Class 11

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 1 Mathematical Reasoning Ex 1(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 1 Mathematical Reasoning Exercise 1(a)

Question 1.
Choose the correct answer from the given choices:

(i) Negation of ‘Paris is in France and London is in England’ is :
(A) Paris is in England and London is in France.
(B) Paris is not in France or Landon is not in England.
(C) Paris is in England or London is in France.
(D) Paris is not in France and London is not in England.
Solution:
(A) Paris is in England and London is in France.

(ii) The conditional (p ∧ q) → p is :
(A) a tautology
(B) a contradiction
(C) neither a tautology nor a contradiction
(D) none of these
Solution:
(A) a tautology

(iii) Which of the following is a contradiction?
(A) (p ∧ q) ∧ ~ (p ∧ q)
(B) p ∨ (~ p ∧ q)
(C) (p → q) → p
(D) None of these
Solution:
(A) (p ∧ q) ∧ ~ (p ∧ q)

(iv) Which of the following is logically equivalent to ~ (~ p → q)?
(A) p ∧ q
(B) p ∧ ~ q
(C) ~ p ∧ q
(D) ~ p ∧ ~ q
Solution:
(D) ~ p ∧ ~ q

(v) (~(~p) ∧ q) is equivalent to
(A) ~ p ∧ q
(B) p ∧ q
(C) p ∧ ~ q
(D) ~ p ∧ ~ q
Solution:
(B) p ∧ q

(vi) If p: It rains today, q: I go to school, r: I shall meet any friend, and s’: I shall go to a movie, then which of the following is the proposition.
If it does not rain or if I do not go to school, then I shall meet a friend and go to a movie.
(A) ∼ (p ∧ q) → (r ∧ s)
(B) ~ (p ∧ q) → (r ∧ s)
(C) ~ (p ∧ q) → (r ∨ s)
(D) None of these
Solution:
(A) ~ (p ∧ q) → (r ∧ s)

(vii) Which of the following is true?
(A) p → q ≡ (~p → ~q)
(B) ~ (p → ~ q) ≡ (~ p ∧ q)
(C) ~ (~p ~ q) ≡ (~ p ∧ q)
(D) ~ (p ↔ q) ≡ [~(p → q)∧~(q → p)]
Solution:
(C) ~ (~p ~ q) ≡ (~ p ∧ q)

(viii)The Inverse of the proposition p ∧ ~ q) → r is:
(A) ~ r (~ p ∨ q)
(B) ~ p ∨ q → ~ r
(C) r → (p ∧ ~q)
(D) None of these
Solution:
(B) ~p ∨ q → ~ r

(ix) The contrapositive of (p ∨ q) → r is
(A) r → (p ∨ q)
(B ) ~r → (p ∨ q)
(C) ~ r → (~p ∧ ~q)
(D) p → (q ∨ r)
Solution:
(C) ~ r → (~p ∧ ~q)

(x) Which of the following is inverse of the proposition: “If a number is a prime, then it is odd.
(A) if a number is not prime, then it is odd.
(B) if a number is not a prime, then it is not odd.
(C) if a number is not odd then it is not a prime.
(D) if a number is not odd, then it is a prime.
Solution:
(B) if a number is not a prime, then it is not odd.

Question 2.
Give examples, five in each case, of , sentences that are
(i) propositions
Solution :
Examples of a proposition:
(a) Rama is a boy.
(b) He is ten years old.
(c) He is reading in class six.
(d) He has 2 brothers and 3 sisters.
(e) 2 + 3 ≥ 5

(ii) not-propositions
Solution:
Examples of not-proposition:
(a) How old are you?
(b) What is he to you?
(c) Read mindfully.
(d) What a beautiful girl!
(e) May God offer you long life.

Question 3.
Illustrate the use of all connectives and the modified ‘not’ in five separate examples of propositions.
Solution:
Conjunction: Hari and Madhu are two friends.
Disjunction: Hari or Madhu stand first in their class.
Implication: If I will be the king, then I will make you my queen.
Double Implication: I will love you if you will love me.
Negation: I don’t like her.

Question 4.
Try to construct an example of a proposition involving all connectives and also the modifier ‘not’.
Solutions:
If she do not come and take my help, then she neither understands the problem nor solves them but she can create other problems.

Question 5.
Which of the following sentences are propositions and which are not? Write with reasons :
(i) 2 < 5.
(ii) Is 9 < 3?
(iii) x is greater than 100.
(iv) Why are you crying?
(v) May God grant you long life.
(vi) Cuttack is a big city.
(vii) It is possible that there is life on Mars.
(viii)Ram is a friend of Hari.
(ix) x² –  x + 1=0
(x) Oh! What scenery!
(xi) You must go to school every day.
(xii) It was raining yesterday.
Solution:
(i) 2 < 5 is a proposition, as it is true.

(ii) Is 9 < 3? Is not a proposition, as it is neither true nor false.

(iii) “x is greater than 100” is not a statement as x is not defined.

(iv) Why are you crying? Is not a statement as it is neither true nor false.

(v) “May God grant you long life” is not a statement as it is neither true nor false.

(vi) “Cuttack is a big city” is not a statement, as it contains the word ‘big’ (not defined).

(vii) “It is possible that there is life on Mars” is not a proposition. (To date it is not confirmed)

(viii)Ram is a friend of Hari. It is a statement as it is true or false.

(ix) “x² – x + 1 = 0” is not a statement as ‘x’ is not defined.

(x) Oh! What scenery! It is not a statement as it is neither true nor false.

(xi) You must go to school every day. It is not a statement as it is neither true nor false.

(xii) It was raining yesterday. It is not a proposition as it is not known to which day yesterday means.

Question 6.
Write down negations of each of the following.
(i) If you read, you will pass.
(ii) John is a friend of Thomas.
(iii) Fifteen is greater than five.
(iv) Either Pramod is clever or he is laborious.
(v) Money is necessary for happiness.
(vi) It is raining and Mahanadi is flooded.
(vii) Pen is might than a sword.
(viii) |x| is equal to either x or – x.
(ix) It is raining and it is cool.
(x) 3 + 6 > 8 and 2 + 3 < 6.
Solution:
(i) It is not true that if you read, you will pass.
(ii) John is not a friend of Thomas.
(iii) Fifteen is not greater than five.
(iv) Pramod is not clever and also not laborious.
(v) Money is not necessary for happiness.
(vi) It is neither raining nor Mahanadi is flooded.
(vii) Pen is not more mighty than a sword.
(viii) |x| is neither x nor – x
(ix) It is not raining or it is not cool.
(x) 3 + 6 ≤ 8 or 2+ 3 ≥ 6.

Question 7.
Translate the following propositions into symbolic form, stating the prime components in each case.
(i) If you do not work hard, you will repent.
(ii) Jamini will be rewarded if and only if he is punctual.
(iii) If there is a will, there is a way.
(iv) Time and tide wait for none.
(v) 29 is a prime number which is a sum of two squares.
(vi) Life is short, but virtue is lasting.
(vii) If the boy is poor, then he will be hungry and if he is hungry, then he cannot be honest.
(viii) A year consists of twelve months while a month does not consist of more than thirty-one days.
(ix) If the government cannot solve the unemployment problem, then public opinion will rise against it which will lead to a strengthening
of opposition.
(x) Chinu and Minu went to Calcutta, but Minu came back earlier since she lost all her money
Solution:
(i) Let p: You work hard, q: you will repent. Then the given statement is ~ p → q.
(ii) Let p: Jamini will be rewarded, q: He is punctual. The given statement is p ↔ q.
(iii) Let p: There is a will, q: There is a way.
∴ The given statement is p → q.
(iv) Let p: Time waits for none. q: Tide waits for none.
∴  Solution is p ∧ q.
(v) Let p: 29 be a prime number. q: It is a sum erf two squares
∴  Solution is p ∧ q.
(vi) Let p: Life is short. q: Virtue is lasting.
Solution is q ∧ q.
(vii) Let p: The boy is poor. q: He will be hungry. r: He can be honest.
Solution is (p → q) ∧ (q → ~r)
(viii) Let p: A year consists of twelve 9. months. q: A month consists of more than 31 days.
∴ Solution is p ∧ ~ q.
(ix) Let p: The Government can solve the unemployment problem. q: Public opinion will rise against it. r: It will lead to a strengthening
of opposition.
∴  Solution is (p → q) → r.
(x) Let p: Chinu went to Calcutta. q: Minu went to Calcutta. r: Minu came back earlier. s: She lost all her money.
Solution is (p ∧ q) ∧ (s → r).

Question 8.
Let p, q, and r denote respectively the statements: “you are honest”, “you are laborious” and “you will receive a promotion”, Translate the following statements into English language :
(i) (p ∨ q) → r
(ii) ~ r → ~ p
(iii) ~ (p ∨ q) → ~ r
(iv) |r ∨ (~ p)| → ~ q
(v) p ∧ q ∧ r
Solution:
Let p: You are honest. q: You are laborious. r: You will receive a promotion.
(i) (p ∨ q) → r. It’s the English language is “If you are honest or laborious then you will receive a promotion.”
(ii) If you will not receive a promotion, then you are not honest.
(iii) If you are neither honest nor laborious then you will not receive a promotion.
(iv) If you will receive a promotion or you are not honest then you are not, laborious.
(v) You are honest and laborious and you will receive a promotion.

Question 9.
Construct truth tables for the following and indicate which of these are tautologies :
Solution:
(i) p ∧ q → p ∨ q

p	q	p ∧ q	p ∨ q	p ∧ q ∧ p ∨ q
T	T	T	T	T
T	F	F	T	T
F	T	F	T	T
F	F	F	F	T

∴ It is a tautology.

(ii) p ∧ q → p
Solution:

p	q	p ∧ q	p ∧ q → p
T	T	T	T
T	F	F	T
F	T	F	T
F	F	F	T

∴ It is a tautology.

(iii) p ∧ (p → q) → q
Solution:

p	q	p → q	p ∧ (p → q)	p ∧ (p → q) → q
T	T	T	T	T
F	T	T	F	T
T	F	F	F	T
F	F	T	F	T

∴ It is a tautology.

(iv) p → p ∧ q
Solution:

p	q	p ∧ q	p → (p ∧ q)
T	T	T	T
T	F	F	F
F	T	F	T
F	F	F	T

∴ It is a not tautology.

(v) p → (~p → q)
Solution:

p	q	~p	~p → q	p → (~p → q)
T	T	F	T	T
T	F	F	T	T
F	T	T	T	T
F	F	T	F	T

∴ It is a tautology.

(vi) ~p ∧ (p ∧ q) → q
Solution:

∴ It is a tautology.

(vii) (p ∨ ~q) ∧ (q ∨ ~p)
Solution:

∴ It is a not tautology.

(viii) p → (~ q ∧ r)
Solution:

∴ It is a not tautology.

(ix) (p → q) → [(q → r) → (p → r)]
Solution:

∴ It is a tautology.

(x) p ∨ → ~(p ∧ q)
Solution:

∴ It is a not tautology.

