Class 9

JAC Board Class 9th Social Science Important Questions Geography Chapter 3 Drainage

I. Objective Type Questions

1. The river system of an area is referred to as:
(a) Water flow
(b) Drainage
(c) Delta
(d) None of these,
Answer:
(b) Drainage

2. Indian river systems can be divided into how many groups?
(a) Three
(b) Four
(c) Six
(d) Two.
Answer:
(d) Two.

3. Most of the peninsular rivers discharge their water in:
(a) Indian Ocean
(b) Bay of Bengal
(c) Arabian Sea
(d) None of these
Answer:
(b) Bay of Bengal

4. Which of the following lakes in Rajasthan is a saltwater lake?
(a) Siliserh
(b) Jaisamand
(c) Pichola
(d) Sambhar.
Answer:
(d) Sambhar.

5. The Wular lake in Jammu and Kashmir is the result of which of the following activities?
(a) Rainfall
(b) Human activity
(c) Tectonic activity
(d) None of these.
Answer:
(c) Tectonic activity

6. In which year was the Ganga Action Plan introduced?
(a) 1955
(b) 1947
(c) 1985
(d) 1995.
Answer:
(c) 1985

II. Very Short Answer Type Questions

Question 1.
What is drainage?
Answer:
The term drainage describes the river system of an area.

Question 2.
What is a drainage basin?
Answer:
The area drained by a single river system is called a drainage basin.

Question 3.
Which river has the largest river basin in the world?
Answer:
The world’s largest drainage basin is that of the Amazon river.

Question 4.
Into how many categories are the Indian rivers divided?
Answer:
The Indian rivers are divided into two major groups:

1. The Himalayan rivers, and
2. The Peninsular rivers.

Question 5.
Name three major rivers, which originate beyond the Himalayas.
Answer:

1. Indus,
2. Satluj,
3. Brahmaputra river.

Question 6.
What do you understand by a river system?
Answer:
A group of a main river alongwith its tributaries is known as a river system.

Question 7.
From where the river Indus originates?
Answer:
The Indus rises in Tibet, near Lake Mansarovar.

Question 8.
What is the total length of the river Indus?
Answer:
2900 km.

Question 9.
Name the major rivers of the Indus river system.
Answer:
The Indus, the Satluj, the Jhelum, the Chenab, the Ravi and the Beas.

Question 10.
When was the Indus Water Treaty signed?
Answer:
In 1960.

Question 11.
How much percent of total Indus water can be used by India according to Indus Water Treaty?
Answer:
20 per cent.

Question 12.
Name the headwater of the Ganga.
Answer:
The Bhagirathi.

Question 13.
Where does the Bhagirathi join the Alaknanda?
Answer:
The Bhagirathi joins the Alaknanda at Devprayag in Uttarakhand.

Question 14.
Name the major tributaries of the Ganga.
Answer:
The Yamuna, the Ghaghara, the Gandak and the Kosi.

Question 15.
Which are the main tributaries of the Ganga that come from the Peninsular uplands?
Answer:
The Chambal, the Betwa and the Son.

Question 16.
Which river flows for the longest length in India?
Answer:
The Ganga river flows (2500 km) for the largest length in India.

Question 17.
Which is the northernmost point of the Ganga Delta?
Answer:
Farakka in West Bengal.

Question 18.
Name the largest delta of the world.
Answer:
Sunderban delta.

Question 19.
Which rivers form the Sunderban delta?
Answer:
The Ganga and the Brahmaputra.

Question 20.
By which name is the river Brahmaputra known in Tibet?
Answer:
Tsang Po.

Question 21.
What is the Sunderban famous for?
Answer:
Sunderban is famous for being the home of the Royal Bengal tiger.

Question 22.
Name four rivers rising in the Western Ghats.
Answer:

1. Godavari,
2. Krishna,
3. Kaveri,
4. Tungabhadra.

Question 23.
In which hills does the Narmada rise?
Or
From which place does the Narmada rises?
Answer:
The Narmada rises in the Amarkantak Hills in Madhya Pradesh.

Question 24.
Name the waterfall formed by the river Narmada.
Answer:
The Dhuadhar Falls.

Question 25.
Which is the largest river of the Peninsular India?
Or
Which river is also known as the ‘Dakshin Ganga’?
Answer:
The Godavari.

Question 26.
Name the main lagoon lakes of India.
Answer:
Chilika, Pulicat and Kolleru Lakes.

Question 28.
Which is the largest freshwater lake in India?
Answer:
The Wular lake (Jammu and Kashmir).

Question 29.
Which river s known as a perennial river?
Or
What are perennial rivers?
Answer:
perennial rivers are those which have water throughout the year.

Question 30.
The Satluj is a tributary of which river?
Answer:
The Satluj is a tributary of Indus River joining in Pakistan.

Question 31.
Where is the Sambhar Lake located? What is its use?
Sambhar Lake istuated near Jaipur in Rajasthan. Its water is used to produce salt.

Question 32.
From where does the Kaveri River originate?
Answer:
The Kaveri River originates from the Brahmagiri range of the Western Ghats.

III. Short Answer Type Questions

Question 1.
Explain the drainage system of India through a line diagram.
Answer:

Question 2.
Mention any two features, of the Himalayan rivers.
Answer:
Two features of the Himalayan rivers are:

1. The Himalayan rivers have long courses from their source to the sea.
2. These rivers perform both erosional as well as depositional activities.

Question 3.
How do the Himalayan rivers perform erosional activities and form depositional features?
Answer:

1. In the upper course, rivers flow with great speed from higher to lower levels, causing erosion.
2. In the middle and the lower course, they carry lots of sediments like silt and sand. So, their speed slows down.
3. Besides, absence of slope in the lower course causes deposition and formation of various features.

Question 4.
Mention any two features of Peninsular rivers.
Answer:
Two features of Peninsular rivers are:

1. A large number of Peninsular rivers are seasonal, as their flow depends on rainfall.
2. Most of the Peninsular rivers originate in the Western Ghats and flow towards the Bay of Bengal.

Question 5.
Why do most of the Peninsular rivers drain into the Bay of Bengal?
Answer:
Most of the Peninsular rivers drain into the Bay of Bengal because:

1. The Eastern Ghats are lower than the Western Ghats. These are discontinuous, allowing the rivers easy passage to the Bay of Bengal.
2. The Deccan plateau has a gentle slope towards the East, which gives easier passage in that direction.

Question 6.
Distinguish between a tributary and a distributary.
Answer:
Difference between a tributary and a distributary:

Tributary	Distributary.
1. When a small stream joins a larger one, the smaller stream is known as the tributary of the larger one.	1. It is formed when a river is forced to break up into branches due to the deposition of sediments in its channel.
2. It can be found in any course of a river.	2. It is found in the lower course of a river.
3. It is useful for transportation and irrigation.	3. It provides a good network for transportation.
4. Example: Yamuna is a tributary of the Ganga.	4. Example: Padma is a distributary of the Ganga.

Question 7.
What do you know about Indus Water Treaty?
Answer:
Indus Water Treaty is a water-sharing treaty between India and Pakistan signed on 19th September, 1960. India can use only 20 percent of the total water carried by the Indus river system. This water is used for irrigation in Punjab, Haryana and Southern and the Western parts of Rajasthan.

Question 8.
Write a note on the Tapi basin.

1. The Tapi river originates from the sacred tank of Multai, in the Satpura ranges, in Betul district of Madhya Pradesh.
2. It is the second-largest, west-flowing river of Peninsular India.
3. The river flows in a rift valley parellel to the Narmada, but it is much shorter in length.
4. The Tapi forms an estuary before falling into the Gulf of Khambhat.
5. Its basin covers part of Madhya Pradesh, Gujarat and Maharashtra.

Question 9.
Write a short note on the Mahanadi basin.

1. The Mahanadi has its source in the highlands of Chhattisgarh.
2. The total length of the river is 860 kms.
3. It covers parts of Maharashtra, Chhattisgarh, Jharkhand and Odisha.
4. It drains into the Bay of Bengal.

Question 10.
Write a note on the Krishna basin.

1. The Krishna river rises near Mahabaleshwar in the Western Ghats.
2. It flows into the Bay of Bengal before forming a large delta.
3. Its length is about 1400 km.
4. The Bhima, the Tungabh ,fra, the Koyna and the Ghatprabha are its major tributanes.
5. It covers Maharashtr

Question 11.
What are the major causes of river pollution?
The major causes of river pollution are as follows:

1. The growing domestic, municipal, industrial and agricultural demand for water from rivers naturally affects the quality of water. As a result, more and more water is being drained out of the rivers, reducing their volume.
2. A heavy load of untreated sewage and industrial effluents are emptied into the rivers. This affects not only the quality of water, but also the self cleansing capacity of the river.
3. Increasing urbanisation and industrialisation is also responsible for increasing pollution level of many rivers.

Question 12.
Briefly explain the National-River Conservation Plan.
Answer:
The river cleaning programme in the country was initiated with the launching of the Ganga Action Plan in 1985. The Ganga Action Plan was expanded to cover other rivers, under the National River Conservation Plan launched in the year 1995. The objective of this programme is to improve the water quality of the rivers, which are the main water sources in the country, through the implementation of pollution control measures.

IV. Long Answer Type Questions

Question 1.
Describe the Indus river system.

1. The Indus river system comprises of the Indus river and its five main tributaries The Jhelum, The Chenab, The Satluj, The Ravi and The Beas.
2. The Indus originates from the glaciers of the Kailash Range in Western Tibet near Mansarovar Lake.
3. It flows west and north-westwards and enters Indian territory in Ladakh.
4. It flows through Ladakh, Baltistan and Gilgit and emerges from the mountains at Attock. Here, it is joined by the Kabul river from Afghanistan.
5. With a total length of 2,900 kilometres, the Indus is considered as one of the longest rivers of the world.
6. The sharing of water by India and Pakistan is regulated by the Indus Water Treaty signed by both the countries.
7. It flows south-westwards across Pakistan to reach the Arabian Sea, east of Karachi.

Question 2.
Write a note on the Ganga river system.
Answer:
The Ganga river system includes the Ganga and its tributaries like the Yamuna, the Gomti, the Ghaghara, the Gandak, the Ramganga, the Mahaganga, the Son and the Kosi, etc.

1. The Ganga rises in Garhwal Himalayas in Uttarakhand at an altitude of about 6,000 metres.
2. The river acquires its name after its head-streams, Alaknanda and Bhagirathi
   which unite at Devaprayag.
3. Flowing south-westwards, the Ganga comes out of Himalayas near Haridwar and enters the plains.
4. The total length of the Ganga is 2,500 km.
5. Beyond Farakka, it flows south-eastwards into Bangladesh where it is known as Padma.
6. Before falling into Bay of Bengal, the Padma joins the Brahmaputra which is known as Jamuna and Meghna there. The delta formed by these rivers is known as the Sunderban delta.

Question 3.
Write the main characteristics of the Brahmaputra river system.
Answer:

1. The river Brahmaputra originates from Chenayungdung glacier near Mansarovar lake in the Kailash range of the Himalayas.
2. With a total length of 2900 km, it is one of the longest rivers of the world.
3. Throughout the whole journey, the river passes through Tibet, India and Bangladesh. The river is known as Tsang Po in Tibet.
4. Towards the end of its journey in Tibet, it takes a southwards turn near Namcha Barwa and enters Arunachal Pradesh as Dihang river. Traversing round the stairs of Garo hills, it bends southwards and enters Bangladesh near Dhubri. In Bangladesh, it is known as the Jamuna.
5. At Goalundo the Jamuna joins the Ganga and is jointly known as the Padma. About 100 km further downstream, the Padma is joined by the Meghna. The river Meghna forms a very broad estuary before pouring into the Bay of Bengal.
6. The Brahmaputra has a braided channel for most of its passage through Assam.
7. With its tributaries like the Dihang, the Lohit, etc. discharging enormous quantities of water and silt, the river causes disastrous floods in every monsoon.

Question 4.
Explain the main features of the Narmada basin.
Answer:
The main features of the Narmada basin are as follows:

1. This river originates from Amarkantak Hills in Madhya Pradesh and flows westwards through a rift valley between the Vindhya range to the North and the Satpura range to the South.
2. The total length of the river from source to mouth is about 1,312 km.
3. The Marble Rocks near Jabalpur where the Narmada flows through a deep gorge and the ‘Dhuadar falls’ where the river plunges over steep rocks are some of the picturesque locations formed by the Narmada.
4. During much of its journey, the Narmada flows through the troughs confined by precipitous hills which do not permit any large tributaries.
5. The river forms an estuary before entering the Gulf of Khambhat. There are several islands in the estuary of the Narmada.The Aliabet is the largest island of the river.
6. The Narmada basin covers parts of Madhya Pradesh and Gujarat.

Question 5.
Explain the main features of the Godavari basin.
Answer:
The main features of the Godavari basin are as follows:

1. The Godavari is the longest river of the Peninsula.
2. It rises from the slopes of the Western Ghats in Nasik district of Maharashtra.
3. It is often referred as the Vridha Ganga or the Dakshin Ganga because of its large size and extent.
4. Its principal tributaries include the Parvara, the Purna, the Manjra, the Penganga, the Wainganga, the Wardha, the Pranhita, the Indravati, the Maner and the Sabari.
5. Its length is about 1500 km and the river drains into the Bay of Bengal.
6. The basin covers parts of Maharashtra, Madhya Pradesh, Odisha and Andhra Pradesh.

Question 6.
Write a note on the Kaveri basin.
Answer:

1. The Kaveri is the most reverred and sacred river of South India.
2. The source of this river lies at Talakaveri on the Brahmagiri range of hills in the Western Ghats.
3. Total length of the river is about 760 km.
4. It flows Eastwards and it reaches the Bay of Bengal south of Cuddalore in Tamil Nadu.
5. The river is unique because it receives rainfall during summer as well as winter.
6. Its main tributaries are Amravati, Bhavani, Hemavati and Kabini.
7. Its basin drains parts of Karnataka, Kerala and Tamil Nadu.

Question 7.
Write a detailed note on the lakes of India.
Or
Lakes are of great value to human beings: Explain the statement with three examples.
Answer:
A lake is the depression filled with water on the Earth’s surface and is entirely surrounded by land. Even after being such a large country, India has comparatively fewer natural lakes. Following are the major types of lakes found in India:
1. Freshwater Lakes:
Most of the freshwater lakes are in the Himalayan region. They are of glacial origin. A glacier is one of the important agents of erosion. The erosive process of glaciers can create U-shaped valleys, and the irregular surface of a glaciated lowland in which water can accumulate. Dal lake, Bhimtal, Nainital, Loktak and Barapani are some of the important freshwater lakes of India.

2. Lakes of Tectonic Origin:
Folding and faulting produce hollows in the Earth’s crust. These hollows may contain either salt or fresh water. The Wular Lake in Jammu and Kashmir is the result of tectonic activity.

3. Saltwater Lake:
Any lake that has no natural drainage outlet, either as a surface stream or as a sustained sub-surface flow, will become saline. The Sambhar in the desert region of Rajasthan is a saltwater lake, and its water is used for producing salt.

4. Man-made Lakes or Artificial Lakes:
In order to harness water for generation of hydel power, to provide irrigation water to crops and to provide drinking water to urban places, a number of lakes have been constructed. Gobind Sagar and Govind Ballabh Pant Sagar are the two most important man-made lakes of India.

Importance of Lakes:

1. Lakes help to regulate the flow of river. During heavy rainfall, they prevent flooding, and during the dry season, they help to maintain an even flow of water.
2. Lakes can also be used for developing hydropower.
3. They moderate the climate of the surroundings, maintain the aquatic ecosystem and enhance natural beauty.
4. They help to develop tourism and provide recreation.

Question 8.
Describe the role of rivers in the national economy.
Or
Rivers have been of fundamental importance throughout human history. Justify the statement.
Answer:
1. Development of Civilisations:
Rivers have played a vital role in the development of civilisations. Most of the ancient civilisations like Indus, Aztec, etc. developed around the rivers. Rivers have been of fundamental importance throughout human history. The banks of the rivers have witnessed great cultural and economic progress since ancient times. Water is a basic natural resource, essential for all human activities,

2. Development of Agriculture:
Rivers and their associated alluvial soil provide the most productive agricultural lands of the country. The Ganga-Brahmaputra basin has been formed by the two great rivers. Irrigation from rivers has been the backbone of the development of Indian agriculture.

3. Settlement:
Their valleys contains dense and concentrated settlements. Most of the large cities are located on river banks. The rivers not only provide us essential water supplies, but they also receive, dilute and transport wastes from settlements.

4. Industrial Development:
Industrial development has flourished along rivers as many industrial processes rely on water as a raw material, as a coolant and for the generation of hydro electricity.

5. Means of Transportation:
Rivers provide primary channels of inland transportation, not only directly in the form of navigable waterways, but also indirectly through their valleys, where roads, railway lines and other routes are built.

Question 1.
On an outline map of India mark the rivers and lakes of India.
Answer:
(a) The Himalayan River System: The Indus, The Ganga and The Satluj.
(b) The Peninsular River: The Narmada, The Tapi, The Kaveri, The Krishna, The Godavri, The Mahanadi

1. Lakes: Wular, Pulicat, Sambhar, Chilika, Vembanad, Kolleru.
2. Mountain Peaks: K2, Kanchanjunga, Anai Mudi
3. Coastal Plains: Konkan, Malabar, Coromandel & Northern Circar (Location & Labelling)

JAC Class 9 Social Science Important Questions

JAC Board Class 9th Social Science Important Questions Geography Chapter 2 Physical Features of India

I. Objective Type Questions

1. Which of the following represents the loftiest and one of the most rugged mountain barriers of the world?
(a) Aravali range
(b) Hindukush
(c) Himalayan mountains
(d) Kunlun mountains.
Answer:
(c) Himalayan mountains

2. The Himalayan mountains form and cover a distance of:
(a) 2510 km
(b) 1750 km
(c) 2400 km
(d) 2100 km.
Answer:
(c) 2400 km

3. Which of the following parts of India is agriculturally a productive part of India:
(a) Indian desert
(b) Northern plains
(c) Peninsular plateau
(d) Coastal plains.
Answer:
(b) Northern plains

4. Which of the following in the Brahmaputra river is the largest inhabited riverine island in the world?
(a) Andamans
(b) Lakshadweep
(c) Majuli
(d) Nicobar
Answer:
(c) Majuli

5. The Indian Desert lies towards the western margins of the :
(a) Aravalli Hills
(b) Shiwalik Hills
(c) Garo Hills
(d) Jointia Hills
Answer:
(a) Aravalli Hills

II. Very Short Answer Type Questions

Question 1.
How many physiographic divisions can India be divided into?
Answer:
India can be divided into the following physiographic divisions—

1. The Himalayan Mountains,
2. The Northern Plains,
3. The Peninsular Plateau,
4. The Indian Desert,
5. The Coastal Plains,
6. The Islands.

Question 2.
Name the highest mountain range of the world.
Answer:
The Himalayas.

Question 3.
Write the expansion of the Himalayas.
Answer:
The Himalayas mountain ranges run in a West-East direction from the Indus to the Brahmaputra.

Question 4.
Which is the northern-most range of the Himalayas?
Answer:
The Himadri.

Question 5.
Which range of Himalayas is the most continuous range?
Answer:
The Northern-most range which is also known as Himadri or inner Himalayas is the most continuous range of Himalayas.

Question 6.
Name the most rugged range of the Himalayas.
Answer:
The Himachal.

Question 7.
Name the sub-ranges of the Himachal Himalayas.
Answer:
The sub-ranges are named as (i) Pir Panjal, (ii) Dhauladhar and (iii) Mahabharat.

Question 8.
What is the variation in height in the Shiwalik mountain range ? .
Answer:
The height of the Shiwalik mountain range varies from 900 to 1100 metres.

Question 9.
What are Shiwalik ranges made of?
Answer:
Shiwalik ranges are composed of unconsolidated sediments brought down by rivers from the main Himalayan ranges.

Question 10.
Name the longitudinal divisions of the Himalayas.
Answer:

1. Punjab Himalayas,
2. Kumaon Himalayas,
3. Nepal Himalayas,
4. Assam Himalayas.

Question 11.
By which rivers the northern-most boundary of the Himalayas formed?
Answer:
The Brahmaputra.

Question 12.
By which name are the mountains spread along the eastern boundary of India- known?
Answer:
Purvachal.

Question 13.
Name the hills running through the Purvachal.
Answer:

1. Patkai,
2. Naga,
3. Mizo,
4. Manipur Hills.

Question 14.
Name the river system that forms the northern plains.
Answer:
The Northern plains are formed by the Indus, the Ganga and the Brahmaputra river systems.

Question 15.
Which is the largest riverine island in the world?
Answer:
Majuli, in the Brahmaputra river, is the largest riverine island in the world.

Question 16.
What do you mean by the word ‘Doab’?
Answer:
‘Doab’ is made up of two words ‘do’, meaning ‘two’ and ‘ab’, meaning ‘water’. Thus, ‘Doab’ means a part between two rivers.

Question 17.
Into how many sections are the northern plains divided?
Answer:

1. The Punjab Plain,
2. The Ganga Plain,
3. The Brahmaputra Plain.

Question 18.
What is Bhabar?
Answer:
The plains formed by the rivers, after descending from the mountains deposit pebbles in a narrow belt lying parallel to the slopes of the Shiwaliks are known as Bhabar.

Question 19.
What is Terai?
To the south of Bhabar belt, the streams and rivers re-emerge and create a wet, swampy and marshy region known as Terai.

Question 20.
The peninsular plateau can be divided into how many divisions?
Answer:
The peninsular plateau can be divided into two divisions

1. The Central Highlands,
2. Deccan Plateau.

Question 21.
How are the Northern Plains and Peninsular Plateau formed?
Answer:
The Northern Plains are formed by the alluvial deposits, while the Peninsular Plateau is formed by igneous and metamorphic rocks.

Question 22.
Which is the ancient landmass of India?
Answer:
Peninsular region.

Question 23.
Name the North-East extensions of the Deccan Plateau.

1. Meghalaya,
2. Karbi-Anglong Plateau,
3. North Cachar hills.

Question 24.
Which is the highest peak in the Western Ghats?
Answer:
Anai Mudi is the highest peak in Western Ghats. Its height is 2695 metres.

Question 25.
Which is the highest peak in the Eastern Ghats?
Answer:
Mahendragiri is the highest peak in the Eastern Ghats. Its height is 1501 metres.

Question 26.
Name the hills that lie at the junction of Eastern and Western Ghats?
Answer:
The Nilgiri Hills in Tamil Nadu lie at the junction of Eastern and Western Ghats.

Question 27.
Which part of the plateau contains black soil of volcanic origin?
Answer:
The Western part of plateau known as the Deccan trap contains black soil of volcanic origin.

Question 28.
What is the Deccan Trap?
Answer:
The black soil area of the western peninsular plateau is known as Deccan Trap.

Question 29.
Where are the Aravali Hills located?
Answer:
The Aravali Hills lie on the Western and North-Western margins of the peninsular plateau.

Question 30.
Which desert is located on the western margin of the Aravali Hills?
Answer:
The Indian Desert (Thar Desert) lies towards the western margins of the Aravali Hills.

Question 31.
Which Indian coastal part is called Konkan?
Answer:
The nor’ hern part of the Indian Western Coast is known as Konkan.

Question 32.
What is the southern part of the Western Coastal Plains known as?
Answer:
The southern part of the Western Costal Plains is known as Malabar.

