CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

Odisha State Board CHSE Odisha Class 12 Sociology Solutions Unit 1 Introducing Indian Society Objective Questions and Answers.

CHSE Odisha 12th Class Sociology Unit 1 Introducing Indian Society Objective Questions

Multiple Choice Questions With Answers

Question 1.
Does unity mean _____?
(a) Integration
(b) difference
(c) Uniformity
(d) Above all
Answer:
(a) Integration

Question 2.
Does diversity mean _____?
(a) Integration
(b) Difference
(c) Uniformity
(d) None of the above all
Answer:
(b) Difference

Question 3.
Which of the following forms of Diversity?
(a) Racial Diversity
(b) Linguistic Diversity
(c) Religious Diversity
(d) Above all
Answer:
(d) Above all

Question 4.
Which of the following Bonds of Unity?
(a) Geographical Unity
(b) Religious Unity
(c) Cultural Unity
(d) Above all
Answer:
(d) Above all

Question 5.
A Race is a ____?
(a) Biological human grouping
(b) A human grouping
(c) Complexion
(d) Above all
Answer:
(a) Biological human grouping

Question 6.
Who says that race is a valid Biological concept? it is a group united by heredity a breed or genetic strain or a subspecies?
(a) A.L. Krober
(b) FrazzBoas
(c) A. W. Green
(d) None of the above
Answer:
(a) A. L. Krober

Question 7.
Who says that In common parlance when we speak of race, we mean of a group of people that have certain blindly and perhaps also mental characteristics in common”?
(a) A.L. Krober
(b) FrazzBoas
(c) A. W. Green
(d) None of the above
Answer:
(b) Frazz Boas

Question 8.
Who says that “A race is a biological human grouping with a member of distinctive inherited characteristics which vary within a certain range”?
(a) A. L. Krober
(b) FrazzBoas
(c) A. W. Green
(d) Above all
Answer:
(c) A. W. Green

Question 9.
Which of the following HerbertRistey’s Racial classification?
(a) The Turko Iranian
(b) Indo Aryan
(c) saythodravidian
(d) Above all
Answer:
(d) Above all

Question 10.
Which of the following classification of A.C. Haddon?
(a) the pre-Dravidian Jungle tribes
(b) the Dravidians who are long-headed and brunette
(c) the Indo-Aryans who are fair-complexioned and long-headed
(d) Above all
Answer:
(d) Above all

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

Question 11.
Which of the following is the classification of B.S Guha in the race?
(a) The Proto-Australoid
(b) Monogoloid
(c) TheTibetomongoloid
(d) Above all
Answer:
(d) Above all

Question 12.
Which of the following religious composition of India?
(a) Hinduism
(b) Islam
(c) Christians
(d) Above all
Answer:
(d) Above all

Question 13.
Which of the following are the linguistic Groups of India?
(a) Indo-Aryan
(b) Dravidriari
(c) A Rastrick
(d) Above all
Answer:
(d) Above all

Question 14.
Which of the following are the tribal groups in India?
(a) North-North Eastern zone
(b) Central Zone
(c) Southern Zone
(d) Above all
Answer:
(d) Above all

Question 15.
Which of the following the classification on the basis of language?
(a) The Sino Tibetan
(b) Austric Linguistic group
(c) The Dravidian Linguistic Group
(d) Above all
Answer:
(d) Above all

Question 16.
Which of the following the classification on the basis of race?
(a) The Mongoloid
(b) The Australoid
(c) TheNegreto
(d) Above all
Answer:
(d) Above all

Question 17.
Which of the following the classification on the basis of the socioeconomic level of Development?
(a) class-I
(b) class-II
(c) class -III
(d) Above all
Answer:
(d) Above all

Question 18.
Which of the following classification of Indian tribes?
(a) Tribal Communities
(b) Semi- Tribal Communities
(c) Accultarated Tribal Communities
(d) Above all
Answer:
(d) Above all

Question 19.
Who says that “Race refers to human stocks that are genetically distinguished to major physiological difference to a remote separation of ancestry”?
(a) Maclver
(b) A.W. Green
(c) D.N.Majumdar
(d) None of the above.
Answer:
(a) Maclver

Question 20.
Who says that “If a group of people who by their possession of a member of common physical traits can be distinguished from others, even of the members of this biological groups are widely scattered they form a race”?
(a) A. W. Green
(b) Maclver
(c) A.L. Krober
(d) D. N. Majumdar.
Answer:
(d) D.N. Majumdar

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

Question 21.
Which of the following classification ofJ.H. Hutton?
(a) Negritos
(b) Proto-Australoid
(c) Pre-Dravidiran
(d) Above all
Answer:
(d) Above all

Question 22.
The 1961 census shows nearly of the Indian population as Hindusim?
(a) 86%
(b) 84%
(c) 85%
(d) 90%
Answer:
(b) 84%

Question 23.
Which of the following classification of tribes on the basis of geographical location?
(a) North-North Eastern Zone
(b) Central Zone
(c) Southern Zone
(d) Above all
Answer:
(d) Above all

Question 24.
Which of the following the classification ofB.S.Guha?
(a) The Negritos
(b) The Proto Australoids
(c) TheMongoids
(d) Above all
Answer:
(d) Above all

Question 25.
Who says that Persia as the land of light Greece the land of grace India- the land of dreams, Rome the land of empire, doubt India is the land of dreams – a dream that strives to blend inextricably her various similarities and differences?
(a) Hegel
(b) Guha
(c) Huddem
(d) None of above
Answer:
(a) Hegel

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

One Word Answers

Question 1.
unity mean ________?
Answer:
Unity means integration

Question 2.
Diversity means _________?
Answer:
Diversity means difference

Question 3.
Mentions one forms of Diversity in India?
Answer:
Racial Diversity

Question 4.
Mentions one Bonds of Unity in India?
Answer:
Geographical Unity

Question 5.
Mentions one racial composition of Indian Society?
Answer:
The Tunku Iranian.

Question 6.
Mentions one religion’s composition?
Answer:
Hinduism

Question 7.
Mentions one linguistic Group?
Answer:
Dravidian Languages.

Question 8.
Mentions one tribal Group?
Answer:
North-North Eastern Zone.

Question 9.
Mentions one on the basis of language?
Answer:
The Sino-Tibetan

Question 10.
Mentions one on the basics of Race?
Answer:
The Mongoloid

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

Question 11.
Mentions one classification on the basis of the socio-economic level of Development?
Answer:
The tribes of class-I

Question 12.
Mentions one of the classifications of Haddon, race?
Answer:
The Pre-Dravidian.

Question 13.
Mention one classification of the J.H. button of race?
Answer:
Mongoloids.

Question 14.
Mention one of the Dr B.S. Guha of race ________?
Answer:
The Negrito.

Question 15.
Mention one of the classification of tribes on the basis of geographical location?
Answer:
North – North – Eastern zone.

Question 16.
Mention one contributing to the unity of India?
Answer:
Religious Unity

Question 17.
Does mention 1971 census show a total languages spoken in India?
Answer:
1108

Question 18.
Who says that A race as a large biological human grouping with a number of distinctive inherited characteristics which very within a certain range?
Answer:
A. W. Green

Question 19.
Who said that Race reforms to human stocks that are genetically distinguished to major physiological differences to a remote separation of ancestry?
Answer:
Maclver

Question 20.
Who says that race as a valid biological concept? It is a group united by hereditary, a breed or genetic strain or a sub-species?
Answer:
A. L. Krober

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

Question 21.
Who says that “If a group of people who by their possession of a number of common physical traits can be distinguished from others, even of the members of thus biological group are widely scattered they form a race”?
Answer:
D.N. Majumdar.

Correct The Sentences

1. Unity means difference?
Answer:
Unity means integration.

2. Diversity means integration?
Answer:
Diversity means difference.

3. India is a museum of the different region?
Answer:
India is a museum of different race?

4. A. R. Desai India presents a spectacle of the museum of tongues?
Answer:
right of all

5. A. L. Krober says The sale a large group of people is intensified by inherited physical differences?
Answer:
BiesazandBiesanz

6. A. W. Green says A race as a biological concept. It is a group united by heredity a breed or genetic strown or sub-species?
Answer:
A.L. Kroeber says a race is a biological concept It is a group united by hereditary a breed or genetic strain or subspecies.

7. Biesaz and Biesanz say in common when we speak of race, are mean of group of people that have certain bodily and perhaps also mental characteristics on common?
Answer:
Frazz Boas says in common parlance when we speak of race we mean of a group of people that have certain bodily and perhaps also mental characteristics in common.

8. A. L. Krober A race as a biological human grouping with a number or distinctive inherited characteristics which very which a certain range?
Answer:
A. W. Green A race as a biological human group with a number of distinctive inherited characteristics which vary within a certain range.

9. A race is a psychological human grouping with a number of distinctive physical characteristics?
Answer:
A race is a biological human grouping with a number of distinctive physical characteristics.

10. India is a Tower port of races?
Answer:
India as a melting pot of races.

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

11. A. R. Desai presents a spectacle of the museum of tongues?
Answer:
Right

12. Animism as a Hinduism faith?
Answer:
Animism is atribal faith.

13. Joins the followers of lord Mahavira?
Answer:
Right

14. Sikhism is founded by Mahama?
Answer:
Sikhism is founded by Guru Nanak.

15. Zoroastrians are followers of Zoroaster?
Answer:
Right

16. Budhism emerged on India during the 7th century B.C Gautam?
Answer:
Buddism emerged in India during the 6th century B.C. Gautam.

17. Islam as the religion of Muslims. Did it extend in India towards the end of the 10th century A.D?
Answer:
Islam as the religion of Muslims. It extended in India towards the end of the 12th century A.D.

18. Muslim in India constitute nearly 12% of the total population?
Answer:
Muslims in India constitutes nearly 10% of the total population.

19. Christians constitute more than 5% of the Indian population?
Answer:
Christians constitute more than 2% of the Indian Population.

20. Tribal population in India constitutes about 10% of the Indian population?
Answer:
The tribal population in India constitutes about 7% of the Indian population.

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

21. Constitutions recognize 210 tribes and these tribes are found in different parts of the country?
Answer:
Constitutions recognize 212 tribes and these tribes are found in different points of the country.

22. Scheduled Tribes’ last modification order 1956, therefore 414 tribes in India?
Answer:
Right

Fill In The Blanks.

1. Unity means ______.
Answer: Integration

2. Diversity means ______.
Answer: difference

3. India is a ______ of different races.
Answer: Museum

4. A. R. Desai India presents a spectacle of ______ of tongues.
Answer: Museum

5. India is a _____ of many religions.
Answer: Lord

6. India is a country of ______.
Answer: Castes

7. A race is a _____ human grouping with a number of distinctive physical characteristics.
Answer: biological

8. race is a valid ______ concept.
Answer: biological

9. _____ religions have coexisted in India in part centuries.
Answer: Different

10. Zoroastrians are followers of _______.
Answer: Zoroaster

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

11. Sikhism was founded by _______.
Answer: GuruNanak

12. Jains the followers of ______.
Answer: LordMahavir

13. Buddhism emerged in India during ______ Century B.C. Gautam.
Answer: 6th

14. Christians Constitute more than _____ of the Indian population.
Answer: 2%

15. Muslim in India Constitute nearly ______ of the total population.
Answer: 10%

16. Islam is the ______ of Muslims.
Answer: Religious

17. Majority of the people of India are ______.
Answer: Hindus.

18. A.R. Desai India presents a ______ of the museum of tongues.
Answer: Spectacle

19. Tribal population in India constitutes about 7% of the ______ population.
Answer: Indian

20. Our Constitution recognizes 212 tribes and these tribes are founded in different parts of the ______.
Answer: Country

CHSE Odisha Class 12 Sociology Unit 1 Introducing Indian Society Objective Questions

21. Tribes Cast modification order 1956 there are _______ tribes in India.
Answer: 414

22. Varrier Elvira has classified Indian tribes into ______classes.
Answer: Four

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 2 Basic Concept Objective Questions and Answers.

CHSE Odisha 11th Class Political Science Unit 2 Basic Concept Objective Questions

Objective Questions With Answers

Question 1.
From which term the word liberty has been derived?
(a) Greek word liber
(b) Latin word liber
(c) French word liber
(d) English word liber
Answer:
(b) Latin word liber

Question 2.
Who says liberty means absence of law.
(a) Ilobbes
(b) Locke
(c) Rousseau
(d) Montesquieu
Answer:
(a) Ilobbes

Question 3.
Which of the following is a safeguard of liberty?
(a) Rule of law
(b) Democratic setup
(c) Constitutional govt.
(d) All of these
Answer:
(d)All of these

Question 4.
What does liberty mean?
(a) Absence of restraints
(b) Unrestrained freedom
(c) Freedom under legal system
(d) None of these
Answer:
(c)Freedom under legal system

Question 5.
Who says liberty and equality are antithetic?
(a) Laski
(b) Pollard
(c) Barker
(d) Lord Acton
Answer:
(d) Lord Acton

Question 6.
Economic equality pre supposes?
(a) Equalisation of income
(b) Adequate opportunity to earn livelihood
(c) Reduction of gap between rich and poor
(d) Equal income for all
Answer:
(b) Adequate opportunity to earn livelihood

Question 7.
What does social equality imply?
(a) Absence of special privilege
(b) Prohibition of discrimination
(c) Equal opportunity to men and women
(d) All the above
Answer:
(d) All the above

Question 8.
Liberty is the product of_________?
(a) Rights
(b) Freedom
(c) Law
(d) Equality
Answer:
(a) Rights

Question 9.
Who enjoy rights in a state?
(a) Citizens
(b) Nationals
(c) Subjects
(d) Leaders
Answer:
(a) Citizens

Question 10.
which of the following is not a political right?
(a) Right to vote
(b) Right to contesting election
(c) Right to form political parties
(d) Right to form association
Answer:
(d) Right to form association

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 11.
Which of the following is not a legal right?
(a) Civil right
(b) Political right
(c) Moral right
(d) Right to contract
Answer:
(c) Moral right

Question 12.
Which of the following is not a civil right?
(a) Right to property
(b) Right to contract
(c) Right to life
(d) Right to residence
Answer:
(d) Right to residence

Question 13.
Which day is observed every year as world Human Rights Day?
(a) January 8
(b) March 15
(c) November 10
(d) December 10
Answer:
(d) December 10

Question 14.
In which year National Human Right Commission was set up?
(a) 1950
(b) 1951
(c) 1981
(d) 1993
Answer:
(d)1993

Question 15.
What does religious liberty mean?
(a) Equality of all religions
(b) Freedom from Religion
(c) Absence of state religion
(d) All of these
Answer:
(d) All of these

Question 16.
Law is opposed to liberty, who says it?
(a) Hobbes
(b) Rousseau
(c) Locke
(d) Laski
Answer:
(b)Rousseau

Question 17.
Who says “Man is born free but everywhere in chains.
(a) Aristotle
(b) Gandhiji
(c) Rousseau
(d) J.S.Mill
Answer:
(c) Rousseau

Question 18.
Which theory regards liberty as absence of restraint?
(a) Individualism
(b) Socialism
(c) Welfare state
(d) Imperialism
Answer:
(a)Individualism

Question 19.
Which liberty believes in maintenance of world peace and brotherhood?
(a) National liberty
(b) Political liberty
(c) International liberty
(d) Natural liberty
Answer:
(b) Political liberty

Question 20.
Which of the following is not a safeguard of liberty?
(a) Rule of law
(b) Constitutional guarantee of rights
(c) Independentjudiciary
(d) Morality
Answer:
(d)Morality

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 21.
What does liberty imply?
(a) Absence of restraint
(b) Righttowork
(c) Natural freedom
(d) Reasonable restraints on individual freedom
Answer:
(d) Reasonable restraints on individual freedom

Question 22.
What does liberty mean in a secular state?
(a) Equality to all religions
(b) Absence of state religion
(c) Religious freedom
(d) All of these
Answer:
(d) All of these

Question 23.
Which of the following is the most important safeguard of liberty?
(a) Equality of rights
(b) Interest for rights
(c) Educated citizens
(d) Eternal vigilance
Answer:
(d) Eternal vigilance

Question 24.
Who says ‘Liberty and equality are complementary’?
(a) I.aski
(b) Lord Acton
(c) A.de Tocqueville
(d) Plato
Answer:
(a) I.aski

Question 25.
What is equality?
(a) Absolute equality
(b) Elimination of gap between rich and poor
(c) Equal right to all
(d) Equal rights and liberty to all
Answer:
(d)Equal rights and liberty to all

Question 26.
Who was the advocate of natural liberty?
(a) Hobbes
(b) Locke
(c) Rousseau
(d) J.S.Mill
Answer:
(c) Rousseau

Question 27.
Which of the following is not a safeguard of liberty?
(a) Organised public opinion
(b) Local government
(c) Fundamental rights
(d) Independent judiciary
Answer:
(b) Local government

Question 28.
Which of the following is not a political right?
(a) Right to public meeting
(b) Right to petition the government
(c) Right to form political party
(d) Right to freedom of speech & expression
Answer:
(d) Right to freedom of speech & expression

29. Which is not a nature of right?
(a) Rights are available in society
(b) Rights are absolute
(c) Rights are recognized by society
(d) Rights change with change in time
Answer:
(b) Rights are absolute

Question 30.
What is the nature of human rights?
(a) Social
(b) Political
(c) Economic
(d) Moral
Answer:
(d) Moral

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 31.
Who is responsible for defending human rights?
(a) state
(b) society
(c) judiciary
(d) All of these
Answer:
(d) All of these

Question 32.
In which year Universal Declaration of Human Rights was approved?
(a) 1945
(b) 1948
(c) 1950
(d) 1952
Answer:
(b) 1948

Question 33.
What is the value of liberty?
(a) Public opinion
(b) Eternal vigilance
(c) Legal Consciousness
(d) Economic equality
Answer:
(b) Eternal vigilance

Question 34.
Who says liberty is the opposite of over-government?
(a) H.J. Laski
(b) P.B. Seeley
(c) J.S.Mill
(d) Johnlocke
Answer:
(b) P.B. Seeley

Question 35.
Which of the following is not a safeguard of liberty?
(a) Rule of law
(b) Free media
(c) Alert public opinion
(d) Social equality
Answer:
(d) Social equality

Question 36.
Which type of equality is established by abolition of untouchability?
(a) Social equality
(b) Political equality
(c) Economic equality
(d) Caste equality
Answer:
(a)Social equality

Question 37.
Which of the following revaluations was the first of its kind against inequality?
(a) American war of Independence
(b) France Revolution
(c) Glorious Revolution
(d) Russian Revolution
Answer:
(b) France Revolution

Question 38.
In which century the concept of equality developed first?
(a) 16th century
(b) 17th century
(c) 18th century
(d) 19th century
Answer:
(c) 18th century

Question 39.
By entry into public service which type of justice prevails?
(a) Legal justice
(b) Political justice
(c) Social justice
(d) Economic justice
Answer:
(b) Political justice

Question 40.
Who was the advocate of distributive justice?
(a) Plato
(b) Aristotle
(c) Milton
(d) Socrates
Answer:
(b) Aristotle

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 41.
What type of right is Right to Residence?
(a) Civil right
(b) Political right
(c) Economic right
(d) Natural right
Answer:
(b) Political right

Question 42.
The western model of development is otherwise known as _________?
(a) Socialist development
(b) Capitalist development
(c) Material development
(d) Liberal development
Answer:
(b) Capitalist development

Question 43.
What is sustainable development?
(a) Present oriented development
(b) Future oriented development
(c) Balanced development with hope for future
(d) Slow and steady development
Answer:
(c) Balanced development with hope for future

Question 44.
What is development?
(a) Individual developments
(b) Social development
(c) Sustainable development
(d) Industrial development
Answer:
(c) Sustainable development

Question 45.
From which Latin term secular has come from?
(a) secular
(b) saicular
(c) saculum
(d) saecutam
Answer:
(c) saculum

Question 46.
what is Indian concept of secularism?
(a) Equal treatment to all religions
(b) Freedom from religious discrimination
(c) Religious tolerance and freedom
(d) All of these
Answer:
(d) All of these

Question 47.
What is western conception of secularism?
(a) Religious freedom
(b) Religious tolerance
(c) Non interference in religious sphere
(d) Unity of all religions
Answer:
(c) Non interference in religious sphere

Question 48.
Which of the following is a principle of capitalist model of development?
(a) Centrally controlled economy
(b) Abolition of economic inequality
(c) Welfare state
(d) Liberal society economy and administration
Answer:
(d) Liberal society economy and administration

Question 49.
What is sustainable development?
(a) Development of society
(b) Development of individual
(c) Modernisation
(d) Development of society, economic and environment
Answer:
(d) Development of society, economic and environment

Question 50.
Which model of development believes in free market economy?
(a) Capitalist development
(b) Socialist development
(c) Sustainable development
(d) None of these
Answer:
(a) Capitalist development

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 51.
Which development model believes in environmental safety?
(a) Socialist development
(b) Capitalist development
(c) Sustainable development
(d) None of these
Answer:
(c) Sustainable development

Answer The Following Questions 

Question 1.
From which word the term liberty derived?
Answer:
Latin word liber

Question 2.
What is negative liberty?
Answer:
Absence of restraint

Question 3.
The freedom which gives an individual the opportunity to participate actively in the affairs of state is _________?
Answer:
Political liberty

Question 4.
What is the other name of legal equality?
Answer:
Civil equality

Question 5.
What is the essence one man one vote?
Answer:
Political equality

Question 6.
What is the motto of justice?
Answer:
Let right be done

Question 7.
Which type of justice eliminates the gap between rich and poor?
Answer:
Economic justice

Question 8.
Which type justice can be maintained by abolition of untouchability?
Answer: Social justice

Question 9.
Reservation of scheduled caste, and scheduled tribes, is meant to ensure which form of justice?
Answer:
Social justice

Question 10.
What emerges from the product of rights?
Answer:
Liberty

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 11.
who says ’man is born free but everywhere in chains?
Answer:
Rousseau

Question 12.
‘Might is right’ symbolizes which type of liberty?
Answer:
Natural liberty

Question 13.
What does national liberty imply?
Answer:
Independence of the state

Question 14.
Absence of special privilege implies which type of equality?
Answer:
Negative equality

Question 15.
Discrimination based on sex and color prohibits which type of equality.
Answer:
Social equality

Question 16.
Who says ‘Liberty and equality are opposed to each other.
Answer:
Lord Acton and A. De Tocqueville

Question 17.
Who says ‘Liberty and equality are complementary.
Answer:
Laski and Barker.

Question 18.
Which body approved the universal declaration of human rights?
Answer:
UN General Assembly

Question 19.
Which type of justice can be realized by universal suffrage?
Answer:
Political justice

Question 20.
John Austin and Thomas Hobbes were the exponents of which form of justice?
Answer:
Legal justice

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 21.
Who says ’Rights are the conditions of social life?
Answer:
Laski

Question 22.
A socialist state opposes which right?
Answer:
Right to property

Question 23.
Which was the first written document on Human Rights?
Answer:
Magnacarta of 1215 AD

Question 24.
Which day is observed as World Human Rights Day?
Answer:
December, 10

Question 25.
Which type of right gives you the opportunity to ask for something from your friend?
Answer:
Moral right

Question 26.
Rights are valueless without which right?
Answer:
Right to life

Question 27.
Which model of development gives priority to market based development?
Answer:
Capitalist model

Question 28.
Which model of development thinks of the present as well as future?
Answer:
Sustainable development

Question 29.
Which secularism approach pleads for separation of Religion from politics?
Answer:
Western Secularism

Question 30.
In which country secularism is considered a slogan for vote bank politics?
Answer:
India

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Fill in the blanks

1. Liberty is derived from the___________word liber.
Answer: Latin

2. National liberty means ___________.
Answer: Independence

3. Liberty is the product of___________.
Answer: Rights

4. Liberty means absence of ___________.
Answer: Restraints

5. __________ is not license.
Answer: Liberty

6. Absence of restraint means ___________ liberty.
Answer: Negative

7. Reasonable restraint on the liberty of individual is, __________ liberty.
Answer: Positive

8. Liberty and __________ are complementary.
Answer: Equality

9. Eternal vigilance is the price of ___________.
Answer: Liberty

10. Equality means absence of ___________.
Answer: Special privilege

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

11. one man one vote is a principle of equality, ___________.
Answer: Political

12. __________ equality is necessary for the successful working of democracy.
Answer: Political

13. The state grants __________for the development of individual personality.
Answer: Rights

14. Right to property is a __________ right.
Answer: Civil

15. Right to vote is a __________ right.
Answer: Political

16. In a __________ state economic rights are secured.
Answer: Socialist

17. Human Rights are __________ rights.
Answer: Moral

18. Political rights are enjoyed only by __________ in a state.
Answer: Citizens

19. The term justice has been derived from the Latin word __________.
Answer: equality

20. _________ was the advocate of natural liberty.
Answer: Rousseau

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

21. Political liberty is valueless without __________.
Answer: Economic

22. Right to freedom of religion seeks to make India a __________ state.
Answer: Secular

23. Rule of law is a condition of __________.
Answer: Safeguard of Liberty

24. Law is a condition of __________.
Answer: Liberty

25. __________ eliminates all discriminations based on caste, religion and regionalism.
Answer: Social equality

26. Sex discrimination violates ___________ equality.
Answer: Social

27. The state by providing basic minimum needs for all establishes __________ justice.
Answer: Economic

28. The eliminates social discriminations to ___________ ensure justice.
Answer: Social

29. Right to life is a __________ right.
Answer: Civil

30. Right to residence is a __________ right.
Answer: Political

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

31. Right to property is a _________ right.
Answer: Civil

32. Right to freedom of speech and expression is a _________ right.
Answer: Civil

33. Right to rest and leisure is a _________ right.
Answer: Economic

34. _________ model of development believes in free economic competition.
Answer: Capitalist

35. Economic inequality considers in a _________ model of development.
Answer: Capitalist

36. _________ development model gives protection to the working class.
Answer: Socialist

37. __________ development model ensures due regard to environmental safety.
Answer: Sustainable

38. Protection of minorities is the catchword of __________ secularism.
Answer: Indian

39. __________ secularism rejects violence and bloodshed in the name of religion.
Answer: Indian

40. The National Human Rights Commission was set up in the year __________.
Answer: 1993

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Answer In One Sentence

Question 1.
What is liberty?
Answer:
Liberty means freedom enjoyed by the people under the law of state.

Question 2.
What is equality?
Answer:
Equality means absence of special privilege and equal opportunity to all.

Question 3.
what is negative liberty?
Answer:
Negative liberty means absence of restraint on individual freedom.

Question 4.
What is positive liberty?
Answer:
The rights and freedom guaranteed by the state to the individuals for their development is known as positive liberty.

Question 5.
What is political liberty?
Answer:
Political liberty consists of those political rights through which an individual takes active part in the affairs of state.

Question 6.
What is economic liberty?
Answer:
Economic liberty means the freedom of an individual from economic exploitation and insecurity.