(xi) (p → ~p) → ~p
Solution:

P	~p	p → ~p	(p → ~p) → ~p
T	F	F	T
F	T	T	T

∴ It is a tautology.

(xii) (~ p ∨ p) → (~ q ∨ q)
Solution:

∴ It is a tautology.

(xiii) (p ∧ q) → p) → q
Solution:

p	q	p ∧ q	(p ∧ q) → p	((p → q) → p) → q
T	T	T	T	T
T	F	F	T	F
F	T	F	T	T
F	F	F	T	F

∴ It is a not tautology.

(xiv) (p ↔ q) ∧ (q ↔ r) → (p ↔ r)
Solution:

∴ It is a tautology.

(xv) [p → (p ∨ q)] → [q → (p ∧ q)]
Solution:

Question 10.
If p has truth value T, what can be said about the truth values of
(i) ~p ∧ q → p ∨ q
Solution:

∴ ~p ∧ q → p v q is always true if p is true.

(ii) p ∨ q → ~p ∧ q
Solution:

∴ p ∨ q → ~ p ∧ q is always false it is true.

Question 11.
Determine the truth values of p ↔  ~ q when the biconditional p ↔ q has truth value (i) F, (ii) T.
Solution:

p	q	-q	p ↔ q	p ↔ ~q
T	T	F	T	F
T	F	T	F	T
F	T	F	F	T
F	F	T	T	F

(i) When p ↔ q is False, p ↔ ~ q is True.
(ii) ∴ When p ↔ q is True, p ↔ ~q is False.

Question 12.
State the converse, inverse and contra-positive of each of the following propositions. Stating it as a conditional, wherever necessary.

(i) If A ABC is equilateral, then its three angles are congruent.
Solution:
If A ABC is equilateral, then its three angles are congruent.
Converse: If the three angles of the A ABC are congruent, then it is equilateral.
Inverse: If A ABC is not equilateral, then its three angles are not congruent.
Contrapositive: If the three angles of the A ABC are not congruent, then it is not equilateral.

(ii) If Gopal is clever, then he is rich.
Solution:
Con: If Gopal is rich, then he is clever.
Inv.: If Gopal is not clever, then he is not rich.
Cont: If Gopal is not rich, then he is not clever.

(iii) p → ~ q
Solution:
p → ~ q
Con: ~ q → p
Inv: ~ p → q
Cont: q → ~ p

(iv) Sum of two odd integers is even.
Solution:
If two integers are odd, then their sum is even.
Con: If the sum of two integers is even, then they are odd.
Inv: If two integers are not odd, then their sum is not even.
Cont: If the sum of two integers is not even then they are not odd.

(v) The square of an integer is a natural number.
Solution:
If a number is an integer, then its square is a natural number.
Con: If the square of a number is a natural number, then it is an integer.
Inv: If a number is not an integer, then its square is not a natural number.
Cont: If the square of a number is not a natural number then it is not an integer.

(vi) A parallelogram that is inscribed in a circle is a rectangle.
Solution:
If a parallelogram is inscribed in a circle, then it is a rectangle.
Con: If a parallelogram is a rectangle, then it is inscribed in a circle.
Inv: If a parallelogram is not inscribed in a circle then it is not a rectangle.
Cont: If a parallelogram is not a rectangle, then it is not inscribed in a circle.

(vii) The ground being wet, there has been rainfall at night.
Solution:
If the ground being wet then there has been rainfall at night.
Con: If there has been rainfall at night then the ground being wet,
Inv: If the ground is not wet then there has been no rainfall at night.
Con: If there has been no rainfall at night then the ground is not wet.

Question 13.
Are the following pair of statements negation of each other?
(i) The number π is not a rational number.
(ii) The number π is not an irrational number.
(iii) The number π is a rational number. The number π is an rational number.
Solution:
(i) No (ii) Yes

Question 14.
Write the component statement of the following compound statements and check whether the compound statement is true or false.
(i) 24 is a multiple of 4 and 6
(ii) The school is closed if there is a holiday or a Sunday.
(iii) 7 is a rational number or an irrational number.
(iv) 57 is divisible by 2 or 3.
(v) All things have two eyes and two legs.
(vi) 2 is an even number and a prime number.
(vii) Every parallelogram is a trapezium or a rhombus.
Solution:

(i) The component statement is
p: 24 is a multiple of 4
q: 24 is a multiple of 6
The truth value of the statement is ‘True’

(ii) The component statements are :
p: There is a holiday or a Sunday
q: The School is closed
The truth value of the compound statement is ‘True’.

(iii) The component statements are
p: 7 is a rational number
q: 7 is an irrational number
The truth value of the compound statement is ‘True’.

(iv) The component statements are
p: 57 is divisible by 2
q: 57 is divisible by 3
The truth value of the compound statement is ‘True’.

(v) The component statements are
p: All things have two eyes.
q: All things have two eyes
The truth value of the compound statement is ‘false’

(vi) The component statements are
p: 2 is an even number
q: 2 is a prime number
The truth value of the compound statement is ‘ True.

(vii) The component statements are
p: Every parallelogram is a trapezium
q: Every parallelogram is a rhombus.
The truth value of the compound statement is “false”.

Question 15.
Identify the Quantifiers of the following statements.
(i) There exists a number that is equal to its square.
(ii) For every real number x, x is less than x + 1.
(iii) There exists a capital for every state of India.
(iv) For all x ∈ R , sin² x + cos² x = 1
(v) There exists an even prime number other than 2.
(vi) For every negative integer x, x³ is also a negative integer.
(vii) For every real number x, x² ≠ x.
Solution:
(i) There exists
(ii) for every
(iii) There exists
(iv) for all
(v) There exists
(vi) for every
(vii) for every

Question 16.
Write the negation of the following statement.
(i) Every living person is not 150 years old.
(ii) There exists x∈ N, x + 3 ≠ 10
(iii) All the students completed their homework.
(iv) There exists a number that is equal to its square.
(v) For every real number x, x + 4 is greater than x.
(vi) Everyone who lives in India is an Indian.
Solution:
(i) There exists a living person who is 150 years old.
(ii) for all x ∈ N, x + 3 ≠ 10
(iii) There exists a student who has not completed his homework.
(iv) Each number is not equal to its square.
(v) There exists a real number x, x + 4 is not greater than x.
(vi) There exists a person who lives in India but is not an Indian.

Odisha State Board Elements of Mathematics Class 11 Solutions CHSE Odisha Chapter 2 Sets Ex 2(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 2 Sets Exercise 2(a)

Question 1.
Construct five different examples of sets. Describe each with the help of a proposition.
Solution:
(i) Collection of all the days of a week.
i.e., D = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}
= {x: x is a day of a week}

(ii) Collection of writing instruments
i.e., A = {pen, pencil, paper, ink}
= {x: x is a writing instrument}

(iii) Collection of all kings having more than one queen.
i.e., B = {x: x is a king having more than one queen.}

(iv) Collection of all nationalized political parties i.e., C = {BJP, Congress, CPI, CPI(M), JD(U), JD(S), JP}
= {x: x is a set of nationalized political parties}

(v) Collection of all integers of multiples of 3.
i.e., D = {0, ± 3, ± 6}
= {x: x is a set of all integers of multiples of 3}

(vi) Collection of all fingers of a hand
i.e., E = {x: x is a finger of hand}

Question 2.
Give an example of a set that has exactly 10 elements and express it through a defining property.
Solution:
Collection of all positive prime numbers less than 30 i.e„ A = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29} = {x: x is a prime number less than 30}

Question 3.
It is possible to express every set through a defining property? Justify your answer.
Solution:
Yes, it is possible to express every set through a defining property, as every set can be written in the set builder form.

Question 4.
If {x: p₁ (x)} = {x: p₂ (x)}, show for each x, p₁ (x) and p₂ (x) have the same truth value.
Solution:
Given that {x : p₁ (x)} = {x : p₂ (x)}
∴ The two sets have the same element.
So p₁ (x) ≠ p₂ (x) i.e., they have the same truth value.

Question 5.
For each of the following words, write down the set of letters forming that word :
(i) Administration,
(ii) Misrepresentation,
(iii) Mathematics,
(iv) Concurrence,
(v) Demonstration
Solution:
(i) {a, d, i, m, n, o, r, s, t }
(ii) {a, e, i, m, n,o,p, r, s, t }
(iii) {a, c, e, h, i, m, s, t }
(iv) {c, e, n, n, o, r, u }
(v) {a, d, e, i, m, n, o, r, s, t }

Question 6.
State with reason, which of the following are sets and which are not :
(i) All big rivers of India.
(ii) All natural numbers having at least one prime factor.
(iii) All sincere students of Ravenshaw college during the academic year 1998 -99.
(iv) All real numbers with negative squares.
(v) All citizens of India earning more than Rs. 10,000/- per month.
(vi) All college teachers who are citizens of India.
(vii) All finite subsets of the set Z of integers.
(viii)Collection of all possible sets.
(ix) Collection of all winged horses.
(x) Collection of all residents of Odisha who will live for more than 100 years.
Solution:
(i) It is not a set, as the word ‘big’ is not properly defined.
(ii) It is a set, as it is properly defined.
(iii) It is not a set, as the word ‘sincere’ is not properly defined.
(iv) It is a set, as it is well-defined.
(v) It is a set, as it is well-defined.
(vi) It is a set, as it is well-defined.
(vii) It is a set, as it is well-defined.
(viii)It is a set, as it is well-defined.
(ix) It is a set, as is it properly defined.
(x) It is not a set, as we do not know, who will live for more than 100 years.

Question 7.
Write the following sets in the form of lists:
(i) {x: x is a prime number and 1 ≤ x ≤ 100}
(ii) {x: x = is an odd integer}
(iii) {x: x = 1 or x = 2 or x = 3 }
(iv) {x: x = can be written as a sum of two odd integers}
(v) Set of all natural numbers that are divisible by 5.
Solution:
(i) {2, 3, 5, 7, …….. 97}
(ii) {± 1, ± 3, ± 5, ……..}
(iii) {1, 2, 3}
(iv) {2, 4, 6, 8, 10, ………}
(v) {5, 10, 15, 20, ……..}

Question 8.
Write the following sets in the intention (or specification form)
(i) {a}
(ii) Φ
(iii) {1, 2}
(iv) {1, 2, 3, 4, 5}
(v) P (Φ)
(vi) {1, 3, 9, 27}
Solution:
(i) {x: x = a}
(ii) {x: x ≠ x}
(iii) {x: x = 1 or x = 2}
(iv) {x: x ∈ N, 1 ≤ x ≤ 5}
(v) {x: x = Φ}
(vi) {x: x =3ⁿ n ∈ Z, 0 ≤ n ≤ 3 }

Question 9.
Determine if set A is a proper subset of the set B where A and B are as given below:

(i) A = { 1, 2, 3, …….}
B = {x: x is a rational number}
Solution:
A is a proper subset of B as all the elements of A are in B.

