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Balbharti Maharashtra State Board Class 12 Geography Solutions Chapter 1 Population Part 1 Textbook Exercise Questions and Answers.

Maharashtra State Board Class 12 Geography Solutions Chapter 1 Population Part 1

1. Identify the correct correlation.

A – Assertion R – Reasoning
Question 1.
A – Areas which have fertile soil have dense population.
R – Fertile soils are good for agriculture.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(c) Both A and R are correct and R is the correct explanation of A.

Question 2.
A – Population of a region does not change.
R – Birth rate, death rate and migration affect the population of a region.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(b) Only R is correct.

Question 3.
A – In stage 2, death rate reduces but birth rate is constant.
R – Population increases rapidly in stage 2.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(c) Both A and R are correct and R is the correct explanation of A.

Question 4.
A – In stage 5 death rate is more than birth rate.
R – Population is declining in stage 5.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(c) Both A and R are correct and R is the correct explanation of A.

Question 5.
A – In stage 1 both death rate and birth rate are high.
R – Population growth is stable in stage 1.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(c) Both A and R are correct and R is the correct explanation of A.

2. Write short notes on.

Question 1.
Impact of relief on population distribution.
Answer:
1. Relief is one of the most important factors influencing the distribution of population.

2. Generally, mountains are thinly populated, plains are thickly populated and plateaus are moderately populated.

3. The mountains and hilly areas are less populated because of limited means of livelihood; agriculture is poorly developed and transportation facilities are limited. For example, north eastern states of India have less population due to hilly and mountainous relief.

4. On the other hand, plains are densely populated because of fertile soil and well-developed agriculture. Due to plain relief, it is easy to construct roads and develop industries. Better employment facilities attract people in these areas. For example, Ganga plains are thickly populated.

5. In short, we can say plains are densely populated and mountains and plateaus are sparsely populated.

Question 2.
Correlation between birth rate and death rate.
Answer:

• Birth rate and death rate are the important components of population change.
• Birth rate is the number of live births in a year per thousand population.
• Death rate is the number of deaths in a year per thousand population.
• Population growth depends upon birth rate and death rate in a year.
• Population growth occurs not only by increasing birth rate but also because of decreasing death rate.
• When birth rate is more than death rate, population increases.
• When birth rate is less than death rate, population decreases.
• If both, birth rate and death rate is same then population is said to remain stable. However, the birth rate and death rate being same is only a hypothetical situation.

Question 3.
Stage 3 of Demographic Transition Theory.
Answer:
1. Stage 3 of Demographic Transition Theory is the stage of expanding population.

2. From second stage to this stage, death rates are decreasing. Birth rates are also decreasing. Decrease in both birth rates and death rates, reduces the rate of growth of population. But actually, population is growing because the birth rates are higher than death rates.

3. In this stage, since the country is making progress, the income of the people is above the subsistence level and there is an improvement in the standard of living of the people. Poverty is also reducing.

4. There is development of technology as a result secondary and tertiary activities develop.

5. Due to increase in education level, people understand the importance of family planning so size of family reduces.

6. In short in stage 3 countries are moving from developing stage to developed stage.

3. Give geographical reasons.

Question 1.
India is passing through Stage 3 of demographic transition.
Answer:

• In India, since there is a decrease in the birth rates and death rates, the growth rate of population is also decreasing.
• Due to the development in the country, income of the people has reached above subsistence level, standard of living is improved, poverty is decreasing, technology is developing.
• Number of people engaged in secondary and tertiary activities are increasing.
• Due to increase in the literacy rate, people have understood the importance of family planning. Therefore, there is a decrease in the size of family.
• Hence, India is passing through Stage 3 of demographic transition.

Question 2.
Population distribution is uneven.
Answer:
1. Distribution of population in the world is very uneven because distribution of population depends upon many physical factors such as relief, climate, availability of water supply, soil etc.

2. For example, if you consider relief factor, mountains and hilly areas are thinly populated. Plateau regions are moderately populated and plains are densely populated. The Himalayan region in India is thinly populated but the Gangatic plains are thickly populated and Deccan plateau region are moderately populated.

3. The distribution of population also depends upon human factors such as agriculture, mining, transportation, urbanisation etc.

4. For example, agriculture or mining activities support large population since they provide source of living to many people.

5. Sometimes government policies also affect population distribution. For example, government provided land, water, electricity at concessional rate in New Mumbai area to attract people and to reduce pressure of population in Mumbai city.

Question 3.
Population increases because of transportation facilities.
Answer:
1. The development of roads and railways makes the region more accessible.

2. Such areas provide favourable conditions for the development and manufacturing industries, which generate employment. Therefore, people from different areas migrate in search of jobs. Thus, such areas become densely populated. For example, Gangetic plain of India, where the density of roads and railways is highest in India.

3. Population increases in port cities due to availability of sea transport for the development of trade. Therefore, the coastal region is densely populated. For example, many port cities like Chennai, Mumbai are developed on the east and west coast of India.

4. Thus, population increases because of transportation facilities.

Question 4.
Secondary and tertiary activities increase in the third stage of demographic transition.
Answer:

• In Stage 3 of demographic transition theory, growth rate of population decreases.
• As a result, the income of the people in the country reaches above subsistence level. Poverty rate decreases and standard of living increases. Therefore, the use of technology increases and this generates an employment in secondary and tertiary activities.
• Due to increase in education level and development of health facilities there is increase in employment in tertiary sector.
• Thus, secondary and tertiary activities increase in the third stage of demographic transition.

Question 5.
Population may increase though birth rates are low.
Answer:
The growth of population depends upon the difference between number of live births in a year per thousand population and number of deaths in a year per thousand population. Therefore, growth of population depends upon both birth rate and death rate.

When birth rate is low and death rate is also low, then though the number of live births per thousand population are less, but due to a smaller number of deaths per thousand population, there is increase in population of the country.

Question 6.
Population density is a function of population and area of a region.
Answer:
The number of people living in any area or country is called total population of the area or country.

Density of population is the ratio between total population and a total area of that region or country.

For example, as per the census of 2011, Density of population in India is 325 persons per sq. km. It is a ratio between total population in India and total area of India in sq. kms.

In some countries total population may be less but the density of population is high due to small area of the country. For example, Bangladesh’s total population is less but area of country is small therefore, density of population is high.

In some countries total population may be more but the density of population is low due to very large area of the country. For example, Brazil has more total population but area of country is also large therefore, density of population is low.

Thus, population density is a function of population and area of a region.

4. Answer the following questions in detail.

Question 1.
Explain the physical factors affecting distribution of population.
Answer:
Physical factors affecting distribution of population are:
(i) Relief
(ii) Climate
(iii) Availability of water
(iv) Soils

(i) Relief

• Distribution of population is greatly affected by relied features.
• Generally, flat plains or gently sloping lands are densely populated.
• Plains are suitable for agricultural activities.
• In these areas it is easier to construct roads and railways and development of industries and trade. As a result, many people are attracted to plains and they become densely populated. For example, Ganga plains are thickly populated.
• On the other hand, in mountainous and hilly areas density of population is low. This is because in such areas agricultural development is difficult.
• The construction and development of transport facilities is very difficult and costly too. Such areas are inaccessible.
• Due to inaccessibility, movement of goods and people are restricted. Therefore, mountainous and hilly areas are thinly populated. For example, north eastern states of India have less population due to hilly and mountainous relief.

(ii) Climate

• Climate is the most important factor of all the factors influencing the distribution of population.
• Areas having very hot or very cold climate, heavy rainfall are very uncomfortable for human settlement. Such areas are thinly populated.
• For example, polar regions where Eskimos and Lapps live are sparsely populated due to extreme cold climate. Sahara Desert is sparsely populated due to extreme hot climate.
• On the other hand, areas with equable climate, that is climate having not much seasonal variation attract people. People feel comfortable to stay in these areas.
• For example, coastal areas have dense population because of equable climate and wide scope for the development of agriculture, industries and trade.

(iii) Availability of water

• Water is the most important factor affecting distribution of population. It is the most essential factor for all human activities.
• Therefore, more people live in areas where potable and sufficient water is available. As a result of this most of the river valleys are densely populated i.e. Nile river valley.
• Even in desert areas there is more population near oasis due to availability of water.

(iv) Soil

• Fertile soils are most important for the development of agriculture.
• The areas having fertile alluvial soil have developed intensive agriculture and support large number of people and hence they are densely populated, e.g., Gangetic Plain, Plains of Mississippi, Irrawaddy and Yangtze etc.
• Similarly, in the areas having very fertile black cotton soil or regur soil, agriculture is well developed and hence such areas are densely populated.
• The volcanic soil is very fertile hence, it supports agriculture. Therefore, slopes of volcanic mountains have dense population. For example, volcanic mountain slopes of Java island.

Question 2.
In the first and fifth stage of the demographic transition, population growth is almost nil. What is the difference between the two stages then?
Answer:

• In the stage 1 both birth rates and death rates are high. The difference between the two is very less and therefore, population is stable.
• In stage 1 birth rates are high due to limited educational opportunities, people feel having many children is good. Therefore, families are big.
• In stage 1, due to lack of sanitation facilities, medical facilities, spread of contagious diseases, malnutrition, etc., death rate is high.
• In stage 5 birth rates and death rates are very low. Birth rates are almost equal to death rates.
• As a result, the population growth is almost minimal or very low or even negative in case of some countries.
• In stage 5, death rate is low because of improved medical facilities, eradication of contagious diseases and healthy environment.
• In stage 5, due to increase in awareness among the people, birth rate is low.

Question 3.
Discuss the problems faced by counties in stage 4 and stage 5.
Answer:
Problems faced by stage 4 countries are as under:

• The death rate is very low and going down as the medical facilities have improved and pandemic like plague, cholera, small pox, etc., are eradicated.
• Birth rate is the same as death rate so population growth is minimal.
• Problems faces by stage 5 countries are as under:
• In this stage the birth rate is very low and death rate is high. Therefore, the growth of population is slow or negative growth of population is seen.
• Due to large number of old people the death rate is high and due to a smaller number of young people birth rate is low.
• Due to large number of old people, dependent population is high.
• Due to less young age population, working population is limited.
• As a result, the size of dependant population is larger than active population and it has adverse effect on economy of the country.

