CBSE Class 10

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

NCERT Solutions for Class 10 English

The Hack Driver NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8

The Hack Driver NCERT Text Book Questions and Answers

The Hack Driver Read and Find out

Question 1.
Why is the lawyer sent to New Mullion? What does he first think about the place?
Answer:
The lawyer is sent to New Mullion to serve summons on a man called Oliver Lutkins. He did not ‘ like to go to a dirty place. He expected New Mullion to be a sweet and simple village unlike the dirty and shadowy corners of the city.

Question 2.
Who befriends him? Where does he take him?
Answer:
The delivery man befriended him. He took him to several places like Fritz’s where there was a chance to meet Lutkins. They also went to some other places in search of Lutkins.

Question 3.
What does he say about Lutkins?
Answer:
He says that Lutkins was a gambler and played the game of poker. He never paid his debts as he was very greedy and did not want to part with his money.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 4.
What more does Bill say about Lutkins and his family?
Answer:
Bill says that Lutkins’ mother is a terror. He described her as a lady who was nine feet tall and four feet thick and she was quick as a cat. She was also very short-tempered.

Question 5.
Does the narrator serve the summons that day?
Answer:
No, the narrator does not serve the summons that day as he was not able to meet Lutkins on whom he had to serve the summons.

Question 6.
Who is Lutkins?
Answer:
Lutkins is the hack driver who is befooling the lawyer as Bill Magnuson.

The Hack Driver Think About It

Question 1.
When the lawyer reached New Mullion, did ‘Bill’ know that he was looking for Lutkins? When do you think Bill came up with his plan for fooling the lawyer?
Answer:
When the lawyer reached New Mullion, ‘Bill’ did not know that he was looking for Lutkins. As the lawyer got down at New Mullion, he found it to be a very messy place. But the presence of the delivery man was the only pleasant sight there. He was a man of forty, red-faced, cheerful and very friendly. When the lawyer enquired about ‘Lutkins’, he immediately came up with his plan of fooling the lawyer because he (Bill) knew that he himself was Lutkins. And the best way to escape from the lawyer was to be with him for the whole time.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 2.
Lutkins openly takes the lawyer all over the village. How is it that no one lets out the secret?
[Hint: Notice that the hack driver asks the lawyer to keep out of sight behind him when they go into Fritz’s.] Can you find other such subtle ways in which Lutkins manipulates the tour?
Answer:
Lutkins openly takes the lawyer all over the village to find ‘Oliver Lutkins’ as he hides his real identity from the lawyer. He knew that the lawyer had come there to serve summons on him because he had not responded to many letters of the court.

No one lets out the secret for the whole day as Lutkins was an oversmart, clever and frivolous person. First of all he tells the lawyer to keep out of sight when they go to Fritz’s to find Lutkins so that nobody could notice him.

Secondly, Bill did not let the lawyer get down from the hack and ask about Lutkins from anyone. He (Bill) himself asked everyone about Lutkins. It seemed that everybody in the village knew about the mischief of Lutkins. Moreover, he tells the lawyer that Lutkins is very smart and never returns anybody’s money back and if he tries to collect in those fancy clothes, he’ll be suspicious and get away from him.

When he meets his mother as ‘Bill’ and introduces himself by saying, ‘Remember me I am Bill Magnuson, the carter and the hack man’, it gives a hint to his mother not to recognise him. In this way, the oversmartness of Bill and the innocence of the lawyer did not let the secret, that Bill was Lutkins, out.

Question 3.
Why do you think Lutkins’ neighbours were anxious to meet the lawyer?
Answer:
The lawyer spent nearly his whole day with Bill at New Mullion to find Oliver Lutkins as he had to serve summons on him in a case as a witness. Lutkins, in the guise of Bill, was with him the whole day. He took the lawyer to all the places wherever Lutkins hung out. At Fritz’s, Gustafs barber shop, Gray’s barber shop and even his mother, almost everybody in the village, had seen the lawyer and laughed at him for his simplicity and innocence and how he was being befooled by Lutkins himself. Only the neighbours of Lutkins had not seen the lawyer so they were anxious to meet him.

Next day when the lawyer is sent again to serve the summons on Lutkins along with a man who had seen Lutkins, the lawyer meets Lutkin’s mother at the station only, she laughs at him and tells him to go to their neighbours to have coffee as they were very anxious to meet him.

Question 4.
After his first day’s experience with the hack driver, the lawyer thinks of returning to New Mullion to practise law. Do you think he would
have reconsidered this idea after his second visit?
Answer:
On the first day, the hack driver spends almost the whole day with the lawyer to find Lutkins as the lawyer had to serve summons on him. The lawyer feels highly obliged and thankful to the hack driver for his kind consideration and concern for even strangers. The hack driver arranges lunch for him, accompanies him everywhere.

The lawyer was too touched and obliged by the behaviour of Bill. He became fond of his simplicity – and humanity. He imagined an honest and happy life beyond the strict limits of universities and law firms. He decided to come to New Mullion and start a new beautiful life.

He must have reconsidered his idea of settling down at New Mullion after realising the fact of being deceived by Lutkins under his nose. He could not foresee the malignant and mischievious intentions of Bill under the cover of simplicity and innocence.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 5.
Do you think the lawyer was gullible? How could he have avoided being taken for a ride?
Answer:
‘Gullible’ means ‘someone easily deceived’. We can say that the lawyer was gullible. ‘Lutkins’ under the facelet of Bill befooled him, deceived him the whole day. He was with him but he never let disclose his real identity to the lawyer.

But the lawyer could have avoided it. He could refuse his offer of ride across the village. He could have taken another hack or cart. Moreover he could have got down from the cart himself and asked about Lutkins from somebody himself. Definitely he would have found Lutkins but he was totally dependant on the hack driver who befooled him.

The Hack Driver Extra Questions and Answers

The Hack Driver Short Answer Questions

Question 1.
Lutkins was really ‘a hard fellow to catch’. How?
Answer:
Lutkins was really a hard fellow to catch. He was a crook. He impressed the narrator by his open friendly and affectionate nature. He disguised himself many times. He had a good relationship with all in his village. So, it was difficult to catch him.

Question 2.
How does Lutkins befool the lawyer?
Answer:
Oliver Lutkins was the hack driver. He impressed the narrator by his simplicity and pleasant appearance. He introduced himself as Bill. The hack driver made a complete fool of the narrator by taking him to all the places where he could find Lutkins but every time missed him by a fraction of minutes. He had a good understanding with his town folks who helped him in befooling the lawyer.

Question 3.
How did the hack driver sketch the character of Lutkins?
Answer:
The hack driver called Lutkins “a good for nothing fellow”. He told that Lutkins did not stick to any single place. The hack driver tried to portray Lutkins as a shrewd and shoddy person. He told the narrator that Lutkins was fond of playing poker. He borrowed money from many people. He was a perfect duper. He was known for taking people for a ride.

Question 4.
What attitude did the lawyer have for country life? How did his experience at New Mullion change it?
Answer:
The lawyer hated city life as he found city people cunning and at times very aggressive. He assumed country life to be sweet and simple but his visit to New Mullion completely changed his attitude. He was disappointed with sights at the countryside and above all, he was duped by Lutkins who changed his assumption that country life was simpler than the city life.

Question 5.
What does the narrator describe as ‘a pretty disrespectful treatment’?
Answer:
The hack driver took the narrator to the farmyard of his mother. He introduced the young lawyer to Lutkins’ mother as a young man representing the court in the city. They followed her to the kitchen. But they ran for cover as she brought out a hot iron rod from the kitchen to shove them away. The lawyer called it ‘a pretty disrespectful treatment’.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 6.
What did the hack driver tell the narrator about Lutkins’ mother?
Answer:
The hack driver told the narrator that Lutkins’ mother was a real terror. She was about nine feet tall and four feet thick and quick as a cat. She could also put people down by talking. It was proved when on meeting the narrator, she did not show respect for him. She chased him with a hot iron ‘ rod.

Question 7.
Describe the young lawyer’s first encounter with the hack driver.
Answer:
When the young lawyer reached New Mullion to serve summons on Oliver Lutkins, he came across a man of forty who was red-faced and cheerful. He introduced himself as Bill, the hack driver. The narrator trusted him and told him about his purpose to visit the place.

Question 8.
Who was the hack driver? What really hurt the narrator’s feelings?
Answer:
The hack driver himself was Oliver Lutkins. He was not Bill Magnuson as he had told the narrator. He had befooled the narrator. The narrator’s feelings were hurt when Lutkins and his mother both laughed at him as though he were a boy of seven.

Question 9.
Which were the places where the narrator and hack driver went to search for Lutkins? How was he missed everywhere?
Answer:
The hack driver took the narrator to many places in New Mullion to locate Lutkins. Some of them were Fritz’s place, Gustaff’s barber shop, Gray’s barber shop, poolroom and his mother’s farmyard. He was missed everywhere by five minutes or so.

Question 10.
How was the hack driver recognised?
Answer:
The lawyer was ordered to go back to New Mullion to fetch Lutkins with a man who had worked with Lutkins. He saw Bill the hack driver with Lutkin’s mother talking and laughing at the platform. His escort told him that Bill was Lutkins himself.

Question 11.
How did the people at the law firm receive the narrator?
Answer:
The Chief of the law firm was very angry with the narrator. The narrator was sent back to New Mullion to trace Oliver Lutkins with another man, who had worked with Lutkins earlier.

Question 12.
Why did the narrator, a young lawyer, not like his job in a law firm?
Answer:
The narrator, a young lawyer, did not like his job in a law firm. He joined the law firm to practise as a lawyer but he was given work of a delivery boy who had to serve summons on people. He had to-go to dirty and shadowy corners of the city. Sometimes, he even got beaten up.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 13.
How did Lutkins’ mother treat the lawyer?
Answer:
The hack driver ‘Bill’ introduced the narrator as a representative of the city court, and that he had a legal right to search all properties of Oliver Lutkins. The mother went inside the kitchen and got an iron rod from the old fashioned store and marched on them shouting and scaring them away.

Question 14.
Why was the narrator disappointed when he reached New Mullion?
Answer:
The narrator was disappointed when he reached New Mullion because he did not like the muddy streets and unpainted looks of shops and houses. It was a small town that held no attraction.

Question 15.
What job did the narrator get after graduation? Did he like his work?
Answer:
The narrator got the job of a junior assistant clerk in a law firm. He was assigned the job of serving summons. He did not like his work as he had to go to muddy and dirty streets and sometimes he was given a beating too. The work was somewhat mean and he wanted to change it.

Question 16.
Why was he happy to go to New Mullion? Why did he go there?
Answer:
He was happy to go to New Mullion, because it was forty miles away and he didn’t have to go to dirty and muddy streets and corners of the city to trace his victims. He had to serve summons on a man called Oliver Lutkins.

Question 17.
What sight did the lawyer find at the station “agreeable”?
Answer:
The delivery man at the station was the only agreeable sight at the station. He left a deep impression on the narrator’s mind. He was a very amiable person, the narrator really admired him. His earnest demeanour, simplicity and humour refreshed the young lawyer.

Question 18.
With what impression did the lawyer come back to the city?
Answer:
The narrator returned to the city fully satisfied and feeling great. He was happily impressed by the town New Mullion and its simple, slow-speaking, wise neighbours. He was so impressed that he wanted to settle down there.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

Question 19.
Why do you think were the neighbours anxious to meet the lawyer?
Answer:
The narrator had accompanied the hack driver ‘Bill’, to find Lutkins, to many neighbourhood houses. One neighbour was left, where the narrator could not go. Lutkins and his mother described the young lawyer as an innocent boy who had been duped by Lutkins. This neighbour was also keen to look at the young lawyer who was duped by Lutkins.

