s Son Will Learn That Bihar Board Question 5.
Why do you think Lincoln wants his son to steer away from envy and learn the secret of quiet laughter?
Answer:
Lincoln wants his son to steer away from envy because envy is such a person who believes that people do not do things for good. He is not sincere. Such type of man is not social, he does every work for his sake only. Rather he wants his son that a man who remains amused all the. can tackle any situation and should enjoy laughing quietly.

Abraham Lincoln Letter To His Son’s Teacher Poem Bihar Board Question 6.
Why does Lincoln not want his son to follow the crowd when everyone is getting on the bandwagon?
Answer:
Lincoln does not want his son to follow the crowd when everyone is getting on the bandwagon because he won’t be able to develop has personal qualities. He would not be a leader but a follower as a puppet.

Abraham Lincoln’s Letter To His Son’s Teacher Questions And Answers Bihar Board Question 7.
What qualities did Lincoln want his son’s teacher to teach him?
Answer:
Lincoln wants his son’s teacher to teach him to know about different types of people and able to face different situations. He wants that he should not have ill thoughts rather he should be always in a happy mood. He wished for his son a higher and higher post. He must be self-dependent.

C.2. Group Discussion

Lincoln’s Son Will Learn That Answer Bihar Board Question 1.
The present system of education is at variance with the learner’s experience.
Answer:
The multiplicity of subjects that we have to study bewilders me. 1 do some times wonder the utility of studying Shakespeare in English literature, History, Geography, Social studies etc. There are a host of other subjects, which have probably no use in our’ later lives. One could understand if we were to study the history and geography of our country. What is perplexing, however, is that we have to learn the history and geography of different countries and continents that we shall probably never even see in our lives. So present system of education is at variance with the learners is useless.

Comprehension Based Questions with Answers

1. He will have to learn, I know,
that all men are not just,
all men are not true.
But teach him also that
for every scoundrel there is a hero;
that for every selfish Politician,
there is a dedicated leader
Teach him for every enemy there is a friend,
It will take time, I now;
but teach him if you can,
that a dollar earned is of far more value than five-pound….

Questions:

1. Name the poem and its poet.
2. What will the pupil have to learn?
3. What does the poet advise the teacher about foe and friend,
4. Which earning is preferable to?

Answers:

1. The name of the poem is “Abraham Lincoln’s letter to his son’s teacher” and the poet is Abraham Lincoln.
2. The pupil will have to learn that all men are not just and true.
3. The poet advises the teacher to teach his pupil that for every enemy there is a friend.
4. A dollar earned honestly is better than five-pound earned otherwise.

Question 2.
Teach him to learn to lose…
and also to enjoy winning.
Steer him away from envy,
if you can,
teach him the secret of
quiet laughter.
Let him learn early that
the bullies are the easiest to lick…
Teach him, if you can,
the wonder of books…
But also give him quiet time
to ponder the eternal mystery of birds in the sky,
bees in the sun,
and the flowers on a green hillside.

Questions:

1. What are the poet’s suggestions for losing and winning?
2. What do you mean by envy?
3. What is an early lesson?
4. What does the poet say about books?
5. What does the poet advise about the mystery?

Answers:

1. The poet suggests the teacher to teach to learn to lose and to enjoy winning.
2. Envy means a feeling of discontent caused by’some else’s good fortune. The poet here asks the teacher to steer away from his son from envy.
3. The poet advises the teacher to give his son an early lesson that the bullies are easiest to be defeated.
4. The poet thinks that there is ‘wonder in books.
5. The poet advises the teacher to teach his son so he may able to think over birds in the sky. bees in the sun and flowers on the green hillside.

3. In the school teach him
it is far honourable to fail
than to cheat…
Teach him to have faith
in his own ideas,
even if everyone tells hint
they are wrong…
Teach him to be gentle
with gentle people,
and tough with the tough.
Try to give my son
the strength not to follow the crowd when everyone is getting oil the bandwagon…

Questions:

1. What does the poet advise the teacher to teach the boy at school?
2. What should he have faith in?
3. How should he behave with people?
4. Find the word from the given stanza which means, “cart”.

Answers:

1. It is far honourable to fail than to cheat.
2. He should have faith in his own ideas.
3. He should be gentle with the gentle and tough with the tough.
4. Wagon.

Question 4.
I each him to listen to all men…
but teach him also to filter
all he hears on a screen of truth,
and take only the good
that comes through.
Teach him if you can.
how to laugh when he is sad…
Teach him there is no shame in tears.
Teach him to scoff at cynics
and to beware of too much sweetness…
Teach him to sell his brawn
and brain to the highest bidders
but never to put a price-tag
on his heart and soul.
Teach him to close his ears
to a howling mob
and to stand and fight
if he thinks he’s right.

Questions:

1. What does the poet advise in the first line?
2. What should he do when he is sad?
3. Whom should he scoff at?
4. Whom should he sell his brawn and brain?
5. What should be done with the howling mob?

Answers:

1. The poet advised in the first line that he should be taught to listen to all men.
2. When hs is said he should learn to laugh.
3. He should be taught to scoff at cynics.
4. He should sell his brawn and brain to the highest bidders.
5. He should not hear it but should stand and fight if he thinks right.

5. Treat him gently,
but do not cuddle him,
because only the test
of fire makes fine steel.
Let him have the courage
to be impatient…
let him have the patience to be brave.
Teach him always
to have sublime faith in himself,
because then he will have
sublime faith in mankind.
This is a big order,
but see what you can do…
He is such a fine fellow, my son!

Questions:

1. What is the suggestion of the poet?
2. How is steel made?
3. What should he always think?
4. How is the son?

Answers:

1. The poet suggests the teacher treat the boy gently but forbade to caddie him.
2. When iron is made hot in fire it becomes fine steel.
3. He should always think about the sublime.
4. His son is very nice.

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Bihar Board Class 10 Maths Solutions Chapter 8 त्रिकोणमिति का परिचय Ex 8.4 Text Book Questions and Answers.

