PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2

Punjab State Board PSEB 9th Class Maths Book Solutions Chapter 1 Number Systems Ex 1.2 Textbook Exercise Questions and Answers.

PSEB Solutions for Class 9 Maths Chapter 1 Number Systems Ex 1.2

Question 1.
State whether the following statements are true or false. Justify your answers:
(i) Every irrational number is a real number.
Answer:
This statement is true. The collection of real numbers contain all the rational numbers and all the irrational numbers.

(ii) Every point on the number line is of the form √m, where m is a natural number.
Answer:
This statement is false. The negative numbers represented on the number line are never of the form √m, where m is a natural number. For natural number m, √m is always a positive number.

(iii) Every real number is an irrational number.
Answer:
This statement is false. The collection of real numbers is made-up of rational numbers and irrational numbers. So, every real number is either a rational number or an irrational number.

PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2

Question 2.
Are the square roots of all positive integers irrational? if not, give an example of the square root of a number that is a rational number.
Answer:
No, The square roots of all positive integers are not irrational. The square root of any perfect square number is always a rational number.
e.g., √4 = 2, √9 = 3, √16 = 4, ……

Question 3.
Show how √5 can be represented on the number line.
Answer:
PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2 1

Start by taking point O on the number line which represents O. Choosing proper unit, locate point A on the number line to represent
1. Draw seg AB of unit length perpendicular to seg OA. Construct seg OB. Then, by Pythagoras’ theorem, OB = √2. Draw seg BC of unit length perpendicular to seg OB. Construct seg OC.
Then, OC = √3. Draw seg CD of unit length perpendicular to seg OC. Construct seg OD.
Then, OD = √4. Draw seg DE of unit length perpendicular to seg OD. Construct seg 0E.
Then, 0E = √5. Draw an arc with centre O and radius OE to Intersect the number line at P Then, point P on the number line represents √5.

Alternate Method:
This can be solved In fewer steps as shown in the following manner:
On the number line l, take a point O corresponding to 0. Choosing the proper unit, take a point A on l such that OA = 2 units. Construct right angled Δ OAP such that ΔOAP = 90° and AP = 1 unit.
PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2 2
Then, by Pythagoras theorem,
OP2 = OA2 + AP2
= (2)2 + (1)2 = 4 + 1 = 5
∴ OP = √5
Draw an arc with centre O and radius OP to intersect l at B. B is the point corresponding to Draw an arc with centre O and radius OP to intersect I at B. B is the point corresponding to √5.

PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2

Question 4.
Classroom activity (Constructing the ‘square root spiral’): Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion. Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn-1Pn by drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3, …………, Pn, ………, and joined them to create a beautiful spiral depicting √2, √3, √4, ………..
PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2 3
Answer:
Take a large sheet of paper and construct the ‘square root spiral’ in the following fashion:
PSEB 9th Class Maths Solutions Chapter 1 Number Systems Ex 1.2 4
Start with a point O and draw a line segment OP1 of unit length. Draw a line segment P1P2 perpendicular to OP1 of unit length (see Fig. 1.9). Now draw a line segment P2P3 perpendicular to OP2. Then draw a line segment P3P4 perpendicular to OP3. Continuing in this manner, you can get the line segment Pn-1Pn by drawing a line segment of unit length perpendicular to OPn-1. In this manner, you will have created the points P2, P3, …………, Pn, ………, and joined them to create a beautiful spiral depicting √2, √3, √4, ………..

PSEB 8th Class Social Science Notes Chapter 13 Colonialism and Tribal Society

This PSEB 8th Class Social Science Notes Chapter 13 Colonialism and Tribal Society will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 13 Colonialism and Tribal Society

→ Tribal society: Tribal society is related to the tribal people of the country who live in ancient conditions in forests, valleys, and in far-off mountains. They basically live in Rajasthan, Gujarat, Bihar, Orissa, and the mountainous region of Madhya Pradesh.