5. Draw a neat labelled diagram for demographic transition theory and its various stages.
Answer:

6. Mark and name the following on the outline map of the world with suitable index.

(a) Highly populated region in Australia.
(b) Sparsely populated region in India.
(c) Any 2 countries in stage 5 of demography transition theory.
(d) Any 2 countries in stage 2 of demographic transition theory.
Answer:

Class 12 Geography Chapter 1 Population Part 1 Intext Questions and Answers

Try These

Question 1.
Observe the pie charts shown in the figure and answer the following questions. (Text book pg.no – 1)

1. Which continent has least population?
2. Which continent has the least landmass and also least population?
3. Which continent has the most land mass as well as most of the population?
4. Which continent is missing in one of the pie charts? Why?

Answer:

1. The continent which has the least population is Australia.
2. The continent which has the least land mass and also least population is Australia.
3. The continent which has the most land mass and also most population is Asia.
4. The continent of Antarctica is missing in population distribution chart, because it has no permanent human settlement.

Question 2.
Look at the below figure and answer the questions that follow:

1. What does the image show?
2. What happens to the population when the deaths are more than births?
3. What happens to the population when births are more than deaths?
4. What happens when both are same? Is it possible?

Answer:

1. The image shows balance between birth rate and death rate.
2. Population growth may be less or in some countries there may be negative growth.
3. When births are more than deaths, then population growth is faster.
4. When both births and deaths are same, population will be stagnant. This is not possible for any country.

Give it a try

Question 1.
The below table shows the 10 most populated countries in the world in 2018 with their areas. Calculate their population densities and complete the table. (Text book pg.no – 1)

Answer:

Question 2.
The satellite image given in Fig. They show the same area from two different periods. (Text book pg.no – 6)

1. What difference do you see?
2. What might have caused these changes?

Answer:
1. The satellite image ‘A’ is image of the year 2005 and satellite image ‘B’ is of the year 2019. That means there is a difference of 14 years in these two images.

2. In image ‘A’ you can see that there are a few roads, limited settlements and most of the areas are covered by agricultural fields, and there is thin population.

3. When we compare the image ‘A’ with the image ‘B’, we find that in image ‘B’ the number of major roads (highway) and minor roads have increased. As a result, the area has become more accessible and thickly populated.

Due to development of industries and employment opportunities there is development of transport.

Question 3.
1. Can you calculate the death rate if the total number of deaths in the above city was 2,986 in the same year?
2. On the basis of the birth rates given in earlier and death rates calculated, what change in population do you observe?
Answer:
1. Total population of a city is 223000 and total deaths in the city are 2986 in that year.
Death Rate = \(\frac {Total number of deaths in a year}{Total population in that year}\) × 1000
Death Rate = \(\frac {2896}{223000}\) × 1000 = 13.39
Therefore, the death rate is 13.39.

2. In earlier example birth rate was 14.57 and the death rates calculated is 13.39. It means death rate have decreased by 1.8. It means the population has increased.

Question 4.
Look at the graph in Fig. carefully. Answer the following questions: (Text book pg.no – 9)

1. What do the blue and black lines indicate?
2. What does the green part in the graph show?
3. What does the blue part in the graph show?
4. In which stages is the birth rate more than the death rate?
5. In which stages is the birth rate same as the death rate?
6. In which stage is the death rate being more than birth rate?

Answer:

1. Blue lines indicate birth rate and black lines indicate death rate.
2. Green part in the graph shows the natural increase of population.
3. Blue part in the graph shows the natural decrease of population.
4. In stage 2 and 3 birth rates is more than death rate.
5. In stage 4 the birth rate is same as the death rate.
6. In stage 5 the death rate is more than birth rate.

Make friends with maps!

Question 1.
Look at the map in Fig. Compare it with the physical map of the world given in Textbook Page No. 83. Try to understand the impact of physical factors on population distribution. Complete the table accordingly. (Text book pg.no – 2)


Answer:

Continent	Physical factors responsible for High population	Physical factors responsible for less population
North America	Coastal Areas	Forest, deserts, snow covered land
Asia	Coastal areas and Fertile Plains	Mountains and deserts
Europe	Coastal areas and fertile Plains	Mountains, snow covered areas
Africa	Coastal Areas	Dense forest, mountains and deserts
South America	Coastal Areas	Mountains, dense forest and deserts
Australia	Coastal Areas	Hilly regions and deserts
Antarctica	–	Snow covered areas

Question 2.
Refer to the map showing rice producing regions of the world in Fig. Relate it with the population map of the world in Fig. Write the conclusions in your own words. (Text book pg.no – 5)


Answer:
Areas of high density of population in Fig 1.2 if we compare with world map Fig 1.4 showing major rice producing areas in the world, we found that the areas of major rice production and areas of high density / thick population are the same areas.
Conclusion:
Rice cultivation is possible only in those areas where there is fertile alluvial soil and assured supply of water.
Rice producing areas and areas of dense population in the world are the river flood plains and delta of rivers like Kaveri, Krishna, Godavari and Ganga in India, Brahmaputra in Bangladesh, Irrawaddy in Myanmar, Yangtze and Yellow in China, Mekong in Laos and Cambodia etc. These areas are high density areas in the world.

Can you tell?

Question 1.
Can you think of the factors besides physiography which affect the distribution of population? Make a list. (Text book pg.no – 3)
Answer:

Physical / Human factors	High density of population	Low density of population
Availability of potable water	River valleys	Deserts
Climate	Equable climate – coastal areas	Extreme climate – polar regions
Availability of resources	Minerals, fertile soil	Limited resources
Economic	Transportation, employment opportunities, urbanisation	Less employment opportunities, poor economic growth
Social	Migration from different parts of India in Mumbai	Out migration from Konkan to Mumbai
Government Policy	Favourable government policies to attract people	Unfavourable government policies

Question 2.
Observe the table 1.4. Arrange data in ascending order for birth rate and death rates respectively. (Text book pg.no – 8)

Country	Crude BR (2017)	Crude DR (2017)
Sweden	11.5	9.1
India	18.1	7.2
Greece	8.2	11.6
China	12.4	7.1
USA	11.8	8.5
Niger	46.5	8.5

Answer:

Question 3.
Look at the Fig. and answer the following questions. (Text book pg.no – 9)

1. If the crude birth rate is 7 and crude death rate is 8 then which stage of demographic transition is the country in?
2. If a country has crude death rate of 20 and crude birth rate of 24, then which stage of demographic transition is the country in? [Text book pg.no – 10]

Answer:

1. The country is in stage 5 of demographic transition.
2. The country is in stage 3 of demographic transition.

Find out.

Question 1.
(i) Are Eskimos still living in their conventional ways?
(ii) What changes can be seen in their lifestyle now? (Text book pg.no – 4)
Answer:
(i) No, Eskimos are not living in their conventional way due to the changing environment as a result of increased contacts with societies to the south.

(ii) Eskimo life has changed greatly because of increased contacts with societies to the south.

• They were using harpoons for hunting, now they are using rifles. They were using dogs for land transport, now they are using snowmobiles.
• Outboard motors, store-bought clothing and many other manufactured products have entered into their culture.
• Women are taking salaried jobs to earn currency for store-bought products. As a result, women are losing their knowledge of traditional skills such as sewing animal skin.
• Many Eskimos are not doing nomadic hunting which was their main activity. Now they are living in northern towns and cities and working in mines and oil fields.
• Some Eskimos in Canada have formed cooperative societies for marketing their handicrafts, fish catches, tourism ventures etc.

Use your brain power!

Question 1.
(i) Can lakes be a factor for concentration of population? Find examples.
(ii) Which water bodies are surrounded by dense population in Maharashtra? (Text book pg.no – 4)
Answer:
(i) Man always likes to settle near a waterbody. People are attracted towards lakes.

Lakes are not only a source of fresh water but also a source of fish. They also provide water supply for industries, agriculture and provide water transport. They provide good sites to develop tourism due to greenery of trees surrounding the lake, scope for boating, cool breeze and pleasant atmosphere.

For example, Lake Victoria in Africa, supports 40 million people, with population density 250 persons per sq. km. The growth rate of the population is 3.5 percent each year, which is among the highest growth rates in the world.

The Victoria lake supports the largest freshwater fishery in the world. The fish catch from the lake is more than one million and it employs two lakh people in direct fishing and supports livelihood to four million people.

Five Great lakes in USA – Superior, Huron, Michigan, Erie and Ontario make up the largest body of freshwater on earth. They support more than 30 million people. This equates to 10 percent of USA residents and 30 percent Canadian residents.

The lakes have been a major source for transportation, trade, fishing, tourism, power, recreation etc.

(ii)

• In Maharashtra the following water bodies are surrounded by dense populations.
• Rankala lake around which dense population of Kolhapur city.
• Powai lake around which dense population of Mumbai city.
• Ambazari lake around which dense population of Nagpur city.
• Pashan lake around which dense population of Pune city.
• Dense population on the bank of Mula-Mutha river of Pune city.
• Dense population on the bank of Nag river – Nagpur city.
• Dense population on the bank of Tapi river – Bhusaval and other cities.
• Dense population on the bank of Godavari river – Nasik city.
• Dense population on the bank of Krishna- Koyana rivers – Karad, Sangli cities.
• Dense population along the coastline of Arabian sea- Mumbai city.

Question 2.
In which stage do you think India is passing right now? (Text book pg.no – 10)
Answer:
India is passing through stage 3 right now.

Question 3.
Find out in what multiples has population increased in the following timeline and write down your findings. For example, in the initial phase, the population took 6 centuries (1000 to 1600 A.D.) to double itself. (Text book pg.no – 11)

Answer:
(i) 1000 to 1600 population increase 2 times in 6 hundred years.
(ii) 1600 to 1900 population increased 3 times in 3 hundred years.
(iii) 1900 to 1960 population increased 2 times in 6 hundred years.
(iv) 1960 to 2000 population increased 2 times in 4 hundred years.

Let’s recall.

Question 1.
Which policy did the Brazilian government promote with respect to decentralisation? (Text book pg.no – 7)
Answer:

1. Last two decades there is highly centralised military rule in Brazil so there was demand for local autonomy. Brazil sought to decentralised government authority and promote citizen participation to establish democracy.
2. Brazil became decentralised federation when it undertook transformation of governance.
3. As result authoritarian military regime came to an end.

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 11.2 8th Std Maths Answers Solutions Chapter 11 Statistics.

