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These DAV Class 8 SST Book Solutions and DAV Class 8 SST Chapter 1 Question Answer – Resources: Utilization and Development are thoughtfully prepared by experienced teachers.

DAV Class 8 SST Ch 1 Question Answer – Resources: Utilization and Development

DAV Class 8 SST Ch 1 Solutions – Resources: Utilization and Development

Something to Know

A. Tick (✓) the correct option.

Question 1.
Future generations will depend on solar energy because it is-
(a) biotic
(b) man-made
(c) inexhaustible
(d) non-renewable
Answer:
(c) inexhaustible

Question 2.
Which one of the following resources can be recycled?
(a) gold
(b) coal
(a) land
(d) natural gas
Answer:
(a) gold

Question 3.
All the abiotic resources include-
(a) living beings
(b) non-living things
(c) inexhaustible resources
(d) renewable resources
Answer:
(b) non-living things

Question 4.
Available resources which are not being tapped fully for the time being are called-
(a) actual resources
(b) man-made resources
(c) biotic resources
(d) potential resources
Answer:
(d) potential resources

Question 5.
Which one does not promote conservation of resources?
(a) use resources more efficiently.
(b) optimum utilisation of resources.
(c) use as much resources as required.
(d) reduce wastage of resources.
Answer:
(c) use as much resources as required.

B. Fill in the blanks.

Question 1.
________ can be used again and again after processing.
Answer:
Metals

Question 2.
On the basis of occurrence, resources are classified into two categories ________ and ________ .
Answer:
natural; man made

Question 3.
With advancement of technology availability of ________ and ________ labour are necessary for resource utilisation.
Answer:
capital; skilled

Question 4.
Developed countries are economically self-sufficient ________ and ________ advanced.
Answer:
technically

Question 5.
The ________ resources need a detailed survey for estimating their quantity and quality.
Answer:
potential

C. Write a technical term or an appropriate word for each of the following statements.

1. Any material which is used to satisfy human needs.
Answer:
Resource

2. Resources which cannot be renewed.
Answer:
Non-renewable resources

3. Resources which are created by human beings.
Answer:
Man-made resources

4. The resource which are surveyed and developed.
Answer:
Actual resources

5. Sustainable and optimum utilisation of resources.
Answer:
Conservation.

D. Answer the following questions in brief.

Question 1.
‘Utility and value of a resource vary from time to time and place’. Give any three examples to support the statement.
Answer:
Utility and value of a resource varies from time to time and place to place. For example,

• Earlier human civilisations flourished along the river valleys as they used water for irrigating fields
• Now, human beings are using water for generating energy, irrigation, navigation and industries, etc.
• China and United States of America (USA) are generating more wind energy than India.

Question 2.
Why are human beings considered the most important resource for development?
Answer:
Human beings are important because of the following reasons:

• Human beings have an intelligent mind which can make best use of nature to create more resources.
• Had humans not been there, different substances would not have been resources.
• Their utility can be only realised by human beings.

Question 3.
Differentiate between biotic and abiotic resources. Give examples for each.
Answer:

• Biotic resources: The resources are obtained from biosphere and have life. For example, birds, animals, etc.
• Abiotic resources: These resources are non-living. For example, land minerals, etc.

Question 4.
Why is there a need for a resource planning? Give any three reasons.
Answer:
There is a need for resource planning because

• resources are rapidly depleting.
• Human beings have always used resources to satisfy their wants. Over-use of many valuable resources have led to their degradation or deterioration in quality.
• Due to deforestation, many plant and animal species have become endangered and are on the verge of becoming extinct.

Question 5.
Mention any six factors on which the utilisation of resources depend.
Answer:
The utilisation of resources depends upon various factors:

• Availability of resources
• Skill of human beings
• Availability of capital
• Advancement of technology (tools, machines, etc.)
• Availability of transport and common certain facilities
• Availability of water.

E. Answer the following questions.

Question 1.
‘Human needs and wants are neither uniform in all parts of the world nor static over the year’. Explain the statement by giving suitable examples.
Answer:

1. It is a fact that human needs and wants are neither uniform in all parts of the world nor static over the years. They generally grow and become complete with the process of change in the society.
2. In ancient times, emphasis was mainly given on satisfying the basic needs, such as food, clothing and shelter which were derived from the natural environment.
3. In advanced societies, greater emphasis has been given to utilisation of resources for satisfying the multifarious needs of human beings.

Question 2.
Distinguish between renewable and non-renewable resources. Which one of the two would you prefer to use and why?
Answer:

Renewable resources	Non-renewable resources
(i) Resources which can be renewed either naturally or by human efforts are called renewable resources.	(i) Resources which take a longer period of time (millions of years) to be renewed are called non-renewable resources.
(ii) Renewable resources are also called inexhaustible resources.	(ii) Non-renewable resources are also called exhaustible resources.
(iii) The quality of these resources can be affected by improper usage.	(ii) Non-renewable resources are also called exhaustible resources.

We would prefer renewable resources because some of the renewable resources are always available.

Question 3.
What is meant by sustainable development? Why is sustainable development the need of the hour?
Answer:
Sustainable development means development that takes place without damaging the environment. It is the need of the hour, because of our resources are limited in their supply. Over-use of many valuable resources has led to their degradation or deterioration in quality, for example, soil, land and water resources. Therefore, resources should be utilised judiciously so that after fulfilling our present requirement, they are also conserved for the future generations.

Question 4.
Describe the various basis of classification of resources with the help of examples.
Answer:
Classification of resources is done on the basis of (a) Renewability (b) Origin (c) Occurrence (d) Development
(a) On the basis of renewability resources are of two types:

• Renewable or inexhaustible resources: These resources can be renewed either naturally or by human effects. For example, solar energy, air and water.
• Non-renewable or exhaustible resources: These resources take millions of years to be renewed. For example, energy resources such as coal, potroleum, etc.

(b) On the basis of origin resources are classified into:

• Biotic resources: The resources are obtained from biosphere and have life. For example, birds, animals, etc.
• Abiotic resources: These resources are non-living. For example, land, minerals, etc.

(c) On the basis of occurrence resources are classified into:

• Natural resources: These resources are available from the nature in the form of water, minerals, forests, etc. and used by human beings to satisfy their needs.
• Man-made resources: These resources are created by human beings to satisfy their needs. For example, roads, machines, etc.

(d) On the basis of level of development of resources, we have two types of resources:

• Actual resources: These resources have been thoroughly surveyed and their quantities are ascestained. For example, Saudi Arabia has 25.9 per cent of the world oil reserved.
• Potential resources: These resources are those whose utility is not known at present or those which are not used despite having utility; instead they may be useful at some time in future. For example, uranium deposits in Ladakh.

Value Based Question

Gandhi said, “there is enough for everybody’s need and not for anybody’s greed”. Earlier humans adopted simple lifestyle by consuming minimum resources from nature. With the advancement in technology, our resource consumption has increased manifold. It created a void in nature. At present, resources are depleting at a fast rate resulting in climate change, loss of biodiversity and death of resources. There is a tremendous consumption of water, energy, food and minerals. For a sustainable society, we all have to change our lifestyle. Especially, the youth has to reduce consumption of resources so that production can be controlled. Minimise the wasteful consumption of resources for a better tomorrow. Adopt sustainable consumption pattern. We have only habitable planet. Care for it.

Question 1.
Technological advancement is a boon as well as a bane to human civilisation. Give one example each to support the statement.
Answer:
Technological advancement is a boon as well as a bane to human civilisation. For example, fossil fuels are needed to provide heat, lighting and power to run vehicles, industries, various gadgets, etc. But at present, they are depleting at a fast rate. Fossil fuels are exhaustible resources. Once consumed they cannot be replaced soon enough. Coal and petroleum reserves have been dwindling all over the world. Today, entire world is facing with an energy crisis.