→ Important Tribes: Gond, Bhil, Santhal, Mizos, Mundas, etc. are the important tribes of the country.

→ Revolts of Tribal people: Many tribal people revolted against the policies of the British government in the 19th century. Bhils in Madhya Pradesh, Mundas in Bihar, Gonds in Orissa, and Santhals in Bihar-Bengal revolted in a great deal.

PSEB 8th Class Social Science Notes Chapter 13 Colonialism and Tribal Society

→ Birsa Munda: Birsa Munda was the leader of the Munda tribe. He was a very powerful person.

→ Revolt of Santhals: Tribal people, living in the mountains of Rajmahal, of the Santhal tribe, revolted in 1855 A.D. under the leadership of Sidhu and Kanhu. They declared themselves independent by defying the company’s rule.

→ The British got control of the situation in 1856 A.D. after using military force. The government made a separate district of the Santhal Pargana so that the Santhal people should remain happy.

→ Result of Revolts of Tribal people: Tribal people became conscious from a social and religious point of view due to these revolts.

PSEB 8th Class Social Science Notes Chapter 12 Rural Life and Society

This PSEB 8th Class Social Science Notes Chapter 12 Rural Life and Society will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 12 Rural Life and Society

→ Land Revenue System of the British:

  • The English East India Company got ‘Diwani’ rights of Bengal, Bihar, and Orissa from the Mughal Emperor Shah Alam in 1765 A.D, As a result, the Company started collecting land revenue from these provinces.
  • The Company wanted to collect more and more revenue.
  • That’s why they adopted many new systems of land.
  • First of all, the company started to give land on contract.
  • The higher bidder was getting the right to collect tax from a particular area.

→ New Land Settlements:

  • After this, the British made land settlements in new different ways in India.
  • Out of these, Permanent Settlement, Ryotwari system, Mahalwari system were important.

PSEB 8th Class Social Science Notes Chapter 12 Rural Life and Society

→ Permanent Settlement of Land:

  • Lord Cornwallis introduced the Permanent Settlement of land in Bengal in 1793.
  • According to it, the landlords or zamindars became the permanent owners of the land and the peasants were crushed.

→ Ryotwari System:

  • This system of land settlement was introduced in Madras and Bombay.
  • According to this system, the government officers directly collected land revenue from the farmers.

→ Mahalwari System: This system of land settlement was introduced in Western U.P, Punjab, and Delhi.

→ Impact of Land Revenue System: Farmers became poor with the land revenue systems of the British and came into the clutches of debt.

PSEB 8th Class Social Science Notes Chapter 11 Administrative Structure, Growth of Colonial Army and Civilian Administration

This PSEB 8th Class Social Science Notes Chapter 11 Administrative Structure, Growth of Colonial Army and Civilian Administration will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 11 Administrative Structure, Growth of Colonial Army and Civilian Administration

→ Regulating Act: This Act was passed in 1773 A.D., now the British government controlled the activities of the English Company.

→ Pitt’s India Act: This Act was passed in 1784 A.D. According to this Act, the position of Governor-General was strengthened.

→ Civil Services: Lord Cornwallis started civil services in India to fill higher government jobs. Indians were kept away from these.

PSEB 8th Class Social Science Notes Chapter 11 Administrative Structure, Growth of Colonial Army and Civilian Administration

→ Police: The British organised the police system in a new way. They started the system of Police-Thanas.

→ Law and Justice: Same laws were introduced in the country. Courts were established in the country and the job was done in the local language.

→ The Charter Act of 1833: According to the Charter Act, all the military and civil rights were grafted to the Governor-General and his council.

→ The Charter Act of 1853: Executive and Legislative were separated from each other through this Act. There were 12 members of the newly established legislature.