Practice Set 11.2 8th Std Maths Answers Chapter 11 Statistics

practice set 11.2 8th class Question 1.
Observe the following graph and answer the questions.

i. State the type of the graph.
ii. How much is the savings of Vaishali in the month of April?
iii. How much is the total of savings of Saroj in the months March and April?
iv. How much more is the total savings of Savita than the total savings of Megha?
v. Whose savings in the month of April is the least?
Solution:
i. The given graph is a subdivided bar graph.
ii. Vaishali’s savings in the month of April is Rs 600.
iii. Total savings of Saroj in the months of March and April is Rs 800.
iv. Savita’s total saving = Rs 1000, Megha’s total saving = Rs 500
∴ difference in their savings = 1000 – 500 = Rs 500.
Savita’s saving is Rs 500 more than Megha.
v. Megha’s savings in the month of April is the least.

practice set 11.2 Question 2.
The number of boys and girls, in std 5 to std 8 in a Z.P. School is given in the table. Draw a subdivided bar graph to show the data. (Scale : On Y axis, 1cm = 10 students)

Standard	5th	6th	7th	8th
Boys	34	26	21	25
Girls	17	14	14	20

Solution:

Standard	5th	6th	7th	8th
Boys	34	26	21	25
Girls	17	14	14	20
Total	51	40	35	45

Statistics class 8 practice set 11.1 Question 3.
In the following table number of trees planted in the year 2016 and 2017 in four towns is given. Show the data with the help of subdivided bar graph.

Year\Town	karjat	Wadgaon	Shivapur	Khandala
2016	150	250	200	100
2017	200	300	250	150

Solution:

Year\Town	karjat	Wadgaon	Shivapur	Khandala
2016	150	250	200	100
2017	200	300	250	150
Total	350	550	450	250

Statistics class 8 Question 4.
In the following table, data of the transport means used by students in 8th standard for commutation between home and school is given. Draw a subdivided bar diagram to show the data.
(Scale: On Y axis: 1 cm = 500 students)

Means of commutation\Town	Paithan	Yeola	Shahapur
Cycle	3250	1500	1250
Bus and auto	750	500	500
On foot	1000	1000	500

Solution:

Means of commutation\Town	Paithan	Yeola	Shahapur
Cycle	3250	1500	1250
Bus and auto	750	500	500
On foot	1000	1000	500
Total	5000	3000	2250

Balbharti Maharashtra State Board Class 12 Geography Solutions Chapter 2 Population Part 2 Textbook Exercise Questions and Answers.

Maharashtra State Board Class 12 Geography Solutions Chapter 2 Population Part 2

1. Identify the correct co-relation

A : Assertion R : Reasoning
Question 1.
A – Increase in the dependency ratio will affect the economy.
R – Medical costs are high when there are more elderly in the population.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(d) Both A and R are correct but R is not the correct explanation of A.

Question 2.
A – In population pyramid, a broad base indicates high number of children in a country.
R – Broad apex is an indicator of high number of elderly people in a country.
(a) Only A is correct.
(b) Only R is correct.
(c) Both A and R are correct and R is the correct explanation of A.
(d) Both A and R are correct but R is not the correct explanation of A.
Answer:
(d) Both A and R are correct but R is not the correct explanation of A.

2. Write short notes on.

Question 1.
Population growth and migration.
Answer:

• When people move from one place to another place, or one city to other city or one country to another country it is called migration.
• The place from where people go out is called donor region.
• The place where people migrate is called recipient region,
• Due to migration there are changes in total population in both the regions.
• From donor region people move outside so donor area population will decrease. Generally, youngsters migrate in large number, so donor region will have less young age population, it will affect fertility rate and there will be slow growth of population.
• In recipient region migrants will be added to the total population of that region. Thus, increasing the population of the region.
• In recipient region more young age population will be added, so fertility rate will increase, and there will be more population growth.

Question 2.
Population pyramid and sex ratio.
Answer:

• The ratio between the number of male and female in the population is called sex ratio.
• Sex ratio is an indicator of status of women in the country.
• In population pyramid X-axis shows the percentage of population in a particular age group and Y-axis, which is at the centre of the graph shows age groups.
• The length of the bar shows number or percentage.
• The left side of the graph shows male population whereas, the right side of the graph shows female population.
• Thus, population pyramid indicates number of percentages of male and female population in different age groups in the country.
  e.g., If we want to know the percentage of male and female in 15-59 age group, we can get it from population pyramid.
• Therefore, we can study age-wise sex ratio using population pyramid.

Question 3.
Occupational structure of population.
Answer:

• In all countries working population is engaged in primary, secondary, tertiary and quaternary activities for their livelihood.
• The percentage of people engaged in these activities is called occupational structure.
• In developing counties percentage of people engaged in primary occupations is high compared to people engaged in secondary, tertiary or quaternary activities.
• In developed countries, percentage of people engaged in secondary, tertiary and quaternary activities is more compared to people engaged in primary activities.
• Trade and infrastructure are advanced. So, more people are required in secondary, tertiary and quaternary activities.
• More people engaged in secondary, tertiary and quaternary activities more the country has been developed.
• Thus, occupation structure of the country is an indicator of the level of economic development of the country.

Question 4.
Literacy rate.
Answer:

• Literacy rate shows proportion of literate people in the country. The people who can read and write are called literate people.
• Every country has different norms to decide literacy. In India, those who can read, write and do arithmetic calculations are called literate.
• Literacy in the country is essential to eradicate poverty and for social, economic and political development.
• Literacy rate in the country depends upon cost of education, standard of living, status of women in the society, availability of educational facilities and government policy etc.
• In general, literacy rate of male is more than female with few exceptions.
• Literacy rate is more than 90% in most of the developed countries of Europe, North America, Australia etc.
• Lowest literacy rate is in Sub-Saharan Africa.

3. Give geographical reasons.

Question 1.
In developed countries, percentage of population engaged in agriculture is low.
Answer:

• In developed counties there is development of industries, infrastructure and trade.
• Therefore, more people are engaged in secondary, tertiary and quaternary activities.
• These countries replace human labour with machinery. So agricultural activities can be carried out with minimum people and can make use of machinery.
• Therefore, the percentage of population engaged in agriculture is low in developed countries.

Question 2.
Literacy rate of a country is an indicator of its socio-economic development.
Answer:

• Socio-economic development of the country is measured by people’s standard of living, social status of female in society, educational facilities in the country and government policies.
• Higher the literacy rate of women, the more women are educated and employed.
• If the literacy rate is high people are educated, employed and well settled. Owing to which the standard of living becomes high.
• If government policies are favourable for education, educational institutes are more developed, more people become educated and employed. This leads to higher standard of living.
• Thus, literacy rate of countries is an indicator of its socio-economic development.

Question 3.
Demographic dividend increases when proportion of working population increases.
Answer:

• The productivity of the country depends upon working and non-working population in the country.
• If more people are working and fewer people are non-working, then resources are invested in other areas, so there is a boost to the country’s economic development.
• Due to boost in economy per capita income increases.
• Thus, there is economic benefit to the country which is dividend and it benefits all in the country.

Question 4.
Migration is not always permanent.
Answer:

• When migrated person never returns to his original place it is called permanent migration.
• In most of the cases migration is seasonal, may be to work as labourer in farm during a particular season or migration of tribal people in search of fodder. This is short term migration.
• In case of migration for jobs to city areas or to other countries, people work in migrated areas but visit their original places once or twice in a year. This is long term migration.
• Thus, in most of the cases migration may be short term or long term and not permanent.

4. Differentiate between.

Question 1.
Donor region and Recipient region
Answer:

Donor Region	Recipient region
(i) Donor region is the region from where people migrate to other areas.	(i) Recipient region is the region, where migration takes place or region where people go.
(ii) In donor region due to reduction in local population there is less utilisation of public facilities like transport, water supply, education, recreation etc.	(ii) In recipient region due to increase in population there is more pressure on public facilities like transport, water supply, education, recreation etc.
(iii) The expenditure on the public facilities is not utilised fully.	(iii) The public facilities are not sufficient for increasing population.
(iv) From donor region mostly young men migrate to other areas in search of jobs, business or education.	(iv) More young men are added to population for job opportunities or business or education.
(v) There are changes in age and sex ratio, there are more women, children and old age population than young age people.	(v) There are changes in age and sex ratio. There are more male than female and more young age population.
(vi) There is more non-working or dependent population, it has adverse effect on economy of that area.	(vi) There is more working age population, with innovative ideas, concepts, etc., which helps technological and economic development of the region.

Question 2.
Expansive pyramid and Constructive pyramid
Answer:

Expansive pyramid	Constrictive pyramid
(i) Expansive pyramid is very broad at the base and becomes narrow at the apex.	(i) Constrictive pyramid is narrow at the base and broader at the apex.
(ii) It shows that there is higher percentage of young people but lower percentage of old age people in the country.	(ii) It shows that there is high percentage of old age people and lower percentage of young age people in the country.
(iii) It indicates high birth rate making the base broad and high death rate making the apex narrow.	(iii) It indicates low birth rate making the base narrow and low death rate making the apex broad.

5. Answer the following questions in detail.

Question 1.
Outline the importance of population pyramids in the study of populations.
Answer:
1.  To study population of any country people use population pyramid.

2. With the help of population pyramid, age-wise and gender-wise population of the country can be studied.

3. Age structure and sex ratio are important aspects of population of the country.

4. In population pyramid, percentage of population in age groups are shown on the X-axis. Whereas markings of age groups are shown on the Y-axis.

5. The right side of the pyramid shows female population and left side shows male population.

6. As the age groups are on Y-axis, the base of pyramid indicates young age population, and apex of pyramid indicates old age population and middle portion of pyramid indicated adult population.

7. When old age population is more, it leads to more non-working population and there is increased expenditure on medical and health facilities.

8. When younger age population is more, it also leads to more non-working and dependent population. This causes a burden on the economy.

9. When adult age population is more, then working population is more. This helps the development of the country.

10. The population pyramid makes us understand age-wise and sex-wise population as per following:

• Broader the base, more young age population.
• Narrower the base less young age population.
• Broader the apex, more old age population.
• Narrower the apex, less old age population.
• Left and right side of pyramid shows male and female population in the country.

11. There are three types of population pyramids which depicts the birth rate and death rate.

• Expansive pyramid- It has abroad base and narrow apex. It shows high birth rate and high death rate.
• Constrictive pyramid- It has narrow base and broad apex. It shows low birth rate and low death rate.
• Stationary pyramid- Here all age groups have same percentage. It shows very low birth rate and very low death rate, that means slow growth of population in the country.

Question 2.
Explain the rural and urban population structure.
Answer:

• The area where more people are engaged in primary activities is called rural area and the people living in rural areas are called rural population.
• The area where more people are engaged in secondary and tertiary activities is called urban area and people living in urban area are called urban population.
• There is a difference in density of population, age structure, sex ratio occupation structure standard of living, lifestyle of people, sources of income, literacy rate etc.
• There is major difference in level of economic development in rural and urban areas.
• There is more use of modern technology in urban areas compared to rural areas. Therefore, development in all fields is very fast.
• Due to more development of industries and infrastructure in urban areas there is an increase in the transportation and trade as compared to rural areas.
• The criteria to differentiate rural and urban population varies from one country to other country.