(ii) A = {x: x is a prime number}
B = {2n – 1: n = 1, 2, 3, …… }
Solution:
A = {x : x is a prime number}
= {2, 3, 5, 7, 11, ……}
B = {2n – 1: n = 1, 2, 3, …. }
= {1, 3, 5, 7, ….}
∴ A ⊄ B, because of 2 ∈ A but 2 ∉.

(iii) A = {-l, 1, 3}
B = {x: x ∈ R and x³ – 2x³ -x + 2 = 0}
Solution:
Solving x³ – 2x² – x + 2 = 0
we have x² (x – 2) – 1 (x – 2) = 0
or, (x – 2) (x²– 1) = 0
∴ x = 1, -1, 2
∴ B ={ -1, 1, 2}
∴ A is not a subset of B.

(iv) A= {1, 2, 3, 4}
B = [n ∈ N, n is a divisor of 60}
Solution:
B = {1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60}
∴ A ⊂ B

Question 10.
For each of the following pairs of sets A and B, determine if A ⊂ B or A ⊄ B:
Solution:
(i) A = Φ, B = {Φ}
Here A ⊂ B, as Φ is the subset of every set

(ii) A = {x : x is an integer}
= 0, ± 1, ± 2……..
B = {3x : x is an integer}
= {0, ± 3, ± 6,……} A ⊄ B.

(iii) A = {x: x is an odd integer}
B = {x: x is real and not an even integer}
∴ A = {± 1, ± 3, ± 5, …….} and B is the set containing all the real numbers except for even integers.
∴ A ⊂ B

(iv) A = {x : x is an integer which is both even and odd}
B = {x: x is an integer, x ≠ x}
∴ A ⊂ B, … A = Φ and B = Φ)

(v) A = |a, b, c|, B = {|a|, |b|,  |c|}
∴ A ⊄ B

Question 11.
Determine the truth of the falsity of the following propositions with reasons.
(a) {1, 2} € {1,2,3}
(b) A ⊂ A for any set A.
(c) Every set has a proper subset.
(d) Every set in a proper subset of the same set
(e) For any object x, there is a set A such that, x ∈ A.
(f) For any object x, there is a set A such that, x ∉ A.
(g) If A, B, C sets, then either A = B or A ⊂ B or B ⊂ A.
(h) a ∈ {(a)}
(i) a ∈ {(a, b), b}, a ≠ b.
(j) If A is a proper subset of B and B is a subset of C, then A is a proper subset of C.
(k) A ⊂ Φ if and only if A = Φ.
Solution:
(a) {1,2} ∈ {1,2,3} is false, as {1, 2} is not an element of { 1, 2, 3} but it is a subset.
(B) A ⊂ A is false, as A is an improper subset of itself, not a proper subset.
(C) ‘Every set has a proper subset is false as Φ has no proper subset.
(d) Every set is a proper subset of the same set is false.
(e) For any object x, there is a set A such that, x ∈ A. It is true.
(f) For every object x, there is a set A such that, x ∉ A. It is true.
(g) If A, B, C sets, then either A = B or A ⊂ B or B ⊂ A. It is false, as there is a possibility for A ≠ B.
e.g. a = {1, 2}, b = {a, b}
(h) a ∈ {{a}}. It is false as ‘a’ is not an element of the set {(a)}.
(i) as ∈ {{a, b}, b}, a ≠ b It is false, as ‘a’ is not an element of the set {{a, b}, b}
(j) If A is a proper subset of B and B is a subset of C, then A is a proper subset of C.
It is true, as
x ∈ A ⇒ x ∈ B ∴ (A ⊂ B)
and x ∈ B ⇒ x ∈ C ∴ (B ⊂ A)
∴ x ∈ A ⇒ x ∈ C means A ⊂ C.
(k) A ⊂ Φ if and only if A = Φ is true.
Proof:
Necessary part: Given A ⊂ Φ and prove A = Φ.
Now A ⊂ Φ       ….(1)
And Φ is the subset of every set.
So Φ ⊂ A           ….(2)
Combining (1) and (2) we get A = Φ.
Sufficient part: Given A = Φ and to prove A ⊂ C.
A = Φ ⇒ A ⊂ Φ and Φ ⊂ A
Thus A ⊂ Φ.

Question 12.
Write down the power set of
(i) {a, b, c}
(ii) {a, {a}}
(iii) Φ
(iv) {Φ}
(v) {a, {a}, {a,b}}
(vi) {{Φ}}
Solution:
(i) Let A = {a, b, c}
P(A) = {{a}, {b}, {c}, {a, b}, {a, c}, {b, c}, A, Φ}

(ii) Let A = {a, {a}} then P(A) = {{a}, {{a}}, Φ, A}

(iii) P (Φ) = {Φ}

(iv) P({Φ})-= {{Φ}, Φ}

(v) Let A = {a, {a}, {a, b}}
∴ P(A) = {{a}, {{a}}, {{a, b}}, {a}, {a}
{{a}, {a,b}}, {a, {a,b}, A, Φ)}

(vi) Let A = {{Φ}}
∴ P(A) = {A, Φ}

Question 13.
Prove that P(A) ⊂ P(B) if and only if A ⊂ B. When is the inclusion P(A) ⊂ P(B) proper?
Solution:
Necessary Part :
Let P(A) ⊂ P(B),
we shall prove that A ⊂ B.
∴ Let x ∈ A
⇒ {x} ∈ P(A)
⇒ {x} ∈ P(B)  (∴ P(A) ⊂P(B)
⇒ x ∈ B
Sufficient Part:
Let A ⊂ B
Let x ∈ P(A)
⇒ x ⊂ A
⇒x ⊂ B (∴ A ⊂ B)
⇒ x ∈ P(B)
Thus P(A) ⊂ P(B)
The inclusion P(A) ⊂ P(B) is proper when A is a proper subset of B.

Question 14.
A set can be finite or infinite (as understood in an informal way). For instance, {1, 2, 3, 4} is a finite set whereas Z is an infinite set. The number of elements of a set A, denoted by |A|, is called its cardinal number. Without going into the necessary technicalities, we may just observe that
|Φ|  = 0, |{x_1, x_2………,x_n }| = n
Two sets A and B are called similar if they have the same cardinal number. Thus, the sets {1, 2, 3} and {2, 4, 6} are similar. We write A ~ B to express the fact that A and B are similar. Now, answer the following questions.
(i) What are the cardinal numbers of the following sets?
{Φ}, {a, {a, b}}, {Z} {0.5}, {0, {5}}, {a, b, {a, b} }, {{Φ}}, {Φ, {Φ}}
(ii) For any natural number n, give an example of a set A such that |A = n|.
(iii) Determine the cardinal number of the set {x: x is real and x³ – x² + x- 1 = 0 }
Solution:
(i) Cardinal number of the set {Φ} is 1.
Cardinal number of the set {a, {a, b} } is 2.
Cardinal number of the set {z} is 1.
Cardinal number of the set {0,5} is 2.
Cardinal number of {0, {5 } } is 2.
Cardinal number of the set {a, b {a, b}) is 3.
Cardinal number of the set {{Φ}} is 1.
Cardinal number of {Φ, {Φ}} is 2.

(ii) Let A = {1, 2, 3}
∴ | A | = 4 where 4 ∈ N for n = 4.

(iii) Let A = {x : x is real and
x³ – x² + x – 1 = 0 }
Solving, x³ – x² + x – 1 = 0
or, x² ( x – 1) + 1 (x – 1 ) = 0
or, (x- 1) (x² + 1) = 0
x – 1 = 0, x² + 1 = 0
x = 1, ± i
As x is real, we have A = {1}
| A | = 1

Question 15.
Which sets are finite and which are infinite?
(i) The set N of positive natural numbers.
(ii) The set Z of integers.
(iii) The set Q of rational numbers.
(iv) The set R of real numbers.
(v) The set of prime numbers.
(vi) The set of even integers.
(vii) The set of human beings.
(viii)The set of integers less than 10.
Solution:
(i) “The set N of positive natural numbers” is an infinite set.
(ii) “The set Z of integers” is an infinite set.
(iii) “The set Q of rational numbers” is an infinite set.
(iv) “The set R of real numbers” is an infinite set.
(v) “The set of prime numbers” is an infinite set.
(vi) “The set of even integers” is an infinite set.
(vii) “The set of human beings” is a finite set.
(viii)“The set of integers less than 10” is an infinite set.

Question 16.
Verify that
| P (Φ) | = 2⁰
| P ({a}) | = 2¹
| P ({a, b}) | = 2²
| P({a, b, c}) | = 2³
Solution:
(i) Let A = Φ, then P(A) = {Φ}
∴ P(A) = 1 = 2⁰

(ii) Let A = {a} then P(A) = {{a}, Φ}
∴ P(A) = 2 = 2¹

(iii) Let A = {a, b)
then P(A) = {{a}, {b}, {a, b}, Φ}
∴ P(A) = 4 = 2²

(iv) Let A = {a, b, c}
P(A) = {{a}, {b}, {c}, {a, b}, {b, c}, A, Φ}
∴ P(A) = 8 = 2³

Question 17.
Find the number of elements of
(i) P(P(Φ))
(ii) P(P(P(Φ)))
(iii) P(P(P(P(Φ))))
Solution:
(i) We have | P (Φ) | = 2⁰ = 1
∴ | P(P(Φ)) | = 2¹ = 2
(ii) | P(P(P(Φ))) | = 2² = 4
(iii) | P(P(P(P(Φ))) | =2⁴ = 16

Question 18.
Prove by the method of induction that if A has n number of elements, then | P (A) | = 2ⁿ.
Solution:
When n = 1, we have, let A = {a₁}
P (A) = {{ a₁ }, Φ} ⇒ | P(A) | = 2 = 2¹
∴ p₁ is true.
Let p_k be true i.e., if A = {a_1, a_{2, ………..} a_k }
then | A | = k and | P(A) | = 2^k
Now let B = {a_1, a_{2, ………..} a_k, a_k+1  }
∴ | B | =k + 1.
Here A has 2^k subsets. These 2^k subsets are also in B. Which includes the additional elements a_k+1 ∈ B.
So there are 2^k. 2 = 2^k+1 subsets in B.
∴ | P(B) | = 2^k+1
i.e., if | A| = k +1 then | P(A) | = 2^k+1
∴ p_k+1 is true.
∴ p_n is true for all values of n ∈ N.
∴ | P(A) | =2ⁿ if | A | = n.

Question 19.
Can you say how many elements P(P(A)) if A has n elements?
Solution:
If | A | = n then | p(A) | =2ⁿ
and | P(P(A)) | = 2⁽²ⁿ⁾ .

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 1 Mathematical Reasoning Ex 1(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 1 Mathematical Reasoning Exercise 1(b)

Question 1.
Check the validity of the following statements.

(i) p: 100 is a multiple of 5 and 4.
(ii) q: 125 is multiple of 5 and 7.
(iii) r: 60 is a multiple of 3 or 5.
Solution:
(i) Here the connective is ‘and’
Step -1: 100 is a multiple of 5 (True)
Step -2: 100 is a multiple of 4 (True)
∴ 100 is a multiple of 5 and 4 is true, i.e. the statement ‘p’ is valid.