PSEB 8th Class Social Science Notes Chapter 10 The Establishment of East India Company

This PSEB 8th Class Social Science Notes Chapter 10 The Establishment of East India Company will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 10 The Establishment of East India Company

→ Discovery of a New Sea Route: A Portuguese sailor Vasco-de-Gama discovered the new sea route to India in 1498 A.D.

→ European Communities in India: The Portuguese, the English, the French, and the Dutch came to India for trade.

→ Factories: Trading centers of European Companies in India were called ‘Factories’.

PSEB 8th Class Social Science Notes Chapter 10 The Establishment of East India Company

→ The British East India Company: The British established the East India Company in 1600 A.D. It opened trade centres in India and checked the expansion of other European trading companies.

→ The French East India Company: Although the French East India Company was established in 1664 A.D., much later than the British company, yet it made great progress in India.

→ Carnatic Wars: The Carnatic Wars were fought between the British and the French. The British won these three wars.

→ Dupleix: Dupleix was the most capable governor of the French possessions in India.

→ Robert Clive: Robert Clive was an able English military commander. He was the founder of the British Empire in India.

→ The victory of Bengal: The British won the battle of Plassey in 1757 A.D. and the battle of Buxar in 1764 A.D. and thus became the real masters of Bengal.

→ Diwani Rights: The Battle of Buxar ended with the Treaty of Allahabad in 1765 A.D. As a result of this treaty, the British got the ‘Diwani Rights’ of Bengal, Bihar, and Orissa. Now the British were in a position to collect land revenue from these territories.

→ Means of Expansion of Empire: The British Empire was expanded through a number of means such as subsidiary alliance, Doctrine of Lapse, war, Discontinuing pension, etc.

→ Maratha Power: The British defeated powerful Maratha rulers one by one and forced them to accept a subsidiary alliance.

→ The victory of Mysore: The British fought four wars with Hyder Ali and Tipu Sultan to conquer Mysore. The British emerged victoriously.

PSEB 8th Class Social Science Notes Chapter 10 The Establishment of East India Company

→ Subsidiary Alliances: Lord Wellesley introduced this system for the expansion of the British Empire. Indian rulers who entered into Subsidiary Alliances with the British came completely under British control.

→ The doctrine of Lapse: This policy was started by Lord Dalhousie. If the ruler of a dependent state had no male child, he could not adopt a son. It meant, if a native ruler died without leaving a son behind, the dependent state would pass automatically into the hands of the British.

PSEB 8th Class Social Science Notes Chapter 9 When, Where and How

This PSEB 8th Class Social Science Notes Chapter 9 When, Where and How will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 9 When, Where and How

→ Division of History:

  • World history has been divided into the ancient period, the medieval period, and the modern period.
  • In the same way, Indian history has also been divided into three periods i.e. ancient period, the medieval period, and the modern period.

→ Modern Period: Modern period in Europe started in the 16th century but in India, it started in the 18th century.

PSEB 8th Class Social Science Notes Chapter 9 When, Where and How

→ Modern Period in India:

  • New powers emerged in the modern period.
  • European powers came to India and British rule was established in India.
  • Consciousness came among Indians with the spread of western education and national movement started in India.
  • It led to the freedom of India in 1947 A.D.

→ Sources of History of Modern India: Main sources of the History of Modern India are:

  • Books
  • Government Documents
  • Newspapers, Magazines, and Pamphlets
  • Historical monuments
  • Paintings and Sculptures
  • Letters of political leaders, etc.

PSEB 8th Class Social Science Notes Chapter 8 Disaster Management

This PSEB 8th Class Social Science Notes Chapter 8 Disaster Management will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 8 Disaster Management

→ Natural Hazard: Any natural event that does not occur frequently but is fast enough to threaten life is called a ‘natural hazard’.

→ Natural disasters: The location of the natural hazards and the intensity with which it occurs lead to what are known as natural disasters. Tsunami, earthquakes, cyclones, floods, etc.