Question 33.
Name two sections of the eastern Coastal Strips.

1. The Northern Circar,
2. The Coromandel Coast.

Question 34.
Where is the Chilika Lake located? Why is it famous?
Answer:
The Chilika Lake lies in the state of Odisha, to the South of the Mahanadi delta. It is the largest salt-water lake in India.

Question 35.
By which name were the Lakshadweep islands known earlier?
Answer:
Earlier, the Lakshadweep islands were known as Laccadive, Minicoy and Amindive.

Question 36.
Where is the administrative headquarters of Lakshadeweep situated?
Answer:
Kavaratti island.

Question 37.
Where is India’s only active volcano located?
India’s only active volcano is found on Barren island in Andaman and Nicobar group of Islands.

Question 38.
What are Corals?
Answer:
Coral polyps are short-lived microscopic organisms which live in colonies in shallow, mudfree and warm water.

Question 39.
What makes up the habitat in which Coral polyps flourish?
Answer:
Coral polyps flourish in a habitat consisting of shallow warm water which does not have mud. This kind of habitat is found in Lakshadweep.

Question 40.
Where is the Great Barrier Reef located?
Answer:
Australia.

Question 41.
What are Barchans?
Answer:
Barchans are crescent-shaped dunes which cover larger area of deserts. They are found in the Indian desert, mainly in Jaisalmer and and near Indo-Pak boundary.

III. Short Answer Type Questions

Question 1.
Write any four features of the Himalayan mountains.
Answer:
Following are the four features of the Himalayan mountains:

1. The Himalayas are a geologically young and structurally fold mountains.
2. The Himalayas act like a natural wall to keep the fertile Indo-Gangetic plains safe from the cold winds coming from Central Asia.
3. The Himalayas are source to perennial rivers like the Indus, the Ganga and the Brahmaputra.
4. The Himalayas are lofty and impassable natural barriers on the Northern border of India.

Question 2.
Why are the Himalayas called young fold mountains?
Answer:
Himalayas are called young fold mountains because:

1. These are young in age compared to several other mountains.
2. They are made of at least three major folds or parallel ranges, e.g. Himadri, Himachal and Shiwaliks.
3. They are characterised by high peaks, gorges, I-shaped valleys, glaciers and steep slopes, which indicate that the mountains are still developing.

Question 3.
Describe the Himadri.
Answer:
The Himadri or the Great or the Inner Himalayas:

1. These are the Northern-most ranges of the Himalayas.
2. The average elevation of the Himadri is more than 6,000 m above the sea level.
3. They contain some of the world’s highest peaks, like, Mt. Everest (8,848 m) in Nepal “,nd Kanchenjunga (8,598 m) in India. Nanga Parbat (8,126 m) and Nanda Devi t ,817m) are the other two important Himalayan peaks in India.
4. The G igotri and the Yamunotri glaciers which gave birth to the Ganga and the Ya mna rivers respectively are located here.

Question 4.
Describe the Middle Himalayas.
Answer:
The Himachal or the Middle Himalayas:

1. Mountains lying to the South of the Himadri are known as Middle or lesser Himalayas or the Himachal.
2. They have an average height of 3,700 m to 4,500 m above the sea level and extend over a width of 50 km.
3. The ranges are mainly composed of highly compressed and altered rocks.
4. All the important hill stations such as Dalhousie, Dharmshala, Shimla Mussoorie, Nainital and Darjeeling lie in this range.
5. pir Panjal, Dhaula Dhar and Mahabharat ranges are its most important range:

Question 5.
Describe the Shiwaliks.
Answer:
The Shiwaliks or the Outer Himalayas:

1. It is the Southern-most range of the Himalayas.
2. The average altitude of Shiwalik-range varies between 900 m and 1,100 m above the sea level and extend over a width of 10-50 km.
3. This range is made of unconsolidated material such as mud, silt, and soft rocks and is prone to earthquake and landslides.
4. Some narrow valleys are found between Shiwaliks and Himachal. They are called ‘duns’. Example Dehradun.

Question 6.
Describe the divisions of the Himalayas from west to east along with Purvachal hills.
Answer:
On the basis of the location, Himalayas can be divided as follows:
1. Western Himalayas (Punjab Himalayas):
The Western section lying between the Indus and the Sutlej is known as the Punjab Himalayas. It covers a large part of Jammu and Kashmir and a part of Himachal Pradesh. They are made up of Ladakh, Zaskar and Pir Panjal ranges.

2. Central Himalayas (Kumaon Himalayas):
The section between the Sutlej and the Kali is known as Kumaon Himalayas. They extend through the state of Uttarakhand in India, and Nepal.

3. Eastern Himalayas (Nepal Himalayas):
The section between the Kali and the Teesta is known as the Nepal Himalayas.

4. Assam Himalayas (Purvachal):
The section between Teesta and Dihang (Tsang po) is known as the Assam Himalayas. They are made up of Patkai, Naga and Mizo Hills. These hills are mainly composed of strong sandstones.

Question 7.
State any three differences-between the Himadri range and Shiwalik range. The differences between Himadri and Shiwalik ranges are:

Features	Himadri Range	Shiwalik Range
1. Location	This is the Northern-most and inner most range of Himalayas.	This is the outermost range of Himalayas.
2. Composition	The core of this part of Himalayas is composed of granite.	This range is composed of uncon-solidated sediment brought down by rivers from the main Himalayan ranges.
3. Altitude	The average altitude of this range is 6000 metres.	The average altitude varies from 900 to 1100 metres.

Question 8.
Make a comparison between the Himachal Himalayas and the Shiwalik based on the following:

1. Composition,
2. Altitude.

Answer:
The comparison between the Himachal Himalayas and the Shiwaliks on the given basis is as follows:

Mountain Range	Composition	Altitude
1. Himachal Himalayas	It is the most rugged mountain system of the Himalayas. It is composed of highly compressed and altered rocks.	It lies south of the Himadri with height varying from 3700 to 4500 metres.
2. Shiwaliks	The composition of Shiwalik is of unconsolidated sediments i.e. thick gravel and alluvium brought down by the Himalayan rivers.	This is the outermost range of the Himalayas with height varying between 900 and 1100 metres.
Mountain Range	Composition	Altitude

Question 9.
Describe the formation of plains.
Answer:

1. To the south of the Himalayas, a basin or depression was formed.
2. It was gradually filled with the alluvium brought by the rivers from north and South.
3. The North Indian Plain was thus followed between the Himalayas and the Peninsular Plateau.

Question 10.
Describe three broad sections of the Northern Plains.
Answer:
1. Punjab Plains:
The Western part of the Northern Plains is referred to as the Punjab plains. It is formed by the river Indus and its tributaries. The larger part of this plain lies in Pakistan. This section of the plain is dominated by the doabs.

2. Ganga Plain:
The Ganga plain extends between Ghaggar and Teesta rivers. It spreads over the states of North India Haryana, Delhi, Uttar Pradesh and Bihar.

3. Brahmaputra Plain:
This plain lies in Assam and partly in Jharkhand and West Bengal.

Question 11.
Describe the divisions of the Northern Plains on the basis of the differences in the relief.
Or
Explain the diverse relief features of the Northen Plains.
Answer:
On the basis of the differences in the relief, the plain is divided into four sections :
1. Bhabar:
It is a narrow belt covered with pebbles lying along the foot of the Shiwaliks from the Indus to the Teesta. They are laid down by numerous streams descending down the hills. This belt is about 8 to 16 km in width.

2. Terai:
It is wet and marshy. It has a thick forest and a variety of wildlife.

3. Bhangar:
It is composed of older alluvium. It is formed higher up in the plains at river terraces. It is less fertile as compared to Khadar.

4. Khadar:
It is composed of newer alluvium. It is formed in the lower levels in the Plains near the river. It is very fertile.

Question 12.
Discuss the importance of the Northern Plains.
Answer:
The importance of the Northern Plains:

1. With their fertile alluvial soils, flat surface, slow moving perennial rivers and favourable climate, the Great Plains of North India are of great economic and social significance.
2. The fertile soil and ample water resources have made these plains a rich agricultural land. These plains are known as the granaries of India.
3. The plains have a good network of roads and railways which has led to large scale industrialisation of the region.
4. As the region has sufficient employment opportunities, so the density of population is high. More than 50% of the total population of India lives in these plains.
5. The Northern plains is the site where the ancient civilization of Mohenjo da and Harappa developed

Question 13.
Write the main characteristics of the Central Highland.
Answer:
The Central Highlands of the Peninsular plateau lie to the north of the river Narmada.

1. These are flanked by the Aravallis in the north-west, and consists of Malwa plateau, Bundelkhand and Baghelkhand plateau and the Chhota Nagpur plateau bound by Rajmahal Hills in the North-East. Its southern boundary is formed by the Vindhyas.
2. The Central Highlands are made of hard, igneous and metamorphic rocks.
3. The Central Highlands are drained by the Southern tributaries of Ganga and

Question 14.
Write a short note on‘Corals’.
Or
What are the types of corals?
Or
How are coral reefs formed? Describe the main features of the islands group which are of coral origin.
Answer:
Corals are short-lived microscopic organisms which live in colonies. They flourish in shallow, mud-free and warm waters. They secrete calcium carbonate. The coral secretion and their skeletons form coral deposits as reefs.
These roofs are mainly of three kinds:

1. Barrier Reef,
2. Fringing Reef,
3. Atolls.

Atolls are circular or horse shoe-shaped coral reefs. In India, Lakshadweep Islands are of coral origin. They cover a small area of 32 sq. km. Karavatti is the administrative headquarters of Lakshadweep. This island group has great diversity of flora and fauna. The uninhabited Pitti island has a bird sanctuary.

IV. Long Answer Type Questions

Question 1.
Name the three longitudinal divisions of the Himalayas. Write the main features of each.
Or
Describe the major divisions of the Himalayas from North to South.
Or
Name the three parallel ranges of Himalayas. Write the major characteristics of each.
Answer:
The longitudinal divisions/parallel ranges/major divisions of the Himalayas are as follows:
1. Himadri

1. The northern most range is called the Great or Inner Himalayas.
2. It is the highest range with an average height of 6000 m.
3. It contains all the prominent Himalayan peaks.
4. The folds of Great Himalayas are assymetrical in nature. The core of this part of the Himalayas is composed of granite.

2. Himachal

1. It is known as the Lesser Himalayas.
2. It lies to the south of Himachal and forms the most rugges mountain system.
3. The altitude varies between 3700 and 4500 metres and width is 50 km.
4. This range consists of the famous valley of Kashmir and the Kangra Valley and Kullu Valley in Himanchal Pradesh.

3. Shiwaliks

1. The outermost range of the Himalayas is known as the Shiwaliks.
2. The Shiwaliks extend over a width of 10 to 50 km and have an altitude varying between 900 to 1100 m.
3. This range is composed of unconsolidated sediments brought down by rivers from the main Himalayan ranges located further North.
4. The valleys are covered with thick gravel and alluvium.

Question 2.
What are the uses of the Himalayas to India?
Answer:
Uses of the Himalayas to India: The Himalayas are beneficial for India in the following ways:

1. The Himalayas are a physical wall protecting the Indian sub-continent from the rest of Asia. In the past, they stood as indestructible barriers against the aggressors from the North. This helped India to maintain its identity.
2. The Himalayas act as a climatic barrier for the Indian sub-continent. They shield India from the cold, bleak winds coming from the Central Asia.
3. The Himalayas also compel rain-bearing monsoon winds to shed bulk of their moisture in the Northern mountains and Northern plains.
4. The Himalayas are snow-covered mountains having many glaciers also. These serve as a source of big perennnial rivers. These rivers have made the Indo-Gangetic plains very fertile. They are important for irrigation, navigation and generation of hydroelectric power.
5. The Himalayas are also home to rich and varied flora and fauna. They are also a storehouse of numerous medicinal herbs.

Question 3.
Describe the Deccan Plateau.
Answer:

1. The part of the Peninsular plateau extending to south of the Vindhyas is called the Deccan plateau.
2. It is triangular in shape. It is at its widest in the North and goes on tapering as we move towards the South.
3. The Satpura ranges and Mahadeo Hills form its northern edge.
4. It is flanked by the Western Ghats in the West and the Eastern Ghats on the east.
5. The Western Ghats and the Eastern Ghats meet to form Nilgiri Mountains along the border of Karnataka and Tamil Nadu.
6. The North-Western part of the Deccan plateau is made up of volcanic lava and is known for its black or regur soil.
7. Unlike the Western Ghats, the Eastern Ghats are discontinuous and broken by long rivers.
8. This plateau is drained by east-flowing rivers – Mahanadi, Godavari, Krishna and Kaveri.

Question 4.
Write the main characteristics of the Western and Eastern Coastal Plains.
Answer:
The main characteristics of the Eastern Coastal Plains are:

1. This plain is located between the Eastern Ghats and the coast of Bay of Bengal.
2. It is a comparatively broader plain with a average width of around 80-100 km.
3. In the Northern part, it is referred to as the Northern Gircar, while the Southern part is known as the Coromandel Coast.
4. Large rivers such as the Mahanadi, the Godavari, the Krishna and the Kaveri have formed extensive deltas in this coast.
5. Lake Chilika is an important feature of this coast.
6. Tuticorin, Chennai, Paradweep, Vishakhapatnam are the major ports of this region.

Question 5.
Write a detailed note on the Lakshadweep and the Andaman and Nicobar islands of India.
The Island Groups of India: The Lakshadweep, and Andaman and Nicobar Islands are the main island groups of India.
The Lakshadweep Islands:

1. The Lakshadweep is located 300 km west coast of Kerala in the Arabian Sea.
2. The Lakshadweep Islands are a group of 36 islands.
3. The Lakshadweep Islands were formerly known as Laccadive, Minicoy and Amindive Islands. They were renamed as Lakshadweep in 1973.
4. The Lakshadweep is the smallest Union Territory in terms of area.
5. Kavaratti Island is the headquarters of Lakshadweep Islands.

The Andaman and Nicobar Islands:

1. The Andaman and Nicobar Islands group is located in the Bay of Bengal.
2. The Southernmost point of India, called the Indira Point, is located in the Great Nicobar Island.
3. The Andaman and Nicobar Islands consist of as many as 200 islands.
4. The Nicobar group consists of 19 islands which are fairly large and more in number than the Lakshadweep Islands.
5. India’s only active volcano erupted on Barren Island in the Andamans on 10th April, 1991.
   The Andaman and Nicobar alongwith the Lakshadweep Islands are known for their great diversity of flora and fauna.

Question 6.
“Physiographic divisions of India are complementary to each other”. Comment the above statement.
Answer:
The Indian sub-continent consists of three structural components:

1. The Great Mountain Wall of the North,
2. The Northern Plains and
3. The Great Peninsular Plateau.

The three geographical physical divisions of India are complementary to each other and have contributed to the growth of the Indian sub-continent as an independent economic entity. The Great Mountain Wall of the North in the form of Himalayas, has provided shelter to the sub-continent against aggression. The snow covering these lofty mountains are big reservoirs of water.

The Northern Plains are sea-level fertile plains. They are well-watered by rains and possess very good irrigation facilities. They are known as the granary of India and support a very large population of India. The Great Peninsular Plateau is the stable block. It is the storehouse of various minerals like iron ore, manganese, mica, bauxite and coal. Rice1 cotton and spices are also produced in large quantities in these regions. The partially-enclosed character of the sub-continent has helped it to evolve a culture of its own.

Question 1.
Physical Features of India
1. Mountain Ranges: The Karakoram, the Zaskar, the Shivalik, the Aravali, the Vindhya, the Satpura, Western & Eastern Ghats

2. Mountain Peaks: K2, Kanchanjunga, Anai Mudi

3. Coastal Plains: Konkan, Malabar, Coromandel & Northern Circar (Location & Labelling)
Answer:

JAC Class 9 Social Science Important Questions

JAC Board Class 9th Social Science Notes  Geography Chapter 2 Socialism in Europe and the Russian Revolution

→ The Age of Social Change

• The French Revolution opened up the possibility of creating a dramatic change in the way in which society was structured.
• The social and political changes that took place all over the European continent can be traced to the French Revolution.
• But not everyone in Europe wanted a complete transformation of the society. Some were conservatives, while others were ‘liberals’, and ‘radicals’.
• Through the revolution in Russia, socialism became one of the most significant and powerful ideas to shape the society in the twentieth century.

→ Liberals, Radical sand Conservatives

• Liberals:
  • These leaders (group of people) wanted a nation which tolerated all religions,
  • Opposed the uncontrolled power of dynastic rulers,
  • Wanted to safeguard the rights of individuals against governments,
  • They argued for a representative, elected parliamentary government, subject to laws -interpreted by a well-trained judiciary that was independent of rulers and officials.
• Radicals:
  • They wanted a nation in which government was based on the majority of a country’s population,
  • They supported women suffragette movements,
  • They opposed the privileges of landowners and wealthy factory owners,
  • They disliked the concentration of property in the hands of a few people.
• Conservatives: They accepted that some changes were inevitable but believed that the past had to be respected and changes had to be brought through a gradual process.

→  Industrial Society and Social Change

• It was the beginning of the industrial revolution. Men, women and children were pushed into the factories for low wages.
• Liberals and radicals who were the factory owners felt that efforts must be encouraged so that benefits of industrialisation may be passed on to the workers.

→ The Coming of Socialism in Europe

• Some socialists believed in the ideas of cooperatives, while others demanded that governments encourage cooperatives.
• These cooperatives were to be the associations of people who produced goods together and divide the profits according to the work done by members. Karl Marx and Friedrich Engels believed that a socialist society would free the workers from capitalism. This would be a communist society.

→ Support for Socialism

• Workers in Germany and England began forming associations to fight for better living conditions.
• They set up funds for members in distress. They wanted reduction of working hours and right to vote.
• By 1905, socialists and trade unionists formed ‘Labour Party’ in Britain and ‘Socialist Party’ in France.
• However, till 1914, socialists did not succeed in forming a government in Europe.

→ The Russian Revolution

• The government in Russia was taken over by the socialists through the October Revolution of 1917.
• The fall of monarchy in February 1917 in Russia and the events of the October Revolution are normally called the Russian Revolution.→ The Russian Tsars had built a vast empire which included part of Poland, Finland, Latvia, Lithuania, Estonia, Ukraine and Belarus.

→ The Russian Empire in 1914

• The major religion of Russia was the orthodox Christianity which grew out the Greek Orthodox Church.
• The empire also included Catholics, Protestants, Muslims and Buddhists.
• At the beginning of the twentieth century, 85 per cent of the Russian population were agriculturists.

→ Economy and Society

• Russia was a major exporter of foodgrains. Russian cultivators produced for the market and for their own needs.
• In Russia, prominent industrial areas were St. Petersburg and Moscow.
• In 1890s, many factories started due to the expansion of the railway network and there was an increase in foreign investment in industries.
• Most industries were private property of industrialists.
• Government supervised large factories to ensure minimum wages and limited hours of work.
• Workers were divided as social groups or by skin. Workers were sometimes united to participate in strikes.
• In the countryside, peasants cultivated most of the land but the nobility, the crown and the orthodox church owned large properties.
• Russian peasants wanted the land of the nobles to be given to them. They refused to pay rent and even murdered the landlords.

→ Socialism in Russia

• All political parties were illegal in Russia before 1914.
• The Russian Social Democratic Workers Party was founded in 1898 by socialists who respected Marx’s ideas.
• Socialists were active in the countryside through the late nineteenth century. They formed the Socialist Revolutionary Party in 1900.
• This party struggled for peasants’ rights and demanded that the property belonging to nobles be transferred to peasants.
• The Social Democratic Party was far divided into two wings, the Bolsheviks and the Mensheviks.
• Vladimir Lenin led the Bolshevik group.

→ A Turbulent Time: The 1905 Revolution

• In the beginning of the 20th century, Russia was still an autocracy and the Tsar was not subject to parliament.
• The year 1904 was bad for Russian workers because of increase in prices of essential goods. Moreover, the real wages declined by 20 percent.
• In 1905, on one Sunday, the procession of workers led by Father Gapon reached the Winter Palace. It was attacked by the police and the Cossacks.
• Over 100 workers were killed and about 300 wounded. This incident, known as Bloody Sunday, started a series of events that came to known as the 1905 Revolution.
• Strike took place all over the country. During the 1905 Revolution, the Tsar allowed the creation of elected consultative parliament or Duma.
• The Tsar dismissed the first Duma within 75 days and the re-elected second Duma within 3 months.
• The Tsar did not want any questioning of his supreme authority.

→ The First World War and the Russian Empire

• In 1914, the First World War started between two European alliances—Germany, Austria and Turkey (the central powers) and France, Britain and Russia (later, Italy and Romania also).
• Russian armies lost badly in Germany and Austria between 1914 and 1916. There were over 7 million Russian casualties by 1917.
• The war had a severe impact on industry. Large supplies of grain were sent to feed the vast army. Food scarcity became common, which sometimes led to riots in bread shops.

→  The February Revolution in Petrograd

• In the winter of 1917, conditions in the capital, Petrograd, were grim.
• In February 1917, a lockout of a factory in Petrograd led to many strikes and demonstrations.
• The Duma was suspended, which ultimately lead to the resign of the Tsar.
• Soviet leaders and Duma leaders formed a provisional movement to-run the country.

→ After February

• In April 1917, the Bolshevik leader Lenin returned from exile and made three demands known as the ‘April Theses’.
• Throughout the summer, the workers’ movement spread.
• Peasants seized land between July and September 1917.

→ The Revolution of October 1917

• The conflict between the provisional government and the Bolsheviks grew.
• On 16 October, 1917, Lenin persuaded the petrograd Soviet and the Bolshevik party to agree to a socialist seizure of power.
• The uprising began on 24th October, 1917.
• There was he ivy fighting between pro-government troops and the Bolsheviks. By December 1917 the Bolsheviks controlled the Moscow-Petrograd area.

→ What changed after October

• The Bolsheviks nationalised banks and industries in November, 1917.
• They declared land as social property and allowed peasants to seize the land of nobles.
• The Bolshevik party was renamed as the Russian Communist Party (Bolshevik).
• In November 1917, the Bolsheviks conducted the elections to the Constituent Assembly, but they failed to gain majority support.
• In January 1918, the Assembly rejected Bolshevik measures and Lenin dismissed the Assembly.
• The Bolsheviks became the only party to participate in the elections to the all Russian Congress of Soviets which was the parliament of the country.

→ The Civil War

• When the Bolsheviks ordered land redistribution, the Russian army began to break up. Soldiers, mostly peasants, wished to go home for the redistribution and deserted.
• The pro Tsarists (the whites) and the socialists (the greens) fought a civil war with the Bolsheviks (the reds) during 1918 and 1919.
• Most non-Russian nationalists were given political autonomy in the USSR created by the Bolsheviks in 1922.

→ Making a Socialist Society

• During the civil war, the Bolsheviks kept industries and banks nationalised.
• They permitted peasants to cultivate the seized land to show collective work.
• A process of centralised planning was introduced and officials made five year plans for the improvement of the economy.
• Rapid construction brought poor working conditions for workers.
• An extended schooling system was developed and arrangements were made for factory workers and peasants to enter universities.
• Creches were established in factories for the children of women workers.