Question 2.
Highlight any two advantages of sustainable lifestyle.
Answer:
(i) The usage of renewable resources is sustainable.
(ii) The diversity of life on the earth is maintained.
(iii) Proper balance between population and utilisation of resources is maintained.
(iv) The resources are used more efficiently in order to reduce wastage. (Any two)

Question 3.
As a young Indian how can you contribute in reversing the adverse impact of human interference on environment?
Answer:
As a young Indian, it is our duty to ensure that
(a) all uses of renewable resources should be sustained.
(b) the diversity of life on earth should be conserved.
(c) the population and distribution of rare and threatened species should be increased.
(d) damage to natural environment should be minimised.
(e) recycling of reusable goods should be increased.
(f) alternative resource is used, if made available.

Map Skill

On an outline political map of the world, show any three developed and developing countries each.
Answer:

Something to Do

Question 1.
Prepare a pictorial chart showing the classification of resources giving at least a suitable example of each category of resource.
Answer:

Classification based on	Name	Examples
1. Renewability	(i) Renewable (ii) Non-renewable	air, water, solar energy, petroleum, coal, natural gas
2. Origin	(i) Biotic (ii) Abiolic	birds, animals, fish, land, water, minerals
3. Occurrence	(i) Natural (ii) Man-made	water, minerals, forests roads, buildings, machines
4. Level of Development	(i) Potential (ii) Actual	uranium deposits in Ladakh oil, reserves in Saudi Arabia

Note: Pictorial work do yourself.

Question 2.
Suggest any five ways to reduce the wastage of resources.
Answer:
Five ways to minimise wastage of resources:

• Swatch off lights when not needed.
• Recycle things and use them again.
• Take bath with a bucket full of water rather than in shower.
• Repair leaking taps.
• Spread awareness among masses.

Question 3.
Look around your home and neighbourhood and list the ways in which water is wasted.
Answer:
Do it on your own observation.

DAV Class 8 Social Science Chapter 1 Question Answer – Resources: Utilization and Development

A. Tick (✓) the correct option.

Question 1.
Which one of the following is a natural resource?
(a) Forests
(b) Roads
(c) Medicines to treat asthma
(d) Television
Answer:
(a) Forests

Question 2.
Which one of the following is a biotic resource?
(a) Birds
(b) Land
(c) Water
(d) Minerals
Answer:
(a) Birds

Question 3.
Coal is a
(a) renewable resource
(b) non-renewable resource
(c) made-made resources
(d) biotic resources
Answer:
(b) non-renewable resource

Question 4.
On the basis of level of development, resources are classified int.
(a) biotic and abiotic
(b) natural and man-made
(c) renewable and non-renewable
(d) potential and actual
Answer:
(d) potential and actual

Question 5.
Which of the following is a recyclable mineral?
(a) Coal
(b) Petroleum
(c) Gold
(d) Natural gas
Answer:
(c) Gold

Question 6.
A vehicle is a
(a) natural resources
(b) man-made resource
(c) renewable resource
(d) biotic resource
Answer:
(b) man-made resource

B. Very Short Answer Type Questions

Question 1.
Define the term conservation.
Answer:
Conservation means using resources carefully and giving them time to get renewed.

Question 2.
WThat do you understand by sustainable development?
Answer:
Sustainable development means development that takes place without damaging the environment. Development that meets the needs of the present without compromising the needs of future generations.

Question 3.
What is the condition for a substance to be called a resource?
Answer:
A substance needs to have some utility to be called a resource.

Question 4.
Mention two disadvantages of over-irrigation.
Answer:
(i) It is responsible for water logging.
(ii) It makes the soil infertile.

Question 5.
Why are human beings considered as a resource?
Answer:
It is only with the help of human skill, that the other resources can be developed.

Question 6.
Why are countries like USA and Japan termed as developed countries?
Answer:
These countries are economically self-sufficient and technologically advanced.

Question 7.
Why are African nations less developed inspite of being rich in resources?
Answer:
Most of the people in African nations are unskilled and illiterate.

Question 8.
What do you mean by resource development?
Answer:
Resource development is the method of utilising our intelligences in order to improve the quality, usability and utility of a resource.

Question 9.
Where are biotic resources derived from?
Answer:
Biotic resources are derived from living things.

Question 10.
What are natural resources?
Answer:
Resources that are drawn directly from nature are called natural resources.

Question 11.
How are man-made resources different from natural resources?
Answer:
Man-made resources have been created by human beings, whereas natural resources are provided by nature.

Question 12.
Which biotic resources take a long period of time to be renewed?
Answer:
Forests are the biotic resources which take a long period of time to be renewed.

Question 13.
Why countries like USA and UK make optimum use of resource as compared to India? What is the reason behind it?
Answer:
These countries are well developed and have technically skilled human resource. India lacks this resource in required number.

Question 14.
How has rapid population growth affected natural resources?
Answer:
Rapid population growth has led to drastic depletion and degradation of natural resources.

Question 15.
What are essential for a long term sustainability of natural resources?
Answer:
Development of technology, human skill and population control are essential for a long term sustainability of natural resources.

Question 16.
How can we contribute to sustainable development?
Answer:
We can contribute to sustainable development by switching off lights when not needed and by recycling things and using them again.

C. Short Answer Type Questions

Question 1.
Mention three features of non¬renewable resources.
Answer:
(i) Non-renewable resources are exhaustible resources as they cannot be renewed.
(ii) They are limited on the earth’s surface and complete utilisation of such resources would result in their exhaustion.
(iii) Some of the minerals like metallic ores i.e., gold and silver are recyclable as the metals may be used again and again after processing.

Question 2.
The quality and quantity of people of a country determine its human resource’. Explain.
Answer:
(i) Healthy and well-educated people contribute to their respective societies in positive ways. They develop resources as per their requirements.
(ii) Malnourished and illiterate people, on the other hand, cannot contribute much to their respective societies. They cannot develop resources as per their needs.
(iii) Resources are well-developed in Japan as people are skilled and technically developed. African nations, inspite of being rich in resources are less developed as most of the people are unskilled and illiterate.

D. Long Answer Type Questions

Question 1.
Differentiate between natural and man-made resources
Answer:

Natural resources	Man-made resources
(i) These resources are taken from nature. They are used without modifying them.	(i) These resources are created by human beings by dint of their intelligence for their own use.
(ii) They provide a base for the development of a country.	(ii) They show how developed a country is.
(iii) Many of these resources are essential for our survival.	(iii) They are essential for us to lead a highly comfortable life.
For examples air, rivers, souls, minerals, trees, mountains, etc. are natural resources.	For examples Roads, buildings, telephone, vehicles, machines, etc. are man-made resources.

Question 2.
Technology plays an important role for the development of resources.’ Explain.
Answer:
(i) Resources are undoubtedly essential for development but merely their presence does not guarantee development. Here, technology plays a vital role.

(ii) Resources become usable when they are processed in several ways by dint of technology.

(iii) For example, wood can be used for making furniture after the trees are fallen and logs are transported to the factory where these are cut, shaped and made into furniture. In the absence of technology, it would be impossible for us to convert wood into several useful items.

(iv) Again, it is technology that turns various natural resources into man¬made resources. The technology of hydroelectricity has made water a source of electricity.

Question 3.
Differentiate between potential and actual resources.
Answer:

Potential resources	Actual resources
(i) These resources are not being used currently.	(i) We can use these resources currently.
(ii) They can prove useful and become actual resources in the future.	(ii) They might have been potential resources in the past. They may end up in the future.
(iii) The entire quantity of potential resources may not be known.	(iii) The actual quantity of these resources is known.
Example: Oil and natural gas reserves beneath the Arctic sea-bed.	Examples: Oil reserves in Saudi Arabia.