Question 3.
Examine the impact of migration on the population structure of a country.
Answer:

• In migration people move from one place to another place for different reasons.
• The place from where people migrate outside is called donor region.
• The place where people migrate to is called recipient region,
• Due to migration of people there are changes in age structure and sex ratio in both the regions.
• In donor region due to migration of young male population there is disturbance in the age structure.
• More females remain in donor area. So, donor area has high sex ratio. In India there is high sex ratio in rural areas due to migration of people from rural to urban areas.
• In donor region there are changes in age structure as well.
• More old age people and children remain in donor region which is non-working/ non-productive population.
• There is shortage of working population.
• In recipient region male population increases due to migration of male into region.
• As a result, sex ratio in recipient region goes down. In many big cities of India sex ratio is less than 85% or 90%.
• In recipient region the percentage of working populatioh increases.
• There is more working population than non-working population, which helps in economic development of the region.

Class 12 Geography Chapter 2 Population Part 2 Intext Questions and Answers

Try this.

Question 1.
In the above figure A, B, C are three population pyramids. Study their shapes and answer the following questions. (Textbook Page No. 12)
(i) In which pyramid(s) the number of children will be the least?
(ii) In which pyramid(s) the number of old people will be the least?
(iii) Which pyramid(s) represents a ‘young country’?
(iv) Which pyramid(s) represents a country with high medical expenditure?
(v) Which pyramid(s) represents a country with large manpower?
(vi) Which pyramid(s) represents developing and developed counties respectively?
Answer:
(i) – C
(ii) – A
(iii) – A
(iv) – C
(v) – B
(vi) – A/B/C

Question 2.
Answer the questions after studying table carefully. (Textbook Page No. 14 and 15)

Country	Retirement Age reforms being implemented or under consideration (in years)
Germany	Retirement age to increase gradually to 66 by 2023 and to 67 by 2029
United States of America	Retirement age to rise gradually to reach 67 for those born in 1960 or later
United Kingdom	Retirement age to increase for both men and women to 66 by October 2020 and further to 67 between 2026-28
Australia	Retirement age scheduled to increase gradually to 67 by 2023
China	By 2045, to increase retirement age for both men and women to 65
Japan	Under consideration to raise the retirement age to 70
India	On an average, 60 years. May vary from 55 years to 65 years according to services

(i) What does the table show?
(ii) Classify these countries into developed and developing.
(iii) What could be the reason behind increasing the retirement age in these countries?
(iv) What will be the impact of increase in the retirement age on the economy of the respective countries?
(v) Why is China considering increasing the age later in 2045?
(vi) Considering these examples from developed countries, will it be good for India to increase its retirement age? Express your views.
(vii) Write a concluding statement about the relationship between age structure, life expectancy and economy of a country.
Answer:
(i) The table shows country wise retirement age reforms implemented or under consideration (in years).

(ii) Germany, United States of America, Australia and Japan are the developed countries and China and India are the developing countries.

(iii) Many countries have considered or considering the increase in retirement age because increase in ageing population increases pressure on pension funding, retirement provisions and medical facilities.

(iv) Due to increase in retirement age and life expectancy people can work for many years. This will reduce pressure on pension funding, retirement provisions and expenses on medical facilities.

(v) China is considering increasing the age of retirement later in 2045 because the proportion of children and young adult population is going to decrease in the age structure of the country.

(vi) From economic point of view, it is yes. India should increase retirement age because in India too expectancy of life in higher age groups is increasing. If we increase retirement age it will reduce pressure on pension fund and medical facilities.

But from the socio-economic point of view, it is not advisable to increase retirement age because the rate at which population in working age group is increasing, job opportunities are not increasing. If you increase retirement age, unemployment in working age population will increase. This will lead to many socio-economic problems.

(vii) A country in which large percentage of population is in working age group and the life, expectancy is high, large human force will be available for the economic development. However, if large percentage population is found in younger age group and elderly age group, dependency ratio will be high and the country will have slow economic development.

Question 3.
You have already made a list of the reasons why migration occurs. Add more reasons to it. Discuss and classify these reasons into pull and push factors and complete the figure. (Textbook Page No. 19)
Answer:

Push factor (Donor Region)	Pull factor (Recipient Region)
(1) Lack of employment	(1) Chances of unemployment
(2) Natural calamities	(2) Increase in number of refugees
(3) Lack of education, health and entertainment facilities	(3) Pressure on educational, medical and entertainment facilities

Question 4.
Complete the following table which shows impact of migration on the population. (Textbook Page No. 20)

Type of migration	Positive effects	Negative effects
Internal migration	Employment is available to migrants. Improves their financial status.	Resources are affected. Sometimes, they might be sent back to their original country.
Rural to urban migration	–	–
Urban to rural migration	–	–
Rural to rural	–	–
Seasonal / Temporary	–	–

Answer:

Type of migration	Positive effects	Negative effects
Internal migration	Employment is available to migrants. Improves their financial status.	Resources are affected. Sometimes, they might be sent back to their original country.
Rural to urban migration	Cheap labour is available	Pressure on civic amenities, housing problems
Urban to rural migration	Migrants enjoy better environment	Difficult to adjust with limited resources
Rural to rural	Improvement in financial conditions	Clashes between locals and migrants
Seasonal / Temporary	Temporary increase in economic activities.	Temporary pressure on civic amenities & housing problem.

Give it a try.

Question 1.
On the basis of the survey done in practical 1, draw a population pyramid for the people in 15 households. Write your conclusions after studying the structure of the population. (Textbook Page No. 13)
Answer:
[Students have to attempt this question on their own.]

Question 2.
Study the below table carefully and answer the following questions. (Textbook Page No. 16)

(i) What does the table show?
(ii) Which sector has the highest occupation? In which year?
(iii) Which sector has the lowest occupation? In which year?
(iv) In which sector is the working population occupation decreasing?
(v) In which sector is the working population increasing?
(vi) Draw a suitable diagram for statistical information showing A, B and C columns from 1901 to 2011.
(vii) Compare the data. Write a concluding paragraph on the graph.
Answer:
(i) The table shows occupational structure of India.
(ii) The primary sector has the highest occupation. It is 72.7 percent in 1951.
(iii) Secondary sector has the lowest occupation. It is 10.00 percent in 1951.
(iv) In the primary sector the working population occupation is decreasing.
(v) In the secondary and tertiary sector, the working population is increasing.
(vi ) Divided Horizontal Percentage Bar Graph

(vii) After studying the occupational structure of India from 1901 to 2011 the following trend is observed:

• There is a continuous fall in the number of persons engaged in primary activities; from 71.9% to 48.96%.
• There is 50% fall (from 50.6% to 26.4%) in the number of persons working as cultivators.
• Even percentage of people engaged in livestock activity, forestry and fishing occupations have gone down by 4 times.
• When it comes to the secondary and tertiary occupations, the number of people working in these activities are increasing continuously. Their number has become almost double.
• The number of people engaged in trade and commerce has become double and there is a four time rise in number of people working in transport and communication.
• In case of other occupations there is a small rise.

Can you tell?

Question 1.
The population pyramid of India is given below. Read the pyramid and answer the following questions. (Textbook Page No. 13)

(i) Which pyramid type does India belong to?
(ii) Comment upon the age structure of its population.
Answer:
(i) The pyramid of India belongs to expansive A type.

(ii) The shape of the India’s population pyramid has a broad base and narrowing apex. This indicates the population below the age 0-15 years is very large and population in the age above 60 years is very small.

• Due to large number of children dependency ratio is very high.
• The narrow apex indicates more people die at the higher age group.
• This also indicates high birth rates and high death rates.

Question 2.
Read the following table and answer the questions that follow: (Textbook Page No. 14)

Decade	Ratio of working / non-working population	Percentage of working population
2001 – 10	1.33 : 1	57.1
2011 – 20	1.53 : 1	60.5
2021 – 30 (projected)	1.81 : 1	64.4
2031 – 40 (projected)	1.72 : 1	63.2

(i) What does the table show?
(ii) What is the relationship between second and third column?
(iii) How will this relationship affect the economy of India?
(iv) What will happen if the ratio decreases over the years?
Answer:
(i) The table shows India’s Demographic Dividend from 2001 to 2004
It contains data of ratio of working population to non-working population and percentage of working population.

(ii) 1. Both columns represent the working, non-working or dependent population in India during each decade.

2. Second column represents this information in the form of ratio of working population to non-working population.

3. Third column represents the same information about working and non-working population in the form of percentage.

4. The relationship between second and third column is very clear as the percentage of working population increases, we find increase in ratio in the second column.

(iii) 1. An economy of any country depends upon the working population, as working population
helps in generation of wealth through various economic activities.

2. When the ratio of working population to non-working population is higher, it helps in increasing economic position of the people, their standard of living and hence this economic benefit percolates in the society by the purchase of goods and services.

3. As per this table, next decade 2021-2030 is the most favorite for the economy of India as both ratio and percentage of working population will be highest in this decade.

(iv) 1. Decrease n the ratio indicates that the non-working population or dependent population is increasing as compared the working population.

2. This is likely to happen when the expectancy of life increases due to improvement in medical facilities, better living conditions.

3. Therefore, more money is required for non-working or dependant population. This may increase financial burden on the economy.

4. We will have to divert more money for non-working population, which would have been useful for other development projects/activities.

Question 3.
Read the following graph and answer the following questions (Textbook Page No. 16)

(i) Which region has the highest literacy rate?
(ii) Which region has the lowest literacy rate?
(iii) In which region does women fare better than men in literacy rate?
(iv) Write a concluding paragraph about the graph.
Answer:
(i) Central Asia region has the highest literacy rate.

(ii) Sub-Saharan Africa region has the lowest literacy rate.

(iii) In no region does women fare better than men because in all the regions the graph shows literacy rate of men is higher than women.

(iv) The graph shows the percentage of literate male and female and total literacy rate of seven regions and the world. In all seven regions the highest literacy rate of both male and female is recorded in Central Asian region, whereas the lowest literacy rate of male and female is recorded in Sub-Saharan Africa.

In all seven regions and world too, male literacy rate is higher than female literacy rate.

Question 4.
On the basis of which other characteristics can you explain the composition of population. Make a list. (Textbook Page No. 17)
Answer:
We can divide population on the basis of many other characteristics as per following.