Question 7.
What is civil liberty?
Answer:
Civil liberty consists of those rights which an individual enjoys as a member of civil society.

Question 8.
What is moral liberty?
Answer:
Moral liberty means respect for moral values and principles and the freedom to act as per the instruction of conscience,

Question 9.
What is natural liberty?
Answer:
Natural liberty is an abstract idea which people enjoyed in the imaginary state of nature.

Question 10.
What is National liberty?
Answer:
National liberty means freedom from foreign control or independence of the state.

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 11.
What is rule of law?
Answer:
Rule of law means law is sovereign and all individuals are equally subjected to it.

Question 12.
What is separation of power?
Answer:
Separation of power means distribution of powers between executive, legislation and judiciary in a state.

Question 13.
What is decentralization of power?
Answer:
Decentralization of power means division of responsibility between Union Government, State and local bodies.

Question 14.
What is natural equality?
Answer:
Natural equality implies that God has gives all individuals with equal psychological traints mental ability and capacity.

Question 15.
What is legal equality?
Answer:
Legal equality means equality before law and equal protection of law to one and all.

Question 16.
What is social equality?
Answer:
Social equality means giving equal social opportunities and privileges to all.

Question 17.
What is political equality?
Answer:
Political equality means equal opportunity to all citizens to participate in the affairs of state.

Question 18.
What is economic equality?
Answer:
Economic equality means to give fair and adequate opportunity to an for work and to earn their livelihood.

Question 19.
What is international equality?
Answer:
International equality means grant of equal status to each state in the international sphere irrespective of its physical and maternal strength.

Question 20.
What is justice?
Answer:
Justice implies rituality, fair treatment to all and maintenance of social discipline.

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 21.
What is legal justice?
Answer:
The justice maintained by the legal system is called legal justice.

Question 22.
What is social justice?
Answer:
Social justice believes in an ideal social order in which social equality and rights are enjoyed by all.

Question 23.
what is political justice?
Answer:
Political justice refers to the freedom and opportunity provided to each individual to participate in the political life of the community.

Question 24.
What is economic justice?
Answer:
Economic justice means freedom from economic Exploitation inequality and die opportunity to earn one’s livelihood.

Question 25.
What is distributive justice?
Answer:
Distributive justice means to give every individual his due on the basis of his caliber and efficiency.

Question 26.
What is corrective justice?
Answer:
Corrective justice means to give compensation to a sufferer and to rectify the wrong done to an individual.

Question 27.
What is right?
Answer:
Rights are the conditions of social life which the state guarantees to all individuals.

Question 28.
What is moral right?
Answer:
The rights which are based on the moral values and conscience of an individual are called moral right.

Question 29.
What is a legal rights?
Answer:
The rights which are guaranteed through the law of state are called legal rights.

Question 30.
What is civil right?
Answer:
Civil right comprises of those rights which enable an individual to lead a decent social life.

CHSE Odisha Class 11 Political Science Unit 2 Basic Concept Objective Questions

Question 31.
What is political right?
Answer:
Political rights are those rights which enable an individual to participate actively in the affairs of state.

Question 32.
What is economic right?
Answer:
The economic rights are those opportunities which provide economic security and necessity to an individual.

Question 33.
What is human right?
Answer:
Human rights are those universal natural rights which enable an individual to lead a dignified life in society.

Question 34.
What is universal declaration of Human Rights?
Answer:
Universal declaration of human rights is a solemn affirmation by the world community about the value and importance of human rights.

Question 35.
What is development?
Answer:
Development is an indication of social political, economic and cultural progress of a nation.

Question 36.
What is sustainable development?
Answer:
Sustainable development refers to a process of development ensuring socio economic progress of the nation along with protection of environment.

Question 37.
What is socialist model of development?
Answer:
Socialist model of development refers to socio economic progress of the nation with state control over production and distribution.

Question 38.
What is capitalist development model?
Answer:
Capitalist model of development believes in industrial technological development of the nation under a liberal free market economy.

Question 39.
What is secularism?
Answer:
Secularism is a policy of keeping die state administration and policy-making process free from religious influence.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Odisha State Board CHSE Odisha Class 12 Political Science Solutions Unit 4 India in World Politics Long Answer Questions.

CHSE Odisha 12th Political Science Unit 4 India in World Politics Long Answer Questions

Long Type Questions With Answers

Question 1.
Identify the basic principles of India’s foreign policy?
Answer:
Every sovereign country has its foreign policy. India too has one. Foreign policy refers to the sum total of principles, interests and objectives which a country promotes while interacting with other countries. Even though there are certain basic features of a foreign policy it is not a fixed .concept. The thrust of foreign policy keeps on changing according to changing international conditions. India’s foreign policy is shaped by several factors including its history, culture, geography and economy. Our Prime Minister, Jawaharlal Nehru, gave a definite shape to the country’s foreign policy.

Preservation of national interest, achievement of world peace, disarmament, independence for Afro-Asian nations have been important objectives of India’s foreign policy. These objectives are sought to be achieved through some principles viz. Panchsheel; no alignment; anti-colonialism, anti-imperialism, anti-racism, and strengthening the UN. It would be befitting to expand these principles.

Question 2.
What is Panchsheel?
Answer:
Nehru was a believer in world peace. He understood the linkage between peace for development and survival of mankind. He had seen the destruction caused by the two world wars and therefore realized that for the progress of a nation a long spell of peace was needed. In its absence social and economic priorities relating to development tend to get pushed to the background.

The production of nuclear weapons strengthened Nehru’s faith in the peaceful philosophy even more. Hence he gave utmost importance to world peace in his policy planning. India’s desired peaceful and friendly relations with all countries, particularly the big powers and the neighbouring nations; while signing an agreement with China, on April 28, 1954, India advocated adherence to five guiding principles known as Panchsheel for the conduct of bilateral relations. It includes the following:

  • Mutual respect for each other’s territorial integrity and sovereignty.
  • Mutual non-aggression.
  • Mutual non-interference in each other’s internal affairs.
  • Equality and mutual benefit.
  • Peaceful co-existence.
  • The Panchsheel agreement enumerates best the principles of peaceful co-existence with neighbours. It is an important component of India’s foreign policy.

Question 3.
Explain the meaning and significance of non-alignment.
Answer:
Non-alignment has been regarded as the most important feature of India’s foreign policy. Non alignment aimed to maintain national independence in foreign affairs by not joining any military alliance formed by the USA and Soviet Union in the aftermath of the Second World War. Non-alignment was neither neutrality nor non-involvement nor isolationism.

It was a dynamic concept which meant not committing to any military bloc but taking an independent stand on international issues according to the merits of each case. The policy of non-alignment won many supporters in the developing countries as it provided an opportunity to them for protecting their sovereignty as also retaining their freedom of action during the tension ridden cold war period.

India played an important role in forging the non-aligned movement (NAM). The concept of NAM emerged through a gradual process. Nehru took the initiative to convene the Asian Relations Conference in New Delhi in 1947. Later on a Conference, of 29 countries of Asia and Africa was held in Bandung (Indonesia) in 1955.

This was the first gathering of its kind which pledged to work together for colonial liberation, peace, cultural, economic and political cooperation. Bandung to Belgrade in 1961 where the first NAM conference was held was a logical process to project an alternative to cold war bloc politics and assertion of newly independent countries of their independent and sovereign rights.

Question 4.
Analyse the relevance of non-alignment in the post cold war period.
Answer:
Cold War was intense rivalry between USA and Soviet Union without fighting a direct war to attract allies in Africa, Asia and Latin America. It started soon after the Second World War and continued for forty five years. These two big countries became two opposite poles known as East and West. The world politics revolved around these two poles. Thus the world became bipolar. Among the non-aligned, Nehru had evolved special relationship with President Tito of Yugoslavia and Nasser of Egypt.

These three are regarded as the founding fathers of the Non-Aligned Movement. The non-aligned movement was a group of the newly independent states who refused to accept the dictates of the former colonial masters and decided to act according to their own judgement on issues of international concern. Non-aligned India and the World movement is anti-imperialist in approach. India as the prime architect of non-alignment and as one of the leading members of the non-aligned movement has taken an active part in its growth.

The Non-Aligned Movement is providing all member states, regardless of size and importance, an opportunity to participate in global decision making and world politics. India hosted the Seventh NAM Summit at New Delhi in 1983. India hoped NAM take up the cause of development, disarmament and the Palestine question.

Since NAM was a product of the cold war scenario and the bipolar world, many scholars have questioned the relevance of NAM after the end of cold war and demise of the Soviet Union. However, even in the present scenario NAM has a significant role to play, First, with the disintegration of Soviet Union, the world faces threat from unipolar world. The NAM can act as a check against US dominance.

Secondly the developed (North) and developing (South) world are divided over several economic issues. The NAM remains a very relevant forum for third world countries to engage the developed nations in a productive dialogue. Moreover, the NAM can prove to be powerful instrument for South-South cooperation. Such a thing is essential if the third world countries are to increase their bargaining power vis-a-vis the developed world. India continues to take active part in the non-aligned movement even after the end of cold war. Finally, the developing countries united under the forum of NAM have to fight for the reform of UN and change it according to the requirements of 21st century.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 5.
Explain the major concerns in India’s foreign policy in the post cold war period.
Answer:
The end of cold war in 1989 has brought about significant changes in the international scene and hence new policy problems for the various states in the developing world including India. The new situation is made by greater uncertainty and complexity. For India, disintegration of the Soviet Union has meant uncertainty on several aspects viz.

supply of weapons system, supply of spare parts, diplomatic support on Kashmir and other politico-strategic issues in and outside the United Nations and as a counter weight to US in South Asia. During the last one decade and a half international politics has undergone major changes.

The cold war has ended, the world has become unipolar, a number of states have disintegrated, cold war military blocs have lost their significance, some such blocs have dissolved and new regional economic blocs are shaping up. Globalisation has given rise to new set of problems such as terrorism, money laundering, proliferation of weapons, global warming etc.

These problems are not endemic to any region but affect all the countries to some extent or the other. This has forced many nation states which were hitherto enemies to cooperate with each other to solve problems which are universal in nature. In this changed international scenario it has become imperative for UN to restructure and reform itself if it is to effectively respond to emerging challenges.

Militancy in Kashmir has emerged as the formost challenge to our foreign policy. Pakistan and the Western countries blamed India for violating human rights and denial of rights to self determination. Gradually, India brought: situation under control. Because of the Kashmir dispute, India’s relations with Pakistan sharply deteriorated. India accused Pakistan of fanning trouble through cross border terrorism in Kashmir and other parts of our country.

India conducted nuclear weapon tests in 1998, followed by Pakistan’s tests. Pakistan resorted to further mischief by secretly sending its soldiers into Kargil in India and the World order to cut off the Kashmir valley from the rest of India. India handled the challenge firmly and effectively. Now engaging Pakistan in a constructive and composite dialogue process remains a challenge to India’s foreign policy, because there is a great deal of push from the United States.

Spread of terrorism to corners beyond Kashmir is a challenge as well as opportunity for our foreign policy nowadays. India is interested in forging anti-terrorism coalition with as many countries as possible. Keeping old friendship and looking for new friendships is another challenge for our foreign policy after the cold war has ended. For example, India is interested in strengthening its relations without damaging its relations with Arab countries.

Similarly,’ India’s foreign policy is tackling new tasks like deepening economic and security cooperation with the United States, while at the same time opposing unilateral actions against Iraq and Yugoslavia. Finally, India is realizing the growing importance of economic aspects of foreign policy. Hence, it is trying to establish a new basis for its relations with neighbouring countries in South Asia, China and the South East Asian counties.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 6.
Recognise India’s contribution to UN efforts for peace and disarmament.
Answer:
The United Nations which came into being on Oct. 24, 1945 has been the most important international organisation since the Second World War. The formal basis for UN activities is the UN charter. The UN has a vital role in world affairs. For more than fifty years UN has helped to manage relations between states and regulate a broad range of international activities.

It has worked to protect the security of people and promote peace and development. One way in which UN has contributed to world peace is by taking up the cause of disarmament India has also contributed immensely to UN’s disarmament efforts. Disarmament is limitation, reduction and possible elimination of dangerous (like nuclear) weapons.

Since independence, India has consistently pursued the objective of global disarmament based on the principles of non-discrimination. Given the destructive capacity of nuclear weapons, India has always believed that a world free of nuclear weapons would enhance global security. Thus India has always advocated that highest priority be given to nuclear disarmament as a first step towards general and complete disarmament.

India has contributed to UN significantly on disarmament in terms of ideas, resolutions, initiatives and bridging differences through action plans. In 1948, India had proposed limiting the use of atomic energy to peaceful purposes and elimination of nuclear weapons from national arsenals. In 1950, India suggested formation of a UN Peace Fund created through peaceful reduction of arms and directing the amount thus released towards development purposes. In 1954, India advocated the cause for a comprehensive nuclear test ban treaty.

India was the first to become party to partial Test Ban Treaty in 1963. Hence India strongly and consistents refused to join the Treaty. In 1964, India took the initiative to place the item ‘non-proliferation of weapons’ on UN agenda. However, the purpose was defeated by the (1968) carried that a large numbering of counties from going nuclear, without firm restrictions on the few nuclear weapon countries activities Nuclear Non¬proliferation Treaty Although our country allged to the oppose to problem.

In 1984, India launched a Six-Nation Five Continent Peace Initiative along with Argentina, Greece, Mexico, Sweden and Tanzania. Four years later (in a joint declaration issued on the occasion of visit of President Gorbachev of Soviet Union the then Prime Minister, Rajiv Gandhi made a forceful plea for the elimination of nuclear weapons.

The Delhi declaration enumerated ten principles for building a nuclear weapon free world). In 1988, Rajiv Gandhi proposed an Action Plan for ushering in a nuclear weapon free and nonviolent world order. The Action Plan envisaged a binding commitment by all nations to the elimination of nuclear weapons in stages by 2010.

India is also an original signatory to the Chemical Weapons Convention, having signed it on Jan. 14, 1993 and was among the first 65 countries to have ratified the treaty. In 1993 India sponsored a resolution on comprehensive test ban along with the US within the overall framework of advancing towards nuclear disarmament. India was distressed when final version of the CTBT was rushed through without consenses. And it failed to address the security reasons of India.

Hence it bravely stood against the steadlity fashion in which some tests use canned while sophisticated nuclear tests were not in a way, India’s conduct of nuclear tests in 1998 could we linked to the unfair framework of CTBT, though many initially misunderstood India’s tests as a negative development for disarmament; India pledged to continue to work for inaugural and non-discriminaly nuclear disarmament.

Question 7.
Explain India’s participation in UN peace keeping and its claim for a permanent seat in the Security Council.
Answer:
India’s history of participation in UN peacekeeping operations is a long one. India’s contribution has been described as excellent by many political observers. In UN. India’s contribution has been acknowledged by members of the international communities.

Peace keeping stands for prevention, containment and termination of hostilities between or within states through the non offensive activities of multinational forces of soldiers, police and civilian people sent unto the authority of the United Nations with the consent of the countries concerned. Peacekeeping nations changed in its scope and nature according to needs of a conflict situation.

India has taken part in 35 of UN peacekeeping operations in four continents. Its most significant contribution has been to peace and stability in Africa and Asia. Presently India is ranked as the largest troop contributor to UN.

The saga of India’s role in UN peace keeping began with the establishment of the United Nation’s Emergency Force (UNEF) in the Gaza strip and the Sinai in 1956 after Israeli war against Egypt ended.The Congo in Africa benefitted significantly from troop presence. India’s contributed to keep unity and integrity of that history in 1960s.

After the end of cold war, India’s contribution to UN peacekeeping remains significant equaly, if not more, military personal at the request of the United Nations Secretery General to Angola, Cambodia, Somalia, El Salvador and Sierra Leone etc. Many of these countries were victims of chaos caused by civil wars. No government machinery collapsed or was discredited. India sent not just troops, but police, doctors, engineers and administrators.

As you already know, the efficiency of peace maintenance in the world depends on the effectiveness of the Security Council but the Council has suffered in this regard due to its outdated, unchanged membership.

Presently the permanent membership of the Security Council is confined to US, Russia, Great Britain, France and China. However, such composition of the Security Council does not take into account the current global power configuration which has changed since the days when these countries were inducted as permanent members.

Since India has emerged as the fourth fastest growing economy and also because of the leadership it has provided in all international fora, its contribution to UN peacekeeping, its track record in espousing the cause of the third world, India has a strong case for a permanent seat in the Security Council. We are getting support from many friendly countries. A final decision on the matter is likely to take some time, because of its complexity.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 8.
India and China are the two great giants of Asia- Explain.
Answer:
Besides being the most populous countries, they are also two of the most ancient civilisations of the world. Historically, several historians have successfully traced the cultural linkages dating back to 2nd century BC. As a result of the communist revolution in 1949, China became the People’s Republic of China (PRC), under the leadership of Mao Tse Tung.

Nehru regarded India as China’s rival for the leadership of the non-white people of the world. India, on the other hand, tried India and the World its best to come close to China. It was the first non-communist country to recognise communist China in 1949. India fully supported China’s claim for membership in the United Nations. It also acknowledged China’s claim over Formosa (Taiwan).

It refused to be a party to peace treaty with Japan without China. In the Korean crisis too, India refused to brand China as aggressor when China intervened on behalf of North Korea. In fact, India supported China even though the Western bloc especially USA was displeased with it.

Nehru’s China policy received the first jolt in 1950, when China occupied Tibet in 1950. It is important to remember in this context that India had long term interests in Tibet because it was a buffer lying between India and China. India even enjoyed certain special privileges in Tibet. Therefore direct Chinese control over Tibet was likely to endanger these, and India’s security.

India’s suggestions for a peaceful settlement of the Tibet problem were treated as interference by the communist regime. Gradually the Tibetans grew restless under China’s yoke and rose in revolt in 1959. China ruthlessly suppressed the movement and declared Tibet as an integral part of China. The head of Tibet, Dalai Lama took shelter in India while Tibet lost whatever autonomy it still enjoyed.

The granting of political shelter to Dalai Lama by India added to China’s distrust. China appreciated India’s neutral and mediatory role in easing the Korean problem (1950-53). Thus, began a period of friendship between the two countries, with the signing of the Sino-Indian Treaty of friendship in 1954. This treaty put a seal of approval upon Chinese suzerainty over Tibet.

The Preamble of the treaty embodies the famous ‘Panchsheel Principles’ about which you have studied (lesson number 26). This agreement initiated a period of relaxed relationship, marked by the slogan of Hindi Chini Bhai Bhai. It is interesting to note that at the Bandung Conference (1955), Nehru actively brought China into the hold of the Afro-Asian solidarity.

Question 9.
Write about the Boundary Dispute between India and China.
Answer:
The 1950s were marked by the boundary dispute between India and China, the- flash point of which unfortunately caused a war between the two countries in 1902. China first started to claim large parts of Indian territory in North East Frontier Agency (NEFA, now Arunachal Pradesh) and Ladakh by publishing maps in which these were shown as included in China. China continued extending its borders and also constructed a 110 mile long road -across Aksai China area (Ladakh) of India in 1956-57.

In 1959, China put claim to some 50, appa sq. miles of Indian territory and also denied the validity of McMahon Line. By. this time Tibet had been fully integrated into China; it was in a strong position at the India-China border with Chinese troops posted all along.

While the two countries were m dispute over the McMahon line issue, China launched a massive attack on India in October. 1962, in the NEFA as well as the Ladakh sector. After overrunning large areas of Indian territory, China announced a unilateral ceasefire after occupying huge territory of India-200’s Question miles in the North Eastern sector and 15,000 s Question miles in Ladakh.

A futile attempt to work out a peaceful settlement between the two countries was made by Sri Lanka. The Colombo Proposals failed because China refused to agree on conditions contained in them. For long in the years following the war, China-India relations did not show any improvement. In fact, China went out of the way to make friends with Pakistan, just to isolate and contain India.

Question 10.
Discuss Normalisation of Relations restored between India and Pakistan.
Answer:
Although the two countries resumed diplomatic relations in 1976 by exchanging ambassadors. The efforts of normalisation of Sino-Indian relations received a boost when then Prime Minister Rajiv Gandhi paid a successful five day visit to China in 1988. The two countries pledged to settle the border dispute through dialogue.

Several high level visits followed including visit by Ex-Prime Minister Atal Bihari Vajpayee in 2003. The two countries agreed to keep the border dispute apart and develop friendly relations in other fields. Until the border dispute is resolved, both countries agreed to maintain peace and tranquillity on the Line of Actual Control (LAC).

One could see a clear shift in the Chinese attitude towards India. The fact that erstwhile USSR had mended fences with China, there were no more apprehensions from the South. Moreover, China’s post-1979 economic transformation demanded big markets for its massive production under economic liberalisation.

President Jiang Zemin’s visit.to India in 1996 witnessed a major consolidation of this progress. This was first ever visit of China’s head of State to India. China’s withdrawal of support to Naga and Mizo rebels; meaningful silence on the status of Sikkim (China considered Sikkim’s status as that of an independent state) and a neutral stand on Kashmir issue could be seen as positive shift in Chinese attitude towards India.

Nevertheless, there was suddenly a brief setback in the mutual ties of the two after the nuclear explosions by India during 1998. These were followed by sharp Chinese reaction and its leading role in getting the resolutions condemning the tests in UN and similar fora, passed. These tests by India were seen as neutralising Chinese prominence in the region.

But the Chinese posture of neutrality during thp Indo-Pak military showdown in Kashmir, Kargil sector in 1999 exhibited China’s inclination to toe a softer and friendly line with India. In fact, Chinese refusal to interfere in the conflict forced Pakistan for cessation of hostilities with India.

However, Ex-Prime Minister Atal Bihari Vajpayee’s 2003 visit to China is a renewed effort in the promotion of close and cordial ties between the two neighbours. The border agreement has recognised the Nathula Pass in Sikkim as a border pass, implying that China no more considers Sikkim- as an independent state.

Another positive breakthrough was the Joint Declaration that underlined the need to explore a framework of a boundary settlement at political level of bilateral relations. This is an acknowledgement that the key issue in resolving the dispute is political.

This is seen as Beijing’s readiness to give up its policy of delaying dialogue. India’s National Security Advisor and Chinese Vice Minister have been appointed for holding the tasks. The developments at the diplomatic and political levels have been supplemented by fresh initiatives at the economic level to strengthen bilateral relations. The border trade between India and China has crossed $ 10 billion quickly.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 11.
India Pakistan relationship.
Answer:
No two countries in the world have so much in common as India and Pakistan. Yet they have perpetually been in a state of undeclared war with varying degree of intensity. Pakistan’s aggression in Kargil (1999) brought the two countries even on the verge of a nuclear confrontation. The legacy of suspicion and mistrust predates the partition of India in 1947. During the freedom struggle the Muslim League, under the leadership of Mohammad Ali Jinnah propounded the two-nation theory, in support of a separate Muslim state.

Jinnah insisted that since Hindus and Muslims, were two communities, two separate states must be constituted for the two communities. The Indian National Congress (INC)’s long rejection of and reluctant acceptance of partition gave room for suspicion in Pakistan that India would try to undo the partition and divide Pakistan.

Moreover, Pakistan was concerned at the possibility of India’s domination in the region and its inability to match India’s power all by itself. Pakistan developed a perception that it is an incomplete state without Kashmir being incorporated into it. On the other hand, India perceives Kashmir’s accession and integration into India as an essential element of its secular and federal democratic structure.

Question 12.
Discuss about the problems of The Kashmir Issue.
Answer:
At the time of partition Jammu and Kashmir (J&K) was one of those several princely states, the fate of which was left uncertain in 1947. Pakistan desired that Kashmir with Muslim majority population should join Muslim country, Pakistan. But the popular leader of National Congress opposed Pakistan’s ideology.

Maharaja Hari Singh did not take a decision until Pakistan sent armed intruders into the Kashmir valley in October 1947. Seeking Indian help to repulse the Pakistani intruders Maharaja signed the ‘Instrument of Accession’ making Jammu and Kashmir a part of Indian Union.

On this occasion, as true democrat, Prime Minister Nehru assured that after Pakistani aggression was cleared* the future status of the state would be decided on the basis of wishes of the people of Kashmir. Since India did not want an open clash with Pakistan, it referred the matter to the United Nations.

Indian forces saved Srinagar from the invaders, pushed back the Pakistanis from the Kashmir Valley. But the whole of Kashmir could not be recaptured, at it would have meant direct and difficult war between the two new nations. India sought United Nations help in 1948. A ceasefire came to be implemented on January 1, 1949.

It left a large part of Jammu and Kashmir (nearly 2/5 of the State) under Pakistan’s possession, which We call Pakistan Occupied Kashmir (POK). In 1950s the UN mediators put forward several plans to resolve the dispute, but they failed to bridge the differences between the two countries.

The problem of Kashmir is still pending. Plebiscite was to be conducted only after Pakistan withdrew its forces from the occupied territory, as per the UN*resolution of 1948, which Pakistan refused to comply. Hence India pleaded that the wishes of the people were ascertained in 1954 in the form the direct election to the Constituent Assembly which satisfied the accession of Jammu and Kashmir to India. The mediation come to an end.

Pakistan was desperate to capture Kashmir. Thinking that India’s army was weak after defeat in the war with China in 1962, Pakistan tried through a war to take Kashmir in 1965. But Indian forces defeated the Pakistani designs. Moreover, Pakistan suffered another humiliation, when its eastern wing, 1000 miles away from West Pakistan successfully waged independence struggle in 1971.

India played a key role in the war to liberate Bangladesh. The birth of Bangladesh proved to be the final burial of two-nation theory on the basis of which Pakistan put a claim to Kashmir. Pakistan was reduced to one-fourth of the size of India.

This altered the power equation in South Asia in India’s favour. In order to normalise relations India invited Pakistan for an agreement, the result of which was the Shimla Pact of 1972.

This Shimla agreement however bears important significance as the two countries agreed to seek the settlement of all bilateral problems, including Kashmir, mutually without the intervention of any third party. Thus under the Shimla Pact, the Kashmir issue cannot be raised in international or any other forum, although Pakistan has not hesitated to ignore the sprit of the agreement. The agreement also talked about the return of Prisoners of War (POW).

Though Pakistan’s territory in India’s possession was returned, a new cease-fire line (in place of the old cease-fire line of 1948-49) was drawn, which is known as the LoC, Pakistan found ways other than open war to destabilise India by encouraging and assisting terrorism in Punjab, and the State-sponsored militancy in Jammu and Kashmir since the mid 1980s.

Pakistan still continues to encourage terrorist and separatist tendencies in Kashmir, operatirigtnainly from terrorist training camps situated in POK.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

The sanctity of the LoC that came to be agreed upon between India and Pakistan under the Shimla Agreement of 1972, was violated by Pakistan in May 1999 as a part of a big plan. This was done when the Pakistani forces infiltrated into India, after crossing the line of control in Kargil, Drass and Batelik sectors of J &K. Indian army once again gave a befitting defeat in a war that continued for about 60 days.