BSEB Bihar Board Class 10 Maths Solutions Chapter 8 त्रिकोणमिति का परिचय Ex 8.4

Bihar Board Class 10 Maths त्रिकोणमिति का परिचय Ex 8.4

Bihar Board Class 10 Math Book Solution In Hindi Pdf Download प्रश्न 1.
त्रिकोणमितीय अनुपातों sin A, sec A और tan A को cot A के पदों में व्यक्त कीजिए
हल
हम जानते हैं कि cot A और cosec A में सम्बन्ध ‘cosec² A = 1 + cot² A’ है और cosec A और sin A में सम्बन्ध प्रतिलोम का है।

Bihar Board Class 10 Math Solution In Hindi प्रश्न 2.
∠A के अन्य सभी त्रिकोणमितीय अनुपातों को sec A के पदों में लिखिए।
हल

Class 10 Maths 8.4 Solution In Hindi Bihar Board प्रश्न 3.

(ii) sin 25° cos 65° + cos 25° sin 65°
हल

(ii) दिया है, sin 25° cos 65° + cos 25° sin 65°
= sin 25° cos (90° – 25°) + cos 25° sin (90° – 25°)
= sin 25° sin 25° + cos 25° cos 25°
[∵ cos (90° – 25°) = sin 25° तथा sin(90° – 25°) = cos 25°]
= sin² 25° + cos² 25°
= 1 [∵ sin² A+ cos² A = 1]
अतः sin 25° cos 65° + cos 25° sin 65° = 1

Bihar Board Class 10 Math Book Solution In Hindi प्रश्न 4.
सही विकल्प चुनिए और अपने विकल्प की पुष्टि कीजिए-
(i) 9 sec² A – 9 tan² A बराबर है-
(A) 1
(B) 9
(C) 8
(C) 0

(ii) (1 + tan θ + sec θ) (1 + cot θ – cosec θ) बराबर है-
(A) 0
(B) 1
(C) 2
(D) -1

(iii) (sec A + tan A)(1 – sin A) बराबर है-
(A) sec A
(B) sin A
(C) cosec A
(D) cos A

(iv) \(\frac{1+\tan ^{2} A}{1+\cot ^{2} A}\) बराबर है-
(A) sec² A
(B) -1
(C) cot² A
(D) tan² A
हल
(i) यहाँ 9 sec² A – 9 tan² A
= 9 (sec² A – tan² A)
= 9 (1 + tan² A – tan² A) [∵ sec² A = 1 + tan² A]
= 9 × (1)
= 9
अत: विकल्प (B) सही है।

(ii) यहाँ (1 + tan θ + sec θ) (1 + cot θ – cosec θ)

Class 10th Math Solution In Hindi Bihar Board Pdf प्रश्न 5.
निम्नलिखित सर्वसमिकाएँ सिद्ध कीजिए, जहाँ वे कोण, जिनके लिए व्यंजक परिभाषित है, न्यूनकोण हैं-

हल

Bihar Board Class 7 Maths Solutions Chapter 8 घातांक Text Book Questions and Answers.

BSEB Bihar Board Class 7 Maths Solutions Chapter 8 घातांक

Bihar Board Class 7 Maths घातांक Ex 8.1

Bihar Board Class 7 Math Solution In Hindi प्रश्न 1.
घातांकीय रूप में व्यक्त कीजिए-
(i) 5 × 5 × 5 × 5
हल :
5⁴
(ii) c × c × c
हल :
c³
(iii) 2 × 2 × 3 × 3 × 3
हल :
2² × 3³
(iv) 6 × 6 × b × b
हल :
6² × b²
(v) a × a × b × b × b × b × b × d
हल :
a² × b⁵ × d

Bihar Board Class 7 Math प्रश्न 2.
मान ज्ञात करें-
(i) 3³
हल :
3³ = 3 × 3 × 3 = 27
(ii) 6⁴
हल :
6⁴ = 6 × 6 × 6 × 6 = 1296
(iii) 9³
हल :
9³ = 9 × 9 × 9 = 729
(iv) 5⁴
हल :
5⁴ = 5 × 5 × 5 × 5 = 625
(v) 4⁴
हल :
4⁴ = 4 × 4 × 4 × 4 = 256

Bihar Board Class 7 Math Solution प्रश्न 3.
घातांकीय संकेतन (रूप) में व्यक्त कीजिए-
(i) 343
(ii) 512
(iii) 729
(iv) 3125
हल :
(i) 343

= 7 × 7 × 7 = 343 = 7³
(ii) 512

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 512 = 2⁹
(iii) 729

= 3 × 3 × 3 × 3 × 3 × 3 = 729 = 3⁶
(iv) 3125

= 5 × 5 × 5 × 5 × 5 = 3125 = 5⁵

Bihar Board 7th Class Math Solution प्रश्न 4.
प्रत्येक में बड़ा कौन है?
(i) 4³ या 3⁴
हल :
4³ = 4 × 4 × 4 = 64
3⁴ = 3 × 3 × 3 × 3 = 81
3⁴ बड़ा है।

(ii) 2⁵ या 5²
हल :
2⁵ = 2 × 2 × 2 × 2 × 2 = 32
5² = 5 × 5 = 25
2⁵ बड़ा है।

(iii) 2⁸ या 8²
हल :
2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
8² = 8 × 8 = 64
2⁸ बड़ा है।

(iv) 100² या 2¹⁰⁰
हल :
100² = 100 × 100
2¹⁰⁰ = 2 × 2 × 2…..2 × 2 = 10000
2¹⁰⁰ बड़ा है।

Class 7 Bihar Board Math Solution प्रश्न 5.
अभाज्य गुणनखण्डों की घातों के गुणनफल के रूप में व्यक्त कीजिए-
(i) 1200
(ii) 720
(iii) 1080
(iv) 2280
(v) 3600
हल :
(i) 1200

= 2⁴ × 3 × 5²
(ii) 720

= 2⁴ × 3² × 5
(iii) 1080

= 2³ × 3³ × 5
(iv) 2280

= 2 × 3² × 5³
(v) 3600

= 2⁴ × 3² × 5²

Class 7 Maths Bihar Board Solution प्रश्न 6.
सरल कीजिए-
(i) 3 × 10²
(ii) 7² × 3²
(iii) (-1)⁵ × (7)³
(iv) 0 × 10²
(v) 3² × 10⁴
(vi) 3⁴ × 2³
हल :
(i) 3 × 10² = 3 × 100 = 300
(ii) 7² × 3² = 49 × 9 = 441
(iii) (-1)⁵ × 7³ = -1 × 343 = -343
(iv) 0 × 10² = 0 × 100 = 0
(v) 3² × 10⁴ = 9 × 10000 = 90000
(vi) 3⁴ × 2³ = 81 × 8 = 648