1. Cast composition
2. Religious composition
3. Linguistic composition
4. Martial status
5. Racial & ethnic composition.

Find out.

Question 1.
Find out India’s sex ratio as per Census 2011. (Textbook Page No. 14)
Answer:
Sex ratio in India as per census 2011 is 943 females per 1000 males.

Question 2.
Find out the minimum age taken into consideration for calculating literacy. (Textbook Page No. 16)
Answer:

1. Brazil – 15
2. USA – 15
3. Germany – 15

Use your brain power!

Question 1.
If you travel to a place for a few days with your family, will it be considered migration?
Answer:
It will be temporary type of migration or migration for pleasure. For example, people go to Kashmir for 10/15 days.

Read the events (Textbook Page No. 17 and 18) and answer the questions that follow:

Question 1.
What similarities do you find in these events?
Answer:
The similarities in these events are that all are migrated from their original place because of physical, economic, social or political reasons. They have left their place and have migrated to other areas as per their requirements.

Question 2.
Is there a change in the location in these events? Why?
Answer:

• Yes, there is change in the location. Change is because of their personal reasons.
• Ram, Prasad and Ritika migrated for jobs.
• Sahmat migrated because of war situation at his original place.
• Babanrao migrated because of drought situation at his original place.
• Ritesh migrated for higher education.
• Latika migrated after marriage.

Question 3.
Arrange these six events according to the difference in the relative distance between the new and old location.
Answer:

New location	Old location	Person migrated
USA	Pune	Ritika
Mumbai	North Indian town	Ramprasad
Sholapur	Satara	Latika
Nashik	Pimpalwadi	Ritesh

Relative distance travelled by Sahmat and Babanrao is very vague and therefore it is not included in the above table.

Question 4.
Make a list of reasons for leaving the original location.
Answer:

Reasons for leaving place	Name of person who left
Economic	Ramprasad and Ritika
Political	Sahmat
Physical	Babanrao
Social	Ritesh and Latika

Question 5.
Classify the reasons into willing and reluctant migration.
Answer:

Willing	Reluctant	Person migrated
Economic	–	Ramprasad, Ritika
–	Political	Sahmat
–	Physical	Babanrao
Social	–	Ritesh, Latika

Question 6.
Make a list of reasons behind migration besides the one given here.
Answer:
The following is the additional list of reasons for migrations. People migrate for

1. Higher education
2. Medical services
3. Riots
4. Partition of a country
5. Pleasure
6. Tourism.

Balbharti Maharashtra State Board Class 9 Maths Solutions covers the Practice Set 4.5 Algebra 9th Class Maths Part 1 Answers Solutions Chapter 4 Ratio and Proportion.

Practice Set 4.5 Algebra 9th Std Maths Part 1 Answers Chapter 4 Ratio and Proportion

Question 1.
Which number should be subtracted from 12, 16 and 21 so that resultant numbers are in continued proportion?
Solution:
Let the number to be subtracted be x.
∴ (12 – x), (16 – x) and (21 – x) are in continued proportion.

∴ 84 – 4x = 80 – 5x
∴ 5x – 4x = 80 – 84
∴ x = -4
∴ -4 should be subtracted from 12,16 and 21 so that the resultant numbers in continued proportion.

Question 2.
If (28 – x) is the mean proportional of (23 – x) and (19 – x), then find the value ofx.
Solution:
(28 – x) is the mean proportional of (23 – x) and (19-x). …[Given]

∴ -5(19 – x) = 9(28 – x)
∴ -95 + 5x = 252 – 9x
∴ 5x + 9x = 252 + 95
∴ 14x = 347
∴ x = \(\frac { 347 }{ 14 }\)

Question 3.
Three numbers are in continued proportion, whose mean proportional is 12 and the sum of the remaining two numbers is 26, then find these numbers.
Solution:
Let the first number be x.
∴ Third number = 26 – x
12 is the mean proportional of x and (26 – x).
∴ \(\frac { x }{ 12 }\) = \(\frac { 12 }{ 26 – x }\)
∴ x(26 – x) = 12 x 12
∴ 26x – x² = 144
∴ x² – 26x + 144 = 0
∴ x² – 18x – 8x + 144 = 0
∴ x(x – 18) – 8(x – 18) = 0
∴ (x – 18) (x – 8) = 0
∴ x = 18 or x = 8
∴ Third number = 26 – x = 26 – 18 = 8 or 26 – x = 26 – 8 = 18
∴ The numbers are 18, 12, 8 or 8, 12, 18.

Question 4.
If (a + b + c)(a – b + c) = a² + b² + c², show that a, b, c are in continued proportion.
Solution:
(a + b + c)(a – b + c) = a² + b² + c² …[Given]
∴ a(a – b + c) + b(a – b + c) + c(a – b + c) = a2 + b2 + c2
∴ a² – ab + ac + ab – b² + be + ac – be + c² = a² + b² + c²
∴ a² + 2ac – b² + c² = a² + b² + c²
∴ 2ac – b² = b²
∴ 2ac = 2b²
∴ ac = b²
∴ b² = ac
∴ a, b, c are in continued proportion.

Question 5.
If \(\frac { a }{ b }\) = \(\frac { b }{ c }\) and a, b, c > 0, then show that,
i. (a + b + c)(b – c) = ab – c²
ii. (a² + b²)(b² + c²) = (ab + be)²
iii. \(\frac{a^{2}+b^{2}}{a b}=\frac{a+c}{b}\)
Solution:
Let \(\frac { a }{ b }\) = \(\frac { b }{ c }\) = k
∴ b = ck
∴ a = bk =(ck)k
∴ a = ck² …(ii)

i. (a + b + c)(b – c) = ab – c²
L.H.S = (a + b + c) (b – c)
= [ck² + ck + c] [ck – c] … [From (i) and (ii)]
= c(k² + k + 1) c (k – 1)
= c² (k² + k + 1) (k – 1)
R.H.S = ab – c²
= (ck²) (ck) – c² … [From (i) and (ii)]
= c²k³ – c²
= c²(k³ – 1)
= c² (k – 1) (k² + k + 1) … [a³ – b³ = (a – b) (a² + ab + b²]
∴ L.H.S = R.H.S
∴ (a + b + c) (b – c) = ab – c²

ii. (a² + b²)(b² + c²) = (ab + bc)²
b = ck; a = ck²
L.H.S = (a² + b²) (b² + c²)
= [(ck²) + (ck)²] [(ck)² + c²] … [From (i) and (ii)]
= [c²k⁴ + c²k²] [c²k² + c²]
= c²k² (k² + 1) c² (k² + 1)
= c4k² (k² + 1)²
R.H.S = (ab + bc)²
= [(ck²) (ck) + (ck)c]² …[From (i) and (ii)]
= [c²k³ + c²k]²
= [c²k (k² + 1)]2 = c⁴(k² + 1)²
∴ L.H.S = R.H.S
∴ (a² + b²) (b² + c²) = (ab + bc)²

iii. \(\frac{a^{2}+b^{2}}{a b}=\frac{a+c}{b}\)

9th Standard Algebra Practice Set 4.5 Question 6. Find mean proportional of \(\frac{x+y}{x-y}, \frac{x^{2}-y^{2}}{x^{2} y^{2}}\).
Solution:
Let a be the mean proportional of \(\frac{x+y}{x-y}\) and \(\frac{x^{2}-y^{2}}{x^{2} y^{2}}\)

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Miscellaneous Problems Set 1 Answers Solutions.

Maharashtra Board Miscellaneous Problems Set 1 Class 7 Maths Solutions

Question 1.
Solve the following:
i. (-16) × (-5)
ii. (72) ÷ (-12)
iii. (-24) × (2)
iv. 125 ÷ 5
v. (-104) ÷ (-13)
vi. 25 × (-4)
Solution:
i. (-16) × (-5) = 80

ii. 72 ÷ (-12) = \(\frac { 72 }{ -12 }\)
= \(\frac{1}{(-1)} \times \frac{72}{12}\)
(-1) × 12
= -6

iii. (-24) × 2 = -48

iv. 125 ÷ 5 = \(\frac { 125 }{ 5 }\)
= 25

v. (-104) ÷ (-13) = \(\frac { -104 }{ -13 }\)
= \(\frac { 104 }{ 13 }\)
= 8

vi. 25 × (-4) = -100

Question 2.
Find the prime factors of the following numbers and find their LCM and HCF:
i. 75,135
ii. 114,76
iii. 153,187
iv. 32,24,48
Solution:
i. 75 = 3 × 25
= 3 × 5 × 5
135 = 3 × 45
= 3 × 3 × 15
= 3 × 3 × 3 × 5
∴ HCF of 75 and 135 = 3 × 5
= 15
LCM of 75 and 135 = 3 × 5 × 5 × 3 × 3
= 675

ii. 114 = 2 × 57
= 2 × 3 × 19
76 = 2 × 38
= 2 × 2 × 19
∴ HCF of 114 and 76 = 2 × 19
= 38
LCM of 114 and 76 = 2 × 19 × 3 × 2
= 228

iii. 153 = 3 × 51
= 3 × 3 × 17
187 = 11 × 17
∴ HCF of 153 and 187 = 17
LCM of 153 and 187 = 17 × 3 × 3 × 11
= 1683

iv. 32 = 2 × 16
= 2 × 2 × 8
= 2 × 2 × 2 × 4
= 2 × 2 × 2 × 2 × 2
24 = 2 × 12
= 2 × 2 × 6
= 2 × 2 × 2 × 3
48 = 2 × 24
= 2 × 2 × 12
= 2 × 2 × 2 × 6
= 2 × 2 × 2 × 2 × 3
∴ HCF of 32, 24 and 48 = 2 × 2 × 2
= 8
LCM of 32,24 and 48 = 2 × 2 × 2 × 2 × 2 × 3
= 96

Question 3.
Simplify:
i. \(\frac { 322 }{ 391 }\)
ii. \(\frac { 247 }{ 209 }\)
iii. \(\frac { 117 }{ 156 }\)
Solution:
i. \(\frac { 322 }{ 391 }\)

ii. \(\frac { 247 }{ 209 }\)

iii. \(\frac { 117 }{ 156 }\)

Question 4.
i. 784
ii. 225
iii. 1296
iv. 2025
v. 256
Solution:
i. 784

∴ 784 = 2 × 2 × 2 × 2 × 7 × 7
∴ √784 = 2 × 2 × 7
= 28

ii. 225

∴ 225 = 3 × 3 × 5 × 5
∴ √225 = 3 × 5
= 15

iii. 1296

∴ 1296 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
∴ √1296 = 2 × 2 × 3 × 3
= 36

iv. 2025

∴ 2025 = 3 × 3 × 3 × 3 × 5 × 5
∴ √2025 = 3 × 3 × 5
= 45

v. 256

∴ 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2
∴ √256 = 2 × 2 × 2 × 2
= 16

Question 5.
There are four polling booths for a certain election. The numbers of men and women who cast their vote at each booth is given in the table below. Draw a joint bar graph for this data.