The purpose of Pakistani operation in Kargil was to create a crisis with a threat of nuclear war, which would in turn ensure intervention by the United States in its favour on Kashmir dispute. Neither United States nor China came to Pakistan’s help. In fact, Pakistan had a diplomatic and military defeat.

Question 13.
Discuss about Nuclear Tests and Efforts Towards Improvement of Relations.
Answer:
Indo-Pakistan relations acquired an entirely new dimension in the context Of nuclear tests by both India and Pakistan in May 1998. The relations between the two neighbours hit a India and the World new low. India has been facing a nuclear threat arising out of China’s clandestine support to build up of the nuclear weapon capability of Pakistan since the mid-seventies.

No doubt, Pakistan’s nuclear policy is targeted against India The extreme bitterness and tension between India and Pakistan in the aftermath of the nuclear tests of May 1998 did bring with it an increasing realisation on both sides that things could not continue in the same manner indefinitely. That, some meeting ground between the two neighbours has to be found.

Thus, foreign secretary level talks started, and a direct bus service between Delhi and Lahore was proposed. Prime Minister Vajpayee’s Bus Diplomacy in 1999 marked a tremendous goodwill between the two countries. The Lahore Declaration signed at the time underlined the need for resolving all outstanding issues, including that of Kashmir, through peaceful meAnswer: While India agreed to bring Kashmir onto the agreed agenda along with other areas of mutual benefits, Pakistan conceded to bilateralism.

The reference to the ‘composite and integrated’ dialogue process implied that the two would not be a hostage to any single issue. Despite the rupture caused by the Kargil war and the terrorist attack against our Parliament (December 2001) the unconditional dialogue has been resumed.

The emphasis in these talks is to promote people to people contacts across LoC, and also improve economic ties between India and Pakistan. Change of government in India has not meant any deviation from our commitment to peaceful and prosperous co-existence with Pakistan.

Question 14.
India Relation with Sri Lanka.
Answer:
Sri Lanka, earlier known as Ceylon (until 1972), is a small island country situated in the Indian Ocean to the south of India. Its total area is 25,332 s Question miles. Of all countries, it has geographical proximity to India. Only 18 miles wide shallow water in the Palk Straits separates Jaffna in northern Sri Lanka from the Southernmost tip of the Indian state of Tamil Nadu.

Its geostrategic location in the Indian Ocean (at the centre of commercial and strategic sea and air routes) and its closeness to US naval base in Deigo Garcia indicates its importance far beyond its size, population and resources. The history of cultural relations between India and Sri Lanka dates back to the ancient times.

Out of the total population of Sri Lanka, about 64 percent believe in Buddhism and about 15 percent believe in Hinduism. Sri Lanka became a British colony in early 19th century. It was granted independence on February 4,1948. India-Sri Lanka relations have generally been cordial, though there have been occasions of tense relations due to the ethnic conflict between Tamils and the Sinhalese.

Despite ethnic problems, India has never sought to impose its will on Sri Lanka and has always based its foreign policy towards this southern neighbour on mutual understanding and friendship.

An important area of common interest between the two neighbours is the foreign policy of non-alignment. Sri Lanka has generally stood neutral in Sino-Indian disputes. In fact, it made efforts to mediate between India and China after the war of 1962. Sri Lanka also showed understanding when India become nuclear. Recently in 2005, India extended valuable help to Sri Lanka after Tsunami devastated the coastal areas of that country.

Question 15.
Write about the Problem of Indian Tamils.
Answer:
Jaffna province of Sri Lanka has large concentration of Tamil population. The problem became serious when Tamilians began demanding a national homeland or “Eelam” in northern Sri Lanka. It is important to understand that there are essentially two categories of Tamilians in Sri Lanka: The Ceylon Tamils whose forefathers had migrated to Sri Lanka centuries ago.

They are estimated to be one million. The second category is of Indian Tamils whose forefathers were taken by the Britishers as plantation workers in the 19th century. They are another one million, many of them without citizenship. The problem of their status dominated early India-Sri Lanka relations. The conflict with Ceylon Tamils came later. The Sinhalese fear Tamil domination, which is the principal reason behind the ethnic conflict.

The difference between the two communities was exploited by British rulers in order to check the growing Sinhalese nationalism. The Tamils were allowed to enter the administration structure and thus gradually took control of the trade and profession. Scarce economic resources and opportunities plus the majority pressure from its own people forced the Government of Sri Lanka to pass series of steps to reducing the importance of Tamils- Indian and the Ceylonese.

The representation of Tamilians in public service in 1948 was 30 percent, but by 1975 it had fallen to mere 5 percent. The Sinhalese were encouraged to settle down in Tamil dominated areas in large numbers. The citizenship law of 1948 and 1949 had deprived about 10 lakh Indian Tamils of political rights. The Tamil youth who had lost faith in non-violence organised themselves into Liberation Tigers. The aim of these ‘Tigers’ is a sovereign Tamil State of Eelam.

The issue of Tamilians, and the policy pursued by government cast a dark shadow on Indo-Sri Lanka relations. India from time to time complained against the discriminatory policy of the Ceylon government. The agreement of 1964 sought to solve the problem of stateless persons (Indian Tamils) in Sri Lanka.

About 3 lakhs of these people were to be granted Sri Lankan citizenship and about 5 lakh 25 thousand persons were to be given citizenship of India. These people were given 15 years time to shift to India in instalments.

Later in 1974, the fate of the rest 1 lakh 50 thousand stateless persons was decided. It was agreed between the two countries that half of them were to be given citizenship of Sri Lanka and rest would become Indian nationals. Thus, the issue of stateless persons was sorted out peacefully between the two countries.

A territorial dispute arose between India and Sri Lanka over the ownership of one mile India and the World long and only 300 yard wide small island known as Kacchativu, in 1968. In 1974 under the agreement signed between the two countries, India accepted Sri Lankan ownership of the island.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 16.
Short Notes on Tamil Separatism.
Answer:
The ethnic problem between Tamils and Sinhalese had a long history. It assumed serious proportions in 1983. As the gulf between the communities developed, militancy, separatist organisations became active. Tamil United Liberation Front (TULF) demanded separate homeland for Tamils in 1988 – Tamil Eelam. A reign of terror was unleashed against the agitating Tamils in 1983. During 1983 – 86, about 2 lakh Tamils were rendered homeless. The worst racial riots in the history of the country made thousands of Tamils refugees in India.

India offered to help resolve the crisis but it was interpreted as “Indian intervention in Sri Lanka” on behalf of the Tamils. When the situation became grim, India and Sri Lanka signed an agreement in 1987. India offered military assistance under the Accord. Indian Peace Keeping Force (IPKF) was sent to Sri Lanka to help restore normalcy in the country.

The deployment of IPKF was also an extension of India’s policy of reminding Sri Lanka and outside powers that if their involvement inside the region were to have an anti-Indian orientation, New Delhi would not remain a mute spectator.

Though the accord of 1987 was a triumph of Indian diplomacy, it proved to be costly for India. India lost about 1200 soldiers and it costed Rs. 2 crore a day on IPKF in the height of its involvement. The worst part was that the Tamils turned against IPKF and a fighting broke out between the two. Rajiv Gandhi, the architect of India-Sri Lanka Accord of 1987 was assassinated in 1991 at the behest of LTTE (Liberation Tigers of Tamil Eelam) leader, Velupillai Prabhakaran.

Question 17.
Short notes on Areas of Mutual Cooperation.
Answer:
Systematic efforts at strengthening economic ties have been taken by India and Sri Lanka since the 1990s, especially after the withdrawal of Indian troops. In 1998, the two countries set up an Indo Sri Lankan Foundation for increasing bilateral exchanges in various fields. They have agreed on a free trade area to facilitate trade, which has gone up greatly.

India encouraged Sri Lanka to invite the peace process between the Tamils and the Sinhalese. In 1998 Sri Lanka invited Norway to work out a peaceful solution to the ethnic problem. India stands for unity of Sri Lanka The greatest milestone of this process was the cease-fire agreement of2002 between LTTE and Sri Lanka and the revival of the dialogue between the two.

From India’s long term point of view, Norway recognised India’s legitimate interests in Sri Lanka and stated that it has no desire to come in the way of any Indian initiative to end the conflict in the region.

Question 18.
Trace the origins of the United Nations (UN).
Answer:
The first half of the twentieth century witnessed two World Wars that caused death to 80million people. Each of those wars strengthened the determination of world leaders and people to set up institutions for peaceful world. Even before the complete defeat of the enemy countries (viz. Germany, Japan, and Italy)in the Second World War, the allied powers led by the USA, former Soviet Union and the UK started planning an organization in place of the League of Nations.

The US president, Roosevelt’ and the British Prime Minister, Winston Churchill signed the Atlantic Charter in August 1941 indicating their desire for a post-war peace institution.

Then, a series of conferences followed at Moscow, Teheran, Dumbarton Oaks and Yalta to discuss various ideas and proposals. Finally, the United States hosted the San Francisco Conference in early 1945 to finalise and sign the Charter of the new organisation, the ‘United Nations’.

The United Nations was established on 24th October 1945. Since then, we celebrate 24th October as UN Day. The Charter is the Constitution of the United Nations. It lists the purposes of the organization,the principles guiding the conduct of both the United Nations and its member countries, the principal organs along with their composition and powers.

Question 19.
Purposes and Principles of the organisation of UN.
Answer:
The Charter indicates, at the very beginning, four broad objectives of the United Nations. They are:

  • to maintain international peace and security through collective measures for
    suppression of aggression and through peaceful settlement of disputes;
  • to develop friendly relations among countries based on full respect for the principle of equality and self-determination;
  • to achieve international cooperation in the economic, social, cultural or humanitarian fields, and
  • to encourage respect for “human rights and fundamental freedoms.

In pursuit of the above objectives, both the United Nations and its member states are required to adhere to a set of important guiding principles. The foremost among them is the principle of equality among countries whether big or small, strong or weak. The United Nations will not interfere in the domestic matters of the member countries.

The member states of the United Nations are expected to resolve their disputes with other states in a peaceful manner without endangering international peace and security. Further, the member states should refrain from threats or use of force against another member. It is the duty of the members to assist the United Nations in the enforcement of peace.

As we have already noted, the maintenance of international peace and security is a very important purpose of the UN. Other purposes are complementary to the purpose of peace. In discussing the role of the UN, we should bear in mind one basic aspect of the world body. It is a political body serving its member governments in the context of global politics. Neither the preferences of governments, nor the trends in international politics are static; they change from time to time.

Hence, in the exercise of its powers, the UN cannot be rigid, mechanical or uniform. The role of the UN is marked, therefore, by flexibility and pragmatism. Generally, the UN preferred not to take a harsh view or condemn the aggressor country whenever it received complaints on a breach of peace. Instead, it directed its efforts to stop the fighting immediately and to seek withdrawal of troops to pre-war locations.

Question 20.
The composition and function of General Assembly.
Answer:
Among the principal organs, the General Assembly is the central body. The principles of sovereign equality and universality are embodied in its composition. All members of the United Nations (presently! 91) are members of the General Assembly. Irrespective of size or strength, every member has one vote in the Assembly.

A vote cast by the United States, for example, is equivalent to the vote of Bhutan or Cuba. The Assembly discusses problems brought to it, makes recommendations on peace and security questions, admits new members, and adopts UN budget. On important matters, it adopts resolutions with the support of two-third majority. Procedural decisions require only a simple majority. The Assembly meets in regular session every year. It has convened 59 such sessions so far.

The Assembly also meets, when need arises, in special sessions and emergency special sessions. The General Assembly is some times called as the world parliament. It can discuss any matter. It discusses matters which include peace and security questions, environmental protection, economic development, problems of colonial administration, disarmament, refugees, population explosion, use of global commons like outer space and deep seaboard.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

It can only make recommendations. As part of this function, the Assembly has adopted a number of important declarations containing principles of international cooperation in political, economic, social and other matters. The Universal Declaration of Human Rights (1948), the Declaration on Decolonisation (1960), Declaration on New International Economic Order (1974), Declaration on Rights of the Child (1989), Declaration on International Terrorism (1994) are only a few examples.

They are common goals desirable for governments to implement in their national policies and programmes. The Declarations are not binding on countries. Yet, they carry great moral and political weight. Therefore, governments find it difficult to ignore them.

The Assembly has also adopted several laws like the covenant on civil, political, economic rights of individuals, the laws of exploitation of seas, laws prohibiting or controlling chemical and biological weapons, and so on. These laws are not like the laws of our Parliament which are automatically binding on all of us whereas these international laws and convention sare legally binding only on those states that agree to comply with them.

The Assembly elects members of various organiser: It appoints the Secretary General. It supervises the work of the Economic and Social Council, the Security Council, the Trusteeship Council and other bodies. The Assembly has the power to approve the budget of the United Nations and to apportion the amount among all the member countries.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 21.
The composition and function of Security Council.
Answer:
The Security Council is the most powerful decision-making body of the United Nations. It has the main responsibility to maintain international peace and security. The Council is a contrast from the General Assembly, in respect of both its composition and the decision-making procedure. Unlike the Assembly, the membership of the Council is limited to 15 countries only, out of which five are permanent members. These five countries are China, France, Russia, the UK and the USA.

The remaining ten members- called non-permanent members are elected by the General Assembly for a term of two years. They represent different geographical regions of the world like Asia, Africa, Latin America, Western and Eastern Europe. It was initially hoped that its small size could make it easy for the Council to take decisions on procedural matters by nine affirmative votes (simple majority).

On substantive questions, the nine affirmative votes should include concurring vote of the permanent members. In other words, the Council cannot take decisions of major significance if any one of the five permanent members casts a negative vote. This special privilege of the permanent members is popularly known as the veto power. To abstain from voting in the Security Council is not veto.

The veto provision has faced criticism from the very beginning. The veto power dilutes the principle of sovereign equality of member countries. The power and functions of the Security Council are limited to the task of maintenance of international peace and security. In case, a dispute arises between two or more countries the Council can make appropriate recommendations in the interest of peaceful settlement of the dispute.

Nevertheless, these recommendations are not binding on the unwilling states. For example, on the Jammu and Kashmir dispute, the Security Council resolutions are not legally binding on either India or Pakistan unless both countries willingly accept them. The Council can use extraordinary power to deal with wars or threats of war between countries.

In such an event, the Council can determine who the aggressor is and can call for necessary steps to restore peace. These steps may include, at the discretion of the Council, economic sanctions like freezing of assets abroad, banning of exports and imports, or military action by land, sea or air.

Notably, whenever the Security Council takes such steps, they are binding not only on the states directly involved in the war but also on all members of the United Nations. Once, the Security Council takes a decision, it is the duty of the member countries to carry out decisions. Obviously, the Council can take such important decisions only with the agreement among the permanent members. In the recent years, after the end of the cold war, the Council has frequently used its binding powers to deal with various problems of international peace and security.

The role of the Security Council in discharging its functions depends on the specific circumstances of each case and the existence of broad agreement among the five permanent members. It is important to note that the Security Council has imposed varying sets of economic and diplomatic sanctions against 25 countries so far. These sanctions included cutting off diplomatic relations, stopping of oil imports and exports, banning weapons supplies, freezing of assets abroad, etc.

Haiti, Iraq, Libya, Somalia, South Africa were among the targets of these sanctions. Since no armed forces are placed under the UN to fight an aggressor even after five decades of the Charter’s commitment to it, it has requested member countries to contribute towards such a force to take military action for restoring peace.

Question 22.
The Economic and Social Council.
Answer:
The Economic and Social Council works to promote international cooperation in economic and social fields. It comprises 54 members all of whom are elected for a term of three years by the General Assembly, giving representation to various geographical regions. Decisions are taken by a simple majority of members present and voting. It considers international economic, social, cultural and humanitarian problems. The Council has set up commissions to study and advise on the status of women, population, human rights, etc.

It has the power to coordinate the activities of various specialized agencies like the International Labour Organisation, the World Health Organisation etc. (which are discussed in a separate lesson in this book). Another important function of the Council is to bring Non-Governmental Organizations (NGOs) to take part in its deliberations.

The powers of the Council are quite modest as compared to its responsibilities. By means of study, discussion and coordination, the Council is expected to promote full employment, higher standards of living and solution of international economic and social problems.

Question 23.
The Trusteeship Council.
Answer:
The Trusteeship Council was created to supervise the working of the international trusteeship system. All the 11 territories, originally placed under the trusteeship system have become free. Now that there is no trust territory to be administered, the Trusteeship Council has ceased to play an active role in the UN system and does not hold meetings. The Charter has to be amended to dissolve this organ.

Question 24.
The International Court of Justice.
Answer:
The International Court of Justice, known as the World Court, located at The Hague (The Netherlands), is the principal judicial organ of the United Nations. The Court consists of 15 judges; who are elected jointly by the General Assembly and the Security Council for a term of nine years. Let us not confuse this court with national court like the Supreme Court of India. Only member nations, not private individuals, can bring cases before the Court. And the judgements are not binding. So far the Court has handled 72 cases.

Question 25.
The Secretariat.
Answer:
The Secretariat General comprises the international staff posted at the UN headquarters, New York and other locations throughout the world. They are expected to be impartial and independent in the discharge of their responsibilities, the United Nations and not any particular member country.

The Chief of the Secretariat is the Secretary General who is appointed by the General Assembly on the recommendation of the Security Council for a term of five years. Since the inception of the Organization, six persons have served as the Secretary-General.

They are; Trygve Lie of Norway, Dag Hammarskjold of Sweden (1953 – 61), U Thant of Myanmar (1961 – 71), Kurt Waldheim of Austria (1972 – 96) and Javier Perez De Cuellar of Peru (1982 – 91) Boutros Boutros-Ghali of Egypt (1992 – 96) Kofi Annan from Ghana. Presently, Ban Kimoon of South Korea is occupying this prestigious office.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

Question 26.
Fight against Colonialism and Racism.
Answer:
As we know India was a British colony for nearly 200 years before Independence in 1947 India was not alone to come under colonial rule. Most parts of Africa and Asia. were not free in 1945 when the United Nations was set up. For UN, ending colonial rule became essential for achieving world peace and progress. Freeing millions of people from foreign colonial rule is a historic achievement of the UN.

The UNs anti-colonial territories covered two categories of dependent population. They were the trust territories for which UN was directly responsible. Then there were several territories administered by western colonial powers like Britain, France, etc.

‘Trust’ territories were placed under the responsibility of the UN until the people of the territories concerned would be able to determine freely their future status. Cameroon, Nauru, New Guinea, the Pacific Islands, Rwanda-Urundi, Somaliland, Tanganyika, Togoland were among them. By 1994 all trust territories became free with the help provided by the UN.

Seven have become independent and four chose to merge with the neighbouring countries. The UN interest in the liberation for subject people extended beyond trust territories.

Its built up this campaign against colonialism was the adoption of the Declaration of Decolonisation by the General Assembly in 1960, demanding immediate independence of all colonial territories and populations. Since that time, 60 territories have become free under the sustained pressure built in the UN.

Namtria, Eritrea, East Timor are among the recent examples of successful fight against colonialism. There are now only very few like western Sahara waiting to exercise their free choice. There is some confusion that the fight against colonialism blesses the right of some disgruntled people to separate from their newly formed independent state. Right to- ‘self-determination’ applies to people under foreign colonial rule only.

The UN opposition to racism in South Africa known as apartheid-is also remarkable. The organizations interest in the matter dates back to early 1946. South African white minority regime did not pay heed to the gentle pleas by the UN. Later pressure was built to force white South African government to end its policy of discrimination against the Black population.

South African teams were passed to participate in international sports events. The Security Council joined the effort later by banning arms sales. South Africa felt the heat and agreed to end its policy in 1993. The widely respected black leader, Nelson Mandela was released after 27 years of imprisonment. The apartheid laws were revoked.

Internationally supervised free elections were held, leading to the installation of a government under President Mandela in 1994. Soon afterwards, the UN revoked all previous punishments and restored to the new South Africa its rightful place in the world body.

Question 27.
Promotion of Human Rights.
Answer:
Promotion of human rights culture through worldwide human rights standards has been another major contribution of the United Nations. Nearly 80 declarations and conventions touching upon various facets of human rights have been adopted by the UN in the past five decades. The Universal Declaration of Human Rights was the first among the UN declarations.

The day of its adoption-10 December 1948 is observed every year as the Human Rights day. The Declaration contains a broad range of civil, political, economic, social and cultural rights that all people are entitled to, without any discrimination. Admittedly, the Universal
Declaration, as any declaration, is not binding on governments.

However, it gave inspiration to the drafting of two legally binding covenants, one on economic, social and cultural rights and the other on civil and political rights. Both these covenants became applicable to the signatory states from 1976 onwards. These two covenants, together with the universal declaration, are known as ‘the International Bill of Rights.

The covenant on economic, social and cultural rights highlights the right to work in just condition, the right to adequate standard of living and the right to social protection. The Covenant on civil and political rights emphasizes freedom of movement, equality before the law, freedom of religion, freedom of participation in elections, and protection of minority rights.

A specially constituted committee monitors the compliance of the signatory states to this covenant on HR. A remarkable feature is the UN is empowered under the civil and political rights covenant to receive and redress complaints from individuals against the behavior of their own respective governments.

The UN has adopted other declarations and covenants with the aim of stopping the practice of torture and racial discrimination or protecting vulnerable section like children, women and migrant workers

The activities of the UN include the convening of periodical conferences on human rights. Recently, in 1993 the UN organized at Vienna an international conference on Human rights. Acting upon the recommendations of the conference, the General Assembly appointed in 1994 the UN high commissioner for HR whose task is to promote more scrupulous respect for human rights throughout the world.

Question 28.
Need for Re-Structureing the United Nation.
Answer:
Although the United Nations has done a responsible job there are some obstacles which limit its performance. For example, a few organs of the United Nations have not changed, though the changes in the world around require it. Let us look at the Security Council as an example. Unlike the General Assembly; the permanent membership of the Security CounciLis limited to 15 countries only.

Out of that, P-5 (China, France, Russia, UK and USA) are permanent. They were given permanent status in 1945 due to some historical arid political reasons. The remaining ten members are non-permanent members elected by the General Assembly for a term of two years. This arrangement is six decades old, when most of Africa and Asian countries were not part of the United Nations. Now with membership of the world body rising by four times, the council’s composion needs to be suitably changed.

There is a strong case to add a few countries like India as permanent members. The member of non-permanent members should also be increased so that different countries can get a feeling that the Council works for their future. The Third World countries are of the opinion that United Nations is an agent of Western countries especially the United States. To correct this image, the number of Permanent members has to be increased.

Japan, India, Germany, Brazil and Nigeria are the claimant for it. Japan and Germany are no longer enemy states and because of their economic strength and contribution to the UN budget are considered as the most eligible for permanent membersnip of the Security Council. India’s contribution in several UN Peacekeeping forces and its active role in peace making processes facilitates its obvious claim to be a permanent member of the Council.

India has been a founder member of the United Nations. Besides India is the second largest populous country and is the largest democracy in the world.

Question 29.
Explain the working of the United Nations Development programme (UNDP).
Answer:
The United Nations structure for planning, coordinating, administering and implementing its economic and social programmes is vast and decentralized. At the apex of the structure are the General Assembly and the Economic and Social Council (ECOSOC). The General Assembly provides general direction and supervision for economic and social activities.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

ECOSOC concentrates solely on this work and has operated with the assistance of functional commissions. These are the Statistical Commission, Human Rights Commission, the Commission on the Status of Women, the Commission for Social Development, the Commission on Narcotic Drugs.

There are also regional economic commissions, which focus on the problems salient to their geographical areas. Five such commissions have been established: the Economic Commission for Europe (ECE); the Economic Commission for Asia and the Pacific (ESC AP), the Economic Commission for Latin America, the Economic Commission for Africa (ECA) and the Economic Commission for Western Asja.

A number of other bodies exist in the economic and. social field which are not as directly subject to ECOSOC direction or control but which are closely related to ECOSOC activities.

These agencies include :
(1) the United Nations Development Programme (UNDP)
(2) The United Nations International Children’s Emergency Fund (UNICEF)
(3) The United Nations High Commissioner for Refugees (UNCR)
(4) The United Nations Conference on Trade and Development (UNCTAD)
(5) The United Nations Industrial Development Organization (UNIDO)
(6) World Food Programme
(7) The United Nations Environment Programme (UNEP).

There are Specialized Agencies of the United Nations. Though these agencies are part of the UN system, they function independently of United Nations organs and are generally described as autonomous organizations. Each has its own headquarters, constitution, staff and budget. Each was created in the same manner as the United Nations by an international conference. Membership of these specialized agencies and membership of the United Nations is not identical.

These agencies are universal in membership. States which are not UN members can be admitted as the members of the specialized agencies (see box) Each specialized Agency is an inter-government agency and is established by international treaty or by an agreement between the agency and the United Nations.

This agreement is negotiated between the agency and ECOSOC subject to approval by the General Assembly. There are about 15 specialized agencies, which operate in affiliation with the United Nations, we shall identify and describe the activities of following UN development agencies, such as UNDP, UNICEF, the World Health Organization (WHO), the United National Educational Scientific and Cultural Organization (UNESCO) and the World Bank.

Question 30.
Describe the role of UNICEF in promoting the welfare of children.
Answer:
Created in 1946, UNICEF concentrates exclusively on the task of improving the lot of disadvantaged children. UNICEF has undertaken projects on health, education, malaria eradication, nutrition, rural development, family and child welfare and emergency aid to promote child welfare. In recognition of its social and humanitarian efforts, UNICEF was awarded the Nobel Peace Prize in 1965.

It focuses on India in a very big way. UNICEF has made an important contribution to a better environment for children in India and identified the problem of excess flouride in groundwater resources. Rajasthan and Andhra Pradesh are the most severely affected states.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Long Answer Questions

WHO’s aims are: (i) preventing the spread of disease, (ii) curing disease and (iii) preventing the outbreak of disease. The means adopted to prevent the spread of disease include Conventions providing international standards for public health.

WHO’s has been a clearing house for scientific knowledge and a exchange of information for curing disease. WHO’s activity in the area of preventing the outbreak of disease is to facilitate the exchange of findings and promotion of research.

It has encouraged research with cheap preventatives, especially vaccines for tuberculosis and DDT for malaria. The campaign against malaria has been one of WHO’s biggest all-out programme.

Since heterosexual transmission of the human immune deficiency virus (HIV) that causes AIDS is becoming the predominant mode of spread of HIV in most countries of the world, WHO is engaged in research for vaccine to cure AIDS for which it needs necessary financial support from rich member countries to meet the challenge of this deadly disease.

A very important WHO programme is Polio Eradication Immunization. Polio is the first disease of the 21 st century to be eradicated. Another important campaign of UN health agency, WHO is against the use of tobacco especially in developing countries.

The Food and Agriculture Organisation (FAO) concentrates on rural development. This Rome based agency works for alleviation of poverty and hunger by promoting agriculture development, improved nutrition and easy access of food. The international Labour Organization (ILO) helps nations in enhancing the living and working standards of industrial workers.