→  Stalinism and Collectivisation

• The period of the early planned economy was linked to the disasters of the collectivisation of agriculture.
• By 1927-1928, the towns in Soviet Russia were facing an acute problem of grain supplies.
• Stalin, who headed the party after the death of Lenin, introduced firm emergency measures.
• He introduced collective farming to reduce the shortage of grains in the country. However, bad harvests during 1930-1933 led to famines with over 4 million people dying.
• Those who criticised Stalin’s policies were charged with conspiracy against socialism.
• By 1939, over 2 million people were imprisoned or sent to labour camps.

→ The Global Influence of Russian Revolution and the USSR

• The impact of the Russian Revolution was felt globally with communist parties being formed in many countries.
• By the time of the outbreak of the Second World War, the USSR had given socialism a global face and world stature. The USSR became a great power.
• Its industries and agriculture had developed and the poor were being fed, But it had denied the essential freedom to its citizens and adopted repressive policies for its developmental projects.
• By the end of the 20th century, the international reputation of the USSR as a socialist country had declined, though it was recognised that socialist ideals still enjoyed respect among its people.
• In each country, the ideas of socialism were re-thought in a variety of different ways.
• Many Indian writers like Jawaharlal Nehru and Rabindranath Tagore were impressed by the Russian Revolution and its ideals.

→ Important Dates and Related Events

• 1850-1880: Debates over socialism in Russia.
• 1898: Formation of the Russian Social Democratic Workers Party.
• 1905: The Bloody Sunday incident and the Revolution of 1905. Formation of Labour Party in Britain and Socialist Party in France.
• 1914: The First World War started.
• 1917: Abdication of the Tsar on 2nd March; Bolshevik uprising in Petrograd on 24th October.
• 1918-20: The Civil War in Russia.
• 1919: Formation of Comintern.
• 1929 : Beginning of Collectivisation in farming.

→ Conservatives: Group of people who believed that the past had to be respected and change had to be brought through a slow process.

→ Liberals: Group of people who opposed the uncontrolled power of dynastic rulers.

→ Radicals: Those who favoured the formation of a government based on the majority of a country’s population.

→ Democrats: Group of people who believed in universal adult Franchise.

→ Suffragette movement: A movement to provide women the right to vote.

→ Jadidists: Muslim reformers within the Russian empire.

→ Real Wage: Reflects the quantities of goods which the wages will actually buy.

→ Duma: Russian Parliament which was created in 1905 for the first time.

→ April Theses: A set of three demands made by Vladimir Lenin in April 1917  War be brought to a close, land be transferred to the peasants and banks be nationalised.

→ Autonomy: The right of a person, an organization, a region etc. to govern his/her/ its own affairs.

→ Nomadism: Lifestyle of those who do not live at one place but move from one place to another to earn their living.

→ Kulaks: The name for well-to-do peasants.

→ Deported: Forcibly removed from one’s own country.

→ Exiled: Forced to live away from one’s own country.

→ Capitalism: It is an economic system under which the means of production are in the hands of private individual or individuals.

→ Socialism: It is an economic system under which the means of production are controlled by the society.

→ Bolsheviks: The majority group of Russian Social Democratic Workers Party
formed in 1898. This group led by Lenin was based on the ideology of Karl Marx and Friedrich Engels. They believed that party should be disciplined and should control the number and quality of its members.

→ Mensheviks: The minority group of Russian Social Democratic Workers Party formed in 1898. They thought that the party should be open to all.

→ Russian Steam Roller: The imperial Russian army came to be known as the Russian steam roller. It was the largest armed force in the world. When this army shifted its loyalty and began supporting the revolutionaries, Tsarist power collapsed.

→ Tsar: The title of the Emperor of Russia.

→ Giuseppe Mazzini: An Italian nationalist politician, journalist and activist who worked to set up a nation where all citizens would have equal rights. He was the spearhead of the Italian revolutionary movement.

→ Robert Owen: A leading English manufacturer, sought to build a co-operative community called New Harmony in Indiana (U.S.A.).

→ Karl Marx: Gave birth to the idea of socialism.

→ Friedrich Engels: Worked along with Karl Marx to give shape to the idea of Socialism.

→ Vladimir Lenin: Led the Bolshevik group to a successful revolution in Russia.

→ Father Gapon: Led the procession of workers that marched to the Winter Palace in 1904.

→ Tsarina Alexandra: Wife of Tsar Nicholas II.

→ Rasputin: Tsarina’s close confidant who had a strong influence on her.

→ Leon Trotskii: Headed the Military Revolutionary Committee appointed by the Soviet.

→ Kerenskii: Prime Minister of Russia in October, 1917.

→ Stalin: Headed the ruling party in Russia after the death of Lenin.

JAC Class 9 Social Science Notes

JAC Board Class 9th Social Science Notes History Chapter 1 The French Revolution

• The French Revolution started on 14th July, 1789 with the storming of the fortress prison- the Bastille, hated by everybody, because it stood for the despotic power of the King. The fortress was demolished.
• The beginning of chain of events started by the middle-class affected and shook the lower class and led to the execution of king in France followed by a revolt against monarchy.

→ Introduction

• The French revolution is a landmark in the history of European continent and the world.
• This revolution ended the monarchical system in France.
• The slogan of French Revolution “liberty, equality and fraternity” became important ideas of the new era.

→ French Society During the Late Eighteenth Century

• In 1774, Louis XVI of Bourbon family became the king of France.
• Due to long years of war and maintenance of an extravagant court of the palace of Versailles, he got an empty treasury.
• King Louis also helped thirteen American colonies to gain their indendence from Britain.
• This war added more than 1 billion livres (unit of currency in France) to the already
  existing debt of more than 2 billion livres. .
• To meet the expenses like maintaining army, court, running government offices or universities etc., the Franch government was forced to increase the taxes.
• French society in the 18th century was divided into three estates and only members of the third estate paid taxes.
• The three estates of France at that time were First Estate (the clergy), Second estate
  (the nobility), Third Estate (businessmen, merchants, court officials, lawyers, peasants, artisans, ladies, labour, servants etc.).

→ The Struggle to Survive

• During 1715-1789, the population of France increased rapidly which led to rapid increase in demand for foodgrains.
• Insufficient production increased the price of bread. But the wages of the workers did not keep pace with the rise in prices.
• Situation became worse when bad weather conditions reduced the harvest. This condition created subsistence crisis.

→ Emergence of Middle Class

• In the 18th century, a new social group emerged which was known as the middle class. They had become rich by expansion of overseas trade and manufacturing goods.
• This group believed that no group of society should be privileged by birth.
• Philosophers like John Locke, Jean Jacques Rousseau and Montesquieu considered that the middle class was solely responsible for the revolution.
• They spread the ideas of freedom, equal laws and opportunities for all.

→ The Outbreak of the Revolution

• On 5th May, 1789 Louis XVI called for an assembly of the Estates General to pass the proposals for new taxes.
• First, second and third estates sent their representatives.
• Peasants, artisans and women were denied entry to the assembly but they sent their demands and grievances through their representatives.
• The members of the third estate demanded that voting should be conducted by taking assembly as a whole. But King Louis XVI rejected this proposal and members of the third estate walked out of the assembly in protest.
• On 20th June, 1789, the representatives of the third estate assembled in the hall of an indoor tennis court in Versailles.
• They declared themselves a National Assembly.
• They also swore to draft a new constitution for France that would limit the powers of the monarch.
• The representatives of the third estate were led by Mirabeau and Abbe Sieyes.
• Due to severe winter, harvest was severely affected in France, which led to the increase in prices of essential commodities.
• After spending many hours in long queues at the bakery, crowds of angry women raided the shops.
• On 14th July, 1789, an agitated craud stormed and destroyeed the Bastille.
• Seeing the power of the revolt, King Louis XVI recognised the proposal of National Assembly that his powers would be checked by a constitution.
• On the night of 4th August, 1789. France passed the law for abolishing the feudal system of obligations and taxes.

→ France Becomes a Constitutional Monarchy

• The National Assembly completed the draft of the constitution in 1791. Its main objective was to limit the powers of the monarch.
• Under the new constitution, the laws were to be made by the National Assembly.
• The constitution began with a declaration of the right of man and citizen.

→  France Abolishes Moranchy and Becomes a Republic

• The National Assembly declared war against Prussia and Austria in April, 1792.
• While men were busy fighting at the front, women had to earn a living and look after their families.
• A large segment of the population was convinced to carry the revolution further, as the constitution of 1791 gave political rights only to the richer section.
• On 10th August, 1792, the Jacobins attacked the palace of the Tuileries with a large number of Parisians.
• They killed the King’s guards and held the king himself as hostage for several hours.
• New election were held and all the men above 21 years of age were allowed to vote.
• The newly elected assembly, the Convention, abolished monarchy on 21st September, 1792 and declared France as a‘Republic’.
• King Louis XVI was sentenced to death by a court on the charge of treason.

→ The Reign of Terror

• The period from 1793 to 1794 is reffered to as the ‘Reign of Terror’ in France.
• Robespierre followed a policy of severe control and punishment.
• Due to his harsh policies, his supporters left him in the end. He was finally convicted by a court and guillotined in July 1794.

→ A Directory Rules France

• After the fall of the Jacobin government, the wealthier middle classes seized power.
• The new constitution was introduced which denied the right to vote to non-propertied society.
• It provided for two elected legislative councils. These councils appointed a Directory, an executive made up of five members.
• The political in stability of the Directory paved the way for the rise of a military dictator- Napoleon Bonaparte.

→  Did Women have a Revolution?

• Women played a very significant role in the French Revolution.
• Women in France were disappointed with the constitution of 1791, as it reduced them to passive citizens who had no
  political rights.
• They demanded political rights, viz., right to vote to be elected to the Assembly and to hold political office.
• Finally in 1946, French women won the right to vote.

→ The Abolition of Slavery

• The most important social reform made by the Jacobin government was to abolish slavery in French colonies.
• After long debates, the National Convention passed a law in 1794. It declared slavery illegal and freed all the slaves in French overseas colonies.
• After two years, Napoleon reintroduced slavery.
• Finally, slavery was abolished in the French colonies in 1848.

→ The Revolution arid Everyday Life

• After 1789, many changes took place in the lives of man, woman, and children in France.
• One important law that come into effect after the storming of the Bastille in the sum¬mer of 1789 was the abolition of censorship.
• With the abolition of censorship and the Declaration of the Right of man and citizen, freedom of speech and expression became a natural right of people.

→ Conclusion

• In 1804, Nepoleon Bonaparte crowned himself as the Emperor of France.
• He conquered the neighbouring European countries, dispossed dynasties and created kingdoms where he placed members of his family.
• He introduced many laws such as the protection of private property and a uniform system of weights and measures provided by the decimal system.
• Napoleon was defeated at the Battle of Waterloo in 1815.
• The ideas of liberty and democratic rights were the most important legacy of the French Revolution.
• Tipu Sultan and Raja Ram Mohan Roy are the two examples of Indian individuals who were inspired by the ideas of the French Revolution.

→ Important Dates and Related Events

• 1774: Louis XVI of the Bourbon family ascended the throne of France and faced empty treasury and growing discontent within the society of the Old Regime.
• 1789: Convocation of Estates General, Third Estate formed National Assembly, the Bastille was demolished, peasants revolted in the countryside, Assembly passed a decree abolishing the feudal system of obligations and taxes.
• 1719: Constitution framed to limit the powers of the king and to guarantee basic rights to all human beings.
• 1792- 93: France became a republic nation. Overthrow of the Jdcobin republic, a Directory which ruled France.
• 1804: Napoleon became the emperor of France, annexed a large part of Europe.
• 1815: Napoleon was defeated at Waterloo.
• 1848: Abolition of slavery in French colonies.
• 1945: Women in France won the right to vote.

→ Revolution: As a historial process, revolution refers to a movement, often violent, to overthrow an old regime and effect complete change in the fundamental institution of society.

→ Livre: Unit of currency in France, discontinued in 1794.

→ Feudal System: This system existed in the Middle Ages in Europe In this system, people received land and protection from a Lord for which they worked and fought.

→ Clergy: Group of persons invested with special functions in the Church.

→ Tithe: A tax levied by the Church, comprising one-tenth of the agricultural produce.

→ Taille: Tax to be paid directly to the state by the members of the Third Instate.

→ Subsistence Crisis: An extreme situation where the basic means of livelihood are endangered.

→ Anonymous: One whose name remains unknown.

→ Manor: An estate consisting of the Lord’s lands and his mansion.

→ Chateau: Castle or stately residence belonging to a king or a nobleman.

→ Marseillaise: The National Anthem of France.

→ Convent: Building belonging to a community devoted to a religious life.

→ Sans-culottes: Jacobins came to be known as the Sans-culottes, literally meaning ‘those without knee breeches’. Sans-culottes men wore in addition the red cap that symbolised liberty.

→ Convention: The newly elected assembly of France in 1792 was called the convention.

→ Republic: A form of government in which the people elect the government including the head of the government.

→ Aristocracy: The highest class in some societies.

→ Guillotine: A machine or a device consisting of two poles and a blade with which a person is beheaded. It was named after Dr. Guillotin who invented it.

→ Directory: It was an executive made up of five members.

→ Treason: Betrayal of one’s country or government.

→ Negroes: A term used for the indigenous people of Africa, south of the Sahara. It is a derogatory term, not in common use any longer.

→ Emancipation: The act of freeing.

→ Militia: An organization that operates like an army but whose members are not professional soldiers.

→ Bastille: A fort in the eastern part of Paris, used as a state prison.

→ Despot: Someone, such as a ruler, who uses power in a cruel and unfair way.

→ Sous: Subordinate (a French prefix).

→ Souvenir: A thing that is kept as a reminder of a person, place or event.

→ Jacobin: A political club of people which was formed to discuss the government policies and plan their own forms of action.

→ Louis XVI: He ascended the throne of France in 1774 and ruled over France during the French Revolution.

→ Rousseau: He was a great philosopher and writer of the book ‘The Social Contract’.

→ Montesquieu: A great philosopher. He wrote the book ‘The Spirit of the Laws’.

→ Abbe Sieyes: He was a priest who led National Assembly which was created in 1789. He wrote an influential pamphlet named “What is the Third Estate”.

→ Mirabeau: He also led the National Assembly. He was born in a noble family. He brought out a journal and delivered powerful speeches.

→ Maximilien Robespierre: Political leader of Jacobins who ruled over France from 1793 to 1794.

JAC Class 9 Social Science Notes

JAC Board Class 9th Social Science Important Questions Economics Chapter 4 Food Security in India

I. Objective Type Questions

1. What is meant by food security?
(a) Availability of food to poor people
(b) Availability of food to rich people
(c) Availability of food to all sections of people
(d) None of these
Answer:
(c) Availability of food to all sections of people

2. Which two food crops have been intensively cultivated in the Green Revolution in India,
(a) Wheat and maize
(b) Wheat and rice
(c) Wheat and mustard
(d) None of these
Answer:
(b) Wheat and rice

3. Buffer stock is created to:
(a) Maintain minimum support price
(b) Distribute food grains in the deficit areas
(c) Run the food-for-work programme
(d) All of the above
Answer:
(b) Distribute food grains in the deficit areas

4. Integrated child development service was introduced in:
(a) 1976
(b) 1978
(c) 1985
(d) 1975
Answer:
(d) 1975

5. In which state of India is the famous cooperative AMUL located:
(a) Rajasthan
(b) Gujarat
(c) Haryana
(d) Tamil Nadu
Answer:
(b) Gujarat

II. Very Short Answer Type Questions

Question 1.
What do you mean by Food Security?
Answer:
Food security means availability, accessibility, and affordability of food to all people at all times.

Question 2.
Who are more vulnerable to food insecurity?
Answer:
The poor are more vulnerable to food insecurity.

Question 3.
What are the three dimensions of food security?
Answer:
The three dimensions of food security are:

1. Availability of food,
2. Accessibility of food,
3. Affordability of food.

Question 4.
When did the great famine of Bengal occur in India?
Answer:
1943.

Question 5.
Who were affected the most by the famine of Bengal:
Answer:

1. The agricultural labourers,
2. Fishermen,
3. Transport workers,
4. Casual labourers.

Question 6.
Name any two states of India that have faced acute food scarcity?
Answer:

1. Bihar
2. West Bengal.

Question 7.
Write two dimensions of hunger.
Answer:

1. Chronic hunger,
2. Seasonal hunger.

Question 8.
Who suffers from chronic hunger?
Answer:
Poor people suffer from chronic hunger.

Question 9.
Which type of hunger is prevalent in rural areas?
Answer:
Seasonal hunger is prevalent in rural areas.

Question 10.
What are the two components of food security System of India?
Answer:
The two components of food security system of India are:

1. Buffer Stock,
2.  Public Distribution System.

Question 11.
What is Buffer stock?
Answer:
Buffer stock is the stock of food grains (wheat and rice) procured by the government through the food corporation of India.

Question 12.
What is PDS?
Answer:
Public Distribution System refers to a system through which the food procured by the FCI is distributed among the poor through government-regulated ration shops by using ration cards.

Question 13.
FCI stands for what?
Answer:
FCI stands for Food Corporation of India.

Question 14.
Why are food-for-work schemes security implemented?
Answer:
To ensure food and nutritional to people living below poverty level.

Question 15.
What is the need of fair price shop?
Answer:
To ensure distribution of food grains to even the poorest of poor at lower than market price. ’

Question 16.
Why does the government give subsidy?
Answer:
To make sure that price of essential commodities should be within the reach of the poorest people.

Question 17.
Which social group is the target of the Annapurna Scheme?
Answer:
The Annapurna Scheme is for indigent senior citizens who are not financially sup-ported by anybody.

Question 18.
Name any two food cooperatives in India.
Answer:

1. Amul,
2. Mother Dairy.

III. Short Answer Type Questions

Question 1.
What are the three dimensions of food security?
Or
Explain the dimensions of food security?
Answer:
Food security has the following dimensions:
1. Availability of food:
It means food production within the country, food imports and the previous years stock stocked in government granaries.

2. Accessibility:
It means food is within reach of every person.

3. Affordability:
It means an individual has enough money to buy sufficient, safe and nutritious food to meet his dietary need.

Question 2.
What was declared in World Food Summit, 1995?
Answer:
The World Food Summit, 1995 declared, “Food security at the individual, household, regional, national and global levels exists when all people, at all times, have physical and economic access to sufficient, safe and nutritious food to meet their dietary needs and food preferences for an active and healthy life.”

Question 3.
How is food security affected during a calamity?
Answer:
Following are the ways in which food security gets affected dring a natural calamity.

1. Due to natural calamity, say drought, total product ion of food grains decreases.
2. Low food production leads to shortage of food in the affected areas.
3. Due to shortage of food, prices go up. At such high prices, many people cannot afford to buy food.
4. If such a calamity happens in a very widespread area or is stretched over a longer time period, it may cause a situation of starvation.
5. A massive starvation might take the turn of famine.

Question 4.
What is a famine? How are people affected by a famine?
Answer:
A famine is characterised by widespread deaths due to starvation and epidemics caused by forced use of contaminated water or decaying food and loss of body re-sistance due to weakening from starvation. This occurs due to a severe shortage of . food resulting from crop failure or other calamity, which increases the price of food, making it unaffordable to the weaker sections of the population.

Question 5.
Why is food security needed in India?
Answer:
The poorest section of the society might be food insecure most of the times while persons above the poverty line might also be food insecure when the country faces a national disaster like earthquake, drought, flood, tsunami, famine, etc. Even today, there are places like Kalahandi and Kashipur in Odisha where famine-like conditions have been existing for many years and where some starvation deaths have also been reported.

Starvation deaths have also been reported in Baran district of Rajasthan, Palamau district of Jharkhand and many other remote areas during the recent years.
Therefore, food security is needed in India to ensure food at all times.

Question 6.
Explain the impact of green revolution on food security in India.
Answer:
Following is the impact of green revolution on food security.

1. It made India self sufficient in food production.
2. After green revolution no food scarcity was felt even during adverse weather conditions.
3. With the increase in per hectare crop production as well as extension of agri-cultural activities in disadvantaged areas, it ensured regular food supply.

Question 7.
What is the need of maintaining buffer stock?
Answer:
Maintenance of Buffer stock is required for the following reasons:

1. It ensures continuous supply of commodities to fair-price shops.
2. It is the stock of country which can be used during any calamity.
3. It helps farmers to sell their surplus crop at a reasonable price.

Question 8.
Write a brief note on the national food security Act, 2013.
Answer:
The national food security Act, 2013 provides for food and nutritional security life at affordable prices and enables people to live their life with dignity. Under this act 75 percent of the rural population and 50 percent of the urban population have been categorised as eligible households for food security aid.

Question 9.
What are the three kinds of ration cards?
Answer:
The three kinds of ration cards are as follows:
1. Antyodaya Cards:
Antyodaya cards for the poorest of the poor.

2. BPL Cards:
Below Poverty Line (BPL) cards for those who are below poverty line.

3. APL Cards:
Above Poverty Line (APL) cards for all others.

Question 10.
Explain any two types of PDS.
Answer:
Two types of PDS are as follows:
1. Revamped Public Distribution System (RPDS):
It was introduced in 1992 in 1,700 blocks in the country. The launch of RPDS was to provide the benefits of PDS to remote and backward areas.

2. Targetted Public Distribution System (TPDS): TPDS was introduced in June 1997 to adopt the principle of targetting the “poor in all areas”. It was for the first time that a differential price policy was adopted for poors and non-poor.

Question 11.
List any three characteristics of public distribution system.
Answer:
Following are the three characteristics of public distribution system.

1. It procures grain from FCl and distributes it among the poorer sections of society.
2. There are almost 5.5 lakh shops under this system reaching the farthest comer of country.
3. It distributes food grains through ration card.

Question 12.
How do fair-price shops help food distribution in India?
Answer:
There are more than 5.5 lakh fair-price shops to help food distribution in India. They provide food stuff like wheat, rice, sugar, and kerosene oil on a monthly basis to ration card holders at lower than the market rates. These rates depend on the category of family, whether they are APL, BPL or Antyodaya families. This enables the poorer sections of society to have food security.

Question 13.
what is MSP? How does it help in food security?
Answer:
The Food Corporation of India (FCI) purchases wheat and rice for the government from the farmers of surplus states at pre-announced prices. This price is called minimum support price (MSP). It helps in ensuring food security in several ways:

1. For farmers it gives surety to their crop price and encourages them to grow certain crops.
2. For government, it ensures that they have enough crop to buy for their buffer stock and public welfare programmes.
3. For public, this ensures that prices of a commodity will be stable and within their reach.

IV. Long Answer Type Questions

Question 1.
Describe the measures adopted by the government of India to achieve self-sufficiency in food grains;
Answer:
Following measures were adopted by government of India to achieve self-sufficiency in food grains.
1. India adopted a new strategy in agriculture, which resulted in green revolution especially in the production of wheat and rice.

2. The government of India has made the provision of buffer stock meant to dis-tribute food grains in the deficit areas and among the poorer strata of society at a price lower than the market price. This also helps to resolve the problem of shortage of food during adverse weather conditions or during the periods of calamity.

3. The government has made provision of Public Distribution System (PDS). This is meant for distribution of food grains trough government regulated ration shops (Fair price shops) among the poorer sections of the society.

4. The government has also initiated other food intervention programmes like Integrated Child Development Services (ICDS), Food-for-Work programme (FFW), Mid-Day meals, Antyodaya Anna Yojana (AAY) etc.

Question 2.
Explain two special schemes launched by the government in 2000.
Answer:
In 2000, two special schemes were launched viz. Antyodaya Anna Yojana and the Annapurna Scheme with special target groups of ‘poorest of the poor’ and ‘indigent senior citizens’, respectively. The functioning of these two schemes was linked with the existing network of the PDS.

