CBSE Class 12 Geography Notes Chapter 22 Geographical Perspective on Selected Issues and Problems is part of Class 12 Geography Notes for Quick Revision. Here we have given NCERT Geography Class 12 Notes Chapter 22 Geographical Perspective on Selected Issues and Problems.

Geography Class 12 Notes Chapter 22 Geographical Perspective on Selected Issues and Problems

Environmental Pollution
Environmental pollution is the release of substances and energy from waste products of human activities. It is of various types. Thus, they are classified on the basis of medium through which pollutants are transported and diffused.
The classification of pollution are as follows:

1. Water pollution
2. Air pollution
3. Noise pollution
4. Land pollution

Water Pollution
Quality of water is majorly degraded by a number of factors i.e. indiscriminate use of water by fast growing population and expansion of industries. No surface water is found in pure form in rivers, canals, lakes, etc as all the water sources contain small quantities of suspended particles, organic and inorganic substances. Water becomes polluted, when quantity of these substances increases in it. It becomes unsuitable for human uses and its self purifying capacity declines.
There are two sources of water pollution:

• Natural Erosion, landslides, decay and decomposition of plants and animals, etc are natural sources that make water polluted.
• Human Industrial, agricultural and cultural activities of human beings make water polluted.
  Water pollution created from human beings are major problem in modern times. Industrial activities of pollution.

Sources of Pollution in the Ganga and the Yamuna Rivers

Most of the industrial wastes, e.g. polluted waste water, poisonous gases, chemical residuals numerous heavy metals, dust, smoke, etc are disposed off in running water, lakes, reservoirs, rivers and other water bodies and thus, destroy the bio-system of these waters. Major culprits are leather, pulp and paper, textiles and chemicals industries.

Today use of various types of chemicals like inorganic fertilizers, pesticides and herbicides are common in agriculture. These chemicals pollute surface water such as rivers, lakes, tanks as well as groundwater by infiltrating into the soil. These fertilizers increase the amount of nitrate content of surface waters. Besides this, cultural activities such as pilgrimage, religious fairs, tourism, etc also cause water pollution. In India, almost all surface water sources are contaminated and unfit for human consumption.

Use of polluted water can harm human health and can cause various water borne diseases, e.g. diarrhoea, intestinal worms, hepatitis, etc. World Health Organisation (WHO) shows that about one-fourth of the communicable diseases in India are water borne.

Air Pollution
A larger proportion of contaminants like dust, fumes, gas, fog, odour, smoke or vapour in air for a long duration is known as air pollution may be harmful to flora and fauna and to property. There is an increase in emission of poisonous gases into the atmosphere because of increasing use of various fuels for energy in various sectors, thus resulting in the pollution of air.
The main sources of air pollution are combustion of fossil fuels, mining and industries which release oxides of sulphur, and nitrogen, hydrocarbons, carbon dioxide, carbon monoxide, lead and asbestos.

Effects of Air Pollution
The effects of air pollution are as follows:

1. Air pollution is responsible for many diseases related to our respiratory, nervous and circulatory systems.
2. Air pollution is responsible for creating smoky fog over cities which is known as urban smog. It has negative effects on human health.
3. Air pollution is also responsible for acid rain. First rain after summer in urban areas always shows high acidic nature of rain water i.e. it shows lower pH level than the subsequent rain.

Noise Pollution
Noise pollution refers to a noise that causes a condition which is unbearable and uncomfortable to human beings. This noise can be from various sources. It is a recent phenomenon which became a serious concern only after a variety of technological innovations. The level of steady noise is measured by sound level expressed in terms of decibels (dB).
Factories, mechanised construction and demolition works, automobiles and aircrafts are major sources of noise that cause noise pollution. Apart from these, there are also some periodic sources of noise pollution such as sirens, loudspeakers in different festivals and programmes and other activities of different communities. Noise produced by traffic is a major source of noise pollution. It creates a huge inconvenience to the people. Intensity and nature of noise made by traffic is dependent on various factors such as type of vehicle (aircraft, train vehicle, etc)/ condition of road and condition of vehicle (in case of automobiles).
In sea traffic, the noise; pollution is limited to the harbour because of loading and unloading activities of containers. Noise pollution from industries is also a serious problem but its intensity varies because of some factors such as type of industry, types of machines and tools, etc.
The intensity of noise pollution decreases as distance from source of pollution (Industrial areas, arteries of transportation, airport, etc) increases. Thus, noise pollution is location specific.

Effects of Noise Pollution
Noise pollution is a major cause of anxiety, tension and some other mental problems and disorders among people in many metropolitan and big cities in India.

Urban Waste Disposal
Overcrowding, congestion, increasing population, improper infrastructure and facilities to support this population, lack of sanitation, foul air, etc are some features of urban areas. Mismanagement of solid wastes and environmental pollution caused by them has now become a major problem.Solid wastes are a variety of old and used articles,for e.g. stained small pieces of metals, broken glass wares, plastic containers, polythene bags,ashes, floppies, CDs, etc dumped at different places.

These discarded materials are also known as refuses, garbage and rubbish,etc and are disposed off from two sources i.e. household or domestic establishments and industrial or commercial establishments. Public lands or private  contractor’s sites are used to disposed off household or domestic wastes. Low lying public grounds (landfill areas) are used to disposed off industrial solid wastes by public (municipal) facilities. Industries, thermal power houses and building constructions and demolitions are contributing with more turn out of ashes and debris in solid wastes.

Disposal of industrial wastes has increased because of the concentration of industrial units in and around urban centres. Urban waste is a bigger problem in small towns and cities than metropolitan cities in the country. About 90% of solid waste is collected and disposed off successfully in Mumbai, Kolkata, Chennai, Bangalore and other metropolitan cities. About 30-50% solid wastes in other towns and cities in country is not collected and disposed off properly. It is a major problem because it accumulates on streets, in open spaces between houses and in wastelands and can cause various health problems.

Impacts of Improper Management of Solid wastes
Improper management of solid wastes has following impacts:

1. Solid wastes are threat to human health and can cause various diseases. It creates foul smell and it harbours flies and rodents that can cause typhoid, diphtheria, diarrhoea, malaria, cholera and other diseases.
2. Solid waste can create inconvenience rapidly if they are not properly handled. Wind and rain water can splitted it and cause a discomfort to people.
3. Industrial solid waste can cause water pollution by dumping it into water bodies. Drains carrying untreated sewage also result into various health problems.
4. Untreated waste release various poisonous biogases such as methane in air by slow fermentation process. These wastes are resources as energy can be generated from them! By compositing these wastes, problem of energy could be solved as well as its management in urban areas.

Rural-Urban Migration
Movement of people from rural area to urban area are caused by various factors such as high demand for labour in urban areas, low job opportunities in rural areas and disparities in terms of development in rural and urban areas. Smaller and medium cities provide low opportunities which force people to bypass these small cities and directly come to the mega cities for their livelihood.

Mostly daily wage workers like, welders; carpenter, etc move to another cities for work, periodically and provide remittances to their families for daily consumption, health care, schooling of children, etc. This has improved their early abject situation into a better one. Simultaneously, due to temporary and transferable job situation, these labourers and their families hear the pain of separation of their near and dear ones.

Sometimes these workers also face difficulty in assimilation to the new culture and environment. Due to these menial jobs at low wages in informal sector in urban areas, the spouses are left behind in
rural areas to look after children and elderly people. Thus, the rural-urban migration stream is dominated by the males.

Trend of Urbanisation in the World
Currently, about 54% of the world’s 7 billion (2011) population lives in urban areas of world . This proportion of urban population will increase in future. It is estimated that between 2025 to 2030, this percentage would be grown with 1.44% per year. This high urban population will pressurise governments to optimise infrastructure facilities in urban areas for giving a standard quality of life.

It is estimated that by 2050, about two-thirds of the world’s population will live in urban areas. It would create a high pressure on existing infrastructure and sanitation, health, crime problems and urban poverty.
There are various factors responsible for growth of urban population:

1. When high birth rate and low morality rate increase.
2. Net in-migration or movement of people from other areas.
3. Reclassification of urban areas to encompass formerly rural settlements.

In India there is a estimation that about 60% India’s urban population has increased after 1961. About 29% of this growth has been caused by rural-urban migration.

Problems of Slums

• Settlement geography differentiate the two concepts namely urban or urban centres and rural. They are also defined differently in different countries.
• These two are differentiated by their functions but sometimes interdependent on each other. These two concepts are also divided in terms of their separate cultural, economic and technological aspects.
• According to 2001 census, about 72% of India’s population is rural (according to 2011, rural population is 68.84%). Most of these rural areas are still in poor conditions and perform primary activities.
• According to Mahatama Gandhi, villages are ideal republics. These work as supplement to the core urban centre forming its hinterland.
• Urban areas are more developed in terms of the socio-economic, politico-cultural, etc than other areas.
• Urban areas have farm house, high income of people and their localities, wide roads, street lights, water and sanitation facilities, lawns, well developed green belts, parks, playgrounds and other facilities, provisions for individual security and right of privacy.
• Apart from these attractions urban areas also have slums, jhuggi jhopari’ clusters and colonies of shanty-structures.
• These are environmentally incompatible and degraded areas of the cities. These are occupied by the migrants who were forced to migrate from rural areas to urban areas for employment and livelihood. But because of high rent and high costs of land, they could not afford proper housing and start to live in these areas.

Characteristics of Slums
Slums have following characteristics:

1. Slums are least choice residential areas that have broken down house, bad hygienic conditions, poor ventilation and does not have basic facilities like drinking water, light and toilet facilities, etc.
2. Slums are overcrowded with people and have many narrow street patterns prone to serious hazards from fire.
3. Most of the slum dwellers works for low wages, high risk-prone and unorganised sectors of the urban economy.
4. They face various health related problems such as malnutrition, illness and prone to various diseases. They are not able to send their children school to provide them education because of low level of income.
5. Dwellers are vulnerable to drug abuse, alcoholism, crime, vandalism, escapism, apathy and social exclusion because of poverty.

Land Degradation
The limited availability and deterioration of quality of land, both are responsible to exert pressure on agricultural land.Soil erosion, water logging, salinisation and alkalinisation of land lead to land degradation which declines productivity of land. In simple words, temporary or permanent decline in productive capacity of the land is known as land degradation. All degraded land may not be considered as wasteland. But if process of degradation is not checked, then a degraded land may be converted into wasteland. Natural and man-made processes, both degrade the quality of land.

Classification of Wastelands

• National Remote Sensing Agency (NRSA) It is an organisation responsible for classification of wastelands in India. It classifies wastelands by using remote sensing techniques on the basis of the processes that have created them.
• Wasteland Caused by Natural Agents Gullied/ ravinous land, desertic or coastal sand, barren rocky areas, steep sloping land, glacial areas, etc are types of wastelands caused by the natural agents. These are considered as wastelands caused by natural agents.
• Wasteland Caused by Natural as well as Human Factors Water logged and marshy areas, land affected by salinity and alkalinity and land with and without scrubs which are degraded by the natural as well as human factors are included in this category.
• Wastelands Caused by Man-made Processes Shifting cultivation area, degraded land under plantation crops, degraded forests, degraded pastures and mining and industrial wastelands are some types of wastelands that are degraded because of human action.

We hope the given CBSE Class 12 Geography Notes Chapter 22 Geographical Perspective on Selected Issues and Problems will help you. If you have any query regarding NCERT Geography Class 12 Notes Chapter 22 Geographical Perspective on Selected Issues and Problems, drop a comment below and we will get back to you at the earliest.

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Environment Class 7 Notes Social Science Geography Chapter 1 SST Pdf free download is part of Class 7 Social Science Notes for Quick Revision. Here we have given Environment Class 7 Geography Chapter 1 Notes.

Environment Class 7 Notes Social Science Geography Chapter 1

Environment
Nature, place, people, things, etc. that surround the living organisms make the environment. The environment can broadly be classified into the natural and human environment. It is a combination of both natural as well as man-made phenomena.

The natural environment comprises biotic (plants and animals) and abiotic-conditions(land, water, air, etc.), whereas the man-made phenomena comprise the activities and interactions among human beings (roads, bridges, etc.).

Natural Environment

• Land, water, air, plants and animals comprise the natural environment.
• Lithosphere, atmosphere, hydrosphere and biosphere are the four domains of the natural environment.
• The lithosphere is the solid crust or the outermost layer of the earth where we live. It contains landforms like mountains, plateaus, plains and valleys.
• The hydrosphere is the domain of water. It comprises water bodies like rivers, lakes, seas, oceans, etc.
• The atmosphere is the thin layer of air that surrounds the earth. It protects us from the harmful rays and scorching heat of the sun.
• The biosphere is a narrow zone of the earth where land, water and air interact with each other to support life.

What is Ecosystem?

• The relation between the living organisms as well as the relation between the organisms and their surrounding form the ecosystem.
• There could be an ecosystem of large rainforest, grassland, desert, mountains, lake, river, ocean and even a small pond.

Human Environment

• Human beings interact with the environment and modify it according to their needs.
• Early humans adapted themselves to their natural surroundings.
• With time, humans learnt to grow new things, domesticate animals and lead a settled life.
• The industrial revolution, transportation and information revolution made communication easier and speedy across the world.
• Man is destroying the environment through deforestation, industrialisation, etc.

The environment in our basic life support system. It provides the air we breathe, the water we drink, the food we eat and the place where we live. Thus, the environment is the most important aspect of our life.

The natural environment consists of land, water, air, plants and animals. It refers to both biotic and abiotic conditions existing on the earth.

While biotic refers to the world of living organisms, such as plants and animals, abiotic refers to the world of non-living elements, such as land.

The human environment refers to the activities, creations and interactions among human beings.

Domains of environment—Lithosphere, hydrosphere, atmosphere and biosphere.

The lithosphere is the solid portion of the earth where we live. It is the domain that provides us forests, grasslands for grazing, land for agriculture and human settlements. It is where we find several minerals.

Hydrosphere refers to the water bodies like rivers, lakes, seas, oceans, etc. that exist on the earth.

The atmosphere is the thin layer of air that surrounds the earth. It protects us from the harmful rays and searching heat of the Sun. It consists of gases, dust and water vapour.

Biosphere or the living world is comprised of plant and animal life. It is a narrow zone of the earth where land, water and air interact with each other to support life.

The relation between the living organisms as well as the relation between the organisms and their surroundings form an ecosystem.

An ecosystem can be found in lakes, mountains, oceans, pond, etc.

Human beings modify the natural environment as per their needs.

Environment: The place, people, things and nature that surround any living organism is called the environment.

Biotic: It refers to the world of living organisms, such as plants and animals.

Abiotic: It refers to the world of non-living elements such as land.

Lithosphere: It is the solid crust or the hard top layer of the earth.

Hydrosphere: It refers to the water bodies like rivers, lakes, seas, oceans, etc. on the earth.

Atmosphere: It is the thin layer of air that surrounds the earth.

Ecosystem: The relation between the living organisms, as well as the relation between the organisms and their surroundings,  form an ecosystem.

Barter system: A trade in which goods are exchanged without the use of money.

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English Workbook Class 10 Solutions Unit 11 Modals-Expressing Attitudes are part of English Workbook Class 10 Solutions. Here we have given CBSE Class 10 English Workbook Solutions Unit 11 Modals-Expressing Attitudes.

CBSE Class 10 English Workbook Solutions Unit 11 Modals-Expressing Attitudes

A. Introduction

A.1. Look at the pictures given below :
See the Workbook on Page 197

Now complete the following dialogues using only one word for each blank on the basis of the pictures given above.

(a) Manav : Suma is playing the violin very well.
Priya : Yes; ________ you play any musical instrument?
Manav : I ________ But I have learnt vocal music.

(b) Peter : It’s suddenly become dark.
Nandiya : Yes ; Thick clouds have gathered in the sky. It ________ rain this evening.

(c) Abdullah : Ma’m, I’m a little late.
______ I enter the class?
Teacher : You ________. I’m afraid late coming has become a habit with you.

(d) Father : Take this. You ________ not forget to wear your helmet while riding your motorbike.
Son : Thanks, Dad. I forgot to pick it up.

Answers:

(a) can, can’t
(b) may
(c) May, may
(d) must

The words that you have used to fill in the blanks denote certain attitudes and functions. Match column (A) with column (B) for the dialogues that you have completed.

The words that you have used are called MODALS. They belong to a large category of auxiliary verbs, ie helping verbs that cannot be used on their own, but to be used in conjunction with other main verbs.
Answer:
You must not forget to wear your helmet while riding your motorbike.
It may rain this evening.
I can.
You may.

A.2.
Given below are some dialogues. Circle the modals and underline the main verbs in the italicised portions of the dialogues :

(a) A: Raju has fractured his arm.
B: But still he can write.

(b) A: I have still some shopping to do. May I leave my bag in your store ?
B: Yes, but please collect it before 8.00 pm.

(c) A: The coffee is rather bitter. Would you please pass some sugar ?
B: No, you must not take any sugar.
Have you forgotten your doctor’s advice ?

(d) A: I’ll not be able to finish my assignment in time.
B: Shall I do the drawings for you ?

(e) A: Jamila hasn’t come yet. It’s already very late.
B: She may come tomorrow.

(f) A: Someone is knocking on the door.
B: I’ll open it- it’ll be the maid.

(g) A: My feet get swollen in the evening.
B: Then you must consult a doctor.

Answers:

A.3.
Match the italicized portions of the dialogues with the attitudes and functions denoted by the modals used in them.


Answers:

A.4.
Here are the modals used in English.
See the Workbook on Page 200

A.5.
Look at the following sentences :

(a) He needn’t come to office tomorrow.
(b) He needed permission to take a day off.

What is the difference in the use of ‘need’ between the above sentences ?

• In sentence (a) ‘need’ is used as a modal verb because there is a hare infinitive after it.
• In sentence (b) ‘need’ is used as a main verb because there is a noun after it.
• Can, could, may, might, shall, should, will and would are called ‘pure’ modals because they

(a) are followed by a main verb in its bare infinitive form (e.g. I must go.)
(b) don’t change in the third person (e.g. He will help and not He wills help.)

• Need and dare are used both as modal verbs and main verbs.

e.g. (1) They needed a lot of money to start a business (main verb).

(2) They need not borrow from the bank to start their business, (modal)
(As a modal, verb ‘need’ is commonly used with ‘not’)

(3) He dare not challenge the authority of his boss, (modal verb)
(As a modal verb dare is also commonly used with ‘not’)

(4) He does not dare to challenge the authority of his boss, (main verb)

A.6.
Complete the following conversation choosing the most appropriate options from those given in the box. There can be more than one option for some of the blanks.

Gautam : I heard that Rahim (1) ________ open a garment shop, though he is a little uncertain.
Sheela : He (2) ________ not plunge into another business proposition ; he (3) ________ forget the colossal failure of his last business venture.
Gautam : You (4) ________ not have any worry on that count. He (5) ________ not be investing any money. His uncle is providing the capital and he said that Rahim (6) ________ be a working partner.
Sheela : In that case, I suppose, he (7) ________ go ahead. I remember how Rahim’s father (8) ________ sit for hours worrying about his son’s future.
Gautam : True. Now that Rahim has learnt his lesson, he (9) ________ be able to live upto the expectations of his father.
Sheela : Whatever you say, Rahim (10) ________ have his own way. he is that way a little obstinate. We (11) ________ only hope that everything turns out well.

Answers:

1. — (a) may
2. — (a) need
3. — (b) shouldn’t
4. — (c) need
5. — (b) will
6. — (b) would
7. — (b) might
8. — (b) would
9. — (a) should
10. — (b) will
11. — (c) can

B. Modals Expressing Possibility

B.1.
Look at the picture. What do you think is happening ? Discuss in small groups. Use the modals given in the box.

could be , might be, must be may be
See the Workbook on Page 203
Answer:

(a) It could be a man balancing himself sitting in the chair at a great height.
(b) It might be a man flying while sitting in his chair.
(c) It must be a magician showing a trick.
(d) It may be a person in his dream.

B.2.
Indira and Mary are discussing their holiday plans. Read the dialogue and fill in the blanks by using suitable modals.

Indira : I’m so thrilled the exams are over.
Let’s go to the North-East this time.
Mary : Yes. I’d love that. Where exactly do you want to go?
Indira : I’d like to go to Cherapunji.
Mary : That’s hardly the place to go to. You see, it ______ raining there, especially at this time of the year. Let’s go to Shillong instead.
Indira : Why Shillong?
IIary : Indira, I’ve lived in that place. You’ll love it and the weather ______ really perfect now.
Indira : Okay, it’s Shillong then. But tell me, do I need to carry woollens?
Mary : Not really. It’s quite pleasant, but the nights ______ chilly, so bring a sweater.
Indira : And what about getting there?
Mary : Well ……… you could fly to Juwahah, and then you can catch a bus to Shillong.
Indira : How far is Shillong?
Mary : It ______ about 80 kilometres. It ______ a three hour drive by taxi.

Answers:
could be, might be, may be, might be, must be, may be

B.3.
‘Can’ and ‘Could’ also denote ability. Rewrite the following sentences as shown in the example using ‘Can’ or ‘Could’.
Example: Parents who are able to support their children should not apply for scholarship.
Parents who can support their children should not apply for scholarship.

(a) After proper investigation the police were able to nail the culprit.
____________________________________________
(b) After the examinations, I shall be able to go home for a week.
____________________________________________
(c) In spite of the sincere efforts of the coach, the team is not able to win a single trophy.
____________________________________________
Did you notice that ‘can’ is used to denote ability in the present and future and ‘could’ is used to denote ability in the past? However, remember that ‘could’ refers to past time only when the context makes the time clear.
Answers:

(a) After proper investigations the police could nail the culprit.
(b) After the examination, I can go home for a week.
(c) In spite of the sincere efforts of the coach, the team can not win a single trophy.

C. Modals – Past, Present & Future

C.1.
Read the following report of a school cricket match and underline all the modals and the verbs accompanying them. Underline the modals red and the verbs green.

Our school cricket team is practicing really hard for the zonal matches. I have no doubt that we will beat the local teams very easily, but when it comes to the outside teams, I am not as confident. Our boys must work very hard. Perhaps they could do some yoga exercises to improve their concentration. They need not worry about their fitness at this stage, but they should follow a strict routine.

Last year they had to struggle to reach the finals. The draw might have been a little unfavourable to them but they shouldn’t have neglected their fielding. This landed them in trouble in the quarter finals. This year our team should try and do better in the field. We lost the finals last year mainly because of floored catches ! A casual approach to this aspect must have been the cause of our failure at the crucial stage. So our team ought to improve its fielding and get its batting to click.
Answer:

C.2.
You will have noticed in C1 that modals are used with a main verb to refer to the past, present or future. In pairs, look at the modals you have underlined and complete the table below. You may have noticed sometimes that the same modal is used to refer to the present as well as the future.

C.3.
Mr Mehta and family decide to drive down to Goa for a holiday. On their way their car develops some problem. Given below is a conversation between the Mehta family members. Read the conversation and complete the conversation using suitable modals from the ones given in the box.

Note: Sometimes there could be more than one correct answer. You may also have to use some of the modals in the box more than once.

must have, will, can’t have, may have, must, may, could, needn’t, can

Mrs Mehta : What is the matter? Why have you stopped?
Mr Mehta : The car is giving some trouble. I have a feeling something is wrong with the engine. Let me check.
Mrs Mehta : Do you think we _____________ run out of petrol?
Mr Mehta : No, we _____________ run out of petrol. I got the tank filled before starting.
Mrs Mehta : If there is a technical fault, do you think you _____________ be able to fix it?
Mr Mehta : Let me first check what is wrong.
Dinu : Dad, look there’s smoke coming out. The engine _____________ become too hot.
Mr Mehta : Dinu, be careful. Don’t take the cap off the radiator. You ___________ not do that. You _____________ get boiling water all over you.
Mrs Mehta : Yes, Dinu, we _____________ have to wait till the engine cools down.
Dinu : And how long do you think it _____________ take for that?
Mr Mehta : I’m not sure. We _____________ have to wait for about fifteen minutes.
Dinu : Dad, I saw a garage about half a mile back. I suppose we _____________ ask them to fix the problem.
Mr Mehta : You _____________ worry. The car _____________ be all right. I got it serviced before starting. I am sure it’s just got too hot. Let’s wait and allow the engine to cool a bit.
Dinu : Mom, I am feeling hungry. _____________ I have something to eat?
Mrs Mehta : There are some sandwiches in the car. You _____________ have them.
Answer:
may have, can’t have, will, must have, must, could, will, may, may, could, needn’t, will, May, can

D. Modals – Referring to the Past

D.1
Respond to the following situations by writing one sentence using might have, must have, should have, could have or ought to have. The first one has been done as an example.

1. Amber was certain that he would be here today, but he hasn’t come yet (miss, flight) Response : He must have missed his flight; nothing else would have held him up.

2.I was asked to be here for a meeting at 10.00 today. It’s already 10.30 and only a few of us are present.(meeting, cancel)
Response : The meeting __________, but you’d better wait for another half an hour.

3. They say they definitely sent the appointment letter by post, but it never arrived, (send fax message)
Response : They __________ instead.

4. The Municipality did not bother about keeping the locality clean. When the epidemic broke out, it claimed many lives.
(take precautions, prevent epidemic)
Response: The Municipality __________

5. The Principal is not in her office. She probably had some urgent work at home, (go, home)
Response : She __________.

6. Asha wasn’t really a big hit as the heroine of the play. The director needn’t have limited his choice to Class XII students alone.
(try, some of the XI class students)
Response : He __________ __________

Answers:

2. might have been cancelled
3. should have sent a fax message
4. ought to have taken precautions which could have prevented the epidemic,
5. must have gone home as she had perhaps some urgent work there,
6. could have tried some of the XI class students instead of restricting his choice to Class XII students only

D. 2
Complete the following paragraph on a school sport meeting by filling in the blanks with could not have, might not have, should not have or would not have.