UN Industrial Development Organization strives for industrial development of developing countries in the era of globalization. With the end of the Second World War, came the conviction that wars begin in the minds of men and the ignorance fosters suspicions and hatreds on which wars breed. It was felt that international collaboration could bring knowledge and greater understanding among people.

Question 31.
Describe the functions of the World Bank as the main UN financial agency for Development.
Answer:
Some of the programmes of the various UN agencies discussed in the previous section entail substantial financial contributions to the purpose of development. For example, an annual budget of approximately 670 million dollars for UNDP is devoted exclusively to aiding the development process. Capital is a primary component for development. The most important financial agencies of the United Nation are the International Bank for Reconstruction and Development (IBRD) or World Bank and the International Monetary Fund (IMF).

These are also called the Bretton Words institutions as these agencies came into being in December 1945 at the Bretton Woods Conference held in New Hampshire, USA. IMF provides temporary funds to aid governments in correcting balance of payment deficits. The World Bank group is the largest multilateral source of funds for development projects for infrastructure development. About 300 billion dollars worth of aid has been given so far for development projects.

However, the World Bank and the IMF are under severe criticism. They are dominated by rich countries. They are also not accountable to the United Nations. Their composition is not democratic. Voting in these institutions is not based on the principle of one nation one vote as in the General Assembly. There is weighted voting i.e. a member country’s number of votes are as per the amount of financial contribution or shares in these bodies.

World Bank’s loan falls into two broad categories. Investment loans are long-term loans aimed to create the physical and social infrastructure necessary for poverty reduction and sustainable development. World Bank loans helped developing countries to construct basic education schools. Other projects include poverty reduction, rural development, water and sanitation, natural resource management and health. Investment loans have accounted for 75 to 80 percent of all World Bank lending.

Adjustment loans have become an important component of World Bank lending and are short-term loans to promote the market structures as well as political institutional reform. During the last 20 years, adjustment loans have accounted for between 20 and 25 percent of all World Bank lending.

Other important sources of multilateral financing for development include regional banks, such as the Inter- American Development Bank and the Asian Development Bank, have been major sources of development financing for hundred of projects within their respective regions.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

Odisha State Board CHSE Odisha Class 12 Political Science Solutions Unit 4 India in World Politics Objective Questions and Answers.

CHSE Odisha 12th Class Political Science Unit 4 India in World Politics Objective Questions

Multiple Choice Questions With Answers

Question 1.
Who is known as the architect of foreign Polity of India?
(a) Mahatma Gandhi
(b) Indira Gandhi
(c) Rajiv Gandhi
(d) Jawaharlal Nehru
Answer:
(d) Jawaharlal Nehru

Question 2.
Non-alignment is totally opposed to:
(a) Military Alliances
(b) Security blocs
(c) Cold War
(d) All the above
Answer:
(d) All the above

Question 3.
The key word that can be used for describing Foreign Policy of India
(a)Non-alignment
(b) Anti-imperialism
(c) Panchsheel
(d) World Peace
Answer:
(a) Non-alignment.

Question 4.
India is a strong contender for a permanent seat in:
(a) ICJ
(b) WTO
(c) World Bank
(d) UN Security Council
Answer:
(d) UN Security Council

Question 5.
Third World Countries means :
(a) Poor Countries
(b) Asian Countries
(c) Latin American Countries
(d) Developing Countries
Answer:
(d) Developing Countries

Question 6.
India became a Nuclear Weapon State in:
(a) January 1950
(b) October 2008
(c) May 1974
(d) May 1998
Answer:
(d) May 1998

Question 7.
India has consistently refused to sign:
(a) PTBT
(b) NPT
(c) NPT & CTBT
(d) CTBT
Answer:
(c) NPT & CTBT

Question 8.
Third World Countries means:
(a) 15 August 1947
(b) 26 January 1950
(c) 26 November 1949
(d) 30 October 1945
Answer:
(d) 30 October 1945

Question 9.
India is totally opposed to:
(a) Racial Discrimination
(b) Uni-Polarism
(c) Colonialism
(d) All the above
Answer:
(d) All the above

Question 10.
Non-Alignment Stands:
(a) Opposition to military alliances
(b) Independence in foreign relations
(c) Opposition to Cold War
(d) All the above
Answer:
(d) All the above

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

Question 11.
China became a Communist Country in the year:
(a) 1947
(b) 1949
(c) 1962
(d) 1967
Answer:
(c) 1962

Question 12.
Bandung Conference of Afro-Asian Countries was held in the year:
(a) 1945
(b) 1949
(c) 1955
(d) 1967
Answer:
(c) 1955

Question 13.
Which line serves as the boundary line between India and China in the Eastern Sector?
(a) Huang Hua border
(b) Me. Mohan Line
(c) Indo-China border
Answer:
(c) Indo-China border

Question 14.
Who is the President of China visited India in the year 1996?
(a) Chou-Enlai
(b) Mao Tse Tung
(c) Jiang Zemin
Answer:
(c) Jiang Zemin

Question 15.
The United Nations Charter was signed in 1945 at the City of:
(a) Geneva
(b) New York
(c) San Francisco
(d) India
Answer:
(c) San Francisco

Question16.
How many countries were the original members of the United Nation?
(a) 45
(b) 51
(c) 172
(d) 191
Answer:
(b) 51

Question 17.
Which organ at the United Nations performs the function of coordinating the activities of the specialized agencies?
(a) General Assembly
(b) Security Council
(c) Economic & Social Council
(d) All the above
Answer:
(c) Economic & Social Council

Question 18.
The Judges of the World Court are elected by:
(a) General Assembly
(b) Security Council
(c) Both Security Council & General Assembly
Answer:
(c) Both Security Council & General Assembly

Question 19.
India has always stood for:
(a) A nuclear weapons free world
(b) A world where every country has nuclear weapons.
(c) A world where nuclear weapons are selectively held by few countries.
Answer:
(a) A nuclear weapons free world

Question 20.
The first Peacekeeping nation with Indian troops was sent to:
(a) Korea
(b) Sinai
(c) Congo
(d) Kalombo
Answer:
b) Sinai

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

Question 21.
Which of the following is not a permanent member of the Security Council?
(a) Russia
(b) Great Britain
(c) India
(d) China
Answer:
(c) India

Question 22.
Which of the following statements is false?
(a) Cold War is over
(b) Soviet Union has disintegrated
(c) Globalisation is a reality
(d) United Nations has been dissolved
Answer:
(d) United Nations has been dissolved

Question 23.
The first peacekeeping nation with Indian troops was sent to
(a) Korea
(b) Sinai
(c) Congo
Answer:
(b) Sinai

Question 24.
Which of the following statements is false?
(a) India is one of the second largest troop contributors to UN peace-keeping.
(b) Peace-keeping was confined to cold war years.
(c) India’s role was significant in protecting the Congo from separation.
Answer:
(c) India’s role was significant in protecting the Congo from separation.

Question 25.
India’s contribution to peacekeeping included
(a) only troops.
(b) only non-military staff.
(c) both military and civilian staff.
Answer:
(c) both military and civilian staff.

Question 26.
Which of the following is not a permanent member of the Security Council?
(a) Russia
(b) Great Britain
(c) India
(d) China
Answer:
(c) India

Question 27.
Which of the following statements is false?
(a) Cold war is over
(b) Soviet Union has disintegrated
(c) Globalisation is a reality
(d) United Nations has been dissolved.
Answer:
(d) United Nations has been dissolved.

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

Fill In The Blanks

1. ______ was the main architect of India’s foreign policy.
Answer:
Nehru

2. The Afro-Asian Conference, 1955 was held at _______.
Answer:
Bandung

3. The first NAM Conference was held at ________ in the year _______.
Answer:
Belgrade, 1961

4. The Panchsheel agreement was signed between _______ and _______.
Answer:
India, China

5. India hosted NAM Summit in _______.
Answer:
New Delhi

6. China became a communist country in the year __________.
Answer:
1949

7. Bandung Conference of Afro-Asian countries was held in the year ________.
Answer:
1955

8. _________ serves as the boundary line between India and China in the eastern sector.
Answer:
McMahon Line

9. China liberalised its economy in ________.
Answer:
Late 1970s

10. ________ the President of China visited India in the year 1996.
Answer:
Jiang Zemin

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

11. The United Nations Charter was signed in 1945 at the city of____________.
Answer:
San Francisco

12. ___________countries were the original members of the United Nations.
Answer:
51

13. The main purpose of the United Nations Charter is _________.
Answer:
Maintenance of international peace and security

14. The permanent members of enjoy the veto power, _______.
Answer:
The Security Council

15. How many territories did The Trusteeship Council used to administer?
Answer:
11

16. Which organ of the United Nations performs the function of coordinating the activities of the specialized agencies?
Answer:
The Economic and Social Council

17. _______ is at present the UN Secretary General.
Answer:
Bam Ki-moon

18. The judges of the World Court are elected by_________.
Answer:
Both the Security Council and the General Assembly

20. When did Sri Lanka gain her independence?
Answer:
February 4, 1948

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

21. Name the two categories of Tamil-speaking people in Sri Lanka.
Answer:
Indian Tamils and Ceylonese Tamils

23. Regarding which island did India surrender her claims to Sri Lanka in 1974?
Answer:
Kacchativu island

24. In what year did India send IPKF to Sri Lanka?
Answer:
1987

True or False

1. Non-alignment and neutrality can be treated as same.
Answer:
False

2. India opposed the policy of apartheid as practised by the government of South Africa.
Answer:
True

3. Nehru along with Tito and Nasser played a major role in the founding of NAM.
Answer:
True

4. International relations in the post cold war period is based upon the bipolar model.
Answer:
False

5. Kashmir issue became the biggest foreign policy problem for India in 1990s.
Answer:
True

6. India’s foreign policy after cold war wants to neglect Arab countries and embrace Israel.
Answer:
False

7. India is trying to forge a coalition of countries to counter terrorism.
Answer:
True

8. The two-nations theory was accepted by Indian National Congress.
Answer:
False

9. Maharaja Hari Singh of Jammu and Kashmir demanded assistance from both India and Pakistan but only India responded.
Answer:
False

10. Pakistan occupied Kashmir is known as Azad Kashmir in Pakistan.
Answer:
True

CHSE Odisha Class 12 Political Science Unit 4 India in World Politics Objective Questions

11. The people of East Pakistan declared themselves independent in April 1971.
Answer:
True

12. The Shimla Agreement was signed between India and Bangladesh in 1972.
Answer:
False

13. Kargil war happened immediately after the nuclear test by India in May l972.
Answer:
False

14. Sovereign equality among the member states is a cardinal principle of the United
Nations.
Answer:
True

15. The United Nations cannot normally take up the domestic problems of its member countries.
Answer:
False

16. The United Nations’ membership has not increased since its existence.
Answer:
False

17. Private individuals can bring disputes before the World Court.
Answer:
False

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 1 Understanding Political Theory Short Answer Questions.

CHSE Odisha 11th Class Political Science Unit 1 Understanding Political Theory Short Answer Questions

Very Short-Answer Type Questions

Question 1.
What is politics?
Answer:
Politics refers to a social, political process which resolves social issues and maintain social orders. It believes in using power for the promotion of self interest.

Question 2.
What are the objectives of politics?
Answer:
Politics seeks to resolve socio-political conflicts. It tries, to bring order out of disorder and restores social integration.

Question 3.
What is the Marxian view of Politics?
Answer:
According to Marx politics is an instrument of class conflict. The rich and powerful make use of it for their self interest.

Question 4.
What is political science?
Answer:
Political science is a social science which studies about state, government and the constitutional system. It also deals with the origin and development of state and its structure and functions.

Question 5.
What is political philosophy?
Answer:
Political philosophy is the abstract of speculative ideas about any political concept or event. It is value oriented study which seeks to explain the ultimate reality.

Question 6.
What is a political system?
Answer:
Political system is a set of arrangement of political actors and institutions in such a way that policy decisions are easily taken. Modern state is a political system as it adjusts itself to the changing environmental stress.

Question 7.
What do you mean by political dynamics?
Answer:
Political dynamics include those external forces and influences that affect the political process. Political parties pressure groups, interest groups and lobbyists are known as political dynamics.

Question 8.
What is the nature of politics?
Answer:
Politics is involved with the totality of interests in our social life. Politics believes in resolution of conflict and controversy by use of power.

Question 9.
What is political theory?
Answer:
Political theory constitute of those ideas, concepts and principles that influence the constitution, government and social life in a systematic manner. It stands for the history of political ideas and it is based on reality.

Question 10.
What is the need of studying political theory?
Answer:
The study of political theory makes people think rationally about political issues and to assess the political events of our time. It informs us about the basic knowledge of political ideas institutions and concepts that shape our day to day life.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 11.
What is the scope of politics?
Answer:
Scope means the subject matter and politics is concerned with the study of state, government, social, political process. Polity making, power structure and administrative process. It also deals with the shaping and sharing of power in society and politics.

Question 12.
What is formal politics?
Answer:
Formal politics refers to the cooperation of a constitutional system of government and publicity defined institutions and procedures. It encompasses the study of political parties, public policy, war and peace, foreign policy etc.

Question 13.
What is informal politices?
Answer:
Informal politics refers to alliance formation, group structure, exercise of power to protect and promote our goals or interests. It is understood as day to day politics that affect our lifestyle.

Question 14.
How politics differs from political science?
Answer:
Political science is the theory whose application is called politics. Political science deals with the origin, nature, working and future of state or a government but politics is concerned with the real issues affecting the system and their solution.

Question 15.
What is state?
Answer:
State is a sovereign political entity. It is the most powerful and universal of all social institutions.

Question 16.
What is Government?
Answer:
Government is the working element of state. It consists of three organs, such as executive, legislature and judiciary.

Question 17.
What is sovereignty?
Answer:
Sovereignty is the most important element of state. It is the supreme and unlimited power of the state over citizens.

Question 18.
Why man is called a social animal?
Answer:
Man is called a social animal because he lives in society and it is society that creates condition for the moral and material development of individual. Man can not live outside society.

Question 19.
What is individualism?
Answer:
Individualism is a political philosophy of 1 9th century. It pleads for maximum liberty to the individual and minimum role to the state. It believes in the economic theory of laissez flare.

Question 20.
What are the functions of a police state?
Answer:
A police state has to defend the state from external aggression. It also maintains law and order and ensures safety and security to the individuals living in the state.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 21.
What is modern individualism?
Answer:
Modern individualism is the individualism of19th century. It gives the state of positive role. It raises its voice against excessive state regulation and control.

Question 22.
What is globalization?
Answer:
Globalization is a policy of economic reforms which aims at reducing trade barriers between the developed and developing countries. It seeks the integration of economies through exchange of ideas, information, technology, labour and capital.

Question 23.
What arc the two main goals of Globalization?
Answer:
The two main goals of Globalization are

  • To secure the benefits of free trade open access to markets and equal participation in securing sustainable development for all the people, and
  • To reduce trade barriers ensuring free flow of capital labour from one Country to the other.

Question 24.
What do you mean by a welfare state?
Answer:
Welfare state is a social service agency which gurantees basic minimum substance to all. It undertakes volumes of social security measures for the poor and backward people.

Question 25.
Why the individualists regard the state as a necessary evil?
Answer:
The state is regarded as a necessary evil because, It interferes in individual liberty and Curtails individual freedom.

Question 26.
What are the two main drawbacks of a welfare state?
Answer:
A welfare state suffers from bureaucratic despotism. It is too much expensive.

Question 27.
What are the two main utilities of Globalization?
Answer:
Globalization accelerates the pace of economic growth. It helps in dissemination of technological knowledge among nations.

Question 28.
Laissez faires
Answer:
The theory of laissez faire is related to individualism. As an economic theory it seeks to give unrestricted freedom to an individual in the economic sphere

Question 29.
Police state
Answer:
Police state concept is developed out of individualism. The individualists consider the state as a police man and argue for giving it only police functions, hence the states is called a police state.

Question 30.
Globalization
Answer:
Globalization is a process of increasing socio-economic industrial and trade relations among the nations all over the world. It seeks to make the whole world a global village. The main trust of globalization is to give the developed nations a free access into the markets of developing nations.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 31.
International Recognition
Answer:
International recognition means the recognition of the international society of nations. It is a formal process by which the existing members of the family of nations accord statehood to a newly born state.

Question 32.
External sovereignty
Answer:
External sovereignty means freedom from outside control or influence. By this aspect of sovereignty a state designs its foreign policy.

Question 33.
Internal sovereignty
Answer:
Internal sovereignty is enforced within the territory of a state. It enables the state to make law for the state administration.

Question 34.
Why state is called a necessary evil?
Answer:
Individualists consider the state as a necessary evil. To them state is necessary for maintenance of law and order and to defend it from aggression. It is an end as it interferes with the liberty of individuals.

Question 35.
What are the two major drawbacks of welfare state?
Answer:
In a welfare state the bureaucracy becomes autocratic and oppressive. It is too costly for a poor and backward country.

Question 36.
Utility of globalization?
Answer:
Globalization accelerates the pace of economic growth. It makes exchange of ideas, capital, raw materials, labour and technology between rich and poor countries easier.

Question 37.
Two major defects of globalization
Answer:
Globalization increases industrialization leading to environmental pollution. It increases unemployment and intervens in the autonomy of states.

Question 38.
What is mixed economy?
Answer:
Mixed economy refers to the coexistence of public and private sector for economic development. This type of economy is found in welfare states.

Question 39.
What is New Deal?
Answer:
New “deal refers to a new programmes of action pursued by USA and other western countries to get rid of economic recession. President Franklin D. Roosevelt of USA was the advocate of this reform programme.

Question 40.
What is Beverage Report?
Answer:
Beverage Report was issued in England in 1942 by William Beverage on social insurance. It envisaged a scheme of social security to fight the evils of want, diseases, ignorance, squalor and idleness.

Question 41.
Negative functions of welfare state
Answer:
A welfare state gives protection against unemployment, poverty and disease. It fights against natural calamities and safeguards children, women and weaker sections of society.

Question 42.
Positive functions of welfare state
Answer:
A welfare state provides the people a wide range of health service and education to the people. It generates employment opportunity and provides social security to old aged and economically disadvantaged sections of society.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 43.
What is modern individualism?
Answer:
Modern individualism is 20th century individualism. It regards the state as a positive and useful institution.

Question 44.
What for state is necessary?
Answer:
State exists for the sake of good life of individuals. It maintains order and helps the individual in realization of his potential.

Question 45.
Theoretical Politics and Applied Politics.
Answer:
Scholars like, Sir Frederich Pollock, Jellinek and Willoughby have distinguished between theoretical and applied politics. Theoretical politics deals with the theory of state, but applied politics deal with structure and working of state. The artificial politics deals with law and administration of state but applied politics with the application of law. Theoretical politics is a science but applied politics is an art.

Question 46.
Politics and Political science
Answer:
The two terms ‘Politics’ and ‘Political Science’ are often used interchangeable, but they differ on the following grounds.

  • Politics is the practical aspect of Political science
  • Political science is the theory which in practice is known as politics.
  • Political science is normative but politics deals with operational aspect.
  • Political science is an academic discipline and its principles are universal, but politics differs from state to state.
  • Politics is an art, but political science is a science,
  • The term politics is much broader a concept than that of political science. In the modern age politics is concerned with the study of conflict and cooperation is society with the help of power.

Question 47.
Political science and Political Philosophy
Answer:
Political science differs from political philosophy on the following ways.
Political science is a science of state and government but political philosophy is a science political values and beliefs. Political science is more empirical than normative, but political philosophy is theory oriented. Political science is more concerned with what is and what ought to be but political philosophy prescribes what is good, just and proper. Political science seeks to analyze political phenomena to frame general laws but, political philosophy is value oriented and normative. Political philosophy is a part and parcel of Political science.

Question 48.
State and Government
Answer:
State is a sovereign political entity, but government is an element of state and it fulfills the purpose of state. State is sovereign, but, government exercises sovereign power. State is permanent but government is temporary. State has a definite territory and population but government consists of a few senior citizens and it works within the state. State is abstract but government is concrete. Membership of state is compulsory but not of government.

Question 49.
Individualism and socialism
Answer:

  • Under individualism individual is the centre of society but under socialism state is central. Individualism pleads for maximum liberty to the individual but socialism pleads for maximum power to the state. Individualism regards the state as a necessary evil, but socialism holds the state a positive good.
  • Individualism gives the state only police functions but socialism gives the state both social economic political and welfare functions. Individualism regards the state as a means, but socialism regards it as an end. Individualism pleads for private property but socialism opposes it.

Question 50.
Traditional and modern individualism
Answer:
Traditional individualism was a philosophy of 17th to 19th century, but modern individualism was a philosophy of 20th century. Traditional individualism was exported by Adamsmith, Herebet Spencer and J.S. Mill, but modern individualism was exposed by Laski, M.P. Follett and Norman Angell.

Traditional individualism regards the state as a necessary evil, but modern individualism regards the state, as a useful institution. Traditional individualism regards the state as a perpetrator of individual liberty, but modern individualism regards it as a coordinator, a facilitator. Traditional individualism insists on individual identity and progress but modern individualism on group identity of individuals. Traditional individualism accords police functions to the state but modern individualism accords welfare functions to the state.

Question 51.
Globalization and internationalism
Answer:
Internationalism stands for increasing cooperation and peaceful co-existence among nations. But, globalization is a process of economic integration of the whole world. Internationalism pleads for avoidance of war and restoration of peace, But, globalization seeks to increase economic and trade relations among nations. Globalization seeks to secure the socio-economic integration and development of all people, but internationalism stands for safety and cooperation of nations. Globalization is an aspect of internationalism.

Question 52.
State and Civil policy
Answer:
State is a sovereign political unit, but civil society is a non governmental voluntary movement for the sake of people. State is sovereign but civil society is not sovereign. State enjoys coercive authority but civil society does not. Civil society exists within the state. State has a territory and population, but civil society has no definite territory nor any fixed population. State can be autocratic but civil society can’t.

Short Questions With Answers 

Question 1.
What is political Science?
Answer:
Political science is a social science deals with the study of state and government. It investigates about the origin and evolution of state, the nature and working of political institutions, processes and principles of conduct. It also analyses about the power structure. It is a science of society and civilization. It is the study of political behaviour and political systems In the modern age it studies about the environment.

Question 2.
Nature of Political Science
Answer:
Political science is a social science. Political science comes closer to a science as it follows scientific method of study. It is an art as it applies the knowledge of science for state administration. It has no agreed principles. It is unpredictable andIts decisions are inexact.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 3.
Political Science is a science
Answer:
Political science is considered to be a subject of science because It believes in scientific method. There is systematic study undertaken on the subject. It studies about individual behaviour, institutions and processes It undertakes experimentation and observation of facts; and To a great extent its decisions are exact. So it may not be a science like physics or chemistry but a science like meteorology or astronomy which can’t make accurate predictions.

Question 4.
Scope of Political Science
Answer:
The scope of political science is vast and expending. It covers the study of state government and legal system. It involves the study of various political systems. Political science also deals with political ideas and ideologies. It encompasses the study, of political parties, pressure groups and other non political institutions. It studies about local and municipal bodies, elections, voting behaviour, inter state relations and about war and peace.

Question 5.
Political science begins and ends with state
Answer:
This statement of Gamer confines the study of political science to state. State is the be all and end all of political science. It investigates about the origin and evolution of state nature of state and working of different states. It also deals with the manifestation and development of state. It covers the study of past, present and future of state.

Question 6.
Political Science is a power science
Answer:
Lasswell and Kaplan along with other modern scholars regard political science as a power science. It deals with power relationship of states. Power is the fundamental principles of every conflict and the ultimate means to any solution. Political science seeks to explain the modes of acquisition of power, exercise of power and sharing of power with others.

Question 7.
Political science is an art
Answer:
Political science is by nature an art, because It applies the knowledge of science in day to day political process. The knowledge of political science is essential for politicians, leaders, diplomats, bureaucrats and for a common man. The knowledge of political science is necessary for begin success in real politics. If not only broadens our knowledge but also helps in the development of state.

Question 8.
Significance of Political Science
Answer:
The knowledge of political science is essential for every individual to know about the state government and other political institutions. It broadens our knowledge of politics to understand the complexities of modern state. It promotes political consciousness and awakens people about their rights and duties. It increases the rate of political participation. Political science teaches us about cooperation, tolerance and national integration. It creates ideal citizens.

Question 9.
Political Science is not a science
Answer:
Political science is not a science because, There is no agreement among scholars as to its meaning methods of study, principles and conclusions. Its principles are not universally valid. It studies human behaviour which is unpredictable. It can’t make objective study of political phenomena. Fully scientific method of investigation is impossible in political science. Its predictions are not exact.

Question 10.
Political Science and Philosophy
Answer:
Political science and Philosophy go hand in hand. Political science is a part and parcel of Philosophy. Philosophy is based on certain ideal doctrines and values which the political leaders and policymakers should practice. Philosophy is a science of knowledge and wisdom which make political thinkers and leaders think about the betterment of society. Both Political science and Philosophy cover some common ground, and both seek to promote good life of the citizens. The laws and policies of the government should be philosophically-sound.

Question 11.
Elements of State
Answer:
State is a sovereign political with four basic elements. Population is essential for a state, because it is a community of persons.State is a territorial unit and without a definite territory no state can exist. Government is the most vital element of state which enacts and enforces laws. Sovereignty is the most essential attribute of state which distinguishes it from other organizations. All these elements vest a state with real statehood.

Question 12.
Why the State is necessary? Or Need of the State
Answer:
State is a natural institution which protects the people and tries to ensure conditions for their happiness prosperity and development. It protects the people from internal disorder and external threat. It regulates economy and formulate and implements all financial policies for the well being of citizens. It undertakes steps for the socio economic, political and cultural development of the people. It ensures safety and security to the life liberty and property ofthe citizens. State creates a moral political order where citizens grow and prosper.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 13.
State is superior to all associations
Answer:
As a sovereign political unit state is considered superior to all other associations. It regulates and controls the activities of all other organizations. All associations exist and work on the basis of the laws of the state. State has the power to Compel all other associations to do as the state demands.

Question 14.
What is Government?
Answer:
Government is an element of state. It is the political organization of the state. The state has no life but the govt gives life to the state. The state acts through the government. The government fulfills the mission of the state. It may come and go but it gives life to the state.

Question 15.
What is sovereignty?
Answer:
Sovereignty is the supreme power of the state over citizens. Using this power the state enacts laws and runs the administration. It resides only with the state and no other association or organization enjoy it. Sovereignty can be internal or external. Internal sovereignty is exercised upon citizens, nationals and organizations. External sovereignty makes the state take final decisions in the outside world.

Question 16.
Internal and External Sovereignty
Answer:
Sovereignty has two aspects, internal and eternal. Internal sovereignty is exercised within the territorial limits of state. But external sovereignty, is exercised in the international sphere. By means of internal sovereignty the state makes law, but by external sovereignty if formulated foreign policy. It is for internal sovereignty people pay allegiance to state, and for external sovereignty no other state can dictate terms to the other. Due to internal sovereignty no other association or organization can disobey the state. But, due to external sovereignty no foreign state can interfere in the internal affairs of state.