Polling Booths	Navodaya Vidyalaya	Vidyaniketan School	City High School	Eklavya School
Women	500	520	680	800
Men	440	640	760	600

Solution:

Question 6.
Simplify the expressions:
i. 45 ÷ 5 + 120 × 4 – 12
ii. (38 – 8) × 2 ÷ 5 + 13
iii. \(\frac{5}{3}+\frac{4}{7} \div \frac{32}{21}\)
iv. 3 × {4 [85 + 5 – (15 – 3)] + 2}
Solution:
i. 45 ÷ 5 + 120 × 4 – 12
= 9 + 80 – 12
= 89 – 12
= 77

ii. (38 – 8) × 2 ÷ 5 + 13
= 30 × 2 ÷ 5 + 13
= 60 ÷ 5 + 13
= 12 + 13
= 25

iii. \(\frac{5}{3}+\frac{4}{7} \div \frac{32}{21}\)
\(\frac{5}{3}+\frac{4}{7} \times \frac{21}{32}\)
\(\frac{5}{3}+\frac{3}{8}=\frac{40}{24}+\frac{9}{24}\)
\(\frac{49}{24}\)

iv. 3 × {4 [85 + 5 – (15 – 3)] + 2}
= 3 × {4[90 – 5] + 2}
= 3 × {4 × 85 + 2}
= 3 × (340 + 2)
= 3 × 342
= 1026

Question 7.
Solve:
i. \(\frac{5}{12}+\frac{7}{16}\)
ii. \(3 \frac{2}{5}-2 \frac{1}{4}\)
iii. \(\frac{12}{5} \times \frac{(-10)}{3}\)
iv. \(4 \frac{3}{8} \div \frac{25}{18}\)
Solution:
i. \(\frac{5}{12}+\frac{7}{16}\)

ii. \(3 \frac{2}{5}-2 \frac{1}{4}\)

iii. \(\frac{12}{5} \times \frac{(-10)}{3}\)
= 4 × (-2)
= -8

iv. \(4 \frac{3}{8} \div \frac{25}{18}\)
= \(\frac{7}{4} \times \frac{9}{5}\)
= \(\frac { 63 }{ 20 }\)

Question 8.
Construct ∆ABC such that m∠A = 55°, m∠B = and l(AB) = 5.9 cm.
Solution:

Question 9.
Construct ∆XYZ such that, l(XY) = 3.7 cm, l(YZ) = 7.7 cm, l(XZ) = 6.3 cm.
Solution:

Question 10.
Construct ∆PQR such that, m∠P = 80°, m∠Q = 70°, l(QR) = 5.7 cm.
Ans:
In ∆PQR,
m∠P + m∠Q + m∠R = 180° …. (Sum of the measures of the angles of a triangle is 180°)
∴ 80 + 70 + m∠R = 180
∴ 150 + m∠R = 180
∴ m∠R = 180 – 150
∴ m∠R = 30°

Question 11.
Construct ∆EFG from the given measures. l(FG) = 5 cm, m∠EFG = 90°, l(EG) = 7 cm.
Solution:

Question 12.
In ∆LMN, l(LM) = 6.2 cm, m∠LMN = 60°, l(MN) 4 cm. Construct ∆LMN.
Solution:

Question 13.
Find the measures of the complementary angles of the following angles:
i. 35°
ii. a°
iii. 22°
iv. (40 – x)°
Solution:
i. Let the measure of the complementary
angle be x°.
35 + x = 90
∴35 + x-35 = 90 – 35
….(Subtracting 35 from both sides)
∴x = 55
∴The complementary angle of 35° is 55°.

ii. Let the measure of the complementary angle be x°.
a + x = 90
∴a + x – a = 90 – a
….(Subtracting a from both sides)
∴x = (90 – a)
∴The complementary angle of a° is (90 – a)°.

iii. Let the measure of the complementary angle be x°.
22 + x = 90
∴22 + x – 22 = 90 – 22
….(Subtracting 22 from both sides)
∴x = 68
∴The complementary angle of 22° is 68°.

iv. Let the measure of the complementary angle be a°.
40 – x + a = 90
∴40 – x + a – 40 + x = 90 – 40 + x
….(Subtracting 40 and adding x on both sides)
∴a = (50 + x)
∴The complementary angle of (40 – x)° is (50 + x)°.

Question 14.
Find the measures of the supplements of the following angles:
i. 111°
ii. 47°
iii. 180°
iv. (90 – x)°
Solution:
i. Let the measure of the supplementary
angle be x°.
111 + x = 180
∴ 111 + x – 111 = 180 – 111
…..(Subtracting 111 from both sides)
∴ x = 69
∴ The supplementary angle of 111° is 69°.

ii. Let the measure of the supplementary angle be x°.
47 + x = 180
∴47 + x – 47 = 180 – 47
….(Subtracting 47 from both sides)
∴x = 133
∴The supplementary angle of 47° is 133°.

iii. Let the measure of the supplementary angle be x°.
180 + x = 180
∴180 + x – 180 = 180 – 180
….(Subtracting 180 from both sides)
∴x = 0
∴The supplementary angle of 180° is 0°.

iv. Let the measure of the supplementary angle be a°.
90 – x + a = 180
∴90 – x + a – 90 + x = 180 – 90+ x
….(Subtracting 90 and adding x on both sides)
∴a = 180 – 90 + x
∴a = (90 + x)
∴The supplementary angle of (90 – x)° is (90 + x)°.

Question 15.
Construct the following figures:
i. A pair of adjacent angles
ii. Two supplementary angles which are not adjacent angles.
iii. A pair of adjacent complementary angles.
Solution:
i.

ii.

iii.

Question 16.
In ∆PQR the measures of ∠P and ∠Q are equal and m∠PRQ = 70°, Find the measures of the following angles.

1. m∠PRT
2. m∠P
3. m∠Q

Solution:
Here, ∠PRQ and ∠PRT are angles in a linear pair.
m∠PRQ + m∠PRT = 180°
∴70 + m∠PRT = 180
∴m∠PRT = 180 – 70
∴m∠PRT = 110°
Now, ∠PRT is the exterior angle of ∆PQR.
∴m∠P + m∠Q = m∠PRT
∴m∠P + m∠P = m∠PRT ….(The measures of ∠P and ∠Q is same)
∴2m∠P = 110
∴m∠P = \(\frac { 110 }{ 2 }\)
∴m∠P = 55°
∴m∠Q =

Question 17.
Simplify
i. 5⁴ × 5³
ii. \(\left(\frac{2}{3}\right)^{6} \div\left(\frac{2}{3}\right)^{9}\)
iii. \(\left(\frac{7}{2}\right)^{8} \times\left(\frac{7}{2}\right)^{-6}\)
iv. \(\left(\frac{4}{5}\right)^{2} \div\left(\frac{5}{4}\right)\)
Solution:
Simplify
i. 5⁴ × 5³
= 5⁴⁺³
= 5⁷

ii. \(\left(\frac{2}{3}\right)^{6} \div\left(\frac{2}{3}\right)^{9}\)

iii. \(\left(\frac{7}{2}\right)^{8} \times\left(\frac{7}{2}\right)^{-6}\)

iv. \(\left(\frac{4}{5}\right)^{2} \div\left(\frac{5}{4}\right)\)

Question 18.
Find the value:
i. 17¹⁶  ÷ 17¹⁶
ii. 10^-3
iii. (2³)²
iv. 4⁶ × 4^-4
Solution:
i. 17¹⁶  ÷ 17¹⁶
= 17⁰
= 1

ii. 10^-3
= \(\frac{1}{10^{3}}\)
= \(\frac{1}{1000}\)

iii. (2³)²
= 2^3×2
= 2⁶
= 2 × 2 × 2 × 2 × 2 × 2
= 64

iv. 4⁶ × 4^-4
= 4^6+(-4)
= 4²
= 4 × 4
= 16

Question 19.
Solve:
i. (6a – 5b – 8c) + (15b + 2a – 5c)
ii. (3x + 2y) (7x – 8y)
iii. (7m – 5n) – (-4n – 11m)
iv. (11m – 12n + 3p) – (9m + 7n – 8p)
Solution:
i. (6a – 5b – 8c) + (15b + 2a – 5c)
= (6a + 2a) + (-5b + 15b) + (-8c – 5c)
= 8a + 10b – 13c

ii. (3x + 2y) (7x – 8y)
= 3x × (7x – 8y) + 2yx (7x – 8y)
= 21x² – 24xy + 14xy – 16y²
= 21x² – 10xy – 16y²

iii. (7m – 5n) – (-4n – 11m)
= 7m – 5n + 4n + 11m
= (7m + 11m) + (-5n + 4n)
= 18m – n

iv. (11m – 12n + 3p) – (9m + 7n – 8p)
= 11m – 12n + 3p – 9m – 7n + 8p
= (11m – 9m) + (-12n – 7n) + (3p + 8p)
= 2m – 19n + 11p

Question 20.
Solve the following equations:
i 4(x + 12) = 8
ii. 3y + 4 = 5y – 6
Solution:
i. 4(x + 12) = 8
∴4x + 48 = 8
∴4x + 48 – 48 = 8 – 48
….(Subtracting 48 from both sides)
∴ 4x = -40
∴ x = \(\frac { -40 }{ 4 }\)
∴ x = -10

ii. 3y + 4 = 5y – 6
∴ 3y + 4 + 6 = 5y – 6 + 6
….(Adding 6 on both sides)
∴ 3y + 10 = 5y
∴ 3y + 10 – 3y = 5y – 3y
….(Subtracting 3y from both sides)
∴ 10 = 2y
∴ 2y = 10
∴ y = \(\frac { 10 }{ 2 }\)
∴ y = 5

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Miscellaneous Problems Set 2 Answers Solutions.

Maharashtra Board Miscellaneous Problems Set 2 Class 7 Maths Solutions

Question 1.
Angela deposited Rs 15000 in a bank at a rate of 9 p.c.p.a. She got simple interest amounting to Rs 5400. For how many years had she deposited the amount?
Solution:
Here, P = Rs 15000, R = 9 p.c.p.a., I = Rs 5400

∴ T = 4
∴ Angela had deposited the amount for 4 years.