At this year’s sports meeting, many records were broken but the reigning sports champion. Ravi, surprisingly could not make it to the finals in any of his favourite events. Perhaps he __________ missed so many of his practice sessions. His coach tends to think that he __________ had the time to get fit enough because of his special classes in the evenings. Even if he had tried, he __________ beaten Ramu, who was much better prepared. If it had not been for Ramu, our school __________ gained a place in the draw of the inter-school tournament.
Answer:
should not have, might not have, could not have, would not have

D.3
Anant has returned from an interview. Read the dialogue, that takes place between Anant and his father. In pairs, fill in the blanks using any suitable modals. To help you, the number of words you need to use is given in brackets.

Father : Well , Anant, how was the interview?
Anant : Father, it was a real nightmare. Just about everything went wrong. I was late. I didn’t have the required papers and the GK questions ……. !
Father : Really ! Anant, please don’t think I’m lecturing you, but I’d like to say something about how you ________ (2) handled the whole business better.
Anant : Father, I wish you ________ (2) say that. You ________ (2) seen the amount of effort I put in.
Father : Well …. I have my doubts about that. First, let’s take up this business about being late.
Anant : Please remember I only got six days’ notice.
Father : No, my dear, it was more than that. If Pm not mistaken, you got the interview call on Saturday itself. If I’d been you, I _________ (2) begun my preparation on Saturday itself. Honestly you __________ (3) gone off on that weekend trip.
Anant : Father you know I’d been planning to go on that trip for ages.
Father : Well …….. if you had stayed home you ___________ (2) made a list of the papers required and filed them systematically,
Anant : Yes, perhaps you’re right, but father. those GK questions ……?
Father : What about them ? Haven’t you been reading the papers regularly?
Anant : Yes of course. But those questions were so outdated. I ___________ (3) answered them even if I had read the paper every single day for the past 10 years.
Father : Anant, there is no point complaining now. You _____ (1)/(2) be prepared to be more alert about these things.
Answer:
could have, would not, must have, would have, should not have, might have, could not have, should

E. Modals – Summary

E.1. Read the following letter and choose the most suitable alternative from those given. Underline your choice. Sometimes more than one alternative is suitable.
Answer:
Dear Mohan

It was lovely to get your letter and to hear the good news that you are going trekking with your friends. You (ought to/ would/ should) have a break after your exams ! You ask me what you (can/ should, will) take. Well, you (might/ can’t/ mustn’t) fit everything in a backpack so you must be selective. You (will/ can/ must) take at least one sweater because it (ought to/ should/ can) get very cold in the mountains. You (needn’t/ could/ should) pack a gas stove because there (could/ may/ will) be plenty of firewood from dead trees.

I’m sure you will have a wonderful time but I (may/ would/ should) give you a word of warning. Don’t get stuck in the Laki Pass at night. Once you’re there you (won’t be able to/ can’t be able to/ not to able to) get down and it’s very dangerous at night. By the way, you (should/ should have to/ should have) told me earlier that you were going and I (should have/ would have/ will have) given you my walking boots !

Anyway, look after yourself and enjoy your holiday.
With love
Daddy

E. 2.
A night at the Theatre – Role Play

Work in pairs. Below is a summary of a discussion between a parent and a child. Read through the notes and decide who will take which role. Then act out the role play. You will probably find that you sometimes need to use modals.
Background to role play

Role A – Daughter/ Son
Yours exams start next week – behind with revision – want to go to theatre to see new play – with friend – his birthday – reduced tickets – good play – need rest from work – find it difficult to concentrate on work.

Role B – Father/ Mother
Disagree with daughter/ son – worried – won’t do well in exam – don’t want them to waste time – for own good – why not worked hard before – if had worked, could go out after exams.

E.3.
When you have finished, you and your partner should team up with another pair and write out the dialogue. Then act it out before the class.
Answers:
A : Father, Today is the birthday of my friend Ram. I want to go to theatre to see a new play. It’s a good play and the tickets are available at reduced rates.
B : I am surprised at you, son. Your exams start next week. Don’t you know you are behind with revision? How can you think of wasting time in a theatre?
A : You are right. But think about it. Can I go on studying all the time? I need some rest from work and I think it is the proper time to do so.
B : Going to the theatre is not to relax. It will be a waste not of just 3 hours but the whole day. You will keep on thinking about the characters of the play all day.
A : Oh no. I believe that I shall be able to concentrate on the books better after that.
B : You say it because you want to get my permission. Otherwise, you know the truth.
A : Father, think about my friend. This is his birthday and we had planned for this day much in advance.
B : Well, you can do what you want. I needn’t keep you against your wish. However, I wish you should have been more careful about your studies.
A : Thanks father. Be sure that I’ll do well in the examination.

We hope the English Workbook Class 10 Solutions Unit 11 Modals-Expressing Attitudes help you. If you have any query regarding CBSE Class 10 English Workbook Solutions Unit 11 Modals-Expressing Attitudes, drop a comment below and we will get back to you at the earliest.

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Political Science Class 12 Important Questions Chapter 4 Alternative Centres of Power is part of Political Science Class 12 Important Questions. Here we have given Political Science Class 12 Important Questions Chapter 4 Alternative Centres of Power.

Political Science Class 12 Important Questions Chapter 4 Alternative Centres of Power

1 Mark Questions

Question 1.
Why was ASEAN established? (Delhi 2016)
Answer:
ASEAN was established to accelerate economic growth and through that social progress and cultural development.

Question 2.
What does the logo on the ASEAN flag symbolise? (All India 2016)
Answer:
On the ASEAN logo, the ten stalks of paddy (Rice) represent the ten South East Asian countries bound together in friendship and solidarity. The circle symbolises the unity of ASEAN.

Question 3.
Under which plan did the USA extend financial support for reviving Europe’s economy after the Second World War? (Delhi 2014)
Answer:
The USA extended massive financial help for reviving Europe’s economy under the plan named ‘Marshall Plan’.

Question 4.
Name any two members of the EU, who are permanent members of the UN Security Council. (Delhi 2014)
Answer:
The two member states of EU, who are permanent members of the UN Security Council are :

• Britain
• France

Question 5.
Trace the evolution process of the European Union, (All indin 2014)
Answer:
The EU has gradually evolved from an economic union to a political union. It became more a nation-state. It does not have its Constitution.

6. What was the objective of founding the European Union? (All indin 2013)
Answer:
The general objectives of the founding the European Union were

• To have an area of freedom, security and justice without internal frontier.
• Promotion of scientific and technological advance.

Question 7.
What is meant by ASEAN way? (All India 2012)
Answer:
It is a kind of interaction which is informal, unofficial, non-confrontationist and cooperative.

Question 8.
What is meant by the ‘Maastricht Treaty’? (All India 2009)
Answer:
‘The Treaty of Maastricht’ was signed on 7th February 1992, establishing the European Union (EU) and laid the foundation for common foreign and security policy, cooperation and justice, home affairs and the creation of a single currency.

Question 9.
In 1992 which regional organisation was formed? (All India 2009)
Answer:
The regional organisation formed in 1992 was the European Union.

Question 10.
What do ASEAN and FTA stand for? (Delhi 2008)
Answer:
ASEAN stands for Association of South East Asian Nations and FTA stands for Free Trade Area.

Question 11.
Mention the full form of the following (Delhi (C) 2008)
(i) CTBT
(ii) ASEAN
Answer:
(i) CTBT—Comprehensive Test Ban Treaty
(ii) ASEAN—Association of South East Nations

2 Marks Questions

Question 1.
State any two features of the European Union that make it an influential organisation. (Delhi 2014)
Answer:
Two features of the European Union that make it an influential organisation are :

1. EU has evolved over time from an economic union to political union. It has its own flag, anthem, founding date and currency.
2. EU’s share of world trade is three times larger than that of the US.

Question 2.
When was the ASEAN regional forum established? What were its main objectives? (Delhi 2013)
Answer:
The ASEAN regional forum was established in 1994. The main objectives of ASEAN were :

1. To accelerate economic growth and through that social progress and cultural development.
2. To promote regional peace and stability based on the rule of law and the principles of the United Nations Charter.

Question 3.
In the European Union Flag, what does the symbol of ‘twelve gold stars in a circle’ signify? (Delhi 2012, 2011)
OR
What does the circle with golden stars on the European Union flag stand for? (Delhi 2010)
Answer:
The circle stands for solidarity and peace among the people of Europe. It contains twelve stars which symbolise perfection, completeness and unity.

Question 4.
Explain India’s improving relationship with China. (Delhi 2011)
Answer:
After the end of the Cold War, significant changes have been seen in the relationship between India and China. Rajiv Gandhi’s visit in December 1988 then both governments have taken measures to contain conflict and maintain ‘peace and tranquillity’ on the border.

Cultural exchanges and cooperation agreements are signed by both. Increased transportation and communication established more sound relationship.

Question 5.
What is the meaning of Panchsheel? (All India 2011)
OR
What does Panchsheel imply? (All India 2009)
Answer:
The five principles of peaceful coexistence are known Panchsheel which formed the bedrock of Indo-China relationship. Their first formal codification in treaty form took place in 1954 when an agreement between India and China was signed. Panchsheel act as guiding principle for Indo-China relation.

Question 6.
Mention any two steps taken by China to improve its economy. (Delhi 2010)
Answer:
Two steps taken by China to improve its economy are:

1. Deng Xiaoping in 1978, announced ‘Open Door Policy’. This aimed at the generation of high productivity by investments of capital and technology from abroad.
2. Privatisation of agriculture and privatisation of industry was done.

Question 7.
What led to the formation of the European Union? (Delhi 2009)
Answer:
European Union was formed after the end of the Cold War. After the disintegration of USSR, the European Union was formed to consolidate the process of reviving the shattered economies of European countries and to get massive US financial help under the Marshall Plan.

Question 8.
What was the Marshall Plan? How did it pave the way for the formation of OEEC (Organisation of European Economic Cooperation)? (All India 2008: Delhi (C) 2008)
Answer:
Marshall Plan was a plan under Mr George C Marshall, US Secretary. America extended huge financial help for reviving Europe’s economy. New collective security structure was created under NATO. Under the Marshall Plan, OEEC was created in 1948, to help West European states. It acted as a platform where the West European states began to cooperate on trade and economic issues.

Question 9.
When was the European Union established? Mention any two kinds of influence that were exercised by the European Union, (All India to 2008)
Answer:
European Union was established on 7th February 1992 after signing the Treaty of Maastricht. Influences that were exercised by the EU are :

1. Economic influence
2. Political and diplomatic influence

4 Marks Questions

Question 1.
Describe India-China relations from 1947 to 1962. (All India, 2017,2016)
OR
Evaluate the causes of the strained relations between India and China. (All India 2015)
OR
Describe India’s relations with China from independence to 1962. (All India 2013)
Answer:
The India-China relations examined are as below: Friendly relations

• After the Chinese Revolution in 1949, India was one of the first countries to recognise the communist government.
• Prime Minister Nehru and Chinese Premier Zhou Enlai adopted Panchsheel, the Five Principles of Peaceful Co-existence on 29 April 1954.

The Chinese invasion and strained relationship

• China annexed Tibet in 1950 and thus removed a historical buffer between the two countries.
• Tibetan spiritual leader Dalai Lama had sought asylum in India in 1959. China alleged that India was allowing anti-China activities in India.
• Boundary disputes arose between the two countries over Aksai-China area in the Ladakh region and NEFA in the Eastern region.
• The boundary disputes led to a massive Chinese invasion in October 1962. Finally, China declared a unilateral ceasefire but relations between the two countries remained strained.

Question 2.
What were the two major policy decisions taken by the Chinese leadership in the 1970s? All India 2016
OR
Describe any four new economic policies of China to make it grow at a faster rate. Delhi 2013
OR
Explain the new economic policies of China since 1978. (All India 2013)
Answer:
China’s economic success has been linked to its rise as a great power :
The major policy decisions new economic policies of China were :

• China ended its political and economic isolation with the establishments of relations with the United States in 1972.
• Four modernisations (agriculture, industry, science and technology and military) were proposed by Premier Zhou Enlai in 1973.
• Den Xiaoping declared the ‘Open Door Policy’ and rapid economic reforms in China. It was meant to generate higher productivity by investments of capital and technology from other countries.
• The privatisation of agriculture in 1982 was followed by the privatisation of industry in 1998.
• The trade barriers were eliminated only in Special Economic Zones (SEZs) where foreign investors could set up enterprises.

Question 3.
In which four ways did the new economic policy of China benefit its economy? (Delhi 2016)
Answer:
The four ways by which the new economic policy of China benefitted its economy are :

1. Privatisation of agriculture led to a remarkable rise in agriculture production and rural incomes.
2. The rural industry too grew due to high personal savings in the rural economy.
3. The SEZs led to a phenomenal rise in foreign trade. It made China the most important destination for foreign direct investment (FDI) anywhere in the world.
4. It helped in strengthening its relations with WTO in 2001 and plans to deepen its integration into the world economy.

Question 4.
Mention any four significant changes in Indo-China relations that have taken place after the Cold War. (Delhi 2016)
Answer:
End of the Cold War marked various changes in the relationship between India and China. Four significant changes in Indo-China relations took place after the Cold war was:

1. Both India and China consider themselves as rising powers in international politics. After the visit of Rajiv Gandhi in 1988, both governments tried to maintain ‘peace and silence’ on the border.
2. Agreements regarding cultural exchanges and cooperation were signed. Four border posts were also opened.
3. Trade between India and China grew at 30 per cent per year since 1999.
4. An increase in bilateral trade from $338 million in 1992 to more than $ 18 billion in 2006 was seen. India and China are following the same policies in international economic institutions like the World Trade Organisation.
5. Leaders from both countries frequently visit each other’s nation and this way they get familiar with each other. Through an increase in transportation and communication links and working on common economic interests development of sound economic relationship has been taking place.

Question 5.
In spite of the improvement in the Chinese economy, there have been negative consequences affecting the people of China. Mention any four such consequences. (Delhi 2016, All India 2016)
OR
Highlight any four drawbacks in the changed Chinese economic system. (Delhi (C) 2008)
Answer:
Even though the Chinese economy has improved dramatically, there have been negative consequences affecting the people of China.
The four negative consequences or drawbacks in the changed Chinese Economic System were :

• The benefits of the reforms have not been equally received. Approximately 100 million people are still unemployed.
• Female employment and conditions of work are as bad as in Europe of the 18th and 19 th centuries.
• Corruption and environmental degradation have increased.
• There has been a rise in economic inequality between rural and urban residents and coastal and inland provinces.

Question 6.
Assess the role of ASEAN as an economic association. (All India 2016)
OR
Why does ASEAN still remain principally an economic community? (Delhi 2015)
Answer:
ASEAN was established primarily for accelerating the economic growth and through that ‘social progress and cultural development,’ It still remains principally an economic community. Though the ASEAN region as a whole is a much smaller economy compared to the US, the EU, and Japan, however, its economy is growing much faster than all these. This accounts for the growth in its influence both in the region and beyond.

The objectives of the ASEAN are to create a common market and production base within ASEAN states. ASEAN as an economic community also committed to improving the existing ASEAN. Dispute Settlement Mechanism to resolve economic disputes. ASEAN has focussed in creating a Free Trade Area (FTA) for investment, labour, and services. The US and China have already negotiated FTA with ASEAN.

The current economic strength of ASEAN particularly its economic relevance as a trading and investment partner to the growing Asian economies such as India and China makes this an attractive proposition. India signed FTA with two ASEAN members, Singapore and Thailand, and trying to sign an FTA with ASEAN itself.

ASEAN’s strength, however, lies in its policies of interaction and consultation with member states, with dialogue partners and with non-aligned organisations.

Question 7.
How has the European Union evolved over time from an economic union to an increasingly political one? (Delhi 2015)
OR
What led the evolution of the European Union from an economic union to an increasingly political one? (Delhi 2011)
Answer:
In the following ways, the European Union was evolved from economic to political union :

1. Its aim was to make Europe politically, economically and culturally strong enough to face powers like the USA, Russia.
2. In order to send grievances of European countries to the UN, two countries i.e. Great Britain and France are members of the Security Council of UNO.
3. Due to the presence of some non-permanent members of the UN Security Council, the EU was able to influence US policies.
4. It has its own flag, anthem, currency, founding date.

Question 8.
Explain the economic and military influence of the European Union. (Delhi 2015)
Answer:
Economic influence EU with more than $12 trillion (2005) is the largest economy in the world surpassing even that of the USA. Euro can cause a danger to the US hegemony of the dollar. The share of the EU is three times greater than that of the US and this makes the EU more powerful in trade disputes with the US and China. Its economy is very impressive and thus, it becomes influential to its neighbours and in Asia and Africa. It plays a significant role in the World Trade Organisation.

Military influence EU stands second in combined armed forces and on total spending on defence. Its members France and Britain have over 550 nuclear warheads and arsenals. EU is the second largest source of space and communication technology. Thus, this super national association has been able to intercede in economic, political and social areas.

But in certain cases, member states have their own foreign relations and defence policies. For example, an Iraqi invasion, where Britain and some other members of the EU joined US-led a coalition of willing, whereas France and Germany opposed the same.

Question 9.
What is meant by the ASEAN way? Mention any two of its objectives. (Delhi 2014)
Answer:
ASEAN way is a kind of interaction which is informal, unofficial, non-confrontationist and cooperative.
The two objectives of ASEAN are :

1. To speed up the economic growth of member countries and through that growth, to bring social and cultural development.
2. Promotion of regional peace and stability based on laws and principles of the UN Charter.

Question 10.
Explain any two causes which led to the formation of ASEAN. (All India 2013)
Answer:
The causes which led to the formation of ASEAN were :

1. The South East Asian Nations suffered the economic and political consequences of repeated colonialisms before and during the Second World War.
2. The end of the Second World War confronted problems of nation-building, the ravages of poverty and economic backwardness and the pressure to align with one great power or another during the Cold War.
3. Hence, South East Asian countries established the Association for South East Asian Nations in order to solve the issues of South East Asian Countries.

Question 11.
What were the objectives behind the formation of the ASEAN in 1967? (All India 2011)
Answer:
Association of South East Asian (ASEAN) Nations was created in 1967 with the following objectives:

1. Primary objective It was to increase economic growth, which will result in social progress and cultural development of the ASEAN. Thus, this objective was related to economic, cultural and social perspectives.
2. Secondary objective Under United Nation Charter, principles and rules of law have been stated. So, the secondary objective of ASEAN nations was to promote stability and regional peace based upon those rules and principles.

Question 12.
Explain the role of emerging alternative centres of power in transforming the different countries into prosperous economies. Delhi 2010
Answer:
The end of the bipolar structure in world politics in the early 1990s interpreted that all alternative centres of economic and political power could limit the dominance by the US.

Two forces were established to compete with this factor. They were the European Union (EU) in Europe and the Association of South East Asian Nations (ASEAN) in Asia.

Both EU and ASEAN have developed alternative institutions and agreements in international law, this converted the countries into prosperous economies. Also, the economic emergence of China has made a substantial impact on world politics.

Question 13.
Why did India and China both, view themselves as rising powers in global politics in spite of the tension between them? Substantiate your answer by giving any four events that have brought cordiality in their relationship. (Delhi 2010)
Answer:
Both India and China view themselves as rising powers in global politics, as their relations now have a strategic as well as economic dimension. Both countries would like to play a major role in the Asian economy and politics.

Four events of friendship between them are:

1. India’s nuclear tests sometimes justified on grounds of threat from China and did not stop their interaction.
2. No issues created problems between both the countries be it Pakistan’s nuclear programme being assisted by China.
3. Increasing transportation and communication link, common economic interests and global concerns establish sound relations.
4. Mutual understanding of concessions’ policy to solve border problems.

Question 14.
How did the European Union exercise its political and diplomatic influence? (Delhi 2008)
Answer:
The political and diplomatic influence of the European Union has considerable significance. Its members Britain and France are permanent members of the UN Security Council. Some non-permanent members of the UNSC are also included in the EU. And this aspect has made EU impact some US policies such as present US position on Iran’s nuclear programme. EU’s usage of negotiations, diplomacy and economic investments proved more fruitful than US coercion and military force. This can be seen in dealings with China on human rights and environmental issues.

Question 15.
Mention any four common features of the European Union. Delhi 2008; (All India 2008)
Answer:
Features of the EU are as follows:

1. EU’s share of world trade is three times larger than that of the US allowing it to be more assertive in trade disputes with the US and China.
2. It has evolved from an economic union to a political one. It has its own flag, anthem, founding date and currency.
3. Its economic power gives it influence over its closest neighbours and on Asia and Africa. It also functions as an important bloc in an international economic organisation such as WTO.
4. EU has political, economic, diplomatic and military influence. GDP of the EU is slightly larger than that of the US.

Question 16.
How can the Euro pass a danger to the US Dollar? (Delhi 2008)
Answer:
European Union has a great economic influence in the world market including the market of the United States. Euro is the currency of the EU.
Euro can pass a danger to the US dollar through:

1. The EU is the world biggest economy with a GDP of more than $ 12 trillion in 2005 and this was slightly larger than the US.
2. Share of EU in world trade is three times larger than that of the US and this is the reason why the EU can be more assertive in trade disputes with the US and China.
3. The economic power of the EU provides great influence over Asia, Africa and its close neighbours.
4. Many countries have joined the EU who are directly linked with the US and carry dollar as their currency. These countries can take economic programmes which are against the interest of the US.

Question 17.
Describe any two aspects each of cordiality and tension in the relationship between India and China. (Delhi to 2008)
Answer:
Two aspects of cordiality in the relationship between India and China are :

1. Bilateral trade between India and China has increased from $ 338 million in 1992 to more than $ 18 billion in 2006.
2. Lately, both countries have agreed upon to cooperate with each other in areas that could otherwise create conflict between both nations.

Two aspects of tension in the relationship between India and China are :

1. When China attacked Tibet in 1950-51, Dalai Lama, a political and religious leader of Tibet took shelter in India. As a result relation between the two countries became bitter.
2. Controversy over MacMohan line, the borderline between India and China and border conflict in 1962, over competing for territorial claims in Arunachal Pradesh and in the Aksai Chin region of Ladakh.

Question 18.
Describe any two similarities and two differences between the USA and the EU. (All India (C) 2008)
Answer:
EU and USA carry similarities as well as differences between them.

Similarities between them are :

• Both have a democratic form of governments.
• Both the USA and the EU are federal structures. USA states whereas the EU is a combination of different states of regional blocs.

Differences between them are :

• USA is a country with the US dollar as its currency, whereas the EU has Euro as its currency.
• Basis of unity in the USA is political and military and EU has econ = nic cooperation as its basis r>l unity.

Question 19.
Give any two reasons why regionally and globally China has become an economic power to reckon with. (All India (C) 2008)
Answer:
Regionally and globally China has become an economic power to reckon to believe with as:

• The integration of China’s economy has considerable influence on trade partners.
• Adjustments through economic considerations have been made with Japan, the US, ASEAN and Russia. Its investments and help in American, African and Latin states have helped it to project itself a major global player for developing states.

6 Marks Questions

Question 1.
Evaluate any three major factors responsible for making the European Union a political force from economic forces. (Delhi 2016)
Answer:
The European Union has gradually evolved from an economic union into a political union. It has become more a nation-state. Though it does not have Constitution, it has its own flag, anthem, founding date and currency. It has a common foreign and security policy in its dealings with other states.

The areas of cooperation have been expanded by the European Union through admitting new members from the former Soviet bloc. This shifting of power of the EU from economic to political force has not been easy as people were not very enthusiastic. There are also reservations about including some new countries within the European Union.

A major factor behind this is

1. Its aim was to make Europe politically, economically and culturally strong enough to face powers like the USA, Russia.
2. In order to send grievances of European countries to the UN, two countries i.e. Great Britain and France are members of the Security Council of UNO.
3. Due to the presence of some non-permanent members of the UN Security Council, the EU will be able to influence US policies.

Question 2.
Analyse any two factors responsible for the European Union to be a highly influential regional organisation. (All India 2015)
OR
Evaluate the role of the European Union as a supranational organisation. (All India 2011, 2009)
OR
How has the European Union risen to be a super-national organisation? What are its limitations? (All India 2008)
Answer:
European Union is considered highly influential.
For types of influences
Economic influence EU with more than $12 trillion (2005) is the largest economy in the world surpassing even that of the USA. Euro can cause a danger to the US hegemony of the dollar. The share of the EU is three times greater than that of the US and this makes the EU more powerful in trade disputes with the US and China. Its economy is very impressive and thus, it becomes influential to its neighbours and in Asia and Africa. It plays a significant role in the World Trade Organisation.

Military influence EU stands second in combined armed forces and on total spending on defence. Its members France and Britain have over 550 nuclear warheads and arsenals. EU is the second largest source of space and communication technology. Thus, this super national association has been able to intercede in economic, political and social areas. But in certain cases, member states have their own foreign relations and defence policies.

For example, in the Iraqi invasion, where Britain and some other members of the EU joined a US-led coalition of willing, whereas France and Germany opposed the same.

Limitations of the European Union European Union as a supranational association has been able to intercede in economic, political and social areas. But there are certain limitations :

• Member states of EU have their own foreign relation and defence policies, that often odds with each other.
• Presence of deep-seated ‘Euro-skepticism’ in some parts of Europe about the EU’s integrationist agenda.

Question 3.
Explain the factors responsible for the rise of the Chinese economy. (Delhi 2009)
Answer:
China is the third major alternative centre of power. It is the fastest growing economy. China at one time was based on the Soviet model and at that time, it broke all the links with the capitalist world. Following are the factors responsible for the rising of the Chinese economy :

• Use of Soviet Model China accepted the Soviet model and relied on its resources. China decided to substitute imports by domestic goods and create state-owned heavy industries from capital produced by agriculture.
• Development of Industrial Economy China used all its resources to develop an industrial economy. All citizens were provided with education and health programmes.
• Relationship with USA China established a relationship with the USA in 1972.
• Modernisation Modernisations in the field of agriculture, industry, military, science and technology were proposed.
• Major Policies Announced Open Door Policy was announced by Deng Xiaoping in 1978, which aimed at a generation of high productivity by investments in capital and technology from abroad.
• The era of Privatisation Privatisation of agriculture in 1982 and privatisation of industry in 1998 was done.
• Establishment of SEZ’s Special Economic Zones was set up. The state had a centralised role in setting up of China’s economy.