These DAV Class 7 SST Book Solutions Pdf and DAV Class 7 SST Chapter 1 Question Answer – Components of Environment are thoughtfully prepared by experienced teachers.

DAV Class 7 SST Ch 1 Question Answer – Components of Environment

DAV Class 7 SST Ch 1 Solutions – Components of Environment

Something To Know

A. Tick (✓) the correct option.

Question 1.
Which one is not a part of biological environment?
(a) plants
(b) water
(c) animals
(d) human beings
Answer:
(b) water

Question 2.
Volcanoes erupt due to
(a) internal disturbance of the earth.
(b) external disturbance of the earth.
(c) climate change.
(d) man-made changes on the earth.
Answer:
(a) internal disturbance of the earth.

Question 3.
Which one brings a sudden change in the environment?
(a) formation of a river
(b) rainfall
(c) growth of a plant
(d) formation of a mountain
Answer:
(b) rainfall

Question 4.
Identify by the term that stands for the topmost layer of the earth comprising of loose material
(a) minerals
(b) soil
(c) sial
(d) sima
Answer:
(c) sial

Question 5.
In which year was the Wildlife Protection Act passed in India?
(a) 1971
(b) 1972
(c) 1973
(d) 1974
Answer:
(b) 1972

B. Give a single term for each of the following statements.

Question 1.
A situation or condition in which an organism lives.
Answer:
Environment.

Question 2.
The only planet in our solar system where life exists.
Answer:
Earth.

Question 3.
The uppermost part of the lithosphere which is rich in silica and aluminium.
Answer:
Soil.

Question 4.
The sphere of air that envelopes the earth.
Answer:
Atmosphere.

Question 5.
Mass of water on the earth’s surface.
Answer:
Hydrosphere.

C. Match the following:

Physical environment includes	(a) Atmosphere
It is the most dynamic in nature	(b) Human beings
A narrow zone supporting life	(c) Non-living things
They are capable of modifying environment	(d) Biosphere
Rocks rich in silica and magnesium	(e) Sima

Answer:

Physical environment includes	(c) Non-living things
It is the most dynamic in nature	(a) Atmosphere
A narrow zone supporting life	(d) Biosphere
They are capable of modifying environment	(b) Human beings
Rocks rich in silica and magnesium	(e) Sima

D. Answer the following questions in brief.

Question 1.
Name the major components of the environment.
Answer:
The major components of the environment are—natural (land, air, water, living things), human-made (buildings, bridges, industries, roads, parks, monuments, etc.), and human (individual, family, community, religion, educational, economic, etc.).

Question 2.
What do you mean by Sima and Sial?
Answer:
The uppermost part of the lithosphere is composed of rocks rich in silica and aluminium called sial. Below the sial layer, the rocks are mainly rich in silica and magnesium and are called sima. It is generally found below the bottom of the ocean basins.

Question 3.
Mention the distribution of water in the Northern and Southern hemispheres.
Answer:
It is estimated that 43% of the total area covered by water lies in the Northern hemisphere; whereas the remaining 57% lies in the Southern hemisphere.

Question 4.
Give the literal meanings of fou spheres of environment.
Answer:
(i) Lithosphere – the ‘sphere of rocks’.
(ii) Atmosphere – the ‘sphere of air’.
(iii) Hydrosphere – the ‘sphere of water’.
(iv) Biosphere – the ‘sphere of life’.

Question 5.
What is the atmosphere composed of?
Answer:
The atmosphere is composed of a mixture of gases like oxygen, nitrogen, carbondioxide, hydrogen, ozone, etc.

E. Answer the following questions.

Question 1.
Differentiate between the physical and the biological environment.
Answer:
The physical environment includes the non-living elements of the environment such as the land, water and air. The biological environment, on the other hand, includes all living things such as, plants, animals and other living organisms.

Question 2.
Why is the earth also called the ‘Blue Planet’?
Answer:
71% of the earth’s surface is covered by waterbodies that include rivers, lakes, seas and oceans. The earth is called the ‘Blue Planet’ because of this abundance of water on its surface.

Question 3.
Define biosphere. Why is it important for us?
Answer:
The word biosphere literally means the ‘sphere of life’. It is the narrow zone where we find land, water and air together. All kinds of life exist in this zone. Therefore, it is important for us.

Question 4.
Explain with the help of an example how physical and biological components of the environment are interdependent.
Answer:
The physical and biological com¬ponents of the environment are interdependent. It means they cannot be separated. Any major change in the physical environment is bound to bring a change in the accompanying biological environment.

Example:
The development of soil takes years together and cannot be noticed through our senses. On the other hand, some changes are very sudden. The occurrence of an earthquake or volcano can bring sudden changes.

Question 5.
Explain two ways in which human beings are disturbing the natural environment.
Answer:
Human beings use the environment for their selfish motives and many times disturb the natural balance of the environment. The two ways in which they are disturbing the natural

environment are –
(i) Technological and scientific development have posed danger.
(ii) Forests are being cut on a large scale. This has reduced the green cover on the earth.

Value-Based Question

1. On 25 April 2015, a massive earthquake of 7.8 magnitude struck 77 km northwest of Nepal’s capital, Kathmandu. It was the most powerful earthquake to have hit Nepal since 1934. It led to heavy loss of life and property. During this earthquake, four men were trapped under the 10 feet rubble. They were rescued by NASA technology, FINDER (Finding Individuals for Disaster and Emergency Response) which sensed their heartbeats. This was the first time when this technology was used in a real-life situation. This is indeed a big step towards disaster management. But this is no way, reduces our responsibilities as human beings.

• Under the circumstances, what best can we do after the disaster?
• Suggest any five ways in which we can help the victims of a disaster.

Answer:
Do it yourself with the help of Internet.

Map Skill

Question 1.
On an outline map of the world, show the given National Parks.
(a) Gir National Park – India
(b) Jim Corbett National Park – India
(c) Yellowstone National Park – USA
(d) Serengeti National Park – Tanzania
(e) Fiord land National Park – New Zealand
Answer:

Something To Do

Question 1.
Hold a class discussion on good and bad environment.
Answer:
Do yourself.

Question 2.
Prepare a diagram showing different spheres of the environment
Answer:

Question 3.
Prepare 20 flash cards showing the wildlife species of India (flora and fauna both), based on this, hold a quiz in the class showing one flash card at a time. For every card, ask the questions like –
(a) Who has seen it live and where?
(b) If not, where can we see it live?
Answer:
Do it yourself.

DAV Class 7 Social Science Chapter 1 Question Answer – Components of Environment

A. Tick (✓) the correct option.

Question 1.
The sphere of the environment where life exists is called
(a) biosphere
(b) hydrosphere
(c) lithosphere
(d) atmosphere
Answer:
(a) biosphere

Question 2.
The sphere of the environment which provides for us land is called
(a) hydrosphere
(b) atmosphere
(c) lithosphere
(d) biosphere
Answer:
(c) lithosphere

Question 3.
The sphere which is the most dynamic in nature is
(a) biosphere
(b) lithosphere
(c) hydrosphere
(d) atmosphere
Answer:
(d) atmosphere

Question 4.
The number of National Parks in India is
(a) 489
(b) 301
(c) 103
(d) 89
Answer:
(c) 103

Question 5.
The uppermost part of the lithosphere is composed of
(a) rocks
(b) minerals
(c) soil
(d) magnesium
Answer:
(a) rocks

Question 6.
The most important component of the biological environment is
(a) plant
(b) man
(c) water
(d) land
Answer:
(b) man

B. Fill in the blanks.

1. The lithosphere is about …………… km in thickness.
2. ………….. and ………….. are the living components in the environment.
3. ………….. The Act 1972 was passed in India to protect the species of plants and animals.
4. …………. is the process which brings out emergence of new species of plants and animals in the environment.
5. ………….. form the major part of water on earth.
Answer:
1. 100
2. Plants; animals,
3. Wildlife Protection,
4. Biodiversity
5. Oceans.