Bihar Board Solution Class 7 Math प्रश्न 7.
(i) (-3)³
(ii) (-1) × (-2)³
(iii) (-4)² × (-3)²
(iv) (-2)³ × (-10)⁴
(v) (-5)² × 2⁴
हल :
(i) (-3)³ = -3 × -3 × -3 = -27
(ii) (-1) × (-2)³ = -1 × -8 = 8
(iii) (-4)² × (-3)² = 16 × 9 = 144
(iv) (-2)³ × (-10)⁴ = -8 × 10000 = -80000
(v) (-5)² × (2)⁴ = 25 × 16 = 400

Bihar Board Class 7 Math Book Solution प्रश्न 8.
निम्न संख्यों की तुलना कीजिए-
(i) 5 × 10¹⁴, 4 × 10⁷
(ii) 2.6 × 10¹² ; 1.6 × 10⁸
(iii) 2.7 × 10¹¹; 3.0 × 10¹⁵
हल :
(i) 5 × 10¹⁴, 4 × 10⁷
5 × 10¹⁴ = 5 × 100000000000000 = 500000000000000
4 × 10⁷ = 4 × 10000000 = 40000000
∴ 5 × 10¹⁴ > 4 × 10⁷

(ii) 2.6 × 10¹² ; 1.6 × 10⁸
2.6 × 10¹² = \(\frac{26}{10}\) × 10000000000000 = 26000000000000
1.6 × 10⁸ = \(\frac{16}{10}\) × 1000000000 = 1600000000
∴ 2.6 × 10¹⁸ > 1.6 × 10⁸

(iii) 2.7 × 10¹¹; 3.0 × 10¹⁵
2.7 × 10¹¹ = \(\frac{27}{10}\) × 1000000000000 = 2700000000000
3.0 × 10¹⁵ = 3 × 10000000000000000 = 30000000000000000
∴ 3.0 × 10¹⁵ > 2.7 × 10¹¹

Bihar Board Math Solution Class 7 प्रश्न 9.
निम्नलिखित को घातांकीय रूप में लिखिए-
(i) \(\frac{8}{729}\)
(ii) \(\frac{81}{343}\)
(iii) \(\frac{243}{1024}\)
हल :

Bihar Board Class 7 Maths घातांक Ex 8.2

Bihar Board Class 7 Maths Solutions प्रश्न 1.
सरल कीजिए और उत्तर को घातांकीय रूप में लिखिए-
(i) 7² × 7⁴ × 7⁸
(ii) 3¹⁰ ÷ 3⁶
(iii) d² × d³
(iv) 5^x × 5²
(v) (5³)² ÷ 5³
(vi) 3⁵ × 5⁵
(vii) a⁴ × b⁴
(viii) (2¹⁰ ÷ 2¹⁰) × 2
(ix) 9^p ÷ 9³
हल :

Bihar Board Class 7 Maths प्रश्न 2.
सरल कीजिए और उत्तर को घातांकीय रूप में लिखिए-
(i) \(\frac{2^{3} \times 3^{4} \times 4}{3^{2} \times 3^{2}}\)
(ii) \(\left[\left(5^{3}\right)^{2} \times 5^{3}\right]+5^{6}\)
(iii) 25⁵ ÷ 5⁴
(iv) 3⁰ + 4⁰ + 5⁰
(v) 3⁰ × 4⁰ × 5⁰
(vi) (4⁰ + 5⁰) × 2⁰
(vii) \(\frac{11^{6} \times 13^{3} \times 3}{39 \times 11^{2}}\)
(viii) \(\frac{5^{7}}{5^{4} \times 5^{3}}\)
(ix) (3³ × 3)³
(x) \(\frac{5^{8} \times a^{5}}{25^{3} \times a^{3}}\)
हल :

प्रश्न 3.
आमाज्य गुणनखंडों की घातों के गुणनफल के रूप में व्यक्त कीजिए-
(i) 1152
(ii) 64 × 81
(iii) 540
(iv) 27 × 48 × 72
(v) 9 × 6 × 15 × 4
हल :
(i) 1152

= 2⁷ × 3²
(ii) 64 × 81
= 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
= 2⁶ × 3⁴
(iii) 540

= 2 × 2 × 3 × 3 × 3 × 5
= 2² × 3³ × 5
(iv) 27 × 48 × 72

= 27 × 48 × 72
= 3 × 3 × 3 × 2 × 2 × 2 × 2 × 3 × 2 × 2 × 2 × 3 × 3
= 3³ × 2⁴ × 3 × 2³ × 3²
(v) 9 × 16 × 15 × 4
= 3 × 3 × 2 × 2 × 2 × 2 × 3 × 5 × 2 × 2
= 3² × 2⁴ × 3 × 5 × 2²

प्रश्न 4.
नीचे दिए गए कथनों में सही/गलत छाँटिए तथा अपने उत्तर का कारण भी दीजिए-
(i) 10⁰ = (1000)⁰
(ii) 4³ × 3² = 12⁵
(iii) 2⁵ = 5²
(iv) 10 × 10⁶ = 100⁶
हल :
(i) 10⁰ = (1000)⁰
10⁰ = 1
(1000)⁰ = 1
10⁰ = (1000)⁰ = 1 (सत्य)

(ii) 4³ × 3² = 125
(2²)³ × 3² = 12⁵
2⁶ × 3² ≠ 12⁵ (असत्य)

(iii) 2⁵ = 5²
32 ≠ 25 (असत्य)

(iv) 10 × 10⁶ = 100⁶
10 × 10000000 = 1000000000000
100000000 ≠ 1000000000000 (असत्य)

प्रश्न 5.
सरल कीजिए-
(i) \(\frac{\left(3^{2}\right)^{5} \times 5^{3}}{9^{3} \times 5^{2}}\)
(ii) \(\frac{9^{2} \times 3^{2} \times a^{8}}{3^{7} \times a^{3}}\)
(iii) \(\frac{3^{5} \times 10^{5} \times 25}{5^{7} \times 6^{5}}\)
हल :