Question 17.
What is a political system?
Answer:
The term political system corresponds to the word state. It includes the working elements of state along with other political forces that influence the state. A political system is a set of inter relationship through which policy decisions are made. It is concerned with power, rule and authority. It includes all governmental and non-governmental organizations, caste groups political parties, pressure groups and the people. Executive, Legislature and Judiciary are the working units of political system.

Question 18.
International Recognition
Answer:
International recognition means the acceptance by the family of nations. It is a formal process of according statehood to a newly born state. It gives a formal recognition to a state to be involved in relationship with other state. It is not an indispensable condition of statehood because, a state can exist even without international recognition. But, it is required for active participation in the field of international cooperation. It is supporting element of state.

Question 19.
State is a called an association of associations
Answer:
State is sovereign political association There are many more associations within the state. As a sovereign and powerful association it coordinates, controls and regulates the activities of other associations. All other associations are subordinated to the sovereign power of the state State is therefore, called an association of associations.

Question 20.
What are the factors responsible for the rise of modern individualism?
Answer:
The factors responsible for the rise of modern individualism are given below The complexities of modern society. The discontentment that developed after the world war. Loss of faith upon parliamentary democracy. Increasing role of bureaucracy. Inability of the individual to face the challenges of modern society.

Question 21.
What are the hindrances before the welfare state?
Answer:
The hindrances faced by a welfare state are Scarcity of production Rapid growth of population Fear of high taxation Increasing corruption Development of narrow loyalties and Environment pollution

Question 22.
What is individualism?
Answer:
Individualism is a political doctrine which grants maximum liberty to the individual against state interference It protects the rights of individuals. Under the system, the state performs only negative functions regulating the activities of individuals. Individualism pleads for free market economy. As a socio political theory it is based on the value of human personality. It believes in the laissez faire theory.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 23.
What are the merits of Individualism?
Answer:
Individualism grants maximum liberty to the individual for his self development. It gives economic freedom to the individual to maximize profit. It gives more opportunity to the talented ones. It helps in increasing production ensuring economic progress. This theory creates condition for the survival of the strong and efficient persons. It expresses full faith upon individual ability and character and therefore grants maximum freedom to the individual to mobilize his resources for himself and society.

Question 24.
What are the demerits on Individualism?
Answer:
State is a welfare agency but the individualists regard it as an evil which is wrong. Individualism considers the individual as the best judge, but actually, individual is swayed by emotion and passion. Individualism wrongly holds that individual and society are antithetic. But in practice individual good and social welfare are not contradictory. Individualism pleads for free competition which will result in the exploitation of the poor by the rich, wastage and unemployment. Its biological argument of survival of the fittest is in human.

Question 25.
What are the functions of an individualist state?
Answer:
The individualists give the state only negative functions such as Protection of the individual against external enemies. Maintenance of law and order within the state. And the enforcement of contracts lawfully made. The state protects the life, liberty and property of individuals and safeguards against them from personal injury and slander.

Question 26.
What is modern individualism?
Answer:
The individualism of the 20th century is called modern individualism of the 20th century is called modern individualism. It believes in the increasing role and functions of the state but protects against excessive state regulation and control. Instead of autonomy of individuals, it gives the groups a separate identity. Modern individualists give the state role of a coordination agency.

Question 27.
Why the individualists consider the state as a necessary evil? Or, State is a necessary evil why?
Answer:
The individualists look upon the state as a necessary evil because of the following reasons. The state is necessary for regulating the activities of selfish and egoistic individuals. It must protect the individual from personal harm, injury and slander. It is an evil, as it interferes in individual liberty and curtails individual freedom. It curtails general interest for individual interest.

Question 28.
What is the meaning of a welfare state?
Answer:
Welfare state is a 20th century phenomenon which is the product a compromise between communism and individualism. It guarantees a minimum standard of subsistence without removing incentives to private enterprise. It is a social service agency which undertakes developmental activities relating to social welfare and security. It puts equal emphasis on the individual and society. It regulates national economy through planning.

Question 29.
Write down the features of welfare state.
Answer:
A welfare state is a social service agency which ensures common good. It always seeks to promote people’s welfare. It is a compromise between extremes of individualism and socialism. It believes in democratic procedure principles. It regulates national economy through planning. The state protects the rights of all equally without discrimination. It guarantees the basic minimum needs to every individual.

Question 30.
What are the demerits of Welfare state?
Answer:
Welfare state is an expensive system for which a huge amount of funds are required. It leads to bureaucratic despotism. It magnifies the state at the expenses of respect for the individual. As the state undertakes all types of activities the role of voluntary associations decline.

Question 31.
What are the obligatory functions of a state?
Answer:
To protect the life, liberty and property of the people. To maintain law and order, peace and security. To protect the country from external attack. To administer free and fair justice to all

Question 32.
What are the voluntary functions of a state?
Answer:
The state provides medical help and hygienic conditions to the people. It seeks to spread education all over the countries. The state regulates trade, industry and development of agriculture. It provides for a variety of social security functions such as insurance old age pension, employment generation and sickness and physically disabled allowance etc. The state regulates public utility services like transport, electricity, postal, and air services.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 33.
What are the political functions of a Welfare State?
Answer:
A welfare state performs the following political functions It safeguards individual rights. It maintains free, fair and periodic elections. It makes provision for the participation of the masses in public affairs. It coordinates the interests and activities of various groups, associations and parties. It eradicates corruption, nepotism and dishonesty. It generates political awareness.

Question 34.
What is the meaning of Globalization?
Answer:
Globalization is the name for the integration of economics through exchange of ideas, information, technologies, goods, and services. It is a policy of economic reforms which aims at reducing trade barriers between the developed and developing countries. It believes in the integration of nation states within the framework of WTO.

Question 35.
What are the objectives of Globalisation?
Answer:
The objectives of globalization are Socio-economic integration of the whole world. Interesting industrial trade cultural relations among the people all over the world. Securing the benefits of free trade, open access to markets and equal participation in securing sustainable development for all the people. Reduction of trade barriers, to ensure free flow of capital and labour from one country to the other. Exchange of goods and services.

Question 36.
What are the features of Globalization?
Answer:
Globalization stands for liberalization of economy. It stands for free flow of trade relations. Globalization of economic activity. Liberalization of import export system. Privatization of means of production and distribution. Economic reforms and increasing collaborations among nations.

Question 37.
What are the social functions of welfare state?
Answer:
The social functions of welfare state are Establishment of social equality among people. Securing social justice. To make provision for social security and welfare of the poor and backward people. Fighting social evils. Rendering social utility services. Spread of education and protection of public health etc.

Question 38.
What are the economic functions of Welfare state?
Answer:
The economic functions undertaken by a welfare state are Improvement in the economic condition of the people. To draw plans for balanced economic development. Development of agriculture and industry Regulation of trade and commerce. Etc

Question 39.
What a modern state can’t do?
Answer:
A modern welfare state can’t interfere in the following spheres of individual. It can’t curtail religious freedom of the people. It can’t suppress public opinion It can’t interfere in the social customs and fashions of the people. It can’t interfere in personal life of the people, and It can’t interfere in cultural and literacy matters of the people.

Question 40.
What role does the state play in an era of Globalization?
Answer:
The role of modern state has changed in an era of globalization. The state continues to be a Welfare State. It acts as a facilitator and co-ordinator economy and it tries to secure stability in the market through macro economic policies. It provides social services like education health and other welfare activities.

Question 41.
What are the evil impacts of globalization?
Answer:
Globalization gives more importance to corporate business capitalists and multi national corporations. It helps the developed nations to control the world economy. It creates difficulty for the developing countries to complete with developed countries. It leads to increase in the gap between rich and poor. Small and medium range industries will suffer a loss. It will lead to neglect of working class.

Question 42.
What are the merits of globalization.
Answer:
Globalization has accelerated the pace of economic integration of the world. It strengthens international peace and stability. It is the best possible means to secure sustainable development of the world. It enhances socio-economic linkages among nations. It helps in dissemination of technical know how among nations. It seeks to encourage interdependence among nations.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 43.
What are the impacts of globalization on Indian Economy?
Answer:
Globalization in India has given rise to export of goods. There are greater flow of foreign investment. Increase in GDP. Neglect of poverty eradication programme. There is sharp decline in employment growth. It resulted in a set back to industry and agriculture.

Question 44.
Good effect of globalization
Answer:
The good effects of globalization on Indian economy are Increase in export of Indian goods and services. Increase in foreign investment coming to India. Consistency in GDP growth. Sharp rise in communication and healthy social order. It is a necessity of modern times.

Question 45
Evil impacts of Globalization and developed nations are exploiting the underdeveloped nations.
Answer:
As a result of globalization the rich and developed nations are exploiting the underdeveloped nations. The foreign countries have entered into Indian markets. The poor people are facing poverty and exploitation. Unemployment has risen. It has badly affected Indian Industry and agriculture. It has given rise to global economic recession.

Question 46.
Nature of politics
Answer:
Politics is concerned with the day to day organized political activities in society. It seeks to resolve the conflicts and controversies arising between two groups or individuals. Power is the be all and end all of politics. Politics is the process of realization of interests or goals by using power. It is found every where in society. In family political parties, religious institutions educational institutions and in all human association. From the point of view of science or art it is by nature an art.

Question 47.
Liberal view of politics
Answer:
The liberals define politics taking the relationship of individual and society into account. Individual is the centre of politics. In society individuals and groups fight with each other for their goals and politics seeks to resolve these conflicts. It brings order out of disorder and promotes the social well being. Politics seeks to bring unity, peace and stability in society.

Question 48.
Marxian view of politics
Answer:
Marxists rejects the liberal view of politics and state that politics results in class struggle. It creates division between rich and poor educated and uneducated and various social grounds. The rich make use of politics to exploit the poor.

Question 49.
Politics is a struggle for power
Answer:
The modern scholars like, Lasswell, Robert Dahl etc. regard politics as a struggle for power. The ongoing conflict between individuals & groups in society for accumulation and use of power is known as politics Politics gives top priority to power & It is concerned with the political process.

Question 50.
What is the scope of politics?
Answer:
Scope implies the subject matter of study of politics and it includes The study of state government, society, socio-political system, policy making etc. The study of conflict, rivatry between individuals and groups. The study of shaping and sharing of power. The study of political process, election, government formation, eradication of poverty corruption, illiteracy, legislation and adjudication etc. Politics also studies about local government, public administration, international policies, war and peace, united nations, foreign policy and relations of national interest.

Question 51.
What is political theory?
Answer:
Political theory refers to the empirical study of political concepts events and issues. It comprises of philosophy, psychology, economics and history within itself. It is factual and based on reality. Political theory is moral reasonable and universal in character. Any systematic statement of political thinkers on any political social issue or event is called political theory.

Question 52.
The usefulness of studying political theory: Or, Significance of studying political theory.
Answer:
The study of political theory is necessary for the study of political events. Issues and conflicts and for their solution. By study of political theory we derive knowledge about political ideals, ideologies and institutions. It also deals with the behaviour of individuals and institutions. It gives us a clear picture of political issues and events where by valid decisions can be made. Political theorem provides stability to the political system and influences politics and society.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 53.
What is modern political theory?
Answer:
Modern political theory refers to the theoretical development in the post world war era. It is scientific in nature and based on reality. It believes in modern techniques like, observation, data collection, analysis objective study of politics and empirical study. It is inter disciplinary in character. Modern political theory seeks to make political research based on facts and evidence so that reasonable decisions can be made.

Question 54.
What is classical political theory?
Answer:
Classical political theory is value oriented and moral in character. The uniting of scholars like, Plato, Aristotle, Machiavelli, Hobbes, Hegel, Rousseau, etc. are all classical in character. It gives priority to ethical politics. It seeks to strike a balance between individual liberty and state control individual state relationship & goals of the state.

Question 55.
Elements of politics
Answer:
Politics is the behavioural dimension of political science. Realisation of interest, conflict over interest and using power for realization of interests are the three basic elements of politics In society people fight for their self interest and whenever they use power and influence for the purpose it is called politics. When power is used for socio political and economic purpose it is called politics.

Question 56.
Evolution of Individualism
Answer:
Individualism developed as a practical theory during 19th century. It emerged from the mercantile individualism of18th and 19th century in Britain, France and Germany. The industrial revolution in Britain in 18th century gave rise to free economic competition and gradually individualism emerged. The French physiocrats were the initial exponents of individualism but it was Adamsmith who gave it the shape of a political theory. Besides Smith, Hobbes, J.S. Mill, Spencer, Hayek, Milton, Nozik, etc. developed it into a full fledged philosophy.

Question 57.
Individual is not the best judge
Answer:
According to individualists indivual is the best judge of his ability, power and self interest. But, it is not always correct state is more matured and capable to judge the self interest of individual. Individual is emotional and he may commit any mistake out of emotion but state is conscious and all actions of state are based on reason and free from passion. The state uses its resources for the well being of individuals.

Question 58.
Individual and state are complementary.
Answer:
Individualism find antipathy between individual interest and states interest but actually, the interests of the state and individual is complementary. State has no interests of its own. Its interest is the sum of individual interest. State resolves all conflicts arising among individuals. The state promotes the interests, security and progress of every individual.

Question 59.
What does survival of the fittest mean?
Answer:
Individualism believes in the principle of survival of the fittest. It means that every time there is a competition among individuals and those who are capable, talented and efficient only survive and the rest perish. There is no scope for the weak, indolent and ignorant people in a state. Charles Darwin and Herbert Spencer were the protagonists of this view. It is scientific and justified also

Question 60.
Laissez fair
Answer:
Laissez fair is a French word which means, let the individual free to take economic or financial decisions. From economic point of view, every individual is conscious of his self interest best. When the individual works for his profit he works with all sincerity and commitment. For the development of agriculture industry and business the individual must be given full freedom.

Question 61.
Features of modern individualism
Answer:
Modern individualism is the 20th century individualism. It gives priority to groups than individuals and recognizes the positive role of state. Graham Walls, Normal Angel, Miss Folel were modern individualists. Modern individualism gives more importance to social welfare than individual good. It pleads that the state can eradicate the obstacles facing individuals.

Question 62.
What is New Deal programme?
Answer:
New Deal was the brain child of former US president F.D. Roosevelt. It was a programme for reform which made the state interfere in the economic sphere creating opportunities for employment and ensure greater social security. During the great economic recession in USA in 1930s, President Roosevelt initiated these reforms to enhance the financial condition of individuals. It generated employment opportunities and provided assistance to the diseased, physically challenged and poor people. This new deal plan created condition for a welfare state.

CHSE Odisha Class 11 Political Science Unit 1 Understanding Political Theory Short Answer Questions

Question 63.
Beverage Report
Answer:
When during the second world war there was world wide recession thousands of people become homeless, unemployed underfed and discussed. In the mean time, William Beverage, a Brithsh national, provided a report in 1942 for introduction of social insurance and national health mission to save the people. As per the report the state shall provide basic minimum health service, insurance and opportunities for income to all. This beverage report led to nationalization of Banks, railways, mines, steel and means of transport etc. It laid the foundation of welfare state.

Question 64.
India is a welfare state.
Answer:
Indian constitution, under Act 38 envisages the goal of a welfare state. The government of India provides basic minimum needs to every individual. Act 39 provides right to work and the right to a decent wage. The state through abolition of poverty, unemployment health service, insurance, social security and spread of education seeks to realize the goal of welfare state. The state also looks after the protection and security of women, children and backward classes.

Question 65.
What were the factors responsible for the evolution of modern Individualism?
Answer:
The following factors led to the evolution of modern Individualism. Problem ridden modern society Public displeasure over the first world war Distruct of parliamentary democracy. Growing importance of Bureaucracy. And the helplessness of the people to face these challenges led to the emergence of modern individualism

Question 66.
Challenges to welfare state
Answer:
The following factors pase a threat to welfare state today Scarcity of production of goods and food grains Population explosion. Increase in rate of taxes. Environmental pollution and Narrow-mindedness of the people

Question 67.
What are the positive impacts of globalization on Indian economy?
Answer:
Globalisation has strengthened Indian economy in the following manner, It has led to the growing demand for Indian goods and services all over the world. Foreign direct investment has increased. Domestic production has increased. There is spread of transport and communication, information and technology. There is growing awareness about human rights and environmental safety.

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(b)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 1 Relation and Function Ex 1(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Exercise 1(b)

Question 1.
Let X={x, y} and Y={u, v}. Write down all the functions that can be defined from X to Y. How many of these are (i) one-one (ii) onto and (ii) one-one and onto?
Solution:
The functions from X = {x, y} to y = {u, v} are:
f1 = {(x, u), (y, v)}
f2 = {(x, v), (y, u)}
f3 = {(x, u), (y, u)}
f4 = {(x, v), (y, v)}

Out of these 4 functions there are:
(i) 2 one-one functions
(ii) 2 onto functions
(iii) 2 one-one and onto function.

Question 2.
Let X and Y be sets containing m and n elements respectively.
(i) What is the total number of functions from X to Y.
(ii) How many functions from X to Y are one-one according as men, m > n and m = n?
Solution:
If | x | = m and | y | = n then
(i) Number of functions =nm
(ii) If m < n then number of one-one functions = nPm.
If m > n then number of one-one functions = 0
If m = n then number of one-one functions = m!

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(b)

Question 3.
Examine each of the following functions if it is
(i) injective (ii) surjective, (iii) bijective and (iv) none of the three
(a) f : R → R, f(x) = x²
(b) f : R → [-1, 1], f(x) = sin x
(c) f : R+ → R + , f(x) = x + 1/x
where R+ = {x ∈ R : x > 0}
(d) f : R → R, f(x) = x³ + 1
(e) f : (-1, 1) → R, f(x) = \(\frac{x}{1-x^2}\)
(f) f : R → R, f(x) = [x] = the greatest integer ≤ x.
(g) f : R → R, f(x) = | x |
(h) f : R → R, f(x) = sgn x
(i) f : R → R, f = idR = the identity function on R.
Solution:
(a) f : R → R, f(x) = x²
for x1, x2 ∈ R
Let f(x1) = f(x2)
⇒ x1² = x2²
⇒ x = ± x2
∴ f is not one-one.
Hence f is not injective or bijective.
Rng f = [0, ∞) ≠ R
∴ f is not surjective.

(b) f : R → [-1, 1], f(x) = sin x
For x1 , x2 ∈ R
let f(x1) = f(x2) ⇒ sin x1 = sin x2 
⇒ x1 = nπ + (- 1)n  x2
⇒ x1 = x2 (not always)
∴ f is not injective and also not bijective.
But f is onto, as ∀ y ∈ [-1, 1]
there is a x ∈ R such that f(x) = sin x.
i.e., f is surjective.

(c) f : R+ → R+ , f(x) = x + \(\frac{1}{x}\)
f(2) = 2 + \(\frac{1}{2}\) = \(\frac{5}{2}\)
f(\(\frac{1}{2}\)) = \(\frac{1}{2}\) + 2 = \(\frac{5}{2}\)
f(2) = f(\(\frac{1}{2}\))
but 2 ≠ \(\frac{1}{2}\)
∴ f is not injective (one-one).
Again, for 1 ∈ R+ (domain)
⇒ there is no x ∈ R+(Dom)
such that x + \(\frac{1}{2}\) = 1
∴ f is not onto.

(d) f : R → R, f(x) = x³ + 1
for x1, x2 ∈ R
Let f(x1) = f(x2)
⇒ x13 = x23
⇒ x1 = x2
∴ f is injective.
Let f(x) = y ⇒ y = x³ + 1
⇒ x³ = y – 1
⇒ x = (y – 1)1/3 which exists ∀ y ∈ R
∴ f is onto.
∴ f is bijective.

(e) f : (-1, 1) → R, f(x) = \(\frac{x}{1-x^2}\)
for x1, x2 ∈ (-1, 1)
Let f(x1) = f(x2) ⇒ \(\frac{x_1}{1-x_1^2}\) = \(\frac{x_2}{1-x_2^2}\)
⇒x1 – x1 x22 = x2 – x12 x2
⇒ x1 – x2 + x12 x2 – x1 x22 = 0
⇒ (x1 – x2) (1 + x1 x2) = 0
⇒ x1 = x2 (for x1 x2 ∈ (-1, 1) x1 x2 ≠ -1)
∴ f is injective.
Again let y = \(\frac{x}{1-x^2}\) ⇒ y – x²y = x
⇒ x²y + x – y = 0
⇒ x = \(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)
= \(\frac{-1 \pm \sqrt{1+4 y^2}}{2 y}\) ∉ (-1, 1) ∀ y ∈¸.
∴f is surjective.
∴f is bijective.

(f) f : R → R
f(x) = [x]
f(1.2) = f(1.5) =1
∴ f is not injective.
Rng f = Z ⊂ R
∴ f is not surjective.
∴ Hence it is not also bijective.

(g) f : R → R
f(x) = | x |
As f(-1) = f(1) = 1
∴ f is not injective.
Again Rng f = [0, ∞) ⊂ R
⇒ f is not surjective.
Thus f is not bijective.

(h) f : R → R
f(x) = Sgn (x) = \(\left\{\begin{array}{cc}
1, & x>0 \\
0, & x=0 \\
-1, & x<0
\end{array}\right.\)
As f(1) = f(2) = 1
We have f is not injective.
Again Rng f = {- 1, 0, 1} ≠ R
∴ R is not surjective.
⇒ R is not bijective.

(i) f : R → R
f = idx
∴ f(x) = x
for x1, x2 ∈ R
Let f(x1) = f(x2) where x2 x2 ∈ R
⇒ x1 = x2
∴ f is one-one.
Again Rng f = R (codomain)
∴ f is onto.
Thus f is a bijective function.

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(b)

Question 4.
Show that the following functions are injective.
(i) f(x) = sin x on \(\left[0, \frac{\pi}{2}\right]\)
(ii) f(x) = cos x [0, π]
(iii) fix) = loga x on (0, ∞), (a > 0 and a ≠ 1)
(iv) f(x) = ax on R. (a > 0 and a ≠ 1)
Solution:
(i) f(x) = sin x . \(\left[0, \frac{\pi}{2}\right]\)
for α, β ∈ \(\left[0, \frac{\pi}{2}\right]\)
Let f(α) = f(β) ⇒ sin α = sin β
⇒ α = β, as α, β ∈ \(\left(0, \frac{\pi}{2}\right)\) and no other values of α is possible.
∴ f is one-one.

(ii) f(x) = cos x, [0, π]
for α, β ∈ [0, π]
Let f(α) = f(β) ⇒ cos α = cos β
⇒ α = β, since α, β ∈ [0, π] and cos x is +ve in 1st quadrant and -ve in 2nd quadrant.
∴ f is one-one.

(iii) f(x) = loga x [1, ∞]
for α, β ∈ [1, ∞]
Let f(α) = f(β)
⇒ loga α = loga β ⇒ α = β
∴ f is one-one.

(iv) f(x) = ax, (a > 0), x ∈ R
for x1, x2 ∈ R
Let f(x1) = f(x2) ⇒ ax1 = ax2
⇒ x1 = x2
∴ f is one-one.

Question 5.
Show that functions f and g defined by f(x) = 2 log x and g(x) = log x2 are not equal even though log x2 = 2 log x.
Solution:
f(x) = 2 log x
g(x) = log x2
Dom f(x) = (0, ∞)
Dom g(x) = R – {0}
As Dom f(x) ≠ Dom g(x) we have f(x) ≠ g(x), though log x2 = 2 log x

Question 6.
Give an example of a function which is
(i) Surjective but not injective.
(ii) injective but not surjective.
(iii) neither injective nor surjective.
(iv) bijective
Solution:
(i) f(x) = sin x
from R → [-1, 1]
which is surjective but not injective.

(ii) f(x) = \(\frac{x}{2}\) from Z → R
is injective but not surjective.

(iii) f : (-1, 1) → R, f(x) = \(\frac{x}{1-x^2}\)
is neither surjective nor injective.
[Refer Q. No. 3(e)].

(iv) f(x) = x3 + 1, f : R → R
is bijective.
[Refer No. 3 (d)].

Question 7.
Prove that the following sets are equivalent:
{1, 2, 3, 4, 5, 6,…}
{2, 4, 6, 8, 10,…}
{1, 7, 5, 7, 9,…}
{1, 4, 9, 16, 25,…}
Solution:
Let A = {1, 2, 3, 4, 5, 6, ……..}
B = {2, 4, 6, 8, 10, …….}
C = {1, 3, 5, 7, 9, ……}
D = {1, 4, 9, 16, 25, ……}
Let f : A → B defined as f(x) = 2x
Clearly f is bijective.
There is a one-to-one correspondence between A and B.
⇒ A and B are equivalent.
Let g : A → C defined as g(x) = 2x – 1
Clearly f is bijective.
⇒ There is a one-to-one correspondence between A to C
∴ A and C are equivalent.
Let h : A → D defined as h(x) = x2.
Clearly h is bijective.
⇒ There is a one-to-one correspondence between A to D.
⇒ A and D are equivalent.
Thus A, B, C and D are equivalent.

Question 8.
Let f = {(1, a), (2, b), (3, c), (4, d)} and g = {{a, x), (b, x), (c, y), (d, x)}. Determine gof and fog if possible. Test whether fog = gof.
Solution:
f = {(1, a), (2, b), (3, c), (4, d)}
g = {{a, x), (b, x), (c, y), (d, x)}
gof (1) = g(a) = x
gof (2) = g(b) = x
gof (3) = g(c) = y
gof (4) = g(a) = x
∴ gof = {(1, x), (2, x), (3, y), (4, x)} Here fog is not defined.

Question 9.
Let f = {(1, 3), (2, 4), (3, 7)} and g = {(3, 2), (4, 3), (7, 1)}. Determine gof and fog if possible. Test whether fog = gof.
Solution:
f = {(1, 3), (2, 4), (3, 7)}
g = {(3, 2), (4, 3), (7, 1)}
We have fog (3) = f (g(3)) = f(2) = 4
fog (4) = f (g(4)) = f(3) = 7
fog (7) = f (g(7)) = f(1) = 3
∴  fog = {(3, 4), (4, 7), (7, 3)}
Again gof (1) = g (f(1)) = g(3) = 2,
gof (2) = g (f(2)) = g(4) = 3,
gof (3) = g (f(3)) = g(7) = 1
∴ gof = {(1, 2), (2, 3), (3, 1)}
∴ gof ≠ fog
So the composition of functions is not necessarily commutative.

Question 10.
Let f(x) =√x and g(x) = 1 – x2.
(i) Find natural domains of f and g.
(ii) Compute fog and gof and find their natural domains.
(iii) Find natural domain of h(x) = 1 – x.
(iv) Show that h = gof only on R0 = {x ∈ R : x ≥ 0} and not on R.
Solution:
Let f(x) = √x, g(x) = 1 – x2
(i) ∴ Dom f = R+ U{0}, Dom g = R

(ii) fog (x) = f (g(x))
= f (1 – x2) = \(\sqrt{1-x^2}\)
∴ fog (x) exists when 1 – x2 ≥ 0
⇒ x2 ≤ 1 ⇒ -1 ≤ x ≤ 1 i.e., x ∈ [-1, 1]
∴ Dom fog = [-1, 1]
Again gof (x) = g (f(x))
= g( √x ) = 1 – ( √x )2 = 1 – x
∴ Dom gof = R0 = (0, ∞)

(iii) Domain of h(x) = 1 – x is R.