(ii) Here the connective is ‘and’
Step – 1: 125 is a multiple of 5 (True)
Step – 2: 125 is a multiple of 7 (false)
∴ The statement ‘q’ is (false), i.e. the statement ‘q’ is not a valid statement

(iii) Here the connective is ‘or’
60 is a multiple of 3 (True)
60 is a multiple of 5 (True)
Thus the component statements are both true.
∴ The statement ‘r’: 60 is a multiple of 3 or is true, i.e. ‘r’ is a valid statement.

Question 2.
Check the validity of the statements given below by the method given against each.
(i) “The sum of an irrational number and a rational number is irrational’’ (by contradiction method).
(ii) “If n is a real number with n > 3, then n² > 9 (by the method of contradiction).
(iii) ‘‘If x, y are integers such that xy is odd then both x and y are odd” (by the method of contrapositive)
(iv) “If x is an integer and x² is even then x is also even” (method of contrapositive).
Solution:
(i) Let the given statement is false.
i.e. the sum of an irrational number and a rational number is rational.
⇒ An irrational number + a rational number = a rational number
⇒ An irrational number = A rational number + rational number = A rational number
Which is absurd.
We arrive at a contradiction.
This is due to our false assumption. Thus, the given statement is true.

(ii) Let the given statement is false.
i.e. for a natural number n > 3 n² > 9
⇒ n² ≤ 3 ⇒ n ≤ 3
(.’. n is a natural number which contradicts the fact that n > 3)
This contradiction is due to our false assumption.
Thus for any natural number
n > 3, n² > 9.

(iii) Let p: x and y are integers such that xy is odd. and q: both x and y are odd. We shall prove the validity of p → q by using the method of contrapositive.
Now ~ q: It is not true that both x and y are odd, i.e. at least one of x (or y) is even.
Let ~ q is true.
Let x is even and x = 2n for some integer n.
⇒ xy = 2ny for some integer n.
⇒ xy is even (not odd)
⇒ ~ p is true.
Thus by the method of contrapositive, we proved ~ q ⇒ ~ p, i.e. p → q is true.

(iv) Let p: x is an integer and x² is even
q : x is even.
Let ~ q is true
⇒ x is not an even integer
⇒ x is an odd integer
Let x = 2n + 1 for some integer ‘n ’
⇒ x² = (2n + 1)² = 4n² + 4n + 1
= 2 (2n² + 2n) + 1
which is odd.
⇒ p is false ⇒ ~ p is true
Thus ~ q ⇒ ~ p
∴ Thus the statement is true.
i.e x is even ⇒x is also even

Question 3.
By giving counter-examples, show that the following statements are not true:
(i) If measures of all the angles of a triangle are equal, then the triangle is an obtuse angled triangle.
(ii) For every real number x and y, x² = y² ⇒ x = y.
(iii) The equation x² – 1 = 0 does not have any root lying between 0 and 2.
Solution:
(i) Let in ΔABC
∠A = ∠B = ∠C = 60°
Clearly, no angle is obtuse.
∴ The triangle is not obtuse-angled.
(ii) for x = – 2, y = 2
x² = y² = 4 but x ≠ y
∴ x² = y² ⇒ x = y
(iii) x = 1 is a root of x² – 1=0
that lies between 0 and 2.
∴ The given statement is false.

Question 4.
Check the validity of “If I do not work, I sleep.
If I am worried, I will not sleep. Therefore, if I am worried, I will work”.
Solution:
Method-1:
Let p: I work
q: I sleep
r: I am worried
“If I do not work, I sleep” can be written as ~ p → q
“If I am worried, I will not sleep” can be written as r → ~ q
‘If I am worried, I will work’’ can be written as r → p
The given statement can be written as [(~ p → q) ∧ (r → ~ q)] → ( r → p)
Let us draw the truth table

As [(~ p → q) ∧ (r → q)] → (r → p)
is a tautology the given statement is logically valid.
Method – 2:
Let p: I do work
q: I sleep
r: I am worried
“If I do not work, I sleep ” can be represented as ~ p → q
“If I am worried, I will not sleep” can be written as r → ~ q
Thus we can write the given statement as
[(~ p → q) ∧ (r → q)] → (r → p)
But a statement and its contrapositive are equivalent.
Thus this can be written as
[(r  → ~ q) ∧  (~ q → p)] → (r → p)
By the principle of syllogism, the given statement is logically valid.

Question 5.
Let a and b be integers. By the law of contrapositive prove that if ab is even then either a is even or b is even:
Solution:
Let p: For integers ‘a and b’ ab is even q: a is even or b is even
we shall check the validity of p → q by the method of contrapositive Let ~ q is true.
⇒ Both a and b are odd
Let a = 2m + 1, b = 2n + 1
for some integers m and n
⇒ ab = (2m + 1) (2n + 1)
= 4mn + 2 (m + n ) + 1
= 2 [2mn + m + n) + 1
Which is odd
⇒  p is false
⇒  ~ p is true
Thus the method of contrapositive p → q is true.
i.e. The given statement is logically valid.

Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Ex 3(c) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Exercise 3(c)

Question 1.
Give an example of a relation that is not a function.
Solution:
Let the relation ‘f’ be defined from
A = {1, 2, 3} to B = {1, 2} as
f = {(1, 1), (1, 2), (2, 1), (3, 2)}
f is not a function because f (1) = 1,
f(1) = 2 but 1 ± 2 i.e. f is one many.

Question 2.
If X and Y are sets containing m and n elements respectively then what is the total number of functions from X to Y?
Solution:
If |X| = m and |Y| = n then the number of functions from X to Y = |Y|^|X| = n^m

Question 3.
Find the domain of the following functions:
(i)\( \sqrt{9-x^2}\)
Solution:
y = f(x) = \(\sqrt{9-x^2}\)
Clearly, f(x) is well-defined for 9 – x² ≥ 0 ⇒ x² ≤ 3² ⇒ – 3 ≤ x ≤ 3
∴ dom f = [ – 3, 3]

(ii) \(\frac{x}{1+x}\)
Solution:
y = f(x) = \(\frac{x}{1+x}\)
f(x) is well defined for all x ∈ R
∴ dom f = R

(iii) 1 – |x|
Solution:
y = f(x) = 1 – |x|
f(x) is well defined for all x ∈ R
∴ dom f = R

(iv) \(\frac{1}{x^2-1}\)
Solution:
y = f(x) = \(\frac{1}{x^2-1}\)
f(x) is well defined for x² – 1 ≠ 0
⇒ x² ≠ 1
⇒ x² ≠ ± 1
∴ dom f = R – { -1, 1}

(v) \(\frac{\sin x}{1+\tan x}\)
Solution:
y – f(x) = \(\frac{\sin x}{1+\tan x}\)
f(x) is well defined for 1 + tan x
≠ 0
⇒ tan x ≠ – 1
⇒ x ≠ n π + \(\frac{3 \pi}{4}\)
∴ dom f = R – {n π + \(\frac{3 \pi}{4}\)}

(vi) \(\frac{x}{|x|}\)
Solution:
y = f(x) = \(\frac{x}{|x|}\)
f(x) is well defined for |x| ≠ 0
⇒ x ≠ 0
∴ dom f = R – {0}

(vii) \(\frac{1}{x+|x|}\)
Solution:
y = f(x) = \(\frac{1}{x+|x|}\)
f(x) is well-defined for
x + |x| ≠ 0
⇒ |x| ≠ – x
⇒ x is not negative
⇒ dom f = [0, – ∞)

(viii) \(\sqrt{\log \left(\frac{12}{x^2-x}\right)}\)
Solution:
y = f(x) = \(\sqrt{\log \left(\frac{12}{x^2-x}\right)}\)
f(x) is well defined for \(\frac{12}{x^2-x}\) ≥ 1
⇒ 12 ≥ x² – x
⇒ x² – x – 12 ≤ 0
⇒ (x – 4) (x + 3) ≤ 0
Let us draw the signing scheme

⇒ x ∈ [ – 3, 4]
∴ dom f =[-3, 4]

(ix) [x] – x
Solution:
y = f(x) = [x] – x
f(x) is well defined for all x ∈ R
∴ dom f = R

(x) \(\frac{1}{\sqrt{1-x^2}}\)
Solution:
y = f(x) = \(\frac{1}{\sqrt{1-x^2}}\)
f(x) is well defined for 1 – x² > 0
⇒ x² < 1 ⇒ – 1 < x < 1
∴ dom f = (-1, 1)

(xi) log (sin x)
Solution:
y = f(x) = log (sin x)
fix) is well-defined for sin x > 0
⇒ x ∈ (2nπ , (2n + l)π), n ∈ Z

Question 4.
Find the range of the following functions:
(i) \(\frac{x^2-1}{x^2+1}\)
Solution:
Let y = f(x) = \(\frac{x^2-1}{x^2+1}\)
⇒ x² – y + y = x² – 1
⇒  x²y – x² = – (1 + y)
⇒ x² (y- 1)=-(1 + y)
⇒ x² = \(\frac{\ – (1+y)}{y-1}=\frac{1+y}{1-y}\)
⇒ x = ± \(\sqrt{\frac{1+y}{1-y}}\)
Now x is well-defined for
\(\frac{1+y}{1-y}\) ≥ 0

∴ rng f = [-1,1)

(ii) \(\sqrt{x-1}\)
Solution:
y = f(x) = \(\sqrt{x-1}\)
⇒ y² = x- 1
⇒ x = y² + 1
x is well difierid for all y ∈ R but
y ≥ 0
∴ rng f = [0, ∞]

(iii) [x] – x
Solution:
y = f(x) = [x], – x
We have [x] ≤ x < [ x] + 1
⇒ 0 ≤ x – [x] < 1
⇒ 0 ≥ [x] – x > – 1
⇒ -1 < [x] – x ≤ 0
⇒ -1 < y ≤ 0
⇒ rng f = ( – 1 , 0]

(iv) \(\frac{x}{1-x}\)
Solution:
y = f(x) = \(\frac{x}{1-x}\)
⇒ y – xy = x
⇒ xy + x = y
⇒ x (y + 1) = y
⇒ x = \(\frac{y}{y+1}\)
x is well defined for y ≠ – 1
∴ Rng f = R – {- 1}

(v) \(\frac{x}{1+x^2}\)
Solution:
y = f(x) = \(\frac{x}{1+x^2}\)
⇒ y + x²y = x
⇒ x²y – x + y = 0
⇒ x = \(\frac{1 \pm \sqrt{1-4 y^2}}{2 y}\)
x is well defined for 1 – 4y² ≥ 0 and y ≠ 0
⇒ y² ≤ \(\frac{1}{4}\) and y ≠ 0
⇒ – \(\frac{1}{2}\) ≤ y ≤ \(\frac{1}{2}\) and y ≠ 0
but for x = 0 we have y = 0
∴ rng f = \(\left[-\frac{1}{2}, \frac{1}{2}\right]\)