Question 4.
Explain the vision of the ASEAN for 2020. (Delhi 2009)
Answer:
ASEAN was established in 1967 with the objective to accelerate economic growth and through that ‘social progress and cultural development’.
ASEAN is rapidly growing into a very important regional organisation. It has a certain vision for 2020. The features of the ASEAN vision 2020 are as follows :

1. Its vision 2020 has defined as an outward-looking role for ASEAN in the international community.
2. This builds on the existing ASEAN policy to encourage negotiations over conflicts in the region. Thus, ASEAN has mediated the end of the Cambodian conflict, the East Timor Crisis and meets annually to discuss East Asian cooperation.
3. ASEAN’s strength, lies in its policies of interaction and consultation with member states, with dialogue partners and with other non-regional organisations.
4. It is the only regional association in Asia that provides a political forum where Asian countries and the major powers can discuss political and security concerns.

Question 5.
Examine the changing Indo-China relations. (All India 2009)
Answer:
For India-China relationship
The India-China relations examined are as below: Friendly relations

• After the Chinese Revolution in 1949, India was one of the first countries to recognise the communist government.
• Prime Minister Nehru and Chinese Premier Zhou Enlai adopted Panchsheel, the Five Principles of Peaceful Co-existence on 29 April 1954.

The Chinese invasion and strained relationship

1. China annexed Tibet in 1950 and thus removed a historical buffer between the two countries.
2. Tibetan spiritual leader Dalai Lama had sought asylum in India in 1959. China alleged that India was allowing anti-China activities in India.
3. Boundary disputes arose between the two countries over Aksai-China area in the Ladakh region and NEFA in the Eastern region.
4. The boundary disputes led to a massive Chinese invasion in October 1962. Finally, China declared a unilateral ceasefire but relations between the two countries remained strained.

Conflict of 1962 and Post-Cold Era marked a major change in Indo-China relations. Indo-China Conflict of 1962 In 1962, border dispute regarding territorial claims in Arunachal Pradesh and in Aksai Chin made India suffer military reverses. This had an impact on relations between both of them.

Till 1976, no progress was seen in the betterment of their relations, but after that, they improved slowly. The change in China’s leadership allowed both countries to improve their relations. Border issues resolution was also started in 1981.

Indo-China Relation After Cold War End of the Cold War marked various changes in the relationship between India and China. Both India and China consider themselves as rising powers in international politics.

After the visit of Rajiv Gandhi in 1988, both governments tried to maintain ‘peace and silence’ on the border.
Agreements regarding cultural exchange and cooperation were signed. Four border posts were also opened. Trade between India and China grew at 30 per cent per year since 1999. An increase in bilateral trade from $ 338 million in 1992 to more than $ 18 billion in 2006 was seen. India and China are following the same policies in international economic institutions like the World Trade Organisation.

The nuclear tests by India in 1998 created tension between the two, but the process of normalisation was continued. No issues created problems between both the countries, be it Pakistan’s nuclear programme being assisted by China.

Leaders from both countries frequently visit each other’s nation and this way, they are becoming familiar with each other. Through an increase in transportation and communication links and working on common economic interests development of sound relationship has been taking place.

Question 6.
Analyse the basis of the projection of China to overtake the US as the world’s largest economy by 2040. (Delhi 2008)
Answer:
China is viewed to dominate the US by the year 2040. The basis of the projection are :

1. China is considered as the driver of East Asian growth because of the economic integration into regions.
2. China is considered to be very powerful and factors such as population, land mass, resources, regional location and political influence add to its strength.
3. China announced ‘Open Door Policy’ in 1978 which aimed at a generation of high productivity by investments in capital and technology from abroad.
4. In the economic sector various steps were taken to encourage investment by Western entrepreneurs for modernisation of:
   • Industry
   • Science and technology
   • Agriculture
   • Military
5. In 1980, China became a member of the World Bank and International Monetary Fund.
6. Privatisation of agriculture and industry helped in growing economy rapidly.
7. Foreign trade grew with the creation of SEZs and new trading plans This resulted in high foreign exchange reserves and this way China became most significant for FDI. The above points show China’s ability to overtake the US as the world’s largest economy by 2040.

Value-Based Question (VBQ)

Question 1.
The conflict of 1962, in which India suffered military reverses, had long-term implications for India-China relations. Diplomatic relations between the two countries were downgraded until 1976. Thereafter, relations bet even the two countries began to ii approve slowly. After the change in China’s political leadership from the mid to late 1970s, China’s policy became more pragmatic and less ideological. So, it was prepared to put off the settlement of contentious issues while improving relations with India. A series of talks to resolve the border issues were also initiated in 1981. (Delhi 2012 )
Study the paragraph given above carefully and answer the following questions
(i) Why did India suffer military reverses as a result of the conflict of 1962?
(ii) Why did the relation between India and China slowly improve?
(iii) What was the change in the policy of China in the seventies?
(iv) Which efforts were made to resolve the border issue between? India and China?
Answer:
(i) China launched a massive attack on Arunachal Pradesh and Aksai Chin in 1962, Indian forces blocked the Chinese on the Western front in Ladakh, they managed to nearly reach the initial point of Assam plains.
(ii) Relationship between India and China started improving from 1976 after the adoption of pragmatic policies by China.
(iii) The policies of China became more pragmatic and less ideological.
(iv) Since Rajiv Gandhi’s visit, both countries have taken measures to contain the conflict and maintain peace.

Map-Based Questions

Question 1.
In the given political outline map of Europe, four member countries of the European Union have been marked A, B, C and D. Identify them with the help of information given below and write their correct names in your answer-book along with with their respective serial number and the alphabet concerned. (Delhi 2013)

(i) An older member of the European Union located between Portugal and France.
(ii) An older member of the European Union located near Belgium and the Netherlands.
(iii) Two new members of the European Union.
Answer:
(i) Spain (A)
(ii) Luxembourg (B)
(iii) Bulgaria (C) and Romania (D)

Question 2.
In the given political outline map of the European Union, identify and write the names of four old members marked as A, B, C and D and four new members marked as P, Q, R and S in your answer-book. (All India 2010)

Answer:
(i) Old members of the European Union are
A-Finland
B-Denmark
C-Austria
D-Ireland

(ii) New members of the European Union
P-Estonia
Q-Poland
R-Hungary
S-Lithuania

Picture Based Question

Question 1.
Study the cartoon given below and answer the following questions (All India 2015, 2014)

(i) Which country does the given cartoon refer to?
(ii) Identify the two symbols in this cartoon which have given you the clue about the related country.
(iii) Where does the cartoon place the related country in international power politics?
Answer:
(i) The country refers to China.
(ii) The Great wall and Dragon.
(iii) The cartoon depicts the economic rise of China.

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Political Science Class 12 Important Questions Chapter 5 Contemporary South Asia is part of Political Science Class 12 Important Questions. Here we have given Political Science Class 12 Important Questions Chapter 5 Contemporary South Asia.

Political Science Class 12 Important Questions Chapter 5 Contemporary South Asia

1 Mark Questions

Question 1.
What is the full form of ‘SAARC’? (All India 2014)
Aus.
The full form of SAARC is the South Asian Association for Regional Cooperation.

Question 2.
Who controls the North-Eastern parts of Sri Lanka? (All India 2014)
Answer:
The LTTE controlled the North-Eastern parts of Sri Lanka. After its defeat the area is now under the control of the Government of Sri Lanka.

Question 3.
Whose mediation resolved the ‘Indus River Waters Dispute’ between India and Pakistan? (All Indio 2012)
Answer:
The World Bank resolved the ‘Indus River Water Dispute’ between India and Pakistan.

Question 4.
Mention any two objectives of SAARC. (Delhi 2011)
Answer:
The two objectives of SAARC are :

1. Cooperation through multilateral ways.
2. Peace and friendly relations among the nations.

Question 5.
Mention any four names of the countries belonging to the SAARC. (All India 2013)
OR
Name the member countries of SAARC? (Delhi 2009, All Indin 2009)
OR
Mention any two member nations of SAARC. (All India 2009)
Answer:
Member countries of SAARC are :

1. India
2. Bangladesh
3. Sri Lanka
4. Maldives
5. Pakistan
6. Nepal
7. Bhutan
8. Afghanistan

Question 6.
What does SAFTA stand for? (Delhi All 2008)
Answer:
SAFTA stands for South Asian Free Trade Agreement.

Question 7.
Mention the names of any four countries of South Asia. (All India 2008)
Answer:
The four countries of South Asia are Bangladesh, Bhutan, India and Pakistan.

2 Marks Questions

Question 1.
Analyse the two political developments of 1940s that led to the decision for the creation of Pakistan. (All India 2017)
Answer:
Two political developments of 1940s that led to the decision for the creation of Pakistan are following

1. Pakistan resolution passed by Muslim League in March 1940 demanding separate homeland for the Muslim.
2. Massive Hindu-Muslim riots on 16 August, 1946 which was observed as Direct Action Day by Muslim League.

Question 2.
Suggest any two measures to have good relations with Pakistan, (All India 2015)
Answer:
Two measures to have good relations with Pakistan are:

1. Pakistan must stop helping the terrorist.
2. Cultural delegates from both the countries must visit each other frequently.

Question 3.
State any two reasons for the instability of democracy in Pakistan. (Delhi 2014)
Answer:
The two factors for Pakistan’s failure of stable democracy are:

1. The social dominance of military.
2. Stiff confrontation for coming to power among political parties.

Question 4.
Before 1971, which two reasons were a source of resentment among the people of East Pakistan (now Bangladesh) against West Pakistan? (Delhi 2013)
Answer:
The two reasons which were source of v resentment (hate) among the people of Pakistan against West Pakistan were :

1. West Pakistan dominated East Pakistan.
2. East Pakistan was forced to use Urdu language.

Question 5.
What were the two main consequences of Indo-Pakistan conflict of 1971? (All India 2013)
Answer:
The consequences of Indo-Pakistan conflict of 1971 are given below :

1. Eastern command of Pakistan military collapsed and East Pakistan was recognised as Bangladesh.
2. Over 93000 Pakistani troops surrendered to the Indian forces making the largest surrender since Second World War.

Question 6.
Explain any two common features relevant to the countries of South Asia. (All India [C] 2008)
Answer:
The common features relevant to the countries of South Asia are :

1. The nations of South Asia do not share same type of political system. Though, all countries of South Asia prefer democratic form of government.
2. South Asian countries stand for diversity in every sense and yet constitute a geo-political space.

4 Marks Questions

Question 1.
‘Democracy is becoming the first choice of the people of South Asia’. Justify the statement. (HOTS; All India 2015)
OR
‘Despite the mixed record of democratic experience, the people of all the countries of South Asia share the aspirations of democracy.’ Explain. (HOTS; Delhi 2012)
Answer:
Democracy is becoming the first choice of the people of South Asia. According to a survey conducted, the results show that all the five countries in the South Asia region supports democracy. People belonging to different religions, ordinary citizens, rich as well as poor, all view the idea of democracy positively and support the institutions of representative ‘ democracy. For instance :

1. Nepal has transformed into a democracy from monarchy.
2. Sri Lanka and India have successfully operated a democratic system since their independence from the British.
3. Bhutan transformed from monarchy to democracy.
4. Maldives from sultanate to Republic with a Presidential form along with Multi-Party system.

Thus, it can be concluded that, despite of mixed record of democratic experience, the people of all countries of South Asia share the aspirations of democracy.

Question 2.
Explain any two points of conflict between India and Bangladesh. (Delhi 2014)
OR
Highlight any four issues of tension between India and Bangladesh. (Delhi 2012)
OR
Highlight any two issues of cooperation as well as confrontation each between India and Bangladesh, (All India 2010)
Answer:
The issues of tension (negative aspects) between India and Bangladesh are :

1. Sharing of river waters of Ganga and Brahmaputra.
2. Indian Government is not happy with Bangladesh’s refusal to act on unlawful immigration to India.
3. Bangladesh’s support to anti-Indian Islamic fundamentalist groups.
4. Bangladesh refused to allow Indian troops to move through its territory to North-East region.
5. Bangladesh refused to export natural gas to India and allow Myanmar to do so through its territory.

The issues of cooperation (positive aspects) between both the countries are :

1. From the last decade, economic relations have been stregthened.
2. India’s Look East Policy does involve Bangladesh that links South-East Asia via Myanmar.
3. Cooperation is noticeable on the grounds of disaster management and environmental issues.
4. Area of cooperation is being broadened by identifying areas of common threat and by responding sensitively to each others needs.

Question 3.
Explain any two reasons for the popular struggle in East Pakistan (now Bangladesh) against West Pakistan during 1971. Delhi 2014
Answer:
The two reasons for the popular struggle in East Pakistan (now Bangladesh) against West Pakistan during 1971 are following :

1. After Independence of both India and Pakistan, Bangladesh was a part of Pakistan and was called East Pakistan. The Government of Pakistan imposed Urdu language forcefully on East Pakistan’s people.
2. The West Pakistan imposed its own culture and it led to unfair treatment on Bengali culture and language. The people of East Pakistan also wanted fair representation in the administration and political power.

Question 4.
Explain any four causes of ethnic conflict in Sri Lanka, (All India 2014)
Answer:
The four causes of ethnic conflict were :

1. The bone of contention was the region of Ceylon which was represented by the majority Sinhala group. They opposed the migration and settlements of Tamilians from India in their region.
2. According to the group Sri Lanka was only for Sinhala people and not for Tamils. This attitude of Sinhala people led to the establishment of Liberation Tigers of Tamil Eelam (LTTE), a militant organisation, which desired for a separate country.
3. There was a pressure on the Government of India by the Tamils of Indian origin to intervene in the matter. Hence, the Government of India tried to negotiate with the Government of Sri Lanka on Tamil question. But direct involvement was in the year 1987. India conceded to sent troops to Sri Lanka for the preservation of relations between Tamils and Sri Lanka Government. Eventually, the Indian troops got into a fight with LTTE.
4. The presence of Indian troops was not liked by many Sri Lankans and hence in 1989, the Indian Peace Keeping Force (IPKF) pulled out of Sri Lanka without attaining its objective.

Question 5.
How is democratisation going on in Nepal since 1990? (All India 2013)
Answer:
Nepal use to be a Hindu kingdom in the earlier period followed by constitutional monarchy in the modern period for many years. The pro-democracy movements forced the king to allow new democratic Constitution in 1990. But it had a short and troubled career.

There was a huge influence of Maoists in many parts of Nepal who believed in armed insurrection against the monarch and the ruling elite. Hence, a triangular conflict among the Monarchist forces, the democrats and the Maoists took place for sometime. The parliament was abolished and the government was dismissed by the king in 2002.

Again in 2006, the king was forced to restore the House of Representatives after a massive country wide pro-democracy protests.
The constituent assembly was formed to write the Constitution for Nepal. The Constitution has come into effect with some amendment process going on.

Question 6.
What does SAARC stand for? Highlight its any three main objectives. (All India 2013)
Answer:
SAARC stands for the South Asia Association for Regional Cooperation. It was founded in 1985. It is a major regional initiative by the South Asian states to evolve cooperation through multilateral meAnswer:
Objectives of SAARC are as follows :

• To promote collective self-reliance through systematic economic growth in the region.
• To suppress menace of terrorism and smuggling of drugs.
• To promote mutual trusts and understanding.

Question 7.
Explain any two factors responsible for Pakistan’s failure in building a stable democracy. (All Indio 2012)
Answer:
The factors that are responsible for Pakistan’s failure in building stable democracy are :

1. The social dominance of military, landowning aristocrats has led to frequent overthrowing of elected governments and development of military governments.
2. Pro-military groups in Pakistan say that democratic government can harm security of Pakistan. And thus, army’s stay is more powerful.

Question 8.
Explain India’s changing relationship with Pakistan. (Delhi 2011)
Answer:
India and Pakistan just after independence got involved in conflict over certain issues. These included Kashmir, control over Siachen glacier, sharing water of rivers etc.
These issues led to wars between them in 1947-1948, 1965 and 1971. The nuclear test by both the countries in 1990’s further deteriorated the relations between them. Steps were taken to improve the relations between India and Pakistan. Some of them include :

• Both the countries signed an agreement in February 2007 on reducing the rise from accident relating to nuclear weapons.
• Both the countries have agreed to have a dialogue for reaching a peaceful settlement on all bilateral issues, including Kashmir.
• Leaders have meet at summits to understand each other better and to find solutions to the major problems between the two neighbours.
• Trade between the two parts of Punjab has increased substantially in the last five years.
• The two countries have agreed to undertake confidence building measures to reduce the risk of war.
• A number of bus route have been opened up between the two countries.

Question 9.
Name the countries included in South Asia. How can peace and cooperation be enhanced in this region? (Delhi Board 2010)
OR
What is meant by SAARC? How can peace and cooperation be enhanced through it? Delhi 2010
Answer:
The countries included in South Asia are Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan, Sri Lanka and Afghanistan. Inspite of many conflicts, the significance of cooperation and friendly relations is very well understood by the nations of South Asia.

To evolve the cooperation by multilateral means, a regional cooperation is being formed under the name of SAARC i.e. the South Asian Association for Regional Cooperation. It was established in 1985. It is a major regional initiative to evolve cooperation through multilateral meAnswer:

SAARC members signed the South Asian Free Trade Agreement (SAFTA) in 2004 which promised the formation of a free trade zone for the whole of South Asia. It aims at lowering trade tarrifs by 20 percent by 2007.

6 Marks Questions
Question 1.
“Nepal and India enjoy a very special relationship that has very few parallels in the world”. Justify the statement with any three suitable arguments. (HOTS; All India 2017)
Nepal and India share a very special relationship that can be illustrated with three suitable examples as follows:

1. A treaty between the two countries allows the citizens of the two countries to travel and work in each other countries without visas and passports.
2. Nepal being a landlocked country enjoys easier access to sea through Indian territory for the purpose of trade and commerce with other nations.
3. Both countries share together trade, scientific cooperation, common natural resources, electricity generation and interlocking water management grids.

Question 2.
Assess the positive and negative aspects of India’s relations with Bangladesh. (Delhi 2015)
Answer:
The issues of tension (negative aspects) between India and Bangladesh are :

• Sharing of river waters of Ganga and Brahmaputra.
• Indian Government is not happy with Bangladesh’s refusal to act on unlawful immigration to India.
• Bangladesh’s support to anti-Indian Islamic fundamentalist groups.
• Bangladesh refused to allow Indian troops to move through its territory to North-East region.
• Bangladesh refused to export natural gas to India and allow Myanmar to do so through its territory.

The issues of cooperation (positive aspects) between both countries are :

• From the last decade, economic relations have been strengthened.
• India’s Look East Policy does involve Bangladesh that links South-East Asia via Myanmar.
• Cooperation is noticeable on the grounds of disaster management and environmental issues.
• Area of cooperation is being broadened by identifying areas of a common threat and by responding sensitively to each other’s needs.

Question3.
Like India, why could democracy not take roots in Pakistan despite the fact that both the countries share a common past? (All India 2011)
OR
Explain the factors responsible for Pakistan’s failure in building a stable democracy. Describe any two pro-democracy factors present in Pakistan which can pave the way for establishing a lasting democratic set up over there. (All indin 2010)
Answer:
Pakistan does not have a good experience with democracy. Several factors contributed to the failure in building a stable democracy in Pakistan. They are as follows :

1. There was always social dominance of military, clergy, and landowning aristocracy which resulted in the downfall of democratic government and the existence of military government.
2. Due to Pakistan’s conflict with India, pro-military groups in Pakistan got strengthened.
3. According to these pro-military groups, political parties and democracy are defective and there is a chance of harm to the security of Pakistan by narrow-minded parties and disorganised democracy.
4. And this way, a justification for the army’s stay in power is provided.
5. Lack of international support has been there in Pakistan for democratic rule.
6. The US and some Western countries moved Pakistan towards authoritarian rule for their own benefits.
7. Military rule in Pakistan is supposed to be a protector of Western interests in West Asia, South Asia as ‘Global Islamic Terrorism’ and nuclear arsenal can only be controlled by the military.

Even though democracy has not been fully successful in Pakistan, there has been a strong pro-democracy sentiment in the country. Pakistan has a courageous and relatively free press and a strong human rights movement.

Question 4.
What are the major differences between the SEC and the European Union as alternative centres of power? (HOTS; All India 2011)
Answer:
The differences between the SAARC and the European Union are as follows

Question 5.
Analyse the common problems of South Asian countries. (All India 2011)
Answer:
South Asia includes countries like India, Pakistan, Bhutan, Bangladesh, Nepal, Maldives and Sri Lanka. The various natural areas such as the Himalayas, Arabian Sea, Bay of Bengal, Indian Ocean are part of this region.

The common problems among them are :

1. Poverty All countries of South Asia suffer from large masses living in poverty. In India, nearly 38 per cent of people are living in poverty.
2. Violation of human rights There exists a great threat to human rights from anti-social elements, communalist and from people with a negative attitude, thinking and approach.
3. A problem faced by democracy Several countries of South Asia aspire to be a democratic country but face a problem.
4. Women employment Women are generally seen at a lower position in most of the South Asian nations. They are restricted and are not as free as their counterparts.

Value Based Questions [VBQs]

Question 1.
Study the following passage carefully and answer the questions those are following (All India 2017)
The lack of genuine international support for democratic rule in Pakistan has further encouraged the military to continue its dominance. The United States and other Western countries have encouraged the military’s authoritarian rule in the past, for their own reasons. Given their fear of the threat of what they call ‘global Islamic terrorism’ and the apprehension that Pakistan’s nuclear arsenal might fall into the hands of these terrorist groups, the military regime in Pakistan has been seen as the protector of Western interests in West Asia and South Asia.
(i) What is meant by ‘Global Islamic Terrorism’?
(ii) Why did Pakistan lack genuine international support for a democratic rule?
(iii) Why was the military regime in Pakistan considered as the protector of Western interests in West Asia and South Asia?
Answer:
(i) Global Islamic Terrorism refers to political violence committed by Islamic fundamentalist to terrorise civilians world widely deliberately to get accepted their demands.
(ii) Pakistan lacks genuine international support for the democratic rule because the USA and other Western countries have fear of the threat of global Islamic terrorism and the nuclear weapon may fall into the hands of terrorist groups under civilian rule.
(iii) The military regime in Pakistan is regarded as the protector of Western interests in West Asia and South Asia because they strictly deal with Islamic fundamentalist and terrorist groups and act as a strategic partner in West Asia and South Asia.

Question 2.
No region exists in a vacuum. It is influenced by outside powers and events no matter how much it may try to insulate itself from non-regional powers. China and the United States remain key players in South Asian politics. Sino-Indian relations have improved significantly in the last ten years, but China’s strategic partnership with Pakistan remains a major irritant. The demands of development and globalisation have brought the two Asian giants closer and their economic ties have multiplied rapidly since 1991. Delhi 2012 Study the paragraph given above carefully and answer the following questions
(i) Which two countries have been referred to as ‘Outside power’?
(ii) Which are the two Asian giants and why have they been called so?
(iii) China’s strategic partnership with Pakistan is a major irritant for which country and why?
Answer:
(i) The two countries referred to outside powers are China and the USA.
(ii) India and China are the two Asian giants. They have been called so because they have emerged as strong economic and military power rapidly.
(iii) The strategic partnership is a major irritant for India because it is causing problems in the normalisation of diplomatic relations between the two countries.

Map-Based Question

Question 1.
In the given outline map of South Asia, five countries have been marked as (A), (B), (C), (D) and (E). Identify them on the basis of the information given below and write their correct names in your answer book with their respective serial number of the information used and the alphabet concerned as per the following format. (All India 2016)

Information used
(i) The country has experienced civilian as well as a military rule both.
(ii) Democracy was restored in this country in 2006.
(iii) This country is still a monarchy.
(iv) The Parliament of this country voted unanimously to introduce a multiparty system in June 2005.
(v) This country is a part of India’s ‘Look East Policy via Myanmar’.
Answer:

We hope the Political Science Class 12 Important Questions Chapter 5 Contemporary South Asia help you. If you have any query regarding Political Science Class 12 Important Questions Chapter 5 Contemporary South Asia, drop a comment below and we will get back to you at the earliest.

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Determinant

1. The symbol is called the determinant of order two. Its value is given by : D = a₁  b₂   − a₂  b₁

2. The symbol   s called the determinant of order three .
Its value can be found as:

OR
.
In this manner we can expand a determinant in 6 ways using elements of ; R₁ , R₂ , R₃ or C₁ , C₂ , C₃.

3. Following examples of short hand writing large expressions are :
(i) The lines:
a₁x + b₁y + c₁ = 0…….. (1 )
a₂x + b₂y + c₂ = 0…….. (2)
a₃x + b₃y + c₃ = 0…….. (3)

Condition for the consistency of three simultaneous linear equations in 2 variables.
(ii) ax² + 2 hxy + by² + 2 gx + 2 fy + c = 0 represents a pair of straight lines if

(iii) Area of a triangle whose vertices are (x_r, y_r) ; r = 1 , 2 , 3 is :

4. Minors: The minor of a given element of a determinant is the determinant of the elements which remain after deleting the row & the column in which the given element stands For example,

Hence a determinant of order two will have “4 minors” & a determinant of order three will have “9 minors” .

5. Cofactor: If M_ij represents the minor of some typical element then the cofactor is defined as: C_ij = (−1)^i+j . M_ij ; Where i & j denotes the row & column in which the particular element lies. Note that the value of a determinant of order three in terms of ‘Minor’ & ‘Cofactor’ can be written as : D = a₁₁M₁₁ − a₁₂M₁₂ + a₁₃M₁₃ OR D = a₁₁C₁₁ + a₁₂C₁₂ + a₁₃C₁₃ & so on …….