Bihar Board Class 7 Maths घातांक Ex 8.3

प्रश्न 1.
निम्नलिखित संख्याओं को विस्तारित रूप में लिखिए-
(i) 389505
(ii) 2005183
(iii) 230829
(iv) 30079
(v) 8324750
हल :
(i) 389505 = 3 × 10⁵ + 8 × 10⁴ + 2 × 10³ + 5 × 10² + 0 + 5 × 1
(ii) 2005183 = 2 × 10⁶ + 0 × 10⁵ + 0 × 10⁴ + 5 × 10³ + 1 × 10² + 8 × 10 + 3 × 1
(iii) 230829 = 2 × 10⁵ + 3 × 10⁴ + 0 × 10³ + 8 × 10² + 2 × 10 + 9
(iv) 30079 = 3 × 10⁴ + 0 × 10³ + 0 × 10² + 7 × 10 + 9
(v) 8324750 = 8 × 10⁶ + 3 × 10⁵ + 2 × 10⁴ + 4 × 10³ + 7 × 10² + 5 × 10

प्रश्न 2.
(i) 9 × 10⁴ + 5 × 10³ + 0 × 10² + 5 × 10² + 4 × 10¹
(ii) 7 × 10⁵ + 8 × 10³ + 4 × 10² + 7 × 10⁰
(iii) 6 × 10⁴ + 5 × 10⁴ + 7 × 10⁰
(iv) 8 × 10⁵ + 3 × 10² + 8 × 10¹
हल :
(i) 9 × 10⁴ + 5 × 10³ + 0 × 10² + 5 × 10² + 4 × 10¹
= 90000 + 5000 + 0 + 500 + 40
= 950540

(ii) 7 × 10⁵ + 8 × 10³ + 4 × 10² + 7 × 10¹
= 700000 + 0000 + 8000 + 400 + 70
= 708470

(iii) 6 × 10⁴ + 5 × 10² + 7 × 10¹
= 60000 + 0000 + 500 + 70
= 60570

(iv) 8 × 10⁵ + 3 × 10² + 8 × 10¹
= 800000 + 00000 + 0000 + 300 + 80
= 800380

प्रश्न 3.
निम्नलिखित संख्याओं को मानक रूप में व्यक्त कीजिए-
(i) 70000000
(ii) 8000000
(iii) 416000000
(iv) 456234
(v) 9634.21
(vi) 72439.62
हल :
(i) 70000000 = 7 × 10⁷
(ii) 8000000 = 8 × 10⁶
(iii) 416000000 = 4 × 10⁸ + 1 × 10⁷ + 6 × 10⁶ = 4.16 × 10⁸
(iv) 456234 = 4 × 10⁵ + 5 × 10⁴ + 6 × 10³ + 2 × 10² + 3 × 10¹ + 4 = 4.56234 × 10⁵
(v) 9634.21 = 9.63421 × 10³
(vi) 72439.62 = 7.243962 × 10⁴

प्रश्न 4.
निम्नलिखित कथनों में प्रकट होने वाली संख्याओं को मानक रूप में व्यक्त कीजिए-
(i) 127560000
(ii) 1027.000000
(iii) 1400000000
(iv) 300000000
(v) 12000000000
(vi) 1000000000000
(vii) 300000000000000000000
(viii) 60230000000000000000000000
(ix) 1353000000
हल :
(i) 127560000 = 1.2756000 × 10⁷
(ii) 1027.000000 = 1.027 × 10⁹
(iii) 1400000000 = 1.4 × 10⁹
(iv) 300000000 = 3 × 10⁸
(v) 12000000000 = 1.2 × 10¹⁰
(vi) 1000000000000 = 1 × 10¹¹
(vii) 300000000000000000000 = 3 × 10²⁰
(viii) 60230000000000000000000000 = 6.023 × 10²²
(ix) 1353000000 = 1.353 × 10⁶

प्रश्न 5.
निम्नलिखित कथनों में प्रकट होने वाली दृश्यों को मानक रूप में व्यक्त करके घटते क्रम में सजायें-
(i) 1433500000000
(ii) 1439000000000
(iii) 149600000000
(iv) 384000000
हल :
(i) 1433500000000 = 1.4335 × 10¹²
(ii) 1439000000000 = 1.439 × 10¹²
(iii) 149600000000 = 1.496 × 10¹¹
(iv) 384000000 = 3.84 × 10⁸

Bihar Board Class 10 Maths Solutions Chapter 4 द्विघात समीकरण Ex 4.3 Text Book Questions and Answers.

BSEB Bihar Board Class 10 Maths Solutions Chapter 4 द्विघात समीकरण Ex 4.3

Bihar Board Class 10 Maths द्विघात समीकरण Ex 4.3

Bihar Board Class 10 Math Book Solution In Hindi Pdf Download प्रश्न 1.
यदि निम्नलिखित द्विघात समीकरणों के मूलों का अस्तित्व हो, तो इन्हें पूर्ण वर्ग बनाने की विधि द्वारा ज्ञात कीजिए।
(i) 2x² – 7x + 3 = 0
(ii) 2x² + x – 4 = 0
(iii) 4x² + 4√3x + 3 = 0
(iv) 2x² + x + 4 = 0
हल
(i) दिया गया द्विघात समीकरण :
2x² – 7x + 3 = 0
⇒ \(x^{2}-\frac{7}{2} x+\frac{3}{2}=0\) [प्रत्येक पद में x² के गुणांक 2 से भाग देने पर]

Bihar Board Class 10 Math Book Solution In Hindi प्रश्न 2.
उपर्युक्त प्रश्न (1) में दिए गए द्विघात समीकरणों के मूल, द्विघाती सूत्र का उपयोग करके ज्ञात कीजिए।
हल
(i) दिया गया द्विघात समीकरण :
2x² – 7x + 3 = 0
उपर्युक्त समीकरण की तुलना व्यापक द्विघात समीकरण ax² + bx + c = 0 से करने पर,
a = 2, b = -7 तथा c = 3

अत: समीकरण के मूल = 3, \(\frac{1}{2}\)

(ii) दिया गया द्विघात समीकरण :
2x² + x – 4 = 0
उपर्युक्त समीकरण की तुलना व्यापक द्विघात समीकरण ax² + bx + c = 0 से करने पर,
a = 2, b = 1 तथा c = -4

(iii) दिया गया द्विघात समीकरण :
4x² + 4√3x + 3 = 0
उपर्युक्त समीकरण की तुलना व्यापक द्विघात समीकरण ax² + bx + c = 0 से करने पर,