PSEB 8th Class Social Science Notes Chapter 8 Disaster Management

→ Earthquake: The sudden mild or violent shaking of a part of the earth is called an earthquake.

→ Seismograph: An instrument is used to record and measure the vibrations of the earthquake.

→ Man-Made disasters: Bomb explosions, terrorism pollution, Dam-burst, industrial accidents, and epidemics.

→ Disaster Management in India: Many institutions have started courses in disaster management. These include:

  • Central Disaster Management Authority, New Delhi.
  • Disaster Management National Centre, New Delhi.
  • Earthquake Information Centre, I.I.T. Kanpur.
  • Disaster Management Institute, Bhopal.
  • Indira Gandhi Open University, New Delhi.
  • Central Board of Secondary Education, New Delhi.

PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture

This PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture

→ Agriculture: It refers to the cultivation of the soil for growing crops and rearing livestock.

→ Crops: The plant species cultivated by human beings for their use.

→ Livestock: Animals and birds which are reared for human use.

→ Crop Specialization: One particular crop suitable for the region is selected by the farmer to be cultivated by him. This is mainly followed for selling the produce in the market.

PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture

→ Organic Farming: In this type of farming, organic manure and natural pesticides are used instead of chemicals.

→ Subsistence Agriculture: Farming in which the product is consumed by the farmer’s household.

→ Commercial Agriculture: Farming in which the produce is grown by the farmer for selling in the market.

→ Intensive Agriculture: The farmer produces more by working hard and using the same field over and over again making use of better agricultural means.

→ Extensive Agriculture: The agriculturist tries to get good output by bringing more and more areas under plough.

→ Mixed Farming: Farming in which animals are also used on the farm while growing crops.

→ Multiple Cropping: When two or more crops are grown at the same time on one and the same field.

→ Sericulture: Commercial rearing of silkworms.

→ Horticulture: Growing vegetables, flowers, and fruits for commercial use.

→ Pisciculture: Breeding of fish in specially constructed tanks and ponds.

→ Viticulture: Cultivation of grapes.

PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture

→ More than half of the world’s population is directly or indirectly engaged in agriculture.

→ Favourable topography of soil and climate is vital for agricultural activity.

→ Agriculture depends largely on the relief of land, climate conditions, fertility of the soil, and economic factors.

→ Soils not only support the plant but also act as a medium to supply moisture and nutrients.

→ In intensive agriculture, the aim is to get higher yields per unit area.

→ Extensive agriculture is done with machines in sparsely populated areas.

→ In commercial agriculture, most of the crops are produced for the market.

→ The production of fruit and flowers is called horticulture.

→ In a co-operative farm, all the members work and earn proportionately.

PSEB 8th Class Social Science Notes Chapter 4 Our Agriculture

→ Crops and livestock are raised together on the same farm in mixed farming.

→ Shifting cultivation is known by different names in different parts of the world, i.e., Juming, Milpa, Ladang, etc.

PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources

This PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources

→ Rock is a natural substance made up of one a more minerals.

→ Minerals: An inorganic substance which is found in the earth’s crust and it has a definite chemical composition.

→ Metallic minerals: Those minerals contain metals.

→ Minerals may be metallic or non-metallic.

PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources

→ Minerals can be ferrous and non-ferrous.

→ Mining: It is an economic activity of extracting valuable minerals from the earth.

→ Mine: It is an excavation in the ground for digging out minerals.

→ Recycling: It means using discarded materials once again.

→ Fossil fuels: They are fuels formed due to the decay of plants and animals millions of years ago.

→ Petroleum: It is derived from Latin words Petra meaning rock and oleum meaning oil. So, petroleum means rock oil.

→ Fossils: The decomposed creatures, minute plants, and animals buried and sedimented for millions of years.

→ Ore: Metals in their raw state as they are extracted from the earth.

→ Grid: Electricity from large power plants is transmitted through a network of power lines.

→ Minerals are extracted by mining, drilling, or quarrying.

PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources

→ Minerals can be conserved by recycling.

→ Mining is of four types:

  • Opencast
  • Shaft
  • Quarrying
  • Drilling

→ All rocks are composed of one or more minerals.

→ Copper was probably the first metal to be discovered and mined by man.

→ Mining is the extraction of minerals from the earth.

→ The distribution of mineral resources is uneven in India.

→ The main sources of power are coal, petroleum, and natural gas.

→ The non-conventional sources of power are sun, wind, tide, falling water, and geothermal sources.

→ Coal is the basis for all industrial development in the world.

→ About 65 percent of the mineral oil resources are found around the Persian Gulf.

→ Metallic minerals contain metal in raw form.

PSEB 8th Class Social Science Notes Chapter 3 Minerals and Energy Resources

→ The Non-Metallic minerals do not contain metals.

→ Switzerland has no known mineral deposits in it.

→ A green diamond is the rarest diamond.

→ The oldest rocks in the world are in Western Australia.

→ Norway was the first country in the world to develop hydroelectricity.

PSEB 8th Class Social Science Notes Chapter 2 Natural Resources

This PSEB 8th Class Social Science Notes Chapter 2 Natural Resources will help you in revision during exams.

PSEB 8th Class Social Science Notes Chapter 2 Natural Resources

→ Conservation: It means using the available resources carefully.

→ Land: The most important resource.

→ Land may be used for agriculture Construction of Roads, Industries, etc.

→ Soil is the uppermost layer of the earth’s crust.

→ Soil Erosion: The removal of soil, especially topsoil, either naturally or as a result of human activity.

PSEB 8th Class Social Science Notes Chapter 2 Natural Resources

→ Land Use: The use of land for different purposes like agriculture, roads, etc.

→ Terrace Farming: The growing of crops on terraces or steps that have been constructed on hillsides.

→ Topography: A detailed account of the features of a tract of country.

→ Strip Cropping: The growing of narrow strips of Cultivated lands, along the contour lines.

→ Shelterbelts: The planting of rows of trees to check the wind movement, to protect the soil.

→ Deforestation: Cutting down trees.

→ Pollution: Contamination of natural resources.

→ Weathering: The breaking up and decay of exposed rocks by temperature changes, plants, animals, etc.

→ Natural vegetation and wildlife are found in the Biosphere.

→ National Park: A natural area designated to protect the ecological integrity of one or more ecosystems for present and future generations.

→ Biosphere resources: Series of protected areas linked through a global network intended to demonstrate the relationship between conservation and development.

→ The land covers about 29 percent of the total surface area of the earth.

PSEB 8th Class Social Science Notes Chapter 2 Natural Resources

→ Land in India actually under cultivation is about 46 percent of the land.

→ The total land resources in our country are fixed.

→ The importance of soils lies in their fertility and capacity to produce crops.

→ Alluvial soils are mostly found in river valleys and floodplains.

→ About 71 percent of the total surface area of the earth is underwater.

→ Wells, tanks, and canals are different sources of irrigation in our country.

→ Natural vegetation can be broadly classified into forests, grasses, and shrubs.

→ Wildlife refers to plants, animals, birds, and other organisms, which live in their natural habitats.

→ Many countries have taken steps to develop ‘biosphere resources’ to protect wildlife.

→ Ninety percent of the world population occupies only thirty percent of the land area.

→ The remaining seventy percent of the land is either sparsely populated or uninhabited.

→ A dripping tap wastes 1200 liters in a year.

→ Soil formation is a very Slow Process. It takes hundreds of years to make just one centimetre of Soil.

→ The thin layer of grainy substance covering the surface of the earth is called soil.

PSEB 8th Class Social Science Notes Chapter 2 Natural Resources

→ In India, soils are of six types.

→ Water can neither be added nor subtracted from the earth.

→ An average urban Indian uses about 135 litres of water every day.