Question 20.
Where did the narrator have his lunch at New Mullion? What was special about the lunch?
Answer:
The narrator was hungry. He wanted to offer lunch to the hack driver too. The hack driver suggested that they would have lunch prepared by his wife on Wade’s Hill. And he charged half a dollar from the narrator. The narrator enjoyed the peaceful scenic beauty of meadows and woods while he had his lunch.

The Hack Driver Long Answer Questions

Question 1.
In life, people who easily trust others are sometimes made to look foolish. One should not be too trusting. Describe how Oliver Lutkins made a fool of the young lawyer. [2018]
Answer:
In the story Oliver Lutkins made a fool of the young lawyer. When the lawyer reached New Mullion, Lutkins came up with his plan to fool the lawyer when the lawyer told him that he was looking for Oliver Lutkins, Lutkins openly takes the lawyer all over the village. When the lawyer said he needed to catch the afternoon train back he realized that he would need to keep him occupied till he left.

He also had to ensure that the lawyer did not speak or question anyone else about him or he would be caught. He therefore told the lawyer that Lutkins never paid anybody a cent and so if he tried to collect money from him in his fancy clothes he would be suspicious and get away. Instead he would go into Fritz’s and ask for Lutkins, and the lawyer was kept out of sight behind him.

NCERT Solutions for Class 10 English Footprints Without Feet Chapter 8 The Hack Driver

In this way Lutkins was always the first to enter a place and prevented the lawyer from directly meeting and speaking to the people. He would then most probably take the people into his confidence so that no one let out the secret of his true identity. At last Bill cornered a friend of Lutkins and made him

admit that he had gone out to his mother’s farm. He then convinced the lawyer that Lutkins’ mother was a terror and so it was best that he dealt with her himself. He introduced himself and the lawyer to her and told her the reason for their visit. This introduction was enough for her to get an idea about what was happening and she too put on an act and did not let out the secret but managed to make a fool of the young lawyer.

Question 2.
Lutkins appeared humble but he was not. Appearances can be deceptive.
Do you think in real life we come across such people frequently? Does it indicate lack of integrity in human?
Answer:
Lutkins appeared humble but he was not. When the lawyer came to the city, he was happy to meet the hack driver. In fact, the hack driver himself was Oliver Lutkins. He impressed the lawyer with his simplicity and nature. He befooled the lawyer by taking him in search of Lutkins. He pretended to be honest and helpful but he just befooled the lawyer.

Yes, in real life we come across such people. Their appearance is deceptive. They present themselves as caring, friendly and cooperative. Initially, they show their care and concern but when they get an opportunity, they show their true colours and dupe us. There is no compassion in them. Yes, it indicates lack of integrity in human values. There is a lack of commitment, honesty and sensitiveness.

Question 3.
Lutkins played with the emotions of the young lawyer. By the end of the story, he was hurt on knowing the truth of the hack driver. Would you call Lutkins an insensitive fellow? Should we hurt the feeling of somone like this?
Answer:
Lutkins played with the emotions of the young lawyer. He impressed him by his deceptive nature. He pretended to help him. But he was making a fool out of him. He roamed around the city with the lawyer in search of Lutkins. He did not reveal that he himself was Lutkins. Wherever he went, he made the lawyer a laughing stock for others.

Everyone was amused to see how Lutkins was making a fool of the lawyer. By the end of the story when the lawyer revisited the place, he was hurt to know how the hack driver had befooled him. No doubt the hack driver was an insensitive human being. He did not care for his emotions. No, we should not hurt someone’s emotions for the sake of self¬entertainment

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NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium)

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium)

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium)

These Solutions are part of NCERT Solutions for Class 10 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 10 Maths Chapter 14 Statistics.

Chapter 14. सांख्यिकी

प्रश्नावली 14.1

Ex 14.1 Class 10 गणित Q1. विधार्थियों के एक समूह द्वारा अपने पर्यावरण संचेतना अभियान के अन्तर्गत एक सर्वेक्षण किया गया, जिसमें उन्होंने एक मोहल्ले के 20 घरों में लगे हुए पौधों से संबंधित निम्नलिखित आँकड़े एकत्रित किए | प्रति घर पौधों की संख्या ज्ञात कीजिए |

NCERT Solutions For Class 10 Maths Statistics 14.1 1

माध्य ज्ञात करने के लिए आपने किस विधि का प्रयोग किया और क्यों ? 

NCERT Solutions For Class 10 Maths Statistics PDF 14.1 2

Ex 14.1 Class 10 गणित Q2. किसी फैक्ट्री के 50 श्रमिकों मज़दूरी के निम्नलिखित बंटन पर विचार कीजिए :

NCERT Maths Solutions For Class 10 Statistics 14.1 3

एक उपयुक्त विधि का प्रयोग करते हुए, इस फैक्ट्री के श्रमिकों की माध्य दैनिक मज़दूरी ज्ञात कीजिए |

हल : प्रत्येक अंतराल के लिए वर्ग-चिन्ह को इस सूत्र से ज्ञात करेंगे

Maths NCERT Solutions For Class 10 Statistics 14.1 4
NCERT Solutions For Maths Class 10 Statistics 14.1 5

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = – 480 + – 280 + 0 + 120 + 400 = – 760 + 520 = – 240

Σfi = 50 और a = 150

Solutions For NCERT Maths Class 10 Hindi Medium Statistics 14.1 6

Ex 14.1 Class 10 गणित Q3. निम्नलिखित बंटन एक मोहल्ले के  बच्चों के दैनिक जेबखर्च दर्शाता है | माध्य जेबखर्च 18 रू है | लुप्त बारंबारता f ज्ञात कीजिए :

NCERT Solutions of Maths For Class 10 Hindi Medium Statistics 14.1 7

हल : 

Maths Solutions For Class 10 NCERT Hindi Medium Statistics 14.1 8

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = 2f – 40,  Σfi = 44 + f और a = 18,

Solutions For Maths NCERT Class 10 Hindi Medium Statistics 14.1 9

Ex 14.1 Class 10 गणित Q4. किसी अस्पताल में, एक डॉक्टर द्वारा 30 महिलाओं की जाँच की गई और उनके ह्रदय स्पंदन (beat) की प्रति मिनट संख्या नोट करके नीचे दर्शाए अनुसार संक्षिप्त रूप में लिखी गई | एक उपयुक्त विधि चुनते हुए, इन महिलाओं के ह्रदय स्पंदन की प्रति मिनट माध्य संख्या ज्ञात कीजिए :

NCERT Books Solutions For Class 10 Maths Hindi Medium Statistics 14.1 10

हल : 

NCERT Maths Book Solutions For Class 10 Hindi Medium Statistics 14.1 11

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = 12,  Σfi = 30 और a = 75.5,

CBSE NCERT Maths Solutions For Class 10 Hindi Medium Statistics 14.1 12

अत: महिलाओं के ह्रदय स्पंदन की प्रति मिनट माध्य संख्या = 75.9 है |

Ex 14.1 Class 10 गणित Q5. किसी फुटकर बाज़ार में, फल विक्रेता पेटियों में रखे आम बेच रहें थे | इन पेटियों में आमों की संख्याएँ भिन्न – भिन्न थी | पेटियों की संख्या के अनुसार, आमों का बंटन निम्नलिखित था : 

CBSE NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 13
एक पेटी में रखे आमों की माध्य संख्या ज्ञात कीजिए | आपने माध्य ज्ञात करने की किस विधि का प्रयोग किया है ?

हल: 

दी गयी श्रृखला समावेशी (inclusive) है जहाँ वर्ग-अंतरालों में 1 का अंतर है | अत: दी गयी श्रृंखला को अपवर्जी (exclusive) श्रृंखला में बदलेंगे |

53 – 52 = 1

NCERT Maths Textbook For Class 10 Solutions Hindi Medium Statistics 14.1 14

= 57 + 0.1875

= 57.1875 या 57.19

आमों की माध्य संख्या = 57.19

Ex 14.1 Class 10 गणित Q6. निम्नलिखित सारणी किसी मोहल्ले के 25 परिवारों में भोजन पर हुए दैनिक व्यय को दर्शाती है:

NCERT Books For Class 10 Maths Solutions Hindi Medium Statistics 14.1 15

एक उपयुक्त विधि द्वारा भोजन पर हुआ माध्य व्यय ज्ञात कीजिए |

हल : 

NCERT Maths Textbook Solutions For Class 10 Hindi Medium Statistics 14.1 16

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 7, Σfi = 25, h = 50 , a = 225

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 17

Ex 14.1 Class 10 गणित Q7. वायु में सल्फर डाई – ऑक्साइड (SO ) की सान्द्रता (भाग प्रति मिलियन में ) को ज्ञात करने के लिए, एक नगर के मोहल्लों से आँकड़े एकत्रित किए गये, जिन्हें नीचे प्रस्तुत किया गया है :

NCERT Solutions For Class 10 Maths PDF Free Hindi Medium Statistics 14.1 18

वायु में SO2  की सांद्रता का माध्य ज्ञात कीजिए |

हल :

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 19

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 31, Σfi = 30, h = 0.04 , a = 0.14

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Textbook Solutions For Class 10 Maths Hindi Medium Statistics 14.1 20
वायु में सल्फर डाई-ऑक्साइड (SO की सान्द्रता का माध्य = 0.099

Ex 14.1 Class 10 गणित Q8. किसी कक्षा अध्यापिका ने पुरे सत्र के लिए अपनी कक्षा के 40 विधार्थियों कि अनुपस्थिति निम्नलिखित रूप में रिकॉर्ड (record) की | एक विधार्थी जितने दिन अनुपस्थित रहा उनका माध्य ज्ञात कीजिए :

NCERT Books Solutions For Class 10 Maths PDF Hindi Medium Statistics 14.1 21

हल :

Download NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 22

विद्यार्थी की अनुपस्थित का माध्य = 12.48 दिन

Ex 14.1 Class 10 गणित Q9. निम्नलिखित सारणी 35 नगरों कि साक्षरता दर (प्रतिशत में ) दर्शाती है | माध्य साक्षरता दर ज्ञात कीजिए :

NCERT Solutions For Class 10 Maths Statistics 14.1 23

 हल : 

NCERT Solutions For Class 10 Maths Statistics PDF 14.1 24

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 2, Σfi = 35, h = 10 , a = 70

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Maths Solutions For Class 10 Statistics 14.1 25

अत: माध्य साक्षरता दर = 69.43 %

प्रश्नावली 14.2

Ex 14. Class 10 गणित Q1. विधार्थियों के एक समूह द्वारा अपने पर्यावरण संचेतना अभियान के अन्तर्गत एक सर्वेक्षण किया गया, जिसमें उन्होंने एक मोहल्ले के 20 घरों में लगे हुए पौधों से संबंधित निम्नलिखित आँकड़े एकत्रित किए | प्रति घर पौधों की संख्या ज्ञात कीजिए |

NCERT Solutions For Maths Class 10 Statistics 14.1 26

माध्य ज्ञात करने के लिए आपने किस विधि का प्रयोग किया और क्यों ? 