1. Antyodaya Anna Yojana (AAY):
This scheme was launched in December 2000. Under the scheme one crore of the poorest among the BPL families covered under the Targetted Public Distribution System were identified. Poor families were identified by the respective state rural development departments through a Below Poverty Line (BPL) survey.

Twenty-five kilograms of food grains were made available to each eligible family at a highly subsidised rate of ₹ 2 per kg for wheat and ₹ 3 per kg for rice. This quantity has been enhanced from 25 to 35 kgs with effect from April 2002. The scheme has been further expanded twice to additional 50 lakh BPL families in June 2003 and in August 2004. With this increase, 2 crore families have been covered under the AAY.

2. Annapurna Scheme:
Annapurna Scheme (APS) was introduced in 2000 as Public Distribution Scheme to support indigent senior citizens with 10 kilograms of food grains free of cost.

JAC Class 9 Social Science Important Questions

JAC Board Class 9th Social Science Important Questions Economics Chapter 3 Poverty as a Challenge

I. Objective Type Questions

1. In India, approximately how many people live in poverty?
(a) 30 crore
(b) 27 crore
(c) 20.2 core
(d) 88.3 crore.
Answer:
(b) 27 crore

2. In rural areas, average calories required person per day are
(a) 2100 calories
(b) 3000 calories
(c) 2400 calories
(d) 1700 calories.
Answer:
(c) 2400 calories

3. The average number of calories required per person per day in urban areas of India are
(a) 3000 calories
(b) 2400 calories
(c) 2900 calories
(d) 2100 calories.
Answer:
(d) 2100 calories.

4. Which of the following states of India has the highest poverty ratio?
(a) Odisha
(b) Bihar
(c) Uttar Pradesh
(d) Assam
Answer:
(b) Bihar

5. When was the Rural Employment Generation programme (REGP) launched?
(a) In 1992
(b) In 2005
(c) In 1993
(d) In 1995
Answer:
(d) In 1995

II. Very Short Answer Type Questions

Question 1.
What is Poverty?
Answer:
Poverty refers to a situation in which a person is not able to get the minimum basic necessities of life, e.g. food, clothing, shelter, etc. for his or her sustenance.

Question 2.
What is one of the biggest challenges of independant India?
Answer:
One of the biggest challenges of independent India is to bring millions of its people out of abject poverty.

Question 3.
What did Mahatma Gandhi always emphasize?
Answer:
Mahatma Gandhi always emphasized that India would be truly independent only when the poorest of its people become free of human suffering.

Question 4.
Name some social indicators through which poverty is seen.
Answer:

1. Illiteracy,
2. Lack of general resistance due to malnutrition,
3. Lack of access to healthcare,
4. Lack of job opportunities,
5. Lack of access to safe drinking water, sanitation, etc.

Question 5.
Define vulnerability to poverty?
Answer:
Vulnerability to poverty is a measure which describes the greater probability of certain communities or individuals becoming or remaining poor in the coming years.

Question 6.
What is poverty line?
Answer:
Poverty line is an imaginary line used by any country to determine its poverty level.

Question 7.
When is a person considered poor?
Answer:
A person is considered poor if his or her income or consumption level falls below a given “minimum level” necessary to fulfil the basic needs.

Question 8.
What is considered when determining the poverty line in India?
Answer:
While determining the poverty line in India a minimum level of food requirement, clothing, footwear, fuel and light, educational and medical requirement, etc. are determined for subsistence.

Question 9.
Why is the calorie requirement of people higher in rural areas as compared to urban areas?
Answer:
The calorie requirement of people in rural areas in higher because the rural people are engaged in more physical labour than people in urban areas.

Question 10.
What is the accepted average calorie requirement in India?
Answer:
The accepted average calorie requirement in India is 2400 calories per person per day in rural areas and 2100 calories per person per day in urban areas.

Question 11.
Which agency conducts the periodical sample surveys for estimating the poverty line in India?
Or
Which organization in India carries the periodical survey for the estimation of poverty?
Answer:
Poverty line is estimated periodically by the National Sample Survey Organisation (NSSO) by conducting sample surveys, generally after every 5 years.

Question 12.
What is the full form of NSSO?
Answer:
The full form of NSSO is National Sample Survey Organisation.

Question 13.
Which are the most Vulnerable groups of poverty?
Answer:
Scheduled castes, scheduled tribes, rural agricultural labour households and urban casual labour households are vulnerable to poverty.

Question 14.
What was the percentage of people living below the poverty line in 2011-12 in India.
Answer:
In 2011-12, 22 per cent of the population was living below the poverty line in India.

Question 15.
Name the two poorest states in India.
Answer:

1. Bihar
2. Odisha.

Question 16.
Name five states having the highest percentage of people below poverty line.
Answer:

1. Bihar,
2. Odisha,
3. Assam,
4. Madhya Pradesh,
5. Uttar Pradesh.

Question 17.
Name five states having the least percentage of people below poverty line.
Answer:

1. Kerala,
2. Himachal Pradesh,
3. Punjab,
4. Andhra Pradesh,
5. Haryana.

Question 18.
How have states like Punjab and Haryana been successful in reducing poverty?
Answer:
States like Punjab and Haryama have been successful in reducing poverty with high agricultural growth rates.

Question 19.
By what method has the state of West Bergal reduced poverty?
Answer:
Proper implementation of land reforms have helped to reduce poverty in West Bengal.

Question 20.
Why has Kerala succeeded in reducing poverty?
Answer:
By focusing more on human resource development.

Question 21.
Which standard is used by the World Bank for the estimation of poverty line?
Answer:
The World Bank uses a uniform standard for poverty line, which is the minimum income of the equivalent of $ 1.90 per person per day.

Question 22.
Why is World Bank important in estimating poverty line?
Answer:
Different countries have different poverty lines as per their existing level of devel¬opment. The World Bank compares countries by presenting a uniform standard for poverty line which is acceptable to all countries.

Question 23.
List some countries having the highest percentage of people below poverty line.
Answer:

1. Nigeria,
2. Bangladesh,
3. India,
4. Pakistan,
5. China.

Question 24.
Name any two causes of poverty in India.
Answer:

1. Low level of economic development during British rule,
2. Inefficient administration.

Question 25.
The current anti-poverty strategy of the government is based broadly on two planks Mention these.
Or
The present anti-poverty strategy of the Government of India is broadly based on what factors?
Answer:
The present anti-poverty strategy of the Government of India is broadly based on two planks :

1. Promotion of economic growth
2. targetted anti-poverty programmes.

Question 26.
Name any two anti-poverty programs.
Answer:

1. Prime Minister Rozgar Yojana (PMRY)
2. Swarna Jayanti Gram Swarozgar Yojana (SGSY).

Question 27.
Write the full form of MNREGA.
Answer:
Full form of MNREGA is Mahatma Gandhi National Rural Employment Guarantee Act.

Question 28.
Which act guarantees minimum 100 days employment per person per year in rural areas?
Answer:
Mahatma Gandhi National Rural Employment Guarantee Act.

Question 29.
When was MNREGA passed?
Answer:
MNREGA was passed in September 2005.

Question 30.
Which scheme has been started to create self-employment opportunities for educated unemployed youth in rural areas?
Answer:
Prime Minister Rozgar Yojana (PMRY).

III. Short Answer Type Questions

Question 1.
How is poverty seen by social scientists?
Answer:
Poverty as seen by social scientists in the following way:

1. Poverty relates to the level of income and consumption.
2. Apart from this, poverty is looked at through other social indicators like illiteracy level, lack of general resistance due to malnutrition, lack of access to healthcare, lack of job opportunities, lack of access to safe drinking weather, sanitation, etc.

Question 2.
What is social exclusion? Explain with an example.
Answer:
Social exclusion is a process through which individuals or groups are excluded from facilities, benefits and opportunities that others enjoy.
Example: The caste system in India in which people belonging to certain castes are” excluded from equal opportunities.

Question 3.
Does poverty line vary with time and place?
Answer:
Yes, poverty line may vary with time and place. A person is considered poor, if his or her income or consumption level falls below a given minimum level that is necessary to satisfy basic needs. What is necessary to satisfy basic needs is different at different times and in different countries. Therefore, poverty line may vary with time and place.

Example: A person not having a car in the USA may be considered poor but in India owning a car is still considered a luxury.

Question 4.
What are the calories and rupees fixed for rural and urban areas for measuring the poverty line?
Answer:
The poverty line fixed for the rural and urban areas in India in the year 2012 was ₹ 186 and ₹ 100 per person per day for urban and rural areas, respectively. It is higher in urban areas because of higher prices of many essential commodities in urban centres. The accepted average calories requirement in India is 2400 calories in rural areas and 2100 in urban areas. It is high in the rural areas because of more physical work done by the rural people.

Question 5.
Briefly explain the principle measures taken in Punjab, Haryana, Kerala and West Bengal to reduce poverty.
Answer:
1. Punjab and Haryana:
These states have succeeded in reducing poverty due to high agricultural growth.

2. Kerala:
It has succeeded in reducing poverty by investing on human resource development. Kerala has the highest literacy rate in the country.

3. West Bengal:
In West Bengal land reform measures have helped in reducing poverty.

Question 6.
How are sociocultural and economic factors responsible for poverty in India?
Answer:
1. Sociocultural causes of poverty: In order to fulfil social obligations and observe religious ceremonies, most people in India including the very poor spend a lot of money. This takes them back to poverty.

2. Economic Causes of Poverty: Small farmers need money to buy agricultural inputs like seeds, fertilizer, pesticides etc. Since poor people hardly have any savings, they borrow money and when there is crop failure they become indebted. This takes pusher them into poverty.

Question 7.
Which circumstances compelled the government to start targetted anti-poverty programmes?
Answer:
Following circumstances compelled the government to start targetted anti-poverty programmes:

1. Since the poor are not able of take advantage of the opportunities created for them, the growth in the agriculture sector is much below expectations.
2. In agriculture sector, a large number of poor people are unemployed for most part of the year, therefore, the need for targetted anti-poverty programmes was felt.

Question 8.
Give the main feature of Rural Employment Generation Programme.
Answer:
Rural Employment Generation Programme (REGP) was launched in 1995. The main features of REGP are:

1. Creation of self-employment opportunities in rural areas and towns.
2. Creation of 25 lakh near Jobs under the tenth five-year plan.

Question 9.
Why were the poverty alleviation programmes not successful in most parts of India?
Answer:
The poverty alleviation programmes were not successful in most parts of India for these reasons:

1. Lack of proper implementation and right targetting.
2. There has been a lot of overlapping of schemes.
3. Every year a huge number is added to the population pool of the country. This makes schemes ineffective.
4. Despite good intentions, the benefits of these schemes do not fully reach to the deserving poor.

IV. Long Answer Type Questions

Question 1.
Analyse poverty on the basis of social exclusion and vulnerability.
Answer:
The analysis of poverty is based on social exclusion and vulnerability as follows:
1. Social exclusion:
Social exclusion means living in a poor surroundings with poor people, excluded from enjoying social equality of better off people in better surrounding. In India, Caste system is based on social exclusion. People belonging to certain castes were prevented from enjoying equal facilities, benefits and opportunities. This caused more poverty than that caused by lower income.

2. Vulnerability:
Vulnerability to poverty is a measure, which describes the greater probability of certain communities becoming or remaining poor in the coming years, e.g. members of a backward caste or individuals like widows, physically handicapped persons and so on. Vulnerability is determined by various options available to different communities in terms of assets, education, job, healthcare, etc. and analyses their ability to face various risks like natural disasters.

Question 2.
Explain the main features of the global poverty scenario.
Answer:
Following are the main features of global poverty scenario:

1. The priducortion of people in developing countries living in extreme economic poverty defined by the World Bank as living on less than $ 1.90 per day has come down from from 36 per cent in 1990 to 10 per cent in 2015.
2. Poverty J.eclined substantially in China and South-East Asian countries as a result ox rapid economic growth and massive investment in human resource development.
3. In the countries of South Asia: India, Pakistan, Sri Lanka, Nepal, Bangladesh, Bhutan, the decline has also been rapid-34 per cent in 2005 to 16.2 per cent in 2013.
4. In sub-Saharan Africa, poverty in fact declined from 51 per cent in 2005 to 41 per cent in 2005.
5. In Latin America, the ratio of poverty has also declined from 10 per cent in 2005 to 4 per cent in 2015.
6. Poverty has also resurfaced in some of the former socialist countries like Russia, where officially it was non-existent earlier.

Question 3.
“There is a strong link between economic growth and poverty reduction” Explain the statement.
Answer:
It is clear that there is a strong link between economic growth and poverty reduction. The higher growth rates have helped significantly in the reduction of poverty. In the 1980s, India’s economic growth was one of the fastest in the world. The growth rate rose from the average of about 3.5% a year in the 1970s to about 6 percent during the 1980s and 1990s.

Economic growth widens opportunities and provides the resources needed to invest in human development. This also encourages people to send their children, including the girl child, to schools in the hope of getting better economic returns from investing in education. Thus, it can be concluded that there is a strong link between economic growth and poverty reduction.

Question 4.
Describe any four poverty alleviation programmes currently being implemented in India.
Or
Describe any four anti-poverty programmes.
Answer:
Following are the four major poverty alleviation programmes implemented by the
Government of India.
1. Mahatma Gandhi National Rural Employment Guarantee Act (MNREGA)

1. This act was passed in September 2005.
2. This act provides 100 days assured employment every year to every rural household.
3. It also aims at sustainable development by addressing the cause of drought, deforestation and soil erosion.
4. One-third of the proposed jobs have been reserved for women.
5. The scheme provided employment to 220 crore mandays of employment to 4.78 crore households.
6. The range of wage rate for different states and union territories lies in between ₹ 281 per day to ₹ 168 per day.

2. Prime Minister Rozgar Yojana (PMRY) .

1. This programme was launched in 1993.
2. It is aimed at providing self-employment opportunities to educated unemployed youth in the rural and small towns.
3. Under this programme, scheduled banks provide loans at a lower interest rate to start small businesses and set up industries.

3. Rural Employment Generation Programme (REGP)

1. This programme was launched in 1995.
2. The aim of the programme is to provide self-employment opportunities to educated unemployed youth in the rural areas and small towns.
3. A target for creating 25 Lakh new Jobs has been set for this programme under the Tenth five-year plan.

4. Pradhan Mantri Gramodaya Yojana (PMGY)

1. This programme was launched in 2000.
2. Under this programme, the Central Government provides additional assistance to the State Government for improving basic services in the village.
3. The major basic services covered under this programme are primary health, primary education, rural shelter, rural drinking water and rural electrification.

Question 5.
Review the future challenges in the context of poverty in India.
Answer:
Despite many plans to reduce poverty in India, the main reason for its partial success is lack of proper implementation and proper targetting. The benefits of these schemes could not be passed on to the poor, even after a good deal of sincere efforts have been made. Poverty has come down due to the implementation of many schemes, but the biggest problem of completely eradicating poverty is still standing before us.

Wide disparities in poverty are visible between rural and urban areas and among . different states. Certain social and economic groups are more vulnerable to poverty. Further, poverty should include not only the factor of adequate amount of food, but also other factors like education, healthcare, shelter, job security, gender equality, dignity and so on. These give as the true concept of human poverty.Poverty reduction is expected to be more effective in next 10-15 years.

In addition to anti-poverty measures, government should focus on the following to reduce poverty:

1. Higher economic growth
2. Universal free elementary education,
3. Decrease in population
4. Empowerment of women and weaker sections.

The official definition of poverty, however, captures only a limited part of what poverty really means to people. It is about a “minimum subsistence level of living rather than a “reasonable” level of living. Many scholars advocate that we must broaden the concept into human poverty. A large number of people many have been able to feed themselves.

But do they have education? or shelter? or healthcare? or job security? or self confidence? Are they free from caste and gender discrimination? Is the practice of child labour still common? World wide experience shows that with development, the definition of poverty is always a moving target.

Hopefully, we will be able to provide the minimum “necessary” in terms of only income to all people by the end of the next decade. But the target will move on for many of the bigger challenges that still remain: Providing healthcare, education and job security for all, and achieving gender equality, and dignity for the poor.

JAC Class 9 Social Science Important Questions

Jharkhand Board JAC Class 9 Maths Important Questions Chapter 12 हीरोन का सूत्र Important Questions and Answers.

JAC Board Class 9th Maths Important Questions Chapter 12 हीरोन का सूत्र

प्रश्न 1.
एक त्रिभुज की भुजाएँ 40 सेमी, 70 सेमी एवं 90 सेमी हैं । त्रिभुज का क्षेत्रफल होगा :
(A) 600\(\sqrt{5}\) वर्ग सेमी
(B) 500\(\sqrt{6}\) वर्ग सेमी
(C) 482\(\sqrt{5}\) वर्ग सेमी
(D) 60\(\sqrt{5}\) वर्ग सेमी
हल :
यहाँ a = 40 सेमी, b = 70 सेमी, c = 90 सेमी
अर्द्ध-परिमाप (s) = \(\frac{a+b+c}{2}=\frac{40+70+90}{2}\)
= \(\frac {200}{2}\) = 100 सेमी

प्रश्न 2.
एक समबाहु त्रिभुज की भुजा 6 सेमी है। त्रिभुज का क्षेत्रफल होगा :
(A) 6\(\sqrt{3}\) वर्ग सेमी
(B) 9\(\sqrt{3}\) वर्ग सेमी
(C) 16\(\sqrt{3}\) वर्ग सेमी
(D) 3\(\sqrt{3}\) वर्ग सेमी
हल :
हम जानते हैं कि
समबाहु त्रिभुज का क्षेत्रफल = \(\frac{a^2 \sqrt{3}}{4}\), जहाँ ‘a’ भुजा है।
= \(\frac{(6)^2 \sqrt{3}}{4}=\frac{36 \sqrt{3}}{4}\)
= 9\(\sqrt{3}\) वर्ग सेमी
अतः विकल्प (B) सही है।

प्रश्न 3.
एक समकोण त्रिभुज का क्षेत्रफल 36 वर्ग सेमी है एवं आधार 9 सेमी है, तो इसके लम्ब की लम्बाई होगी :
(A) 8 सेमी
(B) 4 सेमी
(C) 16 सेमी
(D) 32 सेमी
हल :
त्रिभुज का क्षेत्रफल = \(\frac {1}{2}\) × आधार × लम्ब
⇒ 36 = \(\frac {1}{2}\) × 9 × लम्ब
⇒ 36 × 2 = 9 × लम्ब
∴ लम्ब = \(\frac{36 \times 2}{9}\)
= 4 × 2 = 8 सेमी
अत: सही विकल्प (A) है।

प्रश्न 4.
एक समान्तर चतुर्भुज का क्षेत्रफल 96 सेमी² एवं ऊँचाई 8 सेमी हो तो आधार होगा :
(A) 9.7 सेमी
(B) 8 सेमी
(C) 14 सेमी
(D) 12 सेमी
हल :
समान्तर चतुर्भुज का क्षेत्रपफल आधार ऊँचाई = आधार × ऊँचाई
∴ आधार = समान्तर चतुर्भुज का क्षेत्रफल / ऊँचाई
= \(\frac {96}{8}\) = 12 सेमी
अतः सही विकल्प (D) है।

प्रश्न 5.
यदि किसी समद्विबाहु त्रिभुज की समान भुजाएँ 6 सेमी एवं अन्य भुजा 8 सेमी हो, तो इसका क्षेत्रफल होगा :
(A) 8\(\sqrt{5}\) वर्ग सेमी
(B) 5\(\sqrt{8}\) वर्ग सेमी
(C) 3\(\sqrt{55}\) वर्ग सेमी
(D) 3\(\sqrt{8}\) वर्ग सेमी
हल :
समद्विबाहु त्रिभुज का क्षेत्रफल
= \(\frac {b}{4}\)\(\sqrt{4 a^2-b^2}\)
जहाँ a समान भुजा एवं b अन्य भुजा है।
समद्विबाहु त्रिभुज का क्षेत्रफल
= \(\frac {8}{4}\)\(\sqrt{4(6)^2-(8)^2}\)
= \(\frac {8}{4}\)\(\sqrt{4 \times 36-64}\)
= 2\(\sqrt{144-64}\)
= 2\(\sqrt{80}\) = 2\(\sqrt{4 \times 4 \times 5}\)
= 2 × 4 × \(\sqrt{5}\) = 8\(\sqrt{5}\) वर्ग सेमी
अत: सही विकल्प (A) है।

प्रश्न 6.
यदि किसी समचतुर्भुज के विकर्ण 10 सेमी एवं 8 सेमी हों तो इसका क्षेत्रफल होगा :
(A) 80 वर्ग सेमी
(B) 40 वर्ग सेमी
(C) 9 वर्ग सेमी
(D) 36 वर्ग सेमी
हल :
समचतुर्भुज का क्षेत्रफल
= \(\frac {1}{2}\) × विकर्णों का गुणनफल
= \(\frac {1}{2}\) × 10 × 8
= 5 × 8 = 40 वर्ग सेमी
अत: सही विकल्प (B) है।

प्रश्न 7.
एक त्रिभुज का आधार 14 सेमी एवं ऊँचाई 10 सेमी है, तो त्रिभुज का क्षेत्रफल होगा :
(A) 240 सेमी²
(B) 60 सेमी²
(C) 70 सेमी²
(D) 140 सेमी²
हल :
त्रिभुज का क्षेत्रफल = \(\frac {1}{2}\) × आधार × ऊँचाई
= \(\frac {1}{2}\) × 14 × 10 वर्ग सेमी
= 70 वर्ग सेमी
अत: सही विकल्प (C) है।

प्रश्न 8.
यदि किसी आयत की आसन्न भुजाएँ 3 सेमी व 4 सेमी इसका विकर्ण खींचने पर बने एक त्रिभुज का अर्द्ध-परिमाप होगा :

(A) 6 सेमी
(B) 10 सेमी
(C) 7 सेमी
(D) 12 सेमी।
हल :
ΔABC पाइथागोरस प्रमेय से,
AC = \(\sqrt{3^2+4^2}=\sqrt{9+16}\) = 5 सेमी
∴ ΔABC का अर्द्ध परिमाप = \(\frac{3+4+5}{2}\)
= \(\frac {12}{2}\) = 6 सेमी
अतः सही विकल्प (A) है।

प्रश्न 9.
हीरोन के सूत्र में 3 प्रकट करता है
(A) परिमाप को
(B) क्षेत्रफल को
(C) अर्द्ध परिमाप को
(D) A और B दोनों
हल :
अर्द्धपरिमाप को अत: विकल्प (C) सही है।

प्रश्न 10.
किसी अनियमित आकार के बहुभुजाकार खेत का क्षेत्रफल ज्ञात करने के लिए उसे बाँट लिया जाता है :
(A) आयतों में,
(B) वर्गों में
(C) समचतुर्भुजों में
(D) त्रिभुओं में
हल :
त्रिभुजों में, अतः विकल्प (D) सही है।

प्रश्न 11.
एक समान्तर चतुर्भुज का आधार 18 मीटर एवं क्षेत्रफल 174.60 वर्ग मीटर हो, तो इसकी ऊंचाई ज्ञात कीजिए।
हल :
समान्तर चतुर्भुज का क्षेत्रफल = आधार × ऊँचाई
⇒ 174.60 = 18 × ऊँचाई
∴ ऊँचाई = \(\frac {174.60}{18}\)
= 9.7 मीटर।