C. Very Short Answer Type Questions

Question 1.
What is the atmosphere?
Answer:
It is a gaseous envelope extending about 1600 km above the earth’s surface.

Question 2.
What do you know about the distribution of water in the Northern and Southern hemispheres?
Answer:
The distribution of water is not uniform in the Northern and Southern hemispheres. About 43% of the total area covered by water lies in the Northern hemisphere and 57% lies in the Southern hemisphere.

Question 3.
Where is Sima found?
Answer:
Sima is generally found below the bottom of the ocean basins.

Question 4.
What percentage of the Earth’s surface is covered by water?
Answer:
71 per cent.

Question 5.
How can you say that the ocean is the largest reservoir of water?
Answer:
90 per cent part of water is covered by four oceans, namely, Pacific, Atlantic, Indian and Arctic.

Question 6.
Name two groups of environment.
Answer:
1. Physical environment
2. Biological environment.

D. Short Answer Type Questions

Question 1.
How can you say that environment has both natural and man-made elements?
Answer:
The environment provides us the air we breathe, the water we drink, the food we eat and the land where we live. It also includes plants, animals and a large variety of man-made things which are necessary for our being. Thus, we can say that environment has both natural and man-made elements.

Question 2.
Among the four major elements of the environment, atmosphere is the most dynamic in nature. Explain.
Answer:
It is an atmosphere where changes occur not only from one season to another but also within a short period of time (a few hours). These sudden changes produce changes in weather conditions which affect our life both directly and indirectly.

Question 3.
What do you mean by the term biodiversity? What has the Government of India done to protect and conserve it?
Answer:
Our earth is full of diversities. There is diversities in land, soil, plants and animals. This process of diversification has occurred over a long period of time. As a result of this, new species of plants and animals have emerged. These changes together are known as biodiversity. To protect and conserve this biodiversity, the Government of India has passed the Wildlife Protection Act 1972 under which 103 National Parks and 535 Wildlife Sanctuaries have been established in the country.

Question 4.
What is expected from the human beings?
Answer:
It is expected from the human beings that they live in harmony with their surroundings. This will allow the earth to sustain all forms of life on it. If they exploit various resources available on the earth, they must do it carefully and responsibly.

E. Long Answer Type Questions

Question 1.
What is lithosphere? Give a brief description of it.
Answer:
The lithosphere refers to the solid portion of the earth where we live. It is about 100 km in thickness. The uppermost part of the lithosphere is composed of rocks rich in silica and aluminium called sial. Below this layer, the rocks are mainly rich in silica and magnesium, which together are called sima. It is generally found below the bottom of the ocean basins. This sphere provides for us land which we live on. It provides soil for the plants. It is also a source of different minerals.

Question 2.
Define atomosphere, hydrosphere and biosphere.
Answer:
Atmosphere. The atmosphere is composed of a mixture of gases which forms an envelope around the earth. It is a gaseous envelope extending about 1,600 km above the earth’s surface. Of the total mass of the atmosphere, 99 per cent exits within 32 km of height from the earth’s surface. Hydrosphere. The planet earth is often called the Water Planet or the Blue Planet because of abundance of water on its surface. The water bodies that include rivers, lakes, seas and oceans cover 71 per cent of the earth’s surface.

The distribution of water is not uniform in both the Northern and the Southern Hemispheres. It is estimated that 43 per cent of the total area covered by water lies in the Northern Hemisphere whereas the remaining 53 per cent lies in the Southern Hemisphere. Oceans hold 96.5 per cent water on the earth.

Rest of the water is available in the form of ice, water vapours, underground water, rivers and lakes. Biosphere. It is the narrow zone of contact between all the three spheres of environment where all kinds of life exist. Most of the living organisms like plants, animals and microbes present on the earth are found on or near the earth’s surface of the land, water and air. Human beings are an important part of the biosphere. They are capable of changing it.

Question 3.
Suggest ways in which we can live in harmony with our surroundings and stop the exploitation of the environment.
Answer:
The exploitation of the environment can be stopped through the following measures.

• Hunting and poaching of wild animals should be stopped. We should refuse buying things made from parts of the bodies of animals; such as, their bones, horns, fur, skins and feathers.
• Afforestation should be encouraged
• Population growth should be checked.
• Awareness about environment should be spread.

The DAV Class 7 Maths Book Solutions Pdf and DAV Class 7 Maths Chapter 1 Worksheet 1 Solutions of Rational Numbers offer comprehensive answers to textbook questions.

DAV Class 7 Maths Ch 1 WS 1 Solutions

Question 1.
Which of the following are rational numbers?
(i) -3
(ii) \(\frac{-2}{3}\)
(iii) \(\frac{4}{0}\)
(iv) \(\frac{0}{-5}\)
Answer:
(i) -3 is a rational number.
(ii) \(\frac{-2}{3}\) is a rational number.
(iii) \(\frac{4}{0}\) is not a rational number as
(iv) \(\frac{0}{-5}\) is a rational number.

Question 2.
Write down the rational numbers in the form \(\frac{p}{q}\) whose numerators and denominators are given below.
(i) (-5) × 4 and -5 + 4
Answer:
Numerator = (- 5) × 4 = – 20
Denominator = – 5 + 4 = – 1
Rational Number = \(\frac{-20}{-1}\) or \(\frac{20}{1}\) = 20

(ii) 64 ÷ 4 and 32 – 18
Numerator = 64 + 4 = 16
Denominator = 32 – 18 = 14
Rational Number = \(\frac{16}{14}=\frac{16 \div 2}{14 \div 2}=\frac{8}{7}\)

Question 3.
Which of the following are positive rational numbers?
(i) \(\frac{-2}{9}\)
Answer:
\(\frac{-2}{9}\) is not positive rational number.

(ii) \(\frac{3}{-5}\)
Answer:
\(\frac{3}{-5}\) is not positive rational number.

(iii) \(\frac{4}{9}\)
Answer:
\(\frac{4}{9}\) is the positive rational number.

(iv) \(\frac{-3}{-19}\)
Answer:
\(\frac{-3}{-19}\) is the positive rational number.

(v) \(\frac{0}{-3}\)
Solution:
\(\frac{0}{-3}\) is not positive rational number.

Question 4.
Answer the following.
(i) Which integer is neither positive nor negative?
Answer:
0 is the integer which is neither positive nor negative.

(ii) A rational number can always be written as \(\frac{p}{q}\). Is it necessary that any number written as \(\frac{p}{q}\) is a rational number?
Answer:
No. For example, o is a rational number of the form \(\frac{p}{q}\) where 10 and 1 are integers and q ≠ 0. But \(\frac{p}{q}\) i.e. is not a rational number as p = 0.

Question 5.
State whether the following statements are true. If not, justify your answer with an example.
(i) Every whole number is a natural number.
Answer:
False; because 0 is the whole number but it is not a natural number.

(ii) Every natural number is an integer.
Answer:
True, as the system of integers include all positive zero and all negative numbers.

(iii) Every integer is a whole number.
Answer:
False; as whole numbers are positive whereas integers are negative and positive both, e.g. – 2 is not a whole number.

(iv) Every integer is a rational number.
Answer:
True

(v) Every rational number is a fraction.
Answer:
False : Fractions are never negative whereas rational numbers may be negative.
e.g. \(\frac{-2}{3}\) is not a fraction but it is a rational number.