(iv) We have proved in (ii) that gof (x) = 1 – x.
∴ h(x) = gof (x) ⇒ h = gof only when x ∈ R0 as dom f is R0 = [0, ∞]

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(b)

Question 11.
Find the composition fog and gof and test whether fog = gof when f and g are functions on R given by the following:
(i) f(x) = x3 + 1, g(x) = x2 – 2
(ii) f(x) = sin x, g(x) = x5
(iii) f(x) = cos x, g(x) = sin x2
(iv) f(x) = g(x) = (1 – x3)1/3
Solution:
(i) f(x) = x3 + 1, g(x) = x2 – 2
∴ fog (x) = f (g(x)) = f(x2 – 2)
= (x2 – 2)3 + 1
gof (x) = g (f(x)) = g(x3 + 1)
= (x3 + 1)2 – 1
fog ≠ gof

(ii) f(x) = sin x, g(x) = x5
∴ fog (x) = f (g(x)) = f(x5) = sin x5
∴ gof (x) = g (f(x))
= g(sin x) = (sin x)5 = sin5 x
fog ≠ gof

(iii) f(x) = cos x, g(x) = sin x2
∴ fog (x) = f (g(x))
= f( sin x2) = cos (sin x2)
and gof (x) = g (f(x)) = g(cos x)
= sin (cos x)2 = sin (cos2 x)
fog ≠ gof

(iv) f(x) = g(x) = (1 – x3)1/3
fog (x) = f (g(x))
= (1 – (g(x))3)1/3
= [1 – (1 – x3)]1/3 = x
gof (x) = g (f(x))
= [1 – (f(x))3]1/3 = x
⇒ fog = gof

Question 12.
(a) Let f be a real function. Show that h(x) = f(x) + f(-x) is always an even function and g(x) = f(x) – f(-x) is always an odd function.
(b) Express each of the following function as the sum of an even function and an odd function:
(i) 1 + x + x2 , (ii) x2, (iii) ex, (iv) ex + sin x
Solution:
(a) We have h(x) = f(x) + f(-x)
∴ h(-x) = f(-x) + f(x) = h(x)
∴ h is always an even function.
Further, g(x) = f(x) – f(-x)
∴ g(-x) = f(-x) – f(x)
= – [f(x) – f(-x)] = – g(x).
∴ g is always an odd function.

(b) (i) Let f(x) = 1 + x + x2
∴ f(-x) = 1 – x + x2
∴ g(x) = \(\frac{f(x)+f(-x)}{2}\)
= \(\frac{1+x+x^2+1-x+x^2}{2}\)
= x2 + 1 and
g(-x) = (-x)2 + 1 = x2 + 1
∴ g is an even function.
h(x) = \(\frac{f(x)-f(-x)}{2}\)
= \(\frac{\left(1+x+x^2\right)-\left(1-x+x^2\right)}{2}\) = x
h(-x) = -x = -h(x)
⇒ h is an odd function.
∴ f(x) = g(x) + f(x)
where g is even and h is odd.

(ii) Let f(x) = x2
So that f(-x) = (-x)2 = x2
∴ g(x) = \( \frac{f(x)+f(-x)}{2}\) = \( \frac{x^2+x^2}{2}\) = x2
g(-x) = g(x)
∴ g is an even function.
and h(x) = \( \frac{f(x)-f(-x)}{2}\) = \(\frac{x^2-x^2}{2}\) = 0
h(x) = 0 is both even and odd.
∴ f(x) = g(x) = f(x),
where g is even and h is odd.

(iii) Let f(x) = ex
f(-x) = e-x
g(x) = \( \frac{e^x+e^{-x}}{2}\)
g(-x) = g(x)
g is an even function.
and h(x) = \( \frac{e^x-e^{-x}}{2}\)
h(-x) = \( \frac{e^{-x}-e^x}{2}\) = -h2(x)
⇒ h is an odd function.
∴ f(x) = g(x) + h(x),
where g is even and h is odd.

(iv) Let f(x) = ex + sin x
f(-x) = e-x + sin (-x) = e-x –  sin x
∴ g(x) = \( \frac{f(x)+f(-x)}{2}\)
= \( \frac{e^x+\sin x+e^{-x}-\sin x}{2}\)
= \( \frac{e^x+e^{-x}}{2}\) and h(x) = \( \frac{f(x)-f(-x)}{2}\)
= \( \frac{e^x+\sin x-e^{-x}+\sin x}{2}\)
= \( \frac{e^x-e^{-x}+2 \sin x}{2}\)
∴ f(x) = g(x) + h(x)
where g is even and g is odd.

Question 13.
Let X = {1, 2, 3, 4} Determine whether f : X → X defined as given below have inverses.
Find f-1 if it exists:
(i) f = {(1, 4), (2, 3), (3, 2), (4, 1)}
(ii) f = {(1, 3), (2, 1), (3, 1), (4, 2)}
(iii) f = {(1, 2), (2, 3), (3, 4), (4, 1)}
(iv) f = {(1, 1), (2, 2), (2, 3), (4, 4)}
(v) f = {(1, 2), (2, 2), (3, 2), (4, 2)}
Solution.
(i) x = {1, 2, 3, 4}
f is bijective. Hence f-1 exists.
f-1 = {(4, 1), (3, 2), (2, 3), (1, 4)}

(ii) f(2) = f(3) = 1
⇒ f is not injective
∴ f is not invertible.

(iii) f is bijective. Hence f-1 exists.
f-1 = {(2,1 ), (3, 2), (4, 3), (1, 4)}

(iv) f is not a function as
f(2) = 2 and f(2) = 3

(v) f is not injective hence not invertible.

Question 14.
Let f : X → Y.
If there exists a map g : Y → X such that gof = idx and fog = idy, then show that
(i) f is bijective and (ii) g = f-1
[Hint: Since idx is a bijective function, gof = idx is bijective. By Theorem 2(iv) f is injective. Similarly fog is bijective ⇒ f is surjective by Theorem 2(iii)]
Solution:
Let f : x → y and g : y – x
where gof = idx and fog = idy
we know that idx and idy are bijective functions.
⇒ gof and fog are both bijective functions.
⇒ f is a bijective function.

(ii) As f is bijective (by (i)) we have f-1 exists.
and f-1 : y → x where f-1of = idx and fof-1 = idy
But g : y → x with gof = idx and fog = idy
∴ g = f-1

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(b)

Question 15.
Construct an example to show that f(A ∩ B) ≠ f(A) ∩ f(B) where A ∩ B ≠ Ø
Solution:
Let f(x) = cos x.
Let A = \(\left\{0, \frac{\pi}{2}\right\}\), B = \(\left\{\frac{\pi}{2}, 2 \pi\right\}\).
∴ f(A) = \(\left\{\cos 0, \cos \frac{\pi}{2}\right\}\)
= {1, 0} = {0, 1}
∴ f(B) = \(\left\{\cos \frac{\pi}{2}, \cos 2 \pi\right\}\) = {0, 1}
∴ f(A) ∩ f(B) = {0, 1}
Again,
A ∩ B = \(\left\{\frac{\pi}{2}\right\}\) and f(A ∩ B) = cos \(\frac{\pi}{2}\) = {0}
∴ f(A ∩ B) ≠ f(A) ∩ f(B)

Question 16.
Prove that for any f : X → Y, foidx = f = idyof.
Solution:
Let f : X → Y, so that y = f(x), x ∈ X.
∴ foidx = fof-1 of (x) = fof-1 (f(x))
= f(x) = y (∵ idx = fof-1‍)
Again, (idyof)(x) = (fof-1) of (x)
= (fof-1)(y) = f (f-1(y)) = f(x) = y  ….(2)
∴ From (1) and (2)
we have foidx = f = idyof

Question 17.
Prove that f : X → Y is surjective iff for all B ⊆ Y, f (f-1(B)) = B.
Solution:
Let f : X → Y is surjective.
i.e. for all y ∈ Y, ∃ a x ∈ X such that
y = f(x).
∴ x = f-1(y) ⇔ f(x)
= f (f-1(y)) ∈ f (f-1(B)).
for y = B ⊂ Y ⇔ y ∈ f (f-1(B)).
∴ y ∈ f (f-1(B)) ⇔ y ∈ B
∴ f (f-1(B)) = B

Question 18.
Prove that f : X → Y is injective iff f (f-1(A)) = A for all A ⊆ X.
Solution:
f : X → Y is injective.
Let x ∈ A ⇔ f(x) ∈ f(A) (∵ f is injective)
⇔ x ∈ f (f-1(A))
∴ A = f (f-1(A)) for all A ⊆ X.

Question 19.
Prove that f : X → Y is injective iff for all subsets A, B of X, f(A ∩ B) = f(A) ∩ f(B).
Solution:
f : X → Y is injective.
Let A and B are subsets of X.
Let f(x) ∈ f(A ∩ B)
⇔ x ∈ A ∩ B ⇔ x ∈ A ∧ x ∈ B
⇔ f(x) ∈ f(A) ∧ f(x) ∈ f(B) (∵ f is injective)
⇔ f(x) = f(A) ∩ f(B)
∴ f(A ∩ B) = f(A) ∩ f(B)

Conversely, suppose that
f(A ∩ B) = f(A) ∩ f(B)
Let f is not injective.
The if f(x) ∈ f(A ∩ B) ⇔ x ∈ A ∩ B
⇔ x ∈ A ∧ ⇔ x ∈ B
≠ f(x) ∈ f(A) ∧ ⇔ f(x) ∈ f(B)
⇔ f(x) ∈ f(A) ∩ f(B)
∴ f(A ∩ B) = f(A) ∩ f(B) is false.
so f must be injective.

Question 20.
Prove that f : X → Y is surjective iff for all A ⊆ X, (f(A))‘ ⊆ f(A‘), where A‘ denotes the complement of A in X.
Solution:
f : X → Y is surjective.
Then for all y ∈ Y ∃ x ∈ X
such that f(x) = y.
Let y ∈ [f(A)]‘ ⇒ y ∉ f(A)
⇒ f(x) ∉ f(A) ⇒ x ∉ A ⇒ x ∈ A‘
⇒ f(x) ∈ f(A‘) ⇒ y ∈ f(A‘)
∴ [f(A)]‘ ⊂ f(A‘)

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a)

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Exercise 3(a)

Question 1.
A merchant sells two models X and Y of TV with cost price ₹25000 and ₹50000 per set respectively. He gets a profit of ₹1500 on model X and ₹2000 on model Y. The sales cannot exceed 20 sets in a month. If he cannot invest more than 6 lakh rupees, formulate the problem of determining the number of sets of each type he must keep in stock for maximum profit.
Solution:
To get maximum profit let x TVs of model X and Y TVs of model Y must be kept in stock.
∴ Total profit = Z = 1500x + 2000y which is to be maximum.
According to the question, the sales cannot exceed 20 sets i.e. x + y ≤ 20.
Again total investment does not exceed 6 lakh.
25000x + 50000y ≤ 600000
⇒ x + 2y ≤ 24
∴ The LPP is:
maximise: Z = 1500x + 2000y
subject to: x + y ≤ 20
x + 2y ≤ 24
x, y ≥ 0

Question 2.
A company manufactures and sells two models of lamps L1 and L2, the profit being ₹15 and ₹10 respectively. The process involves two workers W, and W2 who are available for this kind of work 100 hours and 80 hours per month respectively, W1 assembles L1 in 20 and L2 in 30 minutes. W2 paints L1 in 20 and L2 in 10 minutes. Assuming that all lamps made can be sold, formulate the LPP for determining the production figures for maximum profit.
Solution:
Let x units of L1 and y units of L2: are to be produced to get maximum profit.
Total profit = Z = 15x + 10y
According to the question
20x + 30y ≤ 600
and 20x + 10y ≤ 480
=> 2x + 3y ≤ 600
2x + y ≤ 480
.-. The LPP is maximize: Z = 15x + 10y
subject to: 2x + 3y ≤ 600
2x + y ≤ 480
x, y ≥ 0.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a)

Question 3.
A factory uses three different resources for the manufacture of two different products, 20 units of the resource A, 12 units of B and 16 units of C being available. One unit of the first product requires 2, 2 and 4 units of the resources and one unit of the second product requires 4, 2 and 0 units of the resources taken in order. It is known that the first product gives a profit of ₹20 per unit and the second ₹30 per unit. Formulate the LPP so as to earn maximum profit.
Solution:
Let to earn maximum profit the factory produces x units of first product and y units of the second product.
The given data can be summarised as below:

Resource A Resource B Resource C Profit per unit in ₹
Product – I 2 2 4 20
Product – II 4 2 0 30
Availability 20 12 16

Total profit = 20x + 30y
which is to be maximum.
According to the question
2x + 4y ≤ 20
2x + 2y ≤ 12
4x + 0y ≤ 16
.-. The LPP is
maximize: Z = 20x + 30y
subject to: x + 2y ≤ 10
x + y ≤ 6
x ≤ 4
x, y ≥ 0.

Question 4.
A man plans to start a poultry farm by investing at most ₹3000. He can buy old hens for ₹80 each and young ones for ₹140 each, but he cannot house more than 30 hens. Old hens lay 4 eggs per week and young ones lay 5 eggs per week, each egg being sold at ₹5. It costs ₹5 to feed an old hen and ₹8 to feed a young hen per week. Formulate his problem determining the number of hens of each type he should buy so as to earn a profit of more than ₹300 per week.
Solution:
Let to get maximum profit he has to purchase x old hens and y young hens.
Total cost = 80x + 140y ≤ 3000
⇒ 4x + 7y ≤ 150
Total number of hens x + y ≤ 30
Number of eggs per week = 4x + 5y
Total income per week = 20x + 25y
Total cost to feed per week = 5x + 8y
∴ Weekly profit = 15x + 17y
∴ 15x + 17y > 300
and also total profit = z = 15x + 17y is to be maximum.
∴ The LPP is
maximize: Z = 15x + 17y
subject to: 4x + 7y ≤ 150
x + y ≤ 30
15x + 17y ≥ 300
x, y ≥ 0.

Question 5.
An agro-based company produces tomato sauce and tomato jelly. The quantity of material, machine hour, labour (man-hour) required to produce one unit of each product and the availability of raw material ore given in the following table:

Sauce Jelly availability
Man-hour 3 2 10
Machine hour 1 2.5 7.5
Raw material 1 1.2 4.2

Assume that one unit of sauce and one unit of jelly each yield a profit of ₹2 and ₹4 respectively. Formulate the LPP so as to yield maximum profit.
Solution:
Let the company produces x units of sauce and y units of jelly.
Total profit = 2x + 4y to be maximum.
Man hour = 3x + 2y ≤ 10
Machine hour = x + 2.5y ≤ 7.5
⇒ 2x + 5y ≤ 15
Raw material = x + 1.2y ≤ 4.2
⇒ 5x + 6y ≤ 21
∴ The LPP is
maximize: Z = 2x + 4y
subject to: 3x + 2y ≤ 10
2x + 5y ≤ 15
5x + 6y ≤ 21
x, y ≥ 0.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a)

Question 6.
(Allocation Problem.) A farmer has 5 acres of land on which he wishes to grow two crops X and Y. He has to use 4 cart loads and 2 cartloads of manure per acre for crops X and Y respectively. But not more than 18 cartloads of manure is available. Other expenses are ₹200 and ₹500 per acre for the crops X and Y respectively. He estimates profit from crops X and Y at the rates ₹1000 and ₹800 per acre respectively. Formulate the LPP as to how much land he should allocate to each crop for maximum profit.
Solution:
Let x acres are allocated for crop X and y acres for crop Y.
Total profit = 100x + 800y to be maximum.
According to the question
x + y ≤ 5
Manure = 4x + 2y ≤ 1 8 ⇒ 2x + y ≤ 9
∴ The LPP is
maximize: Z = 1000x + 800y
subject to: x + y ≤ 5
2x + y ≤ 9
x, y ≥ 0.

Question 7.
(Transportation Problem) A company has two factories at locations X and Y. He has to deliver the products from these factories to depots located at three places A, B and C. The production capacities at X and Y are respectively 12 and 10 units and the requirements at the depots are 8, 8 and 6 units respectively. The cost of transportation from the factories to the depots per unit of the product is given below.

(Cost in ₹)
To → A B C
From X 210 160 250
Y 170 180 140

The company has to determine how many units of product should be transported from each factory to each depot so that the cost of transportation is minimum. Formulate this LPP.
Solution:
Let x units are transported from X to A and y units from X to B. The transportation matrix is
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a) Q.7

Total cost of transportation
= 210x + 160y + 250 (12 – x – y) +170 (8 – x) +180 (8 – y) + 140 (x + y – 6)
= 4960 – 70x – 130y to be minimum.
Now all costs of transportation are ≥ 0.
∴ x ≥ 0, y ≥ 0.
12 – x – y ≥ 0 ⇒ x + y ≤ 12
8 – x ≥ 0 ⇒ x ≤ 8
8 – y ≥ 0 ⇒ y ≤ 8
x + y – 6 ≥ 0 x + y ≥ 6
∴ The LPP is
Minimize: Z = 4960 – 70x – 130y
subject to: x + y ≤ 12
x ≤ 8
y ≤ 8
x + y ≥ 6
x, y ≥ 0

Question 8.
(Diet Problem) Two types of food X and Y are mixed to prepare a mixture in such a way that the mixture contains at least 10 units of vitamin A, 12 units of vitamin B and 8 units of vitamin C. These vitamins are available in one kg of food as per the table given below.

Vitamins
food A B C
X 1 2 3
Y 2 2 1

One kg. of food X cost ₹16 and one kg. of food Y costs ₹20. Formulate the LPP so as to determine the least cost of the mixture containing the required amount of vitamins.
Solution:
Let x units of food X and y units of food Y are to be mixed to prepare the mixture.
Cost of the mixture = 16x + 20y to be minimum.
According to the question
Vitamin A content = x + 2y ≥ 10
Vitamin B content = 2x + 2y ≥ 12
Vitamin C content = 3x + y ≥ 8
∴ The LPP is
minimize: Z = 16x + 20y
subject to x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(a)

Question 9.
Special purpose coins each weighing 10gms are to be manufactured using two basic metals M1 and M2 and a mix of other metals M3. M1, M2 and M3 cost ₹500, ₹800 and ₹50 per gram respectively. The strength of a coin demands that not more than 7gm. of M1 and a minimum of 3 gm of M1 should be used. The amount of M3 in each coin is maintained at 25% of that of M1. Since the demand for the coin is related to its price, formulate the LPP to find the minimum cost of a coin.
Solution:
Let x gm of M1 and y g of M2 are used to make the coin. According to the demand of the coin \(\frac{x}{4}\) g of M3 is to be mixed.
Cost of the coin = 500x + 800y + \(\frac{50 x}{4}\)
= (512.5)x + 800y
which is to be minimum.
Again weight of the coin = 10g
⇒ x + y + \(\frac{x}{4}\) = 10
⇒ 5x + 4y = 40
According to the question x ≤ 7, y ≤ 3.
Thus the L.P.P is
minimize: Z = (512.5)x + 800y
subject to: 5x + 4y = 40
x ≤ 7
x ≤ 3
x, y ≥ 0.

Question 10.
A company produces three types of cloth A, B and C. Three kinds of wool, say red, green and blue are required for the cloth. One unit length of type A cloth needs 2 metres of red and 3 metres of blue wool; one unit length of type B cloth needs 3 metres of red, 2 metres of green and 2 metres of blue wool and one unit length of type C cloth needs 5 metres of green and 4 metres of blue wool. The firm has a stock of only 80 metres of red, 100 metres of green and 150 metres of blue wool. Assuming that income obtained from one unit length of cloth is ₹30, ₹50 and ₹40 of types A, B and C respectively, formulate the LPP so as to maximize income.
Solution:
Let x units of cloth A, y units of cloth B and z units of cloth C are to be produced from the available materials to get the maximum income. The given data can be summarised as:

Red wool Green wool Blue wool Income
Cloth A 2 3 30
Cloth B 3 2 2 50
Cloth C 5 4 40
Availability 80 100 150

Total Income = 30x + 50y + 40z
which is to be maximum.
According to the question
2x + 3y ≤ 80
2y + 5z ≤ 100
3x + 2y + 4z ≤ 150
Thus the L.P.P. is
minimize: Z = 30x + 50y + 40z
subject to: 2x + 3y ≤ 80
2y + 5z ≤ 100
3x + 2y + 4z ≤ 150
x, y, z ≥ 0

Question 11.
A person wants to decide the constituents of a diet which will fulfil his daily requirements of proteins, fats and carbohydrates at minimum cost. The choice is to be made from three different types of food. The yields per unit of these foods are given in the following table.

food yield/unit cost/unit
Protein Fat Carbonate
f1 3 2 6 45
f2 4 2 3 40
f3 8 7 7 85
Minimum Requirement 100 200 800

Formulate the LPP.
Solution:
Let the diet constitues x units of f1, y units of f2 and z units of f3.
Total cost = 45x + 40y + 85z, which is to be minimum.
According to the question
3x + 4y + 8z ≥ 1000
2x + 2y + 7z ≥ 200
6x + 3y + 7z ≥ 800
Thus the LPP is
Minimize: Z = 45x + 40y + 85z
Subject to: 3x + 4y + 8z ≥ 1000
2x-+2y + 7z ≥ 200
6x + 3y + 7z ≥ 800
x, y, z ≥ 0

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(c)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 1 Relation and Function Ex 1(c) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Exercise 1(c)

Question 1.
Show that the operation ∗ given by x ∗ y = x + y – xy is a binary operation on Z, Q and R but not on N.
Solution:
The operation ∗ given by
x ∗ y = x + y – xy
Clearly for all x, y ∈ Z
x + y – xy ∈ Z
⇒ x ∗ y ∈ Z
∴ ∗ is a binary operation on Z.
For all x, y ∈ Q
x + y – xy ∈ Q
⇒ x ∗ y ∈ Q
⇒ ∗ is a binary operation on Q for all x, y, ∈ R.
x + y – xy ∈ R
⇒ x ∗ y ∈ R
⇒ ∗ is a binary operation on R
Again 3, 4 ∈ N.
3 + 4 – 3 x 4 = 7 – 12 = – 5 ∉ N
i.e., x, y ∈ N
≠ x ∗ y ∈ N
∴ ∗ is not a binary operation on N.

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(c)

Question 2.
Determine whether the following operations as defined by ∗ are binary operations on the sets specified in each case. Give reasons if it is not a binary operation.
(i) a ∗ b = 2a + 3b on Z.
(ii) a ∗ b = ma – nb on Q+ where m and n ∈ N.
(iii) a ∗ b = a + b (mod 7) on {0, 1, 2, 3, 4, 5, 6}
(iv) a ∗ b = min {a, b} on N.
(v) a ∗ b = GCD {a, b} on N.
(vi) a ∗ b = LCM {a, b} on N.
(vii) a ∗ b = LCM {a, b} on {0, 1, 2, 3, 4……, 10}
(viii) a ∗ b = \(\sqrt{a^2+b^2}\) on Q+
(ix) a ∗ b =a × b (mod 5) on {0, 1, 2, 3, 4}.
(x) a ∗ b = a2 + b2 on N.
(xi) a ∗ b = a + b – ab on R – {1}.
Solution:
(i) For all a, b ∈ Z
2a + 3b ∈ Z
⇒ a ∗ b ∈ Z
∗ is a binary operation on Z.

(ii) Let a = 1, b = 2
m = 1, n = 3
ma – nb = 1 – 6 = – 5 ∉ Q+
∴ a, b ∈ Q+ ≠ a ∗ b ∈ Q+
⇒ ∗ is not a binary operation on Q+

(iii) a ∗ b = a + b (mod 7) ∈ {0, 1, 2, 3, 4, 5, 6}
for a, b ∈ 7
∗ is a binary operation on the given set.

(iv) a, b ∈ N ⇒ min {a, b} ∈ N
∴ a ∗ b ∈ N
⇒ ∗ is a binary operation on N.

(v) for all a, b ∈ N, GCD [a, b] ∈ N
⇒ a ∗ b ∈ N
⇒ ∗ is a binary operation on N.

(vi) for all a, b ∈ N, LCM {a, b} ∈ N
⇒ a ∗ b ∈ N
⇒ ∗ is a binary operation on N.

(vii) Let A = {0, 1, 2, ….. 10}
4, 5 ∈ A but 4 ∗ 5 = LCM {4, 5}
= 20 ∉ A
⇒ ∗ is not a binary operation on A.

(viii) for all a, b ∈ Q+
a ∗ b = \(\sqrt{a^2+b^2}\) ∉ Q+
⇒ ∗ is not a binary operation on Q+.

(ix) For all a, b ∈ {0, 1, 2, 3, 4}
a ∗ b = a × b (mod 5) ∈ {0, 1, 2, 3, 4}
∴ ∗ is a binary operation on the given set.

(x) for all a, b ∈ N, a * b = a2 + b2 ∈ N
∴ ∗ is a binary operation on N.

(xi) For all a, b ∈ R – {1}
a ∗ b = a + b – ab ∈ R – {1}
∴ ∗ is a binary operation on R – {1}

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(c)

Question 3.
In case ∗ is a binary operation in Q2 above, test whether it is (i) associative
(ii) commutative, Test further if the identity element exists and the inverse element for any element of the respective set exists.
Solution:
(i) On Z the binary operation is
a ∗ b = 2a + 3b
Commutative:
b ∗ a = 2b + 3a ≠ a ∗ b
∴ ∗ is not commutative.

Associative:
(a ∗ b) ∗ c = (2a + 3b) ∗ c
= 2 (2a + 3b) + 3c
= 4a + 6b + 3c
a ∗ (b ∗ c) = a ∗ (2b + 3c)
= 2a + 3 (2b + 3c)
= 2a + 6b + 9c
As (a ∗ b) ∗ c ≠ a ∗ (b ∗ c)
∗ is not associative.

Existance of identity:
Let e is the identity
∴ e ∗ a = a
⇒ 2e + 3a = a
⇒ e = -2a / 2 = -a
which depends on a.
∴ Identity element does not exist.

(iii) A = (0, 1, 2, 3, 4, 5, 6}
Commutative:
a ∗ b = a + b (mod 7)
= The remainder obtained when a + b is divided by 7.
b ∗ a = b + a (mod 7) = a + b (mod 7)
∴ ∗ is commutative.

Associative:
(a ∗ b) ∗ c = {a + b (mod 7)} ∗ c
= a + b + c (mod 7)
= The remainder obtained if a + b + c is divided by 7.
a ∗ (b ∗ c) = a ∗ {b + c (mod 7)}
= a + b + c (mod 7)
= The remainder obtained if a + b + c is divided by 7.
∴ (a ∗ b) ∗ c = a + (b ∗ c)
∴ ∗ is associative.