(vi) \(\frac{1}{2-\cos 3 x}\)
Solution:
y = f(x) = \(\frac{1}{2-\cos 3 x}\)
we have – 1 ≤ cos 3x ≤ 1
⇒ 1 ≥ – cos 3x ≥ -1
⇒ – 1 ≤- cos 3x ≤ 1
⇒ 2 – 1 < 2 – cos 3x ≤ 3
⇒ 1 ≤ 2 – cos 3x ≤ 3
⇒ 1 ≥ \(\frac{1}{2-\cos 3 x} \geq \frac{1}{3}\)
⇒ \(\frac{1}{3}\) ≤ y ≤ 1
∴ rng f =[\(\frac{1}{3}\), 1]

(vii) log ₁₀ (1 – x)
Solution:
y = f(x) = log₁₀ (1 – x)
Clearly y ∈ R
∴ rng f = R

(viii) \(\sqrt{1+x^2}\)
Solution:
y = f(x) = \(\sqrt{1+x^2}\)
⇒ y² = 1 + x²
⇒  x² = y² – 1
⇒ x = ± \(\sqrt{y^2-1}\)
x is well defined for y² – 1 ≥ 0
⇒ y² ≥ 1
⇒ – 1 ≥ y ≥ 1
But y > 0
∴ rng f = [1, ∞)

Question 5.
Find the domain and range of the following functions:
(i) \(\frac{x^2}{1+x^2}\)
Solution:
y = f(x) = \(\frac{x^2}{1+x^2}\)
Domain:
f(x) is well defined for all x ∈ R
∴ dom f = R
Range (Method – 1):
y = \(\frac{x^2}{1+x^2}\)
⇒ y + yx² = x²
⇒ x² – yx² = y
⇒ x² (1 – y) = y
⇒ x² = \(\frac{y}{1-y}\)
⇒ x = ± \(\sqrt{\frac{y}{1-y}}\)
x is well-defined for \(\frac{y}{1-y}\) ≥ 0

⇒ y 6 [0. 1)
∴ Rng f = [0,1)
Method – 2:
0 ≤ x² < x² + 1
⇒ 0 ≤ \(\frac{x^2}{x^2+1}\) < 1
⇒ 0 ≤ y ≤ 1
∴ rng f = [0, 1)

(ii) \(\sqrt{2 x-3}\)
Solution:
y = f(x) = \(\sqrt{2 x-3}\)
Domain:
f(x) is well defined for 2x- 3 ≥ 0
⇒ x ≥ 3/2
∴ dom f =[\(\frac{3}{2}\), ∞]
Range:
y = \(\sqrt{2 x-3}\) ⇒ y² = 2x – 3
⇒ 2x = y² + 3
⇒ x = \(\frac{y^2+3}{2}\)
x is well defined for all y ∈ R
But y is not negative.
∴ Rng f = [0, ∞)

(iii) log_e |x – 2|
Solution:
y = f(x) = log |x – 2|
Domain:
f(x) is well defined for |x – 2| >0
⇒ x ≠ 2
∴ dom f = R – {2}
Range:
y = log |x – 2| ∈ R ⇒ rng f = R

Question 6.
Give an example of a step function on [- 1, 3] = {x ∈ R| – 1 ≤ x ≤ 3}.
Solution:
f(x) = \(\left\{\begin{array}{c}
-1,-1 \leq x<0 \\
0,0 \leq x<1 \\
1,1 \leq x<2 \\
2,2 \leq x<3 \\
3,3 \leq x<4
\end{array}\right\}\)

Question 7.
Let X ={ a, b, c}, Y = {1, 2, 3, 4}
(a) Find out which of the following relations are functions and which are not and why?
Solution:
X = [a, b, c}, Y = {1, 2, 3, 4}
(i) {(a, 1), (a, 2), (b, 3), (b, 4)}
Solution:
{(a, 1), (a, 2), (b, 3), (b, 4)} is not a function as ‘a’ has two images in Y.

(ii) {(a, 2), (b, 3), (c, 4)}
Solution:
{(a, 2), (b, 3), (c, 4)} is a function from X to Y as the elements of X has unique images in Y.

(iii) {(a, 3), (b, 1), (a, 4), (c, 2)}
Solution:
{(a, 3), (b, 1), (a, 4), (c, 2)} is not a function as ‘a’ and ‘b’ have two images also domain of the function ≠ X.

(iv) {(a, 1), (b, 1), (c, 1)}
Solution:
{(a, 1), (b, 1), (c, 1)} is a function from X to Y.

(v) {(a, 2), (b. 1), (c, 1)}
Solution:
{(a, 2), (b, 1), (c, 1)} is a function from X to Y.

(vi) {(a, a), (b, b), (c, c)}
Solution:
{(a, a), (b, b), (c, c)} is a function from X to X.

(b) Find the domain and range of those relations in a which are functions.
Solution:
(i) The domain of each function is
X = [a, b, c}
Range of functions

(ii) is {2, 3, 4}.
In (iv) is {1} and in (v) is {1, 2}. The range of function in (vi) is X.

(c) Identify the constant function if any.
Solution:
The function in (iv)
i.e. {(a, 1), ib, 1), (c, 1)} is a constant function.

(d) Identify the identity function if any.
Solution:
The function in (vi)
i.e.{(a, a), (b, b), (c, c)} is an identity function.

Question 8.
Find \(f(\sqrt{2})\) and \(\boldsymbol{f}(-\sqrt{3})\) for the function
\(f(x)=\left\{\begin{array}{l}
x^2, \text { if } x<0 \\
x, \text { if } 0 \leq x \leq 1 \\
\frac{1}{x}, \text { if } x>1
\end{array}\right.\)
Solution:
\(f(\sqrt{2})\) = \(\frac{1}{\sqrt{2}}\)
\(\boldsymbol{f}(-\sqrt{3})\) = (√3)² = 3

Question 9.
Find x for which the value of f(x) = x² – 4x + 3 is
Solution:
f(x) = x² – 4x + 3
(i) 0
Solution:
f(x) = 0
⇒ x² – 4x + 3 = 0
⇒ (x – 3) (x – 1) = 0
⇒ x =1, 3

(ii) – 1
Solution:
f(x) = – 1
⇒ x² – 4x + 3 = -1
⇒ x² – 4x + 4 = 0
⇒ (x – 2)² = 0
⇒ x = 2

Question 10.
Find the values of x for which the following functions are not defined:
(i) \(\frac{x^2-4}{x-2}\)
Solution:
y = f(x) = \( \frac{x^2-4}{x-2}\)
Clearly f(x) is not defined for x = 2

(ii) \(\frac{\sin x}{x}\)
Solution:
y = f(x) = \(\frac{\sin x}{x}\)
f(x) is not defined for x = 0

(iii) \(\frac{\log \cos x}{\sec x}\)
Solution:
y = f(x) = \(\frac{\log \cos x}{\sec x}\)
f(x) is not defined for cos x ≤ 0
⇒ for x ∈ x \(\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right]\) or \(\left[\frac{5 \pi}{2}, \frac{7 \pi}{2}\right]\)
In general x ∈ \(\left[(4 n+1) \frac{\pi}{2},(4 n+3) \frac{\pi}{2}\right]\), n ∈ Z

Question 11.
Let f(x) = \(\sqrt{1+x}\), g(x) = \(\sqrt{1-x}\)
Find & Also, find the domain in each case.
Solution:
f(x) = \(\sqrt{1+x}\), g(x) = \(\sqrt{1-x}\)
f(x) is well defined for x + 1 ≥ 0
⇒ x ≥ – 1
∴ dom f = [- 1 , ∞) = D₁
g(x) is well defined for 1 – x ≥ 0
⇒ x ≤ 1
⇒ x ∈ (-∞, 1]
∴ dom g (-∞, 1] = D₂
∴ D₁ ∩ D₂ = [-1, 1]
(i) f + g
Solution:
f + g: [-1, 1] → R
defined as (f + g) (x)
= f(x) + g(x) = \(\sqrt{1-x}\) + \(\sqrt{1-x}\)

(ii) f – g
Solution:
f – g :[-1, 1] → R defined as
(f – g) (x) = \(\sqrt{1-x}\) – \(\sqrt{1-x}\)

(iii) fg
Solution:
fg : [ – 1, 1] → R defined as
(fg) (x) > f(x) g(x)
\(\sqrt{1-x}\)\(\sqrt{1-x}\) = \(\sqrt{1-x^2}\)

(iv) f/g
Solution:
f/g : [- 1,1) → R defined as
\(\left(\frac{f}{g}\right)\)(x) = \(\frac{f(x)}{g(x)}=\frac{\sqrt{1+x}}{\sqrt{1-x}}\)
for (i) to (iii) domain = [- 1, 1]
but for (iv) domain = [- 1, 1)

Question 12.
If(x) = log_e \(\left(\frac{1-x}{1+x}\right)\), then prove that f(x) + f(y) = \(\left(\frac{x+y}{1+x y}\right)\)
Solution:
f(x) = log\(\left(\frac{1-x}{1+x}\right)\)
f(x) + f(y) = log\(\left(\frac{1-x}{1+x}\right)\) + \(\left(\frac{1-y}{1+y}\right)\)

Question 13.
Let f = {(-1, 4), (2, 7), (-2, 11}. (0,1), (1, 2) be a quadratic polynomial from Z to Z, find f(x).
Solution:
Let f(x) = ax² + by² + C is the quadratic polynomial
f(-1) = 4 ⇒ a – b + c = 4    …..(1)
f(0) = 1⇒ c = 1                   ….(2)
f(1) = 2 ⇒ a + + c = 2        ….(3)
∴ a – b + 1 = 4 and a + b + 1 = 2
⇒ a – b = 3 and a + b = 1
⇒ a = 2, b = -1
f(x) = 2x² – x + 1
f(2) = 8 – 2 + 1 = 7
f(- 2) = 8 + 2 + 1 = 1 1
Thus the required function is f(x) = 2x² – x + 1

Question 14.
Sketch the graphs of the following functions.
(i) f(x) = x³
(ii) f(x) = 1 + \(\frac{1}{x^2}\)
(iii) f(x) = (x-1)²
Solution:
(i) f(x) = x³

x	0	1	2	– 1	-2	3
y	1	1	8	-1	-8	27

(ii) f(x) = 1 + \(\frac{1}{x^2}\)

x	1	-1	2	– 2	3	-3
y	2	2	5/4	5/4	10/9	10/9

(iii) f(x) = (x-1)²

x	-1	0	1	2	3	4
f(x)	4	1	0	1	4	9

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 4 Constitution at Work-I Short Answer Questions.

CHSE Odisha 11th Class Political Science Unit 4 Constitution at Work-I Short Answer Questions

Very Short-Answer Type Questions

Question 1.
What is an Election?
Answer:
The election is a process of choosing representatives.

Question 2.
What are the different types of elections?
Answer:
The election is of two types
(a) Direct election
(b) Indirect election.

Question 3.
What is a direct election?
Answer:
Direct election is a process where the voters cast their vote directly in favor of candidates.