(vi) Every fraction is a rational number.
Answer:
False, fraction cannot be negative whereas rational numbers may be negative.
e.g. \(\frac{-2}{3}\) is a rational number but \(\frac{-2}{3}\) is not a fraction.

DAV Class 8 Maths Chapter 1 Worksheet 1 Notes

Natural Numbers:
All positive numbers starting from 1 are called natural numbers. These numbers are used for counting.
1, 2, 3, 4, 5, 6, ………………….. are all natural numbers.

Whole Numbers:
All positive numbers including zero are called whole numbers.
0, 1, 2, 3, 4, 5 ………………….. are all whole numbers.

Integers:
All positive numbers and their corresponding negatives along with zero, constitute a system of integers.
………………….., -5, – 4, – 3, – 2, – 1, 0, 1, 2, 3, 4, 5, ………………….

Fraction:
Fraction is a part of a whole number
e.g. \(\frac{1}{4}\), \(\frac{3}{8}\), \(\frac{7}{5}\) …………………..

Rational Numbers:
The numbers which are represented in the form \(\frac{a}{b}\) where a and b are co-primes and b ≠ 0 are called rational numbers.
e.g. \(\frac{2}{3}, \frac{1}{6}, \frac{5}{7}, \frac{-3}{-4}\) are all positive rational numbers and \(\frac{-2}{3}, \frac{1}{-6}, \frac{-11}{12}, \frac{3}{-4}\) are all negative rational numbers.

Properties of Rational Numbers:

• If \(\frac{p}{q}\) be a rational number and m be any integer different from zero, then \(\frac{p}{q}=\frac{p \times m}{q \times m}\)
• If \(\frac{p}{q}\) be a rational number and m be a common divisor of p and q, then \(\frac{p}{q}=\frac{p \div m}{q \div m}\)
• Two rational numbers \(\frac{p}{q}\) and \(\frac{r}{s}\) are said to be equivalent (equal) if p × s = q × r.

Standard form of a Rational Number:
A rational number \(\frac{p}{q}\) is said to be in standard form if q is positive and HCF of p and q is 1.

Absolute Value of a Rational Number:

• Absolute value of every rational number other than zero is positive.
• The absolute value of zero is zero itself.
• Absolute value of a rational number is greater than or equal to the number itself.

Comparing Rational Numbers:

(i) By representing on number line:
Rational numbers can be compared easily when they are represented on the number line. Any number on the number line is greater than any other number lying to the left of it. Any number on a number line is less than any other number lying to the right of it.

(ii) Without representing on number line:
If and are two rational numbers with q and s positive integers then
if \(\frac{p}{q}>\frac{r}{s}\) if p × s > q × r,
\(\frac{p}{q}<\frac{r}{s}\) if p × s < q × r and
\(\frac{p}{q}=\frac{r}{s}\) if p × s = q × r

Example 1:
Which of the following are positive rational numbers?
(i) \(\frac{-1}{-2}\)
(ii) \(\frac{5}{-6}\)
(iii) \(\frac{2}{3}\)
(iv) \(\frac{-4}{7}\)
Answer:
(i) \(\frac{-1}{-2}\) is a positive rational number as the numerator and the denominator have the same sign.
(ii) \(\frac{5}{-6}\) is not a positive rational number as the sign of the numerator and the denominator are different.
(ii) \(\frac{2}{3}\) is a positive rational number.
(iv) \(\frac{-4}{7}\) is not a positive rational number.

Example 2:
Show that \(\frac{-2}{7}\) and \(\frac{6}{-21}\) are equivalent rational numbers.
Answer:
(- 2) × (- 21) = 6 × 7
42 = 42
Hence, \(\frac{-2}{7}\) and \(\frac{6}{-21}\) are equivalent rational numbers.

Example 3:
Write two rational numbers which are equivalent to \(\frac{2}{3}\).
Answer:
Multiplying the numerator and the denominator of the given fraction by the same number, we get
\(\frac{2}{3}=\frac{2 \times 2}{3 \times 2}=\frac{4}{6}\),
\(\frac{2}{3} \times \frac{3}{3}=\frac{6}{9}\)
Hence, the required rational numbers are \(\frac{4}{6}\) and \(\frac{6}{9}\).

Example 4:
Express \(\frac{24}{-54}\) in the standard form.
Answer:
HCF of 24 and 54 is 6
∴ Dividing the numerator and denominator by 6, we get
\(\frac{24 \div 6}{-54 \div 6}=\frac{4}{-9}\)
Hence, the simplest standard form \(\frac{4}{-9}\)

Example 5:
Find the value of x such that the given rational numbers become equivalent.
\(\frac{x}{36}=\frac{5}{12}\).
Answer:
\(\frac{x}{36}=\frac{5}{12}\) will be equivalent if
x × 12 = 5 × 36
⇒ x =
= 15
Hence, x = 15

Example 6.
What is absolute value of a rational number? Find the absolute values of the given rational numbers.
\(\frac{-2}{3}, \frac{6}{-7}, \frac{2}{3}\), – 4, 0
Answer:
The absolute value of a rational number is its numerical value without its sign.
Here, absolute values of the given rational numbers are
\(\left|\frac{-2}{3}\right|=\frac{2}{3},\left|\frac{6}{-7}\right|=\frac{6}{7},\left|\frac{2}{3}\right|=\frac{2}{3},|-4|=4,|0|=0\).

Example 7:
Represent the following rational numbers on number line.
\(\frac{-3}{2}, \frac{1}{2}, \frac{-1}{2}, \frac{5}{2}, \frac{-5}{2}\)
Answer:

Example 8:
Compare \(\frac{2}{3}\) and \(\frac{3}{5}\).
Answer:
To compare the two rational numbers, first we make their denominators same.
\(\frac{2}{3} \times \frac{5}{5}=\frac{10}{15}\)
and \(\frac{3}{5} \times \frac{3}{3}=\frac{9}{15}\)
Now comparing their numerators, we get
10 > 9
∴ \(\frac{2}{3}>\frac{3}{5}\).

The DAV Class 8 Maths Book Solutions and DAV Class 8 Maths Chapter 1 Worksheet 1 Solutions of Squares and Square Roots offer comprehensive answers to textbook questions.

DAV Class 8 Maths Ch 1 WS 1 Solutions

Question 1.
Which of the following numbers are perfect squares?
11, 16, 32, 36, 50, 64, 75
Solution:
11 = 11 × 1 the prime factors are not in pair.
∴ 11 is not a perfect square number.

16 = 2 × 2 × 2 × 2, the prime factors are in pair.
∴ 16 is a perfect square number.

32 = 2 × 2 × 2 × 2 × 2, all the prime factors are not in pair.
∴ 32 is not a perfect square number.

36 = 2 × 2 × 3 × 3, all the prime factors are in pair.
∴ 36 is a perfect square number.

50 = 2 × 5 × 5, all the prime factors are not in pair.
∴ 50 is not a perfect square number.

64 = 2 × 2 × 2 × 2 × 2 × 2, all the prime factors are in pair.
∴ 64 is a perfect square number.

75 = 3 × 5 × 5, all the prime factors are not in pair.
∴ 75 is not a perfect square number.

Question 2.
Which of the following numbers are perfect squares of even numbers?
121, 225, 784, 841, 576, 6561
Solution:
As the numbers with their end digit even, their squares will also have their end digit even.
∴ 121 is not a perfect square of even number.
225 is not a perfect square of even number.
784 is a perfect square of even number.
841 is not a perfect square of even number.
576 is a perfect square of even number,
6561 is not a perfect square of even number.

Question 3.
Which of the following numbers are perfect squares?
100, 205000, 3610000, 212300000
Solution:
Any number ending with odd number of zeros is never a perfect square.
100 is a perfect square as it is ending with even zeros.
205000 is not a perfect square as it has odd number of zeros.
3610000 is a perfect square as it has even number of zeros.
212300000 is not a perfect square as it has odd number of zeros.