Solutions For NCERT Maths Class 10 Hindi Medium Statistics 14.1 27

Ex 14.2 Class 10 गणित Q2. किसी फैक्ट्री के 50 श्रमिकों मज़दूरी के निम्नलिखित बंटन पर विचार कीजिए :

NCERT Solutions of Maths For Class 10 Hindi Medium Statistics 14.1 28

एक उपयुक्त विधि का प्रयोग करते हुए, इस फैक्ट्री के श्रमिकों की माध्य दैनिक मज़दूरी ज्ञात कीजिए |

हल : प्रत्येक अंतराल के लिए वर्ग-चिन्ह को इस सूत्र से ज्ञात करेंगे

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 29
Maths Solutions For Class 10 NCERT Hindi Medium Statistics 14.1 30

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = – 480 + – 280 + 0 + 120 + 400 = – 760 + 520 = – 240

Σfi = 50 और a = 150

Solutions For Maths NCERT Class 10 Hindi Medium Statistics 14.1 31

Ex 14.2 Class 10 गणित Q3. निम्नलिखित बंटन एक मोहल्ले के  बच्चों के दैनिक जेबखर्च दर्शाता है | माध्य जेबखर्च 18 रू है | लुप्त बारंबारता f ज्ञात कीजिए :

NCERT Books Solutions For Class 10 Maths Hindi Medium Statistics 14.1 32

हल : 

NCERT Maths Book Solutions For Class 10 Hindi Medium Statistics 14.1 33

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = 2f – 40,  Σfi = 44 + f और a = 18,

CBSE NCERT Maths Solutions For Class 10 Hindi Medium Statistics 14.1 34

Ex 14.2 Class 10 गणित Q4. किसी अस्पताल में, एक डॉक्टर द्वारा 30 महिलाओं की जाँच की गई और उनके ह्रदय स्पंदन (beat) की प्रति मिनट संख्या नोट करके नीचे दर्शाए अनुसार संक्षिप्त रूप में लिखी गई | एक उपयुक्त विधि चुनते हुए, इन महिलाओं के ह्रदय स्पंदन की प्रति मिनट माध्य संख्या ज्ञात कीजिए :

CBSE NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 35

हल : 

NCERT Maths Textbook For Class 10 Solutions Hindi Medium Statistics 14.1 36

कल्पित माध्य विधि (Assume mean Method) से

Σfidi = 12,  Σfi = 30 और a = 75.5,

NCERT Books For Class 10 Maths Solutions Hindi Medium Statistics 14.1 37

अत: महिलाओं के ह्रदय स्पंदन की प्रति मिनट माध्य संख्या = 75.9 है |

Ex 14.2 Class 10 गणित Q5. किसी फुटकर बाज़ार में, फल विक्रेता पेटियों में रखे आम बेच रहें थे | इन पेटियों में आमों की संख्याएँ भिन्न – भिन्न थी | पेटियों की संख्या के अनुसार, आमों का बंटन निम्नलिखित था : 

NCERT Maths Textbook Solutions For Class 10 Hindi Medium Statistics 14.1 38

एक पेटी में रखे आमों की माध्य संख्या ज्ञात कीजिए | आपने माध्य ज्ञात करने की किस विधि का प्रयोग किया है ?

हल: 

दी गयी श्रृखला समावेशी (inclusive) है जहाँ वर्ग-अंतरालों में 1 का अंतर है | अत: दी गयी श्रृंखला को अपवर्जी (exclusive) श्रृंखला में बदलेंगे |

53 – 52 = 1

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 39

= 57 + 0.1875

= 57.1875 या 57.19

आमों की माध्य संख्या = 57.19

Ex 14.2 Class 10 गणित Q6. निम्नलिखित सारणी किसी मोहल्ले के 25 परिवारों में भोजन पर हुए दैनिक व्यय को दर्शाती है:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 40

एक उपयुक्त विधि द्वारा भोजन पर हुआ माध्य व्यय ज्ञात कीजिए |

हल : 

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 41

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 7, Σfi = 25, h = 50 , a = 225

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 42

Ex 14.2 Class 10 गणित Q7. वायु में सल्फर डाई – ऑक्साइड (SO ) की सान्द्रता (भाग प्रति मिलियन में ) को ज्ञात करने के लिए, एक नगर के मोहल्लों से आँकड़े एकत्रित किए गये, जिन्हें नीचे प्रस्तुत किया गया है :

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 43

वायु में SO2  की सांद्रता का माध्य ज्ञात कीजिए |

हल :

NCERT Textbook Solutions For Class 10 Maths Hindi Medium Statistics 14.1 44

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 31, Σfi = 30, h = 0.04 , a = 0.14

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Books Solutions For Class 10 Maths PDF Hindi Medium Statistics 14.1 45

वायु में सल्फर डाई-ऑक्साइड (SO की सान्द्रता का माध्य = 0.099

Ex 14.2 Class 10 गणित Q8. किसी कक्षा अध्यापिका ने पुरे सत्र के लिए अपनी कक्षा के 40 विधार्थियों कि अनुपस्थिति निम्नलिखित रूप में रिकॉर्ड (record) की | एक विधार्थी जितने दिन अनुपस्थित रहा उनका माध्य ज्ञात कीजिए :

Download NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 46

हल :

Solutions For NCERT Maths Class 10 Hindi Medium Statistics 14.1 47

विद्यार्थी की अनुपस्थित का माध्य = 12.48 दिन

Ex 14.2 Class 10 गणित Q9. निम्नलिखित सारणी 35 नगरों कि साक्षरता दर (प्रतिशत में ) दर्शाती है | माध्य साक्षरता दर ज्ञात कीजिए :

NCERT Solutions of Maths For Class 10 Hindi Medium Statistics 14.1 48

 हल : 

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 49

पग-विचलन विधि (Step-deviation Method) से माध्य :

Σfiui = – 2, Σfi = 35, h = 10 , a = 70

पग-विचलन विधि के सूत्र में उपरोक्त मानों (values) को रखने पर

NCERT Books Solutions For Class 10 Maths Hindi Medium Statistics 14.1 50

अत: माध्य साक्षरता दर = 69.43 %

प्रश्नावली 14.3 

Ex 14. Class 10 गणित Q1. निम्नलिखित बारंबारता बंटन किसी मोहल्ले के 68 उपभोक्ताओं की बिजली कि मासिक खपत दर्शाता है | इन आँकड़ों के Ex माध्यक, माध्य और बहुलक ज्ञात कीजिए | इनकी तुलना कीजिए |

NCERT Maths Book Solutions For Class 10 Hindi Medium Statistics 14.1 51
हल :

CBSE NCERT Maths Solutions For Class 10 Hindi Medium Statistics 14.1 52

माध्यक (Median) के लिए : 

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 53

34 संचयी बारंबारता के 42 में शामिल है |

इसलिए, माध्यक वर्ग 125 – 145 है |

अत: l = 125, f = 20, cf = 22 (माध्यक वर्ग से ठीक ऊपर वाला संचयी बारंबारता) और

h = 20, 

CBSE NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 54

बहुलक के लिए :

सारणी से हमें ज्ञात होता है कि वर्ग 125 – 145 की बारंबारता सबसे अधिक है इसलिए बहुलक वर्ग 125 – 145 है

अत: l = 125, f0 = 13, f1 = 20, f2 = 14 और h = 20

NCERT Maths Textbook For Class 10 Solutions Hindi Medium Statistics 14.1 55

माध्यक = 137, माध्य = 137.058 और बहुलक = 135.76 

Ex 14.3 Class 10 गणित Q2. यदि नीचे दिए हुए बंटन का माध्यक 28.5 हो तो x और y के मान ज्ञात कीजिए :

NCERT Books For Class 10 Maths Solutions Hindi Medium Statistics 14.1 56

हल : 

NCERT Maths Textbook Solutions For Class 10 Hindi Medium Statistics 14.1 57

दिया है, माध्यक = 28.5,

अत: 28.5 वर्ग-अन्तराल 20 – 30 में शामिल है |

इसलिए, l = 20, f = 20, h = 10 और cf = 5 + x

N = 60,

NCERT Solutions For Class 10 Maths PDF Free Hindi Medium Statistics 14.1 58

अब,  45 + x + y = 60

अथवा x + y = 60 – 45

x + y = 15

8 + y = 15   समी० (1) से

y = 15 – 8

y = 7

x = 8, और y = 7 

Ex 14.3 Class 10 गणित Q3. एक जीवन बीमा एजेंट 100 पॉलिसी धारकों कि आयु के बंटन के निम्नलिखित आँकड़े ज्ञात करता है | माध्यक आयु परिकलित कीजिए, यदि पॉलिसी केवल उन्हीं व्यक्तियों को दी जाती है,  जिनकी आयु 18 वर्ष या उससे अधिक हो, 60 वर्ष से कम हो |

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 59

हल :

Ex 14.3 Class 10 गणित Q4. एक पौधे कि 40 पत्तियों कि लंबाइयाँ निकटतम मिलीमीटरों में मापी जाती है तथा प्राप्त आँकड़ों को निम्नलिखित सारणी के रूप में निरुपित किया जाता है :

NCERT Textbook Solutions For Class 10 Maths Hindi Medium Statistics 14.1 60

पत्तियों की माध्यक लंबाई ज्ञात कीजिए |

संकेत : माध्यक ज्ञात करने के लिए, आँकड़ों को सतत वर्ग अंतरालों में बदलना पड़ेगा, क्योंकि सूत्र में वर्ग अंतरालों को सतत मन गया है | तब ये वर्ग 117.5 – 126.5 – 135.5,…,171.5 – 180.5 में बदल जाते हैं |  

हल :

Ex 14.3 Class 10 गणित Q5. निम्नलिखित सारणी 400 नियाँन लैंपों के जीवनकालों (life time) को प्रदर्शित करती है :

NCERT Books Solutions For Class 10 Maths PDF Hindi Medium Statistics 14.1 61

  एक लैंप का माध्यक जीवन काल ज्ञात कीजिए |

हल :

Ex 14.3 Class 10 गणित Q6. एक स्थानीय टेलीफ़ोन निर्देशिका से 100 कुलनाम (surnames) लिए और उनमें प्रयुक्त अंग्रेज़ी वर्णमाला के अक्षरों की संख्या का निम्नलिखित बारंबारता बंटन प्राप्त हुआ :

Download NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 62

हल :

कुलनामों में माध्यक अक्षरों कि संख्या ज्ञात कीजिए |  कुलनामों में माध्य अक्षरों कि संख्या ज्ञात कीजिए | साथ ही, कुलनामों का बहुलक ज्ञात कीजिए |

Ex 14.3 Class 10 गणित Q7. नीचे दिया हुआ बंटन एक कक्षा के 30 विधार्थियों के भार दर्शा रहा है | विधार्थियों का माध्यक भार ज्ञात कीजिए |

NCERT Solutions For Class 10 Maths Statistics 14.1 63

हल :

प्रश्नावली 14.4

Ex 14.4 Class 10 गणित Q1. निम्नलिखित बंटन किसी फैक्ट्री के 50 श्रमिकों कि दैनिक आय दर्शाता है :

NCERT Solutions For Class 10 Maths Statistics PDF 14.1 64

‘उपरोक्त बंटन को एक कम प्रकार ‘ के संचयी बारंबारता बंटन में बदलिए और उसका तोरण खींचिए |

हल : ‘से कम प्रकार’ का संचयी बारंबारता बंटन सारणी :

NCERT Maths Solutions For Class 10 Statistics 14.1 65

‘से कम प्रकार’ के तोरण के लिए क्रमित युग्म (order pairs) :

(120, 12), (140, 26), (160, 34), (180, 40) और (200, 50)

Maths NCERT Solutions For Class 10 Statistics 14.1 66

Ex 14.4 Class 10 गणित Q2. किसी कक्षा के 35 विधार्थियों कि मेडिकल जाँच के समय, उनके भार निम्नलिखित रूप में रिकॉर्ड किए गए :

NCERT Solutions For Maths Class 10 Statistics 14.1 67

उपरोक्त आँकड़ों के ‘लिए कम प्रकार का तोरण’ खींचिए | इसके बाद माध्यक भार ज्ञात कीजिए |