Question 4.
What is an indirect election?
Answer:
The indirect election is a process in which the voters elect an intermediary group or body which again elects the true representative.

Question 5.
When the Indian election commission was set up?
Answer:
The Indian election commission was set on 26th January 1950

Question 6.
What is the function of the election commission?
Answer:
The election commission conducts free, fair, and impartial elections for the office of the President, Vice President, members of parliament, and the state legislature.

Question 7.
On what ground is the election? commissioners can be removed?
Answer:
The members of the Election Commission can be removed on grounds of proven misbehavior or incapacity.

Question 8.
Which act regulates the election to the office of president and vice president?
Answer:
The presidential Vice-Presidential Election Act. 1952 regulates the election of the President and Vice President.

Question 9.
By which amendment Act the voting age of votes is reduced from 21 to 18 years?
Answer:
The (51st Amendment Act of 1988 has reduced the voting age from 21 to 18 years.

Question 10.
What is the tenure of office of Election Commissions?
Answer:
The tenure of office of each election commission is 6 years but he may retire before if he attains the age of 65.

Question 11.
How the chief election commissioner can be removed?
Answer:
The chief election commissioner can be removed on grounds of proof, of misbehavior or incapacity if a proposal to that effect is passed in both houses of parliament by a special majority.

Question 12.
What is the voter list of the Electoral roll?
Answer:
The electoral roll or voter list is the list containing the names of valid voters of a constituency.

Question 13.
Where do the candidates file their nominations?
Answer:
The candidates file their nomination before the District Returning Officer.

Question 14.
What is repolling?
Answer:
When polling takes place for the second time after the election in a both is countermanded due to irregularities, it is called repolling.

Question 15.
What do you mean by electoral reforms?
Answer:
Electoral reform is an attempt to restrict the effects of the prevailing electoral process.

Question 16.
What is the relative majority?
Answer:
The relative majority refers to a number that is not about half of the voters who cast their vote in an election but is a majority in comparison to all other contesting candidates.

Question 17.
What is a by-election?
Answer:
When an election to an office is held due to runtime death or resignation of the office bearer before the normal term is known as buy election.

Question 18.
What is a mid-term poll?
Answer:
The election held before the end-of normal figure of Loksabha or Vidhansabha for unusual dissolution of the house is called a mid-term poll.

Question 19.
What is constituency?
Answer:
Constituency refers to an electoral segment constituted by taking the voters in that area from which one candidate is elected.

Question 20.
What is the electorate?
Answer:
Electorate refers to the valid voters of a definite constituency.

Question 21.
What is universal suffrage?
Answer:
Universal suffrage means an extension of voting rights to all adults irrespective of caste, color, sex, education, and property qualification.

Question 22.
To whom does the constitution deprive of voting rights?
Answer:
As per Art. 326, the constitution deprived the voting rights to aliens, criminals, lunatics, and bankrupt persons.

Question 23.
What is a single-member – constituency?
Answer:
One candidate can win in a definite election

Question 24.
What is a general election?
Answer:
The general election is a process where all the voters of the nation or state participate and so the election to Lok sabha and Vidhansabha is called a general election.

Question 25.
Who are the constituents of Parliament?
Answer:
The parliament constitutes of Loksabha, RajyaSabha, and the President of India.

Question 26.
What is a quorum?
Answer:
Quorum means the minimum number of members to be present in any house for a day for transacting its business.

Question 27.
How the members of the Rajya Sabha are elected?
Answer:
The members of RajyaSabha are elected indirectly by state legislative assemblies through proportional representation single transferable vote

Question 28.
What is the consolidated fund?
Answer:
The fund in which all the receipts of income of the union government are deposited is called the consolidated fund of India.

Question 29.
What is a contingency fund?
Answer:
The contingency fund is a reserve fund in the hands of the president from which sanctions can be made to meet any unavoidable situation or natural calamity.

Question 30.
What is the financial year?
Answer:
The financial year is a time period that lasts from April 1 st to March 31 st.

Question 31.
What s question hour?
Answer:
Question hour is the very first hour of every parliamentary ‘ session that continues from 11 AM to 12 Noon every day.

Question 32.
What is zero hours?
Answer:
Zero hour refers1 to one hour of parliamentary business that extends from 12 Noon to 1 PM every working day.

Question 33.
What is an adjournment motion?
Answer:
An adjournment motion is a legislative motion introduced in either house to discuss any matter of public importance in place of the regular course of business in a house.

Question 34.
What is half an hour discussion?
Answer:
Half an hour discussion is a brief discussion on administrative lapses arid negligence in the parliament.

Question 35.
What is a censure motion?
Answer:
A censure motion is a parliamentary motion that condemns corruption and inefficiency of any executive department.

Question 36.
What is the bill?
Answer:
Bill is a draft proposal pending legislation.

Question 37.
What is the public bill?
Answer:
A public bill is a bill that affects all or most of the residents in a state.

Question 38.
What is the private bill?
Answer:
A private bill relates to any private person, company or organization or section of the population.

Question 39.
What is the ordinary bill?
Answer:
The ordinary bill includes all bills except money bills and constitutional amendment bills.

Question 40.
What is an appropriation bill?
Answer:
An appropriation bill is a proposal for sanctioning of funds out of the consolidated fund for any specific department.

Question 41.
What is a vote on Account?
Answer:
A vote on the account is a temporary measure sought by the government if it fails to pass the general.budget before 31st March.

Question 42.
What is territorial representation?
Answer:
Territorial representation is also known- as geographical representation. In this process, the entire state is divided into a number of constituencies and from each such constituency, a representative is elected.

Question 43.
What is functional representation?
Answer:
Functional representation is a form of minority representation. It gives representation to people belonging to various functional groups and associations like industry, trading, corporations, medical association, lawyers, engineers, teachers, etc.

Question 43.
What is proportional representation?
Answer:
Proportional representation is a technique of minority representation. In this method, a political party secures seats in proportion to the votes secured. It is further divided into a single transferable vote system and a list system.

Question 44.
What is universal suffrage?
Answer:
When voting right is extended to all adults irrespective of caste, religion, sex, property and educational qualification, it is called universal suffrage. Art. 326 of the constitution deals with it.

Question 45.
Lok Sabha
Answer:
Lok Sabha is the lower house of the Indian Parliament. It consists of 545 by citizen voters of the country.

Question 46.
Rajya Sabha
Answer:
Rajya Sabha is the upper house oi parliament. It is a permanent chamber and its members are elected indirectly b> state legislative assemblies.

Question 47.
Speaker of Lok Sabha
Answer:
Speaker is the chairman and presiding officer of Lok Sabha. He conducts the proceedings of Lok Sabha.

Question 48.
Answer:
The vice-President of India is the ex-officio chairman of the Rajya Sabha. He presides over the meetings of the Rajya Sabha and conducts its proceedings.

Question 49.
Consolidated fund of India
Answer:
Art. 266 of the constitution deals with the consolidated fund. All incomes, revenues, and taxes collected from various sources are deposited in this fund.

Question 50.
Contingency Fund
Answer:
Art. 267 provides for the contingency fund of India. It is under the disposal of the president and funds can be sanctioned to meet unforeseen expenditures.

Question 51.
What is call-attention motion?
Answer:
During the parliamentary discussion, if some members draw the attention of the house with due permission from the speaker about any vital issue affecting the general interest of the nation it is called a call attention motion. The opposition parties use it as a weapon to obstruct government policies and discussions.

Question 52.
What is privilege motion?
Answer:
When any minister is actions, behavior or words affect the dignity of any member or the house as a whole it results in a breach of privilege. The opposition may bring a privilege motion to criticize the ruling party.

Question 53.
What is no confidence motion?
Answer:
A no-confidence motion is introduced by any members of Lok Sabha condemning the behavior and role of the government. If it is passed in the Lok Sabha by a simple majority of votes then the government has to resign.

Question 54.
What is the budget?
Answer:
The budget is the annual estimate of the income and expenditure of the government. It has to be passed in both houses of parliament before the beginning of the new financial year.

Question 55.
What are the financial powers of Parliament?
Answer:

• The parliament approves the annual budget of the state.
• Without its approval no new tax can be levied nor exempted.

Question 56.
What is question hour?
Answer:
Question hour is the very first hour of every working day when the parliament is in session. During this hour the members may ask various questions to the government about different issues.

Question 57.
What is an ordinance?
Answer:
The ordinance is an emergency legislation proclaimed either by the president of India or the Governor of any state. It is declared during the recess of parliament.

Question 58.
Joint sitting of Parliament.
Answer:
The joint sitting of Parliament is held as per Art. 108 of the constitution. The President may convene a joint sitting to settle the dispute sing between the two houses over the passage of an ordinary bill.

Question 59
What is a vote on Account?
Answer:
A vote on the account is a temporary measure taken by parliament when the annual budget can’t be passed before 31st March.  In this process, the Govt has to pass budgetary allocation for two to three months.

Question 60.
What is a closure?
Answer:
The program advisory committee of the Lok Sabha determines the time limit for discussing the demand for grants of every department during the budget. If it is not passed within the time then no discussion demand for grants takes place and that is called closure.

Question 61.
What is the guillotine?
Answer:
During budget discussion, if the demand for grants of various departments can it be discussed then those are simply placed for a vote of the house, which is called the guillotine. It marks the end of the discussion on the demand for grants.

Question 62.
What is cut motion?
Answer:
During a discussion of the demand for grants of different departments, the opposition may initiate a cut motion. This motion proposes to bring down the expenditure of a department to Re.l.

Question 63.
What is the point of order?
Answer:
When any member of parliament seeks the intervention of the honorable Speaker citing irregularities in the parliamentary procedure it is called a point of order. It can be introduced for discussion if the speaker gives permission.

Question 64.
Independence of election commission
Answer:
The independence and autonomy of the Election Commission is essential for the conduct of a free and fair poll. Therefore, the constitution has kept the election commission free from politically arid bureaucratic interference.

Question 65.
Qualifications of an MLA.
Answer:
The qualification prescribed by the constitution for being an MLA is He/she must be a citizen of India. He/ she must be above 25 years of. He/she must pass all other qualifications as prescribed by parliament.

Question 66.
How the Vidhansabha exercises control over the state council of ministers?
Answer:
The members of Vidhansabha may ask questions, supplementary questions, motions, and resolutions to criticize the government. It can introduce not confidence motion to remove the ministry from office.

Question 67.
How the legislature controls the purse of the nation?
Answer:
The legislature passes the annual budget and approves all proposals for imposition, repeal, or collection of taxes. The government can’t raise or spent one rupee without the approval of the legislature. It also controls all incomes and expenditures incurred y the executive.

Question 68.
What are the functions of the speaker of Lok Sabha?
Answer:
The speaker of Lok Sabha presides over the Lok Sabha. He conducts the proceedings of the house as an impartial umpire.

Question 69.
How the Lok Sabha exercises control over the union council of ministers?
Answer:
The Lok Sabha exercises control over the Union Council of Ministers by passing a vote of the no-confidence motion. It can also initiate cut motion, call attention motion, censure motion and put questions to ministers to keep the government under control.