Question 2.
Ten men take 4 days to complete the task of tarring a road. How many days would 8 men take?
Solution:
Let us suppose that 8 men require x days to tar the road.
Number of days required by 10 men to tar the road = 4
The number of men and the number of days required to tar the road are in inverse proportion.
∴ 8 × x = 10 x 4
∴ \(x=\frac{10 \times 4}{8}\)
∴ x = 5
∴ 8 men will require 5 days to tar the road.

Question 3.
Nasruddin and Mahesh invested Rs 40,000 and Rs 60,000 respectively to start a business. They made a profit of 30%. How much profit did each of them make?
Solution:
Total amount invested = Rs 40,000 + Rs 60,000
= Rs 1,00,000
Profit earned = 30%
∴ Total profit = 30% of 1,00,000
= \(\frac { 30 }{ 100 }\) × 100000
= Rs 30000
Proportion of investment = 40000 : 60000
= 2:3 …. (Dividing by 20000)
Let Nasruddin’s profit be Rs 2x and Mahesh’s profit be Rs 3x.
∴ 2x + 3x = 30000
∴ 5x = 30000
∴ x = \(\frac { 30000 }{ 5 }\).
∴ x = 6000
∴ Nasruddin’s profit = 2x = 2 × 6000 = Rs 12000
Mahesh’s profit = 3x = 3 × 6000 = Rs 18000
∴ The profits of Nasruddin and Mahesh are Rs 12000 and Rs 18000 respectively.

Question 4.
The diameter of a circle is 5.6 cm. Find its circumference.
Solution:
Diameter of the circle (d) = 5.6 cm
Circumference = πd
= \(\frac{22}{7} \times 5.6\)
= \(\frac{22}{7} \times \frac{56}{10}\)
= 17.6 cm
∴ The circumference of the circle is 17.6 cm.

Question 5.
Expand:
i. (2a – 3b)²
ii. (10 + y)²
iii. \(\left(\frac{p}{3}+\frac{q}{4}\right)^{2}\)
iv. \(\left(y-\frac{3}{y}\right)^{2}\)
Solution:
i. Here, A = 2a and B = 3b
∴ (2a – 3b)² = (2a)² – 2 × 2a × 3b + (3b)²
…. [(A – B)² = A² – 2AB + B²]
= 4a² – 12ab + 9b²

ii. Here, a = 10 and b = y
(10 + y)² = 102 + 2 × 10xy + y²
…. [(a + b)² = a² + 2ab + b²]
= 100 + 20y + y²

iii. Here, a = \(\frac { p }{ 3 }\) and b = \(\frac { q }{ 4 }\)
\(\left(\frac{p}{3}+\frac{q}{4}\right)^{2}=\left(\frac{p}{3}\right)^{2}+2 \times \frac{p}{3} \times \frac{q}{4}+\left(\frac{q}{4}\right)^{2}\)
…. [(a + b)² = a² + 2ab + b²]
\(\frac{p^{2}}{9}+\frac{p q}{6}+\frac{q^{2}}{16}\)

iv. Here, a = y and b = \(\frac { 3 }{ y }\)
\(\left(y-\frac{3}{y}\right)^{2}=y^{2}-2 \times y \times \frac{3}{y}+\left(\frac{3}{y}\right)^{2}\)
…. [(a – b)² = a² – 2ab + b²
= \(y^{2}-6+\frac{9}{y^{2}}\)

Question 6.
Use a formula to multiply:
i. (x – 5)(x + 5)
ii. (2a – 13)(2a + 13)
iii. (4z – 5y)(4z + 5y)
iv. (2t – 5)(2t + 5)
Solution:
i. Here, a = x and b = 5
(x – 5)(x + 5) = (x)² – (5)²
…. [(a + b)(a – b) = a² – b²]
= x² – 25

ii. Here, A = 2a and B = 13
(2a – 13)(2a + 13) = (2a)² – (13)²
…. [(A + B)(A – B) = A² – B²]
= 4a² – 169

iii. Here, a = 4z and b = 5y
(4z – 5y)(4z + 5y) = (4z)² – (5y)²
…. [(a + b)(a – b) = a² – b²]
= 16z² – 25y²

iv. Here, a = 2t and b = 5
(2t – 5)(2t + 5) = (2t)² – (5)²
…. [(a + b)(a – b) = a² – b²]
= 4t² – 25

Question 7.
The diameter of the wheel of a cart is 1.05 m. How much distance will the cart cover in 1000 rotations of the wheel?
Solution:
Diameter of the wheel (d) = 1.05 m
∴ Distance covered in 1 rotation of wheel = Circumference of the wheel
= πd
= \(\frac{22}{7} \times 1.05\)
= 3.3 m
∴ Distance covered in 1000 rotations = 1000 x 3.3 m
= 3300 m
= \(\frac { 3300 }{ 1000 }\) km …[1m = \(\frac { 1 }{ 1000 }\)km]
= 3.3 km
∴ The distance covered by the cart in 1000 rotations of the wheel is 3.3 km.

Question 8.
The area of a rectangular garden of length 40 m, is 1000 sq m. Find the breadth of the garden and its perimeter. The garden is to be enclosed by 3 rounds of fencing, leaving an entrance of 4 m. Find the cost of fencing the garden at a rate of Rs 250 per metre.
Solution:
Length of the rectangular garden = 40 m
Area of the rectangular garden = 1000 sq. m.
∴ length × breadth = 1000
∴ 40 × breadth = 1000
∴ breadth = \(\frac { 1000 }{ 40 }\)
= 25 m
Now, perimeter of the rectangular garden = 2 × (length + breadth)
= 2 (40 + 25)
= 2 × 65
= 130 m
Length of one round of fence = circumference of garden – width of the entrance
= 130 – 4
= 126 m
∴ Total length of fencing = length of one round of wire × number of rounds = 126 × 3
= 378 m
∴ Total cost of fencing = Total length of fencing × cost per metre of fencing
= 378 × 250
= 94500
∴ The cost of fencing the garden is Rs 94500.

Question 9.
From the given figure, find the length of hypotenuse AC and the perimeter of ∆ABC.
Solution:

In ∆ABC, ∠B = 90°, and l(BC) = 21, and l(AB) = 20
∴ According to Pythagoras’ theorem,
∴ l(AC)² = l(BC)² + l(AB)²
∴ l(AC)² = 21² + 20²
∴ l(AC)² = 441 + 400
∴ l(AC)² = 841
∴ l(AC)² = 29²
∴ l(AC) = 29
Perimeter of ∆ABC = l(AB) + l(BC) + l(AC)
= 20 + 21 + 29
= 70
∴ The length of hypotenuse AC is 29 units, and the perimeter of ∆ABC is 70 units.

Question 10.
If the edge of a cube is 8 cm long, find its total surface area.
Solution: ,
Total surface area of the cube = 6 × (side)²
= 6 × (8)²
= 6 × 64
= 384 sq. cm
The total surface area of the cube is 384 sq.cm.

Question 11.
Factorize: 365y⁴z³ – 146y²z⁴
Solution:
= 365y⁴z³ – 146y²z⁴
= 73 (5y⁴z³ – 2y²z⁴)
= 73y² (5y²z³ – 2z⁴)
= 73y²z³(5y² – 2z)

Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 5.4 8th Std Maths Answers Solutions Chapter 5 Expansion Formulae.

Practice Set 5.4 8th Std Maths Answers Chapter 5 Expansion Formulae

Question 1.
Expand:
i. (2p + q + 5)²
ii. (m + 2n + 3r)²
iii. (3x + 4y – 5p)²
iv. (7m – 3n – 4k)²
Solution:
i. (2p + q + 5)² = (2p)² + (q)² + (5)² + 2(2p) (q) + 2(q) (5) + 2(2p) (5)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 4p² + q² + 25 + 4pq + 10q + 20p

ii. (m + 2n + 3r)² = (m)² + (2n)² + (3r)² + 2(m) (2n) + 2(2n) (3r) + 2(m) (3r)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= m² + 4n² + 9r² + 4mn + 12nr + 6mr

iii. (3x + 4y – 5p)² = (3x)² + (4y)² + (- 5p)² + 2(3x) (4y) + 2(4y) (- 5p) + 2(3x) (- 5p)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 9x + 16y² + 25p² + 24xy – 40py – 30px

iv. (7m – 3n – 4k)² = (7m)² + (- 3n)² + (- 4k)² + 2(7m) (- 3n) + 2 (- 3n) (- 4k) + 2 (7m) (- 4k)
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 49m² + 9n² + 16k² – 42mn + 24nk – 56km

Question 2.
Simplify:
i. (x – 2y + 3)² + (x + 2y – 3)²
ii. (3k – 4r – 2m)² – (3k + 4r – 2m)²
iii. (7a – 6b + 5c)² + (7a + 6b – 5c)²
Solution:
i. (x – 2y + 3)² + (x + 2y – 3)²
= [(x)² + (- 2y)² + (3)² + 2 (x) (- 2y) + 2 (- 2y) (3) + 2 (x) (3)] + [(x)² + (2y)² + (- 3)² + 2 (x) (2y) + 2 (2y) (- 3) + 2 (x) (- 3)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= x² + 4y² + 9 – 4xy – 12y + 6x + x² + 4y² + 9 + 4xy – 12y – 6x
= x + x² + 4y² + 4y² + 9 + 9 – 4xy + 4xy – 12y – 12y + 6x – 6x
= 2x² + 8y² + 18 – 24y

ii. (3k – 4r – 2m)² – (3k + 4r – 2m)²
= [(3k)² + (- 4r)² + (- 2m)² + 2 (3k) (- 4r) + 2 (- 4r) (- 2m) + 2 (3k) (- 2m)] – [(3k)² + (4r)² + (- 2m)² + 2 (3k) (4r) + 2 (4r) (- 2m) + 2 (3k) (- 2m)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= (9k² + 16r² + 4m² – 24kr + 16rm – 12km) – (9k² + 16r² + 4m² + 24kr – 16rm – 12km)
= 9k² + 16r² + 4m² – 24kr + 16rm – 12km – 9k² – 16r² – 4m² – 24kr + 16rm + 12km
= 9k² – 9k² + 16r² – 16r² + 4m² – 4m² – 24kr – 24kr + 16rm + 16rm – 12km + 12km
= 32rm – 48kr

iii. (7a – 6b + 5c)² + (7a + 6b – 5c)²
= [(7a)² + (- 6b)² + (5c)² + 2(7a) (-6b) + 2(-6b) (5c) + 2(7a) (5c)] + [(7a)² + (6b)² + (- 5c)² + 2 (7a) (6b) + 2 (6b) (- 5c) + 2 (7a) (- 5c)]
… [(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac]
= 49a² + 36b² + 25c² – 84ab – 60bc + 70ac + 49a² + 36b² + 25c² + 84ab – 60bc – 70ac
= 49a² + 49a² + 36b² + 36b² + 25c² + 25c² – 84ab + 84ab – 60bc – 60bc + 70ac – 70ac
= 98a² + 72b² + 50c² – 120bc

Maharashtra Board Class 8 Maths Chapter 5 Expansion Formulae Practice Set 5.4 Intext Questions and Activities

Question 1.
Fill in the boxes with appropriate terms in the steps of expansion. (Textbook pg. no. 27)
(2p + 3m + 4n)²
= (2p)² + (3m)² + __ + 2 × 2p × 3m + 2 × __ × 4n + 2 × 2p × __
= __ + 9m² + __ + 12pm + __ + __
Solution:
(2p + 3m + 4n)²
= (2p)² + (3m)² + (4n)² + 2 x 2p x 3m + 2 x 3m x 4n + 2 x 2p x 4n
= 4p² + 9m² + 16n² + 12pm + 24mn + 16pn

Balbharti Maharashtra State Board Class 7 Maths Solutions covers the 7th Std Maths Practice Set 12 Answers Solutions Chapter 3 HCF and LCM.