हल : ‘से कम प्रकार के‘ तोरण के लिए संचयी बारंबारता सारणी

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 68

से कम प्रकार’ के तोरण के लिए के लिए क्रमित युग्म (Order pairs) :

(38, 0), (40, 3), (42, 5), (44, 9), (46, 14), (48, 28), (50, 32), (52, 35)

NCERT Solutions of Maths For Class 10 Hindi Medium Statistics 14.1 69

Ex 14.4 Class 10 गणित Q3. निम्नलिखित सारणी किसी गाँव के 100 फार्मों में हुआ प्रति हेक्टेयर (ha) गेंहूँ का उत्पादन दर्शाते हैं :

Maths Solutions For Class 10 NCERT Hindi Medium Statistics 14.1 70

इस बंटन को ‘अधिक के प्रकार के ‘ बंटन में बदलिए और फिर उसका तोरण खींचिए |

हल : ‘से अधिक प्रकार के‘ तोरण के लिए संचयी बारंबारता सारणी:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) 14.1 71

‘से अधिक प्रकार’ के तोरण के लिए के लिए क्रमित युग्म (Order pairs) :

(50, 100), (55, 98), (60, 90), (65, 78), (70, 54), (75, 16)

Solutions For Maths NCERT Class 10 Hindi Medium Statistics 14.1 72

प्रश्नावली 14.5

अतिरिक्त एवं महत्वपूर्ण प्रश्न : 

Ex 14.5 Class 10 गणित Q1. निम्न आँकडें आरोही क्रम में लिखे गए हैं। यदि आँकडों का माध्यक 14.5 है तो x का मान ज्ञात कीजिए।

11, 12, 13, 7x, 7x + 1, 16, 16, 18, 20

Ex 14.5 Class 10 गणित Q2. 5 संख्याओं का माध्य 18 है | यदि एक संख्या निकल दी जाए, तो माध्य 16 हो जाता है | तो निकाली गयी संख्या ज्ञात कीजिए | 

Ex 14.5 Class 10 गणित Q3. 20 संख्याओं का माध्य 17 है, यदि प्रत्येक संख्या में 3 जोड़ा जाए तो नया माध्य ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q4. ‘से कम प्रकार’ तथा ‘से अधिक’ के तोरण के प्रतिच्छेदन बिन्दु का भुज किस केन्द्रीय प्रवृत्ति की माप को दर्शाता है ?

Ex 14.5 Class 10 गणित Q5. यदि 2,3,5,4,2,6,3,5,5,2 और x का बहुलक 2 है, तो ‘x’ का मान ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q6. 2,3,6,0,1,4,8,2,5 की माध्यिका ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q7. x, x + 1, x + 2, x + 3, x + 4, x + 5 और x + 6 का माध्य ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q8. प्रथम 10 विषम संख्याओं का माध्य ज्ञात कीजिए | 

Ex 14.5 Class 10 गणित Q9. यदि आरोही क्रम में लिखे प्रेक्षणों 24, 25, 26, x + 3, 30, 31, 34 की माध्यिका 27.5 है, तो ‘x’ का मान ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q10. 40 प्रेक्षणों का माध्य 160 था | जाँच करने पर ज्ञात हुआ कि 165 गलती से 125 लिखा गया था, सही माध्य ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q11. एक मैचों की श्रृंखला में एक बास्केट बॉल टीम द्वारा हासिल किए गए मैचों में अंक इस प्रकार था :

  17, 2, 7, 27, 25, 5, 14, 18 , 10, 24, 10, 8, 7, 10
  तो आंकड़ों का माध्य, माध्यक और बहुलक ज्ञात कीजिए |

Ex 14.5 Class 10 गणित Q12. 40, 42, 80, 69, 56, 47 का परिसर क्या है ?

Ex 14.5 Class 10 गणित Q13. यदि 25, 30, 32, x, 43 का समान्तर माध्य 34 है तो x का मान ज्ञात कीजिए | 

Ex 14.5 Class 10 गणित Q14. निम्नलिखित आंकड़ों का बहुलक ज्ञात कीजिए |

     5, 7, 6, 5, 9, 8, 6, 7, 11, 10, 5, 7, 6, 8, 6, 9, 10.

Ex 14.5 Class 10 गणित Q15. 34, 32, x, x-1, 19, 15, 11 का माध्यक ज्ञात कीजिए जहाँ x आँकड़ें 10, 20, 30, 40, 50 का माध्य है |

Ex 14.5 Class 10 गणित Q20. एक मोहल्ले के 20 घरों में लगे हुए पौधों से संबंधित निम्नलिखित आँकडें एकत्रित किए प्रति घर पौधों की माध्य संख्या ज्ञात कीजिए ।

NCERT Books Solutions For Class 10 Maths Hindi Medium Statistics 14.1 73

Ex 14.5 Class 10 गणित Q21. किसी फैक्टरी के कुछ श्रमिकों की दैनिक मजदूरी के बंटन का माध्य 145.20 है तो f का मान ज्ञात कीजिए ।

NCERT Maths Book Solutions For Class 10 Hindi Medium Statistics 14.1 74

Ex 14.5 Class 10 गणित Q22. निम्न सारणी कुछ परिवारों में भोजन पर हुए दैनिक व्यय का माध्य व्यय 211 रू है तो f का मान ज्ञात कीजिए ।

CBSE NCERT Maths Solutions For Class 10 Hindi Medium Statistics 14.1 75

Ex 14.5 Class 10 गणित Q23. नीचे दिया हुआ बंटन एकदिवसीय क्रिकेट मैचों में, गेंदबाजों द्वारा लिए गए विकटों का माध्य ज्ञात कीजिए ।

CBSE NCERT Solutions For Class 10 Maths Hindi Medium Statistics 14.1 76

Ex 14.5 Class 10 गणित Q24. निम्न ऑकडों का माध्य, माध्यक और बहुलक ज्ञात कीजिए ।

NCERT Maths Textbook For Class 10 Solutions Hindi Medium Statistics 14.1 77

Ex 14.5 Class 10 गणित Q25. एक सर्वेक्षण के आँकडे दिए गए है जो दशवीं कक्षा के लडकियों का ऊँचाई है। निम्न आँकडों से माध्यक ऊँचाई ज्ञात कीजिए ।   

NCERT Books For Class 10 Maths Solutions Hindi Medium Statistics 14.1 78

Ex 14.5 Class 10 गणित Q26. p का मान ज्ञात कीजिए यदि दिए गए बंटन का माध्य 20 हो |

NCERT Maths Textbook Solutions For Class 10 Hindi Medium Statistics 14.1 79

Ex 14.5 Class 10 गणित Q27. निम्न आँकडों से माध्य, माध्यक और बहुलक ज्ञात कीजिए ।

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 80

Ex 14.5 Class 10 गणित Q28. निम्न आँकडों का माध्यक 525 है। यदि बारम्बारताओं का योग 100 है, तो x और y का मान ज्ञात कीजिए ।

NCERT Solutions For Class 10 Maths PDF Free Hindi Medium Statistics 14.1 81

Ex 14.5 Class 10 गणित Q29. उपयुक्त आँकडों से ‘से कम प्रकार’ का तोरण खींचिए। प्राप्त ग्राफ से माध्यक ज्ञात कीजिए |

NCERT Book Solutions For Class 10 Maths Hindi Medium Statistics 14.1 82

Hope given NCERT Solutions for Class 10 Maths Chapter 14 are helpful to complete your homework.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics (Hindi Medium) Read More »

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry (Hindi Medium)

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry (Hindi Medium)

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry (Hindi Medium)

These Solutions are part of NCERT Solutions for Class 10 Maths in Hindi Medium. Here we have given NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry.

Chapter 9. त्रिकोणमिति का अनुप्रयोग

प्रश्नावली 9.1

Ex 9.1 Class 10 गणित Q1. सर्कस का एक कलाकार एक 20 m लंबी डोर पर चढ़ रहा है जो अच्छी तरह से तनी हुई है और भूमि पर सीधे लगे खंभे के शिखर से बंध हुआ है। यदि भूमि स्तर के साथ डोर द्वारा बनाया गया कोण 30° का हो तो खंभे की ऊँचाई ज्ञात कीजिए (देखिए आकृति)|

Solution: 

माना खंभे की ऊँचाई = h मीटर

NCERT Solutions For Class 10 Maths 9.1 1

डोरी की लंबाई = 20 मीटर

θ = 30

समकोण त्रिभुज ABC में;

NCERT Solutions For Class 10 Maths PDF 9.1 2

Ex 9.1 Class 10 गणित Q2. आँधी आने से एक पेड़ टूट जाता है और टूटा हुआ भाग इस तरह मुड़ जाता है कि पेड़ का शिखर जमीन को छूने लगता है और इसके साथ 30 का कोण बनाता है। पेड़ के पाद-बिंदु की दूरी, जहाँ पेड़ का शिखर जमीन को छूता है, 8 m है। पेड़ की ऊँचाई ज्ञात कीजिए।

Solution:

माना पेड़ की ऊँचाई BC’ है और पेड़ बिंदु A से टूटकर

NCERT Maths Solutions For Class 10 9.1 3

जमीन पर बिंदु C पर झुकी है |

θ = 30°, BC = 8 m

समकोण त्रिभुज ABC में, AB भुजा के लिए,

Maths NCERT Solutions For Class 10 9.1 4

Ex 9.1 Class 10 गणित Q3. एक ठेकेदार बच्चों को खेलने के लिए एक पार्क में दो फिसलनपट्टी लगाना चाहती है। 5 वर्ष से कम उम्र के बच्चों के लिए वह एक ऐसी फिसलनपट्टी लगाना चाहती है जिसका शिखर 1.5 m की ऊँचाई पर हो और भूमि के साथ 30° के कोण पर झुका हुआ हो, जबकि इससे अधिक उम्र के बच्चों के लिए वह 3 m की ऊँचाई पर एक अधिक ढाल की फिसलनपट्टी लगाना चाहती है, जो भूमि के साथ 60° का कोण बनाती हो। प्रत्येक स्थिति में फिसलनपट्टी की लंबाई क्या होनी चाहिए?