Question 70.
What do you mean by the parliament of India?
Answer:
Parliament is the Union Legislature in India. It comprises the Lok Sabha, the Rajya Sabha, and the President of India. It is the most powerful organ of the state.

Question 71.
What are the two special powers of the Rajya Sabha?
Answer:
Rajya Sabha can pass a resolution by 2/3rds majority authorizing the parliament to make law on the state list. It can pass a resolution in respect of the creation or abolition of posts of All India Services.

Question 72.
What are the privileges of Members of Parliament?
Answer:
Members of Parliament enjoy unrestricted freedom to express their views in the house. During their tenure, they can’t be detained for any civil offense during and 40 days before and after the session of the house.

Question 73.
What is an appropriation bill?
Answer:
The appropriation bill contains all the demands for grants of all the departments and the amount charged to the consolidated fund of India. The Parliament by approval of this bill allows the government to incur expenditures for various departments under the government.

Question 74.
What is Finance Bill?
Answer:
The finance bill contains all proposals for taxation in the budget. It is introduced after the enactment of the Appropriation bill. The passage of the finance bill marks the end of the budget process.

Question 75.
How the second chamber of a state legislature can be created or abolished?
Answer:
The second chamber of a State legislature can be created or abolished if a proposal to that effect is passed in the concerned State Legislative Assembly by 2/3rds of its members present and voting. After that parliament reserves the right to take the final decision.

Question 76.
How the members of Lok Sabha are elected?
Answer:
The members of Lok Sabha are elected directly by the people through single-member constituencies on the basis of a universal adult franchise. They are elected through a simple majority vote system.

Short-Answer Type Questions

Question 1.
Distinguish between direct and indirect elections.
Answer:
Direct election is a single election where the voters directly cast their votes in favor of the actual representative. But indirect election involves two elections, the first one by voters to elect the intermediary group, and by the second the true representatives are elected. In direct election close contact between the voters and the representatives is established. But in the indirect election so contact is established.

Direct election makes people conscious and responsible, but indirect election does not stimulate public interest. Direct election is suitable for developed countries but indirect election is useful for backward countries. Direct election is expensive but indirect election is less expensive.

Question 2.
Election Commission.
Answer:
The Indian constitution under Art. 324 has provided for an independent election commission. It ensures free, fair, and impartial elections in India. It conducts an election for President. Vice President Parliament and the state legislature. It comprises three members appointed by the president. It recognizes political parties and allows party symbols.

Question 3.
Functions of the election commission.
Answer:
The election commission discharges the following functions

• Preparation and revision of electoral rolls.
• Conduct of elections to the office of president, Vice-President, Parliament and state legislature
• Recognition of political parties and allotment of party symbols.
• Appointment of Returning officers, observers, election officers, and polling officers.

Question 4.
Independence of Election commission.
Answer:
The Indian constitution has secured the independence of the election commission. The members of the election commission are appointed by the president as per the law made by the parliament. They can’t be removed from office unless a proposal to that effect is passed in both houses of parliament by a special majority. The salary and allowances of the members of the election commission can’t be lowered during their term of office. They enjoy equal status as that of the judges of the Supreme Court.

Question 5.
Electoral reforms.
Answer:
Electoral reforms are necessary for every democratic system because with changes in time the drawbacks of the election process need modification. The Government of India has therefore introduced some reforms in the election process and some more reforms are self-indispensable. The voting age of voters has been reduced from 21 to 18. Electronic voting machines have been introduced to conduct free and fair polls and speedy counting of results. The voters have been given photo identity cards. To avoid fake candidates number of proposers and seconders has been increased and the security deposit has also been hiked.

Question 6.
Chief Election Commissioner.
Answer:
The senior member of the election commission is known as the chief election commissioner. He is appointed and removed in the same process and enjoys equal powers with the other two members He enjoys a 6 years term and retires at the age of 65 years. He is removed on grounds of proven misbehavior or incapacity if a resolution to that effect is passed in both houses of parliament by a special majority. He has to coordinate the activities of the other two members of the election commission.

Question 7.
Features of an ideal election system.
Answer:

1. After ideal election system is vital for the success of democracy.
2. It must be free from political and . bureaucratic influence.
3. There should be an independent judiciary to adjudicate election disputes.
4. Public trust and support towards the election commission is an indicators of an ideal electoral system.
5. It must have efficient administrative machinery to ensure free polling.

Question 8.
Importance of election for a democracy.
Answer:

• An independent election system is vital for the success of democracy.
• It enables voters to elect efficient and capable representatives.
• Election leads to the formation of a stable government and a good election system makes people repose their faith on government.
• Election lets the representatives enact good laws.
• An ideal election system keeps criminals and evil-minded people away from the democratic process.

Question 9.
Challenges to Indian Election Commission.
Or, Problems with the Indian electoral system
Answer:
The Indian election commission is now facing a few challenges which obstruct its efficiency, and these are

• Use of black money & muscle power in elections.
• The prevailing pattern of the relative majority system
• Abuse of power by central and state employees.
• Defects in the preparation of pectoral rolls.
• Influence of caste, religion, language, communal and regional feelings electoral process. Entry of criminals and anti-socials into the process.

Question 10.
Universal suffrage
Answer:
Universal suffrage is the very basis of representation in a democracy. It believes in the granting of voting rights to all adults irrespective of their caste, color, sex, religious discrimination, and education or property qualification. It supports the one-man-one-vote principle. It ensures more participation of younger people and women in elections and this makes democracy real.

Question 11.
Merits of Universal suffrage.
Answer:
Universal suffrage makes democracy successful. It ensures political, equality and justice. It promotes political awareness among people and develops the self-respect of each voter. Universal suffrage makes the legislature a true representative chamber of various interest groups. It enables women and backward classes to safeguard their own interests.

Question 12.
Demerits of Adult Suffrage.
Answer:
The drawbacks of adult suffrage are as follows:
Universal suffrage gives voting rights to poor illiterate people who do not understand the value of a vote. So it tends to be abusing voting rights. It often results in the selling of votes for a meager amount. Those backward people make a mockery of their voting right. It makes democracy weak because illiterate votes can’t judge good candidates. Universal suffrage further affects the dignity of women and their feminine qualities.

Question 13.
Women suffrage.
Answer:
Women’s suffrage means a grant of voting rights to women. Women’s suffrage makes women equal to men. It develops a spirit of service and sacrifice in women. Women’s Suffrage was first of all granted in the USA in 1919. England in 1928, Switzerland in 1970. India in 1950 and European countries from 1940-50.

Question 14.
Merits of Women suffrage.
Answer:
John Stuart Mill Sidquick and Esmein support women’s suffrage on the following grounds. As in a democracy, women are treated at par with men, There is no, ground to deprive them of voting right. Women’s suffrage will make them safeguard their own rights and privilege. Today women are capable of doing everything even if they are joining- the army and airforce, so it will be an injustice today for them to vote right.

Women’s suffrage will bring a major change in the social setup. Women are less tolerant of corruption. Crime and favoritism so by giving them political rights they can abolish exploitation and inequality in society.

Question 15.
Demerits of women suffrage.
Answer:
Women’s suffrage may lead to disruptions in family life. It will lead to neglect of children and the old. Women joining politics may develop a rift between husband and wife. As women are by nature fearful and apprehensive they may not discharge their duties properly. Unless they are educated it is not at all justifiable to give them voting right.

Question 16.
What is a direct election?
Answer:
Direct election is a process where the citizen voters directly cast their vote at a pooling booth to elect their representatives. It gives the opportunity and freedom to each voter to vote for his / her candidate of choice. In this election, the person who gets the maximum vote is declared elected. Direct election is democratic and it is seen everywhere. The members of Lok Sabha and Vidhan Sabha are elected by direct election.

Question 17.
Merits of direct election.
Answer:
Direct election gives every voter the freedom to vote for the candidate of his choice. In this process, each Voter gets the satisfaction that he is selecting the government. It establishes close contact between the votes and representatives. It promotes political consciousness. It makes voters accountable and develops the attitude of service.

Question 18.
Demerits of direct election
Answer:
The poor and ignorant people while casting their vote can not make the proper choices of representatives. Indirect election votes are swayed by election waves and do not make good choices. It is too much expensive, so poor people rarely get a chance to win. Violence and muscle power influence the outcome of a direct election.

Question 19.
Indirect election.
Answer:
The indirect election is a process where the voters elect their representatives indirectly that is through an intermediary group. It involves two elections, first, the intermediary group is elected and by second the group elects the real representatives. The Indian President, Vice-President and members of the Rajya Sabha are elected in this method.  It is less expensive and more representative. It may be carried out either by list system.

Question 20.
Minority Representation.
Answer:
Minority representation refers to the representation of minorities. Proportional representation is a technique of minority representation. Each group and party secures seats in proportion to the votes secured. It enables each minority to safeguard its interests.

Question 21.
Merits of indirect election.
Answer:
Indirect election eliminates the evils of the party system, therefore more capable and efficient representatives are elected. Here merit of the candidates counts over the election wave. It is suitable for poor and backward countries. It is less influenced by the evils of party politics.

Question 22.
Demerits of Indirect Election.
Answer:
The indirect election is undemocratic as the voters are not given the scope to elect representatives directly. There is no direct contact between the voters and representatives. It discourages voters in a democracy. Here the party dominates over individual choice. It encourages corruption, bribery, and illegal activities.

Question 23.
Single transferable vote system.
Answer:
A single transferable vote system is a form of proportional representation. It was invented by Thomas Hare of England. It is suitable for multi-member constituencies. In this system, each voter cast his vote in order of preference. The 1st preference votes are taken into account first, and those who secure the required quota of votes are declared elected. Here the 2nd preference vote is transferred to another candidate for which it is called a single transferable vote system.

Question 24.
Proportional Representation.
Answer:
Proportional representation is a form of indirect election. It rectifies the defects of a single-member constituency. In this system, a representative is elected on the basis of votes cast in his favor. So every vote is taken into consideration. It provides an opportunity to smaller parties and groups to win some seats in proportion to their votes. No vote is wasted in this system.

Question 25.
Demerits of Proportional representation.
Answer:
Propositional Representation is a complex process that ordinary voters can not understand. It encourages small parties and factionalism in a democracy. If encourages a multi-party system and most of the time coalition ministries are formed. It establishes no links or relationships between voters and representatives. In this system, the voters are bound by partly decisions and policies.

Question 26.
Communal Representation.
Answer:
Communal representation means the formation of electoral constituencies on the basis of Hindu, Muslim, Christian and Sikh religious communities, This system was encouraged by Britishers during pre-independence In this system, representatives are elected from every religious community. It can be ensured by reservation of seats bn communal lines. The Indian constitution has rejected communal representation.

Question 27.
Functional Representation.
Answer:
Functional Representation means the election of representatives from specific functional groups and units. It is an alternative to the system of territorial representation. This type of representation is prevailing in socialist and communist countries where representatives are chosen from farmers. It tends to neglect general interest for the sake of functional gr I p interest.