HCF and LCM Class 7 Practice Set 12 Answers Solutions Chapter 3

Question 1.
i. 25, 40
ii. 56, 32
iii. 40, 60, 75
iv. 16, 27
v. 18, 32,48
vi. 105, 154
vii. 42, 45, 48
viii. 57, 75, 102
ix. 56, 57
x. 777, 315, 588
Solution:
i. 25, 40

∴ 25 = 5 × 5
40 = 2 × 2 × 2 × 5
∴ HCF of 25 and 40 = 5

ii. 56, 32

∴ 56 = 2 × 2 × 2 × 7
32 = 2 × 2 × 2 × 2 × 2
∴ HCF of 56 and 32 = 2 × 2 × 2
∴ HCF of 56 and 32 = 8

iii. 40, 60, 75

∴ 40 = 2 × 2 × 2 × 5
60 = 2 × 2 × 3 × 5
75 = 3 × 5 × 5
∴ HCF of 40, 60 and 75 = 5

iv. 16, 27

∴ 16 = 2 × 2 × 2 × 2 × 1
27 = 3 × 3 × 3 × 1
∴ HCF of 16 and 27 = 1

v. 18, 32,48

∴ 18 = 2 × 3 × 3
32 = 2 × 2 × 2 × 2 × 2
48 = 2 × 2 × 2 × 2 × 3
∴ HCF of 18, 32 and 48 = 2

vi. 105, 154

∴ 105 = 3 × 5 × 7
154 = 2 × 2 × 11
∴ HCF of 105 and 154 = 7

vii. 42, 45, 48

∴ 42 = 2 × 3 × 7
45 = 3 × 3 × 5
48 = 2 × 2 × 2 × 2 × 3
∴ HCF of 42,45 and 48 =3

viii. 57, 75, 102

∴ 57 = 3 × 19
75 = 3 × 5 × 5
102 = 2 × 3 × 17
∴ HCF of 57, 75 and 102 = 3

ix. 56, 57

∴ 56 = 2 × 2 × 2 × 7 × 1
57 = 3 × 19 × 1
∴ HCF of 56 and 57 = 1

x. 777, 315, 588

∴ 777 = 3 × 7 × 37
315 = 3 × 3 × 5 × 7
588 = 2 × 2 × 3 × 7 × 7
∴ HCF of 777, 315 and 588 = 3 × 7
HCF of 777, 315 and 588 = 21

Question 2.
Find the HCF by the division method and reduce to the simplest form:
i. \(\frac { 275 }{ 525 }\)
ii. \(\frac { 76 }{ 133 }\)
iii. \(\frac { 161 }{ 69 }\)
Solution:
i. \(\frac { 275 }{ 525 }\)

ii. \(\frac { 76 }{ 133 }\)

iii. \(\frac { 161 }{ 69 }\)

Maharashtra Board Class 7 Maths Chapter 3 HCF and LCM Practice Set 12 Intext Questions and Activities

Question 1.
In each of the following examples, write all the factors of the numbers and find the greatest common divisor. (Textbook pg. no. 17)
i. 28, 42
ii. 51, 27
iii. 25, 15, 35
Solution:
i. Factors of 28 = 1,2,4, 7, 14, 28
Factors of 42 = 1,2, 3, 6, 7, 14, 21, 42
∴ HCF of 28 and 42 = 14

ii. Factors of 51 = 1, 3, 17, 51
Factors of 27 = 1, 3, 9, 27
∴ HCF of 51 and 27 = 3

iii. Factors of 25 = 1, 5, 25
Factors of 15 = 1, 3, 5, 15
Factors of 35 = 1, 5, 7, 35
∴ HCF of 25, 15 and 35 = 5

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 16 Quadrilaterals Class 6 Practice Set 37 Answers Solutions.

6th Standard Maths Practice Set 37 Answers Chapter 16 Quadrilaterals

Question 1.
Observe the figures below and find out their names:

Solution:
i. Pentagon (5 sides)
ii. Hexagon (6 sides)
iii. Heptagon (7 sides)
iv. Octagon (8 sides)

Maharashtra Board Class 6 Maths Chapter 16 Quadrilaterals Practice Set 37 Intext Questions and Activities

Question 1.
Observe the figures given below and say which of them are quadrilaterals. (Textbook pg. no. 81)

Solution:
Is a quadrilateral: (i)

Question 2.
Draw a quadrilateral. Draw one diagonal of this quadrilateral and divided it into two triangles. Measures all the angles in the figure. Is the sum of the measures of the four angles of the quadrilateral equal to the sum of the measures of the six angles of the two triangles? Verity that this is so with other quadrilaterals. (Textbook pg. no. 84)
Solution:

m∠PQR = 104°
m∠QRP = 26°
m∠RPQ = 50°
m∠PRS = 34°
m∠RSP = 106°
m∠SPR = 40°
∴ Sum of the measures of the angles of quadrilateral = m∠PQR + m∠QRP + m∠RPQ + m∠PRS + m∠RSP + m∠SPR
= 104° + 26° + 50° + 34° + 106° + 40°
= 360°
Also, we observe that
Sum of the measures of the angles of quadrilateral = Sum of the measures of angles of the two triangles (PQR and PRS)
= (104°+ 26°+ 50°)+ (34° + 106° + 40°)
= 180° + 180°
= 360°
[Note: Students should drew different quadrilaterals and verify the property.]

Question 3.
For the pentagon shown in the figure below, answer the following: (Textbook pg. no. 84)

1. Write the names of the five vertices of the pentagon.
2. Name the sides of the pentagon.
3. Name the angles of the pentagon.
4. See if you can sometimes find players on a field forming a pentagon.

Solution:

1. The vertices of the pentagon are points A, B, C, D and E.
2. The sides of the pentagon are segments AB, BC, CD, DE and EA.
3. The angles of the pentagon are ∠ABC, ∠BCD, ∠CDE, ∠DEA and ∠EAB.
4. The players shown in the above figure form a pentagon. The players are standing on the vertices of

Question 4.
Cut out a paper in the shape of a quadrilateral. Make folds in it that join the vertices of opposite angles. What can these folds be called? (Textbook pg. no. 83)

Solution:
The folds are called diagonals of the quadrilateral.

Question 5.
Take two triangular pieces of paper such that . one side of one triangle is equal to one side of the other. Let us suppose that in ∆ABC and ∆PQR, sides AC and PQ are the equal sides. Join the triangles so that their equal sides lie B side by side. What figure do we get? (Textbook pg. no. 83)

Solution:
If we place the triangles together such that the equal sides overlap, the two triangles form a quadrilateral.

Balbharti Maharashtra State Board Class 6 Maths Solutions covers the Std 6 Maths Chapter 2 Angles Class 6 Practice Set 3 Answers Solutions.

6th Standard Maths Practice Set 3 Answers Chapter 2 Angles

Question 1.
Use the proper geometrical instruments to construct the following angles. Use the compass and the ruler to bisect them:

1. 50°
2. 115°
3. 80°
4. 90°

Solution:

Maharashtra Board Class 6 Maths Chapter 2 Angles Practice Set 3 Intext Questions and Activities

Question 1.
Construct an angle bisector to obtain an angle of 30°. (Textbook pg. no. 11)
Solution: .
In order to get a bisected angle of a given measure, the student has to draw the angle having twice the measurement of required bisected angle.

For getting measurement of 30° (for the bisected angle), one has to make an angle of 60° (i.e. 30° × 2).

Step 1:
Draw ∠ABC of 60°.

Step 2:
Cut arcs on the rays BA and BC. Name these points as D and E respectively.

Step 3:
Place the compass point on point D and draw an arc inside the angle.
Without changing the distance of the compass, place the compass point on point E and cut the previous arc. Name the point of intersection as O

Step 4:
Draw ray BO.
Ray BO is the angle bisector of ∠ABC.
i.e. m∠ABO = m∠CBO = 30°

Question 2.
Construct an angle bisector to draw an angle of 45°. (Textbook pg. no. 11)
Solution:
For getting measurement of 45° (for the bisected angle), one has to make an angle of 90° (i.e. 45° × 2).
Step 1:
Draw ∠PQR of 90°.

Step 2:
Cut arcs on the rays QP and QR.
Name these points as M and N respectively.

Step 3:
Place the compass point on point M and draw an arc inside the angle.
Without changing the distance of the compass, place the compass point on point N and cut the

Step 4:
Draw ray QO.
Ray QO is the angle bisector of ∠PQR.
i.e. m∠PQO = m∠RQO = 45°

Question 3.
Ask three or more children to stand in a straight line. Take two long ropes. Let the child in the middle hold one end of each rope. With the help of the ropes, make the children on either side stand along a straight line. Tell them to move so as to form an acute angle, a right angle, an obtuse angle, a straight angle, a reflex angle and a full or complete angle in turn. Keeping the rope stretched will help to ensure that the children form straight lines. (Textbook pg. no. 6)
Solution:

Question 4.
Look at the pictures below and identify the different types of angles. (Textbook pg. no. 8)

Solution:
i. Complete angle
ii. Reflex and Acute angle
iii. Acute and Obtuse angle