Solution: 

NCERT Solutions For Maths Class 10 9.1 5
Solutions For NCERT Maths Class 10 Hindi Medium 9.1 6

Ex 9.1 Class 10 गणित Q4. भूमि के एक बिंदु से, जो मीनार के पाद-बिंदु से 30 m की दूरी पर है, मीनार के शिखर का उन्नयन कोण 30° है। मीनार की ऊँचाई ज्ञात कीजिए।

Solution:

NCERT Solutions of Maths For Class 10 Hindi Medium 9.1 7

माना मीनार AB की ऊँचाई = h मीटर

बिंदु C से मीनार के पाद बिंदु B की दुरी = 30 m

समकोण  ΔABC में,

Maths Solutions For Class 10 NCERT Hindi Medium 9.1 8

Ex 9.1 Class 10 गणित Q5. भूमि से 60 m की ऊँचाई पर एक पतंग उड़ रही है। पतंग में लगी डोरी को अस्थायी रूप से भूमि के एक बिंदु से बांध् दिया गया है। भूमि के साथ डोरी का झुकाव 60° है। यह मानकर कि डोरी में कोई ढील नहीं है, डोरी की लंबाई ज्ञात कीजिए।

Solution:

Solutions For Maths NCERT Class 10 Hindi Medium 9.1 9
NCERT Books Solutions For Class 10 Maths Hindi Medium 9.1 10

Ex 9.1 Class 10 गणित Q6. 1.5 m लंबा एक लड़का 30 m ऊँचे एक भवन से कुछ दूरी पर खड़ा है। जब वह ऊँचे भवन की ओर जाता है तब उसकी आँख से भवन के शिखर का उन्नयन कोण 30° से 60° हो जाता है। बताइए कि वह भवन की ओर कितनी दूरी तक चलकर गया है।

Solution:

माना कि वह लड़का x m दूर भवन की ओर गया |

लडके ऊंचाई छोड़कर भवन की ऊंचाई (AB) = 30 m – 1.5 m

= 28.5 m

NCERT Maths Book Solutions For Class 10 Hindi Medium 9.1 11

समकोण त्रिभुज ABC में,

CBSE NCERT Maths Solutions For Class 10 Hindi Medium 9.1 12

Ex 9.1 Class 10 गणित Q7. भूमि के एक बिंदु से एक 20 m ऊँचे भवन के शिखर पर लगी एक संचार मीनार के तल और शिखर के उन्नयन कोण क्रमशः 45° और 60° है। मीनार की ऊँचाई ज्ञात कीजिए।

CBSE NCERT Solutions For Class 10 Maths Hindi Medium 9.1 13

Solution:

माना संचार मीनार की ऊंचाई (AD) = h m

भवन की ऊंचाई (DC) = 20 m

माना भूमि पर वह बिंदु B है |

भवन सहित मीनार की ऊंचाई (AC) = (20 + h) m

समकोण त्रिभुज BCD में,

NCERT Maths Textbook For Class 10 Solutions Hindi Medium 9.1 14

Ex 9.1 Class 10 गणित Q8. एक पेडस्टल के शिखर पर एक 1.6 m ऊँची मूर्ति लगी है। भूमि के एक बिंदु से मूर्ति के शिखर का उन्नयन कोण 60° है और उसी ¯बदु से पेडस्टल के शिखर का उन्नयन कोण 45° है। पेडस्टल की ऊँचाई ज्ञात कीजिए।

NCERT Books For Class 10 Maths Solutions Hindi Medium 9.1 15

Solution:

माना पेडस्टल की ऊंचाई h मीटर है |

मूर्ति की ऊंचाई = 1.6 m

समकोण त्रिभुज BCD में,

NCERT Maths Textbook Solutions For Class 10 Hindi Medium 9.1 16

Ex 9.1 Class 10 गणित Q9. एक मीनार के पाद-बिंदु  से एक भवन के शिखर का उन्नयन कोण 30o है और भवन के पाद-बिंदु से मीनार के शिखर का उन्नयन कोण 60° है। यदि मीनार 50m ऊँची हो, तो भवन की ऊँचाई ज्ञात कीजिए।

Solution:

NCERT Book Solutions For Class 10 Maths Hindi Medium 9.1 17

माना भवन की ऊंचाई = h m

समकोण त्रिभुज ABC में,

NCERT Textbook Solutions For Class 10 Maths Hindi Medium 9.1 18

Ex 9.1 Class 10 गणित Q10. एक 80 m चैड़ी सड़क के दोनों ओर आमने-सामने समान लंबाई वाले दो खंभे लगे हुए हैं। इन दोनों खंभों के बीच सड़क के एक बिंदु से खंभों के शिखर के उन्नयन कोण क्रमशः 60° और 30° है। खंभों की ऊँचाई और खंभों से बिंदु की दूरी ज्ञात कीजिए।

Solution:

NCERT Books Solutions For Class 10 Maths PDF Hindi Medium 9.1 19

माना भूमि पर वह बिंदु B है |

और खंभों की ऊंचाई = h मीo,

B बिंदु से एक खंभे की दुरी = x m

तो दुसरे खंभे की दुरी = (80 – x) m

समकोण त्रिभुज ABC में,

Download NCERT Solutions For Class 10 Maths Hindi Medium 9.1 20
NCERT Solutions For Class 10 Maths Some Applications of Trigonometry (Hindi Medium) 9.1 21

Ex 9.1 Class 10 गणित Q11. एक नहर के एक तट पर एक टीवी टॉवर उर्ध्वार्धर खड़ा है टॉवर के ठीक सामने दूसरे तट के एक अन्य बिंदु से टॉवर के शिखर का उन्नयन कोण 60° है। इसी तट पर इस बिंदु से 20 m दूर और इस बिंदु को मीनार के पाद से मिलाने वाली रेखा पर स्थित एक अन्य बिंदु से टावर के शिखर का उन्नयन कोण 30° है । टॉवर की ऊँचाई और नहर की चैड़ाई ज्ञात कीजिए।

Solution:

NCERT Solutions For Class 10 Maths PDF Some Applications of Trigonometry (Hindi Medium) 9.1 22

माना टॉवर (AB) की ऊंचाई = h मीo

नहर BC की चौड़ाई = x मीo

समकोण त्रिभुज ABC में,

NCERT Maths Solutions For Class 10 Some Applications of Trigonometry (Hindi Medium) 9.1 23

Ex 9.1 Class 10 गणित Q12. 7 m ऊँचे भवन के शिखर से एक केबल टावर के शिखर का उन्नयन कोण 60° है और इसके पाद का अवनमन कोण 45o है। टॉवर की ऊँचाई ज्ञात कीजिए।

Solution:

NCERT Solutions For Maths Class 10 Some Applications of Trigonometry (Hindi Medium) 9.1 24

माना टॉवर की ऊँचाई = h मीटर

भवन DE की ऊंचाई = 7 मीo

DE = BC = 7 मीo

AB की लंबाई = h – 7 मीo

समकोण त्रिभुज EDC में,

Solutions For NCERT Maths Class 10 Hindi Medium Some Applications of Trigonometry (Hindi Medium) 9.1 25

Ex 9.1 Class 10 गणित Q13.  समुद्र-तल से 75 m ऊँची लाइट हाउस के शिखर से देखने पर दो समुद्री जहाजों के अवनमन कोण 30° और 45° हैं। यदि लाइट हाउस के एक ही ओर एक जहाज दूसरे जहाज के ठीक पीछे हो तो दो जहाजों के बीच की दूरी ज्ञात कीजिए।

Solution:

NCERT Solutions of Maths For Class 10 Hindi Medium 9.1 26

माना दो जहाजों A तथा B है

जिनका अवनमन कोण क्रमश: 45° और 30° है |

लाइट-हाउस DC की ऊंचाई = 75 m

चूँकि अवनमन कोण उन्नयन कोण के बराबर होता है |

∴ ∠DAC = 45o और ∠DBC = 30o

Maths Solutions For Class 10 NCERT Hindi Medium 9.1 27

Ex 9.1 Class 10 गणित Q14.  1.2 m लंबी एक लड़की भूमि से 88.2 m की ऊँचाई पर एक क्षैतिज रेखा में हवा में उड़ रहे गुब्बारे को देखती है। किसी भी क्षण लड़की की आँख से गुब्बारे का उन्नयन कोण 60° है। कुछ समय बाद उन्नयन कोण घटकर 30° हो जाता है | इस अन्तराल के दौरान गुब्बारे द्वारा तय की गयी दुरी ज्ञात कीजिए | 

Solution:

लड़की की ऊंचाई = 1.2 m

भूमि से गुब्बारे की ऊंचाई = 88.2 m

लड़की को छोड़कर गुब्बारे की ऊंचाई = 88.2 – 1.2

Solutions For Maths NCERT Class 10 Hindi Medium Some Applications of Trigonometry 9.1 28

AB = DE = 87.0 m

तय दुरी = BE

समकोण DABC में,

NCERT Books Solutions For Class 10 Maths Hindi Medium 9.1 29

अर्थात इस अन्तराल के दौरान गुब्बारे द्वारा तय की गयी दुरी 87√3 m है |

Ex 9.1 Class 10 गणित Q15.  एक सीध राजमार्ग एक मीनार के पाद तक जाता है। मीनार के शिखर पर खड़ा एक आदमी एक कार को 30° के अवनमन कोण पर देखता है जो कि मीनार के पाद की ओर एक समान चाल से जाता है। छः सेकंड बाद कार का अवनमन कोण 60° हो गया। इस बिंदु से मीनार के पाद तक पहुँचने में कार द्वारा लिया गया समय ज्ञात कीजिए।

Solution:

माना कार को बिंदु C से मीनार के पाद B तक पहुँचने में x सेके ण्ड लगता है |

CBSE NCERT Solutions For Class 10 Maths Hindi Medium Chapter 9 9.1 30
NCERT Maths Textbook For Class 10 Solutions Hindi Medium 9.1 31

Ex 9.1 Class 10 गणित Q16.  मीनार के आधर से और एक सरल रेखा में 4 m और 9 m की दूरी पर स्थित दो ¯बदुओं से मीनार के शिखर के उन्नयन कोण पूरक कोण हैं। सिद्ध कीजिए कि मीनार की ऊँचाई 6 m है।

NCERT Books For Class 10 Maths Solutions Hindi Medium 9.1 32
Solution:

माना मीनार की ऊँचाई = h मीटर है |

समकोण त्रिभुज ABC में,
NCERT Maths Textbook Solutions For Class 10 Hindi Medium 9.1 33

Hope given NCERT Solutions for Class 10 Maths Chapter 9 are helpful to complete your homework.

NCERT Solutions for Class 10 Maths Chapter 9 Some Applications of Trigonometry (Hindi Medium) Read More »

NCERT Solutions for Class 10 English First Flight Poem 11 For Anne Gregory

NCERT Solutions for Class 10 English

For Anne Gregory NCERT Solutions for Class 10 English First Flight Poem 11

For Anne Gregory NCERT Text Book Questions and Answers

For Anne Gregory Thinking about the Poem

Question 1.
What does the young man mean by ‘great honey-coloured ramparts at your ear?’ Why does he say that young men are ‘thrown into despair’ by them?
Answer:
“Great honey-coloured/Ramparts at your ear” means white hair of the beloved. White hair reflects the maturity and the growing age of the beloved. The young are thrown into despair on seeing her white hair because they find her unattractive and too old to be a beloved.

NCERT Solutions for Class 10 English First Flight Poem 11 For Anne Gregory

Question 2.
What colour is the young woman’s hair? What does she say she can change it to? Why would she want to do so?
Answer:
The colour of the young woman’s hair is grey. She is ready to use any colour, say, black or brown or carrot for dying her hair. She wants to impress her despaired lover who had not seen her inner beauty.

Question 3.
Objects have qualities which make them desirable to others. Can you think of some objects (a car,a phone, a dress) and say what qualities make one object more desirable than another? Imagine you were trying to sell an object: what qualities would you emphasise?
Answer:
Usefulness, quality, durability, utility, price and looks of an object are some factors which make the object desirable.

For Anne Gregory Extra Questions and Answers

For Anne Gregory Reference-to-Context Questions

Read the stanza given below and answer the questions that follow:

Question 1.
But I can get a hair-dye
And set such colour there,
Brown, or black, or carrot,
That young men in despair
May love me for myself alone
And not my yellow hair.

(a) Anne Gregory wants to argue on the point that a young man will love her alone.
Answer:
for herself

(b) Anne wants to change the …………. of her hair to make her lover love her and not her hair.
Answer:
colour

(c) Anne would give her hair orange, yellow or carrot colour. (True/False)
Answer:
False

(d) Find the antonym of ‘hope’ in the extract.
Answer:
despair.

NCERT Solutions for Class 10 English First Flight Poem 11 For Anne Gregory

Question 2.
“I heard an old religious man
But yesternight declare
That he had found a text to prove
That only God, my dear,
Could love you for yourself alone
And not your yellow hair.”