6. Properties Of Determinants:

• Property 1: The value of a determinant remains unaltered , if the rows & columns are inter changed . e.g.
  
  If D′ = − D then it is Skew Symmetric determinant but D′ = D ⇒ 2 D = 0 ⇒ D = 0 ⇒ Skew symmetric determinant of third order has the value zero.
• Property 2: If any two rows (or columns) of a determinant be interchanged, the value of determinant is changed in sign only. e.g.
  
  Then D′ = − D.
• Property 3: If a determinant has any two rows (or columns) identical , then its value is zero . e. g.
  
  then it can be verified that  D=0
• Property 4: If all the elements of any row (or column) be multiplied by the same number , then the determinant is multiplied by that number.
  e.g.
  
  Then D′ = KD
• Property 5: If each element of any row (or column) can be expressed as a sum of two terms then the determinant can be expressed as the sum of two determinants . e.g.
  
• Property 6: The value of a determinant is not altered by adding to the elements of any row (or column) the same multiples of the corresponding elements of any other row (or column) .e.g.
  
  Then D′ = D.
  Note: that while applying this property Atleast One Row (Or Column)  must remain unchanged.
• Property 7: If by putting x = a the value of a determinant vanishes then (x − a) is a factor of the determinant.

7.Multiplication Of Two Determinants:

Similarly two determinants of order three are multiplied.

where A_i, B_i, C_i are cofactors
Proof: Consider

Note : a₁A₂ + b₁B₂ + c₁C₂ = 0 etc. therefore,

8. System Of Linear Equation (In Two Variables):
(i) Consistent Equations: Definite & unique solution. [ intersecting lines ]
(ii) Inconsistent Equation: No solution. [ Parallel line ]
(iii) Dependent equation: Infinite solutions. [ Identical lines ]
Let a₁x + b₁y + c₁ = 0 & a₂x + b₂y + c₂ = 0 then:

&

9. Cramer’ S Rule :[ Simultaneous Equations Involving Three Unknowns ]
Let ,a₁x + b₁y + c₁z = d₁ …(I) ; a₂x + b₂y + c₂z = d₂ …(II) ; a₃x + b₃y + c₃z = d₃ …(III)
Then,

Where

Note: (a) If D ≠ 0 and alteast one of D₁ , D₂ , D₃ ≠ 0 , then the given system of equations are
consistent and have unique non trivial solution .
(b) If D ≠ 0 & D₁ = D₂ = D₃ = 0 , then the given system of equations are consistent and have trivial solution only
(c) If D = D₁ = D₂ = D₃ = 0 , then the given system of equations are consistentand have infinite solutions . In case

represents these parallel planes then also D = D₁ = D₂ = D₃ = 0 but the system is inconsistent.
(d) If D = 0 but atleast one of D₁ , D₂ , D₃ is not zero then the equations are inco ns istent and have no solution .

10. If x , y , z are not all zero , the condition for a₁x + b₁y + c₁z = 0 ; a₂x + b₂y + c₂z = 0 & a₃x + b₃y + c₃z = 0 to be consistent in x , y , z is that

Remember that if a given system of linear equations have Only Zero Solution for all its variables then the given equations are said to have Trivial Solution.

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Conjugate Complex | Complex Numbers

If z = a + ib then its conjugate complex is obtained by changing the sign of its imaginary part & is denoted by z. i.e. = a − ib.

Note:

• z + = 2 Re(z)
• z − = 2i Im(z)
• z = a² + b² which is real
• If z lies in the 1^st quadrant then lies in the 4^th quadrant and lies in the 2^nd quadrant.

Algebraic Operations | Complex Numbers

The algebraic operations on complex numbers are similar to those on real numbers treating i as a polynomial. Inequalities in complex numbers are not defined. There is no validity if we say that complex number is positive or negative.
e.g. z > 0, 4 + 2i < 2 + 4 i are meaningless .
However in real numbers if a² + b² = 0 then a = 0 = b but in complex numbers,
z₁² + z₂² = 0 does not imply z₁ = z₂ = 0.

Equality in Complex Number

Two complex numbers z₁ = a₁ + ib₁ & z₂ = a₂ + ib₂ are equal if and only if their real & imaginary parts coincide.

Representation of Complex Number in Various Forms

• Cartesian Form (Geometric Representation):
  Every complex number z = x + i y can be represented by a point on the cartesian plane known as complex plane (Argand diagram) by the ordered pair (x, y). length OP is called modulus of the complex number denoted by |z| & θ is called the argument or amplitude
  e.g. |z| =
  
  θ = tan⁻¹
  (angle made by OP with positive x−axis)
  Note:
  1. |z| is always non-negative. Unlike real numbers is not correct
  2. Argument of a complex number is a many valued function . If θ is the argument of a complex number then 2 nπ + θ ; n ∈ I will also be the argument of that complex number. Any two arguments of a complex number differ by 2nπ.
  3. The unique value of θ such that – π < θ ≤ π is called the principal value of the argument.
  4. Unless otherwise stated, amp z implies principal value of the argument.
  5. By specifying the modulus & argument a complex number is defined completely. For the complex number 0 + 0 i the argument is not defined and this is the only complex number which is given by its modulus.
  6. There exists a one-one correspondence between the points of the plane and the members of the set of complex numbers.
• Trignometric / Polar Representation:
  z = r (cos θ + i sin θ) where | z | = r ; arg z = θ ; = r (cos θ − i sin θ)
  Note: cos θ + i sin θ is also written as CiS θ.
  Also
• Exponential Representation:
  z = re^iθ ; | z | = r ; arg z = θ ; = re^-iθ

Important Properties of Conjugate/ Moduli/ Amplitude | Complex Numbers

If z , z₁ , z₂ ∈ C then ;

• z + = 2 Re (z) ; z − = 2 i Im (z) ; ; ;
  ; ; ; z₂ ≠ 0
• |z₁ + z₂|² + |z₁ – z₂|² = 2 [|z₁|² + |z₂|²]
  ||z₁| − |z₂|| ≤ |z₁ + z₂| ≤ |z₁| + |z₂|
• (i) amp (z₁ . z₂) = amp z₁ + amp z₂ + 2 kπ. k ∈ I
  (ii) amp = amp z₁ – amp z₂ + 2kπ; k ∈ I
  (iii) amp(zⁿ) = n amp(z) + 2kπ .
  where proper value of k must be chosen so that RHS lies in (− π , π ].

Vectorial Representation Of A Complex Number

Every complex number can be considered as if it is the position vector of that point. If the point P represents the complex number z then, & || = |z|

Note:

• If = z = re^iθ then = z₁ = re^{i(θ + φ)} = z . e^iφ. If and are of unequal magnitude then φ
• If A, B, C & D are four points representing the complex numbers z₁, z₂, z₃ & z₄ then is purely real ;
  is purely imaginary ]
  
• If z₁, z₂, z₃ are the vertices of an equilateral triangle where z0 is its circumcentre then (a) (b)

Demoivre’S Theorem

Statement: cos nθ + i sin nθ is the value or one of the values of (cos θ + i sin θ)ⁿ ¥ n ∈ Q. The theorem is very useful in determining the roots of any complex quantity
Note: Continued product of the roots of a complex quantity should be determined using theory of equations.

Cube Root Of Unity | Complex Numbers

• The cube roots of unity are 1,
• If w is one of the imaginary cube roots of unity then 1 + w + w² = 0. In general 1 + w^r + w²^r = 0 ; where r ∈ I but is not the multiple of 3.
• In polar form the cube roots of unity are:
  
• The three cube roots of unity when plotted on the Argand plane constitute the vertices of an equilateral triangle.
• The following factorisation should be remembered:
  (a, b, c ∈ R & ω is the cube root of unity)

a³ − b³ = (a − b) (a − ωb) (a − ω^²b); x² + x + 1 = (x − ω) (x − ω²);
a³ + b³ = (a + b) (a + ωb) (a + ω²b);
a³ + b³ + c³ − 3abc = (a + b + c)(a + ωb + ω²c)(a + ω²b + ωc)

n^th Roots Of Unity | Complex Numbers

If 1 ,₁ ,α₂ , α₃ ….. α_{n − 1} are the n, nth root of unity then:

• They are in G.P. with common ratio e^i(2π/n) &
• if p is not an integral multiple of n
  = n if p is an integral multiple of n
• (1 − α₁) (1 − α₂) …… (1 − α_{n – 1}) = n &
  (1 + α₁) (1 + α₂) ……. (1 + α_n − 1) = 0 if n is even and 1 if n is odd.
• 1 . α₁ . α₂ . α₃ ……… α_{n − 1} = 1 or −1 according as n is odd or even.

The Sum Of The Following Series Should Be Remembered:

Straight Lines & Circles In Terms Of Complex Numbers:

• If z₁ & z₂ are two complex numbers then the complex number z =mn
  divides the joins of z₁ & z₂ in the ratio m : n.
  Note:
  (i) If a , b , c are three real numbers such that az₁ + bz₂ + cz₃ = 0 ; where a + b + c = 0 and a,b,c are not all simultaneously zero, then the complex numbers z₁, z₂ & z₃ are collinear.
  (ii) If the vertices A, B, C of a ∆ represent the complex nos. z₁, z₂, z₃ respectively, then:
  (a) Centroid of the ∆ ABC =
  (b)  Orthocentre of the ∆ ABC = OR
  (c)  Incentre of the ∆ ABC = (az₁ + bz₂ + cz₃) ÷ (a + b + c)
  (d) Circumcentre of the ∆ ABC = :
  (Z₁ sin 2A + Z₂ sin 2B + Z₃ sin 2C) ÷ (sin 2A + sin 2B + sin 2C)
• amp(z) = θ is a ray emanating from the origin inclined at an angle θ to the x− axis.
• |z − a| = |z − b| is the perpendicular bisector of the line joining a to b.
• The equation of a line joining z₁ & z₂ is given by;
  z = z₁ + t (z₁ − z₂) where t is a parameter.
•  z = z₁ (1 + it) where t is a real parameter is a line through the point z₁ & perpendicular to oz₁.
• The equation of a line passing through z₁ & z₂ can be expressed in the determinant form as
  
  This is also the condition for three complex numbers to be collinear.
• Complex equation of a straight line through two given points z₁ & z₂ can be written as
  which on manipulating takes the form as where r is real and α is a non zero complex constant.
• The equation of circle having center z₀ & radius ρ is: |z − z₀| = ρ or
  which is of the form , r is real centre − α & radius
  . Circle will be real if .
• The equation of the circle described on the line segment joining z₁ & z₂ as diameter is:
  
• Condition for four given points z₁, z₂, z₃ & z₄ to be concyclic is, the number .  is real. Hence the equation of a circle through 3 non collinear points z₁, z₂ & z₃ can be taken as    is real ⇒

Reflection points for a straight line: Two given points P & Q are the reflection points for a given straight line if the given line is the right bisector of the segment PQ. Note that the two points denoted by the complex numbers z₁ & z₂ will be the reflection points for the straight line if and only if; where r is real and α is non zero complex constant.

Inverse points w.r.t. a circle:
Two points P & Q are said to be inverse w.r.t. a circle with center ‘O’ and radius ρ, if :

• the point O, P, Q are collinear and on the same side of O.
• OP. OQ = ρ².

Note that the two points z₁ & z₂ will be the inverse points w.r.t. the circle
if and only if .

Ptolemy’s Theorem:

It states that the product of the lengths of the diagonals of a convex quadrilateral inscribed in a circle is equal to the sum of the lengths of the two pairs of its opposite sides.
i.e. |z₁ − z₃| |z₂ − z₄| = |z₁ − z₂| |z₃ − z₄| + |z₁ − z₄| |z₂ − z₃|.

Logarithm Of A Complex Quantity

• Log_e(α + iβ) = ½Log_e(α² + β²) + i( 2nπ + tan⁻¹ where n ∈ I.
• iⁱ represents a set of positive real numbers given by 

The post Complex Numbers Definition, Examples, Formulas, Polar Form, Amplitude and Application appeared first on Learn CBSE.

Quadratic Equations

Quadratic Equations have been around for centuries! Indian mathematicians Brahmagupta and Bhaskara II made some significant contributions to the field of quadratic equations. Although quadratic equations look complicated and generally strike fear among students, with a systematic approach they are easy to understand. In this Article You will find Solving of Quadratic Equations, Nature of Roots, Applications of Quadratic Roots, Quadratic Equation Formulas, Roots of Quadratic Equation, General Form of Quadratic Equation, Maximum and Minimum Value, Theory of Equations, Location of Roots, and Logarithmic Inequalities.

The general form of a quadratic equation in x is , a x² + bx + c = 0 , where a , b , c ∈ R & a ≠ 0.

• The solution of the quadratic equation , ax² + bx + c = 0 is given by x = The expression b2 – 4ac = D is called the discriminant of the quadratic equation.
• If α & β are the roots of the quadratic equation ax² + bx + c = 0, then;
  (i) α + β = – b/a
  (ii) α β = c/a
  (iii) α – β =
• Nature Of Roots:
  (A) Consider the quadratic equation ax² + bx + c = 0 where a, b, c ∈ R & a≠ 0 then
  (i) D > 0 ⇔ roots are real & distinct (unequal).
  (ii) D = 0 ⇔ roots are real & coincident (equal).
  (iii) D < 0 ⇔ roots are imaginary.
  (iv) If p + i q is one root ofa quadratic equation, then the other must be the conjugate p − i q & vice versa. (p , q ∈ R & i = )
  (B) Consider the quadratic equation ax2 + bx + c = 0 where a, b, c ∈ Q & a ≠ 0 then;
  (i) If D > 0 & is a perfect square , then roots are rational & unequal.
  (ii) If α = p + is one root in this case, (where p is rational & q is a surd) then the other root must be the conjugate of it i.e. β = p − & vice versa.
• A quadratic equation whose roots are α & β is (x − α)(x − β) = 0 i.e.
  x² − (α + β) x + α β = 0 i.e. x² − (sum of roots) x + product of roots = 0.
• Remember that a quadratic equation cannot have three different roots & if it has, it becomes an identity.
• Consider the quadratic expression , y = ax² + bx + c , a ≠ 0 & a , b , c ∈ R then
  (i) The graph between x , y is always a parabola . If a > 0 then the shape of the parabola is concave upwards & if a < 0 then the shape of the parabola is concave downwards.
  (ii) ∀ x ∈ R , y > 0 only if a > 0 & b² − 4ac < 0 (figure 3) .
  (iii) ∀ x ∈ R , y < 0 only if a < 0 & b² − 4ac < 0 (figure 6) .
  Carefully go through the 6 different shapes of the parabola given below.
  
• Solution Of Quadratic Inequalities:
  ax² + bx + c > 0 (a ≠ 0).
  (i) If D > 0, then the equation ax² + bx + c = 0 has two different roots x₁ < x₂.
  Then a > 0 ⇒ x ∈ (−∞, x₁) ∪ (x₂, ∞)
  a < 0 ⇒ x ∈ (x₁, x₂)
  (ii) If D = 0, then roots are equal, i.e. x₁ = x₂.
  In that case a > 0 ⇒ x ∈ (−∞, x₁) ∪ (x₁, ∞)
  a < 0 ⇒ x ∈ φ
  (iii)Inequalities of the form 0 can be quickly solved using the method of intervals.
• Maximum & Minimum Value of y = ax² + bx + c occurs at x = − (b/2a) according as ; a < 0 or a > 0.
• Common Roots of 2 Quadratic Equations [Only One Common Root]:
  Let α be the common root of ax² + bx + c = 0 & a′x2 + b′x + c′ = 0 Thereforea α² + bα + c = 0 ; a′α² + b′α + c′ = 0. By Cramer’s Rule   Therefore, α = . So the condition for a common root is (ca′ − c′a)² = (ab′ − a′b)(bc′ − b′c).
• The condition that a quadratic function
  f(x , y) = ax² + 2 hxy + by² + 2 gx + 2 fy + c may be resolved into two linear factors is that;  abc + 2 fgh − af2 − bg2 − ch2 = 0 OR
  
• Theory of Equations: If α₁, α₂, α₃, ……α_n are the roots of the equation;
  f(x) = a₀xⁿ + a₁x^n-1 + a₂x^n-2 + …. + a_n-1x + a_n = 0 where a₀, a₁, …. a_n are all real & a₀ ≠ 0 then, ,
  Note:
  (i) If α is a root of the equation f(x) = 0, then the polynomial f(x) is exactly divisible by (x − α) or (x − α) is a factor of f(x) and conversely .
  (ii) Every equation of nth degree (n ≥ 1) has exactly n roots & if the equation has more than n roots, it is an identity.
  (iii) If the coefficients of the equation f(x) = 0 are all real and α + iβ is its root, then α − iβ is also a root. i.e. imaginary roots occur in conjugate pairs.
  (iv) If the coefficients in the equation are all rational & α + is one of its roots, then α − is also a root where α, β ∈ Q & β is not a perfect square.
  (v) If there be any two real numbers ‘a’ & ‘b’ such that f(a) & f(b) are of opposite signs, then f(x) = 0 must have atleast one real root between ‘a’ and ‘b’ .
  (vi) Every eqtion f(x) = 0 of degree odd has atleast one real root of a sign opposite to that of its last term.
• Location Of Roots: Let f(x) = ax² + bx + c, where a > 0 & a, b, c ∈ R.
  (i) Conditions for both the roots of f (x) = 0 to be greater than a specified number ‘d’ are b² − 4ac ≥ 0; f(d) > 0 & (− b/2a) > d.
  (ii) Conditions for both roots of f(x) = 0 to lie on either side of the number ‘d’ (in other words the number ‘d’ lies between the roots of f(x) = 0) is f(d) < 0.
  (iii) Conditions for exactly one root of f(x) = 0 to lie in the interval (d , e) i.e. d < x < e are b²− 4ac > 0 & f(d) . f(e) < 0.
  (iv) Conditions that both roots of f(x) = 0 to be confined between the numbers p & q are (p < q). b2 − 4ac ≥ 0; f(p) > 0; f(q) > 0 & p < (− b/2a) < q.
• Logarithmic Inequalities
  (i) For a > 1 the inequality 0 < x < y & log_a x < log_a y are equivalent.
  (ii) For 0 < a < 1 the inequality 0 < x < y & log_a x > log_a y are equivalent.
  (iii) If a > 1 then log_a x < p ⇒ 0 < x < a^p
  (iv) If a > 1 then log_a x > p ⇒ x > a^p
  (v) If 0 < a < 1 then log_a x < p ⇒ x > a^p
  (vi) If 0 < a < 1 then log_a x > p ⇒ 0 < x < a^p

The post Solving of Quadratic Equations, Nature of Roots, Formulas, Applications and Examples appeared first on Learn CBSE.

Results:

• A Useful Notation : n! = n (n − 1) (n − 2)……… 3. 2. 1 ; n ! = n. (n − 1) !0! = 1! = 1 ; (2n)! = 2n. n ! [1. 3. 5. 7…(2n − 1)] Note that factorials of negative integers are not defined.
• If ⁿP_r denotes the number of permutations of n different things, taking r at a time, then
  
• If ⁿC_r denotes the number of combinations of n different things taken r at a time, then
  where r ≤ n ; n ∈ N and r ∈ W.
• The number of ways in which (m + n) different things can be divided into two groups containing m & n things respectively is: If m = n, the groups are equal & in this case the number of subdivision is ; for in any one way it is possible to interchange the two groups without obtaining a new distribution. However, if 2n things are to be divided equally between two persons then the number of ways 
• Number of ways in which (m + n + p) different things can be divided into three groups containing m , n & p things respectively is ,  m ≠ n ≠ p. If m = n = p then the number of groups   . However, if3n things are to be divided equally among three people then the number of ways
• The number of permutations of n things taken all at a time when p of them are similar & of one type, q of them are similar & of ano ther type, r o f them are similar & of a third type & the remaining n – (p + q + r) are all different is:
• The number of circular permutations of n different things taken all at a time is ; (n − 1)!. If clockwise & anti−clockwise circular permutations are considered to be same, then it is
  Note: Number of circular permutations of n things when p alike and the rest different taken all at a time distinguishing clockwise and anticlockwise arrangement is
• Given n different objects, the number of ways of selecting atleast one of them is , ⁿC₁ + ⁿC₂ + ⁿC₃ +…..+ ⁿC_n = 2ⁿ − 1. This can also be stated as the total number of combinations of n distinct things.
• Total number of ways in which it is possible to make a selection by taking some or all out of p + q + r +…… things , where p are alike of one kind, q alike of a second kind , r alike of third kind & so on is given by: (p + 1) (q + 1) (r + 1)…….. –1.
  (x) Number of ways in which it is possible to make a selection of m + n + p = N things , where p are alike of one kind , m alike of second kind & n alike of third kind taken r at a time is given by coefficient of x^r in the expansion of (1 + x + x² +…… + x^p) (1 + x + x² +…… + x^m) (1 + x + x² +…… + xⁿ).
  Note: Remember that coefficient of x^r in (1 − x)^-n = ^n+r-1C_r (n ∈ N). For example the number of ways in which a selection of four letters can be made from the letters of the word Proportion is given by coefficient of x⁴ in (1 + x + x² + x³) (1 + x + x²) (1 + x + x²) (1 + x) (1 + x) (1 + x).
• Number of ways in which n distinct things can be distributed to p persons if there is no restriction to the number of things received by men = pⁿ.
• Number of ways in which n identical things may be distributed among p persons if each person may receive none , one or more things is ; ^n+p−1C_n.
• a. ⁿC_r = ⁿCn−r ; ⁿC₀ = ⁿC_n = 1;
  b. ⁿC_x = ⁿC_y ⇒ x = y or x + y = n
  c. ⁿC_r + ⁿC_r-1 = ⁿ⁺¹C_r
• ⁿC_r is maximum if :
  (a) if n is even.
  (b) if n is odd.
• Let N = p^a. q^b. r^c…… where p , q , r…… are distinct primes & a , b , c….. are natural numbers then:
  (a) The total numbers of divisors of N including 1 & N is = (a + 1)(b + 1)(c + 1)…..
  (b) The sum of these divisors is = (p⁰ + p¹ + p² +…. + p^a) (q⁰ + q¹ + q² +…. + q³) (r⁰ + r¹ + r² +…. + r^c)….
  (c) Number of ways in which N can be resolved as a product of two factors is = if N is not a perfect square
  if N is a perfect square
  (d) Number of ways in which a composite number N can be resolved into two factors which are relatively prime (or coprime) to each other is equal to 2^n-1 where n is the number of different prime factors in N. [ Refer Q.No.28 of Ex−I ]
• Grid Problems and tree diagrams.
  Dearrangement: Number of ways in which n letters can be placed in n directed letters so that no letter goes into its own envelope is
• Some times students find it difficult to decide whether a problem is on permutation or combination or both. Based on certain words/phrases occurring in the problem we can fairly decide its nature as per the following table:
• Problems on Combinations
  • Selections, choose
  • Distributed group is formed
  • Committee
  • Geometrical problems
• Problems on Permutations
  • Arrangements
  • Standing in a line seated in a row
  • problems on digits
  • Problems on letters from a word

The post Permutation and Combination Questions, Formulas and Examples appeared first on Learn CBSE.

Matrices

1. Definition: Rectangular array of mn numbers. Unlike determinants, it has no value.

Abbreviated as: A = [ a_ij ] 1 ≤ i ≤ m ; 1 ≤ j ≤ n, i denotes the row and j denotes the column is called a matrix of order m × n.

2. Special Type Of Matrices:

• Row Matrix: A = [ a₁₁ , a₁₂ , …… a_1n ] having one row . (1 × n) matrix. (or row vectors)
• Column Matrix:
  
  having one column. (m × 1) matrix (or column vectors)
• Zero or Null Matrix: (A = O_m×n ) An m × n matrix all whose entries are zero .
  
  is a 3 × 2 null matrix &
  
  is 3 × 3 null matrix
• Horizontal Matrix: A matrix of order m × n is a horizontal matrix if n > m.
  
• Verical Matrix: A matrix of order m × n is a vertical matrix if m > n.
  
• Square Matrix: (Order n)If number of row = number of column ⇒ a square matrix.
  Note:
  (i) In a square matrix the pair of elements a_ij & a_ji are called Conjugate Elements .e.g.
  
  (ii) The elements a₁₁ , a₂₂ , a₃₃ , …… a_nn are called Diagonal Elements . The line along which the diagonal elements lie is called “Principal or Leading” diagonal. The qty Σ a_ii = trace of the matrice written as , i.e. t_r A Triangular Matrix Diagonal Matrix denote as ddia (d₁ , d₂ , ….., d_n) all elements except the leading diagonal are zero diagonal Matrix Unit or Identity Matrix
  Note: Min. number of zeros in a diagonal matrix of order n = n(n – 1) “It is to be noted that with square matrix there is a corresponding determinant formed by the elements of A in the same order.”

3. Equality Of Matrices:
Let A = [a_ij ] & B = [b_ij ] are equal if ,

• both have the same order.
• a_ij = b_1ij for each pair of i & j.

4.Algebra Of Matrices:
Addition: A + B = [ a_ij + b_ij ] where A & B are of the same type. (order)

• Addition of matrices is commutative. i.e. A + B = B + A, A = m × n; B = m × n
• Matrix addition is associative .(A + B) + C = A + (B + C) Note : A , B & C are of the same type.
• Additive inverse. If A + B = O = B + A A = m × n

5. Multiplication Of A Matrix By A Scalar:

6.Multiplication Of Matrices: (Row by Column)AB exists if, A = m × n & B = n × p 2 × 3 3 × 3
AB exists , but BA does not ⇒ AB ≠ BA
Note: In the product AB,

A = (a₁ , a₂ , …… a_n) &

1 × n n × 1 A B = [a₁b₁ + a₁b₂ + …… + a_nb_n]
If A = [ a_ij ] m × n & B = [ b_ij] n × p  matrix , then

Properties Of Matrix Multiplication:

• Matrix multiplication is not commutative.
  