Existance of identity:
Let e is the identity
⇒ e ∗ a = a ∗ e = a
⇒ e + a mod 7 = a
⇒ e = 0
∴ 0 is the identity.

Existance of inverse:
Let a-1 = the inverse of a
⇒ a ∗ a-1 = a-1 ∗ a = e = 0
⇒ a + a-1 (mod 7) = 0
⇒ a + a-1 is divisible by 7.
1-1 = 6, 6-1 = 1
2-1 = 5, 5-1 = 2
3-1 = 4, 4-1 = 3

(iv) a ∗ b = min {a, b} on N.
Commutative:
a ∗ b = min {a, b}
b ∗ a – min {b, a} = a ∗ b
∴ ∗ is commutative.
Associative:
(a ∗ b) ∗ c = min {a, b} ∗ c
= min {a, b, c}
a ∗ (b ∗ c)= a ∗ min {b, c}
= min {a, b, c}
⇒ a ∗ (b ∗ c) = (a ∗ b) ∗ c
∴ ∗ is associative.

Existance of Identity:
Let e is the identity
∴ For all a ∈ N
e ∗ a = a ∗ e = a
⇒ min {e, a} = a
No such element exists in N.
∴ ∗ has no identity element on N.

(v) a ∗ b = GCD {a, b} on N.
b ∗ a = GCD {b, a} = GCD {a, b} = a ∗ b
∴ ∗ is commutative.
Associative:
(a ∗ b) ∗ c = GCD {a, b} ∗ c
= GCD {a, b, c}
a ∗ (b ∗ c) = a ∗ GCD {b, c}
= GCD {a, b, c}
⇒ (a ∗ b) ∗ c = a ∗ (b ∗ c)
⇒ ∗ is associative.

Existance of Identity:
Let e is the identity
∴ a ∗ e = e ∗ a = a
⇒ GCD {e, a} = a
No such element exists in N
⇒ ∗ has no indentity element.

(vi) a ∗ b = LCM {a, b} on N
Commutative:
a ∗ b = LCM {a, b}
= LCM {b, a}
= b ∗ a
∴ ∗ is commutative.

Associative
(a ∗ b) ∗ c = LCM {a, b} ∗ c
= LCM {a, b, c}
a ∗ (b ∗ c) =» a ∗ LCM {b, c}
= LCM {a, b, c}
⇒ (a ∗ b) ∗ c = a ∗ (b ∗ c)
∴ ∗ is associative.

Existance of Identity:
Let e is the identity
∴ e ∗ a = a ∗ e = a
⇒ LCM {e, a} = a
⇒ e – 1
∴ 1 is the identity element.

Existance of inverse:
Let a-1 is the inverse of a
⇒ a * a-1 = e = 1
⇒ LCM [a, a-1} = 1
a = a-1 = 1
Only 1 is invertible with 1-1 = 1.

(ix) a ∗ b = a × (mod 5) on {0, 1, 2, 3, 4}

Commutative:
a ∗ b = a x b (mod 5)
= Remainder on dividing a x b by 5
= Remainder on dividing b x a by 5
= b x a (mod 5)
= b x a
∴ ∗ is commutative.

Associative:
(a ∗ b) ∗ c=a x b (mod 5) ∗ c
= a x b x c (mod 5)
a and a ∗ {b ∗ c} = a ∗ {b x c (mod 5)}
= a x b x c (mod 5)
∴ (a ∗ b) ∗ c -=a ∗ (b ∗ c)
⇒ ∗ is associative.

Existance of identity:
Let e is the identity
∴ For all a ∈ {0, 1, 2, 3, 4}
a ∗ a = e ∗ a = a
a × e (mod 5) = a
⇒ e = 1
∴ 1 is the identity element.

Existance of inverse:
Let a-1 is the inverse of a
∴ a ∗ a-1= a-1 ∗ a = e = 1
⇒ a x a-1 (mod 5) = 1
⇒ 1-1 = 1
2-1 = 3, 3-1 = 2, 4-1 = 4
0 has no inverse.

(x) a ∗ b = a2 + b2 on N.
Commutative:
a ∗ b = a2 + b2
b ∗ a = b2 + a2 = a2 + b2 = a ∗ b
∴ ∗ is commutative.

Associative:
(a ∗ b) ∗ c = (a2 + b2) ∗ c
= (a2 + b2)2 + c2
a ∗ (b ∗ c) = a ∗ (b2 + c2)
= a2 + (a2 + b2)2
(a ∗ b) ∗ c ≠ a ∗ (b ∗ c)
∴ ∗ is not associative.

Existance of Identity:
Let e is the identity
a ∗ e = e ∗ a = a
⇒ a2 + e2 = a
⇒ e = \( \sqrt{a-a^2}\) which depends on a
∴ Identity does not exist.

(xi) a ∗ b = a + b – ab on R – {1}
Commutative:
a ∗ b = a + b – ab
b ∗ a = b + a – ba
a ∗ b = b ∗ a
∴ ∗ is commutative.

Associative:
a ∗ (b ∗ c) = a ∗ (b + c – bc)
= a + (b + c – bc) – a (b + c – bc)
= a + b + c – bc – ab – ac + abc
(a ∗ b) ∗ c = (a + b – ab) ∗ c
= a + b – ab + c – (a + b – ab) c
= a + b + c – ab – bc – ca + abc
∴ (a ∗ b) ∗ c = a ∗ (b ∗ c)
⇒ ∗ is associative.

Existance of Identity:
Let e is the identity
∴ e ∗ a = a ∗ e = a
⇒ a + e – ae = a
⇒ e (1 – a) = 0
⇒ e = 0 ( a ≠ 1)
∴ 0 is the identity.

Existance of inverse:
Let a-1 is the inverse of a
⇒ a ∗ a-1 = a-1 ∗ a = e
⇒ a + a-1 – aa-1 = 0
⇒ a-1 (1 – a) = – a
⇒ a-1 = \(\frac{a}{a-1}\) for a ∈ R – {1}

CHSE Odisha Class 12 Math Solutions Chapter 1 Relation and Function Ex 1(c)

Question 4.
Construct the composition table/multiplication table for the binary operation ∗ defined on {0, 1, 2, 3, 4} by a ∗ b = a × b {mod 5). Find the identity element if any. Also find the inverse elements of 2 and 4.
[This operation is called multiplication moduls 5 and denoted by x5. In general, on a finite subset of N, xm denotes the operation of multiplication modulo m where m is a fixed positive integer].
Solution:
A = {0. 1, 2, 3, 4}
a ∗ b = a × b mod 5

0 1 2 3 4
0 0 0 0 0 0
1 0 1 2 3 4
2 0 2 4 1 3
3 0 3 1 4 2
4 0 4 3 2 1

As 3rd row is identical to the first row we have 1 is the identity clearly 2-1 = 3 and 4-1 = 4.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Odisha State Board CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Exercise 3(b)

Question 1.
Maximize Z = 5x1+ 6x2
Subject to: 2x1 + 3x2 ≤ 6
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraint as equation, we get 2x1 + 3x2 = 6
Step – 2 Let us draw the graph

x1 3 0
x2 0 0

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.1
Step – 3 Clearly (0,0) statisfies 2x1 + 3x2 ≤ 6
The shaded region is the feasible region with vertices 0(0,0), A(3,0), B(0,2).
Step – 4

Corner point Z = 5x1+ 6x2
0(0.0) 0
A(3,0) 15 → maximum
B(0,2) 12

Z is maximum at A (3,0)
∴ The solution of LPP is x1 = 3, x2 = 0
Zmax = 15

Question 2.
Minimize: Z = 6x1 + 7x2
Subject to: x1 + 2x2 ≥ 4
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraint as equation we get x1 + 2x2 = 0
Step – 2 Let us draw the graph of x1 + 2x2 = 4

x1 0 4
x2 2 0

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.2
Step – 3 Clearly 0(0,0) does not satisfy
x1 + 2x2 > 4, x1 > 0, x2 > 0 is the first quadrant.
The feasible region is the shaded region with vertices A(4, 0), B(0, 2).
Step – 4 Z (4, 0) = 24
Z (0, 2) = 14 → minimum
Step – 5 As the feasible region is unbounded we cannot immediately decide Z is minimum at B (0, 2).
Let us draw the half-plane 6x1 + 7x2 < 14

x1 0 3.5
x2 2 -1

As this half-plane has no point common with the feasible region, we have Z is minimum for x1= 0, x2 = 2 and the minimum value of Z = 14.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Question 3.
Maximize Z = 20x1+ 40x2
Subject to: x1 + x2 ≤ 1
6x1 + 2x2 ≤ 3
x1, x2 ≥ 0.
Solution:
Step – 1 Treating the constraints as equations
x1 + x2 = 1    …. (1)
6x1 + 2x2 = 3   …. (2)
x1, x2 ≥ 0
Step – 2 Let us draw the graph:
Table – 1

x1 0 1
x2 1 0

Table – 2

x1 0 0.5
x2 1.5 0

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.3
Step – 3 As (0, 0) satisfies both the inequations the shaded region is the feasible region.
Step – 4 Solving
x1 + x2 = 1
6x1 + 2x2 = 3
we have x1 = ¼ x2 = ¾
The vertices are O(0, 0), A(0.5, 0), B(0,1) and C(¼, ¾)
Now Z(O) = 0
Z(A) = 10
Z(B) = 40
Z(C) = 20 × ¼ + 40 × ¾ = 35
∴ Z attains maximum at B for x1= 0, x2 = 1
Zmax = 40

Question 4.
Minimize: Z = 30x1 + 45x2
Subject to: 2x1 + 6x2 ≥ 4
5x1 + 2x2 ≥ 5
x1, x2 ≥ 0
Solution:
Step – 1 Consider the constraints as equations
2x1 + 6x2 = 4
5x1 + 2x2 = 5
Step – 2
Table – 1

x1 2 -1
x2 0 1

Table – 2

x1 1 0
x2 0 2.5

Step – 3 Clearly 0(0,0) does not satisfy 2x1 + 6x2 ≥ 4 and 5x1 + 2x2 ≥ 5.
Thus the shaded region is the feasible region.
Solving the equations we get
x1 = \(\frac{11}{13}\), x2 = \(\frac{5}{13}\).
∴ The vertices are A(2, 0)
B(\(\frac{11}{13}\), \(\frac{5}{13}\)) and C(0, \(\frac{5}{2}\)).
Step – 4 Z(A) = 60
Z(B) = \(\frac{555}{13}\) → minimum
Z(C) = \(\frac{225}{2}\)
Step – 5 As the feasible region is unbounded we cannot immediately decide Z is minimum at B(\(\frac{11}{13}\), \(\frac{5}{13}\))
Let us draw the half plane
30x1 + 45x2 < \(\frac{555}{13}\)

x1 \(\frac{11}{13}\) 0
x2 \(\frac{5}{13}\) \(\frac{27}{39}\)

As this half plane and the feasible region has no point in common we have Z is minimum for x1 = \(\frac{11}{13}\), x2 = \(\frac{5}{13}\), and Zmin = \(\frac{555}{13}\)

Question 5.
Maximize: Z = 3x1+ 2x2
Subject to: -2x1 + x2 ≤ 1
x1 ≤ 2
x1+ x2 ≤ 3
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations
-2x1 + x2 = 1        …..(1)
x1 = 2                   …..(2)
x1+ x2 = 3            …..(3)
Step – 2 Let us draw the lines.
Table – 1

x1 0 -1
x2 1 -1

Table – 2

x1 2 2
x2 0 1

Table – 3

x1 0 3
x2 3 0

Step – 3 (0, 0) satisfies all the constraints and x1, x2 > 0 is the 1st quadrant the shaded region is the feasible region.
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.5
Step – 4 Solving -2x1 + x2 = 1
x1+ x2 = 3
we have 3x1 = 2
⇒ x1 = \(\frac{2}{3}\), x2 = 3 – \(\frac{2}{3}\) = \(\frac{7}{3}\)
From x1+ x2 = 3 and x1 = 2 we have x1 = 2, x2 = 1
∴ The vertices are 0(0, 0), A(2, 0), B(2, 1), C(\(\frac{2}{3}\), \(\frac{7}{3}\)), D(0, 1)
Z(0) = 0, Z(A) = 6, Z(B) = 8, Z(C) = 3.\(\frac{2}{3}\) + 2.\(\frac{7}{3}\) = \(\frac{20}{3}\), Z(D) = 2
Z is maximum at B.
∴ The solution of given LPP is x1 = 2, x2 = 1, Z(max) = 8.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Question 6.
Maximize: Z = 50x1+ 60x2
Subject to: x1 + x2 ≤ 5
x1+ 2x2 ≤ 4
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
x1 + x2 = 5     ….(1)
x1+ 2x2 = 4    ….(2)
Step – 2 Let us draw the graph
Table – 1

x1 5 5
x2 0 0

Table – 2

x1 4 0
x2 0 2

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.6
Step – 3 0(0,0) satisfies x1 + x2 ≤ 5 and does not satisfy x1+ 2x2 ≤ 4
Thus the shaded region is the feasible region.
Step – 4 The corner points are A(4,0), B(5,0), C(0,5) , D(0,2)

Corner point z = 50x1+ 60x2
A(4,0) 200
B (5,0) 250 → maximum
C(0,5) 300
D(0,2) 120

Z is maximum for x1 = 0, x2 = 5, Z(max) = 300.

Question 7.
Maximize: Z = 5x1+ 7x2
Subject to: x1 + x2 ≤ 4
5x1+ 8x2 ≤ 30
10x1+ 7x2 ≤ 35
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get,
x1 + x2 = 4           …. (1)
5x1+ 8x2 = 30      …. (2)
10x1+ 7x2 = 35    …. (3)
Step – 2 Let us draw the graph
Table – 1

x1 4 0
x2 0 4

Table – 2

x1 6 2
x2 0 2.5

Table – 3

x1 0 3.5
x2 5 0

Step – 3 0(0,0) satisfies all the constraints.
Thus the shaded region is the feasible region.
From (1) and (2) we get (\(\frac{2}{3}\), \(\frac{10}{3}\))
From (1) and (3) we get
x1 = \(\frac{7}{3}\), x1 = \(\frac{5}{3}\)
∴ The corner points are 0(0,0), A(\(\frac{7}{2}\), 0), B(\(\frac{7}{3}\), \(\frac{5}{3}\)), C(\(\frac{2}{3}\), \(\frac{10}{3}\)), D(0, \(\frac{15}{4}\))
Step – 4

Corner point z = 5x1+ 7x2
0(0,0) 0
A(\(\frac{7}{2}\), 0) \(\frac{35}{2}\)
B(\(\frac{7}{3}\), \(\frac{5}{3}\)) \(\frac{70}{3}\)
C(\(\frac{2}{3}\), \(\frac{10}{3}\)) \(\frac{80}{3}\)
D(0, \(\frac{15}{4}\)) \(\frac{105}{4}\)

Z attains its maximum value \(\frac{80}{3}\) for x1 = \(\frac{2}{3}\) and x2 = \(\frac{10}{3}\).

Question 8.
Maximize: Z = 14x1 – 4x2
Subject to: x1 + 12x2 ≤ 65
7x1 – 2x2 ≤ 25
2x1+ 3x2 ≤ 10
x1, x2 ≥ 0
Also find two other points which maximize Z.
Solution:
Step – 1 Treating the constraints as equations we get
x1 + 12x2 = 65   …. (1)
7x1 – 2x2 = 25    …. (2)
2x1 + 3x2 = 10   …. (3)
Step – 2 Let us draw the graph
Table – 1

x1 65 5
x2 0 5

Table – 2

x1 5 10
x2 5 22.5

Table – 3

x1 5 2
x2 0 2

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.8
Step – 3 Clearly 0(0,0) satisfies x1 + 12x2 ≤ 65 and 7x1 – 2x2 ≤ 25 but does not satisfy 2x1+ 3x2 ≤ 10. Thus shaded region is the feasible region.
Equation (1) and (2) meet at (5, 5).
From (2) and (3)
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.8.1
∴ The corner points of the feasible region are A(0, \(\frac{10}{3}\)), B(\(\frac{19}{5}\), \(\frac{4}{5}\)), C(5, 5), D(0, \(\frac{65}{12}\)).
Step – 4

Corner point z = 14x1 – 4x2
A(0, \(\frac{10}{3}\)) \(\frac{-40}{3}\)
B(\(\frac{19}{5}\), \(\frac{4}{5}\)) 50 → maximum
 C(5, 5) 50 → maximum
D(0, \(\frac{65}{12}\)) \(\frac{65}{3}\)

Z is maximum for x1 = \(\frac{19}{5}\), x2 = \(\frac{4}{5}\) or x1 = 5, x2 = 5 and Zmax = 50
There is no other point that maximizes Z.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Question 9.
Maximize: Z = 10x1 + 12x2 + 8x3
Subject to: x1 + 2x2 ≤ 30
5x1 – 7x3 ≤ 12
x1 + x2 + x3 = 20
x1, x2 ≥ 0
[Hints: Eliminate x3 from all expressions using the given equation in the set of constraints, so that it becomes an LPP in two variables]
Solution:
Eliminating x3 this LPP can be written as Maximize Z = 2x1 + 4x2 + 160
Subject to: x1 + 2x2 ≤ 30
5x1 – 7x3 ≤ 12
x1, x2 ≥ 0
Step – 1 Treating the consraints as equations we get
x1 + 2x2 = 30    …..(1)
5x1 – 7x3 = 12   …..(2)
Step – 2 Let us draw the graph
Table – 1

x1 30 0
x2 0 15

Table – 2

x1 8 1
x2 8 20

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.9
Step – 3 Clearly 0(0,0) satisfies x1 + 2x2 ≤ 30 and does not satisfy 12x1 + 7x2 ≤ 152
∴ The shaded region is the feasible region.
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.9.1
Step – 4
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.9.2
Z is maximum for x1 = 30, x2 = 0 and Zmax = 220

Question 10.
Maximize: Z = 20x1 + 10x2
Subject to: x1 + 2x2 ≤ 40
3x1 + x2 ≥ 30
4x1+ 3x2 ≥ 60
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equalities we have:
x1 + 2x2 = 40   ….(1)
3x1 + x2 = 30   ….(2)
4x1+ 3x2 = 60  ….(3)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.10
Step – 3 (0, 0) satisfies x1 + 2x2 ≤ 40 and does not satisfy 3x1 + x2 ≥ 30 and 4x1+ 3x2 ≥ 60, x1, x2 ≥ 0 is the first quadrant.
∴ The shaded region is the feasible region.
Step – 4 x1 + 2x2 = 40 and 3x1 + x2 = 30
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.10.1

∴ The vetices are A(15, 0), B(10, 0), C(4, 18) and D(6, 12)
Z(A) = 300, Z(B) = 800
Z (C) = 20 x 4 + 10 x 18 = 260
Z (D) = 120 + 120 = 240
Z attains minimum at D(6 ,12).
∴ The required solution x1 = 6, x2 =12 and Zmin = 240

Question 11.
Maximize: Z = 4x1 + 3x2
Subject to: x1 + x2 ≤ 50
x1 + 2x2 ≥ 80
2x1+ x2 ≥ 20
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations
x1 + x2 ≤ 50    ….(1)
x1 + 2x2 ≥ 80  ….(2)
2x1+ x2 ≥ 20   ….(3)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.11
Step – 3 (0, 0) satisfies x1 + x2 < 50, x1 + 2x2 < 80 but does not satisfy
2x1 + x2 > 20, x1 > 0, x2 > 0 is the 1st quadrant.
Hence the shaded region is the feasible region.
Step – 4 x1 + x2 = 50
x1 + 2x2 = 80
=> x2 = 30, x1 = 20
The vertices of feasible region are
A(10, 0), B(50, 0), C(20, 30), D (0, 40) and E (0, 20)

Point Z = 4x1 + 3x2
A(10,0) 40
5(50,0) 200
C(20,30) 170
D(0,40) 120
E(0,120) 60

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Question 12.
Optimize: Z = 5x1 + 25x2
Subject to: -0.5x1 + x2 ≤ 2
x1 + x2 ≥ 2
-x1+ 5x2 ≥ 5
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations
-0.5x1 + x2 = 2   ….(1)
x1 + x2 = 2         ….(2)
-x1+ 5x2 = 5      ….(3)
Step – 2 Let us draw the graph.
D:\BSE Odisha.guru\Image\CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.12.png
Step – 3 (0, 0) satisfies -0.5x1 + x2 ≤ 2, but does not satisfy x1 + x2 ≥ 2 and -x1+ 5x2 ≥ 5, x1 > 0, x2 > 0 is the 1st quadrant.
The shaded region is the feasible region with vertices A(\(\frac{5}{6}\), \(\frac{7}{6}\)) and B(0, 2).
Step – 4 Z can be made arbitrarily large.
∴ Problem has no maximum.
But Z(A) = \(\frac{100}{3}\), Z(B) = 50
Z is minimum at A(\(\frac{5}{6}\), \(\frac{7}{6}\)).
But the feasible region is unbounded.
Hence we cannot immediately decide, Z is minimum at A.
Let us draw the half plane
5x1 + 25x2 < \(\frac{100}{3}\)
⇒ 3x1 + 15x2 < 20
As there is no point common to this half plane and the feasible region.
we have Z is minimum for x1 = \(\frac{5}{6}\), x2 = \(\frac{7}{6}\) and the minimum value = \(\frac{100}{3}\)

Question 13.
Optimize: Z = 5x1 + 2x2
Subject to: -0.5x1 + x2 ≤ 2
x1 + x2 ≥ 2
-x1+ 5x2 ≥ 5
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations
-0.5x1 + x2 = 2   ….(1)
x1 + x2 = 2         ….(2)
-x1+ 5x2 = 5      ….(3)
Step – 2 Let us draw the graph.
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.13
Step – 3 The shaded regian is feasible region which is unbounded, thus Z does not have any maximum.
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.13(1)
As Z can be made arbitrarily large, the given LPP has no maximum.
Z is minimum at B (0, 2). But we cannot immediately decide, Z is minimum at B.
Let us draw the half plane 5x1 + 2x2 < 4

x1 0 4/5
x2 2 0

As there is no point common to this half plane and the feasible region,
we have Z is minimum for x1 = 0, x2 = 2 and the minimum value of Z = 4.

Question 14.
Optimize: Z = -10x1 + 2x2
Subject to: -x1 + x2 ≥ -1
x1 + x2 ≤ 6
x2 ≤ 5
x1, x2 ≥ 0
Solution:
Step – 1 Treating the constraints as equations
-x1 + x2 = -1     ….(1)
x1 + x2 = 6        ….(2)
x2 = 5                ….(3)
Step – 2 Let us draw the graph
Table – 1

x1 1 0
x2 0 -1

Table – 2

x1 6 0
x2 0 1

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.14
Step – 3 Clearly 0(0,0) satisfies all the constraints.
Thus the shaded region is the feasible region.
The vertices are 0(0,0) , A(1,0), B(\(\frac{7}{2}\), \(\frac{5}{2}\)) ,C(1, 5) and D (0, 5)
Step – 4 Z(O) = 0
Z(A) = -10
Z(B) = – 30
Z(C) = 0
Z(D) = 10
∴ Z is maximum for x1= 0, x, = 5 and Z(max) = 10
Z is minimum for x1 = \(\frac{7}{2}\)  x2 = \(\frac{5}{2}\) and Z(min) = -30

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

Question 15.
Solve the L.P.P.s obtained in Exercise 3(a) Q.1 to Q. 9 by graphical method.
(1) Maximise: Z = 1500x + 2000y
Subject to: x + y < 20
x + 2y < 24
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
x + y = 20
x + 2y = 24
Step – 2 Let us draw of graph.
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(1)
Step – 3 Clearly 0(0,0) satisfies all the constraints.
Thus the shaded region is the feasible region.
From (1) and (2) we get
y = 14
x = 16
With vertices 0(0, 0), A(20, 0), B(16, 4), C(0, 12).
Step – 4 Z(0) = 0
Z(A) = 30,000
Z(B) = 32,000 → Maximum
Z(C) = 24000
Z is maximum for x = 16, y = 4 with Z = 32000
To get maximum profit he must keep 16 sets of model X and 4 sets of model Y.
Maximum profit = 1500 × 16 + 2000 × 4 = ₹32,000

(2) Maximize: 15x + 10y
Subject: x + 3y ≤ 600
2x + y ≤ 480
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
2x +3y = 600
2a + y = 480
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(2)
Step – 3 Clearly 0(0,0) satisfies all the constraints.
The corner point are 0(0, 0), A (240, 0) B(210, 60),C(0, 200)
Step – 4 Z(0) = 6
Z(A) = 3600
Z(B) = 3150 + 600
= 3750 → maximum
Z(C) = 2000
Thus Z is maximum for x = 210 and y = 60
and Z(max) = 3750

(3) Maximize: Z = 20x + 30y
Subject to: x + 2y ≤ 10
x + y ≤ 6
x ≤ 4
x, y ≥ 0.
Solution:
Step – 1 Treating the constraints as equations we get
x + 2y = 10       …(1)
x + y = 6           …(2)
x = 4
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(3)
Step – 3 As 0(0,0) satisfies all the constraints the shaded region is the feasible region.
Solving (1) and (2) we get x = 2, y = 4.
The vertices and 0(0, 0) , A(4, 0), B(4, 2), C(2, 4), D (0, 5).
Step – 4 Z(0) =0
Z(A) = 80
Z (B) =140
Z(C) = 1 60 → maximum
Z (D) = 150
∴ Z is Maximum when x = 2, y = 4 and Z(max) = 160

(4) Maximize: Z = 15x + 17y
Subject to: 4x + 7y ≤ 150
x + y ≤ 30
15x + 17y > 300
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
4x + 7y = 150      ….(1)
x + y = 30            ….(2)
15x + 17y = 300  ….(3)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(4)
Step – 3 Clearly 0(0,0) satisfies all the constraints.
4x + 7y ≤ 150, x + y ≤ 30, but does not satisfy 15x + 17y ≥ 300.
∴ The shaded region is the feasible region.
From (1) and (2) we get
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(4.1)
∴ Z is maximum for x = 20. y = 10 and Z(max) = 470

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

(5) Maximize: Z = 2x + 4y
Subject to: 3x + 2y ≤ 10
2x + 5y ≤ 15
5x + 6y ≤ 21
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
3x + 2y = 10  …(1)
2x + 5y = 15  …(2)
5x + 6y = 21  …(3)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(5)
Step – 3 As 0(0,0) satisfies all the constraints the shaded region is the feasible region.
From (1) and (3) we get
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(5.1)
From (2) and (3) we get
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(5.2)
Step-4 Z(O) = 0
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(5.3)

(6) Maximize: Z = 1000x + 800y
Subject to: x + y ≤ 5
2x + y ≤ 9
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
x + y = 5    ….(1)
2x + y = 9  ….(2)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(6)
Step – 3 Clearly 0(0,0) satisfies all the constraints.
∴ Thus the shaded region is the feasible region.
From (1) and (2) we get x = 4, y = 1.
∴ The vertices are A(0, 0), A(4.5, 0), B(4, 1) and C(0, 5).
Step – 4 Z(0) =0
Z (A) = 4500
Z (B) = 4800 → Maximum
Z (C) = 4000
Z is maximum for x = 4 and y = 1, Z(max) = 4800

(7) Minimize: Z = 4960 – 70x – 130y
Subject to: x + y ≤ 12
x + y ≥ 6
x ≤ 8
y ≤ 8
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
x + y = 12   ….(1)
x + y = 6     ….(2)
x = 8           ….(3)
y = 4           ….(4)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(7)

Step – 3 Clearly 0(0,0) satisfies all the constraints except x + y > 6.
The shaded region is the feasible region.
The vertices are A(6, 0), B(8, 0), C(8, 4), D(4, 8), E(0, 8) and F(0, 6).
Step – 4 Z (A) = 4540
Z (B) = 4400
Z (C) = 3880
Z (D) = 3640 → Minimum
Z (E) = 3920
Z (F) = 4180
∴ Z is maximum for x = 4 and y = 8 and Z(min) = 3640.