(a) The old religious man wants to give the from a religious text.
Answer:
evidence

(b) The yellow hair refers to the colour of the hair and the
Answer:
age

(c) Only God can love us for ourselves. (True/False)
Answer:
True

(d) Find the same meaning of ‘saintly’ in the extract.
Answer:
religious.

NCERT Solutions for Class 10 English First Flight Poem 11 For Anne Gregory

For Anne Gregory Long Answer Question

Question 1.
The poet in the poem, ‘For Anne Gregory’ conveys that we should give importance to the inner beauty and not to the physical appearance. Elaborate with reference to the poem. [Delhi 2019]
Answer:
The lady has attractive yellow hair, but shuns any suitor who falls for her hair rather than herself. The lady asserts that she can dye her hair into shades of brown, black, or carrot to ward off desperate men and assert that a genuine lover should love her for herself and not for her hair. The poet declares that human love is fickle and drawn to exterior appearances. The poet declares that loving a person for his true character rather than the external accoutrements, is a godly quality. God loves a human being for their true selves and not for their yellow hair, proving that a gay coat does not make a person a gentleman.

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NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

NCERT Solutions for Class 10 English

A Letter to God NCERT Solutions for Class 10 English First Flight Chapter 1

A Letter to God NCERT Text Book Questions and Answers

A Letter to God Oral Comprehension Check

Question 1.
What did Lencho hope for?
Answer:
Lencho hoped for getting a better crop that year.

Question 2.
Why did Lencho say the raindrops were like ‘new coins’?
Answer:
Lencho said that the raindrops were like new coins because they were round in shape and almost of the same size. Secondly, he knew that good rain meant good crop which ultimately meant good money.

Question 3.
How did the rain change? What happened to Lencho’s fields?
Answer:
The pleasant and auspicious rain changed into a large hailstorm as a strong wind began to blow. Lencho’s field was covered with snow and it looked white as if it were covered with salt.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 4.
What were Lencho’s feelings when the hail stopped?
Answer:
When the hail stopped, Lencho was disappointed to see that the whole crop was spoiled. He felt very sad.

Question 5.
Who or what did Lencho have faith in? What did he do?
Answer:
Lencho had faith in God alone. He wrote a letter to God.

Question 6.
Who read the letter?
Answer:
The postmaster read the letter.

Question 7.
What did the postmaster do then?
Answer:
The postmaster collected some money from the employees and sent it to the poor farmer.

Question 8.
Was Lencho surprised to find a letter for him with money in it?
Answer:
No, Lencho was not surprised to find a letter for him from God with money in it. He took it very casually.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 9.
What made him angry?
Answer:
Lencho became angry to see only seventy pesos instead of hundred pesos.

A Letter to God Thinking about the Text

Question 1.
Who does Lencho have complete faith in? Which sentences in the story tell you this?
Answer:
Lencho had complete faith in God. The lines which show his extreme faith in God are:
(i) Lencho thought only of his one hope: the help of God.
(ii) God, if you don’t help me, my family and I will go hungry this year.
‘Lencho showed not, the slightest surprise on seeing the money.’
‘God could not have made a mistake’.
‘God: Of the money I asked for, only seventy pesos reached me, send me the rest.’

Question 2.
Why does the postmaster send money to Lencho? Why does he sign the letter ‘God’?
Answer:
The postmaster sent money to Lencho because he was extremely impressed by the extreme faith of a poor farmer in the supreme power of God. He signed the letter God because he didn’t want to shake the poor man’s faith in God.

Question 3.
Did Lencho try to find out who had sent the money to him? Why/Why not?
Answer:
No, Lencho did not try to find out who had sent the money to him because he could not think that anybody other than God could have given him the money.

Question 4.
Who does Lencho think has taken the rest of the money? What is the irony in the situation. (Remember that the irony of a situation is an unexpected aspect of it. An ironic situation is strange or amusing because it is the opposite of what is expected.)
Answer:
Lencho thought that the post office employees had taken the money. The irony is that the post office employees donated the money to help Lencho but he accused them of stealing the money from the envelope sent by God.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 5.
Are there people like Lencho in the real world? What kind of a person would you say he is?
Answer:
Yes, there are people like Lencho, who are innocent enough to think that the God would certainly help them as they have full faith in the supreme power of God. Lencho is a very simple man who had extreme faith in God; he is a man of clear conscience.

Lencho is a simple and innocent fellow who is naive but not stupid. It was his firm faith in God that he thought of writing a letter to God. He has an unquestioning attitude.

Though Lencho has immense faith in God, he is a poor judge of human nature. He lacks the value of gratefulness. What I like most about him is his immense faith in God and his simplicity.

Question 6.
There are two kinds of conflicts in the story ‘A letter to God’: between humans and nature and between humans themselves. How are these conflicts illustrated?
Answer:
It is true that there are two kinds of conflicts in the story between humans and nature and between humans themselves. In the beginning of the story, Lencho is shocked to see the hailstorm wipe out the happiness along with the crop in the field. The moment Lencho was rejoicing at the rainfall, he did not know that it was the end of his happiness. On the other hand, Lencho who had extreme faith in the power of Almighty does not have the slightest trust in the employees of the post office. He considers them a bunch of crooks though they tried to help him.

A Letter to God Extra Questions and Answers

A Letter to God Reference-to-Context Questions

Read the following extract carefully and answer the questions that follow.

Question 1.
The house — the only one in the entire valley — sat on the crest of a low hill. From this height one could see the river and the field of ripe corn dotted with the flowers that always promised a good harvest. The only thing the earth needed was a downpour or at least a shower. Throughout the morning Lencho — who knew his fields intimately — had done nothing else but see the sky towards the north-east.

(а) The house was located on the
Answer:
crest of a low hill

(b) The only thing the earth needed was
Answer:
a downpour

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

(c) One could see huts and the field of ripe corn dotted with the flowers from the height of the hill. (True/False)
Answer:
False

(d) Find the word from the passage which means ‘top of a hill’.
Answer:
crest

Question 2.
“Now we’re really going to get some water, woman.” The woman who was preparing supper, replied, “Yes, God willing”. The older boys were working in the field, while the smaller ones were playing near the house until the woman called to them all, “Come for dinner”. It was during the meal that, just as Lencho had predicted, big drops of rain began to fall. In the north-east huge mountains of clouds could be seen approaching. The air was fresh and sweet. The man went out for no other reason than to have the pleasure of feeling the rain on his body, and when he returned he exclaimed, “These aren’t raindrops falling from the sky, they are new coins. The big drops are ten-cent pieces and the little ones are fives.”

(a) Lencho compared the raindrops with the
Answer:
silver coins

(b) The family was happy as the rain was much needed for a good
Answer:
harvest

(c) The woman heard from Lencho that it was going to rain. (True/False)
Answer:
True

(d) Find the word from the passage which means ‘symbol of prosperity’.
Answer:
new coins.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 3.
With a satisfied expression he regarded the field of ripe corn with its flowers, draped in a curtain of rain. But suddenly a strong wind began to blow and along with the rain very large hailstones began to fall. These truly did resemble new silver coins. The boys, exposing themselves to the rain, ran out to collect the frozen pearls.

(a) Lencho was satisfied as the rain outside was much for a good harvest.
Answer:
needed

(b) Suddenly a strong wind began to blow and along with the rain very large began to fall.
Answer:
hailstones

(c) Very large stones that came along with the rain resembled golden pearls. (True/False)
Answer:
False

(d) Find the words from the passage which means ‘hailstones’.
Answer:
‘Frozen pearls’.

Question 4.
“It’s really getting bad now,” exclaimed the man. “I hope it passes quickly.” It did not pass quickly. For an hour the hail rained on the house, the garden, the hillside, the cornfield, on the whole valley. The field was white, as if covered with salt. Not a leaf remained on the trees. The corn was totally destroyed. The flowers were gone from the plants. Lencho’s soul was filled with sadness. When the storm had passed, he stood in the middle of the field and said to his sons, “A plague of locusts would have left more than this. The hail has left nothing. This year we will have no corn.”

(a) Lencho exclaimed with sadness that the ………….. was getting bad as it was raining with hailstones.
Answer:
weather

(b) Lencho was worried about how his family would …………… as the hailstones had completely destroyed the cornfield.
Answer:
survive

(c) The hailstorm not only destroyed Lencho’s cornfield but also damaged the whole valley. (True/False)
Answer:
True

(d) ‘A plague of locusts’ means
Answer:
a large number of insects that can cause great damage to the crops.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 5.
That night was a sorrowful one. “All our work, for nothing.”
“There’s no one who can help us.” “We’ll all go hungry this year”. But in the hearts of all who lived in that solitary house in the middle of the valley, there was a single hope: help from God.
“Don’t be so upset, even though this seems like a total loss. Remember, no one dies of hunger.”
“That’s what they say: no one dies of hunger.” All through the night, Lencho thought only of his one hope: the help of God, whose eyes, as he had been instructed, see everything, even what is deep in one’s conscience. Lencho was an ox of a man, working like an animal in the fields, but still he knew how to write. The following Sunday, at daybreak, he began to write a letter which he himself would carry to town and place in the mail. It was nothing less than a letter to God.

(a) The single hope for the family was
Answer:
help from God.

(b) Lencho at last decided to write to God.
Answer:
a letter

(c) Lencho believed that God does not let anyone die of hunger. (TFue/Faise)
Answer:
True

(d) Give the meaning of the word ‘conscience’ with reference to the extract.
Answer:
a person’s moral sense of right and wrong.

Question 6.
“God,” he wrote, “if you don’t help me, my family and I will go hungry this year. I need a hundred pesos in order to sow my field again and to live until the crop comes, because the hailstorm….”
He wrote ‘To God’ on the envelope, put the letter inside and, still troubled, went to town. At the post office, he placed a stamp on the letter and dropped it into the mailbox.

(a) Lencho requested God to send him
Answer:
a hundred pesos

(b) At the post office Lencho placed a on the letter and dropped it into the mailbox.
Answer:
stamp

(c) Lencho wrote the letter to God because God will sow his field again. (iVue/False)
Answer:
False

(d) Find the synonym of the word ‘anxious’ from the extract.
Answer:
‘troubled’

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 7.
One of the employees, who was a postman and also helped at the post office, went to his boss laughing heartily and showed him the letter to God. Never in his career as a postman had he known that address. The postmaster — a fat, amiable fellow — also broke out laughing, but almost immediately he turned serious and, tapping the letter on his desk, commented, “What faith! I wish I had the faith of the man who wrote this letter. Starting up a correspondence with God!”

(a) The postman laughed heartily because he saw the letter to God.
Answer:
addressed

(b) The postmaster became serious suddenly and was impressed to see Lencho’s in God.
Answer:
faith

(c) The postmaster was an amiable man and praised Lencho’s faith in God. (True/False)
Answer:
True

(d) Give the synonym of ‘letter writing’ from the extract.
Answer:
‘correspondence’.

Question 8.
So, in order not to shake the writer’s faith in God, the postmaster came up with an idea: answer, the letter. But when he opened it, it was evident that to answer it he needed something more than goodwill, ink and paper. But he stuck to his resolution: he asked for money from his employees, he himself gave part of his salary, and several friends of his were obliged to give something ‘for an act of charity’.

It was impossible for him to gather together the hundred pesos, so he was able to send the farmer only a little more than half. He put the money in an envelope addressed to Lencho and with it a letter containing only a single word as a signature: God.

(a) It was impossible for the postmaster together together the
Answer:
hundred pesos

(b) When the postmaster opened the letter, he needed something more than, ink and paper.
Answer:
goodwill

(c) The postmaster managed a hundred pesos from his friends. (True/False)
Answer:
False

(d) Give the synonym of ‘grateful’ from the extract.
Answer:
‘obliged’.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 9.
The following Sunday Lencho came a bit earlier than usual to ask if there was a letter for him. It was the postman himself who handed the letter to him while the postmaster, experiencing the contentment of a man who has performed a good deed, looked on from his office.
Lencho showed not the slightest surprise on seeing the money; such was his confidence — but he became angry when he counted the money. God could not have made a mistake, nor could he have denied Lencho what he had requested.