द्विघात समीकरण के दो मूल होते हैं और यहाँ b² – 4ac = 0 है।
अत: दोनों मूल समान होंगे। तब समीकरण के मूल = \(-\frac{\sqrt{3}}{2},-\frac{\sqrt{3}}{2}\)

(iv) दिया गया समीकरण :
2x² + x + 4 = 0
उपर्युक्त समीकरण की तुलना व्यापक द्विघात समीकरण ax² + bx + c = 0 से करने पर,
a = 2, b = 1 तथा c = 4

√-31 एक अधिकल्पित संख्या है।
x के मान अधिकल्पित होंगे।
अत: दिए गए समीकरण के मूलों का अस्तित्व नहीं है।

Bihar Board Class 10th Math Solution In Hindi प्रश्न 3.
निम्न समीकरणों के मूल ज्ञात कीजिए :
(i) x – \(\frac{1}{x}\) = 3, x ≠ 0
(ii) \(\frac{1}{x+4}-\frac{1}{x-7}=\frac{11}{30}\), x ≠ -4, 7
हल

Bihar Board Class 10 Math Solution प्रश्न 4.
3 वर्ष पूर्व रहमान की आयु (वर्षों में) का व्युत्क्रम और अब से 5 वर्ष पश्चात् आयु के व्युत्क्रम का योग \(\frac{1}{3}\) है। उसकी वर्तमान आयुज्ञात कीजिए।
हल
माना रहमान की वर्तमान आयु x वर्ष है।
3 वर्ष पूर्व उसकी आयु = (x – 3) वर्ष
3 वर्ष पूर्व उसकी आयु का व्युत्क्रम = \(\frac{1}{x-3}\)
5 वर्ष पश्चात् उसकी आयु = (x + 5) वर्ष
5 वर्ष पश्चात् उसकी आयु का व्युत्क्रम = \(\frac{1}{x+5}\)
प्रश्नानुसार, दोनों व्युत्क्रमों का योग = \(\frac{1}{3}\)
\(\frac{1}{x-3}+\frac{1}{x+5}=\frac{1}{3}\)

धनात्मक (+) चिह्न लेने पर, x = 2 + 5 = 7
ऋणात्मक (-) चिह्न लेने पर, x = 2 – 5 = -3
परन्तु आयु ऋणात्मक नहीं होती; अत: x का मान -3 स्वीकार्य नहीं है
∴ x = 7
अत: रहमान की वर्तमान आयु 7 वर्ष है।

Bihar Board 10th Math Solution In Hindi प्रश्न 5.
एक क्लास टेस्ट में शेफाली के गणित और अंग्रेजी में प्राप्त किए गए अंकों का योग 30 है। यदि उसको गणित में 2 अंक अधिक और अंग्रेजी में 3 अंक कम मिले होते, तो उनके अंकों का गुणनफल 210 होता। उसके द्वारा दोनों विषयों में प्राप्त किए अंक ज्ञात कीजिए।
हल
माना शेफाली ने गणित में x अंक प्राप्त किए।
अंग्रेजी और गणित दोनों के प्राप्तांकों का योग = 30
अंग्रेजी में प्राप्तांक = (30 – x)
यदि उसको गणित में 2 अंक अधिक मिलते अर्थात् गणित में (x + 2) अंक मिलते और अंग्रेजी में 3 अंक कम मिलते अर्थात् अंग्रेजी में (30 – x – 3) या (27 – x) अंक मिलते, तो अंकों का गुणनफल (x + 2) (27 – x) होता अर्थात्
गुणनफल = (x + 2) (27 – x)
= 27x – x² + 54 – 2x
= 25x – x² + 54
प्रश्नानुसार, गुणनफल = 210
⇒ 25x – x² + 54 = 210
⇒ x² – 25x – 54 + 210 = 0 [पक्षान्तरण करने पर]
⇒ x² – 25x + 156 = 0 [सरल करने पर]
उपर्युक्त समीकरण की तुलना मानक द्विघात समीकरण ax² + bx + c = 0 से करने पर,
a = 1, b = -25 तथा c = 156

तब, शेफाली ने गणित में या तो 12 अंक प्राप्त किए या फिर 13 अंक प्राप्त किए।
यदि शेफाली ने गणित में 12 अंक प्राप्त किए, तो अंग्रेजी में (30 – 12) = 18 अंक प्राप्त किए
और यदि शेफाली ने गणित में 13 अंक प्राप्त किए, तो अंग्रेजी में (30 – 13) = 17 अंक प्राप्त किए।
अतः शेफाली ने गणित व अंग्रेजी में क्रमश: 12 व 18 अंक अथवा 13 व 17 अंक प्राप्त किए।

Bihar Board Class 10 Maths Solution प्रश्न 6.
एक आयताकार खेत का विकर्ण उसकी छोटी भुजा से 60 मी अधिक लम्बा है। यदि बड़ी भुजा छोटी भुजा से 30 मी अधिक हो, तो खेत की भुजाएँ ज्ञात कीजिए।
हल
माना आयताकार खेत की छोटी भुजा x मी है।
बड़ी भुजा छोटी भुजा से 30 मी अधिक है।
बड़ी भुजा = (x + 30) मी
तब खेत की लम्बाई = (x + 30) मी तथा चौड़ाई = x मी
प्रश्नानुसार, आयताकार खेत का विकर्ण, छोटी भुजा (चौड़ाई) से 60 मी अधिक है।
आयताकार खेत का विकर्ण = (x + 60) मी
परन्तु आयत के लिए,
लम्बाई² + चौड़ाई² = विकर्ण²
⇒ (x + 30)² + x² = (x + 60)²
⇒ x² = (x + 60)² – (x + 30)²
⇒ x² = (x + 60 + x + 30) (x + 60 – x – 30) [∵ a² – b² = (a + b) (a – b)]
⇒ x² = (2x + 90) (30)
⇒ x² = 60x + 2700
⇒ x² – 60x – 2700 = 0 [पक्षान्तरण करने पर]
⇒ x² – (90 – 30)x – 2700 = 0 [मध्यपद का विखण्डन करने पर]
⇒ x² – 90x + 30x – 2700 = 0
⇒ x(x – 90) + 30(x – 90) = 0
⇒ (x – 90)(x + 30) = 0
⇒ (x – 90)(x + 30) = 0
यदि x – 90 = 0 हो, तो x = 90
और यदि x + 30 = 0 हो, तो x = -30
परन्तु भुजा की लम्बाई ऋणात्मक नहीं हो सकती; अत: x का मान -30 स्वीकार्य नहीं है।
∴ x = 90
दूसरी भुजा = (x + 30) मी = (90 + 30) = 120 मी
अत: आयताकार खेत की भुजाएँ 90 मी व 120 मी हैं।