प्रश्न 12.
उस समबाहु त्रिभुज की भुजा की लम्बाई ज्ञात कीजिए, जिसका क्षेत्रफल 9\(\sqrt{3}\) वर्ग सेमी है।
हल :
समबाहु त्रिभुज का क्षेत्रफल = \(\frac{a^2 \sqrt{3}}{4}\), जहाँ भुजा है।
⇒ 9\(\sqrt{3}\) = \(\frac{a^2 \sqrt{3}}{4}\)
⇒ 9 × 4\(\sqrt{3}\) = a²\(\sqrt{3}\)
⇒ a² = \(\frac{9 \times 4 \times \sqrt{3}}{\sqrt{3}}\) = 9 × 4
⇒ a² = 36
∴ a = 6 सेमी
अतः समबाहु Δ की भुजा की लम्बाई = 6 सेमी।

प्रश्न 13.
एक समद्विबाहु त्रिभुज की दो समान भुजाओं में प्रत्येक 5 सेमी एवं तीसरी भुजा 4 सेमी लम्बी है, तो त्रिभुज का क्षेत्रफल ज्ञात कीजिए।
हल :
माना कि a = 5 सेमी, b = 4 सेमी
अतः समद्विबाहु त्रिभुज का क्षेत्रफल
= \(\frac {b}{4}\) × \(\sqrt{4 a^2-b^2}\)
= \(\frac {b}{4}\) × \(\sqrt{4 \times 25-16}\) वर्ग सेमी
= \(\sqrt{84}\) वर्ग सेमी
= 2\(\sqrt{21}\) वर्ग सेमी।

प्रश्न 14.
उस समबाहु त्रिभुज की ऊँचाई ज्ञात कीजिए जिसकी एक भुजा 2a है।
हल :

दिया है : भुजा = 2a
समबाहु त्रिभुज में शीर्ष से खींचा गया लम्ब सम्मुख भुजा को समद्विभाजित करता हैं। अत: समबाहु ΔABD में
∠ADB = 90°
AD²= AB² – BD²
(पाइथागोरस प्रमेय से)
= (2a)² – (a)²
= 4a² – a² = 3a²
AD = \(\sqrt{3}\)a इकाई
∴ त्रिभुज की ऊँचाई = \(\sqrt{3}\)a

प्रश्न 15.
एक त्रिभुजाकार खेत की भुजाएँ 20 मीटर, 51 मीटर एवं 37 मीटर हैं। 2 × 3 वर्ग मीटर माप की कितनी क्यारियाँ इस खेत में बनाई जा सकती हैं ?
हल :
त्रिभुजाकार खेत की भुजाएँ a = 20 मीटर, b = 51 मीटर, c = 37 मीटर
खेत का अर्द्ध परिमाप (s) = \(\frac{a+b+c}{2}\)
= \(\frac{20+51+37}{2}\)
= \(\frac {108}{2}\) = 54 सेमी
त्रिभुजाकार खेत का क्षेत्रफल = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{54(54-20)(54-51)(54-37)}\)
= \(\sqrt{54 \times 34 \times 3 \times 17}\)
= 306 वर्ग मीटर
एक क्यारी का क्षेत्रफल = 2 × 3 वर्ग मीटर
= 6 वर्ग मीटर
क्यारियों की संख्या = खेत का क्षेत्रफल / एक क्यारी का क्षेत्रफल
= 306 वर्ग मीटर / 6 वर्ग मीटर
= 51 क्यारियाँ

प्रश्न 16.
उस समबाहु त्रिभुज का क्षेत्रफल एवं ऊंचाई ज्ञात कीजिए जिसकी एक भुजा 6 सेमी हो।
हल :
माना कि एक भुजा a = 6 सेमी
समबाहु त्रिभुज का क्षेत्रफल
= \(\frac{\sqrt{3}}{4}\)a² = \(\frac{\sqrt{3}}{4}\) × (6)²
= 9\(\sqrt{3}\) वर्ग सेमी
त्रिभुज की ऊँचाई = 2 × क्षेत्रफल / आधार
= \(\frac{2 \times 9 \sqrt{3}}{6}\)
= 3\(\sqrt{3}\) सेमी
अतः त्रिभुज का क्षेत्रफल 9\(\sqrt{3}\) वर्ग सेमी एवं ऊँचाई 3\(\sqrt{3}\) सेमी है।

प्रश्न 17.
किसी समान्तर चतुर्भुज की दो आसन्न भुजाएँ क्रमश: 5 सेमी एवं 3.5 सेमी तथा विकर्ण 6.5 सेमी है। समान्तर चतुर्भुज का क्षेत्रफल ज्ञात कीजिए।
हल :
समान्तर चतुर्भुज का विकर्ण उसे दो बराबर क्षेत्रफल वाले त्रिभुओं में बाँटता है।
∴ समान्तर चतुर्भुज ABCD का क्षेत्रफल
= 2 × (ΔABC का क्षेत्रफल)

अतः समान्तर चतुर्भुज का क्षेत्रफल
= 2 × 5\(\sqrt{3}\) वर्ग सेमी
= 10\(\sqrt{3}\) वर्ग सेमी।

प्रश्न 18.
उस चतुर्भुज का क्षेत्रफल ज्ञात कीजिए, जिसकी भुजाएँ क्रमशः 9 सेमी, 40 सेमी, 28 सेमी एवं 15 सेमी हैं एवं प्रथम दो भुजाओं के मध्य का कोण समकोण है।
हल :
माना चतुर्भुज ABCD में भुजाएँ AB, BC, CD और DA
क्रमशः 9 सेमी, 40 सेमी, 28 सेमी और 15 सेमी हैं।
AB तथा BC के मध्य कोण 90° है।

AC विकर्ण खींचा, जो चतुर्भुज ABCD को दो त्रिभुजों (ΔABC और ΔACD) में विभक्त कर देता है।
ΔABC का क्षेत्रफल
= \(\frac {1}{2}\) × (आधार × ऊँचाई )
= \(\frac {1}{2}\) × 9 × 40 = 9 × 20 = 180 वर्ग सेमी
∴ ΔABC में, पाइथागोरस प्रमेय से,
(कर्ण)² = (आधार)² + (लम्ब)²
AC² = BC² + AB²
AC² = (40)² + (9)² = 1600 + 81
AC² = 1681 वर्ग सेमी
∴ AC = \(\sqrt{1681}\) = 41 सेमी
अतः ΔACD में,
AC = 41 सेमी, CD = 28 सेमी, DA = 15 सेमी
अर्द्ध परिमाप (s) = \(\frac{41+28+15}{2}\)
= \(\frac {84}{2}\) = 42 सेमी
ΔACD का क्षेत्रफल
= \(\sqrt{42(42-41)(42-28)(42-15)}\)
= \(\sqrt{42 \times 1 \times 14 \times 27}\)
= \(\sqrt{14 \times 3 \times 14 \times 3 \times 3 \times 3}\)
= 14 × 3 × 3 = 126 वर्ग सेमी
अत: चतुर्भुज ABCD का क्षेत्रफल
= ΔABC का क्षेत्रफल + ΔACD का क्षेत्रफल
= 180 वर्ग सेमी + 126 वर्ग सेमी
= 306 वर्ग सेमी।

प्रश्न 19.
उस समलम्ब चतुर्भुज का क्षेत्रफल ज्ञात कीजिए जिसकी समान्तर भुजाएँ क्रमशः 55 सेमी एवं 40 सेमी हैं तथा असमान्तर भुजाएँ क्रमश: 20 सेमी एवं 25 सेमी हैं।
हल :

समलम्ब चतुर्भुज ABCD में समान्तर भुजाएँ AB = 55 सेमी, व DC = 40 सेमी एवं असमान्तर भुजाएँ AD = 20 सेमी एवं BC = 25 सेमी हैं। ΔBEC में,
रचना : AD || EC एवं CF ⊥ AB खींचा।
अत: EB = AB – AE = 55 – 40 = 15 सेमी एवं EC = 20 सेमी

समान्तर चतुर्भुज AECD का क्षेत्रफल
= AE × CF
= 40 × 20
= 800 वर्ग सेमी
अतः समलम्ब चतुर्भुज ABCD का क्षेत्रफल
= (स.च. AECD का क्षे.) + (ΔBEC का क्षे.)
= 800 वर्ग सेमी + 150 वर्ग सेमी
= 950 वर्ग सेमी।

प्रश्न 20.
सोनिया के पास एक खेत है जो एक समचतुर्भुज के आकार का है। वह अपनी एक पुत्री और एक पुत्र से यह चाहती थी कि वे उस खेत पर काम करके अलग-अलग फसलों का उत्पादन करें। उसने इस खेत को दो बराबर भागों में विभाजित कर दिया। यदि इस खेत का परिमाप 400 मीटर है और एक विकर्ण 160 मीटर है, तो प्रत्येक को खेती के लिए कितना क्षेत्रफल प्राप्त होगा ?
हल :
माना ABCD समचतुर्भुजाकार खेत है जिसका परिमाप 400 मीटर है। विकर्ण AC इस खेत को दो बराबर भागों में विभाजित करता है।

∴ प्रत्येक भुजा = \(\frac {परिमाप}{4}\) = \(\frac {400}{4}\) = 100 मीटर
विकर्ण = 160 मीटर
ΔABC का अर्द्ध परिमाप
s = \(\frac{100+100+160}{2}\)
= \(\frac {360}{2}\)
= 180 मीटर
∴ ΔABC का क्षेत्रफल
= \(\sqrt{180(180-100)(180-100)(180-160)}\)
= \(\sqrt{180 \times 80 \times 80 \times 20}\) = 4800 मीटर²
अतः प्रत्येक को खेती करने के लिए 4800 मीटर² क्षेत्रफल प्राप्त होगा।

वैकल्पिक विधिः
CE ⊥ BD
∵ समद्विबा के शीर्ष से असमान भुजा पर डाला गया लम्ब उसे अद्धित करता है ।
और चूँकि विकर्ण
BD = 160 मी.
∴ DE = \(\frac {180}{2}\) = 80 मी.
अब समकोण त्रिभुज CED में
CE = \(\sqrt{(C D)^2-(D E)^2}\)
= \(\sqrt{100^2-80^2}\)
= \(\sqrt{10000-6400}\)
= \(\sqrt{3600}\)
= 60 मी.
क्षेत्रफल ΔBCD
= \(\frac {1}{2}\) × आधार × ऊँचाई
= \(\frac {1}{2}\) × 160 × 60
= 80 × 60
= 4800 मी²

प्रश्न 21.
कमला के पास 240 मीटर, 200 मीटर और 360 मीटर भुजाओं वाला एक त्रिभुजाकार खेत है, जहाँ वह गेहूँ उगाना चाहती है। इसी खेत से संलग्न 240 मीटर, 320 मीटर और 400 मीटर भुजाओं वाला एक अन्य खेत है, जहाँ वह आलू और प्याज उगाना चाहती है। उसने इस खेत की सबसे लम्बी भुजा के मध्य बिन्दु को सम्मुख शीर्ष से जोड़कर उसे दो भागों में विभाजित कर दिया। इनमें से एक भाग में उसने आलू उगाये और दूसरे भाग में प्याज उगाई गेहूँ, आलू और प्याज के लिए कितने-कितने क्षेत्रफलों (हेक्टेअर में) का प्रयोग किया गया है। (1 हेक्टेअर = 10000 वर्ग मीटर) ।
हल :
माना कि ABC वह खेत है जहाँ गेहू उगाया गया है और ACD वह खेत है जिसकी सबसे लम्बी भुजा AD के मध्य-बिन्दु E को C से जोड़कर इस खेत को दो भागों में बाँटा गया है।

ΔABC का क्षेत्रफल :
a = 200 मीटर
b = 240 मीटर
c = 360 मीटर
s = \(\frac{200+240+360}{2}\)
s = 400 मीटर
∴ गेहूँ उगाने के लिए ΔABC का क्षेत्रफल
= \(\sqrt{400(400-200)(400-240)(400-360)}\)
= \(\sqrt{400 \times 200 \times 160 \times 40}\)
= 16000\(\sqrt{2}\) वर्ग मीटर
= 1. 6\(\sqrt{2}\) हेक्टेअर
= 1·6 × 1.414 = 2.26 हेक्टेअर (लगभग)
आलू और प्याज उगाने के लिए ΔACD का क्षेत्रफल :
s = \(\frac{240+320+400}{2}\) = 480 मीटर
ΔACD का क्षेत्रफल
= \(\sqrt{480(480-240)(480-320)(480-400)}\)
= \(\sqrt{480 \times 240 \times 160 \times 80}\)
= 38400 वर्ग मीटर
= 3.84 हेक्टेअर
CE, ΔACD की माध्यिका है। यह त्रिभुज को दो बराबर भागों में बाँटेगी।
आलू उगाने के लिए क्षेत्रफल = प्याज उगाने के लिए क्षेत्रफल
= \(\frac {3.84}{2}\)
= 1.92 हेक्टेअर
अतः गेहूँ उगाने के लिए क्षेत्रफल = 2.26 हेक्टेअर
आलू उगाने के लिए क्षेत्रफल = 1.92 हेक्टेअर
और प्याज उगाने के लिए क्षेत्रफल = 1.92 हेक्टेअर ।

प्रश्न 22.
किसी स्कूल के विद्यार्थियों ने सफाई अभियान के लिए एक रैली निकाली। उन्होंने दो समूहों में, विभिन्न गलियों में चलकर मार्च किया। एक समूह ने गलियों AB, BC और CA में मार्च किया। फिर उन्होंने इन गलियों द्वारा घेरे गये भागों को साफ किया। यदि AB = 9 मीटर, BC = 40 मीटर, CD = 15 मीटर, DA = 28 मीटर और ∠B = 90° है, तो किस समूह ने अधिक सफाई की और कितनी अधिक ? विद्यार्थियों द्वारा सफाई किया गया कुल क्षेत्रफल भी ज्ञात कीजिए।
हल :

AB = 9 मीटर
BC = 40 मीटर
∠B = 90°
पाइथागोरस प्रमेय से,
AC = \(\sqrt{A B^2+B C^2}\)
= \(\sqrt{9^2+40^2}\)
= \(\sqrt{81+1600}\)
= \(\sqrt{1681}\) = 41 मीटर
पहले समूह द्वारा की गई सफाई का क्षेत्रफल
= समकोण ΔABC का क्षेत्रफल
= \(\frac {1}{2}\) × BC × AB
= \(\frac {1}{2}\) × 40 × 9
= 180 वर्ग मीटर
दूसरे समूह द्वारा की गई सफाई का क्षेत्रफल = ΔACD का क्षेत्रफल
जहाँ a = 41 मी., b = 15 मी. , c = 28 मीटर
∴ S = \(\frac{41+15+28}{2}=\frac{84}{2}\)
= 42 मीटर
ΔACD का क्षेत्रफल = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{42(42-41)(42-15)(42-28)}\)
= \(\sqrt{42 \times 1 \times 27 \times 14}\)
= 126 वर्ग मीटर
∴ पहले समूह ने दूसरे समूह की अपेक्षा (180 – 126) = 54 वर्ग मीटर अधिक सफाई की है।
सभी विद्यार्थियों द्वारा की गई सफाई का कुल क्षेत्रफल
= 180 + 126
= 306 वर्ग मीटर।

प्रश्न 23.
एक समबाहु त्रिभुज की माध्यिका की लम्बाई x सेमी है तो उस त्रिभुज का क्षेत्रफल ज्ञात करो ।
हल :
दिया है त्रिभुज ABC समबाहु त्रिभुज है जिसकी प्रत्येक भुजा a (माना) है।

ΔAPC मैं,
AC² = AP² + PC²
a² = x² + (\(\frac {a}{2}\))²
⇒ a² = x² + \(\frac{a^2}{4}\)
⇒ a² – \(\frac{a^2}{4}\) = x²
⇒ \(\frac{3 a^2}{4}\) = x²
⇒ a² = \(\frac{4 x^2}{3}\)
⇒ a = \(\sqrt{\frac{4 x^2}{3}}\)
∴ a = \(\frac{2 x}{\sqrt{3}}\)
अब, त्रिभुज ABC का क्षेत्रफल
= \(\frac {1}{2}\) × BC × AP
= \(\frac {1}{2}\) × a × x
= \(\frac {1}{2}\) × \(\frac{2 x}{\sqrt{3}}\) × x
= \(\frac{x^2}{\sqrt{3}}\)
अतः क्षेत्रफल = \(\frac{x^2}{\sqrt{3}}\) वर्ग इकाई

प्रश्न 24.
एक त्रिभुजाकार प्लाट की भुजाओं का अनुपात 3 : 5 : 7 है तथा उसका परिमाप 300 मीटर है। इस प्लाट का क्षेत्रफल ज्ञात कीजिए।
हल :
मान लीजिए त्रिभुजाकार प्लॉट की भुजाएँ 3x, 5x तथा 7x हैं।
∴ परिमाप = 3x + 5x + 7x = 300
⇒ 15x = 300
∴ x = \(\frac {300}{15}\) = 20 मीटर
∴ प्लॉट की भुजाएँ,
a = 3 × 20 = 60 मीटर
b = 5 × 20 = 100 मीटर
c = 7 × 20 = 140 मीटर
अब, s = \(\frac{60+100+140}{2}=\frac{300}{2}\) = 150 मीटर
∴ त्रिभुज का क्षेत्रफल = \(\sqrt{s(s-a)(s-b)(s-c)}\)
= \(\sqrt{150(150-60)(150-100)(150-140)}\)
= \(\sqrt{150 \times 90 \times 50 \times 10}\)
अत: क्षेत्रफल = 1500\(\sqrt{3}\) वर्ग मीटर ।

प्रश्न 25.
यदि किसी त्रिभुज की प्रत्येक भुजा को दुगुना कर दिया जाय तो इस त्रिभुज के क्षेत्रफल में कितने प्रतिशत की वृद्धि हो जायेगी।
हल :
माना कि किसी त्रिभुज की भुजाएँ क्रमश: x, y तथा z हैं एवं s इसका अर्द्ध परिमाप है। अतः
s = \(\frac{x+y+z}{2}\)
अब पुनः माना कि नये त्रिभुज की भुजाएँ 2x, 2y तथा 2z हैं एवं s’ इसका अर्द्ध परिमाप है। अतः
s’ = \(\frac{2 x+2 y+2 z}{2}\)
= \(\frac{2(x+y+z)}{2}\) = 2s
∴ s’ = 2s
अब माना कि दोनों त्रिभुजों के क्षेत्रफल क्रमश A तथा A’ हैं तो

∴ त्रिभुज के क्षेत्रफल में वृद्धि = A’ – A = 4S – S = 3S
प्रतिशत वृद्धि = \(\frac {3S}{S}\) × 100 = 300%
अतः क्षेत्रफल में वृद्धि = 300%

Jharkhand Board JAC Class 9 Maths Important Questions Chapter 11 रचनाएँ Important Questions and Answers.

JAC Board Class 9th Maths Important Questions Chapter 11 रचनाएँ

प्रश्न 1.
एक त्रिभुज ABC की रचना कीजिए जिसमें ∠B = 45°, ∠C = 60° और A से BC पर लम्ब AD = 4 सेमी।
हल :
दिया है ΔABC में, ∠B = 45°, ∠C = 60° तथा शीर्ष लम्ब AD = 4 सेमी।

रचना :

1. सर्वप्रथम XY रेखाखण्ड खींचा।
2. XY रेखाखण्ड पर कोई बिन्दु D लिया।
3. D से ED ⊥ XY खींचा।
4. AD = 4 सेमी काटा।
5. A बिन्दु से XY के समान्तर PQ खींची।
6. XY के बिन्दु A पर क्रमश: ∠PAB = 45° और ∠QAC = 60° के कोण बनाती हुई रेखाएँ खींची जो XY को B तथा C बिन्दुओं पर मिलती हैं।
7. इस प्रकार प्राप्त ΔABC ही अभीष्ट त्रिभुज है।

प्रश्न 2.
त्रिभुज ABC की रचना कीजिए, जिसकी परिमिति 12 सेमी एवं आधार कोण 50° और 70° हों।
हल :

रचना :

1. सर्वप्रथम PQ = 12 सेमी का रेखाखण्ड खींचा।
2. PQ के बिन्दु P से कोण RPQ = \(\frac {50°}{2}\) = 25° बनाती हुई रेखा PR खींची तथा PQ के बिन्दु Q से कोण SQP = \(\frac {70°}{2}\) = 35° का कोण बनाती हुई QS रेखा खींची जो परस्पर A बिन्दु पर काटती है।
3. AP और AQ के लम्ब समद्विभाजक खींचे जो PQ को क्रमश: B और C बिन्दुओं पर मिलते हैं।
4. A को B व C को 4 से मिलाया।
5. इस प्रकार प्राप्त त्रिभुज ABC ही अभीष्ट त्रिभुज है, जिसमें AB + BC + CA = 12 सेमी है।

प्रश्न 3.
त्रिभुज ABC की रचना कीजिए जिसमें BC = 6 सेमी, AB – AC = 2 सेमी और ∠C = 30° हो ।
हल :

रचना :

1. रेखा BC = 6 सेमी की खींची।
2. बिन्दु C पर 30° का कोण बनाती हुयी रेखा CY खींचा।
3. CY में से CD = 2 सेमी काटा।
4. BD को मिलाया।
5. BD का लम्ब समद्विभाजक खींचा जो CY की A बिन्दु पर काटता है।
6. AB को मिलाया।
   अतः अभीष्ट त्रिभुज ABC प्राप्त हुआ।

प्रश्न 4.
त्रिभुज PQR की रचना कीजिए, जिसमें RQ = 6 सेमी, ∠Q = 60° और PQ + PR = 8 सेमी है।
हल :

रचना :

1. सर्वप्रथम भुजा RQ = 6 सेमी की खींची।
2. भुजा RQ के बिन्दु Q पर 60° का कोण बनाती हुयी रेखा QT खींची।
3. QT से QS = (PQ + PR = 8 सेमी) काटा।
4. S को R से मिलाया।
5. RS का लम्ब समद्विभाजक खींचा जो SQ को बिन्दु P पर काटता है।
6. P को R से मिलाया।
   ΔPQR ही अभीष्ट त्रिभुज है जिसमें PQ + PR = 8 सेमी है।

प्रश्न 5.
त्रिभुज ABC की रचना कीजिए, जिसमें AB = 4 सेमी, AC = 3 सेमी और भुजा BC पर शीर्ष लम्ब 2.5 सेमी लम्बा हो ।
हल :
रचना :
1. सर्वप्रथम XY रेखा खींची।
2. XY रेखाखण्ड पर कोई बिन्दु D लिया उस पर PD लम्ब खींचा।
3. PD में से AD = 2.5 सेमी काटा।

4. A को केन्द्र मानकर क्रमशः 4 सेमी और 3 सेमी की त्रिज्या लेकर चाप लगाये जो XY को क्रमश: B और C बिन्दुओं पर काटते हैं।
5. A को B और C को 4 से मिलाया।
6. प्राप्त ΔABC ही अभीष्ट त्रिभुज है।

प्रश्न 6.
त्रिभुज ABC की रचना कीजिए जिसमें AB = AC = 8 सेमी, ∠A = 75°, ∠B का समद्विभाजक खींचिए जो सामने की भुजा को मिले।
हल :
रचना :
1. भुजा AB = 8.0 सेमी की खींची।
2. बिन्दु A पर 75° का कोण बनाती हुयी AX रेखा खींची तथा AC = 8 सेमी काटा।
3. बिन्दु A को केन्द्र मानकर 8.0 सेमी त्रिज्या का एक चाप लगाया जो RA को C पर काटता है।

4. C को B से मिलाया।
5. B को केन्द्र मानकर किसी भी त्रिज्या का एक चाप PQ लगाया जो AB और BC को क्रमश: Q और P बिन्दुओं पर काटता है।
6. अब P और Q को केन्द्र मानकर दो चाप खींचे जो एक-दूसरे को S बिन्दु पर काटते हैं।
7. B और S को मिलाती हुयी रेखा खींची जो AC को M पर मिलती है।
8. इस प्रकार बना त्रिभुज AMB ही अभीष्ट त्रिभुज है।

प्रश्न 7.
ΔABC की रचना कीजिए जिसमें a = 7 सेमी, b = 5 सेमी और c = 4 सेमी। A से BC पर लम्ब डालिए ।
हल :
दिया है ΔABC में a = 7 सेमी, b = 5 सेमी और c = 4 सेमी अर्थात् BC = 7 सेमी, AC = 5 सेमी, AB = 4 सेमी।
रचना :
1. सर्वप्रथम रेखाखण्ड BC = 7 सेमी खींचा।
2. B को केन्द्र मानकर 4 सेमी त्रिज्या से तथा C को केन्द्र मान कर 5 सेमी की त्रिज्या से चाप लगाए जो परस्पर A बिन्दु पर काटते हैं।

3. A को B से व C को A से मिलाया। यही अभीष्ट त्रिभुज ABC है।
4. अब बिन्दु A को केन्द्र मानकर चाप खींचा जो BC को क्रमश: P और Q बिन्दुओं पर काटता है।
5. P और Q को क्रमशः केन्द्र मानकर तथा उचित त्रिज्या से दो चाप BC के नीचे की ओर खींचे जो एक-दूसरे को R बिन्दु पर काटते हैं।
6. A को R से मिलाया, जो BC भुजा को S पर काटता है।
7. अत: AS, ही A से BC पर खींचा गया अभीष्ट लम्ब है।

Jharkhand Board JAC Class 9 Maths Solutions Chapter 13 पृष्ठीय क्षेत्रफल एवं आयतन Ex 13.5 Textbook Exercise Questions and Answers.