(a) Lencho became angry because he did not get the that he requested God.
Answer:
amount

(b) Lencho came to the post office the following to ask if there was any letter for him.
Answer:
Sunday

(c) The postmaster had performed a good deed by helping Lencho. (True/False)
Answer:
True

(d) Give the meaning of the word ‘a conscious action’ from the extract. ”
Answer:
deed

Question 10.
Immediately, Lencho went up to the window to ask for paper and ink. On the public writing-table, he started to write, with much wrinkling of his brow, caused by the effort he had to make to express his ideas. When he finished, he went to the window to buy a stamp which he licked and then affixed to the envelope with a blow of his fist. The moment the letter fell into the mailbox the postmaster went to open it. It said: “God: Of the money that I asked …. for, only seventy pesos reached me. Send me the rest, since I need it very much. But don’t send it to me through the mail because the post office employees are a bunch of crooks. Lencho.”

(a) Lencho called the post office employees ………. because he thought that they had cheated him.
Answer:
a bunch of crooks

(b) There were wrinkles on his brow because he was ………….
Answer:
angry

(c) Lencho wrote in his second letter that he received seventy pesos only. (True/False)
Answer:
False

(d) Give the meaning of the word’ “creased” from the extract.
Answer:
‘wrinkling’.

A Letter to God Short Answer Questions

Answer the following questions in 30 – 40 words each:

Question 1.
(i) Where was ‘the house’ located?
(ii) Why do you think it is called ‘the’ house and not ‘a’ house?
Answer:
(i) The house was located on the top of a low hill.
(ii) It is called ‘the house’ because it is the only house on the top of the hill.

Question 2.
Why did Lencho keep gazing at the sky?
Answer:
Lencho knew that his fields needed water immediately. He was eagerly waiting for the rain, therefore he gazed at the sky.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 3.
“Now we’re really going to get some water, woman.” Is Lencho sure that it is going to rain? Give a reason for your answer.
Answer:
Lencho was sure that it was going to rain because he kept watching the sky throughout the day. Through his experience, he knew that the clouds would certainly bring rain.

Question 4.
(i) How did Lencho feel when it started raining?
(ii) What was the effect of the rain on the crops?
Answer:
(i) Lencho was excited when he came out of his house to have the pleasure of feeling the rain on his body. He compared the raindrops with coins, as he knew that a good rain would mean a good crop and a good crop would mean a lot of money.
(ii) The rain brought with it destruction. There was hailstorm for about an hour and it covered the field. The corn was totally destroyed.

Question 5.
What are the raindrops compared to and why?
Answer:
Raindrops are compared to coins. He compares big raindrops to ten-cent coins and smaller ones to five-cent coins. He knew that the raindrops would certainly be helpful in giving him rich harvest. Naturally, it would make him get more money.

Question 6.
Lencho had only ‘one hope’. What was it?
Answer:
Lencho was a God-fearing man and had a firm faith in the benevolence of God, who he thought would certainly help him. God was his only hope.

Question 7.
Did the letter reach God? Why did the postmaster send a reply to Lencho?
Answer:
The letter did not reach God but it certainly reached the postmaster who was a God-fearing and kind-hearted man. He decided to send a reply to Lencho as he was moved by the firm faith of a farmer in God, and he did not want to disappoint him.

Question 8.
Lencho describes the post office employees as ‘a bunch of crooks’.
(i) Were they ‘a bunch of crooks’?
(ii) How would you describe them?
Answer:
(i) The post office employees were really very good people who tried to help a poor farmer. They were not a bunch of crooks.
(ii) They can be described as kind-hearted, generous, helpful and God-fearing men.

A Letter to God Long Answer Questions

Question 1.
Describe the character of Lencho in the light of his faith and attitude towards God and man.
Answer:
Lencho was a hardworking farmer who had immense faith in God. He had such an immense faith in the existence and helpfulness of God that he started communicating with him. He wrote a letter to God requesting him to send him one hundred pesos. When he received seventy pesos, he was not surprised at all. He even doubted the integrity of the post office employees who, he thought, had stolen his thirty pesos. He was a poor judge of human nature. His attitude towards man was negative. He could not think of a help from man.

NCERT Solutions for Class 10 English First Flight Chapter 1 A Letter to God

Question 2.
Lencho called the post office employees ‘a bunch of crooks’. What does it show about his attitude towards men? Was he not A person of humility, appreciation and gratefulness? Elaborate.
Answer:
Lencho called the post office employees a bunch of crooks as he thought that they had stolen his money sent by God. He was not correct in his assessment of the employees. It shows that he had a negative attitude towards mankind. He was not a fair judge of man’s nature.

It seems he was too naive to have the sense of humility, appreciation and gratefulness. He hurt the feelings of the post office employees unintentionally. He was a simple man who had immense faith in God but could not think of any help from men. His anger and attitude towards them shows that he did not have any faith in men. He did not credit the post office employees for their help out of ignorance but he should not have called them a bunch of crooks.

Question 3.
What kind of people were the post office employees? What do you like about the gesture of the postmaster?
Answer:
The post office employees were very generous, kind and helpful people. When they received the letter for God from Lencho, they were impressed with his faith in God althought initially they made fun of it.They did not want to hurt his feelings and shake his faith in god. They decided to help him by sending him money.

It was a noble gesture on their part. All of them contributed by giving a share of their salaries. It shows their kindness and generosity. They could have told Lencho the truth about God but their sensitivity stopped them from doing so. They did not want to hurt his feelings. They had sympathy and compassion for Lencho. The postmaster’s generosity, his sensitivity, initiative and his noble gesture make him a good human being in the eyes of the readers.

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NCERT Solutions for Class 10 Science Chapter 5 Periodic Classification of Elements (Hindi Medium)

NCERT Solutions for Class 10 Science Chapter 5 Periodic Classification of Elements (Hindi Medium)

NCERT Solutions for Class 10 Science Chapter 5 Periodic Classification of Elements (Hindi Medium)

These Solutions are part of NCERT Solutions for Class 10 Science in Hindi Medium. Here we have given NCERT Solutions for Class 10 Science Chapter 5 Periodic Classification of Elements.

Chapter 5. तत्वों के आवर्त वर्गीकरण

अध्याय-समीक्षा 

  • सन् 1800 तक केवल 30 तत्वों का पता चला था। इन सभी तत्वों की संभवतः भिन्न-भिन्न विशेषताएँ थीं।
  • जैसे-जैसे विभिन्न तत्वों की खोज हो रही थी, वैज्ञानिक इन तत्वों के गुणधर्मों के बारे में अधिक से अधिक जानकारी एकत्र करने लगे।
  • सबसे पहले, ज्ञात तत्वों को धातु एवं अधातु में वर्गीकृत किया गया। जैसे-जैसे तत्वों एवं उनके गुणधर्मों के बारे में हमारा ज्ञान बढ़ता गया, वैसे-वैसे उन्हें वर्गीकृत करने के प्रयास किए गए।
  • सन् 1817 में जर्मन रसायनज्ञ, वुल्फगांग डॉबेराइनर ने समान गुणधर्मों वाले तत्वों को समूहों में व्यवस्थित करने का प्रयास किया। उन्होंने तीन-तीन तत्व वाले कुछ समूहों को चुना एवं उन समूहों को त्रिक कहा |
  • डॉबेराइनर ने बताया कि त्रिक के तीनों तत्वों को उनके परमाणु द्रव्यमान के आरोही क्रम में रखने पर बीच वाले तत्व का परमाणु द्रव्यमान, अन्य दो तत्वों के परमाणु द्रव्यमान का लगभग औसत होता है। उदाहरण के लिए लिथियम (Li) सोडियम (Na) एवं पोटैशियम (K) है |
  • डॉबेराइनर की त्रिक में तत्वों के वर्गीकरण की यह पद्धति सफल नहीं रही क्योंकि उस समय तक ज्ञात तत्वों में केवल तीन त्रिक ही ज्ञात कर सके थे।
  • डॉबेराइनर ने ही सबसे पहले प्लैटिनम को उत्प्रेरक के रूप में पहचाना तथा समान त्रिक की खोज की जिससे तत्वों की आवर्त सारणी का विकास हुआ।
  • सन् 1866 में अंग्रेज़ वैज्ञानिक जॉन न्यूलैंड्स ने ज्ञात तत्वों को परमाणु द्रव्यमान के आरोही क्रम में व्यवस्थित किया। उन्होंने सबसे कम परमाणु द्रव्यमान वाले तत्व हाइड्रोजन से आरंभ किया तथा 56वें तत्व थोरियम पर इसे समाप्त किया।
  • न्यूलैंड्स का अष्टक नियम: “प्रत्येक आठवें तत्व का गुणधर्म पहले तत्व के गुणधर्म के समान हैं |”
  • न्यूलैंड्स के अष्टक में लीथियम एवं सोडियम के गुणधर्म समान थे। सोडियम, लीथियम के बाद आठवाँ तत्व है। इसी तरह बेरिलियम एवं मैग्नीशियम में अधिक समानता है।
  • ऐसा देखा गया कि अष्टक का सिद्धांत केवल कैल्सियम तक ही लागू होता था, क्योंकि कैल्सियम के बाद प्रत्येक आठवें तत्व का गुणधर्म पहले तत्व से नहीं मिलता।
  • न्यूलैंड्स ने कल्पना की कि प्रकृति में केवल 56 तत्व विद्यमान हैं तथा भविष्य में कोई अन्य तत्व नहीं मिलेगा। लेकिन, बाद में कई नए तत्व पाए गए जिनके गुणधर्म, अष्टक सिद्धांत से मेल नहीं खाते थे।
  • अपनी सारणी में इन तत्वों को समंजित करने के लिए न्यूलैंड्स ने दो तत्वों को एक साथ रख दिया और कुछ असमान तत्वों को एक स्थान में रख दिया।
  • इस प्रकार, न्यूलैंड्स अष्टक सिद्धांत केवल हल्के तत्वों के लिए ही ठीक से लागू हो पाया।
  • तत्वों के वर्गीकरण का मुख्य श्रेय रूसी रसायनज्ञ डमित्राी इवानोविच मेन्डेलीफ को जाता है। तत्वों की आवर्त सारणी के प्रारंभिक विकास में उनका प्रमुख योगदान रहा। उन्होंने अपनी सारणी में तत्वों को उनके मूल गुणधर्म, परमाणु द्रव्यमान तथा रासायनिक गुणधर्मों में समानता के आधार पर व्यवस्थित किया।
  • जब मेन्डेलीफ ने अपना कार्य आरंभ किया तब तक 63 तत्व ज्ञात थे। उन्होंने तत्वों के परमाणु द्रव्यमान एवं उनके भौतिक तथा रासायनिक गुणधर्मों के बीच संबंधों का अध्ययन किया |
  • रासायनिक गुणधर्मों के अंतर्गत मेन्डेलीफ ने तत्वों के ऑक्सीजन एवं हाइड्रोजन के साथ बनने वाले यौगिकों पर अपना ध्यान केन्द्रित किया। उन्होंने ऑक्सीजन एवं हाइड्रोजन का इसलिए चुनाव किया क्योंकि ये अत्यंत सक्रिय हैं तथा अधिकांश तत्वों के साथ यौगिक बनाते हैं। तत्व से बनने वाले हाइड्राइड एवं ऑक्साइड के सूत्र को तत्वों के वर्गीकरण के लिए मूलभूत गुणधर्म माना गया।