• 
  ⇒ AB = O ⇒/ A = O or B = O
  Note: IfA and B are two non- zero matrices such that AB = O then A and B are called the divisors of zero. Also if [AB] = O ⇒ |AB| ⇒ |A||B| = 0 ⇒ |A| = 0 or |B| = 0 but not the converse. IfA and B are two matrices such that
  (i) AB = BA ⇒ A and B commute each other
  (ii) AB = – BA ⇒ A and B anti commute each other

3. Matrix Multiplication Is Associative:
If A , B & C are conformable for the product AB & BC, then (A . B) . C = A . (B . C)

4. Distributivity:

Provided A, B & C are conformable for respective products

5. Positive Integral Powers Of A Square Matrix:
For a square matrix A , A² A = (A A) A = A (A A) = A³.
Note that for a unit matrix I of any order, I^m = I for all m ∈ N.

6. Matrix Polynomial:
If f (x) = a₀xⁿ + a₁x^n-1 + a₂x^n-2  + ……… + a_nx⁰ then we define a matrix polynomial f(A) = a₀Aⁿ + a₁A^n-1 + a₂A^n-2 + ….. + a_nIⁿ where A is the given square matrix. If f (A) is the null matrix then A is called the zero or root of the polynomial f (x).
Definitions:

• Idempotent Matrix: A square matrix is idempotent provided A² = A.
  Note that Aⁿ = A ∀ n ≥ 2, n ∈ N.
• Nilpotent Matrix: A square matrix is said to be nilpotent matrix of order m, m ∈ N, if A^m = O , A^m-1 ≠ O.
• Periodic Matrix: A square matrix is which satisfies the relation A^k+1 = A, for some positive integer K, is a periodic matrix. The period of the matrix is the least value of K for which this holds true.
  Note that period of an idempotent matrix is 1.
• Involutary Matrix: IfA² = I, the matrix is said to be an involutary matrix.
  Note that A = A^-1 for an involutary matrix.

7. The Transpose Of A Matrix: (Changing rows & columns)
Let A be any matrix. Then, A = a_ij of order m × n
⇒ AT or A′ = [ a_ij ] for 1 ≤ i ≤ n & 1 ≤ j ≤ m of order n × m
Properties of Transpose of a Matrix:
If A^T & B^T denote the transpose of A and B ,

• (A ± B)^T = A^T ± B^T ; note that A & B have the same order.
• (AB)^T = B^TA^T A & B are conformable for matrix product AB.
• (AT)^T = A
• (kA)^T = kA^T k is a scalar.
• General : (A₁, A₂, …… A_n)^T = A_n^T , ……. , A₂^T , A₁^T (reversal law for transpose)

8. Symmetric & Skew Symmetric Matrix:
A square matrix A = [ a_ij] is said to be , symmetric if, a_ij = a_ji ∀ i & j (conjugate elements are equal)
(Note A = A^T)
Note: Max. number of distinct entries in a symmetric matrix of order n is
and skew symmetric if , a_ij = − a_ji  ∀ i & j (the pair of conjugate elements are additive inverse of each other) (Note A = –AT ) Hence If A is skew symmetric, then a_ii = − aii ⇒ a_ii = 0 ∀ i Thus the digaonal elements of a skew symmetric matrix are all zero , but not the converse.
Properties Of Symmetric & Skew Matrix:

• Property 1: A is symmetric if A^T = A
  s skew symmetric if A^T = − A
• Property 2: A + ATis a symmetric matrix A − AT is a skew symmetric matrix. Consider (A + A^T)^T = A^T + (A^T)^T = A^T + A = A + A^T
  A + A^T is symmetric.
  Similarly, we can prove that A − A^T is skew symmetric.
• Property 3: The sum of two symmetric matrix is a symmetric matrix and the sum of two skew symmetric matrix is a skew symmetric matrix. Let A^T = A; B^T = B where A & B have the same order. (A + B)^T = A + B Similarly we can prove the other.
• Property 4: If A & B are symmetric matrices then,
  (a) AB + BA is a symmetric matrix
  (b) AB − BA is a skew symmetric matrix .
• Property 5: Every square matrix can be uniquely expressed as a sum of a symmetric and a skew symmetric matrix.
  

9. Adjoint Of A Square Matrix:
Let

be a square matrix and let the matrix formed by the cofactors of [a_ij ] in determinant

Then,

Theorem: A (adj. A) = (adj. A).A = |A| In , If A be a square matrix of order n.
Note: If A and B are non singular square matrices of same order, then
(i) |adj A| = |A|^n-1
(ii) adj (AB) = (adj B) (adj A)
(iii) adj(KA) = K^n-1 (adj A), K is a scalar
Inverse Of A Matrix (Reciprocal Matrix): A square matrix A said to be invertible (non singular) if there exists a matrix B such that, AB = I = BA
B is called the inverse (reciprocal) of A and is denoted by A^-1. Thus
A^-1 = B ⇔ AB = I = BA . We have,  A . (adj A) = |A| I_n
A^-1 A (adj A) = A^-1I|Α|;
I_n (adj A) = A^-1  |A| I_n
∴
Note: The necessary and sufficient condition for a square matrix A to be invertible is that |A| ≠ 0.
Theorem: IfA & B are invertible matrices ofthe same order , then (AB)^-1 = B^-1 A^-1 . This is reversal law for inverse
Note: (i)If A be an invertible matrix , then A^T is also invertible & (A^T)^-1 = (A^-1)^T .
(ii) If A is invertible, (a) (A −1) −1 = A ; (b) (A^k)^-1 = (A^-1)k = A^-k, k ∈ N
(iii) IfA is an Orthogonal Matrix. AA^T= I = A^T
(iv) A square matrix is said to be orthogonal if , A^-1= A^T.

System Of Equation & Criterian For Consistency
Gauss – Jordan Method
x + y + z = 6, x − y + z = 2, 2 x + y − z = 1
or

A X = B ⇒ A −1 A X = A −1 B ⇒

Note:
(1)If |A| ≠ 0, system is consistent having unique solution
(2)If |A| ≠ 0 & (adj A) . B ≠ O (Null matrix) , system is consistent having unique non − trivial solution.
(3) If |A| ≠ 0 & (adj A) . B = O (Null matrix) , system is consistent having trivial solution
(4) If

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Geometric Progression (GP) | Sequences and Series

GP is a sequence of numbers whose first term is non zero & each of the succeeding terms is equal to the proceeding terms multiplied by a constant . Thus in a GP the ratio of successive terms is constant. This constant factor is called the COMMON RATIO of the series & is obtained by dividing any term by that which immediately proceeds it. Therefore a, ar, ar², ar³, ar⁴, …… is a GP with a as the first term & r as common ratio.

• nth term = ar^{n –1}
• Sum of the Ist n terms i.e.
• Sum of an infinite GP when |r| < 1 when n → ∞ rⁿ → 0 if |r| < 1 therefore,
  
• If each term of a GP be multiplied or divided by the same non-zero quantity, the resulting sequence is also a GP.
• Any 3 consecutive terms of a GP can be taken as a/r, a, ar; any 4 consecutive terms of a GP can be taken as a/r³, a/r, ar, ar³ & so on.
• If a, b, c are in GP ⇒ b² = ac.

Harmonic Progression (HP) | Sequences and Series

A sequence is said to HP if the reciprocals of its terms are in AP.If the sequence a1, a2, a3, …. , an is an HP then 1/a1, 1/a2, …. , 1/an is an AP & converse. Here we do not have the formula for the sum of the n terms of an HP. For HP whose first term is a & second term is b, the nth term is

If a, b, c are in HP ⇒

Sequences and Series | Means

Arithmetic Mean:
If three terms are in AP then the middle term is called the AM between the other two, so if a, b, c are in AP, b is AM of a & c . AM for any n positive number a₁, a₂, … , a_n is ;

n – Arithmetic Means Between Two Numbers:
If a, b are any two given numbers & a, A₁, A₂, …. , A_n, b are in AP then A₁, A₂, … A_n are the n AM’s between a & b.

where
Note: Sum of n AM’s inserted between a & b is equal to n times the single AM between a & b i.e.
where A is the single AM between a & b.

Geometric Means:
If a, b, c are in GP, b is the GM between a & c.
b² = ac, therefore b = ; a > 0, c > 0.
n-Geometric Means Between a, b:
If a, b are two given numbers & a, G₁, G₂, ….. , G_n, b are in GP. Then
G₁, G2, G₃ , …., G_n are n GMs between a & b
G₁ = a(b/a)^{1 /n+1} ,G₂ = a(b/a)^{2 /n+1} = ar , ……., G_n = a(b/a)^{n /n+1} = ar ,
G₁ = ar ,                G₂ = ar² ,                      ……., G_n = arⁿ ,  where r = (b/a)^{1 /n+1}

Note: The product of n GMs between a & b is equal to the n^th power of the single GM between a & b  i.e.

where G is the single GM between a & b.

Harmonic Mean:
If a, b, c are in HP, b is the HM between a & c, then b = 2ac/[a + c].
Theorem:
If A, G, H are respectively AM, GM, HM between a & b both being unequal & positive then,

• G² = AH
• A > G > H (G > 0). Note that A, G, H constitute a GP.

Arithmetic-Geometric Series | Sequences and Series

A series each term of which is formed by multiplying the corresponding term of an AP & GP is called the Arithmetico-Geometric Series. e.g. 1 + 3x + 5x² + 7x³ + …..
Here 1, 3, 5, …. are in AP & 1, x, x², x³ ….. are in GP.
Standard appearance of an Arithmetic-Geometric Series is
Let S_n = a + (a + d) r + (a + 2 d) r² + ….. + [a + (n − 1)d] rⁿ⁻¹
Sum To Infinity:
If |r| < 1 & n → ∞ then

Sigma Notations Theorems:

• 
  where k is a constant.

Results:

•   (sum of the first n natural nos.)
•   (sum of the squares of the first n natural numbers)
•   (sum of the cubes of the first n natural numbers)

Method Of Difference | Sequences and Series

If T₁, T₂, T₃, …… , T_n are the terms of a sequence then some times the terms T₂ − T₁, T₃ − T₂ , ……. constitute an AP/GP. n^th term of the series is determined & the sum to n terms of the sequence can easily be obtained.
Remember that to find the sum of n terms of a series each term of which is composed of r factors in AP, the first factors of several terms being in the same AP, we “write down the nth term, affix the next factor at the end, divide by the number of factors thus increased and by the common difference and add a constant. Determine the value of the constant by applying the initial conditions”.

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Probability Formulas

Introduction to Probability

• Sample–Space: The set of all possible outcomes of an experiment is called the Sample–Space(S).
• Event: A subset of sample−space is called an Event.
• Complement Of An Event A: The set of all out comes which are in S but not in A is called the Complement Of An Event A Denoted By Or A^c.
• Compound Event: If A & B are two given events then A∩B is called Compound Event and is denoted by A∩B or AB or A & B.
• Mutually Exclusive Events: Two events are said to be Mutually Exclusive Events (or disjoint or incompatible) if the occurence of one precludes (rules out) the simultaneous occurence of the other. If A & B are two mutually exclusive events then P (A & B) = 0.
• Equally Likely Events: Events are said to be Equally Likely when each event is as likely to occur as any other event.
• Exhaustive Events: Events A,B,C …….. L are said to be Exhaustive Events if no event outside this set can result as an outcome of an experiment. For example, if A & B are two events defined on a sample space S, then A & B are exhaustive ⇒ A∪B = S⇒ P (A∪B) = 1.
• Classical Def. Of Probability: If n represents the total number of equally likely, mutually exclusive and exhaustive outcomes of an experiment and m of them are favourable to the happening of the event A, then the probability of happening of the event A is given by P(A) = m/n.
  Note:
  (1) 0 ≤ P(A) ≤ 1
  (2) P(A) + P( ) = 1, Where = Not A .
  (3) If x cases are favourable to  & y cases are favourable to A then P(A) = and P( ) =
  We say that Odds In Favour Of A are x: y & odds against A are y : x

Comparative study of Equally likely , Mutually Exclusive and Exhaustive events.

Results − 2

AUB = A+ B = A or B denotes occurence of at least A or B. For 2 events A & B : (See fig.1)

• P(A∪B) = P(A) + P(B) − P(A∩B) = P(A. ) + P( .B) + P(A.B) = 1 − P( )
• Opposite of “atleast A or B” is Niether A nor B i.e. = 1-(A or B) = ∩
  Note that P(A+B) + P( ) = 1.
• IfA & B are mutually exclusive then P(A∪B) = P(A) + P(B).
• For any two events A & B, P(exactly one of A , B occurs)
  = P (A ∩ ) + P (B ∩ ) = P (A) + P (B) − 2P (A ∩ B)
  = P (A ∪ B) − P (A ∩ B) = P (A^c ∪ B^c ) − P(A^c ∩ B^c )
• If A & B are any two events P(A∩B) = P(A).P(B/A) = P(B).P(A/B), Where P(B/A) means conditional
  probability of B given A & P(A/B) means conditional probability ofA given B. (This can be easily seen
  from the figure)
• DE MORGAN’S LAW : − IfA & B are two subsets of a universal set U , then
  • (A∪B)c = Ac∩Bc &
  • (A∩B)c = Ac∪Bc
• A ∪ (B∩C) = (A∪B) ∩ (A∪C) & A ∩ (B∪C) = (A∩B) ∪ (A∩C)

Result − 3

For any three events A,B and C we have (See Fig. 2)

• P(A or B or C) = P(A) + P(B) + P(C) − P(A∩B) − P(B∩C)− P(C∩A) + P(A∩B∩C)
• P (at least two of A,B,C occur) = P(B∩C) + P(C∩A) + P(A∩B) − 2P(A∩B∩C)
• P(exactly two of A,B,C occur) = P(B∩C) + P(C∩A) + P(A∩B) − 3P(A∩B∩C)
• P(exactly one of A,B,C occurs) = P(A) + P(B) + P(C) − 2P(B∩C) − 2P(C∩A) − 2P(A∩B)+3P(A∩B∩C)
  Note: If three events A, B and C are pair wise mutually exclusive then they must be mutually exclusive.
  i.e P(A∩B) = P(B∩C) = P(C∩A) = 0 ⇒ P(A∩B∩C) = 0. However the converse of this is not true.

Result − 4
Independent Events: Two events A & B are said to be independent if occurence or non occurence of one does not effect the probability of the occurence or non occurence of other.

• If the occurence of one event affects the probability of the occurence of the other event then the events are said to be Dependent or Contingent. For two independent events A and B : P(A∩B) = P(A). P(B). Often this is taken as the definition of independent events.
• Three events A , B & C are independent if & only if all the following conditions hold;
  P(A∩B) = P(A) . P(B) ; P(B∩C) = P(B) . P(C)
  P(C∩A) = P(C) . P(A) & P(A∩B∩C) = P(A) . P(B) . P(C)
  i.e. they must be pairwise as well as mutually independent.
  Similarly for n events A₁, A₂, A₃, …… A_n to be independent, the number of these conditions is equal to ⁿc₂ + ⁿc₃ + ….. + ⁿc_n = 2ⁿ − n − 1.
• The probability of getting exactly r success in n independent trials is given by P(r) = ⁿC_r p^r q^n-r
  where: p = probability of success in a single trial q = probability of failure in a single trial. note : p + q = 1
  Note: Independent events are not in general mutually exclusive & vice versa. Mutually exclusiveness can be used when the events are taken from the same experiment & independence can be used when the events are taken from different experiments.

Result − 5:
Baye’s Theorem Or Total Probability Theorem:
If an event A can occur only with one of the n mutually exclusive and exhaustive events B₁, B₂,… B_n & the probabilities P(A/B₁), P(A/B₂) ……. P(A/B_n) are known then,


Proof:
The events A occurs with one of the n mutually exclusive & exhaustive events B₁, B₂,B₃,……..B_n; A = AB₁ + AB₂ + AB₃ + ……. + AB_n

Note: A ≡ event what we have;
B₁ ≡ event what we want ;
B₂, B₃, ….B_n are alternative event .
Now, P(AB_i) = P(A) . P(B_i/A)
= P(B_i) . P(A/B_i)

Result − 6
If p1 and p2 are the probabilities of speaking the truth of two indenpendent witnesses A and B thenP (their combined statement is true)

In this case it has been assumed that we have no knowledge of the event except the statement made by A and B. However, if p is the probability of the happening of the event before their statement then P (their combined statement is true)

Here it has been assumed that the statement given by all the independent witnesses can be given in two ways only, so that if all the witnesses tell falsehoods they agree in telling the same falsehood. If this is not the case and c is the chance of their coincidence testimony then the Pr. that the statement is true = P p₁ p₂ Pr. that the statement is false = (1−p).c (1−p₁)(1−p₂)
However, chance of coincidence testimony is taken only if the joint statement is not contradicted by any witness.

Result − 7

• A Probability Distribution spells out how a total probability of 1 is distributed over several values of a random variable.
• Mean of any probability distribution of a random variable is given by
    ( Since Σ p_i = 1 )
• Variance of a random variable is given by, σ² = ∑ ( x_i − µ)² . pi
  σ² = ∑ p_i x²_i − µ² ( Note that SD = + )
• The probability distribution for a binomial variate ‘X’ is given by; P ( X = r ) = ⁿC_rpⁿ q^n-r  where all symbols have the same meaning as given in result 4. The recurrence formula
  is very helpful for quickly computing P(1) , P(2). P(3) etc. if P(0) is known.
• Mean of BPD = np ; variance of BPD = npq.
• If p represents a persons chance of success in any venture and ‘M’ the sum of money which he will receive in case of success, then his expectations or probable value = pM expectations = pM

Result − 8:
Geometrical Applications: The following statements are axiomatic:

• If a point is taken at random on a given staright line AB, the chance that it falls on a particular segment PQ of the line is PQ/AB .
• If a point is taken at random on the area S which includes an area σ, the chance that the point falls on σ is σ/S .

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Relations and Functions

Relations and Functions: If to every value of x belonging to some set E there corresponds one or several values of the variable y, then y is called a multiple valued function of x defined on E.Conventionally the word “FUNCTION” is used only as the meaning of a single valued function, if not otherwise stated. Pictorially:
y is called the image of x & x is the pre-image of y under f. Every function from A → B
satisfies the following conditions.

• f ⊂ A x B
• ∀ a ∈ A ⇒ (a, f(a)) ∈ f and
• (a, b) ∈ f & (a, c) ∈ f ⇒ b = c

Domain, Co−Domain & Range Of A Function

Let f : A → B, then the set A is known as the domain of f & the set B is known as co-domain of f. The set of all f images of elements of A is known as the range of f. Thus

Domain of f = { a | a ∈ A, (a, f(a)) ∈ f} Range of f = { f(a) | a ∈ A, f(a) ∈ B}
It should be noted that range is a subset of co−domain. If only the rule of function is given then the domain of the function is the set of those real numbers, where function is defined. For a continuous function, the interval from minimum to maximum value of a function gives the range.

Important Types Of Functions

• Polynomial Function:
  If a function f is defined by f (x) = a₀xⁿ + a₁x^n-1 + a₂x^n-2 + … + a_n-1x + a_n where n is a non negative integer and a₀, a₁, a₂, …, a_n are real numbers and a₀ ≠ 0, then f is called a polynomial function of degree n
  Note:
  (a) A polynomial of degree one with no constant term is called an odd linear function. i.e. f(x) = ax , a ≠ 0
  (b) There are two polynomial functions, satisfying the relation; f(x).f(1/x) = f(x) + f(1/x). They are:
  (i) f(x) = xⁿ + 1 &
  (ii) f(x) = 1 − xⁿ , where n is a positive integer.
• Algebraic Function: y is an algebraic function of x if it is a function that satisfies an algebraicequation of the form
  P₀(x) yⁿ + P₁ (x) y^n-1 + ……. + P_n-1 (x) y + P_n (x) = 0 Where n is a positive integer and
  P₀(x), P₁(x) ……….. are Polynomials in x.
  e.g. y = |x| is an algebraic function, since it satisfies the equation y² − x² = 0.
  Note that all polynomial functions are Algebraic but not the converse. A function that is not algebraic is called Transcedental Function.
• Fractional Rational Function: A rational function is a function of the form.
  
  where g (x) & h (x) are polynomials & h (x) ≠ 0.
• Absolute Value Function: A function y = f (x) = |x| is called the absolute value function or Modulus function. It is defined as:
  
• Exponential Function: A function f(x) = a^x = e^xlna  (a > 0 , a ≠ 1, x ∈ R) is called anexponential function. The inverse of the exponential function is called the logarithmic function . i.e. g(x) = log_ax.
  Note that f(x) & g(x) are inverse of each other & their graphs are as shown.
  
• Signum Function:
  A function y= f (x) = Sgn (x) is defined as follows:
  
  
  It is also written as Sgn x = |x|/ x ; x ≠ 0 ; f (0) = 0
• Greatest Integer Or Step Up Function:
  The function y = f (x) = [x] is called the greatest integer function where [x] denotes the greatest integer less than or equal to x . Note that for:
  − 1 ≤ x < 0 ; [x] = − 1 0 ≤ x < 1 ; [x] = 0
  1 ≤ x < 2 ; [x] = 1 2 ≤ x < 3 ; [x] = 2 and so on .
  
  Properties of greatest integer function:
  
  • [x] ≤ x < [x] + 1 and x − 1 < [x] ≤ x , 0 ≤ x − [x] < 1
  • [x + m] = [x] + m if m is an integer.
  • [x] + [y] ≤ [x + y] ≤ [x] + [y] + 1
  • [x] + [− x] = 0 if x is an integer = − 1 otherwise.
• Fractional Part Function:
  It is defined as:
  g (x) = { x} = x − [x] .
  e.g. the fractional part of the no. 2.1 is
  2.1− 2 = 0.1 and the fractional part of − 3.7 is 0.3. The period of this function is 1 and graph of this function is as shown.
  

Domains And Ranges Of Common Function

Equal Or Identical Function | Relations and Functions

Two functions f & g are said to be equal if :

• The domain of f = the domain of g.
• The range of f = the range of g and
• f(x) = g(x) , for every x belonging to their common domain.
  eg. f(x) = & g(x) = are identical functions.

Classification Of Functions

One − One Function (Injective mapping):
A function f : A → B is said to be a one−one function or injective mapping if different elements of A have different f images in B. Thus for x₁, x₂ ∈ A & f(x₁), f(x₂) ∈ B , f(x₁) = f(x₂) ⇔ x₁ = x₂ or x₁ ≠ x₂ ⇔ f(x₁) ≠ f(x₂) .
Diagrammatically an injective mapping can be shown as

Note:

• Any function which is entirely increasing or decreasing in whole domain, then f(x) is one−one.
• If any line parallel to x-axis cuts the graph of the function atmost at one point, then the function is one−one.

Many–one function:
A function f : A → B is said to be a many one function if two or more elements of A have the same  f image in B. Thus f : A → B is many one if for; x₁, x₂ ∈ A, f(x₁) = f(x₂) but x₁ ≠ x₂
Diagrammatically a many one mapping can be shown as

Note:

• Any continuous function which has atleast one local maximum or local minimum, then f(x) is many−one. In other words, if a line parallel to x−axis cuts the graph of the function atleast at two points, then f is many−one.
• If a function is one−one, it cannot be many−one and vice versa.

Onto function (Surjective mapping): If the function f : A → B is such that each element in B (co−domain) is the f image of atleast one element in A, then we say that f is a function of A ‘onto’ B. Thus f : A → B is surjective iff ∀ b ∈ B, ∃ some a ∈ A such that f (a) = b.
Diagramatically surjective mapping can be shown as

Note: if range = co−domain, then f(x) is onto.

Into function:
If f : A → B is such that there exists atleast one element in co−domain which is not the image of any element in domain, then f(x) is into.
Diagrammatically into function can be shown as

Note: If a function is onto, it cannot be into and vice versa. A polynomial of degree even will always be into. Thus a function can be one of these four types:

• one−one onto (injective & surjective)
  
• one−one into (injective but not surjective)
  
• many−one onto (surjective but not injective)
  
• many−one into (neither surjective nor injective)
  

Note:
(i) If f is both injective & surjective, then it is called a Bijective mapping. The bijective functions are also named as invertible, non singular or biuniform functions.
(ii) If a set A contains n distinct elements then the number of different functions defined from A→ A is nn & out of it n ! are one one.
Identity function: The function f: A → A defined by f(x) = x ∀ x ∈ A is called the identity of A and is denoted by IA. It is easy to observe that identity function is a bijection.
Constant function: A function f: A → B is said to be a constant function if every element ofA has the same f image in B. Thus f: A → B; f(x) = c, ∀ x ∈ A, c ∈ B is a constant function. Note that the range of a constant function is a singleton and a constant function may be one-one or many-one, onto or into.

Algebraic Operations On Functions

If f & g are real valued functions of x with domain set A, B respectively, then both f & g are defined in A ∩ B. Now we define f+g, f−g, (f. g) & (f/g) as follows:

(iii) domain is { x | x ∈ A ∩ B s . t g(x) ≠ 0}.

Composite Of Uniformly & Non-Uniformly Defined Functions

Let f : A → B & g : B → C be two functions . Then the function gof : A → C defined by (gof) (x) = g (f(x)) ∀ x ∈ A is called the composite of the two functions f & g .
Diagrammatically . Thus the image of every x ∈ A under the function gof is the g−image of the f−image of x.
Note that gof is defined only if ∀ x ∈ A, f(x) is an element of the domain of g so that we can take its g-image. Hence for the product gof of two functions f & g, the range of f must be a subset of the domain of g.
Properties Of Composite Functions:
(i) The composite of functions is not commutative i.e. gof ≠ fog .
(ii) The composite of functions is associative i.e. if f, g, h are three functions such that fo (goh) & (fog) oh are defined, then fo (goh) = (fog) oh .
(iii) The composite of two bijections is a bijection i.e. if f & g are two bijections such that gof is defined, then gof is also a bijection.