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b)

(8) Minimize: Z = 16x + 20y
Subject to x + 2y ≥ 10
x + y ≥ 6
3x + y ≥ 8
x, y ≥ 0
Solution:
Step – 1 Treating the constraints as equations we get
x + 2y = 10  ….(1)
x + y = 6      …(2)
3x + y = 8    …(3)
Step – 2 Let us draw the graph
CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(8)
Step – 3 Clearly 0(0,0) satisfies all the constraints. Thus the shaded region is the feasible region.
From (1) and (2) we get y = 4, x = 2.
From (2) and (3) we get x = 1, y = 5.
The vertices are A(10, 0), B(2, 4), C(1, 5), D(0, 8).
Step – 4 Z (A) = 160
Z (B) = 112 → Minimum
Z (C) =116
Z (D) = 160
As the region is unbounded, let us draw the half plane Z < Z(min)
⇒ 16x + 20y < 112
⇒ 4x + 5y < 28

x1 7 0
x2 0 5.6

There is no point common to the shaded region and the half plane 4x + 5y ≤ 28 other than B(2, 4).
∴ Z is minimum for x = 2, y = 4 and Z(min) = 112.

(9) Minimize: Z = (512.5)x + 800y
Subject to: 5x + 4y = 40
x ≤ 7
x ≤ 3
x, y ≥ 0
Solution:
Step – 1 Let us draw the graph of
5x + 4y = 40
x = 7, y = 3

x1 8 0
x2 0 10

CHSE Odisha Class 12 Math Solutions Chapter 3 Linear Programming Ex 3(b) Q.15(9)
Step – 1 Let us draw the graph of
5x + 4y = 40
x = 7, y = 3
Step – 2 The line segment AB is the feasible region.
Step – 3 Z (A) = 3587.5 + 1000 = 4587.5
Z (B) = 2870 + 2400 = 5270
Clearly Z is minimum for
x = 7, y = \(\frac{5}{4}\) and Z(min) = 4587.5

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

Odisha State Board Elements of Mathematics Class 12 Solutions CHSE Odisha Chapter 2 Inverse Trigonometric Functions Ex 2 Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Exercise 2

Question 1.
Fill in the blanks choosing correct answer from the brackets:
(i) If A = tan-1 x, then the value of sin 2A = ________. (\(\frac{2 x}{1-x^2}\), \(\frac{2 x}{\sqrt{1-x^2}}\), \(\frac{2 x}{1+x^2}\))
Solution:
\(\frac{2 x}{1+x^2}\)

(ii) If the value of sin-1 x = \(\frac{\pi}{5}\) for some x ∈ (-1, 1) then the value of cos-1 x is ________. (\(\frac{3 \pi}{10}\), \(\frac{5 \pi}{10}\),\(\frac{3 \pi}{10}\))
Solution:
\(\frac{3 \pi}{10}\)

(iii) The value of tan-1 x (2cos\(\frac{\pi}{3}\)) is ________. (1, \(\frac{\pi}{4}\), \(\frac{\pi}{3}\))
Solution:
\(\frac{\pi}{4}\)

(iv) If x + y = 4, xy = 1, then tan-1 x + tan-1 y = ________. (\(\frac{3 \pi}{4}\), \(\frac{\pi}{4}\), \(\frac{\pi}{3}\))
Solution:
\(\frac{\pi}{2}\)

(v) The value of cot-1 2 + tan-1 \(\frac{1}{3}\) = ________. (\(\frac{\pi}{4}\), 1, \(\frac{\pi}{2}\))
Solution:
\(\frac{\pi}{4}\)

(vi) The principal value of sin-1 (sin \(\frac{2 \pi}{3}\)) is ________. (\(\frac{2 \pi}{3}\), \(\frac{\pi}{3}\), \(\frac{4 \pi}{3}\))
Solution:
\(\frac{\pi}{3}\)

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

(vii) If sin-1 \(\frac{x}{5}\) + cosec-1 \(\frac{5}{4}\) = \(\frac{\pi}{2}\), then the value of x = ________. (2, 3, 4)
Solution:
x = 3

(viii) The value of sin (tan-1 x + tan-1 \(\frac{1}{x}\)), x > 0 = ________. (0, 1, 1/2)
Solution:
1

(ix) cot-1 \(\left[\frac{\sqrt{1-\sin x}+\sqrt{1+\sin x}}{\sqrt{1-\sin x}-\sqrt{1+\sin x}}\right]\) = ________. (2π – \(\frac{x}{2}\), \(\frac{x}{2}\), π – \(\frac{x}{2}\))
Solution:
π – \(\frac{x}{2}\)

(x) 2sin-1 \(\frac{4}{5}\) + sin-1 \(\frac{24}{25}\) = ________. (π, -π, 0)
Solution:
π

(xi) if Θ = cos-1 x + sin-1 x – tan-1 x, x ≥ 0, then the smallest interval in which Θ lies is ________. [(\(\frac{\pi}{2}\), \(\frac{3 \pi}{2}\)), [0, \(\frac{\pi}{2}\)), (0, \(\frac{\pi}{2}\)])
Solution:
(0, \(\frac{\pi}{2}\)]

(xii) sec2 (tan-1 2) + cosec2 (cot-1 3) = ________. (16, 14, 15)
Solution:
15

Question 2.
Write whether the following statements are true or false.
(i) sin-1 \(\frac{1}{x}\) cosec-1 x = 1
Solution:
False

(ii) cos-1 \(\frac{4}{5}\) + tan-1 \(\frac{2}{3}\) = tan-1 \(\frac{17}{6}\)
Solution:
True

(iii) tan-1 \(\frac{4}{3}\) + cot-1 (\(\frac{-3}{4}\)) = π
Solution:
True

(iv) sec-1 \(\frac{1}{2}\) + cosec-1 \(\frac{1}{2}\) = \(\frac{\pi}{2}\)
Solution:
False

(v) sec-1 (-\(\frac{7}{5}\)) = π – cos-1 \(\frac{5}{7}\)
Solution:
True

(vi) tan-1 (tan 3) = 3
Solution:
False

(vii) The principal value of tan-1 (tan \(\frac{3 \pi}{4}\)) is \(\frac{3 \pi}{4}\)
Solution:
False

(viii) cot-1 (-√3) is in the second quadrant.
Solution:
True

(ix) 3 tan-1 3 = tan-1 \(\frac{9}{13}\)
Solution:
False

(x) tan-1 2 + tan-1 3 = – \(\frac{\pi}{4}\)
Solution:
False

(xi) 2 sin-1 \(\frac{4}{5}\) = sin-1 \(\frac{24}{25}\)
Solution:
False

(xii) The equation tan-1 (cotx) = 2x has exactly two real solutions.
Solution:
True

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

Question 3.
Express the value of the foilowing in simplest form.
(i) sin (2 sin-1 0.6)
Solution:
sin (2 sin-1 0.6)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(1)

(ii) tan (\(\frac{\pi}{4}\) + 2 cot-1 3)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(2)

(iii) cos (2 sin-1 x)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(3)

(iv) tan (cos-1 x)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(4)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(4.1)

(v) tan-1 (\(\frac{x}{y}\)) – tan-1 \(\frac{x-y}{x+y}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(5)

(vi) cosec (cos-1 \(\frac{3}{5}\) + cos-1 \(\frac{4}{5}\))
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(6)

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

(vii) sin-1 \(\frac{1}{\sqrt{5}}\) + cos-1 \(\frac{3}{\sqrt{10}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(7)

(viii) sin cos-1 tan sec √2
Solution:
sin cos-1 tan sec √2
= sin cos-1 tan sec \(\frac{\pi}{4}\)
= sin cos-1 1 = sin 0 = 0

(ix) sin (2 tan-1 \(\sqrt{\frac{1-x}{1+x}}\))
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(9)

(x) tan \(\left\{\frac{1}{2} \sin ^{-1} \frac{2 x}{1+x^2}+\frac{1}{2} \cos ^{-1} \frac{1-y^2}{1+y^2}\right\}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(10)

(xi) sin cot-1 cos tan-1 x.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(11)

(xii) tan-1 \(\left(x+\sqrt{1+x^2}\right)\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.3(12)

Question 4.
Prove the following statements:
(i) sin-1 \(\frac{3}{5}\) + sin-1 \(\frac{8}{17}\) = cos-1 \(\frac{36}{85}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(1)

(ii) sin-1 \(\frac{3}{5}\) + cos-1 \(\frac{12}{13}\) = cos-1 \(\frac{33}{65}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(2)

(iii) tan-1 \(\frac{1}{7}\) + tan-1 \(\frac{1}{13}\) = tan-1 \(\frac{2}{9}\)
Solution:
L.H.S = tan-1 \(\frac{1}{7}\) + tan-1 \(\frac{1}{13}\)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(3)

(iv) tan-1 \(\frac{1}{2}\) + tan-1 \(\frac{1}{5}\) + tan-1 \(\frac{1}{8}\) = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(4)

(v) tan ( 2tan-1 \(\frac{1}{5}\) – \(\frac{\pi}{4}\) ) + \(\frac{7}{17}\) = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(5)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.4(5.1)

Question 5.
Prove the following statements:
(i) cot-1 9 + cosec-1 \(\frac{\sqrt{41}}{4}\) = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(1)

(ii) sin-1 \(\frac{4}{5}\) + 2 tan-1 \(\frac{1}{3}\) = \(\frac{\pi}{2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(2.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(2.2)

(iii) 4 tan-1 \(\frac{1}{5}\) – tan-1 \(\frac{1}{70}\) + tan-1 \(\frac{1}{99}\) = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(3.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(3.2)

(iv) 2 tan-1 \(\frac{1}{5}\) + sec-1 \(\frac{5 \sqrt{2}}{7}\) + 2 tan-1 \(\frac{1}{8}\) = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(4.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(4.2)

(v) cos-1 \(\frac{12}{13}\) + 2 cos-1 \(\sqrt{\frac{64}{65}}\) + cos-1 \(\sqrt{\frac{49}{50}}\) = cos-1 \(\frac{1}{\sqrt{2}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(5.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(5.2)
(vi) tan2 cos-1 \(\frac{1}{\sqrt{3}}\) + cot2 sin-1 \(\frac{1}{\sqrt{5}}\) = 6
Solution:
tan2 cos-1 \(\frac{1}{\sqrt{3}}\) + cot2 sin-1 \(\frac{1}{\sqrt{5}}\)
= tan2 tan-1 √2 + cot2 cot-1 (2)
= 2 + 4 = 6

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

(vii) cos tan-1 cot sin-1 x = x.
Solution.
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.5(7)

Question 6.
Prove the following statements:
(i) cot-1 (tan 2x) + cot-1 (- tan 2x) = π
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(1)

(ii) tan-1 x + cot-1 (x + 1) = tan-1 (x2 + x + 1)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(2)

(iii) tan-1 (\(\frac{a-b}{1+a b}\)) + tan-1 (\(\frac{b-c}{1+b c}\)) = tan-1 a – tan-1 c.
Solution:
tan-1 (\(\frac{a-b}{1+a b}\)) + tan-1 (\(\frac{b-c}{1+b c}\))
= tan-1 a – tan-1 b + tan-1 b – tan-1 c
= tan-1 a – tan-1 c.

(iv) cot-1 \(\frac{p q+1}{p-q}\) + cot-1 \(\frac{q r+1}{q-r}\) + cot-1 \(\frac{r p+1}{r-p}\) = 0
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(4)

(v)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(5.1)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(5.2)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.6(5.3)

Question 7.
Prove the following statements:
(i) tan-1 \(\frac{2 a-b}{b \sqrt{3}}\) + tan-1 \(\frac{2 b-a}{a \sqrt{3}}\) = \(\frac{\pi}{3}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(1)

(ii) tan-1 \(\frac{1}{x+y}\) + tan-1 \(\frac{y}{x^2+x y+1}\) = tan-1 \(\frac{1}{x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(2.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(2.2)

(iii) sin-1 \(\sqrt{\frac{x-q}{p-q}}\) = cos-1 \(\sqrt{\frac{p-x}{p-q}}\) = cot-1 \(\sqrt{\frac{p-x}{x-q}}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(3.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(3.2)

(iv) sin2 (sin-1 x + sin-1 y + sin-1 z) = cos2 (cos-1 x + cos-1 y + cos-1 z)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(4)

(v) tan (tan-1 x + tan-1 y + tan-1 z) = cot (cot-1 x + cot-1 y + cot-1 z)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.7(5)

Question 8.
(i) If sin-1 x + sin-1 y + sin-1 z = π, show that x\(\sqrt{1-x^2}\) + x\(\sqrt{1-y^2}\) + x\(\sqrt{1-z^2}\) = 2xyz
Solution:
Let sin-1 x = α, sin-1 y = β, sin-1 z = γ
∴ α + β + γ = π
∴ x = sin α, y = sin β, z = sin γ
or, α + β = π – γ
or, sin(α + β) = sin(π – γ) = sin γ
and cos(α + β) = cos(π – γ) = – cos γ
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.8(1)

(ii) tan-1 x + tan-1 y + tan-1 z = π show that x + y + z = xyz.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.8(2)

(iii) tan-1 x + tan-1 y + tan-1 z = \(\frac{\pi}{2}\). Show that xy + yz + zx = 1
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.8(3)
or, 1 – xy – yz – zx = 0
⇒ xy + yz + zx = 1

(iv) If r2 = x2 +y2 + z2, Prove that tan-1 \(\frac{y z}{x r}\) + tan-1 \(\frac{z x}{y r}\) + tan-1 \(\frac{x y}{z r}\) = \(\frac{\pi}{2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.8(4)

(v) In a triangle ABC if m∠A = 90°, prove that tan-1 \(\frac{b}{a+c}\) + tan-1 \(\frac{c}{a+b}\) = \(\frac{\pi}{4}\). where a, b, and c are sides of the triangle.
Solution:
L.H.S. tan-1 \(\frac{b}{a+c}\) + tan-1 \(\frac{c}{a+b}\)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.8(5)

Question 9.
Solve
(i) cos (2 sin-1 x) = 1/9
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(1)

(ii) sin-1 x + sin-1 (1 – x) = \(\frac{\pi}{2}\)
Solution:
sin-1 x + sin-1 (1 – x) = \(\frac{\pi}{2}\)
or, sin-1 (1 – x) = \(\frac{\pi}{2}\) – sin-1 x = cos-1 x
or, sin-1 (1 – x) = sin-1 \(\sqrt{1-x^2}\)
or, 1 – x = \(\sqrt{1-x^2}\)
or, 1 + x2 – 2x = 1 – x2
or, 2x2 – 2x  = 0
or, 2x (x – 1) = 0
∴ x = 0 or, 1

(iii) sin-1 (1 – x) – 2 sin-1 x = \(\frac{\pi}{2}\)
Solution:
sin-1 (1 – x) – 2 sin-1 x = \(\frac{\pi}{2}\)
⇒ – 2 sin-1 x = \(\frac{\pi}{2}\) – sin-1 (1 – x)
⇒ cos-1 (1 – x)
⇒ cos (– 2 sin-1 x) = 1 – x      ….. (1)
Let sin-1 Θ ⇒ sin Θ
Now cos (– 2 sin-1 x) = cos (-2Θ)
= cos 2Θ = 1 – 2 sin2 Θ = 1 – 2x2
Using in (1) we get
1 – 2x2 = 1 – x
⇒ 2x2 – x = 0 ⇒ x (2x – 1) = 0
⇒ x = 0, ½, But x = ½ does not
Satisfy the given equation, Thus x = 0.

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

(iv) cos-1 x + sin-1 \(\frac{x}{2}\) = \(\frac{\pi}{6}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(4)

(v) tan-1 \(\frac{x-1}{x-2}\) + tan-1 \(\frac{x+1}{x+2}\) = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(5)

(vi) tan-1 \(\frac{1}{2 x+1}\) + tan-1 \(\frac{1}{4 x+1}\) = tan-1 \(\frac{2}{x^2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(6)

(vii) 3 sin-1 \(\frac{2 x}{1+x^2}\) – 4 cos-1 \(\frac{1-x^2}{1+x^2}\) + 2 tan-1 \(\frac{2 x}{1-x^2}\) = \(\frac{\pi}{3}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(7)

(viii) cot-1 \(\frac{1}{x-1}\) + cot-1 \(\frac{1}{x}\) + cot-1 \(\frac{1}{x+1}\) = cot-1 \(\frac{1}{3x}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(8)

(ix) cot-1 \(\frac{1-x^2}{2 x}\) =  cosec-1 \(\frac{1+a^2}{2 a}\) – sec-1 \(\frac{1+b^2}{1-b^2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(9)

(x) sin-1 \(\left(\frac{2 a}{1+a^2}\right)\) + sin-1 \(\left(\frac{2 b}{1+b^2}\right)\) = 2 tan-1 x
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(10)

(xi) sin-1 y – cos-1 x = cos-1 \(\frac{\sqrt{3}}{2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(11)

(xii) sin-1 2x + sin-1 x = \(\frac{\pi}{3}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.9(12)

Question 10.
Rectify the error ifany in the following:
sin-1 \(\frac{4}{5}\) + sin-1 \(\frac{12}{13}\) + sin-1 \(\frac{33}{65}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.10

Question 11.
Prove that:
(i) cos-1 \(\left(\frac{b+a \cos x}{a+b \cos x}\right)\) = 2 tan-1 \(\left(\sqrt{\frac{a-b}{a+b}} \tan \frac{x}{2}\right)\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.11(1)

(ii) tan \(\left(\frac{\pi}{4}+\frac{1}{2} \cos ^{-1} \frac{a}{b}\right)\) + tan \(\left(\frac{\pi}{4}-\frac{1}{2} \cos ^{-1} \frac{a}{b}\right)\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.11(2.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.11(2.2)

(iii) tan-1 \(\sqrt{\frac{x r}{y z}}\) + tan-1 \(\sqrt{\frac{y r}{y x}}\) + tan-1 \(\sqrt{\frac{z r}{x y}}\) = π where r = x + y +z.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.11(3)

Question 12.
(i) If cos-1 (\(\frac{x}{a}\)) + cos-1 (\(\frac{y}{b}\)) = Θ, prove that \(\frac{x^2}{a^2}\) – \(\frac{2 x}{a b}\) cos Θ + \(\frac{y^2}{b^2}\) = sin2 Θ.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(1.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(1.2)

(ii) If cos-1 (\(\frac{x}{y}\)) + cos-1 (\(\frac{y}{3}\)) = Θ, prove that 9x2 – 12xy cos Θ + 4y2 = 36 sin2 Θ.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(2)

(iii) If sin-1 (\(\frac{x}{a}\)) + sin-1 (\(\frac{y}{b}\)) = sin-1 (\(\frac{c^2}{a b}\)) prove that b2x2 + 2xy \(\sqrt{a^2 b^2-c^4}\) a2y2 = c2
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(3)

(iv) If sin-1 (\(\frac{x}{a}\)) + sin-1 (\(\frac{y}{b}\)) = α prove that \(\frac{x^2}{a^2}\) + \(\frac{2 x y}{a b}\) cos α + \(\frac{y^2}{b^2}\) = sin2 α
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(4)

CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2

(v) If sin-1 x + sin-1 y + sin-1 z = π prove that x2 + y2 + z2 + 4x2y2z2 = 2 ( x2y2 + y2z2 + z2x2 )
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.12(5)

Question 13.
Solve the following equations:
(i) tan-1 \(\frac{x-1}{x+1}\) + tan-1 \(\frac{2 x-1}{2 x+1}\) = tan-1 \(\frac{23}{36}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.13(1)

(ii) tan-1 \(\frac{1}{3}\) + tan-1 \(\frac{1}{5}\) + tan-1 \(\frac{1}{7}\) + tan-1 x = \(\frac{\pi}{4}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.13(2)

(iii) cos-1 \(\left(x+\frac{1}{2}\right)\) + cos-1 x+ cos-1 \(\left(x-\frac{1}{2}\right)\) = \(\frac{3 \pi}{2}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.13(3.1)
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.13(3.2)

(iv) 3tan-1 \(\frac{1}{2+\sqrt{3}}\) – tan-1 \(\frac{1}{x}\) = tan-1 \(\frac{1}{3}\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 2 Inverse Trigonometric Functions Ex 2 Q.13(4)

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b)

Odisha State Board Elements of Mathematics Class 12 CHSE Odisha Solutions Chapter 4 Matrices Ex 4(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Exercise 4(b)

Question 1.
State which of the following matrices are symmetric, skew-symmetric, both or not either:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.1
Solution:
(i) Symmetric
(ii) Neither Symmetric nor skew-symmetric
(iii) Symmetric
(iv) Skew symmetric
(v) Both
(vi) Neither symmetric nor skew-symmetric
(vii) Skew symmetric

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b)

Question 2.
State ‘True’ or ‘False’:
(i) If A and B are symmetric matrices of the same order and AB – BA ≠ 0, then AB is not symmetric.
Solution:
True

(ii) For any square matrix A, AA’ is symmetric.
Solution:
True

(iii) If A is any skew-symmetric matrix, then A2 is also skew-symmetric.
Solution:
False

(iv) If A is symmetric, then A2, A3, …, An are all symmetric.
Solution:
True

(v) If A is symmetric then A – A1 is both symmetric and skew-symmetric.
Solution:
False

(vi) For any square matrix (A – A1)2 is skew-symmetric.
Solution:
True

(vii) A matrix which is not symmetric is skew-symmetric.
Solution:
False

Question 3.
(i) If A and B are symmetric matrices of the same order with AB ≠ BA, final whether AB – BA is symmetric or skew symmetric.
Solution:
A and B are symmetric matrices;
Thus A’ = A and B’ = B
Now (AB – BA)’ = (AB)’ – (BA)’
= B’A’ – A’B’
= BA – AB = – (AB – BA)
∴ AB – BA is skew symmetric.

(ii) If a symmetric/skew-symmetric matrix is expressed as a sum of a symmetric and a skew-symmetric matrix then prove that one of the matrices in the sum must be zero matrix.
Solution:
We know that zero matrix is both symmetric as well as skew-symmetric.
Let A is symmetric.
∴ A = A + O where A is symmetric and O is treated as skew-symmetric. If B is skew-symmetric then we can write B = O + B where O is symmetric and B is skew-symmetric.

Question 4.
A and B are square matrices of the same order, prove that
(i) If A, B and AB are all symmetric, then AB – BA = 0
Solution:
Let A, B and AB are all symmetric.
∴A’ = A, B’ = B and (AB)’ = AB
⇒ B’A’ = AB
⇒ BA = AB
⇒ AB – BA = 0

(ii) If A, B and AB are all skew symmetric then AB + BA = 0
Solution:
Let A, B and AB are all skew symmetric matrices
∴ A’ = -A, B’ = -B and (AB)’ = -AB
Now (AB)’ = -AB
⇒ B’A’ = -AB
⇒ (-B) (-A) = -AB
⇒ BA = -AB
⇒ AB + BA = 0

Question 5.
If A = \(\left[\begin{array}{rrr}
1 & 2 & 0 \\
0 & 1 & 3 \\
-2 & 5 & 3
\end{array}\right]\), then verify that A’ = \(\left[\begin{array}{ccc}
1 & 0 & -2 \\
2 & 1 & 5 \\
0 & 3 & 3
\end{array}\right]\)

(i) A+A’ is symmetric
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.5

(ii) A-A’ is skew-symmetric
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.5(2)

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b)

Question 6.
Prove that a unit matrix is its own inverse. Is the converse true?
IfA = \(\left[\begin{array}{rrr}
0 & 1 & -1 \\
4 & -3 & 4 \\
3 & -3 & 4
\end{array}\right]\) show that A2 = I and hence A= A-1.
Solution:
No the converse is not true for example:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.6

Question 7.
Here A is an involuntary matrix, recall the definition given earlier.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.7

Question 8.
Show that \(\left[\begin{array}{ll}
\mathbf{0} & \mathbf{1} \\
\mathbf{1} & \mathbf{0}
\end{array}\right]\) is its own inverse.
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.8

Question 9.
Express as a sum of a symmetric and a skew symmetric matrix.
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9
Solutions:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(1)

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(3)
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(4)
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(5)
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(6)
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.9(7)

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b)

Question 10.
What is the inverse of
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.10

Question 11.
Find inverse of the following matrices by elementary row/column operation (transformations):
(i) \(\left[\begin{array}{ll}
1 & 2 \\
3 & 5
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(1)

(ii) \(\left[\begin{array}{ll}
2 & 5 \\
1 & 3
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(2)

(iii) \(\left[\begin{array}{cc}
4 & -2 \\
3 & 1
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(3)

(iv) \(\left[\begin{array}{ll}
2 & 5 \\
1 & 3
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(4)

(v) \(\left[\begin{array}{cc}
1 & 0 \\
2 & -3
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(5)

(vi) \(\left[\begin{array}{cc}
1 & 0 \\
0 & -1
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.11(6)

CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b)

Question 12.
Find the inverse of the following matrices using elementary transformation:
(i) \(\left[\begin{array}{lll}
\mathbf{0} & \mathbf{0} & 2 \\
\mathbf{0} & \mathbf{2} & \mathbf{0} \\
\mathbf{2} & \mathbf{0} & \mathbf{0}
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.12(1)

(ii) \(\left[\begin{array}{lll}
0 & 1 & 2 \\
1 & 2 & 3 \\
3 & 1 & 1
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.12(2)

(iii) \(\left[\begin{array}{ccc}
3 & -2 & 3 \\
2 & 1 & -1 \\
4 & -3 & 2
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.12(3)

(iv) \(\left[\begin{array}{lll}
1 & 1 & 2 \\
0 & 1 & 2 \\
1 & 2 & 1
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.12(4)

(v) \(\left[\begin{array}{lll}
1 & 2 & 3 \\
2 & 1 & 4 \\
1 & 0 & 2
\end{array}\right]\)
Solution:
CHSE Odisha Class 12 Math Solutions Chapter 4 Matrices Ex 4(b) Q.12(5)