JAC Board Class 9 Maths Solutions Chapter 13 पृष्ठीय क्षेत्रफल एवं आयतन Exercise 13.5

प्रश्न 1.
माचिस की डिब्बी की माप 4 सेमी × 2.5 सेमी × 1.5 सेमी है। ऐसी 12 डिब्बियों के एक पैकेट का आयतन क्या होगा ?
हल:
माचिस की डिब्बी की माप
∴ l = 4 सेमी, b = 2.5 सेमी तथा h = 1.5 सेमी
∴ माचिस की डिब्बी का आयतन = lbh
= 4 × 2.5 × 1.5 घन सेमी
= 15 घन सेमी
अतः 12 माचिसों के पैकेट का आयतन = 15 × 12
= 180 घन सेमी।

प्रश्न 2.
एक घनाभाकार पानी की टंकी 6 मीटर लम्बी, 5 मीटर चौड़ी और 4.5 मीटर गहरी है। इसमें कितने लीटर पानी आ सकता है? (1 घन मीटर = 1000 लीटर)
हल:
घनाभाकार टंकी की लम्बाई (l) = 6 मीटर,
चौड़ाई (b) = 5 मीटर और गहराई (h) = 4.5 मीटर।
∴ टंकी का आयतन = lbh
= 6 × 5 × 4.5 घन मीटर
= 135 घन मीटर
∴ टंकी में समाहित हो सकने वाले पानी का आयतन
= 135 घन मीटर
= 135 × 1000 लीटर
= 1,35,000 लीटर
अतः टंकी में 1,35,000 लीटर पानी आ सकता है।

प्रश्न 3.
एक घनाभाकार बर्तन 10 मीटर लम्बा और 8 मीटर चौड़ा है। इसको कितना ऊँचा बनाया जाए कि इसमें 380 घन मीटर द्रव आ सके ?
हल:
लम्बाई (l) = 10 मीटर, चौड़ाई (b) = 8 मीटर और आयतन = 380 मीटर³
माना बर्तन की ऊँचाई = h
बर्तन का आयतन = लम्बाई × चौड़ाई × ऊँचाई

प्रश्न 4.
8 मीटर लम्बा, 6 मीटर चौड़ा और 3 मीटर गहरा एक घनाभाकार गड्ढा खुदवाने में 30 रुपये प्रति घन मीटर की दर से होने वाला व्यय ज्ञात कीजिए।
हल:
घनाभाकार गड्ढे की लम्बाई (l) = 8 मीटर.
चौड़ाई (b) = 6 मीटर तथा गहराई (h) = 3 मीटर
∴ गड्ढे का आयतन = lbh
= 8 × 6 × 3 घन मीटर
= 144 घन मीटर
घनाभाकार गड्ढे को खुदवाने का व्यय = गड्डे का आयतन × दर = 30 × 144 = ₹ 4,320
अतः गड्ढा खुदवाने में होने वाला व्यय = ₹ 4,320

प्रश्न 5.
एक घनाभाकार पानी की टंकी की धारिता 50,000 लीटर है। यदि इस टंकी की लम्बाई और गहराई क्रमश: 2.5 मीटर और 10 मीटर है तो इसकी चौड़ाई ज्ञात कीजिए।
हल:
माना टंकी की चौड़ाई b मीटर है।
∵ टंकी की लम्बाई (l) = 2.5 मीटर और टंकी की गहराई (h) = 10 मीटर।
∴ घनाभाकार टंकी का आयतन = lbh
= 2.5 × b × 10 घन मीटर
= 256 घन मीटर
∴ टंकी की धारिता = 25b घन मीटर
= 25b × 1000 लीटर [∵ 1 घन मीटर 1000 लीटर]
प्रश्नानुसार
टंकी का आयतन = टंकी की धारिता
= 50,000 लीटर
∴ 25,000b = 50,000
∴ b = \(\frac{50,000}{25 \times 1000}\) = 2 मीटर
अतः टंकी की चौड़ाई 2 मीटर।

प्रश्न 6.
एक गाँव जिसकी जनसंख्या 4000 है, को प्रतिदिन प्रति व्यक्ति 150 लीटर पानी की आवश्यकता है। इस गाँव में 20 मीटर × 15 मीटर × 6 मीटर मापों वाली एक टंकी बनी हुई है। इस टंकी का पानी वहाँ कितने दिन के लिए पर्याप्त होगा ?
हल:
गाँव की जनसंख्या = 4000
प्रति व्यक्ति प्रतिदिन पानी की आवश्यकता = 150 लीटर
∴ प्रतिदिन गाँव के लिए आवश्यक पानी की मात्रा = 4000 × 150 लीटर
= 6,00,000 लीटर
= 600 घन मीटर
(∵ 1000 लीटर = 1 घन मीटर)
टंकी का आयतन = 20 × 15 × 6 घन मीटर
= 1800 घन मीटर
जल की पर्याप्तता (दिनों में)

अतः टंकी का जल 3 दिन के लिए पर्याप्त होगा।

प्रश्न 7.
किसी गोदाम की माप 40 मीटर × 25 मीटर × 15 मीटर है। इस गोदाम में 1.5 मीटर × 1.25 मीटर × 0.5 मीटर माप वाले लकड़ी के कितने अधिकतम क्रेट (crate) रखे जा सकते हैं?
हल:
गोदाम का आयतन (40 × 25 × 15) मीटर³
1 क्रेट का आयतन = (1.5 × 1.25 × 0.5 ) मीटर³
गोदाम में रखे जा सकने वाले क्रेटों की संख्या

प्रश्न 8.
12 सेमी भुजा वाले एक ठोस घन को बराबर आयतन वाले 8 घनों में काटा जाता है। नये घन की क्या भुजा होगी? साथ ही, इन दोनों घनों के पृष्ठीय क्षेत्रफलों का अनुपात भी ज्ञात कीजिए।
हल:
बड़े घन की भुजा = 12 सेमी
∴ आयतन = (भुजा)³ = (12)³ सेमी³
= 12 × 12 × 12 सेमी³
यह घन 8 बराबर आयतन के घनों में काटा जाता है।

अतः नये घन की भुजा \(\sqrt[3]{6 \times 6 \times 6}\) सेमी
= 6 सेमी।
बड़े घन का पृष्ठीय क्षेत्रफल = 6 × (भुजा)²
= 6 × (12)² वर्ग सेमी
= 864 वर्ग सेमी
छोटे प्रत्येक घन का पृष्ठीय क्षेत्रफल = 6 × (भुजा)²
= 6 × (6)² वर्ग सेमी
= 6 × 6 × 6 वर्ग सेमी
= 216 वर्ग सेमी
∴ दोनों घनों के पृष्ठीय क्षेत्रफल का अनुपात = 864 : 216 = 4 : 1
अतः नये घन की भुजा 6 सेमी और दोनों घनों के पृष्ठीय क्षेत्रफल का अनुपात = 4 : 1.

प्रश्न 9.
3 मीटर गहरी और 40 मीटर चौड़ी एक नदी 2 किमी प्रति घण्टा की चाल से बहकर समुद्र में गिरती है। एक मिनट में समुद्र में कितना पानी गिरेगा ?
हल:
नदी की गहराई (h) = 3 मीटर और चौड़ाई (b) = 40 मीटर
∴ नदी का परिच्छेद क्षेत्रफल = लम्बाई × चौडाई
= 3 × 40
= 120 वर्ग मीटर
∵ नदी के पानी की चाल 2 किमी प्रति घण्टा है।
∴ 1 मिनट में नदी के विस्थापित पानी की लम्बाई = \(\frac{2 \times 1000}{60}\) मीटर
= \(\frac{100}{3}\) घन मीटर
∴ 1 मिनट में बहने वाले पानी का आयतन = नदी के परिच्छेद का क्षेत्रफल × नदी की प्रति मिनट चाल
= 120 × \(\frac{100}{3}\) घन मीटर
= 4000 घन मीटर।
अतः 1 मिनट में समुद्र में 4000 घन मीटर पानी गिरेगा।

Jharkhand Board JAC Class 9 Science Solutions Chapter 10 गुरुत्वाकर्षण Textbook Exercise Questions and Answers.

JAC Board Class 9 Science Solutions Chapter 10 गुरुत्वाकर्षण

Jharkhand Board Class 9 Science गुरुत्वाकर्षण Textbook Questions and Answers

प्रश्न 1.
यदि दो वस्तुओं के बीच की दूरी को आधा कर दिया जाए तो उनके बीच गुरुत्वाकर्षण बल किस प्रकार बदलेगा?
उत्तर:
सूत्र F = \(\frac{\mathrm{G} m_1 m_2}{r^2}\) से

अतः दूरी को आधा करने पर गुरुत्वाकर्षण बल चार गुना हो जाएगा।

प्रश्न 2.
सभी वस्तुओं पर लगने वाला गुरुत्वीय बल उनके द्रव्यमान के समानुपाती होता है। फिर एक भारी वस्तु, हल्की वस्तु के मुकाबले तेजी से क्यों नहीं गिरती?
उत्तर:
∵ F ∝ m
अर्थात् F = km
जहाँ K = नियतांक
अत: सूत्र F = ma से,
वस्तु का त्वरण a = \(\frac { F }{ m }\)
अर्थात् a = \(\frac { γm }{ m }\) = K ( नियतांक)
इससे स्पष्ट होता है कि भले ही गुरुत्वीय बल वस्तु के द्रव्यमान के समानुपाती होता है, परन्तु वस्तुओं के मुक्त पतन का त्वरण सभी वस्तुओं के लिए नियत है। अब चूँकि कोई वस्तु कितनी तेजी से गिरेगी यह वस्तु के त्वरण पर निर्भर करता है (न कि गुरुत्वीय बल पर); अतः त्वरण के नियत होने के कारण हल्की तथा भारी सभी वस्तुएँ समान तेजी से गिरती हैं।

प्रश्न 3.
पृथ्वी तथा उसकी सतह पर रखी किग्रा की वस्तु के बीच गुरुत्वीय बल का परिमाण क्या होगा? (पृथ्वी का द्रव्यमान 6 x 10²⁴ किग्रा है तथा पृथ्वी की त्रिज्या 6.4 x 100 मीटर है)।
हल:
पृथ्वी का द्रव्यमान M = 6.4 x 10²⁴ किग्रा, पृथ्वी की त्रिज्या R = 6.4 x 10⁶ मीटर, m = 1 किग्रा, d = R.
G = 6.67 × 10^-11 न्यूटन मीटर² / किग्रा²
∴ पृथ्वी तथा वस्तु के बीच गुरुत्वीय बल
F = G\(\frac{\mathrm{M} m}{d^2}\) = 6.67 x 10^-11 x \(\frac{6 \times 10^{24} \times 1}{\left(6.4 \times 10^6\right)^2}\) न्यूटन
= \(\frac{6.67 \times 6 \times 10}{6.4 \times 6.4}\)
= 9.77 न्यूटन

प्रश्न 4.
पृथ्वी तथा चन्द्रमा एक-दूसरे को गुरुत्वीय बल से आकर्षित करते हैं। क्या पृथ्वी जिस बल से चन्द्रमा को आकर्षित करती है वह बल, उस बल से जिससे चन्द्रमा पृथ्वी को आकर्षित करता है बड़ा है या छोटा है या बराबर है? बताइए, क्यों?
उत्तर:
क्रिया-प्रतिक्रिया के नियम से पृथ्वी का चन्द्रमा पर आकर्षण बल चन्द्रमा के पृथ्वी पर आकर्षण बल के बराबर है।

प्रश्न 5.
यदि चन्द्रमा पृथ्वी को आकर्षित करता है तो पृथ्वी चन्द्रमा की ओर गति क्यों नहीं करती है?
उत्तर:
चन्द्रमा और पृथ्वी दोनों एक-दूसरे पर समान परिमाण का आकर्षण बल लगाते हैं, परन्तु चन्द्रमा का द्रव्यमान पृथ्वी के द्रव्यमान की तुलना में बहुत कम होने के कारण, समान बल होने पर भी चन्द्रमा का पृथ्वी की ओर त्वरण, पृथ्वी के चन्द्रमा की ओर त्वरण से बहुत अधिक है। इसीलिए चन्द्रमा पृथ्वी के चारों ओर गति करता है, पृथ्वी चन्द्रमा की ओर गति करती प्रतीत नहीं होती।

प्रश्न 6.
दो वस्तुओं के बीच लगने वाले गुरुत्वाकर्षण बल का क्या होगा, यदि –
(i) एक वस्तु का द्रव्यमान दो गुना कर दिया जाए?
(ii) वस्तुओं के बीच की दूरी दोगुनी अथवा तीन गुनी कर दी जाए?
(iii) दोनों वस्तुओं के द्रव्यमान दोगुने कर दिए जाएँ?
उत्तर:
(i) ∵ F ∝ m₁ m₂
∵ एक वस्तु का द्रव्यमान दोगुना कर देने पर बल भी दोगुना हो जाएगा।

(ii) ∵ F ∝ \(\frac{1}{d^2}\)
∴ दूरी दोगुनी करने पर बल एक-चौथाई रह जाएगा। जबकि दूरी तीन गुनी कर देने पर बल 9वाँ भाग रह जाएगा।

(iii) ∵ F ∝ m₁ m₂ अतः दोनों वस्तुओं के द्रव्यमान दोगुने करने पर बल चार गुना हो जाएगा।

प्रश्न 7.
गुरुत्वाकर्षण के सार्वत्रिक नियम के क्या महत्व हैं?
उत्तर:
गुरुत्वाकर्षण के सार्वत्रिक नियम का महत्व – यह नियम अनेक ऐसी परिघटनाओं की व्याख्या करता है, जो प्राचीनकाल में असम्बद्ध मानी जाती थीं; जैसे-

• इस नियम द्वारा सूर्य के चारों ओर ग्रहों की गति की व्याख्या की जाती है।
• इस नियम द्वारा पृथ्वी के चारों ओर चन्द्रमा की गति की व्याख्या की जाती है।
• इस नियम द्वारा वस्तुओं के पृथ्वी की ओर गिरने की व्याख्या की जाती है।
• इस नियम द्वारा समुद्र में आने वाले ज्वार भाटा की व्याख्या की जाती है।

पृथ्वी की कक्षा में कृत्रिम उपग्रह स्थापित करना, चन्द्रमा तथा अन्य ग्रहों तक खोजी यान भेजना तथा अन्तरिक्ष स्टेशन स्थापित करना आदि इसी नियम का ज्ञान प्राप्त होने के बाद ही सम्भव हो पाया है।

प्रश्न 8.
मुक्त पतन का त्वरण क्या है?
उत्तर:
मुक्त पतन का त्वरण- किसी ऊँची मीनार की छत से छोड़ी गई किसी वस्तु का पृथ्वी की ओर त्वरण, मुक्त पतन का त्वरण कहलाता है, जिसे g से प्रदर्शित करते हैं। पृथ्वी तल पर मुक्त पतन के त्वरण का मान 9.8 मीटर/सेकण्ड² है।

प्रश्न 9.
पृथ्वी तथा किसी वस्तु के बीच लगने वाले गुरुत्वीय बल को हम क्या कहेंगे?
उत्तर:
उस वस्तु का भार कहेंगे।

प्रश्न 10.
एक व्यक्ति A अपने मित्र के निर्देश पर ध्रुवों पर कुछ ग्राम सोना खरीदता है वह इस सोने को विषुवत् वृत्त पर अपने मित्र को देता है क्या उसका मित्र इस खरीदे हुए सोने के भार से सन्तुष्ट होगा? यदि नहीं, तो क्यों?
उत्तर:
मित्र सोने के भार से सन्तुष्ट नहीं होगा इसका कारण यह है कि विषुवत् वृत्त पर तौलने पर सोने का भार, ध्रुवों पर उसके भार की तुलना में कम होगा (g के मान में कमी के कारण)।

प्रश्न 11.
एक कागज की शीट उसी प्रकार की शीट को मोड़कर बनाई गई गेंद से धीमी क्यों गिरती है?
उत्तर:
ऐसा वायु के प्रतिरोध के कारण होता है। वायु कागज की शीट पर गेंद की अपेक्षा अधिक प्रतिरोध लगाती है; अतः कागज की शीट गेंद की तुलना में धीमी गिरती है।

प्रश्न 12.
चन्द्रमा की सतह पर गुरुत्वीय बल, पृथ्वी की सतह पर गुरुत्वीय बल की अपेक्षा 1/6 गुना है। एक 10 किग्रा द्रव्यमान की वस्तु का चन्द्रमा पर तथा पृथ्वी पर न्यूटन में भार कितना होगा?
हल:
दिया है वस्तु का द्रव्यमान m = 10 किग्रा,
पृथ्वी पर गुरुत्वीय त्वरण g = 9.8 मीटर / सेकण्डर²
∴ पृथ्वी पर वस्तु का भार W₁ = mg
= 10 × 9.8 = 98 न्यूटन
अब चूँकि चन्द्रमा पर गुरुत्वीय बल
= \(\frac { 1 }{ 6 }\) x पृथ्वी पर गुरुत्वीय बल
∴ चन्द्रमा पर वस्तु का भार W₂
= \(\frac { 1 }{ 6 }\) x पृथ्वी पर वस्तु का भार (W₁)
= \(\frac { 1 }{ 2 }\) x 98 न्यूटन
= 16.33 न्यूटन
अतः पृथ्वी पर वस्तु का भार = 98 न्यूटन
तथा चन्द्रमा पर वस्तु का भार = 16.33 न्यूटन।

प्रश्न 13.
एक गेंद ऊर्ध्वाधर दिशा में ऊपर की ओर 49 मीटर / सेकण्ड के वेग से फेंकी जाती है। परिकलन कीजिए- (i) अधिकतम ऊंचाई जहाँ तक कि गेंद पहुँचती है। (ii) पृथ्वी की सतह पर वापस लौटने में लिया गया समय।
हल:
दिया है, गेंद का वेग 49 मीटर / सेकण्ड ऊपर की ओर
गुरुत्वीय त्वरण g = 9.8 मीटर/सेकण्ड² नीचे की ओर
माना कि गेंद। ऊँचाई तक ऊपर जाती है तथा ऊपर तक जाने में समय लेती है।
ऊपर की दिशा को धनात्मक तथा नीचे की दिशा को ऋणात्मक मानने पर,
सूत्र v² = u² + 2as से, (उच्चतम बिन्दु पर वेग v = 0)

कोई वस्तु जितना समय उच्चतम बिन्दु तक जाने में लेती है, उतना ही समय पृथ्वी तल तक आने में लेती है।
∴ पृथ्वी की सतह तक लौटने में लगा समय = 2 + उच्चतम बिन्दु तक जाने में लगा समय
= 25 10 सेकण्ड
∴ अधिकतम ऊँचाई / 122.5 मीटर
कुल समय = 10 सेकण्ड।

प्रश्न 14.
19.6 मीटर ऊँची मीनार की चोटी से एक पत्थर छोड़ा जाता है। पृथ्वी पर पहुँचने से पहले उसका अन्तिम वेग ज्ञात कीजिए।
हल:
दिया है मीनार की ऊँचाई h = 19.6 मीटर,
पत्थर छोड़ते समय वेग v = 0,
त्वरण g = 9.8 मीटर / सेकण्ड² नीचे की ओर
सूत्र v² = u² + 2as से,
= 0² + 2 × 9.8 × 19.6
= 19.6 × 19.6 या v² = (19.6)²
∴ v = 19.6 मीटर/सेकण्ड
अतः पृथ्वी से टकराने से पहले अन्तिम वेग = 19.6 मीटर / सेकण्ड।

प्रश्न 15.
कोई पत्थर ऊर्ध्वाधर दिशा में ऊपर की ओर 40 मीटर / सेकण्ड के प्रारम्भिक वेग से फेंका गया है। g 10 मीटर / सेकण्ड लेते हुए ग्राफ की सहायता से पत्थर द्वारा पहुँची अधिकतम ऊँचाई ज्ञात कीजिए नेट विस्थापन तथा पत्थर द्वारा चली गई कुल दूरी कितनी होगी?
हल:
दिया है प्रारम्भिक वेग u = 40 मीटर / सेकण्ड ऊपर की ओर
गुरुत्वीय त्वरण g = 10 मीटर / सेकण्ड² नीचे की ओर
माना कि पत्थर को उच्चतम बिन्दु तक जाने में t सेकण्ड लगते हैं जहाँ उसका वेग v = 0 हो जाता है तब y = u- gt से,
0 = 40 – 10 x t
10t = 40
∴ t = \(\frac { 40 }{ 10 }\) = 4 सेकण्ड
अर्थात् अधिकतम ऊँचाई तक पहुँचने में पत्थर को 4 सेकण्ड लगते हैं।
पुन: सूत्र v = u – gt में g = 10 मीटर / सेकण्ड² तथा क्रमशः t = 0, 1, 2, 3, 4 प्राप्त होती है-

t (सेकण्ड में)	0	1	2	3	4
v (मीटर/सेकण्ड मे)	40	30	20	10	0

उपर्युक्त सारणी की सहायता से खींचा गया वेग- समय ग्राफ चित्र 10.7 में प्रदर्शित है।
वेग-समय ग्राफ से,
पत्थर द्वारा प्राप्त अधिकतम ऊँचाई
h = वेग समय ग्राफ के नीचे घिरा क्षेत्र
= ∆OAB का क्षेत्रफल
= \(\frac { 1 }{ 2 }\) OA × OB