Homogeneous Functions | Relations and Functions

A function is said to be homogeneous with respect to any set of variables when each of its terms is of the same degree with respect to those variables.
For example 5x² + 3y² − xy is homogeneous in x & y . Symbolically if, f(tx , ty) = tⁿ .f(x , y) then f(x , y) is homogeneous function of degree n.

Bounded Function | Relations and Functions

A function is said to be bounded if |f(x)| ≤ M , where M is a finite quantity.

Implicit & Explicit Function | Relations and Functions

A function defined by an equation not solved for the dependent variable is called an Implicit Function. For eg. the equation x³+y³ = 1 defines y as an implicit function. If y has been expressed in terms of x alone then it is called an Explicit Function.

Inverse of A Function | Relations and Functions

Let f : A → B be a one−one & onto function, then their exists a unique function g : B → A such that f(x) = y ⇔ g(y) = x, ∀ x ∈ A & y ∈ B . Then g is said to be inverse of f. Thus g = f^-1: B → A = { (f(x), x) | (x, f(x)) ∈ f}.

Properties of Inverse Function

• The inverse of a bijection is unique.
• If f : A → B is a bijection & g : B → A is the inverse of f, then fog = IB and gof = I_A , where I_A & I_B are identity functions on the sets A & B respectively.
  Note that the graphs of f & g are the mirror images of each other in the line y = x . As shown in the figure given below a point (x ‘,y ‘) corresponding to y = x² (x >0) changes to (y ‘,x ‘ ) corresponding to y = , the changed form of x = .
  
• The inverse of a bijection is also a bijection .
• If f & g two bijections f : A → B , g : B → C then the inverse of gof exists and (gof)−1 = f−1o g−1

Odd and Even Functions | Relations and Functions

If f (−x) = f (x) for all x in the domain of ‘f’ then f is said to be an even function. e.g. f (x) = cos x ; g (x) = x² + 3 . If f (−x) = −f (x) for all x in the domain of‘f’ then fis said to be an odd function. e.g. f (x) = sin x ; g (x) = x³ + x .

Note:

• f (x) − f (−x) = 0 => f (x) is even & f (x) + f (−x) = 0 => f (x) is odd.
• A function may neither be odd nor even.
• Inverse of an even function is not defined.
• Every even function is symmetric about the y−axis & every odd function is symmetric about the origin.
• Every function can be expressed as the sum of an even & an odd function. e.g.
  
• only function which is defined on the entire number line & is even and odd at the same time is f(x)= 0.
• If f and g both are even or both are odd then the function f.g will be even but if any one of them is odd then f.g will be odd.

Periodic Function | Relations and Functions

A function f(x) is called periodic if there exists a positive number T (T > 0) called the period of the function such that f(x + T) = f(x), for all values of x with in the domain of x e.g. The function sin x & cos x both are periodic over 2π & tan x is periodic over π
Note:

• f (T) = f (0) = f (−T) , where ‘T’ is the period.
• Inverse of a periodic function does not exist.
• Every constant function is always periodic, with no fundamental period.
• If f(x) has a period T & g (x) also has a period T then it does not mean that f(x) + g (x) must have a period T. e.g. f(x) = |sinx| + |cosx|.
• If f(x) has a period p, then also has a period p.
• If f(x) has a period T then f(ax+b) has a period T/a (a>0).

General: If x, y are independent variables, then:

• f (xy) = f(x) + f(y) ⇒ f(x) = k ln x or f(x) = 0 .
• f(xy) = f(x) . f(y) ⇒ f(x) = xⁿ , n ∈ R
• f(x + y) = f(x) . f(y) ⇒ f(x) = a^kx.
• f(x + y) = f(x) + f(y) ⇒ f(x) = kx, where k is a constant.

The post Relations and Functions appeared first on Learn CBSE.

Inverse Trigonometric Functions (Inverse Trig Functions)

Inverse trig functions: sin^-1x , cos^-1x , tan^-1x etc. denote angles or real numbers whose sine is x , whose cosine is x and whose tangent is x, provided that the answers given are numerically smallest available. These are also written as arc sinx , arc cosx etc . If there are two angles one positive & the other negative having same numerical value, then positive angle should be taken.

Principal Values And Domains Of Inverse Circular Functions

• y = sin^-1x where −1 ≤ x ≤ 1 ;   and sin y = x.
• y = cos^-1x where −1 ≤ x ≤ 1 ; 0 ≤ y ≤ π and cos y = x.
• y = tan^-1x where x ∈ R ; and tan y = x.
• y = cosec^-1x where x ≤ − 1 or x ≥ 1 ; , y ≠ 0 and cosec y = x
• y = sec^-1x where x ≤ −1 or x ≥ 1 ; 0 ≤ y ≤ π ; and sec y = x.
• y = cot^-1x where x ∈ R , 0 < y < π and cot y = x .
  Note:
  (i) 1st quadrant is common to all the inverse functions.
  (ii) 3rd quadrant is not used in inverse functions.
  (iii) 4th quadrant is used in the Clockwise Direction i.e.

Properties Of Inverse Circular Functions | Inverse Trigonometric Functions

• Property 1:
  
  • sin (sin^-1x) = x , −1 ≤ x ≤ 1
  • cos (cos^-1x) = x , −1 ≤ x ≤ 1
  • tan (tan^-1 x) = x , x ∈ R
  • sin^-1(sin x) = x ,
  • cos^-1(cos x) = x ; 0 ≤ x ≤ π
  • tan^-1(tan x) = x ;
• Property 2:
  
  • cosec^-1x = sin^-1 ; x ≤ −1 , x ≥ 1
  • sec^-1x = cos^-1  ; x ≤ −1 , x ≥ 1
  • cot^-1x = tan^-1 ; x > 0 = π + tan^-1 ; x < 0
• Property 3:
  
  • sin^-1(−x) = − sin^-1x , −1 ≤ x ≤ 1
  • tan^-1(−x) = − tan^-1x , x ∈ R
  • cos^-1(−x) = π − cos^-1x , −1 ≤ x ≤ 1
  • cot^-1(−x) = π − cot^-1x , x ∈ R
• Property 4:
  
  • sin^-1x + cos^-1x = −1 ≤ x ≤ 1
  • tan^-1x + cot^-1x =   x ∈ R
  • cosec^-1x + sec^-1x = |x|≥1
• Property 5:
  • where x > 0 , y > 0 & xy < 1
    where x > 0 , y > 0 & xy > 1
  • where x > 0 , y > 0
• Property 6:
  
  • where x ≥ 0 ,y≥0 & (x²+y²)≤1
    Note: x²+y²≤ 1 ⇒ 0 ≤ sin^-1x + sin^-1y ≤
  •   where x≥0,y ≥ 0 & x²+y²>1
    Note: x² + y² >1 ⇒ < sin^-1x + sin^-1y < π
  •   where x > 0 , y > 0
  •   where x ≥ 0 , y ≥ 0
• Property 7:
  If tan^-1x + tan^-1y + tan^-1z =
  Note:
  (i) If tan^-1x + tan^-1y + tan^-1z = π then x + y + z = xyz
  (ii) If tan^-1x + tan^-1y + tan^-1z = then xy + yz + zx = 1
• Property 8:
  

  Note very carefully that:
  
  
  

  Remember That:
  (i) sin^-1x + sin^-1y + sin^-1z =   ⇒ x = y = z = 1
  (ii) cos^-1x + cos^-1y + cos^-1z = 3π ⇒ x = y = z = −1
  (iii) tan^-11 + tan^-12 + tan^-13 = π and tan^-11 + tan^-1 + tan^-1 =

Inverse Trigonometric Functions | Some Useful Graphs

1. y = sin^-1x , |x| ≤ 1 , y ∈

2. y = cos^-1x , |x| ≤ 1 , y ∈ [0 , π]

3. y = tan^-1x, x ∈ R , y ∈

4. y = cot^-1x, x ∈ R, y ∈ (0 , π)

5. y = sec^-1x, |x| ≥ 1, y ∈

6. y = cosec^-1x, |x| ≥ 1, y ∈

7. (a) y = sin^-1(sin x) , x ∈ R , y ∈
Periodic with period 2 π

7.(b) y = sin (sin^-1x) ,
= x, x ∈ [− 1 , 1] , y ∈ [− 1 , 1] , y is  a periodic

8. (a) y = cos^-1(cos x), x ∈ R, y ∈ [0, π],
= x periodic with period 2 π

8. (b) y = cos (cos^-1x),
= x,  x ∈ [− 1 , 1] , y ∈ [− 1 , 1], y is a periodic

9. (a) y = tan (tan^-1x) , x ∈ R , y ∈ R , y is a periodic
= x

9. (b)y = tan^-1(tan x) ,
= x
, periodic with period π

10. (a) y = cot^-1(cot x),
= x
x ∈ R − { nπ} , y ∈ (0 , π) , periodic with π

10. (b) y = cot (cot^-1x) ,
= x
x ∈ R , y ∈ R , y is a periodic

11. (a) y = cosec^-1(cosec x),
= x
x ε R − { nπ , n ε I }, y ∈
y is periodic with period 2 π

11. (b) y = cosec (cosec^-1x) ,
= x
|x| ≥ 1, |y| ≥ 1, y is aperiodic

12. (a) y = sec −1 (sec x) ,
= x
y is periodic with period 2π ;

12. (b) y = sec (sec −1 x), |x| ≥ 1 ; |y| ≥ 1], y is a periodic

The post Inverse Trigonometric Functions appeared first on Learn CBSE.

NCERT English Workbook Class 10 Solutions Unit 13 Reported Speech are part of English Workbook Class 10 Solutions. Here we have given CBSE Class 10 English Workbook Solutions Unit 13 Reported Speech.

CBSE Class 10 English Workbook Solutions Unit 13 Reported Speech

A.1.
Read and enjoy the following article.

The Road to English
(Adapted from an article by Arishban Bagchi (Hindu college) [The Hindustan Times, 4 October 1996]

1. The great question, after you have failed to put yourself in an engineering or medical college in contemporary Indian society, is whether you’ll ever find a job.
2. “Oh ! He showed such promise during his early days,” says the sister of the neighbour of your aunt in Timbuctoo. “Now look at my Bittoo,” she goes on. “In spite of being so brilliant and all, he could only barely manage a grade A+ at MIT, and then he only just managed a well-paid job. How difficult getting jobs must be.”
3. The next line reads, “I wonder how your son will find a job, being a non-engineer, and that too in India.”
4. Your father’s friend, a prosperous doctor, decides to come visiting. Quite predictably, his first question on seeing you is the inevitable, “Why in heaven’s name did you not qualify in the pre-medical test ?’ Followed by the equally inevitable, “Now what are you going to do ?”
5. He raves on about his nephew who has just gone to the UK for his FRCS, and his daughter who has just completed her MBBS from AIIMS with top results, and what exciting prospects they have.
6. Your father into whose eyes you haven’t dared to look for quite some time, speaks up. “I have lost all hope for him. However, educating him is my duty and I won’t shirk from it.”
7. Someone speaks up. “Let him go to college to study Physics or Chemistry.” Everyone sits in silence. You cannot help feeling a little proud. At length, someone plucks up the courage: “It’s quite impossible to educate him any further. Youngsters these days never seem to listen to what we have to say.”
8. “I will study English Literature,” you say, dropping a bombshell, fearless of the consequences. Amazingly, it works. The crowd hurries to disperse. You are so relieved to see their backs that you don’t care. Thankfully, your parents voice no objection, remembering, perhaps, that you did manage to score highly in English in your Board exams.
9. So you finally take English literature as your subject of study.

A. 2.
Work in pairs and list the speakers in the passage you have just read.
Answer:

1. The author (Arishban Bagchi)
2. Bittoo’s mother
3. A doctor
4. Bittoo’s father
5. Someone

Still working in pairs, answer the following.

1. Did anyone actually say (or write) “Oh ! He showed such promise during his early days ?” (Yes/No) How can you tell ?

2. Is “Now look at my Bittoo”, said by the same person as the extract in 1 above ? (Yes/No) How do you know ?

3. In paragraph 4, who says “Now what are you going to do ?”
What words help you to know ?

4. (i) ln paragraph 5, who is the speaker ? ____________
Discues and work out what must have been his exact words. Then write them below. (To be discussed as desired)
(ii) Underline the verb which tells you how the person must have said this.
[Hint: Try to work out the meaning of this verb.]

5. How many of the nine paragraphs in the passage are reporting what someone has said ?

6. How many paragraphs include the exact words of the various speakers (direct speech)?

7. How many paragraphs have reported them ‘indirectly’ (indirect speech) ?

8. What is your conclusion about how writers report what someone says or has said in a newspaper article such as this ?

Answers:

1. Yes … It has been put in ‘inverted commas’.

2. Yes … ‘she goes on’ indicates it.

3. Father’s friend, a prosperous doctor
The words which help us to know are : ‘his first question on seeing you …………..’ ‘followed by the equally inevitable, “________ ”

4. (i) Father’s friend, a prosperous doctor.
“Look at my nephew who has just gone to the UK for his FRCS, and my daughter who has just completed her MBBS from AIIMS with top results. What exciting results they have !”
(ii) The verb to be underlined is – ‘raves’
Meaning = talks furiously and wildly

5. Six

6. Six

7. Three

8. In a newspaper article, the writers report some very important words in direct speech ie, as they are spoken. They report some in indirect speech adding the words from their own side to exactly report the underlining emotions, feelings, moods or manners.

B. Reporting Verbs

B. 1.
A reporting verb is used in both direct and indirect (reported) speech. The reporting verb usually adds to the meaning of each sentence for instance, it may show the speaker’s MOOD (e.g. agreed), PURPOSE (e.g. asked), MANNER OF SPEAKER (e.g. shouted). An example is :

The tourist complained that the hotel was hot and noisy.

In this sentence, the reporting word ‘complained’ shows that the tourist was clearly unhappy about the arrangements.

Now work in groups of four. Read the following sentences carefully, and circle the reporting verbs. Then discuss and write the ways in which each reporting verb adds to the meaning of its arrangement.

1. “When I was in school, I used to skip a few classes, especially Moral Science because of the bookish manner in which it was treated,” confessed the retired IAS Officer.
2. Saurav’s friends protested that he should have been included in the school badminton team, on the basis of his fine performance in the inter-house matches.
3. “Make a circle, make a circle !” Mira shouted, firmly pulling and pushing the children till a kind of vague circle was formed.
4. The music teacher warned the children against getting carried away and getting out of tune.
5. “Father, you must tell me what you meant exactly when you said that I was the same as every other teenager,” Varun insisted.
6. “Oh God ! She is coming again,” the children whispered to each other, when they saw Mrs Sharma striding towards their classroom for the third time that day.

Answers:

1. ‘Confessed’ to be circled is the reporting verb used in the sentence. It reveals the mood of the speaker as he admits his weakness of skipping the class which was contrary to rules.
2. ‘protested’ is to be circled in the reporting verb used in the sentence.
   The verb shows Saurav’s friends’ mood.
3. ‘shouted’ is to be circled in the reporting verb in the sentence.
   ‘Shouted’ shows Mira’s mood ie, irritable manner.
4. ‘warned’ is to be circled in the reporting verb in the sentence.
   It reflects music teacher’s manner of speaking to the children ie, threatening manner.
5. ‘insisted’ is to be circled in the reporting verb in the sentence.
   This verb shows Varan’s emphatic manner.
6. ‘whispered’ is to be circled in the reporting verb in the sentence.
   This verb shows children’s tone and manner i.e. afraid and disliking.

B. 2.
Look at the following example.
See the Workbook on Page 251

The exact words of the Prime Minister : “I shall lead this great country on the path of peace and prosperity. Not only that, but I assure you that I will lower taxes and do everything in my power to reduce inflation.”

[Situation : A newsreader reports the words of the Prime Minister on the radio.]

“The new prime Minister said that he would lead the country on the path of peace and prosperity. He also promised to lower taxes and reduce inflation.”

Working in pairs, note the changes the newsreader made while reporting the PM’s speech.

Fill in the table below.

Answer:

Now do the same with this situation. The following is a conversation that took place between Neeta and Shobhna (in the presence of Shohhna’s mother) last week.

Neeta : Can I borrow ₹25 ? I have lost all my money on the bus this morning.
Shobhna : But you asked me for a loan last week as well, you haven’t repaid that yet. Sorry, But I can’t lend you any more.

Imagine it is now next week. Shobhna’s mother talks about it to her husband in her own words.

“Neeta came in last week and asked Shobhna if she could borrow twenty five rupees. She explained she had lost all her money on the bus that morning. Shobhna reminded Neeta that she had asked her for a loan the previous week as well, and still hadn’t repaid it. So she decided she couldn’t lend Neeta any more.


Answer:

Read the exact words of Mrs Bhattacharya, a resident of Park Street, Kolkata.

“Where do the two of you live ? You shouldn’t make such a noise in the street. If you do it again, I’ll have to complain to the police. So, be careful.”

Now think of a situation in which Mrs Bhattacharya has to report what she said to somebody but not exactly as she has said above (eg. to a neighbour.)
Answer:
Situation. Mrs Bhattacharya reports this to her husband.

Now report Mrs Bhattacharya’s words. Remember : You can decide whether to use direct or indirect speech forms.
Answer:
When two boys were making a loud noise, (Mrs Bhattacharya) I asked them where they lived. I advised them not to make such a noise. Then I warned them to be careful as if they did it again, I would have to complain to the police.

Work with your partner. Read the following. Decide on a likely situation in which what was said has been repeated. Then use your imagination and recreate the original (“direct”) speech.

Everyone at the hospital looked after me very well. As soon as I arrived, a nurse asked me how I felt. Then she asked me where I lived and whether she could contact my parents. I explained that you were out today, so she couldn’t contact you. After that she asked me how that accident had happened and I said I didn’t know.
Answer:
Situation. A boy telling his parents about an accident he had met that day, and how he was treated in the hospital.

Direct speech (in dialogue form)

Nurse : How do you feel?
Boy : i am feeling nervous.
Nurse : Where do you live ? Can I contact your parents ?
Boy : i live in Model Town. You can’t contact my parents because they are out today.
Nurse : Do you know how this accident happened?
Boy : i don’t know anything about it.

C. Practising Reported Speech

C.1.
Statements : Rewrite the following in reported speech :

(a) Sheela to Rashmi: “You can come and stay at my place if you’re ever in Delhi”.
(b) Anand to Renu : “I don’t know what Gayathri is doing these days. She hasn’t visited us for ages”.
(c) Teacher to Students : “We shall go on a field trip to study water pollution”.

Answer:

(a) Sheela told Rashmi that she could come and stay at her place if she was ever in Delhi.
(b) Anand told Renu that he didn’t know what Gayathri was doing those days as she had not visited them for ages.
(c) The teacher informed the students that they would go on a field trip to study water pollution.

Changes
See the Workbook on Pages 255-258

C.2.
Questions in indirect speech.

Rewrite the following in indirect speech :

(a) He said, “Who has moved into the neighbouring house ?”
(b) He said, “What have you bought for Deepawali ?”
(c) He said to me, “Why didn’t you wear your new dress for the party ?”
(d) “Is anyone there ?” he asked.
(e) “Shall I wait for the doctor or come again tomorrow ?” she asked the receptionist.

Answer:

(a) He asked who had moved into the neighbouring house.
(b) He asked her what she had bought for Deepawali.
(c) He asked me why I had not worn my new dress for the party.
(d) He enquired if anyone was there.
(e) She asked the receptionist if she would wait for the doctor or come again the following day.

Points to Remember

• If the direct question begins with a question word (when, where, who, how, why, what etc), the question word is repeated.
• Tenses, pronouns, possessive adjectives and adverbs of time and place change as in statements.
• The interrogative form of the verb changes to the affirmative form. The question mark (?) is therefore replaced by a full stop.
  • He said, “Where does she live ?”
  • He asked where she lived. .
• If the introductory verb is ‘say’, it must be changed to a verb of inquiry, e.g. ask, inquire, wonder, want to know etc.
• If the direct question does not have a question word, ‘if’ or ‘whether’ must be used.

C.3.
Commands, requests and advice in indirect speech :
Rewrite the following in indirect speech :

(a) The General said,” Move the tanks to the battlefield immediately.”
(b) “Don’t drive too fast”, the instructor said to me.
(c) “If I were you, I’d buy that property immediately”, the agent said to Anwar.
(d) “Why don’t you change into something more comfortable ?” he said to his guest.
(e) “Go on, taste it”, said the cook to the guest.

• You will notice that direct commands, requests and advice are usually expressed by a suitable reporting verb in indirect speech (Refer Section B)

Answers:

(a) The General ordered to move the tanks to the battlefield immediately.
(b) The instructor warned me not to drive too fast.
(c) The agent told Anwar that if he were him, he would buy that property immediately.
(d) He asked his guest why he didn’t change into something more comfortable.
(e) The cook urged the guest to taste it (the dish).

C.4.
Let’s, let him etc.

Examples

1. He said, “Let’s have our lunch before starting the journey”.
He suggested that they should have their lunch before starting the journey.
Or
He suggested having their lunch before starting the journey.
See the Workbook on Pages 260-261

C.5.
Exclamations
See the Workbook on Pages 261-262

C.6.
Change the following into indirect speech. Change tense and time expressions only when necessary. You may use a variety of reporting verbs from the box below.

1. “Human nature changes,” sighed the old man.
2. “We’ll win the match next week.” said Vasu optimistically,
   (reporting just after he said it)
3. “I saw him with Akanksha yesterday,” she whispered.
4. “Sanjay, I’m sorry we didn’t visit you in Bombay (now Mumbai) last week,” Arun said (reporting immediately after he said it)
5. “This rice tastes awful,” he muttered.
6. “Would you like to come to the party with us tomorrow, Gopa ?” Sushila asked, (reporting later in the week.)
7. “Please, Ma, please,” they begged. “We’ll play on the veranda and porch. We won’t take a step off the veranda.”
   (reporting immediately after)
8. “Don’t be a fool,” Raghu said roughly, pushing him aside. Even Mira said, “Stop howling, Ravi. If you want to play, you can stand at the end of the line,” and she put him there very firmly.
   (reporting immediately after)

Answers:

1. The old man exclaimed that human nature changes.
2. Vasu assured that they would win the match next week.
3. She confided that she had seen him with Akanksha the previous day or the day before.
4. Arun apologised to Sanjay saying that they hadn’t visited him in Bombay last week.
5. He complained that that rice tasted awful.
6. Sushila asked Gopa if she would like to go to the party with them the next day.
7. They pleaded their mother to let them play on the veranda and porch assuring her that they won’t take a step off the veranda.
8. Pushing him aside, Raghu warned Ravi not to be a fool. Even Mira scolded him to stop howling and putting him there very firmly she advised him to stand at the end of the line if he wanted to play.

C.7.
Correct the errors in the following sentences. Write out the correct sentence in the space provided.

1. The nurse enquired how I am.
2. He said he live in Connaught Circus.
3. They asked when I have arrived.
4. The taxi driver asked where I want to go.
5. I warn Sanjay to be careful while crossing the road.
6. Rohit couldn’t understand where all the children are gone.

Answers:

1. The nurse enquired how I was.
2. He said that he lived at Connaught (Place) Circus.
3. They asked when I had arrived.
4. The taxi driver asked where I wanted to go.
5. I warned Sanjay to be careful while crossing the road.
6. Rohit couldn’t understand where all the children were gone.

C.8.
You said that …………
Look at the horoscope page from a newspaper. Find your zodiac sign. Imagine that you have come to the end of the week and nothing has happened, according to the horoscope. Write a letter of complaint to Madam Kiran. Report what Madam Kiran said would happen and then describe what actually happened. You may wish to write something similar to the letter in the example below.

Dear Madam Kiran,

I am writing to complain about your horoscope prediction for Virgo last week.

Firstly, you said that my relationships would be successful. In fact I had terrible squabbles with my mother and with no fewer than three different friends. You assured me that there would be a new admirer in my life who would make me feel confident about my future. Well, I have a new admirer but he is making my life a misery for me …….
Answer:
I requested for his help in a friendly manner. But, he took it otherwise. This has added to my worry. Now I am in a fix what to do.

Secondly, you said that I would enjoy a new closeness or affinity with my husband. But he is still his old self. He is still indifferent and detached. I saw some silver lining in your prediction. But alas ! this has proved all wrong.

Thirdly, your prediction about the money matters proved totally wrong. On the contrary, I have been given an increment in my salary. Also, my husband has been promoted with a big raise in his salary.

I regret that your horoscope predictions for Virgo proved wrong in my case.

Yours
Pragya Verma

See the Workbook on Page 265

D. Reported Speech – Summary

D.1.
Read the following extract from Oliver Twist, a novel by Charles Dickens.

“Where is my little brother ?” cried Nancy, when she reached the police station.

“There are no little boys here, madam,” answered an officer.

“Where is he, then ?” she persisted, and began describing what oliver looked like

The officer informed her that he had been driven to the home of a gentleman in Pentonville. When Fagin heard the news, he exploded, “The boy must be found, even if we have to kidnap him.”

Working in pairs, (a) note down the reporting verbs used in the above passage. Then, (b) describe in a few words the mood or purpose of the speakers.

Reporting Verbs

1. cried
2. answered
3. persisted
4. describing
5. informed
6. exploded

Mood/Purpose/Manner

1. worried, anxious, upset,
2. polite, responsible
3. curious, emphatic, demanding
4. anxious, demanding
5. conscious of duty, responsible
6. angry, emphatic, worried, restless

D.2.
Below are some common remarks made by youngsters, their parents and guardians. They show the differences of opinions on modern music and film between the three groups. First read them carefully.

On the basis of the above comments, write an article for your school magazine, entitled : “Yesterday, Today and Tomorrow. ” Here are some tips :

1. Make your article interesting and readable by reporting the feeling in the above speech bubbles.
2. Use both ‘direct’ and ‘indirect’ ways of reporting.
3. Use a variety of reporting verbs to suit the mood, purpose, and manner of the speakers above. You may wish to use some of the reporting verbs listed below.
   