पाठगत-प्रश्न:

पेज – 91

1. क्या डॉबेराइनर के त्रिक, न्यूलैंड्स के अष्टक के स्तंभ में भी पाए जाते हैं? तुलना करके पता कीजिए।
उत्तर : हाँ , त्रिक  न्यूलैंड्स के अष्टक के स्तंभ में भी मिलते है | उदहारण :- Li , Na व K |

2. डॉबेराइनर के वर्गीकरण की क्या सीमाएँ हैं?
उत्तर :  डॉबेराइनर केवल तीन तत्वों के त्रिक को उस समय पहचान सके एवं सभी तत्वों का वर्गोंकरण उनके त्रिक के अनुसार नहीं हो सका |

3. न्यूलैंड्स के अष्टक सिद्धात की क्या सीमाएँ हैं?
उत्तर :  न्यूलैंड्स का अष्टक  सिद्धात कैल्सियम तक केव परमाणु भर वाले तत्वों का वर्गोंकरण कर पाया |

पेज – 94

1. मेन्डेलीफ की आवर्त सारणी का उपयोग कर निम्नलिखित तत्वों वेफ ऑक्साइड के सूत्र का अनुमान कीजिए: K,C,Al,Si,Ba |
उत्तर : K – K2O , O – O2 , Al – Al2O2 ,Si – SiO2 , Ba – BaO |

2. गैलियम के अतिरिक्त, अब तक कौन-कौन से तत्वों का पता चला है जिसके लिए मेन्डेलीफ ने अपनी आवर्त सारणी में खाली स्थान छोड़ दिया था? दो उदाहरण दीजिए।
उत्तर : स्कैंडियम व जर्मेनियम |

3. मेन्डेलीफ ने अपनी आवर्त सारणी तैयार करने के लिए कौन सा मापदंड अपनाया?
उत्तर :  मेन्डेलीफ ने तत्वों को उनके परमाणु के अनुसार अलग किया | उनहोंने एक समान गुणों वाले तत्वों को एक समूह में रखने का प्रयास किया |

4. आपके अनुसार उत्कृष्ट गैसों को अलग समूह में क्यों रखा गया?
उत्तर :
 उत्कृष्ट गैसों अक्रियाशील होती है अत: अलग वर्ग में रखा गया |

पेज – 100

1. आधुनिक आवर्त सारणी द्वारा किस प्रकार से मेन्डेलीफ की आवर्त सारणी की विविध विसंगतियों को दूर किया गया?
उत्तर :

  1. आधुनिक आवर्त सारणी में तत्वों को उनके परमाणु क्रमांकों के अनुसार अलग किया गया | हाइड्रोजन को प्रथम समूह में स्थान दिया गया |
  2. आवर्त सारणी में तत्वों की सिथति से उनकी रासायनिक  अभिक्रियाशीलता का पता चलता है |
  3. तत्वों को उनके भार के अनुसार भारी व हल्के अलग-अलग क्रम में रखा गया |

2. मैग्नीशियम की तरह रासायनिक अभिक्रियाशीलता दिखाने वाले दो तत्वों के नाम लिखिए? आपके चयन का क्या आधर है?
उत्तर : बैरीलियम (Be) तथा  कैल्सियम (Ca) दोनों ही मैग्नीशियम की तरह  अभिक्रियाशीलता दर्शाते है | दोनों के ही बाह्य किश में 2 संयोजी इलेक्ट्रॉन होते है |Be(2,2) तथा Ca(2,8,8,2)|

3. के नाम बताइएः
(a) तीन तत्वों जिनके सबसे बाहरी कोश में एक इलेक्ट्रॉन उपस्थित हो।
(b) दो तत्वों जिनके सबसे बाहरी कोश में दो इलेक्ट्रॉन उपस्थित हों।
(c)तीन तत्वों जिनका बाहरी कोश पूर्ण हो।

उत्तर :
(a) लिथियम (Li) , सोडियम (Na) , पोटैशियम (K) |
(b) मैग्नीशियम (Mg) ,  कैल्सियम (Ca) |
(c)  निऑन (Ne) , आर्गन (Ar) , क्रिप्टोंन (Kr) |

4.
(a) लीथियम, सोडियम, पोटैशियम, ये सभी धातुएँ जल से अभिक्रिया कर हाइड्रोजन गैस मुक्त करती हैं। क्या इन तत्वों के परमाणुओं में कोई समानता है?
(b) हीलियम एक अक्रियाशील गैस है जबकि निऑन की अभिक्रियाशीलता अत्यंत कम है। इनके परमाणुओं में कोई समानता है?

उत्तर :
(a) ‘ हाँ ‘ इन तत्वों के परमाणुओं में समानता है | इनके बाह्यतम कोष में केवल 1 इलेक्ट्रॉन है | इनकी संयोजकताएँ भी समान है |
(b) ‘ हाँ ‘ इनमें भी समानता है |  दोनों संयोजकता  ‘ o ‘ है तथा इनके बाह्यतम कोश पूर्ण है |

5. आधुनिक आवर्त सारणी में पहले दस तत्वों में कौन सी धातुएँ हैं?
उत्तर : लिथियम एवं बेरीलियम धातुएँ है |

6. आवर्त सारणी में इनके स्थान के आधार पर इनमें से किस तत्व में सबसे अधिक धात्विक अभिलक्षण की विशेषता है?
Ga , Ge , As , Se , Be |
उत्तर : Be |

अभ्यास

1. आवर्त सारणी में बाईं से दाईं ओर जाने पर, प्रवृत्तियों के बारे में कौन सा कथन असत्य है?
(a) तत्वों की धात्विक प्रकृति घटती है।
(b) संयोजकता इलेक्ट्रॉनों की संख्या बढ़ जाती है।
(c) परमाणु आसानी से इलेक्ट्रॉन का त्याग करते हैं।
(d) इनके ऑक्साइड अधिक अम्लीय हो जाते हैं।

उत्तर : (c) परमाणु आसानी से इलेक्ट्रॉन का त्याग करते हैं।

2. तत्व X, XCl2 सूत्र का वाला एक क्लोराइड बनाता है जो एक ठोस है तथा जिसका गलनांक अधिक है। आवर्त सारणी में यह तत्व संभवतः किस समूह के अंतर्गत होगा?
(a) NA
(b) Mg
(c) Al
(d) Si

उत्तर : (b) Mg |

3. किस तत्व में

(a)दो कोश हैं तथा दोनों इलेक्ट्रॉनों से पूरित हैं?
(b) इलेक्ट्रॉनिक विन्यास 2, 8, 2 है?
(c) कुछ तीन कोश हैं तथा संयोजकता कोश में चार इलेक्ट्रॉन हैं?
(d) कुछ दो कोश हैं तथा संयोजकता कोश में तीन इलेक्ट्रॉन हैं?
(e) दूसरे कोश में पहले कोश से दोगुने इलेक्ट्रॉन हैैं?

उत्तर :
(a) निऑन (Ne)
(b) मैग्नीशियम (Mg)
(c) सिलिकॉन (Si)
(d) बोरॉन (B)
(e) कार्बन (C)

4.
(a) आवर्त सारणी में बोरान के स्तंभ के सभी तत्वों के कौन से गुणधर्म समान हैं?
(b) आवर्त सारणी में फलुओरीन के स्तंभ के सभी तत्वों के कौन से गुणधर्म समान हैं?

उत्तर :
(a) सामान गुणधर्म :- 

  1. सभी तत्व धातुएँ है |
  2. ऊपर से नीचे जाने पर आकर एवं धात्विक गुण बढता जाता है |
  3. सभी विघुत के सुचालक होते है |

(b) सामान गुणधर्म :- 

  1. सभी तत्व अधातुएँ है तथा संयोजकता 7 होती है |
  2. सभी विघुत के कुचालक है |

5. एक परमाणु का इलेक्ट्रॉनिक विन्यास 2, 8, 7 है।
(a) इस तत्व की परमाणु-संख्या क्या है?
(b) निम्न में किस तत्व के साथ इसकी रासायनिक समानता होगी? ;परमाणु-संख्या कोष्ठक में दी गई है |
N(7) , F(9) , P(15) , Ar(18) 

उत्तर :
(a) इसकी परमाणु संख्या 17 है |
(b) F(9) – 2,7 के साथ रासायनिक गुणों में समानता होगी |

6. आवर्त सारणी में तीन तत्व । A,B तथा C की स्थिति निम्न प्रकार है:
समूह 16       समूह 17
—                 —

    —                  A

    —                 —

    B                   C

अब बताइए कि:
(a) धातु है या अधातु।
(b)की अपेक्षा  अधिक अभिक्रियाशील है या कम?
(c) का साइज़  से बड़ा होगा या छोटा?
(d) किस प्रकार आयन, धनायन या ऋणायन बनाएगा?

उत्तर :
(a) A- अधातु है |
(b) C कम क्रियाशील है |
(c) C का आकार B से छोटा है
(d) तत्व A ऋणायन बनायेगा |

7. नाइट्रोजन (परमाणु-संख्या7)तथा परमाणु-संख्या 15के आवर्त सारणी के समूह 15 के तत्व हैं। इन दोनों तत्वों का इलेक्ट्रॉनिक विन्यास लिखिए। इनमें से कौन सा तत्व अधिक ऋण विद्युत होगा और क्यों?

उत्तर : नाइट्रोजन की परमाणु संख्या 7 (2,5) है अत: यह अधिक विद्युत ऋणात्मक होगा | फॉस्फोरस और नाइट्रोजन दोनों ही अधातुएँ है परन्तु फॉस्फोरस 15 (2,8,5) नाइटोजन से नीचे की ओर आता है और इस प्रकार ऋणात्मक घटती है |

8. तत्वों के इलेक्ट्रॉनिक विन्यास का आधुनिक आवर्त सारणी में तत्व की स्थिति से क्या संबंध है?

उत्तर : तत्वों का उनके इलेक्ट्रॉनिक विन्यास के अनुसार वर्गोंकरण किया गया है | किसी तत्व की बाह्यतम कोश में उपसिथत इलेक्ट्रॉन से उसकी संयोजकता पता चलती है तथा कोशों की कुल संख्या उसकी आवर्त संख्या होत |

9. आधुनिक आवर्त सारणी में कैल्सियम (परमाणु-संख्या 20) चारों ओर 12, 19 21 तथा 38 परमाणु-संख्या वाले तत्व स्थित हैं। इनमें से किन तत्वों के भौतिक एवं रासायनिक गुणधर्म कैल्सियम के समान हैं?

उत्तर : आवर्त सारणी में C(20) के चारों ओर 12,19,21 व 38 परमाणु संख्या वाले तत्व है | इनमें से परमाणु संख्या 21 (2,8,9,2) तथा परमाणु संख्या 38 (2,8,18,2) वाले तत्वों के रासायनिक व भौतिक गुणधर्म सामान होंगे |

10. आधुनिक आवर्त सारणी एवं मेन्डेलीफ की आवर्त सारणी में तत्वों की व्यवस्था की तुलना कीजिए।

उत्तर :
आधुनिक आवर्त सारणी :-

  1. यह परमाणु संख्या के अनुसार क्रमित है |
  2. इसमें 18 वर्ग है |
  3. इनमें अक्रिय गैसों को 18वें वर्ग में रखा गया है |

मेन्डेलीफ की आवर्त सारणी :-

  1. यह परमाणु द्रव्यमान पर आधारित है |
  2. इसमें 8 समूह है |
  3. इनमें अक्रिय गैसों को कोई स्थान नहीं मिला है |

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