Question 4.
By just observing the digits at ones place, tell which of the following can be perfect squares?
1026, 1022, 1024, 1027
Solution:
The number ending with 2, 3, 7 and 8 are not perfect squares.
∴ 1026 and 1024 may be perfect squares whereas
1022 and 1027 may not be perfect squares.

Question 5.
How many non-square numbers lie between the following pairs of numbers?
(i) 7² and 8²
(ii) 10² and 11²
(iii) 40² and 41²
(iv) 80² and 81²
(v) 101² and 102²
(vi) 205² and 206²
Solution:
The non-perfect square numbers between the square of the numbers n and n + 1 is 2n.
(i) 7² and 8²
Here n = 7 and n + 1 = 8
∴ Number of non-perfect squares between 7² and 8²
= 2 × 7 = 14.

(ii) 10² and 11²
Here n = 10 and n + 1 = 11
∴ Non-perfect numbers between 10² and 11²
= 2 × 10 = 20.

(iii) 40² and 41²
Here n = 40 and n + 1 = 41
∴ Non-perfect square numbers between 40² and 41²
= 2 × 40 = 80.

(iv) 80² and 81²
Here n = 80 and n + 1= 81
∴ Non-perfect square numbers between 80² and 81²
= 2 × 80 = 160.

(v) 101² and 102²
Here n = 101 and n+ 1= 102
∴ Non-perfect square numbers between 101² and 102²
= 2 × 101 = 202.

(vi) 205² and 206²
Here n = 205 and n + 1 = 206
∴ Non-perfect square numbers between 205² and 206²
= 2 × 205 = 410.

Question 6.
Write down the correct number in the box:
(i) 100² – 99² = ______ = ______
(ii) 27² – 26² = ______ = ______
(iii) 569² – 568² = ______ = ______
Solution:
(i) 100² – 99² = 100 + 99 = 199
(ii) 27² – 26² = 27 + 26 = 53
(iii) 569² – 568² = 569 + 568 = 1137

Question 7.
Observe the pattern in the following and find the missing numbers:
121 = \(\frac{(22)^2}{1+2+1}\)

12321 = \(\frac{(333)^2}{1+2+3+2+1}\)

1234321 = ______
123454321 = ______
12345654321 = ______
Solution:
1234321 = \(\frac{(4444)^2}{1+2+3+4+3+2+1}\)

12345321 = \(\frac{(55555)^2}{1+2+3+4+5+4+3+2+1}\)

12345654321 = \(\frac{(666666)^2}{1+2+3+4+5+6+5+4+3+2+1}\)

Question 8.
Which of the following triplets are Pythagorean?
(3, 4, 5), (6, 7, 8), (10, 24, 26), (2, 3, 4)
[Hint: Let the smallest even number be 2m and find m for it. Then, fmd (2m, m² – 1, m² + 1). If you get the triplet, it is Pythagorean).
Solution:
(i) Taking the triplet (3, 4, 5)
Here, the smallest even number = 4
∴ 2m = 4 ⇒ m = 2
∴ Pythagorean triplets are 2m, m² – 1 and m² + 1
= 2 × 2, (2)² – 1 and (2)² + 1 = 4, 3, 5
Hence (3, 4, 5) is a Pythagorean triplet.

(ii) Taking the triplet (6, 7, 8)
Here, the smallest even number = 6
∴ 2m = 6 ⇒ m = 3
∴ Pythagorean triplets are 2m, m² – 1 and m² + 1
= 2 × 3, (3)² – 1 and (3)² + 1 = 6, 8, 10
Hence (6, 7, 8) is not a Pythagorean triplet.

(iii) Taking the triplet (10, 24, 26)
Here, the smallest natural number = 10
∴ 2m = 10 ⇒ m = 5
∴ Pythagorean triplets are 2m, m² – 1 and m² + 1
⇒ 2 × 5, (5)² – 1 and (5)² + 1 ⇒ 10, 24 and 26
Hence (10, 24, 26) is a Pythagorean triplet.

(iv) Taking the triplet (2, 3, 4)
Here, the smallest even number = 2 2m = 2 m = 1
Pythagorean triplets are 2m, m² – 1 and m² + 1
= 2 × 1, (1)² – 1 and (1)² + 1 = 2, 0 and 2
Hence (2, 3, 4) are not Pythagorean triplet.

Additional Questions:

Question 1.
Which of the following numbers are not perfect squares?
(i) 1057
(ii) 7928
(iii) 22222
(iv) 23453
(v) 2061
(vi) 1069
(vii) 256
(viii) 36124
Solution:
The numbers ending with 2, 3, 7 or 8 can never be perfect squares.
(i) 1057 = ending with 7, so it is not a perfect square.
(ii) 7928 = ending with 8, so it is not a perfect square.
(iii) 22222 = ending with 2, so it is not a perfect square.
(iv) 23453 = ending with 3, so it is not a perfect square.
(v) 2061 = It may be a perfect square as it is ending with 1 (other than 2, 3, 7, or 8).
(vi) 1069 = It may be a perfect square number as it is ending with 9 (other than 2, 3, 7, or 8).
(vii) 256 = It may be a perfect square number as it is ending with 6.
(viii) 36124 = It may be a perfect square number as it is ending with 4 (other than 2, 3, 7, 8).

Question 2.
Which of the following squares would end with digit 1?
123², 77², 82², 56², 161², 109²
Solution:
If a number has 1 or 9 in the unit’s place, then it is square ends in 1.
∴ only 161² and 109² would end with 1 as they have 1 and 9 respectively in the unit’s place.

Question 3.
Which of the following numbers would have digit 6 at unit place?
(i) 19²
(ii) 24²
(iii) 26²
(iv) 36²
(v) 34²
Solution:
When a square number ends, the number whose square it is, will have either 4 or 6 in unit’s place.
(i) 19² is not a number which will have 6 in its unit’s place.
(ii) 24² is the number which will have 6 in its unit’s place.
(iii) 26² is the number which will have 6 in its units place.
(iv) 36² is the number which will have 6 in its unit’s place.
(v) 34² is the number which will have 6 in its unit’s place.

Question 4.
Which of the following numbers are perfect squares of even numbers?
225, 121, 1024, 1296, 361, 289, 576
Solution:
A number having even number digits at its unit place, will have even numbers at the unit place of its square.
∴ Only 1024, 1296 and 576 are the perfect squares of even numbers.

Question 5.
What will be the number of zeros in the square of the following numbers?
(i) 60
(ii) 400
(iii) 2000
(iv) 150000
Solution:
(i) Square of 60 will have two zeros in the end.
(ii) Square of 400 will have four zeros in the end.
(iii) Square of 2000 will have six zeros in the end.
(iv) Square of 150000 will have eight zeros in the end.

Question 6.
How many non-square numbers lie between the following pairs of numbers?
(i) 8² and 9²
(ii) 110² and 111²
(iii) 205² and 206²
Solution:
There are ‘2n’ non-perfect square numbers between the squares of ‘n’ and ‘(n + 1)’.

(i) 8² and 9²
Here n – 8 and (n + 1) = 9
∴ Non-perfect square numbers between 8² and 9² are 2 × 8 = 16,

(ii) 110² and 111²
Here n = 110 and n + 1 = 111
∴ Non-perfect square numbers between 110² and 111² are 2 × 110 = 220.

(iii) 205² and 206²
Here n = 205 and n + 1 = 206
∴ Non-perfect square numbers between 205² and 206² are 2 × 205 = 410.