Class 10th Math Solution In Hindi Bihar Board Pdf प्रश्न 7.
दो संख्याओं के वर्गों का अन्तर 180 है। छोटी संख्या का वर्ग बड़ी संख्या का आठ गुना है। दोनों संख्याएँ ज्ञात कीजिए।
हल
माना छोटी संख्या x है।
छोटी संख्या का वर्ग बड़ी संख्या का 8 गुना है।
बड़ी संख्या × 8 = छोटी संख्या का वर्ग
बड़ी संख्या × 8 = x²
बड़ी संख्या = \(\frac{x^{2}}{8}\)
प्रश्नानुसार, वर्गों का अन्तर = 180
(बड़ी संख्या)² – (छोटी संख्या)² = 180
⇒ \(\left(\frac{x^{2}}{8}\right)^{2}-(x)^{2}=180\)
⇒ \(\frac{x^{4}}{64}\) – (x)² = 180
⇒ x⁴ – 64x² = 11520
⇒ x⁴ – 64x² – 11520 = 0
माना x² = X, तब उक्त समीकरण :
X² – 64X – 11520 = 0
उपर्युक्त समीकरण की तुलना मानक द्विघात समीकरण AX² + BX + C = 0 से करने पर,
A = 1, B = -64 तथा C = -11520

धनात्मक (+) चिह्न लेने पर, x = 32 + 112 = 144
ऋणात्मक (-) चिह्न लेने पर, x = 32 + 112 = -80
X = x²
⇒ x² = 144 या -80
⇒ x = ±12 या √-80 जो कि अधिकल्पित संख्या है।
तब, छोटी संख्या = 12 या -12
तब, बड़ी संख्या = \(\frac{x^{2}}{8}=\frac{144}{8}=18\)
अतः संख्याएँ = 12, 18 अथवा -12, 18

Bihar Board Solution Class 10 Math प्रश्न 8.
एक रेलगाड़ी एकसमान चाल से 360 km की दूरी तय करती है। यदि यह चाल 5 km/h अधिक होती, तो वह उसी यात्रा में 1 घंटा कम समय लेती। रेलगाड़ी की चाल ज्ञात कीजिए।
हल
माना रेलगाड़ी की चाल x km/h है।
सूत्र; समय = \(\frac{\text { दूरी }}{\text { चाल }}\) से
360 किमी दूरी तय करने में लगा समय = \(\frac{360}{x}\) घंटा
यदि रेलगाड़ी की चाल 5 km/h अधिक होती अर्थात् चाल (x + 5) km/h होती, तो
360 km दूरी तय करने में लगा समय = \(\frac{360}{x+5}\) घंटा


रेलगाड़ी की चाल ऋणात्मक नहीं हो सकती जिससे x का मान -45 स्वीकार्य नहीं है, तब x = 40
अत: रेलगाड़ी की चाल = 40 km/h

Bihar Board 10th Math Solution प्रश्न 9.
दो पानी के नल एक-साथ एक हौज को 9\(\frac{3}{8}\) घंटों में भर सकते हैं। बड़े व्यास वाला नल हौज को भरने में, कम व्यास वाले नल से 10 घंटे कम समय लेता है। प्रत्येक द्वारा अलग से हौज को भरने के समय ज्ञात कीजिए।
हल
माना कम व्यास वाला नल पानी के हौज को x घंटे में भरता है।
बड़े व्यास वाला नल हौज को भरने में 10 घंटे कम समय लेता है।
बड़े व्यास वाला नल हौज को (x – 10) घंटे में भरेगा।
पहले नल द्वारा हौज को भरने की प्रति घंटा दर = \(\frac{1}{x}\) भाग
इसी प्रकार, दूसरे नल द्वारा हौज को भरने की प्रति घंटा दर = \(\frac{1}{x-10}\) भाग
यदि दोनों नल एक-साथ खुले हों, तो 1 घंटे में हौज का \(\left(\frac{1}{x}+\frac{1}{x-10}\right)\) भाग भर जाएगा। परन्तु दिया है कि 9\(\frac{3}{8}\) घंटे या \(\frac{75}{8}\) घंटे में पूरा हौज भर जाएगा


अत: छोटा नल हौज को 25 घंटे या 3\(\frac{3}{4}\) घंटे में भर सकता है।
जब दोनों नल हौज को भरते हैं, तब 9 घंटे से अधिक समय लगता है तब केवल एक नल उसे 3\(\frac{3}{4}\) घंटे में भर दे यह असम्भव एवं असंगत है।
अत: छोटा नल उसे 25 घंटे में भरता है, तब बड़ा नल उसे 25 – 10 = 15 घंटे में भर सकता है।
अत: कम व्यास वाला नल हौज को 25 घंटे में और अधिक व्यास वाला नल उसे 15 घंटे में भर सकता है।

Bihar Board Class 10 Math Solution In Hindi प्रश्न 10.
मैसूर और बैंगलौर के बीच के 132 km यात्रा करने में एक एक्सप्रेस रेलगाड़ी, सवारी गाड़ी से 1 घंटा समय कम लेती है (मध्य के स्टेशनों पर ठहरने का समय ध्यान में न लिया जाए)। यदि एक्सप्रेस रेलगाड़ी की औसत चाल, सवारी गाड़ी की औसत चाल से 11 km/h अधिक हो, तो दोनों रेलगाड़ियों की औसत चाल ज्ञात कीजिए।
हल
माना सवारी गाड़ी की औसत चाल x km/h है।
एक्सप्रेस रेलगाड़ी की औसत चाल सवारीगाड़ी की अपेक्षा 11 km/h अधिक है।
एक्सप्रेस रेलगाड़ी की औसत चाल = (x + 11) km/h.
तब, 132 km यात्रा में सवारी गाड़ी द्वारा लिया समय = \(\frac{\text { दूरी }}{\text { चाल }}=\frac{132}{x}\) घंटा
और उसी यात्रा में एक्सप्रेस रेलगाड़ी द्वारा लिया समय = \(\frac{132}{x+11}\) घंटा
प्रश्नानुसार, एक्सप्रेस रेलगाड़ी 1 घंटा कम समय लेती है।