4. You may like to read the article “The Road to English” (A1) again, for some ideas.

Answers:
‘Yesterday, Today and Tomorrow’
(By: Prerna XA)

Modern music and films have undergone a drastic change for the last two decades. New electronic instruments have brought a sea-change in rhyme, rhythm and pitch in the songs. But my father’s friend has declared that it is not music. It is simply an ear¬splitting noise which almost maddens a man. My father said, “It is no music at all” because of fast beats. I tried to assert that it was lively. I asked if they could imagine a party with the sort of music that they had about 20 years ago.

And films, the elderly people don’t like modern films. My aunt protested, “The films today are so cheap that no one can see them with one’s family.” At this my friend contended, “The actors and actresses today are so natural.” Another friend of mine added that he couldn’t stand the theatrical and ‘sing-song’ way in which actors delivered their lines in old films. Modern day films are more and convincing realistic. Another uncle of mine announced that the films in their time had meaningful stories. The argument came to an end with a concluding remark of my grandfather. He said, “Everyone thinks their time was the best.”

On the whole, trends change with the changing times. ‘Change is the Law of Nature.’

D. 3.
Read the following excerpt from a newspaper report.
Tiger numbers up, but habitat a worry

New Delhi : India’s tiger population has gone up. On Monday, environment minister Jairam ramesh will announce an increase of over 100 tigers across the country at a three-day international conference of experts on tigers.

But can India keep this rising numbers intact ? According to the government’s own study on tiger reserves, India cannot hold more than 1000 to 1200 tigers, with its forests having witnessed a degradation in the last two decades.

“Where is the habitat to keep so many tigers safe ?” asked Vivek Menon, chief executive officer of the Wildlife Trust of India. “Constant habitat destruction and illegal mining is causing wildlife stress,” said Dharmendra Kandhal, a wildlife biologist.

Hindustan Times-March 28, 2011

• Where do you find sentences in direct speech in the above excerpt ?
• Why has the reporter used the exact words of Mr. Menon and Mr. Kandhal ?
• Change the sentences in direct speech to indirect speech and then read the excerpt. Does it sound better or worse ? Why ?

Answer:

• Sentences in direct speech are in the last para of the text.
  “Where is the habitat to keep so many tigers safe ?” asked Vivek Menon, chief executive officer of the Wildlife Trust of India.
  “Constant habitat destruction and illegal mining is causing wildlife stress” said Dharmendra Kandhal, a wildlife biologist.
• The reporter has used the exact words of Mr Menon and Mr Kandhal as they are very important words. It is to emphasise their viewpoints.
• Vivek Menon, chief executive officer of the Wildlife Trust of India asked where the habitat to keep so many tigers was safe. Dharmendra Kandhal, a wildlife biologist said that constant habitat destruction and illegal mining were causing wildlife stress.

— It sounds worse in Indirect speech because the meaning has changed due to past form of verbs.

D.4.
Given below are notes on a news report covering an operation by Indian Navy that nabbed 16 pirates. Using the notes write a newspaper report. Remember to use a combination of direct and indirect speech. Make the report interesting and dramatic.
Navy sinks ship, nabs 16 pirates
1.1 Indian navy- intensifying search for pirates- following approval of government for aggressive measures.

1.2 Saturday-sinking of ‘private mother ship’- 400 nautical miles west of Lakshadweep Islands.

1.3 16 pirates captured- 12 Iranian and 4 Pakistani sailors held as hostages rescued- 120 pirates captured in last two months- In earlier three operations 104 pirates captured- facing trial in Mumbai courts.

2 Saturday operation- began 10 am-naval patrol aircraft spotted ‘Morteza’- Iranian traveler used as ‘mother vessel’ by brigands- offshore patrol vessel INS Suvarna and coast Guard Ship Sangram sent to intercept Morteza- Pirates given warning- ordered to stop- but they fired- Suvarna returned limited fire- disabled Morteza- people seen abandoning ship- according to an official.

2.1 Later 16 pirates and 16 sailors picked up from the waters.

2.2 All being taken to Mumbai; will be handed over to police for investigation said official. You may write this report in 3-4 paragraphs.
Answer:
Indian navy sinks ship, nabs 16 pirates

Lakshadweep Island (PTI): India Navy has succeeded in capturing the all 16 pirates who had held 12 Iranian and 4 Pakistani sailors as hostages on Saturday in an aggressive operation. The operation began at 10:00 am. A naval patrol aircraft spotted 6 Morteza’ Iranian traveler used as mother vessel by brigands offshore patrol vessel. INS Suvarna and coast Guardship Sangram were sent to intercept ‘Morteza’.

The pirates were warned and ordered to stop but they fired. ‘Suvama’ returned limited fire. Morteza was disabled. According to an official, people were seen abandoning the ship. The ship sank in the sea area of 400 nautical miles west of Lakshadweep Islands. Later, 16 pirates and 16 sailors were picked up from the waters. All are being taken to Mumbai. “They will be handed over to police for investigation,” said an official.

In the last two months, 120 pirates have been captured. 104 pirates, who were captured in earlier three operations, are facing trials in Mumbai Court.

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NCERT English Workbook Class 10 Solutions Integrated Grammar Practice 8 are part of English Workbook Class 10 Solutions. Here we have given CBSE Class 10 English Workbook Solutions Integrated Grammar Practice 8.

CBSE Class 10 English Workbook Solutions Integrated Grammar Practice 8

Question 1.
Given below are instructions for opening a bank account. Use these to complete the paragraph that follows.

• obtain form from the bank
• fill in the form with all the relevant details
• ask an account-holder to countersign your form
• submit two passport-size photographs
• deposit the minimum amount required

First a form must be (a) __________ All relevant details (b) __________. The form must then (c) __________. Two passport- size photographs along with proof of residence (d) __________. Finally the minimum amount required (e) __________.

Answers:

(a) obtained from the bank
(b) must be filled in the form.
(c) be countersigned by an account holder
(d) must be submitted.
(e) must be deposited.

Question 2.
Given below are a few news headlines. Using information from the same, complete the sentences that follow.

1. India Allows Airspace to Pak
In the first public move to diffuse tension between the two countries, India _________ through Indian airspace.

2. Research Work at AIIMS Stalled for Want of Animals
More than 50 research projects at the prestigious All India Institute of Medical Sciences _________ to conduct experiments on.

3. After making Toilets, MCD Looks for Users
About 250 toilet complexes constructed by the Municipal Corporation of Delhi with Japanese aid have turned into liabilities as apparently _________.

4. Selling Kidneys to make a Living
Starving Tribals of Idduki district _________ to make a living.

5. Kidneys Donated without Medical Inspection
Most of the kidney donation procedures _________ the required medical examination in Indian hospitals.

Answers:

1. has allowed Pak to fly
2. have been stalled for want of animals
3. MCD is looking for users
4. have to sell kidneys/are selling kidneys
5. are done without

Question 3.
The following passage has not been edited. There is one error in each of the lines. Write the incorrect word and the correction in the space provided.

Question 4.
Complete the following paragraph on one of the earlier voyages of Columbus by choosing the correct options.

Christopher Columbus, (a) __________ born in 1451 AD. Unlike the people of his time, (b) __________ In order to prove his belief he said (c) __________ Japan. Queen Isabella of Spain supported him. Columbus sailed west (d) __________ three ships. Unfortunately, one of the ships was wrecked. Columbus returned to Spain (e) __________ colony.

(a) (i) a skilled sailor and an explorer, was
(ii) was skilled sailor and an explorer
(iii) being a skilled sailor and an explorer was
(iv) a skilled sailor and an explorer is

(b) (i) but Columbus believed that the Earth was round
(ii) Columbus had believed that the Earth was round
(iii) but Columbus believed that the Earth is round
(iv) Columbus believed that the Earth was round

(c) (i) if he sails west from Europe
(ii) if he is sailing west of Europe
(iii) if he sailed west from Europe
(iv) if he sailed west to Europe

(d) (i) with a crew of ninety men on
(ii) having a crew of ninety men in
(iii) with a crew of ninety men having
(iv) going with a crew of ninety men on

(e) (i) left behind forty men in the island of Hispaniola
(ii) leaving behind forty men on the island of Hispaniola
(iii) has left forty men on the island of Hispaniola
(iv) is leaving forty men on the island of Hispaniola

Answers:

(a) — (i) a skilled sailor and an explorer, was
(b) — (iv) Columbus believed that the Earth was round
(c) — (iii) if he sailed west from Europe
(d) — (i) with a crew of ninety men on
(e) — (ii) leaving behind forty men on the island of Hispaniola

Question 5.
Complete the following passage by choosing the correct options from those given below.Electronic commerce, it seems, still has (a) __________ limits, even in the Silicon Valley. For all the feverish excitement (b) __________ the tripling of electronic shopping last holiday season, the total money (c) __________ by American consumers online still (d) __________ to only about one percent of its total sales-barely a tenth (e) __________ the revenues from (f) __________ method of distance selling that has been (g) __________ for a century; the catalogue. This may be because electronic shopping (h) __________ on quite a narrow range of goods, mainly books, toys and music. Worse, there (i) __________ many stories of failed and late deliveries. And, more recently, a string of hackers’ attacks (j) __________ temporarily disabled some of the best-known e-commerce websites.

(a) (i) their
(ii) a
(iii) the
(iv) its

(b) (i) about
(ii) of
(iii) in
(iv) for

(c) (i) spend
(ii) spending
(iii) spent
(iv) being spent

(d) (i) amount
(ii) amounted
(iii) amounts
(iv) amounting

(e) (i) of
(ii) for
(iii) by
(iv) upon

(f) (i) another
(ii) other
(iii) some
(iv) the other

(g) (i) user
(ii) used
(iii) uses
(iv) in use

(h) (i) concentrated
(ii) is concentrating
(iii) was concentrated
(iv) had concentrated

(i) (i) were
(ii) have been
(iii) has been
(iv) was

(j) (i) has
(ii) have
(iii) having
(iv) had

Answers:

(a) — (iv) its
(b) — (i) about
(c) — (iii) spent
(d) — (iii) amounts
(e) — (i) of
(f) — (iv) the other
(g) — (ii) used
(h) —(ii) is concentrating
(i) — (ii) have been
(j) — (i) has

Question 6.
In the passage given below, one word has been omitted in each line. Write the missing word along with the word that comes before and the word that comes after it in your answer sheet against the correct blank number. Ensure that the word that forms your answer is underlined.

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Political Science Class 12 Important Questions Chapter 10 Challenges of Nation Building is part of Political Science Class 12 Important Questions. Here we have given Political Science Class 12 Important Questions Chapter 10 Challenges of Nation Building.

Political Science Class 12 Important Questions Chapter 10 Challenges of Nation Building

1 Mark Questions

Question 1.
Name the leader of the freedom movement of India who was popularly known as Frontier Gandhi. (Delhi 2014)
Answer:
Khan Abdul Gaffar Khan.

Question 2.
Name the leader who played a historic role in negotiating with the rulers of princely states to join the Indian Union. (Delhi 2014)
Answer:
Sardar Vallabhbhai Patel.

Question 3.
Mention the main recommendation of the State Reorganisation Commission of 1953. (All India 2014)
OR
What was the basis of the report of the States Reorganisation Commission? (All India 2012)
Answer:
The basis of report of the States Reorganisation Commission was that the boundaries of the states should reflect boundaries of different languages.

Question 4.
What is the ‘Two Nation Theory’ advanced by Muslim League? (Delhi 2013)
Answer:
According to the ‘Two-Nation Theory’, India consisted of not one but two ‘people’, Hindus and Muslims. That is why it demanded Pakistan, a separate country for the Muslims.

Question 5.
Which four princely states of India initially resisted to join the Indian Union? (Delhi 2013)
Answer:
Princely states of Junagadh, Hyderabad, Kashmir and Manipur initially resisted to join the Indian Union.

Question 6.
What was the huge obstacle in nation building at the time of India’s independence? (Delhi 2011)
OR
What was the biggest obstacle in nation building at the time of India’s independence? (Delhi 2011)
Answer:
The huge obstacle in nation building at the time of India’s independence was to shape a nation that was united, yet accommodative of the diversity in our society.

Question 7.
Why were the states reorganised on linguistic basis in India in 1956? (HOTS; Delhi 2011)
Answer:
The states were reorganised on linguistic basis under the pressure of people and leaders and also it helped to preserve the diverse culture of India.

Question 8.
Which two princely states refused to join either Pakistan or India at the time of Independence? (Delhi 2011)
Answer:
Hyderabad, Junagadh and Kashmir refused to join either Pakistan or India at the time of Independence.

Question 9.
What do you understand by ‘instrument of accession’? (Delhi 2010)
Answer:
The ‘Instrument of accession’ was a legal document created in 1947. It was executed by Government of India to princely states which was signed by most of the rulers.

Question 10.
When and by whom was the ‘tryst with destiny’ speech delivered? (Delhi, 2010)
Answer:
‘Tryst with destiny’ speech was delivered by JawAllar Lai Nehru at midnight on 14th-15 th August, 1947.

Question 11.
Which theory was behind the partition of India in 1947? (Delhi 2009)
Answer:
The two-nation theory of Muslim League was behind the partition of India in 1947.

Question 12.
How many princely states were in India at the time of its independence? (Delhi (C) 2008)
Answer:
At the time of Independence there were 565 princely states in India.

Question 13.
Where was the ‘Tryst with Destiny’ speech delivered by Pt. Nehru? (All India (C) 2008)
Answer:
Pt. Nehru delivered ‘Tryst with Destiny’ speech from Red Fort, Delhi on 15th August, 1947.

Question 14.
Give the name of two provinces which were also divided during the partition of India? (All India 2008)
Answer:
The two provinces which were divided during the partition of India were Punjab and Bengal.

Question 15.
Why did the leaders of the National Movement cherish the ideal of the secular nation? Give any one reason. (HOTS; All India 2008)
Answer:
The leaders of the National Movement cherished the ideal of the secular nation because they knew that India i.e. Bharat is a land of many religions and faiths. So, in order to survive as a unified country India had to follow secular ideals.

2 Marks Questions

Question 1.
Analyse the two political developments of 1940s that led to the decision for the creation of Pakistan, (HOTS; Delhi 2016)
Answer:
During 1940s in India, there were many political developments which led to the decision for the creation of Pakistan.
Two prominent among them were :

1. The political competition between the Congress and the Muslim League was taking place. The Congress wanted to make a nation that reflect democratic government, whereas the Muslim League propounded Two-Nation Theory to gain power and status for minority community in politics.
2. The British were also playing their role of ‘divide and rule policy’ and accepted the Two-Nation Theory for partition of India. Thus, in 1947 the two-nation i.e. India and Pakistan came into existence.

Question 2.
While the rest of the country was reorganised on linguistic lines in 1950s, why had Punjab to wait till 1966? (Delhi 2016)
Answer:
Except Punjab rest of the country was reorganised on linguistic lines in 1950s. Punjab had to wait till 1966 due to following reasons :

• In Punjab, there were two linguistic groups, Hindi-speaking and Punjabi-speaking.
• The Punjabi-speaking people demanded a separate state. Finally in 1966 Haryana and Himachal Pradesh were separated from Punjab.

Question 3.
Identify any two consequences of the partition of India in 1947. (All India 2014)
OR
Highlight any two outcomes of partition or division of India into India and Pakistan, (All India, (C) 2008)
Answer:
Two consequences of the partition of India in 1947 are following:

• There were killings and atrocities on both sides of the border.
• Political division of the country led to the administrative failure.

Question 4.
What is meant by ‘Two Nation Theory’? (Delhi 2014)
Answer:
The ‘Two Nation Theory’ means the cultural, political, religious, economic and social dissimilarities between the two major communities living in India; Hindus and Muslim. This theory gave rise the demand of two separate countries/nations one for Muslims (Pakistan) and one for Hindus (India).

Question 5.
Name the original states from which the following states were carved out.
(i) Meghalaya
(ii) Gujarat (All India 2012)
Answer:
Meghalaya was carved out from Assam in 1972. Gujarat was carved out from Bombay state in 1960.

Question 6.
What two challenges were faced by India at the time of her independence? (Delhi 2012; 2008 (C); All India 2010)
OR
Mention any two challenges that India faced just after independence. (Delhi 2012)
OR
Mention any two challenges that India faced just after independence. (Delhi 2012)
Answer:
The two challenges faced by India just after independence were:

• Challenge to shape a nation which is accommodative of the diversity in our society.
• Challenge to establish democracy.
• Challenge to ensure development and well-being of the entire society.

Question 7.
What was meant by princely states? How many princely states were there in India at the time of independence? (All India 2011)
Answer:
During colonial period there were several large and small states ruled by princes were called Princely States. There were 565 princely states at the time of independence.

Question 8.
Explain the role played by Sardar Patel in the unification of princely states in India. (Delhi 2011, 2009)
OR
Mention the role of Sardar Vallabhbhai Patel towards India’s integration. (Delhi 2009)
Answer:
Sardar Patel played following roles in the unification of princely states in India

• He procured letter of accession from the princely states through diplomacy and negotiation.
• He used force and persuation with the states of Hyderabad, Junagadh, Manipur and Kashmir for their merger.

4 Marks Questions

Question 1.
What does the special status given to Jammu and Kashmir under Article 370 mean? (All India 2014)
Answer:
After partition Hari Singh, the Hindu ruler of Kashmir signed an ‘Instrument of Accession’ with the Government of India. Sheikh AbdullAll who was against joining Pakistan, became the Prime Minister and Indian Government agreed to maintain the autonomy of Jammu and Kashmir. Jammu and Kashmir was given a special status in Article 370 of Indian Constitution.

Jammu and Kashmir is included in the first schedule as one of the states after signing the instrument of Accession. Article 370 says that except defence, foreign affairs, communication and ancillary matters, the Indian Parliament needs the permission of State Government’s for applying all other laws.

Article 370 grant special autonomous status to the State of Jammu and Kashmir. Thus, the state has separate set of law, including those related to citizenship, ownership of property and Fundamental Rights.

Question 2.
How did the state of Hyderabad became a part of the Indian Union after partition? (HOTS; All India 2009)
Answer:
Hyderabad, the largest of the princely states covered almost l/3rd part of South India. Nizam signed Standstill Agreement with the Government of India and state emerged as an independent state after India’s independence. Many movements took place in Hyderabad; State specially in Telangana region where many peasants were victimised and oppressed by Nizans

Nizam sent his para-military force, Razakars. Razakars murdered, raped and looted particularly the non-Muslims. Therefore, Central Government ordered the army to tackle the situation on 13th September, 1948, Indian army marched in Hyderabad and on the 17th September, 1948. Hyderabad surrendered. This way Hyderabad became a part of the Indian Union after partition.

Question 3.
What was the approach of the Government of India towards the princely states immediately after the partition of India in 1947? All India 2009
Answer:
At the time of India’s independence, there were 565 princely states. Immediately after partition communal violence was at its culmination. In this environment, the government’s approach towards princely states was guided by following three considerations:

1. Firstly, the people of most of the princely states clearly wanted to become part of the Indian union.
2. Secondly, the government was prepared to be flexible in giving autonomy to some regions. The idea was to accommodate plurality and adopt a flexible approach in dealing with the demands of the regions.
3. Thirdly, in the backdrop of partition which brought into focus the contest over demarcation of territory, the integration and consolidation of the territorial boundaries of the nation had assumed supreme importance.

Question 4.
Describe the outcomes of States Reorganisation Commission appointed in 1953. (Delhi 2009)
Answer:
The States Reorganisation Act was passed in 1956. This led to the creation of 14 states and 6 Union Territories. Earlier there were demands of separate states on the basis of linguistic line, but leaders did not support this.

Thereafter a lot of movements occurred and provinces suffered from it therefore under popular pressure, finally decision was taken in favour of linguistic states. It was hoped that if we accept the demand of linguistic claims then the separatism and division would be reduced. Thus, these divisions reflected the true democracy.

Question 5.
Describe briefly any four problems faced in the process of partition of India. (Delhi 2008)
Answer:
The major problems faced by India at the time of partition were as follows :

1. The country faced communal riots in almost every parts of India.
2. Problem of integration of the territories which were divided on the basis of language, religion and culture.
3. Problem of well being of the entire society particularly the minorities and other weaker sections.
4. Challenge to shape a nation which just got the independence.
5. Challenge to establish democracy and make a constitution for all.

Question 6.
Describe how the princely states of Manipur and Junagadh acceded to India. (All India 2008)
Answer:
Accession of Manipur After the independence in 1947, MAllaraja of Manipur Bodhachandra Singh, signed the Instrument of Accession with Indian Union on the assurance that the internal autonomy of Manipur would be maintained. Under the pressure of people of Manipur, MAllaraja held the election in June, 1948 and state became a constitutional monarchy.

Thus, Manipur was the first state to hold an election on the basis of adult franchise. The legislators of the regional parties of Manipur did not want to merge with India but state Congress wanted to.

Government of India pressurised the Manipur MAllaraja and succeeded to do so. MAllaraja accepted the agreement and signed it without consulting the Legislative Assembly. This led to lot of anger and resentment in Manipur, the repercussions of which are still being felt.

Accession of Junagadh In case of Junagadh, the Nawab of Junagadh wanted to merge with Pakistan or wanted to remain independent. The people of Junagadh wanted to merge with Indian Union. This lead to several events and also a plebiscits which resulted in the integration of Junagadh into India.

The successful negotiations brought many states to sign Instrument of Accession which means that states wanted to accept the sovereignty of India.

6 Marks Questions

Question 1.
Analyse any six consequences of the partition of India in 1947. (HOTS; All India 2016)
OR
Assess any six consequences of the partition of British India in 1947. (Delhi 2014)
OR
Explain any three consequences of partition of British India in 1947. (Delhi 2013)
OR
Explain any two causes of the partition of India in 1947. Analyse its any four major consequences. (Delhi 2011)
OR
Assess any two causes of the partition of India in 1947. Explain any four of its consequences. (All India 2010)
OR
What were the consequences of partition of India in 1947? (All India 2008)
Answer:
Muslim League advanced ‘Two-Nation Theory’ which advocated India consisted of not one but two ‘people’, Hindus and Muslims. That is why Muslim League demanded Pakistan, a separate country for the Muslims. The two main causes of partition in 1947 were as follows :

• Political competition between the Congress and the Muslim League.
• The role of Britishers in dividing the Hindus and Muslims by their policy of ‘divide and rule’.

The consequences of partition of India in 1947 are as follows:
1. Division of provinces according to majority The implementation of partition was very difficult because there was no single belt of Muslims majority in British India. The concentration of Muslims were in Punjab which was in the West and Bengal which was in East. The problems lied in these areas as concentration of non-Muslims were more. Therefore, it was decided that these two provinces would be bifurcated according to the majority at the district or even lower level.

2. Exploitation of minorities Further there were problems with the minorities on both side of the borders, they were easily targeted and there was no option except to leave their own land and homes and go across the border.

This transfer is said to be most abrupt, largest and unplanned transfer known in the human history. There were killings and atrocities on both sides of border in the name of religion. The minorities on both sides fled from their homes and often secured temporary shelter in refugee camps. Even they were not safe in refugee camps so, they travelled to the other side by all means railways, roads and by foot.

3. Exploitation of women During this journey, women were oftf n attacked and killed. Women were abdi cted and raped and also forcefully conve :ted to other religion. Therefore, family members killed their girls and women. 80 lakh people migrated across the new border and between 5 to 10 lakh people were killed during partition. Thus, partition of India established the deep trauma within minds of the citizens.

4. Problem with refugee Those who did manage to cross the border found that they had no home. For lakhs of these ‘refugees’ the country’s freedom meant life in ‘refugees camps’, for months and sometimes for years.

5. Administrative failure There were competing political interests behind communal conflicts. The Muslim league was formed to protect the interests of the Muslims in colonial India. It was in the forefront of the demand for a separate Muslim nation. Similarly there were organisations, which were trying to organise the Hindus in order to turn India into a Hindu nation. This situation led to administrative failure in the country.

6. Distribution of financial assets The financial assets and things like tables, chairs, typewriters, paper-clips, books and also musical instruments of the police band were divided. The employees of the government and the railways were also ‘divided’. It was a violent separation of communities who had hitherto to lived together as neighbours.

Question 2.
“The accommodation of regional demands and the formation of linguistic states were also seen as more democratic.” Justify the statement with any three suitable arguments, (HOTS; Delhi 2016)
Answer:
This statement can be justified by following three arguments:

1. Regional aspirations are very much a part of democratic politics. Expression of regional issues is not an aberration or an abnormal phenomenon. A large and diverse democracy like India must deal with regional aspirations on a regular basis.
2. The best way to respond to regional aspirations is through democratic negotiations rather than through suppression.
3. Regional imbalance in economic development contributes to the feeling of regional discrimination. Regional imbalance is a fact of India’s development experience.

Question 3.
How did the reorganisation of states take place in India after its independence? Explain. (All India 2014)
OR
What forced the Union Government of India to appoint the States Reorganisation Commission in 1953? Mention its two main recommendations. Name any four new states formed after 1956. (Delhi 2014)
OR
Explain the process and basis of the Reorganisation of States of Indian Union. (Delhi 2013)
OR
What was the States Reorganisation Commission? When was it constituted? What was the most important recommendation of this commission? (Delhi 2010)
OR
What was the States Reorganisation Commission? What were its important recommendations? (Delhi to 2008)
Answer:
State Reorganisation Commission The formation of Andhra Pradesh spurred the struggle for making of other states on linguistic basis in other parts of the country. These struggle forced the Central Government into appointing a States Reorganisation Commission in 1953 to look into

Recommendations of State Reorganisation Commission were :

1. To look into the question of redrawing of the boundaries of states.
2. This commission in its report accepted that the boundaries of the state should reflect the boundaries different languages. On the basis of its report the States Reorganisation Act was passed in 1956.

Process and the basis of Reorganisation of States of Indian Union After partition the challenge was to draw the internal boundaries of the Indian states. The boundaries had to be drawn in a way so that the linguistic and cultural plurality of the country could be reflected without affecting the unity of the nation. Indian National Congress and many leaders recognised the linguistic principle as reorganisation of new states’ boundaries.