Question 7.
Fill in the blank boxes with correct numbers:
(i) 89² – 88² = ______ = ______
(ii) 56² – 55² = ______ = ______
(iii) 105² – 104² = ______ = ______
(iv) 576² – 575² = ______ = ______
(v) 112² – 111² = ______ = ______
Solution:
(i) 89² – 88² = 89 + 88 = 117
(ii) 56² – 55² = 56 + 55 = 111
(iii) 105² – 104² = 105 +104 = 209
(iv) 576² – 575² = 576 + 575 = 1151
(v) 112² – 111² = 112 + 111 = 223

Question 8.
Observe the following pattern in the following and fill in the blanks:
(i) 1 = ______ = ______
(ii) 1 + 3 = ______ = ______
(iii) ______ = 9 = ______
(iv) 1+ 3 + 5 + 7 = ______ = ______
(v) ______ = ______ = 5²
Solution:
(i) 1 = 1 = 1²
(ii) 1 + 3 = 4 = 2²
(iii) 1 + 3 + 5 = 0 = 3²
(iv) 1 + 3 + 5 + 7 = 16 = 4²
(v) 1 + 3 + 5 + 7 + 9 = 25 = 5²

Question 9.
Express the following as the sum of two consecutive integers:
(i) 11²
(ii) 13²
(iii) 19²
(iv) 21²
(v) 33²
Solution:
n² = \(\frac{n^2-1}{2}+\frac{n^2+1}{2}\)

(i) 11² =
⇒ 60 + 61
Hence 11² = 60 + 61

(ii) 13² =
⇒ 84 + 85
Hence 13² = 84 + 85

(iii) 19² =
⇒ 180 + 181
Hence 19² = 180 + 181

(iv) 21² =
⇒ 220 + 221
Hence 21² = 220 + 221

(v) 33² =
⇒ 544 + 545
Hence 32² = 544 + 545

Question 10.
Fill in the blank boxes with correct numbers.
(i) 1² = ___
(ii) 11² = 1 ___ 1
(iii) 111² = 12 ___ 21
(iv) 1111² = 123 ___ 321
(v) 11111² = 1234 ___ 4321
(vi) 111111² = ______
Solution:
(i) 1² = 1
(ii) 11² = 121
(iii) 111² = 12321
(iv) 1111² = 1234321
(v) 11111² = 123454321
(vi) 111111² = 12345654321

Question 11.
Observe the following following and fill in the blanks:
1 + 3 = 2²
1 + 3 + 5 = 3²
1 + 3 + 5 + 7 = 4²
1 + 3 + 5 + 7 + 9 = ______
1 + 3 + 5 + 7 + 9 + 11 = ______
1 + 3 + 5 + 7 + ………. upto n terms = ______
Solution:
1 + 3 + 5 + 7 + 9 = 5²
1 + 3 + 5 + 7 + 9 + 11 = 6²
1 + 3 + 5 + 7 + …… upto n terms = n²

Question 12.
Fill in the blank boxes with correct numbers:
(i) 7² = 49
(ii) 67² = 4489
(iii) 667² = 444889
(iv) 6667² = ______
(v) 66667² = ______
(vi) 666667² = ______
Solution:
(iv) 6667² = 4444889
(v) 66667² = 4444488889
(vi) 666667² = 444444888889

Question 13.
Observe the following pattern and supply the missing numbers:
(i) 11² = 121
(ii) 101² = 10201
(iii) 10101² = 102030201
(iv) 1010101² = ___________
(v) 101010101² = ___________
(vi) 10101010101² = ___________
Solution:
(iv) 1020304030201
(v) 10203040504030201
(vi) 102030405060504030201.

Question 14.
Using the given pattern, find the missing entries:
(i) 1² + 2² + 2² = 3²
(ii) 2² + 3² + 6² = 7²
(iii) 3² + 4² + ___ = 13²
(iv) 4² + 5² + ___ = 21²
(v) ___ + 6² + 30² = ___
(vi) 6² + 7² + ___ = 43²
Solution:
(iii) 12²
(iv) 5²
(v) 20²
(vi) 42²

Question 15.
Find the squares of the following numbers without actual multiplications:
(i) 39
(ii) 42
(iii) 61
(iv) 75
(v) 85
Solution:
(i) 39² = (30 + 9)²
= 30(30 + 9) + 9(30 + 9)
= 30² + 30 × 9 + 9 × 30 + 9²
= 900 + 270 + 270 + 81
= 900 + 540 + 81 = 1521

(ii) 42² = (40 + 2)²
= 40(40 + 2) + 2(40 + 2)
= 402 + 40 × 2 + 2 × 40 + 2²
= 1600 + 80 + 80 + 4 = 1764

(iii) 61² = (60 + 1)²
= 60 (60 + 1) + 1(60 + 1)
= 60² + 60 × 1 + 1 × 60 + 1²
= 3600 + 60 + 60 + 1 = 3721

(iv) 75² = (70 + 5)²
= 70(70 + 5) + 5(70 + 5)
= 70² + 70 × 5 + 5 × 70 + 5²
= 4900 + 350 + 350 + 25 = 5625

(v) 85² = (80 + 5)²
= 80(80 + 5) + 5(80 + 5)
= 80² + 80 × 5 + 5 × 80 + 5²
= 6400 + 400 + 400 + 25 = 7225.

Question 16.
Which of the triplets are Pythagoreans?
(i) (12, 35, 37)
(ii) (8, 15, 17)
(iii) (7, 8, 12)
(iv) (2, 3, 5)
(v) (6, 8, 10)
Solution:
The Pythagorean triplets are 2 m, m² – 1 and m² + 1
if 2 m is the smallest even number of the triplet.
(i) (12, 35, 37)
Here 12 is the smallest even number
∴ 2m = 12 ⇒ m = 6
∴ triplets are 2m = 2 × 6 = 12
m² – 1 = 6² – 1 = 36 – 1 = 35
and m² + 1 = (6)² + 1 = 36 + 1 = 37
Hence (12, 35, 37) is the Pythagorean triplet.

(ii) (8, 15, 17)
Here the smallest even number is 8
2m = 8
∴ m = 4
m² – 1 = (4)² – 1 = 16 – 1 = 15
and m² + 1 = (4)² + 1 = 16 + 1 = 17
Hence (8, 15, 17) is a Pythagorean triplet.

(iii) (7, 8, 12)
Here the smallest even number is 8
2m = 8
∴ m = 4
m² – 1 = (4)² – 1 = 16 – 1 = 15
m² + 1 = (4)² + 1 = 16 + 1 = 17
So, (7, 8, 12) is not a Pythagorean triplet.

(iv) (2, 3, 5)
Here smallest even number is 2
2m = 2
∴ m = 1
m² – 1 = 1² – 1 = 0
m² + 1 = 1² + 1 = 2
Hence (2, 3, 5) is not a Pythagorean triplet.

(v) (6, 8, 10)
Here 6 is the smallest even number
2m = 6
∴ m = 3
m² – 1 = (3)² – 1 = 9 – 1 = 8 and
m² + 1 = (3)² + 1 = 9 + 1 = 10
Hence (6, 8, 10) is a Pythagorean triplet.

Note: [All Pythagorean triplets may not be obtained using this form of 2 m, m² – 1 and m² + 1. example: (5, 12, 13) and (7, 24, 25). Although they have 12 and 24 as their due of the members.]

Question 17.
Fill in the following blanks:
(i) 1 + 3 + 5 = (___)²
(ii) 1 + 3 + 5 + 7 = (___)²
(iii) 1 + 3 + 5 + 7 + 9 = (___)²
(iv) 1 + 3 + 5 + 7 + 9 + 11 = (___)²
(u) 1 + 3 + 5 + 7 + 9 + 11+ 13 = (___)²
Solution:
(i) 3
(ii) 4
(iii) 5
(iv) 6
(v) 7.