= \(\frac { 1 }{ 2 }\) (40 मीटर/सेकण्ड ) x (4 सेकण्ड)
= 80 मीटर।
पत्थर उच्चतम बिन्दु पर क्षणिक विराम की अवस्था में आता है और फिर नीचे की ओर गिरता हुआ अपने प्रारम्भिक बिन्दु पर वापस पहुँच जाता है।
∴ पत्थर का कुल विस्थापन = प्रारम्भिक व अन्तिम बिन्दु के बीच सरल रेखीय दूरी = 0
जबकि कुल तय दूरी = तय किए गए पथ की लम्बाई
= 2 x अधिकतम ऊँचाई = 2 x 80 = 160 मीटर।

प्रश्न 16.
पृथ्वी तथा सूर्य के बीच गुरुत्वाकर्षण बल का परिकलन कीजिए।
दिया है, पृथ्वी का द्रव्यमान 6 x 10²⁴ किग्रा, सूर्य का द्रव्यमान = 2 x 10³⁰ किग्रा
दोनों के बीच औसत दूरी 1.5 x 10¹¹ मीटर है।
हल:
m₁ = 6 × 10²⁴ किग्रा, m₂ = 2 x 10³⁰ किग्रा,
d = 1.5 x 10¹¹ मीटर
G = 6.67 x 10^-11 न्यूटन मीटर²/किग्रार²
∴ पृथ्वी तथा सूर्य के बीच गुरुत्वाकर्षण बल
F = G\(\frac{m_1 m_2}{d^2}\)
= 6.67 × 10^-11 x \(\frac{6 \times 10^{24} \times 2 \times 10^{30}}{\left(1.5 \times 10^{11}\right)^2}\)
= \(\frac{6.67 \times 6 \times 2}{1.5 \times 1.5}\)
= 3.56 x 10²² न्यूटन।

प्रश्न 17.
कोई पत्थर 100 मीटर ऊँची मीनार की चोटी से गिराया गया और उसी समय कोई दूसरा पत्थर 25 मीटर / सेकण्ड के वेग से ऊर्ध्वाधर दिशा में ऊपर की ओर फेंका गया। परिकलन कीजिए कि दोनों पत्थर कब और कहाँ मिलेंगे?
हल:
माना कि दोनों पत्थर, छोड़े जाने के क्षण से सेकण्ड बाद, पृथ्वी तल से t ऊँचाई पर मिलते हैं, तब मिलते क्षण तक नीचे से फेंका गया पत्थर ऊपर की ओर ऊँचाई तय कर चुका होगा; अतः
अतः
h = u₂ x t – \(\frac { 1 }{ 2 }\) gt² … (1)
जबकि मीनार की चोटी से छोड़ा गया पिण्ड नीचे की ओर (100-h) दूरी गिर चुका होगा; अतः

100 – h = u₁ x t + \(\frac { 1 }{ 2 }\)gt²
या 100 – h = \(\frac { 1 }{ 2 }\) gt² [∵ u₁ = 0] … (2)
समीकरण (1) व (2) को जोड़ने पर,

t = 4 सेकण्ड तथा g 10 मीटर / सेकण्ड² समीकरण (2) में रखने में,
100 – h = \(\frac { 1 }{ 2 }\) × 10 × (4)²
या 100 – h = 80 या h = 100 – 80 = 20 मीटर
अतः पत्थर, प्रारम्भिक क्षण से 4 सेकण्ड बाद, पृथ्वी तल से 20 मीटर की ऊँचाई पर मिलेंगे।.

प्रश्न 18.
ऊर्ध्वाधर दिशा में ऊपर की ओर फेंकी गई एक गेंद 6 सेकण्ड पश्चात् फेंकने वाले के पास लौट आती है। ज्ञात कीजिए-
(a) यह किस वेग से ऊपर फेंकी गई?
(b) गेंद द्वारा प्राप्त की गई अधिकतम ऊँचाई, तथा
(c) 4 सेकण्ड बाद गेंद की स्थिति।
हल:
(a) माना कि गेंद u वेग से ऊपर की ओर फेंकी गई थी।
चूँकि गेंद 6 सेकण्ड पश्चात् प्रारम्भिक बिन्दु पर लौट आती है
अत: t = 6 सेकण्ड में गेंद का विस्थापन s = 0
जबकि त्वरण a = – g = – 9.8 मीटर/सेकण्डर²
∴ s = ut + \(\frac { 1 }{ 2 }\) at² से,
0 = u × 6 + \(\frac { 1 }{ 2 }\) (- 9.8) × 6²
या 6u = \(\frac { 1 }{ 2 }\) x 9.8 × 6 × 6 या u = 3 x 9.8 = 29.4
अत: गेंद 29.4 मीटर/सेकण्ड के वेग से फेंकी गई थी।

(b) माना कि गेंद अधिकतम ऊँचाई तक जाती है, तब s = h ऊँचाई पर वेग = 0
∴ v² = u² + 2as से,
0² = (29.4)² + 2 × (- 9.8) × h
या 2 × 9.8 × h = 29.4 × 29.4
∴ h = \(\frac{29.4 \times 29.4}{2 \times 9.8}\) = 44.1 मीटर

(c) माना कि t = 4 सेकण्ड बाद गेंद पृथ्वी तल से h₁ ऊँचाई पर है,
तब S = ut + \(\frac { 1 }{ 2 }\) at² से,
h₁ = 29.4 × 4 + \(\frac { 1 }{ 2 }\) x (- 9.8) × 4²
= 117.6 – 78.4
= 39.2 मीटर
अतः 4 सेकण्ड बाद गेंद पृथ्वी तल से 39.2 मीटर ऊपर होगी।

प्रश्न 19.
किसी द्रव में डुबोई गई वस्तु पर उत्प्लावन बल किस दिशा में कार्य करता है?
उत्तर:
उत्प्लावन बल सदैव भार के विपरीत दिशा में अर्थात् ऊपर की और कार्य करता है।

प्रश्न 20.
पानी के भीतर किसी प्लास्टिक के गुटके को छोड़ने पर यह पानी की सतह पर क्यों आ जाता है?
उत्तर:
चूँकि प्लास्टिक का घनत्व, पानी के घनत्व से कम होता है, इस कारण प्लास्टिक के गुटके को जल में डुबोने पर उस पर लगने वाला उत्प्लावन बल गुटके के भार से अधिक होगा। अतः गुटका पानी की सतह पर आ जाता है।

प्रश्न 21.
50 ग्राम के किसी पदार्थ का आयतन 20 सेमी है। यदि पानी का घनत्व 1 ग्राम / सेमी हो तो पदार्थ तैरेगा या डूबेगा?
हल:
पदार्थ का द्रव्यमान 50 ग्राम
तथा आयतन 20 सेमी³
जल का घनत्व = 1 ग्राम/सेमी³

∵ पदार्थ का घनत्व > जल का घनत्व
∴ यह पदार्थ जल में डूब जाएगा।

प्रश्न 22.
500 ग्राम के एक मुहरबन्द पैकेट का आयतन 350 सेमी है। पैकेट 1 ग्राम / सेमी³ घनत्व वाले पानी में तैरेगा या डूबेगा? इस पैकेट द्वारा विस्थापित पानी का द्रव्यमान कितना होगा?
हल:
पैकेट का द्रव्यमान = 500 ग्राम तथा आयतन = 350 सेमी³
जल का घनत्व = 1 ग्राम / सेमी³

∵ पैकेट का घनत्व > जल का घनत्व
∴ पैकेट जल में डूब जायेगा।
∵ पैकेट पूरा डूब जाएगा, अतः यह अपने आयतन (350 सेमी³) के बराबर पानी को विस्थापित करेगा।
∴ विस्थापित पानी का द्रव्यमान विस्थापित पानी का आयतन x पानी का घनत्व
= 350 सेमी³ x 1 ग्राम / सेमी³
= 350 ग्राम।

Jharkhand Board Class 9 Science गुरुत्वाकर्षण InText Questions and Answers

क्रियाकलाप 10.1. (पा. पु. पू. सं. 145)
धागे का एक टुकड़ा लेकर इसके सिरे पर एक छोटा पत्थर बाँधकर दूसरे सिरे से पकड़कर पत्थर को वृत्ताकार पथ में घुमाइए तथा पत्थर की गति की दिशा देखिए। अब धागे को छोड़िए तथा फिर से पत्थर की गति की दिशा को देखिए।

निष्कर्ष-धागे को छोड़ने से पहले पत्थर एक निश्चित चाल से वृत्ताकार पथ में गति करता है तथा प्रत्येक बिन्दु पर उसकी गति की दिशा बदलती है। वस्तु को वृत्ताकार पथ पर गतिशील रखने वाला बल, जिसके कारण त्वरण होता है, अभिकेन्द्रीय बल कहलाता है।

पृथ्वी के चारों ओर चन्द्रमा की गति अभिकेन्द्रीय बल के कारण है। अभिकेन्द्रीय बल पृथ्वी के आकर्षण बल के कारण होता है। हमारे सौर परिवार में सभी ग्रह सूर्य की परिक्रमा करते हैं। सूर्य तथा ग्रह के बीच एक बल विद्यमान है जो गुरुत्वाकर्षण बल कहलाता है।

न्यूटन के निष्कर्ष के आधार पर विश्व के सभी पिण्ड एक दूसरे को आकर्षित करते हैं।

खण्ड 10.1 से सम्बन्धित पाठ्य-पुस्तक के प्रश्नोत्तर (पा. पु. पृ. सं. 149)

प्रश्न 1.
गुरुत्वाकर्षण का सार्वत्रिक नियम बताइए।
उत्तर:
दो वस्तुओं के बीच लगने वाला बल, दोनों वस्तुओं के द्रव्यमान के गुणनफल के समानुपाती तथा उनकी बीच की दूरी के वर्ग के व्युत्क्रमानुपाती होता है। यह गुरुत्वाकर्षण का सार्वत्रिक नियम कहलाता है।

प्रश्न 2.
पृथ्वी तथा उसकी सतह पर रखी किसी वस्तु के बीच लगने वाले गुरुत्वाकर्षण बल का परिमाण ज्ञात करने को सूत्र लिखिए।
उत्तर:
सूत्र F = G\(\frac{\mathrm{M} m}{d^2}\) से पृथ्वी की सतह के लिए d = R अत: F = \(\frac{\mathrm{GM} m}{R^2}\)

क्रियाकलाप 10.2. (पा.पु. पृ. सं. 149)
एक पत्थर लेकर ऊपर की ओर फेंकिए। यह एक निश्चित ऊँचाई तक पहुँचता है और फिर नीचे की ओर गिरने लगता है।

पृथ्वी सभी वस्तुओं को अपनी ओर आकर्षित करती है। पृथ्वी के इस आकर्षण बल को गुरुत्वीय बल कहते हैं। वस्तुओं के पृथ्वी की ओर गिरने पर वस्तुओं को मुक्त पतन में होना कहा जाता है। गिरते समय वस्तुओं की गति की दिशा में कोई परिवर्तन नहीं होता है परन्तु पृथ्वी के आकर्षण के कारण वेग के परिमाण में परिवर्तन होता है जिससे त्वरण उत्पन्न होता है तथा इस त्वरण को पृथ्वी के गुरुत्वीय बल के कारण त्वरण या गुरुत्वीय त्वरण g कहते हैं।

गति के दूसरे नियम से हमें ज्ञात है कि द्रव्यमान तथा त्वरण का गुणनफल, बल कहलाता है। माना पत्थर का है तथा गिरती हुई वस्तुओं में गुरुत्वीय बल के द्रव्यमान कारण त्वरण लगता है और इसे g से प्रदर्शित करते हैं।
अतः
F = mg … (i)
तथा न्यूटन के गुरुत्वाकर्षण के नियम से
F = \(\frac{\mathrm{GMm}}{d^2}\) … (ii)
समी. (i) व (ii) से,
mg = \(\frac{\mathrm{GMm}}{d^2}\)
या g = \(\frac{\mathrm{GM}}{d^2}\)
जहाँ M पृथ्वी का द्रव्यमान तथा वस्तु और पृथ्वी के बीच की दूरी है।
यदि वस्तु पृथ्वी पर या इसके पृष्ठ के पास है तो d के स्थान पर पृथ्वी की त्रिज्या R रखनी होगी। इस प्रकार पृथ्वी के पृष्ठ पर या इसके समीप रखी वस्तुओं के लिए
g = \(\frac{\mathrm{GM}}{R^2}\)
पृथ्वी की त्रिज्या ध्रुवों से विषुवत रेखा की ओर जाने पर बढ़ती है अतः g का मान ध्रुवों पर विषुवत रेखा की अपेक्षा अधिक होता है।

क्रियाकलाप 10.3. (पा. पु. पू. सं. 150)
कागज की एक शीट तथा एक पत्थर लीजिए तथा दोनों को किसी इमारत की पहली मंजिल से एक साथ गिरा कर देखिए कि क्या दोनों एक साथ धरती पर पहुँचते हैं?

निष्कर्ष – हम यह पाते हैं कि कागज धरती पर पत्थर की अपेक्षा कुछ देर से पहुँचता है। ऐसा वायु के प्रतिरोध के कारण होता है। गिरती हुई गतिशील वस्तुओं पर घर्षण के कारण वायु प्रतिरोध लगाती है। कागज पर लगने वाला वायु का प्रतिरोध पत्थर पर लगने वाले प्रतिरोध से अधिक होता है।

यदि इस प्रयोग को ऐसे जार में करें जिसमें से वायु निकाल दी गई है तो कागज तथा पत्थर एक ही दर से नीचे गिरेंगे।

पृथ्वी के निकट g का मान स्थिर है अतः एक समान त्वरित गति के सभी समीकरण त्वरण a के स्थान पर g रखने पर भी मान्य रहेंगे, ये समीकरण निम्न हैं-

सरल रेखीय	गुरुत्व के अधीन
v = u + at	v = u + gt
s = ut + \(\frac { 1 }{ 2 }\)at²	h = ut + \(\frac { 1 }{ 2 }\)gt²
v² = u² + 2as	v² = u² + 2gs

जहाँ
u – वस्तु का प्रारस्भिक वेग
v – वस्तु का अन्तिम वेग
s – वस्तु द्वारा t समय में चली गई दूरी
नोट- यदि त्वरण गति की दिशा में लग रहा हो तो इसे धनात्मक लेते हैं तथा यदि त्वरण गति की दिशा के विपरीत लग रहा हो तो इसे ऋणात्मक लेते हैं।

उदाहरण 10.2.
एक कार किसी कगार से गिरकर 0.55 में धरती पर आ गिरती है। परिकलन में सरलता के लिए g का मान 10 मी / से.2 लीजिए।
(i) धरती पर टकराते समय कार की चाल क्या होगी?
(ii) 0.5 से. के दौरान इसकी औसत चाल क्या होगी?
(iii) धरती से कगार कितनी ऊँचाई पर है?
हल:
प्रश्नानुसार समय t = 0.58
प्रारम्भिक वेग u = 0 ms^-1
गुरुत्वीय त्वरण g = 10 m s^-2
कार का त्वरण a = + 10m/sec² (अधोमुखी)
(i) चाल v = at से
v = 10 मी/से.² x 0.5 से.
= 5 मी./से.^-1

(ii) औसत चाल = \(\frac { u+v }{ 2 }\)
= (0 मी/से +5 मी/से.^-1) / 2 = 2.5 मी/से.

(iii) तय की गई दूरी s = \(\frac { 1 }{ 2 }\) at² + \(\frac { 1 }{ 2 }\) x 10 मी/से.² x (0.5 से.)²
= \(\frac { 1 }{ 2 }\) x 10 मी/से.^-2 x 0.25 से.²
अतः = 1.25 मीटर
(i) धरती पर टकराते समय इसकी चाल 5मी/से.^-1
(ii) 0.5 सेकण्ड के दौरान इसकी औसत चाल = 2.5 मी/से.^-1
(iii) धरती से कगार की ऊँचाई = 1.25 मी.

उदाहरण 10.3.
एक वस्तु को ऊर्ध्वाधर दिशा में ऊपर की ओर फेंका जाता है और यह 10 मीटर की ऊँचाई तक पहुँचती है। परिकलन कीजिए-
(i) वस्तु कितने वेग से ऊपर फेंकी गई तथा
(ii) वस्तु द्वारा उच्चतम बिन्दु तक पहुँचने में लिया गया समय।
हल:
तय की गई दूरी s = 10 मी
अन्तिम वेग v = 0 मी/से.
गुरुत्वीय त्वरण g = 9.8 मी/से.²
वस्तु का त्वरण a = – 9.8 मी / से.² (ऊर्ध्वमुखी)
(i) v² = u² + 2as
0 = u² + 2 × (- 9.8 मी / से.²) x 10m
– u² = – 2 × 9.8 × 10 मी² / से.²
u = \(\sqrt{196}\) मी/से.
u = 14 मी/से.

(ii) v = u + at
0 = 14 मी / से. – 9.8 मी / से.² x 1
t = 1.43 से
(i) प्रारम्भिक वेग u = 14 मी / से. तथा
(ii) लिया गया समय t = 1.43 सेकण्ड।

खण्ड 10.2 से सम्बन्धित पाठ्य पुस्तक के प्रश्नोत्तर (पा.पु. पृ. सं. 152)

प्रश्न 1.
मुक्त पतन से क्या तात्पर्य है?
उत्तर:
वस्तुएँ पृथ्वी की ओर गुरुत्वीय आकर्षण बल के कारण गिरती हैं। इसे हम कहते हैं कि वस्तुएँ मुक्त पतन में हैं।

प्रश्न 2.
गुरुत्वीय त्वरण से आप क्या समझते हैं?
उत्तर:
जब कोई वस्तु पृथ्वी की ओर गिरती है तो पृथ्वी के आकर्षण के कारण वेग के परिमाण में परिवर्तन होता है। वेग में यह परिवर्तन त्वरण उत्पन्न करता है। यह त्वरण पृथ्वी के गुरुत्वीय बल के कारण है। इसलिए इसे गुरुत्वीय त्वरण कहते हैं।

खण्ड 10.3 एवं 10.4 से सम्बन्धित पाठ्य पुस्तक के प्रश्नोत्तर (पा.पु. पृ. सं. 153)

प्रश्न 1.
किसी वस्तु के द्रव्यमान तथा भार में क्या अन्तर है?
उत्तर:
द्रव्यमान तथा भार में अन्तर

द्रव्यमान	भार
1. किसी वस्तु में उपस्थित पदार्थ की मात्रा ही उसका द्रव्यमान होती है।	किसी वस्तु का भार उस बल के बराबर होता है जिससे पृथ्वी उस वस्तु को आकर्षित करती है।
2. द्रव्यमान का मात्रक किलोग्राम है।	भार का मात्रक न्यूटन या किलोग्राम-भार है।
3. किसी वस्तु के द्रव्यमान का मान प्रत्येक स्थान पर समान रहता है।	वस्तु का भार (m g) गुरुत्वीय त्वरण g के परिवर्तन के कारण भिन्न-भिन्न स्थानों पर भिन्न-भिन्न होता है।
4. द्रव्यमान अदिश राशि है।	भार सदिश राशि है।
5. द्रव्यमान को भौतिक तुला से तोला जाता है।	भार को कमानीदार तुला से तोला जाता है।

प्रश्न 2.
किसी वस्तु का चन्द्रमा पर भार पृथ्वी पर इसके भार का 1/6 गुना क्यों होता है?
उत्तर:
चन्द्रमा का द्रव्यमान, पृथ्वी के द्रव्यमान की तुलना में काफी कम है, इस कारण चन्द्रमा की सतह पर चन्द्रमा के कारण गुरुत्वीय त्वरण का मान, पृथ्वी पर गुरुत्वीय त्वरण के मान का 1/6 होता है। अब चूँकि किसी स्थान पर किसी वस्तु का भार उस स्थान पर गुरुत्वीय त्वरण के समानुपाती होता है; अंतः चन्द्रमा पर किसी वस्तु का भार पृथ्वी पर उसके भार का 1/6 गुना होता है।

क्रियाकलाप 10.4. (पा. पु. पृ. सं. 155)
प्लास्टिक की एक खाली बोतल लेकर उसके मुँह को एक वायुरुद्ध डाट से बन्द करके इसे एक पानी की बाल्टी में रखिए। बोतल को पानी में धकेलने पर ऊपर की ओर एक धक्का महसूस होता है तथा इसे और नीचे धकेलने में आपको कठिनाई महसूस होगी। पानी द्वारा बोतल पर ऊपर की ओर एक बल लगाया जाता है जिसे उत्प्लावन बल कहते हैं।

क्रियाकलाप 10.5. (पा.पु. पृ. सं. 156)
एक बीकर लेकर उसमें भरे पानी की सतह पर एक लोहे की कील रखिए। कील पानी में डूब जाती है। इस प्रकार का उत्तर जानने के लिए एक क्रियाकलाप करते हैं।

क्रियाकलाप 10.6 (पा.पु. पू. सं. 156)
पानी से भरा बीकर लेकर एक कील तथा समान द्रव्यमान का एक कॉर्क का टुकड़ा लेकर उन्हें पानी की सतह पर रखा। आप पायेंगे कि कील पानी में डूब जाती है जबकि कॉर्क का टुकड़ा पानी के ऊपर तैरता
रहता है।

कारण- कॉर्क तैरता है जबकि कील डूब जाती है। ऐसा उनके घनत्वों में अन्तर के कारण होता है। किसी पदार्थ का घनत्व, उसके एकांक आयतन के द्रव्यमान को कहते हैं। कॉर्क का घनत्व पानी के घनत्व से कम है अर्थात् कॉर्क पर पानी का उत्प्लावन बल, कॉर्क के भार से अधिक है इसलिए यह तैरता है।

इस प्रकार द्रव के घनत्व से कम घनत्व की वस्तुएँ द्रव पर तैरती हैं। द्रव के घनत्व से अधिक घनत्व की वस्तुएँ द्रव मैं डूब जाती हैं।

खण्ड 10.5 से सम्बन्धित पाठ्य पुस्तक के प्रश्नोत्तर (पा.पु. पू. सं. 157)

प्रश्न 1.
एक पतली तथा मजबूत डोरी से बने पट्टे की सहायता से स्कूल बैग को उठाना कठिन होता है, क्यों?
उत्तर:
यदि स्कूल बैग को पतली तथा मजबूत डोरी से बने पट्टे की सहायता से हाथ में उठाया जाए अथवा कन्धे से लटकाया जाए तो यह पट्टा हाथ अथवा कन्धे के छोटे से क्षेत्रफल के सम्पर्क में होगा। तब बैग का सम्पूर्ण भार इस छोटे से क्षेत्रफल पर लगेगा जिसके फलस्वरूप इस क्षेत्रफल पर दाब बहुत अधिक होगा और पट्टा हाथ या कन्धे में गढ़ जाएगा।

प्रश्न 2.
उत्प्लावकता से आप क्या समझते हैं?
उत्तर:
उत्प्लावकता- किसी द्रव का वह गुण जिसके कारण वह द्रव में छोड़ी गई किसी वस्तु पर ऊपर की ओर एक बल लगाता है, उत्प्लावकता’ कहलाता है।