रेलगाड़ी की चाल ऋणात्मक नहीं हो सकती जिससे x का मान -44 स्वीकार्य नहीं है।
∴ x = 33
अत: सवारी गाड़ी की चाल 33 km/h तथा एक्सप्रेस गाड़ी की चाल (33 + 11) = 44 km/h है।

Bihar Board Class 10 Math Book Solution In Hindi Pdf Download प्रश्न 11.
दो वर्गों के क्षेत्रफलों का योग 468 m2 है। यदि उनके परिमापों का अन्तर 24 m हो, तो दोनों वर्गों की भुजाएँ ज्ञात कीजिए।
हल
माना एक वर्ग की भुजा x m है।
तब, उस वर्ग का परिमाप = 4x m
दोनों वर्गों के परिमापों में 24m का अन्तर है।
दूसरे वर्ग का परिमाप = (4x + 24) m
तब, दूसरे वर्ग की भुजा = (\(\frac{4 x+24}{4}\)) m = \(\frac{4(x+6)}{4}\) m = (x + 6) m
पहले वर्ग का क्षेत्रफल = x² m²
तथा दूसरे वर्ग का क्षेत्रफल = (x + 6)² m² = (x² + 12x + 36) m²
प्रश्नानुसार, दोनों वर्गों के क्षेत्रफलों का योग = 468 m²
⇒ x² + (x² + 12x + 36) = 468
⇒ 2x² + 12x + 36 – 468 = 0
⇒ 2x² + 12x – 432 = 0
⇒ 2(x² + 6x – 216) = 0
⇒ x² + 6x – 216 = 0
⇒ x² + 2 × x × 3 + (3)² – 216 – (3)² = 0 [3² जोड़ने व घटाने पर]
⇒ (x + 3)² – 225 = 0
⇒ (x + 3)² – (15)² = 0 [पूर्ण वर्ग बनाने पर]
⇒ (x + 3 + 15) (x + 3 – 15) = 0 [∵ a² – b² = (a + b) (a – b)]
⇒ (x + 18) (x – 12) = 0
⇒ (x + 18) (x – 12) = 0
यदि x + 18 = 0 हो तो x = -18
या x – 12 = 0 हो, तो x = 12
वर्ग की भुजा x = -18 ऋणात्मक नहीं हो सकती; अत: x का मान -18 स्वीकार्य नहीं है।
छोटे वर्ग की भुजा = 12 m
तब, बड़े वर्ग की भुजा = x + 6 = 12 + 6 = 18 m
अत: वर्गों की भुजाएँ क्रमश: 12 m व 18 m हैं।

Get Updated Bihar Board Class 9th English Book Solutions in PDF Format and download them free of cost. Bihar Board Class 9 English Book Solutions Poem 5 Sound Questions and Answers provided are as per the latest exam pattern and syllabus. Access the topics of Panorama English Book Class 9 Solutions Poem 5 Sound through the direct links available depending on the need. Clear all your queries on the Class 9 English Subject by using the Bihar Board Solutions for Poem 5 Sound existing.

Panorama English Book Class 9 Solutions Poem 5 Sound

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Bihar Board Class 9 English Sound Text Book Questions and Answers

A. Work in small groups and discuss the questions given below:

Bihar Board Class 9 English Book Solution Question 1.
How do trees help us?
Answer:
Trees help us in many ways. They purify the air, they give us oxygen. They give shelter to wild animals and birds. They also give us fruits and fuel. They check the soil erosion and act as a balance to ecology.

Bihar Board 9th Class English Book Solution Question 2.
Should you cut trees?
Answer:
We should never cut trees.

English Poem For Class 9 Bihar Board Question 3.
Name the frees which you have in your school garden.
Answer:
The trees are mango, guava, peapal, neem and a big bunyan trees.

Bihar Board 9th Class English Book Question 4.
Have you planted trees in your locality? If not, would you do it?
Answer:
I live in a city. There is no place to plant a tree, so, I have not planted any tree. Yes, I like to do it.

B. Answer the following questions very briefly:

Bihar Board English Book Class 9 Pdf Download Question 1.
What happens to a trees in the woods?
Answer:
A tree is hacked in the woods.

Bihar Board Class 9 English Question 2.
Do the halves express their grief?
Answer:
Yes, the halves express their grief to each other.

Bihar Board 9th Class English Book Pdf Question 3.
Do they make a sound because they are in pain?
Answer:
Yes. they make a sound because they are in pain.

English Poems For Class 9 Bihar Board Question 4.
Where do the logs go?
Answer:
The logs are driven from each other and go to different places.

Class 9 English Book Bihar Board Question 5.
Who knows the predicament of trees?
Answer:
The wind knows the predicament of trees.

Sound Class 9 Solutions Bihar Board Question 6.
Can all men sense the agonies of trees.
Answer:
No, all men cannot sense the agonies of trees.

Bihar Board Class 9 English Book Pdf Question 7.
Why does the poet call the songs not song but just sounds?
Answer:
The poet does not call them songs but sounds because they are the cries of lamentation.

English Poems For Class 9 On Nature Bihar Board Question 8.
What will be the ultimate end of such sounds?
Answer:
Such sounds would be choked to death as they would be confined to script only.

C.1. Long Answer Type Questions

Question 1.
The poet has given a touching account of a tree which has been cut down. Don’t you think that this is a sad poem in memory of a felled tree?
Answer:
Yes, I agree to this point that through cutting of tree the poet presents a sad memory of a felled tree. The tree which has been cut mercilessly must have felt agonies. Its branches are driven away far off places. The whispering of the logs present its sad plight. So this poem is decidedly a sad poem.