DAV Class 8 Maths Chapter 1 Worksheet 1 Notes

The number obtained by multiplying any number by itself is called the square of the number.

For example:
1 × 1 = 1 = 1²
2 × 2 = 4 = 2²
3 × 3 = 9 = 3²
4 × 4 = 16 = 4²
n × n = n²
Numbers, such as 1, 4, 9, 16, 25 … are called perfect squares.

Significance of a perfect square:

(i) Squares of even numbers are also even.
e.g. 4² = 16,
6² = 36 and
8² = 64, etc.

(ii) Squares of odd numbers are always odd.
e.g. 9² = 81,
11² = 121 and
13² = 169, etc.

(iii) The numbers ending with an odd number of zeros are never perfect squares.
e.g. 180, 36000, etc.

(iv) The difference between the squares of two consecutive natural numbers is equal to their sum.
e.g. 5² – 4² = 25 – 16 = 9 = 5 + 4
7² – 6² = 49 – 36 = 13 = 7 + 6
9² – 8² = 81 – 64 = 17 = 9 + 8

(v) The numbers ending with 2, 3, 7 and 8 are not perfect squares.
e.g. 12, 23, 67, 238 and 353, etc.

(vi) The square of a natural number n’ is equal to the sum of the first n odd natural numbers.
e.g. 3² = 1 + 3 + 5 = 9
5² = 1 + 3 + 5 + 7 + 9 = 25
6² = 1 + 3 + 5 + 7 + 9 + 11 = 36

(vii) Squares of natural numbers composed of the only digit 1, follow a particular pattern.
e.g. 1² = 1 = 1²
11² = 121 = 1 + 2 + 1 = 4 = 2²
111² = 12321 = 1 + 2 + 3 + 2 + 1 = 9 = 3²
1111² = 1234321 = 1 + 2 + 3 + 4 + 3 + 2 + 1 = 16 = 4²

(viii) The square of a number other than 0 and 1 is either a multiple of 3 or exceeds the multiple of 3 by 1,
e.g. 3² = 9
4² = 16 = (15 + 1)
7² = 49 = (48 + 1)

(ix) The square of a number other than 0 and 1 is either a multiple of 4 or exceeds a multiple of 4 by 1.
e.g. 4² = 16
5² = 25 = 24 + 1)
6² = 36
7² = 49 = (48 + 1)

Numbers between two square numbers:

Let us take any two consecutive numbers n and (n + 1). The number of non-squares between n² and (n + 1)² is 2n.

e.g.
(i) 1² = 1 and 2² = 4
∴ Non-square numbers between 1 and 4 are 2, 3.
1, 2, 3, 4 → 2 non-square numbers i.e. 2 × 1

(ii) 2 = 4 and 32 = 9
∴ Non-square numbers between 4 and 9 are 5, 6, 7, 8.
4, 5, 6, 7, 8, 9 → 4 non-square numbers i.e. 2 × 2

(iii) 3² = 9 and 4² = 16
∴ Non-square numbers between 9 and 16 are 10, 11, 12, 13, 14, 15.
9, 10, 11, 12, 13, 14, 15, 16 → 6 non-square number i.e. 2 × 3
Hence, there are 2n non-square natural numbers between the two consecutive perfect square numbers.

These DAV Class 8 Science Notes and DAV Class 8 Science Chapter 1 Notes – The Cell Its Structure and Functions act as excellent revision resources, particularly in preparation for board exams.

The Cell Its Structure and Functions Class 8 DAV Notes

→ Cell: The basic structural and functional unit of living organisms is called cell.

→ Discovery of Cell: Robert Hooke was the first scientist who observed thin slices of cork with the help of his self-designed microscope. He observed honeycomb-like structure and called the compartments as cell.

→ Celi Number: Some organisms are composed of a single cell. These are called unicellular organisms. Some organisms are composed of more than one cell. These are called multicellular organisms.

→ Cell Shape: The shape of cells differs in different organisms, as well as in different organs of the same organism. A cell may be oval, spherical, cuboidal, fibre-like or polygonal. The shape of a cell is influenced by its location and the function it serves.

→ Cell Size: The size of cells varies from 0.1 micron to 170 mm. Mycoplasma is a unicellular organism which is 0.1 micron in size. An egg of ostrich is the largest known living cell and is 170 mm in diameter.

→ Parts of a Cell: A cell is composed of protoplasm which is surrounded by a cell membrane. The protoplasm consists of cytoplasm and nucleus. There are a number of cell organelles in the cytoplasm and nucleus.

→ Cell Membrane: All living cells are bound by a thin membrane called plasma membrane or cell membrane. The cell membrane provides protection to the contents of the cell and controls the entry and exit of various substances as per a cell’s requirement.

→ Cell Wall: In plants, fungi and bacteria, the cell is surrounded by a cell wall in addition of the cell membrane also. Cell wall provides additional rigidity to the cell.

→ Cytoplasm: The part of the protoplasm which lies between the cell membrane and nucleus is called cytoplasm. It acts like a matrix for various cell organelles. It is made up of carbohydrates, proteins, fats, minerals, vitamins and water.

→ Nucleus: The nucleus lies in the centre of the cell. It controls all the activities of the cell. The protoplasm of the nucleus is called nucleoplasm. Nucleus is surrounded by a nuclear membrane. The nucleus has thread-like network called chromatin. The chromatin network is composed of chromosomes which become visible during cell division. Chromosomes are responsible for inheritance of characters.

→ Plastids: These are found in plant cells only. They are large and capsule-shaped. Plastids are in many colours. The green coloured plastids are called chloropiasts. Photosynthesis happens in chloroplast. Plastids are responsible for imparting colour to a plant part.

→ Mitochondria: Mitochondria are capsule-shaped structures. Cellular respiration takes place in mitochondria and energy is generated. Due to this, mitochondria are also called the powerhouse of the cell.

→ Endoplasmic Reticulum: It is a network of tube-like structures. It provides a skeletal framework to the cell and also facilitates transportation of substances.

→ Golgi Complex: These are sac-like structures stacked over one another. They store materials which are produced by cells. Due to this, Golgi complex is also called the store house of the cell.

→ Vacuole: These are fluid filled spaces inside cells. Vacuoles are very large in plant cells. Excess water and waste products are held in vacuoles. Food vacuoles are present in Amoeba.

→ Ribosomes: These are tiny granules which lie scattered in the cytoplasm. Ribosomes help in protein synthesis.

→ Cilia and Flagella: Some cells have special structures on them for locomotion. Paramecium has cilia, while Euglena has flagella.

Levels of Organisation in Organisms

→ Cellular Level: This level of organization is found in unicellular and in some simple multicellular organisms. In such organisms, a single cell is responsible for all life functions.

→ Tissue Level: This level of organization is found in some simple multicellular organisms in which a group of cells, i.e. tissue is responsible for all life functions.

→ Organ Level: Organisms; like hookworm and roundworm show organ level of organization.

→ Organ System Level: Many organs group together to form an organ system. Complex organisms show organ system level of organization.

→ Organism: An organism is an independent entity which can live on its own.

→ Cell : The basic structural and functional unit of living beings.

→ Cytology : The branch of biology in which we study about cells.

→ Protoplasm : The jelly like substance inside the cell.

→ Cytoplasm : The protoplasm which is present between cell membrane and nuclear membrane.

→ Nucleoplasm : The protoplasm which is present inside the nucleus.

→ Chromosomes : Rod-like stwctures inside nucleus which are responsible for transmission of genetic traits.

Comparison between plant cell and animal cell

Cell components	Plant cell	Animal cell
Cell wall	Present	Absent
Cell membrane	Present	Present
Plastids	Present	Absent
Mitochondria	Present	Present
Nucleus	Present	Present
Vacuoles	Large in size and more in number	Small in size and may be absent