But our leader further felt that carving out states on the basis of language might lead to disruption and disintegration and would draw attention away from other social and economic challenges that the country faced.

Thus, protests began in the Telugu speaking areas of the old Madras province. The Vishalandhra Movement (the movement for a separate Andhra) demanded that the Telugu speaking areas should be separated from the Madras province and be made into a separate Andhra province.

The movement gathered momentum. Potti Sriramulu, a Congress leader and a Veteran Gandhian, went on an indefinite fast that led to his death after 56 days. This caused great unrest and resulted in violent outbursts in Andhra region. Finally, the Prime Minister announced the formation of a separate Andhra State in December 1952.

New States formed after 1956 were :

1. This commission led to the creation of 14 states and six union territories. Maharashtra, Gujarat, Punjab, Haryana, Himachal Pradesh, Tripura, Meghalaya, Arunachal Pradesh, Uttarakhand, Chhattisgarh and Jharkhand are the new states formed after 1956.
2. Uttarakhand from Uttar Pradesh, Chhattisgarh from Madhya Pradesh and Jharkhand from Bihar all of these created in 2000.
3. In 2014, another state is created after bifurcation of Andhra Pradesh, namely Telangana. As a result Gujarat was formed out by Bombay. Haryana was from Punjab, Himachal Pradesh was formed out from Punjab. Tripura, Meghalaya, Arunachal Pradesh were created from AssAnswer:

Question 4.
Explain any three challenges faced by India at the time of its independence. (Delhi 2014)
OR
Explain any three challenges that India faced at the time of her independence. (Delhi 2010)
Answer:
The major challenges faced by India at the time of its independence are as follows:

1. To shape a United Nation Immediately after independence, there was a challenge to make India an unified nation. There were diversities of cultures, languages, religions etc increased the questions on India’s future.

2. To establish democracy However, India is seventh largest country in the world and has different values, cultures norms etc. According to the Constitution, India has adopted the democratic government on the basis of adult franchise. The challenge was how to maintain democracy.

3. To ensure the development and well-being The Constitution laid down in Fundamental Rights that all citizens are equal and all of them are free to practise their own religion. In DPSP laid down welfare state. Although the Preamble of the Constitution laid down that the Principles of justice, liberty, equality and fraternity were adopted to develop the society. However, the challenges were how to overcome the poverty and how to develop economy of India through the peoples’ participation.

4. Integration of princely states After independence, there were 565 Princely States. The Independence Act, 1947 says that British India divided into two nations India and Pakistan. And Princely States may be merged with both the countries or stayed independent. The British left India with multiple problems. This was certain and very serious challenge raised in front of India.

Question 5.
What were the major challenges of building democracy in India? (All India 2011)
Answer:
There were three major challenges of building democracy in India. These were as follows :
1. Communalism Indian polity is secular in nature, but communalism is thriving in the country and now it constitutes a serious problem of Indian states. India respects all religions and the major religious communities are Hindus, Muslims, Jains, Buddhists, Parsis, Christians and Anglo-Indians The Muslims constitute the largest minority community. The Hindus constitute more than 80 per cent of population of the country. Most of Hindu leaders believed that India does not have diverse communities.

2. Caste This is the biggest threat to India as political parties candidates are of the same caste as that of the majority voters, who favour him on caste basis although politics has moved towards casteism. It has brought a balance in caste equation, because not only the advanced castes but other castes also are eligible for participation in a representative democracy. The association of politics with caste has led democracy to a greater rationality vis-a-vis the caste system. The political parties while selecting the candidates, see whether the candidate will be able to get the support of voters of his caste or not.

3. Multi-party system After independence, many regional parties have formed, whether on religious basis or caste basis or any other basis. These multi-party systems further lead to coalition government this is also big threat to Indian democracy.

Question 6.
Discuss the problem related to Kashmir between India and Pakistan. (HOTS: All India 2010)
Answer:
The Congress party has evolved its politics on Kashmir on the basis of major global and domestic developments.

Pt. Jawaharlal Nehru repeated his commitment to find the will of the people of Kashmir in the Constituent Assembly of India. The problems of Kashmir between Indian and Pakistan are :
1. Accession to India India was satisfied that the most important political leader and party of Kashmir had accepted accession to India. The leader like Sheikh AbdullAll of National Conference represented the democratic will of the people of Kashmir and they were unambiguously acceeded to India. The Congress party also assured internal autonomy to the people of Jammu and Kashmir through the Constitution of India.

2. Article 370 and political consensus The Article 370 of Constitution can be altered in favour of the centre. Many other parties have supported this article, but Bharatiya Jan Sangh (now BJP) rejected every premise and every policy of the Congress and wanted to omit Article 370. Two extremely polarised position on Kashmir are represented by Congress and the BJP and it is impossible to evolve any minimal national consensus on Kashmir in India.

3. Emergence of terrorism Further the emergence of terrorism in the valley has accentuated polarisation among political parties in India because Pakistan is directly involved in terrorist activities.

4. Inter-regional dispute Another dimensions that Kashmir valley, Jammu and Ladakh have involved is, inter-regional disputes and competition. Ladakh’s political parties say that Kashmir discriminated them. But after the entry of centre all the movements were discontinued. If Jammu and Kashmir valley are separated from each other, then another two-nation theory could be faced by Indian Union. That’s why the political parties have to maintain legitimacy and democracy with all.

Question 7.
What were the main consideration for bringing princely states with Indian Union? Who played the historic role in this task? (Delhi 2008)
Answer:
The British paramountacy was over on the princely States after independence and these states may go with India or Pakistan or stay independent. There were 565 princely states.

Problem started because of following reasons:

1. The decision was totally upto the ruler not on the people this was a serious problem and big threat on the existence of a united India.
2. After Independence ruler of Travancore declared himself ‘ independent after a few days Hyderabad made same declaration.
3. Nawab of Bhopal was averse to join Constituent Assembly. This kind of differences might futher divide India into small states or countries.

Government Approaches Government took forward step and negotiated with the Princely State ruler and saw that the people of these states wanted to become a part of the Indian Union. Then government adopted flexible diplomacy and gave autonomy to some states. India held plebiscite and acceded the Princely States into Indian Union and operations which government operationalised accessed the Princely States, e.g., in Junagadh Government held plebiscite, operation Vijay in Goa and operation Polo in Hyderabad. Therefore, after all these efforts integrated Princely States.

Sardar Patel who was the Deputy Prime Minister and Home Minister that time, played an important role in negotiating with Princely States rulers and brought them into the Indian Union.

Passage-Based Question

Question 1.
Read the paragraph given below carefully and answer the following questions. (Delhi 2010)
We have a Muslim minority who are so large in numbers that they cannot, even if they want, go anywhere else. That is a basic fact about which there can be no argument. Whatever the provocation from Pakistan and whatever the indignities and horrors inflicted on non-Muslims there, we have got to deal with this minority in a civilised manner. We must give them security and the rights of citizens in a democratic state. If we fail to do so, we shall have a festering sore which will eventually poison the whole body politic and probably destroy it. Jawaharlal Nehru, Letter to Chief Minister, 15th October, 1947 :
(i) In spite of indignities and horrors inflicted on Non-Muslims by Pakistan, why Jawaharlal Nehru wanted to deal with the Muslim minority in a civilised way?
(ii) Why this minority should be given the security and rights on the same footing as to all others in a democratic system?
(iii) If this minority was not provided security and rights what kind of scenario is envisaged?
Answer:
(i) At the time of partition Pakistan inflicted horrors on non-Muslims. Despite this fact Nehru wanted to deal with the Muslim minority in a civilised way because out of the then minority communities in India Muslims were large in numbers. They had no option to go anywhere.
(ii) India is a democratic and secular country, where all religions are treated equally. Because of this factor the Muslim minority should be given security and rights on the same footings in India.
(iii) If this minority was not provided security and rights it will poison the whole Indian political system and the Indian democratic set-up would come to an end.

Value Based Questions (VBQs)

Question 1.
Sardar Patel in a letter to princely rulers in 1947 said, “I hope the Indian states shall realise fully that if we do not cooperate and work together in general interest, anarchy and chaos will overwhelm us all, great and small, and lead us to total ruin.”
Answer the following questions
(i) What general interest has been referred to?
(ii) What situation would lead to total ruin? (All India 2008)
Answer:
(i) The general interest referred to raise the country to new greatness. Lack of unity will expose India to unexpected calamities.
(ii) Sardar Patel said that Indian states should realise fully that if they do not cooperate and work together in general interest, anarchy and chaos will lead the nation to total ruin.

Question 2.
Malama Gandhi said on 14th August, 1947, “Tomorrow will be a day rejoicing as well as mourning”. (Delhi 2008)
OR
According to MAllatma Gandhi, why would 15th August, 1947 (tomorrow) be a day of rejoicing as well as mourning?
Answer:
Malama Gandhi referred to the 15th August, 1947 both a day of rejoicing as well as mourning beause on one hand India was about to get independence from the British rule, whereas on the other hand gruesome riots between Hindus and Muslims were taking place in the country due to partition.

We hope the Political Science Class 12 Important Questions Chapter 10 Challenges of Nation Building help you. If you have any query regarding Political Science Class 12 Important Questions Chapter 10 Challenges of Nation Building, drop a comment below and we will get back to you at the earliest.

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NCERT Books for Class 1 All Subjects

NCERT Books for Class 1 हिंदी

रिमझिम – 1

• पाठ 1: झूला
• पाठ 2: आम की कहानी
• पाठ 3: आम की टोकरी
• पाठ 4: पत्ते ही पत्ते
• पाठ 5: पकौड़ी
• पाठ 6: छुक-छुक गाड़ी
• पाठ 7: रसोईघर
• पाठ 8: चूहो! म्याऊँ सो रही है
• पाठ 9: बंदर और गिलहरी
• पाठ 10: पगड़ी
• पाठ 11: पतंग
• पाठ 12: गेंद-बल्ला
• पाठ 13: बंदर गया खेत में भाग
• पाठ 14: एक बुढ़िया
• पाठ 15: मैं भी
• पाठ 16: लालू और पीलू
• पाठ 17: चकई के चकदुम
• पाठ 18: छोटी का कमाल
• पाठ 19: चार चने
• पाठ 20: भगदड़
• पाठ 21: हलीम चला चाँद पर
• पाठ 22: हाथी चल्लम चल्लम
• पाठ 23: सात पूँछ का चूहा

NCERT Books for Class 1 English

Marigold – 1

• Unit 1:
  • A Happy Child
  • Three Little Pigs
• Unit 2:
  • After a Bath
  • The Bubble, the Straw and the Shoe
• Unit 3:
  • One Little Kitten
  • Lalu and Peelu
• Unit 4:
  • Once I Saw a Little Bird
  • Mittu and the Yellow Mango
• Unit 5:
  • Merry-Go-Round
  • Circle
• Unit 6:
  • If I Were an Apple
  • Our Tree
• Unit 7:
  • A Kite
  • Sundari
• Unit 8:
  • A Little Turtle
  • The Tiger and the Mosquito
• Unit 9:
  • Clouds
  • Anandi’s Rainbow
• Unit 10:
  • Flying Man
  • The Tailor and his Friend

NCERT Books for Class 1 English (Special Series)

Raindrops – 1

• Chapter 1: Clap, Clap, Clap
• Chapter 2: One, Two
• Chapter 3: The Little Bird
• Chapter 4: Bubbles
• Chapter 5: Chhotu
• Chapter 6: Animals and Birds
• Chapter 7: Fruits and Vegetables
• Chapter 8: Who Am I?
• Chapter 9: Hide and Seek

NCERT Books for Class 1 Maths in English Medium

Maths Magic – 1

• Chapter 1: Shapes and Space
• Chapter 2: Numbers from One to Nine
• Chapter 3: Addition
• Chapter 4: Subtraction
• Chapter 5: Number form Ten to Twenty
• Chapter 6: Time
• Chapter 7: Measurement
• Chapter 8: Numbers form Twenty-one to Fifty
• Chapter 9: Data Handling
• Chapter 10: Patterns
• Chapter 11: Numbers
• Chapter 12: Money
• Chapter 13: How Many

NCERT Books for Class 1 Maths in Hindi Medium

गणित का जादू – 1

• अध्याय 1: आकृतियाँ और स्थान
• अध्याय 2: एक से नौ तक की संख्याएँ
• अध्याय 3: जोड़
• अध्याय 4: घटाव
• अध्याय 5: दस से बीस तक की संख्याएँ
• अध्याय 6: समय
• अध्याय 7: माप
• अध्याय 8: 21 से 50 तक की संख्याएँ
• अध्याय 9: आंकड़ों का उपयोग
• अध्याय 10: पैटर्न
• अध्याय 11: संख्याएँ
• अध्याय 12: मुद्रा
• अध्याय 13: बताओ कितने

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NCERT English Workbook Class 10 Solutions Unit 14 Prepositions are part of English Workbook Class 10 Solutions. Here we have given CBSE Class 10 English Workbook Solutions Unit 14 Prepositions.

CBSE Class 10 English Workbook Solutions Unit 14 Prepositions

Question 1.
You are already very familiar with common prepositions such as at, on and in. So, this short unit will focus on some of the less common but very useful ones. They are listed in the diagram below.

See the Workbook on Page 275

Question 2.
Look at the following :

See the Workbook on Page 276

Which one of the following explanations matches the above sentences ? Write the letter in the box.
Answer:

Question 3.
Read this paragraph. Underline the two prepositions from A.1 above. Then circle the time period they are referring to.

When the Nalaban Bird Sanctuary was flooded during (the monsoons), the flamingos disappeared temporarily. Some of them were spotted on other islands in the lake. However, the long-legged birds flew back to the lake throughout (the winter months). A record amount of migration was noticed in (the first week of January).
Answer:
When the Nalaban Bird Sanctuary was flooded during the (monsoons) disappeared temporarily. Some of them were spotted on other islands in the lake. However, the long-legged birds flew back to the lake throughout (the winter months) A record amount of migration was noticed in (the first week of january)

Match each of the two prepositions above with its dictionary definition below :

Answer:

Question 4.
Complete the sentences below with appropriate prepositions.

1. My grandfather is always complaining ________ the pain in his back.
2. The pilot blamed his colleague losing ________ their way.
3. An infant depends ________ its mother for food.
4. He is worried ________ his bad results.
5. They’re very fond ________ tennis
6. You were absent ________ the science club yesterday
7. I was angry ________ my brother for breaking my tape recorder.

Answers:

1. of
2. for
3. upon/on
4. over/about
5. of
6. from
7. with

Now refer to a dictionary and find out the prepositions that are normally used with the following words :

complain, blame, depend, fond, absent and angry.

Answers:

• complain about, complain of, complain to
• blame for
• depend upon, depend on
• fond of
• absent from
• angry with, angry at, angry to

Question 5.
Take five different prepositions from the chart in A.1. Then write five sentences containing one each of those prepositions on a piece of paper. But leave out the prepositions in each. Then hand your piece of paper to a partner. She/he must complete your sentences, using the correct prepositions.

1. There is a garden __________ my house.
2. Distribute the sweets __________ forty children.
3. The son was sitting __________ his father’s knee.
4. My house is just __________ the street.
5. Rishi was a quick waLker. He soon got __________ the others.

Answers:

1. in front of
2. among
3. astride
4. across
5. ahead of

Question 6.
Fill appropriate prepositions in the blanks in the following sentences :

(a) Since Raju is clever __________ painting, he should join an art academy.
(b) They accused their neighbours __________ dumping garbage in front of their house.
(c) The students agreed __________ their teacher’s suggestion regarding the choice of place for an excursion.
(d) He had to leave the firm because his superiors did not agree __________ him on many issues.
(e) We should abide __________ the constitution of our country.
(f) All the furniture in my office is made __________ wood.
(g) Sugar is made __________ sugar beet and sugarcane.
(h) The two countries entered __________ an agreement to increase bilateral trade.
(i) Though Rahul does not like his rather imperious uncle, he tries to be polite __________ him.
(j) The principal congratulated the school basketball team __________ their success in the inter-school tournament.

Answers:

(a) at
(b) of
(c) to
(d) with
(e) by
(f) of
(g) from
(h) into
(i) with
(j) on

Question 7.
Correct the following sentences.

(a) It is essential that we discuss about your proposal before reaching any decision.
(b) The class fell silent as the teacher entered into the classroom.
(c) I have been living here since four years.
(d) The tournament will be held between Monday to Friday.
(e) Rani closely resembles to her maternal aunt.
(f) As the train was approaching to the station, someone pulled the chain and brought it to a halt.
(g) Connectors are also called as discourse markers.

Study sentences (a), (b), (e), (f) and (g). What conclusion can you draw from these examples about the correct use of prepositions ?

Answers:

(a) It is essential that we discuss your proposal before reaching any decision.
(b) The class fell silent as the teacher entered the classroom.
(c) I have been living here for four years.
(d) The tournament will be held from Monday to Friday.
(e) Rani closely resembles her maternal aunt.
(f) As the train was approaching the station, someone pulled the chain and brought it to a halt.
(g) Connectors are also called discourse markers.

In sentences (a), (b), (e), (f) and (g), prepositions are not required. The verbs used in them do not need prepositions.

Question 8.
Read the following sentences in which prepositions occur before particular words and expressions.

(a) Let’s go in the car instead of by bus.
(b) Seen from his point of view, the proposal seems quite reasonable.

Now fill appropriate prepositions in the blanks to complete the following sentences.
Answers:

(a) In my opinion, he should have accepted the offer.
(b) Who is the woman in a dark red saree ?
(c) Is there any good show on the TV tonight ?
(d) The old man would have died if he had not been taken to the hospital in time.
(e) The Chairman of the Board wanted the meeting to start exactly on time.

Question 9.
Pilloo has always had problems with prepositions. Edit this letter for him. Delete the incorrect prepositions and/ or insert the correct one wherever you think it is necessary. (There are eight mistakes altogether.)

Anand Bhawan Udaipur
27 January 20 — —
Dear Binod

I must say time really flies ! Because of lack of time, I couldn’t write to you earlier. The great news is Anil is marrying with a Sikkimese girl. I must say he’s a lucky guy ! Reena wasn’t too happy for it and Anil was very rude with her. He said he didn’t care for her opinion. She wasn’t nice with me either.

I’ve had no time for practice so I’m not taking part at the Athletics meet. I’m no good at either the high jump or the long jump and going there without practice would make it worse.

Yes, do write to Yak and Yeti Travels asking for details from their special offer. If it’s within our budget, it’ll be a great holiday. Write when you can.

Love
Pilloo

Answer:

Anand Bhawan
Udaipur
27 January, 20 — —

Dear Binod

I must say time really flies ! Because of lack of time, I couldn’t write to you earlier. The great news is Anil is marrying a Sikkimese girl. I must say he’s a lucky guy ! Reena wasn’t happy with it and Anil was very rude to her. He said he didn’t care for her opinion. She wasn’t nice to me either.

I’ve had no time for practice so I’m not taking part in the Athletics meet. I’m no good in either the high jump or the long jump and going there without practice would make it worse.

Yes, do write to Yak and Yeti Travels asking details about their special offer. If it’s in our budget, it’ll be a great holiday. Write when you can.

Love
Pilloo

We hope the NCERT English Workbook Class 10 Solutions Unit 14 Prepositions help you. If you have any query regarding CBSE Class 10 English Workbook Solutions Unit 14 Prepositions, drop a comment below and we will get back to you at the earliest.

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NCERT Exemplar Class 7 Science Chapter 13 Motion and Time are part of NCERT Exemplar Class 7 Science. Here we have given NCERT Exemplar Class 7 Science Solutions Chapter 13 Motion and Time.

NCERT Exemplar Class 7 Science Solutions Chapter 13 Motion and Time

Multilple Choice Questions

Question 1.
Which of the following cannot be used for measurement of time?
(a) A leaking tap.
(b) Simple pendulum.
(c) Shadow of an object during the day.
(d) Blinking of eyes.
Solution:
(d) Eyes do not blink at fixed interval of time.

Question 2.
Two clocks A and Bare shown in figure. Clock A has an hour and a minute hand, whereas clock B has an hour hand, minute hand as well as a ‘ second hand. Which of the following statement is correct for these clocks?

(a) A time interval of 30 seconds can be measured by clock A.
(b) A time interval of 30 seconds cannot be measured by clock B.
(c) Time interval of 5 minutes can be measured by both A and B.
(d) Time interval of 4 minutes 10 seconds can be measured by clock A.
Solution:
(c) Clock A can not measure seconds as it has not a second hand. Clocks A and B both have minute hands, so time interval of 5 minutes can be measured by both of them.

Question 3.
Two students were asked to plot a distance¬time graph for the motion described by table A and table B.


The graph given in figure is true for
(a) both A and B.
(b) A only.
(c) Sonly.
(d) neither A nor B.
Solution:
(a) Distance time graph for uniform motion shows a straight line. Slope is same for both table A and table B.

Question 4.
A bus travels 54 km in 90 minutes. The speed of the bus is
(a) 0.6 m/s
(b) 10 m/s
(c) 5.4 m/s
(d) 3.6 m/s

Question 5.
If we denote speed by 5, distance by D and time by T, the relationship between these quantities is
(a) S=D × T
(b) T=S/D
(c) S=1/T x D
(d) S=T/D
Solution:
(c)

Question 6.
Observe figure.

The time period of a simple pendulum is the time taken by it to travel from
(a) A to B and back to A.
(b) OtoA, 4 to 6 and 8 to 4.
(c) B to A, A to B and B to O.
(d) A to B.
Solution:
(a)

Question 7.
Figure shows an oscillating pendulum.

Time taken by the bob to move from A to C is f, and from C to O is f2. The time period of this simple pendulum is
(a) (t₁ + t₂)
(b) 2 (t₁ + t₂)
(c) 3 (t₁ + t₂)
(d) 4 (t₁ + t₂)
Solution:
(d) Time taken by the bob to move from

Question 8.
The correct symbol to represent the speed of an object is
(a) 5 m/s
(b) 5 mp
(c) 5 m/s^-1
(d) 5 s/m
Solution:
(a)

Question 9.
Boojho walks to his school which is at a distance of 3 km from his home in 30 minutes. On reaching he finds that the school is closed and comes back by a bicycle with his friend and reaches home in 20 minutes. His average speed in km/h is
(a) 8.3
(b) 7.2
(c) 5
(d) 3.6
Solution:

Very Short Answer Type Questions

Question 10.
A simple pendulum is oscillating between two points A and B as shown in figure. Is the motion of the bob uniform or non-uniform?

Solution:
Motion of the bob is non-uniform as its speed keeps changing.

Question 11.
Paheli and Boojho have to cover different distances to reach their school but they take the same time to reach the school. What can you say about their speed?
Solution:
Paheli and Boojho have different speeds.

Question12.
If Boojho covers a certain distance in one hour and Paheli covers the same distance in two hours, who travels in a higher speed?
Solution:
Boojho moves at a higher speed as he covers the same distance in a lesser time than Paheli.

Question 13.
Complete the data of the table given below with the help of the distance-time graph given in figure.

Solution:

Question 14.
The average age of children of Class VII is 12 years and 3 months. Express this age in seconds.
Solution:
12 years 3 months
= 12 x 365 + 3 x 30 = 4470 days
= 4470 x 24 x 60 x 60 s = 386208000 s

Question 15.
A spaceship travels 36,000 km in one hour. Express its speed in km/s.
Solution:
Speed of spaceship = 36,000 km/h

Question 16.
Starting from A, Paheli moves along a rectangular path ABCD as shown in figure 7. She takes 2 minutes to travel each side. Plot a distance-time graph and explain whether the motion is uniform or non-uniform.

Solution:
Since the distance covered per unit time for the entire rectangular path covered is not the same, the motion is non-uniform.

Question 17.
Plot a distance-time graph of the tip of the second hand of a clock by selecting 4 points on x-axis and y-axis respectively. The circumference of the circle traced by the second hand is 64 cm.
Solution:


Long Answer Type Questions

Question 18.
Figure given below is the distance-time graph of the motion of an object.

(i) What will be the position of the object at 20 s?
(ii) What will be the distance travelled by the object in 12 s?
(iii) What is the average speed of the object?
Solution:
(i) At 20 s, the object will be 8 m away from the starting point.
(ii) In 12 s, distance travelled by the object will be 6 m.
(iii) Average speed of the object Total distance=Total distance/Time taken=8m/20s=0.4m/s

Question 19.
Figure given below is the distance-time graph of the motion of an object.
Distance between Bholu’s and Golu’s house is 9 km. Bholu has to attend Golu’s birthday party at 7 o’clock. He started from his home at 6 o’clock on his bicycle and covered a distance of 6 km in 40 minutes. At that point he met Chintu and he spoke to him for 5 minutes and reached Golu’s birthday party at 7 o’clock. With what speed did he cover the second part of the journey? Calculate his average speed for the entire journey.
Solution:
Distance between Bholu’s and Golu’s house = 9 km
Distance covered by Bholu in first part of the journey = 6 km
Time taken to cover 6 km = 40 min
Distance covered by Bholu in second part of the journey = 9-6 = 3 km
Time taken to cover 3 km = 60 – (40+5)=15 min

Question 20.
Boojho goes to the football ground to play football. The distance-time graph of his journey from his home to the ground is given as figure.

(a) What does the graph between point B and C indicate about the motion of Boojho?
(b) Is the motion between 0 to 4 minutes uniform or non-uniform?
(c) What is his speed between 8 and 12 minutes of his journey?
Solution:
(a) Graph between point B and C is a horizontal line which indicates that Boojho is at rest, i.e. his speed is zero.
(b) Motion between 0 to 4 minutes is non-uniform as distance-time graph for this time interval is not a straight line.

We hope the NCERT Exemplar Class 7 Science Chapter 13 Motion and Time will help you. If you have any query regarding NCERT Exemplar Class 7 Science Solutions Chapter 13 Motion and Time, drop a comment below and we will get back to you at the earliest.

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