Question 2.
Why has the poet indulged in reminiscences? Has anything ever compelled you to reminisce?
Answer:
The felled tree has touched the sensitivity of the poet so she goes on thinking. She has become emotional. She saw the sad mood of the tree insight in him. She has indulged herself with the sad tree. It is mind which makes me sad or happy. It is also true that trees eat, drink and breath. They grow like human beings. They also take rest .at night. They enjoy the pleasure and suffer the furies of nature. When they are hacked they must feel pain. So the poet thinks so.
Once I was going to my school hostel. I was waiting for the train. Suddenly a lady came to me and made friendship with me. She called me son. She took me to the canteen and both had a good break fast there. She talked me a lot. When the train came I boarded into the train I looked at her. She was too looking at me and made me see off. That day always reminisces me.

Question 3.
What does ‘the wind know and what the wind blowing a din’ suggest?
Answer:
The wind knows how the tree suffered when it was tossed. It knows that the tree bore all seasons rain. The wind is blowing and making din. This is to suggest that the wind crying over the pain of the tree.

Question 4.
“Many a man is blunt, so blunt,/ He doesn’t even sense the agonies caught/Even in simple words.” Explain the lines.
Answer:
The given lines are very suggestive. The poet says that majority of men have got their sensitivity blunted. So much so that they fail to perceive the agonies behind the simple words. In fact the poem conveys that it is because of their blunted sensitivity v that men fell trees.

Question 5.
Justify the title of the poem.
Answer:
Cutting of tree compel the halves to cry. The wind is also crying over the loss of the tree. The poet also laments such loss and pain. But all these make sound only. The effect is unknown. They fall flat on him as me resounds. Hence, the title ‘sound’ very subtly but aptly conveys the feeling of the poem.

Question 6.
The poem suggests that the writer of this poem is an environmentalist. She is deeply concerned with protecting and preserving the natural environment. Do you agree with it? Write your opinion.
Answer:
The way of thinking shows that the writer of the poem is an environmentalist and that she is deeply concerned with protecting and preserving the natural environment. She does not want that even a tree should be cut. I agree that she has tried to make us aware of the importance of trees and plant life.

Question 7.
‘A lot of people are insensitive to the agonies of trees’. Comment.
Answer:
The poet describes the cutting of the tree as if it were duty of insensitive people. The tree is the symbol of Nature and the environment and the poem can be read as a parable on what man has been doing to nature. Man is entitled to exploit the reasources of nature to make a living. But there is no justification Tor exploiting a tree to satisfy his greed. In this sense man does not foci the agonies of a tree.

Question 8.
What is the theme of the poem? Could you suggest another r title?
Answer:
The theme of the poem ‘Sound’ is the degradation nature has suffered at the hands of modem men who are blunt and insensitive to the agonies of trees. ‘Sound’ is of Nature’s love lover poem which lays bare before us man’s wanton destruction of the environment to satisfy his greed. Another title may be ‘Echo’.

Question 9.
Do trees have souls? Give your opinion.
Answer:
The great Indian scientist Jagdish Chandra Bose has already proved that plants are living things. They eat, drink and breathe. They grew like the human beings. They also take rest at night. Their green leaves produce all the starch. They enjoy the pleasures and suffer the furies of nature like the human beings. Hence wc can say that trees are alive and have souls.

Question 10.
Imagine yourself to be a branch which has just been hacked out. Describe your feelings to your parent tree.
Answer:
What happened to me that cannot be borne. It is a matter of regret that I have been hacked. Oh! the pain is unbearable I am fallen on the ground lifeless. I am helpless. I ani dying. My agony can’t he understood by blunt people who have hacked me. I was y.our inseparable part but these rude and blunt people have cut me apart.

C.2. Group Discussion

Discuss the following in groups or pairs:

Question 1.
Trees are our friends; we must not cut them.
Answer:
Trees play a key role in our life. The people play and refresh themselves in their cool shade. They give us fire wood and fruits. They give us Limber and building macrial. Paper is also tiude of wood. Trees supply oxygen to the alomosphere. They absorb Carbon dioxide. Their leaves produce Oxygen and release ¡milo the air. The green leaves also produce starch. It is an essential pari bi the food of men and animals. The leaves of trees breathe out a lot of water vapour. It helps to cool the air. So it is often cooler under a tree than inside a building. Forest attracts rain. Trees prevent floods. They protect the soil from being washed off. Trees are home of birds. They support to live wild animals as well. Thus it is clear that trees are our friends.

Question 2.
Save trees today for a better tomorrow.
Answer:
This should be always remembered save trees to day for a better tomorrow children of today will be the elders of tomorrow. Then they will need trees. Thinking this the Indian Government has started a festival. It is called “Vanmahotsava’ or the “Forest Festival”. This festival is held every year in order to make the people realise the value of trees’ in the present period and in future. Large number of trees are planted on this day. The people are apprised of their duty to look after the trees well and protect them from every harm.

Comprehension Based Questions with Answers

1. A tree in the woods is hacked
Its branch breaking away
what do the halves
whisper to each other?
Do they moan and groan
In the heart of their hearts?
And do these logs driven from each other Reminisce?

Questions:

1. Name the poem and its poet.
2. What happened to the tree in the woods?
3. What pain do the halves feel?
4. What do the logs do?

Answers:

1. The name of the poem is ‘Sound’ and its poet is Rajani Parulekar.
2. The tree was cut down in the woods.
3. The halves moan and groan in pain.
4. The logs reminisce their past life.

2. Do they remember how the wind tossed them?
How they got drenched.in the rain?
And the blossoms in the spring And the fall in autumn?
Oh! But the wind knows
The wind blowing with a din
In places forlorn Sings such songs.

Questions:

1. What does the tree remember?
2. Which season is mentioned in the poem?
3. Who knows everything that happens to the tree?
4. Find the word from the poem which mean ‘Sad state’.

Answers:

1. The tree remembers how the wind tossed it.
2. Autumn’ has been mentioned in the poem.
3. The wind knows every thing that happens to the tree.
4. Forlorn.

3. Those songs not all could praise
Many a man is blunt,
He doesn’t even sense
The agonies caught
Even in simple words!
What then of these songs
They are just sounds
Such sounds as would be choked to death
If confined in the strokes and coils of the script.

Questions:

1. Could all praise those songs?
2. What type of men are mentioned here?
3. What does the poet think about the songs?
4. What will be to such sound?
5. What is confined?

Answers:

1. No, those songs could not be praised by all.
2. Blunt people are mentioned here.
3. The poet thinks that the songs are not effective.
4. Such sound will be choked to death.
5. They will be confined to the strokes and coils or script only.

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