प्रश्न 3.
पानी की सतह पर रखने पर कोई वस्तु क्यों तैरती या डूबती है?
उत्तर:
जब किसी वस्तु को पानी की सतह पर रखा जाता है तो उस वस्तु पर दो बल कार्य करते हैं- प्रथम वस्तु पर पृथ्वी का गुरुत्वाकर्षण बल (वस्तु का भार) नीचे की ओर तथा द्वितीय वस्तु पर पानी का उत्प्लावन बल ऊपर की और।
किसी वस्तु का पानी में डूबना या तैरना उपर्युक्त दोनों बलों के आपेक्षिक मानों पर निर्भर करता है।

• यदि वस्तु का भार उत्प्लावन बल से अधिक है तो वस्तु पानी में डूब जाएगी।
• यदि वस्तु का भार उत्प्लावन बल से कम है तो वस्तु पानी में तैरेगी।
• यदि वस्तु का भार उत्प्लावन बल के बराबर है तो वस्तु पानी में पूरी डूबकर तैरती रहेगी।

किसी वस्तु के जल में तैरने या डूबने का ज्ञान उस वस्तु के घनत्व से प्राप्त किया जा सकता है। यदि वस्तु का घनत्व जल के घनत्व से कम है तो वह वस्तु जल में तैरेगी। इसके विपरीत यदि वस्तु का घनत्व, जल के घनत्व से अधिक है तो वह वस्तु जल में डूब जाएगी।

क्रियाकलाप 10.7. (पा.पु. पू. सं. 157)
एक पत्थर के टुकड़े को किसी कमानीदार तुला या रबड़ की डोरी के एक सिरे से बाँधकर लटकाएँ (चित्र 10.5 a) पत्थर के भार के कारण रबड़ की डोरी की लम्बाई में वृद्धि या कमानीदार तुला का पाठ्यांक नोट कीजिए। अब पत्थर को पानी से भरे एक बर्तन में डुबोइए (चित्र 10.5 b) डोरी की लम्बाई या तुला की माप में हुए परिवर्तन को नोट कीजिए।

आप देखेंगे कि पानी में डुबाने पर डोरी की लम्बाई या तुला के पाठ्यांक में कमी आती है। यह कमी पत्थर द्वारा हटाए गए पानी के भार के बराबर होगी।

“जब किसी वस्तु को किसी तरल में पूर्ण या आंशिक रूप में डुबोया जाता है तो वह ऊपर की दिशा में एक बल का अनुभव करती हैं जो वस्तु द्वारा हटाए गए तरल के भार के बराबर होता है। इसे आर्किमिडीज का सिद्धान्त कहते हैं।”

आर्किमिडीज के सिद्धान्त के बहुत से अनुप्रयोग हैं। यह जलयानों तथा पनडुब्बियों के डिजाइन बनाने में काम आता हैं। हाइड्रोमीटर तथा दुग्धमापी भी इसी सिद्धान्त पर आधारित हैं।

प्रश्न 1.
पनडुब्बियां किस सिद्धान्त पर कार्य करती हैं?
उत्तर:
आर्किमिडीज के सिद्धान्त पर

प्रश्न 2.
आर्किमिडीज का सिद्धान्त क्या है?
उत्तर:
जब किसी वस्तु को पूर्ण या आंशिक रूप से द्रव में डुबोया जाता है तो वह ऊपर की ओर एक बल का अनुभव करती है, जो उस वस्तु द्वारा हटाए गए द्रव के भार के बराबर होता है।

खण्ड 10.6 से सम्बन्धित पाठ्य पुस्तक के प्रश्नोत्तर (पा.पु. पृ. सं. 158)

प्रश्न 1.
एक तुला पर आप अपना द्रव्यमान 42 किग्रा नोट करते हैं। क्या आपका द्रव्यमान 42 किग्रा से अधिक है या कम?
उत्तर:
चूँकि हम किसी वस्तु का द्रव्यमान वायु में मापते हैं; अतः वायु की उत्प्लावकता के कारण तुला का पाठ्यांक सदैव ही वस्तु के वास्तविक द्रव्यमान से कम होता है। अतः हमारा वास्तविक द्रव्यमान 42 किग्रा से अधिक होगा, यद्यपि यह अन्तर अत्यन्त कम होगा।

प्रश्न 2.
आपके पास एक रुई का बोरा तथा एक लोहे की छड़ है। तुला पर मापने पर दोनों 100 किग्रा द्रव्यमान दर्शाते हैं। वास्तविकता में एक दूसरे से भारी है। क्या आप बता सकते हैं कि कौन-सा भारी है और क्यों?
उत्तर:
वायु की उत्प्लावकता के कारण तुला दोनों का ही द्रव्यमान कम मापती है। चूँकि समान द्रव्यमान की रुई का आयतन लोहे की तुलना में अधिक है। अतः रुई पर उत्प्लावकता का प्रभाव अधिक होगा अर्थात् रुई के वास्तविक द्रव्यमान तथा प्रेक्षित द्रव्यमान में अन्तर लोहे के वास्तविक तथा प्रेक्षित द्रव्यमानों में अन्तर की तुलना में अधिक होगा। अतः रुई का वास्तविक द्रव्यमान लोहे के वास्तविक द्रव्यमान से अधिक होगा। अर्थात् रुई लोहे की तुलना में भारी होगी।

Jharkhand Board JAC Class 9 Maths Important Questions Chapter 14 सांख्यिकी Important Questions and Answers.

JAC Board Class 9th Maths Important Questions Chapter 14 सांख्यिकी

बहुविकल्पीय प्रश्न :

प्रश्न 1.
8, 3, 7, 10, 5, 6, 14, 19, 21, 25 का परिसर है :
(A) 22
(B) 17
(C) 25
(D) 14
हल :
परिसर = आँकड़ो की उच्चतम सीमा – उनकी निम्नतम सीमा = 25 – 3 = 22
सही विकल्प (A) है।

प्रश्न 2.
आँकड़ों के आलेखीय निरूपण में चर प्रदर्शित किए जाते हैं।
(A) X- अक्ष पर
(B) Y-अक्ष पर
(C) क्रमश: दोनों अक्षों पर
(D) मूल बिन्दु पर
हल :
सही विकल्प (B) है।

प्रश्न 3.
किसी वर्ग के अन्तर को कहते हैं :
(A) वर्ग की चौड़ाई
(B) वर्ग की माप
(C) वर्ग-अन्तराल
(D) ये सभी
उत्तर :
सही विकल्प (D) है।

प्रश्न 4.
किसी समस्या के 10 पदों में सबसे अन्तिम पद की संचयी आवृत्ति 60 है। तो N का मान होगा :
(A) 10
(B) 6
(C) 600
(D) 60
हल :
अन्तिम पद की संचयी बारम्बारता = समस्त बारंबारताओं का योग (N) = 60
सही विकल्प (D) है।

प्रश्न 5.
आँकड़ों में दिए गए 1 – 10, 11 – 20 …….. वर्गों की सतत बनाने के लिए :
(A) निम्न सीमा में से 0.5 घटाएगें
(B) निम्न सीमा में 0.5 जोड़ेंगे
(C) निम्न सीमा में से 0.5 घटाएगें और उच्च सीमा में 0.5 जोड़ेगे,
(D) सतत बन ही नहीं सकता।
हल :
सही विकल्प (C) है।

प्रश्न 6.
आयत चित्र में आयतों की ऊँचाइयाँ उन वर्गों की :
(A) बारम्बारताओं के व्युत्क्रमानुपाती होती हैं.
(B) बारम्बारताओं के समानुपाती होती हैं
(C) वर्ग-अन्तराल के समानुपाती होती हैं।
(D) वर्ग-अन्तराल के व्युत्क्रमानुपाती होती हैं।
हल :
सही विकल्प (B) है।

प्रश्न 7.
असमान वर्ग-अन्तराल की स्थिति में आयत चित्र बनाने के लिए वर्ग की बारम्बारता को पुनः निर्धारित करने का सूत्र है :
पुनः निर्धारित बारम्बारता = ?

हल :
सही विकल्प (A) है।

प्रश्न 8.
वर्ग – चिह्न ज्ञात करने का सूत्र है :
(A) ऊपरी सीमा – निम्न सीमा / 2
(B) (ऊपरी सीमा ÷ निम्न सीमा) × बारम्बारता
(C) ऊपरी सीमा + निम्न सीमा / 2
(D) (ऊपरी सीमा + निम्न सीमा) ÷ बारम्बारता
हल :
सही विकल्प (C) है।

प्रश्न 9.
चार छात्रों के सांख्यिकी में प्राप्तांक 53, 75, 42, 70 हैं। उनके प्राप्तांकों का समान्तर माध्य है :
(A) 42
(B) 64
(C) 60
(D) 56.
हल :
समान्तर माध्य = प्राप्तांकों का योग / छात्रों की संख्या = \(\frac{53+75+42+70}{4}=\frac{240}{4}\) = 60
सही विकल्प (C) है।

प्रश्न 10.
यदि 5, 7, 9, x का समान्तर माध्य 9 हो, तो x का मान है :
(A) 11
(B) 15
(C) 18
(D) 16
हल :
समान्तर माध्य = आँकड़ों का योग / पदों की संख्या
9 = \(\frac{5+7+9+x}{4}=\frac{21+x}{4}\)
⇒ 9 × 4 = 21 + x
⇒ 36 = 21 + x
∴ x = 36 – 21 = 15
सही विकल्प (B) है।

प्रश्न 11.
बंटन 1, 3, 2, 5, 9 की माध्यिका है :
(A) 3
(B) 4
(C) 2
(D) 20.
हल :
सही विकल्प (A) है।
पदों को आरोही क्रम में रखने पर 1, 2, 3, 5, 9
यहाँ पदों की संख्या (N) = 5 है, जो कि विषम है।
अतः माध्यिका = (\(\frac{N+1}{2}\)) वें पद का मान = (\(\frac{5+1}{2}\)) वें पद का मान = (\(\frac {6}{2}\)) वें पद का मान
= 3 वें पद का मान = 3

प्रश्न 12.
बंटन 3, 5, 7, 4, 2, 1, 4, 3, 4 का बहुलक है :
(A) 7
(B) 4
(C) 3
(D) 1.
हल :
सही विकल्प (B) है।
ऊपर दी गई सारणी को देखने से स्पष्ट होता है कि 4 की बारम्बारता सबसे अधिक (3 बार) है। अतः इसका बहुलक 4 होगा । अतः सही विकल्प (B) है।

प्रश्न 13.
माध्य के अन्य नाम हैं :
(A) समान्तर माध्य
(B) औसत
(C) मध्यमान
(D) ये सभी
हल :
सही विकल्प (D) है।

प्रश्न 14.
प्रथम 7 विषम संख्याओं का माध्यक होगा :
(A) 7
(B) 8
(C) 9
(D) 5.
हल :
प्रथम 7 विषय संख्याएँ है: 1, 3, 5, 7, 8, 11, 13.
अत : माध्यक = \(\frac{N+1}{2}\) वाँ पद = 7.
सही विकल्प (A) है।

प्रश्न 15.
प्रथम 11 पूर्ण संख्याओं का माध्य होगा :
(A) 11
(B) 10
(C) 5
(D) 55.
हल :
प्रथम 11 सपूर्ण संख्याएँ हैं 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
अतः \(\bar{x}\) = \(\frac{0+1+2+3+4+5+6+7+8+9+10}{11}\) = \(\frac {55}{11}\) = 5
सही विकल्प (C) है।

लघु एवं दीर्घ प्रश्नोत्तर :

प्रश्न 1.
निम्नलिखित बारम्बारता बंटन का परिसर ज्ञात कीजिए : 2.7, 27, 2.8, 21, 2.4, 3.2, 3.1, 2.8, 3.2.
हल :
बारम्बारता का अधिकतम मान = 3.2
बारम्बारता का न्यूनतम मान = 2.1
∴ परिसर (परास) = अधिकतम मान – न्यूनतम मान = 3.2 – 2.1 = 1.1

प्रश्न 2.
प्राथमिक आँकड़े क्या हैं?
हल :
सांख्यिकीय अन्वेषक जिन आँकड़ों का स्वयं या अपने कार्यकर्ताओं के द्वारा पहली बार संग्रहीत करता है, उन्हें प्राथमिक आँकड़े कहते हैं।

प्रश्न 3.
गौण आँकड़े अर्थात् द्वितीयक आँकड़े क्या हैं?
हल :
वे आँकड़े जिनका पूर्व में अन्य किसी व्यक्ति या संस्था द्वारा संकलन किया जा चुका हो, जो प्रकाशित या अप्रकाशित हो सकते हैं, ऐसे आँकड़ों को द्वितीयक आँकड़े कहते हैं ।

प्रश्न 4.
एक गाँव में जन्मे 30 बच्चों का भार (किग्रा में) निम्न प्रकार था :
3.4, 3.6, 3.0, 3.8, 3.6, 3.8, 2.9, 3.4, 2.9, 3.4, 3.0, 3.4, 3.2, 3.1, 3.2, 3.2, 3.1, 3.2, 3.4, 3.0, 3.1, 3.2,3.5, 3.7, 3.1, 3.0, 2.9, 3.0, 3.1, 3.2
उपर्युक्त को बारम्बारता बंटन सारणी में निरूपित कीजिए ।
हल :
बारम्बारता सारणी :

प्रश्न 5.
निम्नलिखित असतत बारम्बारता बंटन सारणी को सतत बारम्बारता बंटन सारणी में बदलिए, जिसमें एक कक्षा के 38 विद्यार्थियों के भार दिये गये हैं और यह भी बताइए कि 35.5 किग्रा तथा 40.5 किग्रा के भार वाले विद्यार्थी किस वर्ग-अन्तराल में रखे जायेंग ?

भार (किग्रा में)	विद्यार्थियों की संख्या
31-35 36-40 41-45 46-50 51-55 56 60 61-65 66-70 71-75	9 5 14 3 1 2 2 1 1
योग	38

हल :
वर्ग 31-35 और 36-40 से
वर्ग 36-40 की निम्न सीमा = 36
वर्ग 31-35 की ऊपरी सीमा = 35
न्यूनतम अन्तर (h) = 36 – 35 = 1
अन्तर का आधा (\(\frac {h}{2}\)) = \(\frac {1}{2}\) = 0.5
इस प्रकार प्रत्येक वर्ग की निम्न सीमा से 0.5 घटा कर और ऊपरी सीमा में 0.5 जोड़कर सतत वर्ग-अन्तराल बनाते हैं।

भार (किग्रा में)	विद्यार्थियों की संख्या
30.5-35.5 35.5-40.5 40.5-45.5 45.5-50.5 50.5-55.5 55.5-60.5 60.5-65.5 65.5-70.5 70.5-75.5	9 5 14 3 1 2 21 1
योग	38

अतः 35.5 किग्रा भार को 35.5 – 40.5 वर्ग – अन्तराल में और 40.5 किग्रा भार को 40.5 – 45.5 वर्ग – अन्तराल में रखते हैं।

प्रश्न 6.
एक परिवार ने जिसकी मासिक आय ₹ 20,000 है। विभिन्न मदों के अन्तर्गत हर महीने होने वाले खर्च की योजना बनाई थी :

मद	खर्च
ग्रासरी (परचून का समा) किराया बच्चों की शिक्षा दवाइयाँ ईंधन मनोरंजन विविध	4000 5000 5000 2000 2000 1000 1000

ऊपर दिये गये आँकड़ों का दण्ड आलेख बनाइए ।
हल :
दण्ड आलेख बनाने की विधि :
(i) पहले X- अक्ष और Y – अक्ष खींचते हैं।
(ii) X-अक्ष पर अचर (मद) को निरूपित करते हैं। दो मदों के मध्य समान दूरी रखी जाती है ।
माना पैमानाः 1 सेमी = 1 मद
(iii) Y-अक्ष चर (विभिन्न ) पर खर्च को निरूपित करते हैं। पैमाना : 1 सेमी = ₹ 1,000 ।
(iv) अब दिये गये आँकड़ों के अनुसार तथा दो क्रमागत आयताकार दण्डों के बीच 1 सेमी का खाली स्थान छोड़कर (समान चौड़ाई) आयताकार दण्ड प्रदर्शित करते हैं।

प्रश्न 7.
निम्न बारम्बारता सारणी से आयत चित्र बनाइए :

हल :
यहाँ बारम्बारता बंटन वर्गीकृत एवं सतत है। वर्ग अन्तराल भी समान हैं।
(i) X- अक्ष पर पैमाना : 1 सेमी = 5 इकाई मानकर वर्ग-अन्तराल को निरूपित करते हैं जो आयत की चौड़ाई को व्यक्त करता है।
(ii) Y – अक्ष पर पैमानाः 1 सेमी = 2 इकाई मानकर बारम्बारता को अंकित करते हैं जो आयत की ऊँचाई को निरूपित करता है।

प्रश्न 8.
निम्न बारम्बारता बंटन के लिए बारम्बारता बहुभुज का निर्माण कीजिए :

हल :

X – अक्ष पर पैमाना (1 सेमी = 5 इकाई) लेकर विचर अंकित किये और Y – अक्ष पर पैमाना (1 सेमी = 2 इकाई) लेकर बारम्बारता अंकित कीं ।
अब बिन्दु (5, 2), (10, 6), (15, 4), (20, 1), (25, 5) और (30, 2) अंकित किये। प्रथम विचर से पहले विचर का मान शून्य आता है। अब बिन्दु (5, 2) को बिन्दु (0, 0) से मिलाया । इसी प्रकार अन्तिम विचर से आगे वाला विचर 35 है। अतः अंतिम बिन्दु (30, 2) को बिन्दु (35, 0) से मिलाया ।
इस प्रकार प्राप्त लेखाचित्र दिए गए बारम्बारता बंटन के लिए बारम्बारता बहुभुज होगा ।

प्रश्न 9.
प्रथम दस विषम संख्याओं का समान्तर माध्य ज्ञात कीजिए ।
हल :
प्रथम दस विषम संख्याएँ क्रमशः 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 हैं।
अतः समान्तर माध्य (\(\bar{x}\)) = \(\frac{1+3+5+7+9+11+13+15+17+19}{10}\) = \(\frac {100}{10}\) = 10

प्रश्न 10.
एक विद्यालय के सहायक कर्मचारियों का मासिक वेतन (रुपयों में) 1,720, 1,750, 1,760 तथा 1,710 है, तो समान्तर माध्य ज्ञात कीजिए ।
हल :
समान्तर माध्य = कर्मचारियों के मासिक वेतन का योग / कर्मचारियों की संख्या
= \(\frac{1,720+1,750+1,760+1,710}{4}\) = \(\frac {6940}{4}\) = ₹ 1735
अतः समान्तर माध्य = ₹ 1735

प्रश्न 11.
निम्नलिखित बंटन का समान्तर माध्य ज्ञात कीजिए :

हल : 

x	f	fx
0.1 0.2 0.3 0.4 0.5 0.6	30 60 20 40 10 50	3 12 6 16 5 30
	Σf = 210	Σfx = 72

अतः समान्तर माध्य (\(\bar{x}\)) = \(\frac {Σfx}{Σf}\) = \(\frac {72}{210}\)
= 0.342.

प्रश्न 12.
निम्न आँकड़ों की माध्यिका ज्ञात कीजिए : 19, 25, 59, 48, 35, 31, 30, 32, 51.
हल :
दिये गये आँकड़ों को आरोही क्रम में रखने पर,
19, 25, 30, 31, 32, 35, 48, 51, 59
यहाँ कुल पद (n) = 9, जो कि विषम पद है।
अतः माध्यिका = (\(\frac{n+1}{2}\)) वाँ पद = (\(\frac{9+1}{2}\))वाँ पद
= (\(\frac {10}{2}\))वाँ पद = 5वाँ पद = 32
अतः माध्यिका 32।

प्रश्न 13.
आरोही क्रम में व्यवस्थित चर मान (x) निम्नानुसार हैं : 8 11 12 16 16 + x 20 25 30 यदि माध्यिका 18 हो, तो x का मान ज्ञात कीजिए ।
हल :
यहाँ कुल चरों की संख्या 8 है जो कि समसंख्या है।

⇒ 32 + x = 36 ⇒ x = 36 – 32 = 4
अतः x का मान = 4.

प्रश्न 14.
एक कक्षा के 20 छात्रों की आयु (वर्षों में) निम्न प्रकार है :
15 16 13 14 14 13 15 14 13 13 14 12 15 14 16 13 14 14 13 15
इन्हें बारम्बारता बंटन सारणी में व्यक्त कर बहुलक ज्ञात कीजिए ।
हल :

सारणी से स्पष्ट है कि सबसे अधिक बारम्बारता 7, आयु 14 वर्ष की है।
अतः बहुलक 14 है।

प्रश्न 15.
कुछ विद्यार्थियों के प्राप्तांक नीचे दिये हुए हैं, प्राप्तांकों का बहुलक ज्ञात कीजिए :

हल :
सारणी से स्पष्ट है कि 40 अंक प्राप्त करने वाले विद्यार्थियों की संख्या सर्वाधिक 26 है
अत: बहुलक 40 है।

प्रश्न 16.
क्रिकेट के एक खिलाड़ी ने 10 पारियों में क्रमश: 60, 62, 56, 64, 0, 57, 33, 27, 9 और 71 रन बनाये । उनके इन पारियों के रनों का औसत ज्ञात कीजिए।
हल :

प्रश्न 17.
यदि 3, 4, 8, 5, x, 3, 2, 1 अंकों का समान्तर माध्य 4 हो, तो x का मान ज्ञात कीजिए ।
हल :
समान्तर माध्य (\(\bar{x}\)) = पदों का योग / पदों की संख्या
4 = \(\frac{3+4+8+5+x+3+2+1}{8}\)
⇒ 4 × 8 = 26 + x
⇒ 32 = 26 + x
∴ x = 32 – 26 = 6
अत: x = 6.

प्रश्न 18.
यदि 6, 9, 5, 8, x, 4 अंकों का समान्तर माध्य 7 हो, तो x का मान ज्ञात कीजिए ।
हल :
चूँकि समान्तर माध्य (\(\bar{x}\)) = \(\frac{\Sigma x_i}{N}\)
\(\bar{x}\) = \(\frac{6+9+5+8+x+4}{6}\)
⇒ \(\bar{x}\) = \(\frac{32+x}{6}\) = 7 (∵ \(\bar{x}\) = 7)
⇒ 32 + x = 42
⇒ x = 42 – 32
∴ x = 10

प्रश्न 19.
किसी बारम्बारता बंटन का समान्तर माध्य 18.50 है तथा Σf = 20, तो Σfx का मान ज्ञात कीजिए ।
हल :
हम जानते है कि,
\(\bar{x}\) = \(\frac {Σfx}{Σf}\)
⇒ समान्तर माध्य, 18.50 = \(\frac {Σfx}{20}\)
⇒ Σfx = 18.50 × 20
∴ Σfx = 370

प्रश्न 20.
किसी फुटबाल खिलाड़ी ने कुछ मैचों में 3 गोल प्रति मैच की औसत से 39 गोल किए। खिलाड़ी द्वारा खेले गए मैचों की संख्या बताइए।
हल :
औसत \(\bar{x}\) = 8 तथा कुल गोल Σx = 39.
∴ \(\bar{x}\) = \(\frac {Σfx}{N}\)
⇒ 3 = \(\frac {39}{N}\)
⇒ 3 × N = 39
⇒ N = \(\frac {39}{N}\) = 13