Question 28.
Challenges to Indian Election System.
Answer:
The Indian election system is facing, a lot of challenges in the nature

• Lot-of challenges in the nature of
• Increase in corruption and entry of criminals into politics.
• Politicization of caste, religion, communal and regional issues.
• Increasing violence, booth capturing arid rigging during the poll.
• Most of political parties are trying to misguide and confuse voters especially the poor and weaker sections of society.

Question 29.
Difference between money bill and finance bill.
Answer:
The difference between money bills and financial bills is more systematic than real. Art. 110 deals with money bills while Art. li 7 deals with financial bills. Financial bills are mostly bills dealing with income and expenditure and some portions of money bills also deal with similar issues. But all financial bills are not many bills. A finance bill is a mixture of an ordinary bill and a money bill. Money bills can’t be amended by Rajya Sabha but financial bills can be.

Question 30.
Ordinary Bill and Money Bill.
Answer:
An ordinary bill may be a public bill or a private bill, but a money bill is always a public bill. Ah, the ordinary bill can be introduced into either House of Parliament, but a money bill can only be introduced into the Lok Sabha. A money bill is introduced with the prior permission of the President, but an ordinary bill requires no such permission. The President may or may not approve an ordinary bill, but can’t disapprove a motley bill. The Rajya Sabha can reject an ordinary bill, but it can’t reject a money bill.

Question 31.
Bill and Act.
Answer:
Bill is a draft proposal for legislation. It is the preliminary stage of an Act, but Act is the final stage of a bill. A bill is a legislative proposal that after parliamentary action becomes an Act. A bill is not enforceable either by the executive or judiciary but an Act is enforced by the executive and applied in law courts. A bill carries no legal sanction but an Act carries legal sanction.

Question 32.
How does the legislature act as the custodian of the national purse?
Answer:
Without the approval of the budget by the legislature, no money can be raised or spent by the government. Without legislative sanction, no expenditure can be charged out of the consolidated fund, and no tax can be levied or exempted. It maintains a strict vigil over financial transactions made by executives. It appoints legislative committees like public accounts. Committee and Estimates Committee for the purpose.

Question 33.
How the Union Parliament is organized?
Answer:
Union Parliament is bicameral in structure, its Lower House is called Lok Sabha, and its Upper House as Rajya Sabha. Lok Sabha is the popular house and its members are elected directly by the citizen voters for five years. Rajya Sabha is the Upper House and its strength is 250 of which 238 members are elected indirectly from states and Union Territory Legislative Assembles for six years. The rest 12 are nominated by President.

Lok Sabha enjoys a five years tenure but Rajya Sabha is permanent.

Question 34.
What are the required qualifications for a member of the Rajya Sabha?
Answer:
A member of the Rajya Sabha is required to possess the following qualifications.

• He must be a citizen of India.
• He must be above 30 years of age.
• He should not be insolvent or of unsound mind,
• He should not hold any office or profit either under the Union of State Gate.

Question 35.
What are the required qualifications for a member of the Lok Sabha?
Answer:
A member of Lok sabha should satisfy the following qualifications.

• He must be a citizen of India.
• He must be above 25 years of age.
• He must not be insolvent or of unsound mind.
• He must not hold any office of profit either under the Union Govt or of slate.

Question 36.
Joint sitting of Parliament.
Answer:
The President summons the joint sitting of parliament under Art. 108 . to resolve the deadlock between the two houses of parliament over the passage of an ordinary bill. The meeting is held in. the central Hall of Parliament with the speaker of Lok Sabha in the chair. The matter is discussed and finally, a vote is taken. The decision of the majority is taken for granted. The Lok Sabha due to its, numerical strength usually wins.

Question 37.
Role of Rajya Sabha in the passage of a money bill.
Answer:
Rajya Sabha is the second chamber of the union parliament and it plays an insignificant role in the passage of a money bill. No money bill can be introduced into the House. A bill after approval of Lok Sabha comes to the house and it is given a period of 14 days to approve the bill. The House can’t amend or reject a money bill, but can suggest amendments. The lower house may consider such a suggestion or not. Under no circumstances it can delay a money bill beyond 14 days.

Question 38.
Write the special powers of RajyaSabha.
Answer:

• Under Art. 249, Rajya Sabha can pass a resolution authorizing the Parliament to enact laws on any item of state list in the national interest.
• The House can initiate a proposal for the removal of the Vice President.
• Under Art. 312, it can pass a resolution authorizing the union Govt, either for the creation of addition of posts belonging to all Indian services.

Question 39.
What is a No-confidence motion?
Answer:
No confidence motion is an instrument in the hands of the Lok Sabha to control the ministry. It is moved by the members of the opposition bench to criticize and remove the government. It is initialed by at least l/4th members of the House and the Speaker gives a 14 days notice to the Govt. On the appointed date, the matter is discussed vividly and a final vote is taken. If the majority of the members are present and the voting vote is in favor of the motion the govt, resigns.

Question 40.
What are the functions of the Speaker of Lok Sabha?
Answer:

• The Speaker is the presiding officer of the Lok Sabha.
• He presides over its meetings and maintains decorum
• He conducts the business of the House.
• He protects the privileges and freedom of the members
• He interprets the rules of business of the House and decides on the admissibility of questions, resolutions and motions.
• In case of a tie, he casts his vote.

Question 41.
Estimate Committee.
Answer:
The estimates committee is a parliamentary committee. It consists of 30 members elected from Parliament. It examines the estimates of various ministries and suggests alternative policies to bring efficiency and economy to administration. The committee also works to bring about improvements in organization and efficiency in administration.

Question 42.
What are the privileges of members of Parliament?
Answer:
The members of parliament enjoy the following privileges. They enjoy freedom of speech, and for that, no legal action can be taken. They are immune from all legal proceedings for any act committed inside the House. No, a member can be arrested or detained by the public authority during – the session without the permission of the speaker.

Question 43.
Appropriation Bill.
Answer:
After a discussion of demands for grants, the Appropriation Bill is prepared by taking the demands passed by Lok Sabha and expenditure charged upon the Consolidated Fund of India. This bill is presented to the Lok Sabha and it has to pass through all the stages as any other bill.

Question 44.
Finance Bill.
Answer:
All the taxation proposals contained in the budget are known as Finance Bill. It is presented to the Lok Sabha after the enactment of the Appropriation Bill. It is passed in the same process as money bills. The passing of finance bills marks the completion of the budget.

Question 45.
What is a Vote on Account?
Answer:
The financial year of the Govt ends on 31 st March and as per the rules, the Budget must be passed by 31st March. If for any reason the budget can’t be passed within the time then the Govt can seek an affirmative vote from the Parliament to make necessary expenditures on Adhoc basic. This is called Vote on Account.

Question 46.
What are the required qualifications for membership of the Legislative Assembly?
Answer:
As per 173 of the constitution, a member of the State Legislative Assembly is required to satisfy the following qualifications He must be a citizen of India. He must be above 25 years of age. He must possess all other qualifications as prescribed by the law of Parliament.

Question 47.
What, are the disqualifications for membership of the State Legislative Assembly?
Answer:
A person shall be disqualified for membership of a State Legislative Assembly if.He/she holds any office of profit either under the State or Union government. He /she is of unsound mind. He/she is an undischarged insolvent. He/she has voluntarily acquired the citizenship of a foreign state. He/she is disqualified by any law made by Parliament.

Question 48.
How the membership of an MLA can be terminated?
Answer:
Termination of membership of an MLA is a controversial issue and the final decision in this regard is given by the State Governor. The Governor before disqualifying a member has to obtain the view of the Election Commission and act accordingly. His decision is final and can not be questioned in any court of law. The membership of a disqualified member shall be terminated by the Assembly by passing a resolution to that, effect.

Question 49:
What are the required qualifications of a member of the Legislative Council?
Answer:
A person should possess the following qualifications to become a member of the legislative council. He must be a citizen of India. He/she must be above 30 years of age. He/she must possess such other qualifications as may be prescribed by the law of parliament.

Question 50.
How the Second Chamber of the State Legislature can be abolished?
Answer:
The Second Chamber of a State Legislature can be abolished in accordance with Art. 169 of the Constitution. It can be done if a resolution to that effect is passed by a majority of the total membership of the Assembly and a two-thirds majority of members present and voting of the concerned state legislative assembly. This resolution must be followed by the Act of Parliament after which the President orders for the abolition of the Second Chamber.

Question 51.
Which states in India have bicameral legislature?
Answer:
Five of 25 states in India have a bicameral legislature. These states are

• Uttar Pradesh.
• Bihar.
• Maharastra.
• Jammu and Kashmir.

Question 52.
Legislative Council is a superfluous chamber.
Answer:
Legislative Council is the Second Chamber of a State Legislature. It is a weak chamber that exercises limited and negligible influence over the lower chamber in the legislative sphere. It can neither check the money bills nor ordinary bills against the wish of the Lower House. It has no control over the executive. It does not participate in the amendment of the Constitution and the election of the President. Thus, in comparison to the Lower House, the Legislative Council is weaker in all aspects for which it is criticized as a superfluous chamber.

Question 53.
What are the functions of the Speakers of the Legislative Assembly?
Answer:
Speaker is the Presiding officer of the Legislative Assembly and he performs the following functions. He presides over the sessions of the Assembly. He maintains decorum in the House and interprets the rules of business. He is the final authority to admit questions, motions, and resolutions. He conducts the proceedings and votes within the House He can cast his vote in case of a tic. He safeguards the privileges of the members of the House.

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 4 Constitution at Work-I Long Answer Questions Part-2.

CHSE Odisha 11th Class Political Science Unit 4 Constitution at Work-I Long Answer Questions Part-2

Long Questions With Answers

Question 1.
Explain the functions of the election commission of India.
Answer:
The election commission of India is an independent body that conducts elections to the office of the President, Vice-President members of Parliament, and state legislatures, the functions of the commission can be enumerated below.

The Election/Commission revises electoral rolls before the every-general election. It exercises supervision and control over all matters pertaining to the election of the President, Vice-President, Members of Parliament, and State legislatures. It tenders advice to the President and Governors in matters of disqualification of members of parliament and state legislatures.

The commission gives recognition to political parties and allots election symbols. It makes appointments of election officials to enquire about disputes arising out of election arrangements. It issues notification of the election of schedules indicating the date and time of elections. The commission also regulates the campaigning of political parties through TV. and Radio.

It also requires the necessary states for the conduct of the poll. The commission has to determine the code of conduct of the political parties and candidates during elections. It has to decide about cases of rigging, booth capturing and. countermanding of polls, and also on repoll. The commission undertakes delimitation of constituencies every 10 years or so. The commission has to make all arrangements to conduct the peaceful poll.

Question 2.
Write an essay on the Independence of the Election Commission.
Answer:
Free and fair elections are indispensable for a democratic polity, The founding fathers were well aware of the situation and they tried their best to ensure the independence and integrity of the Election Commission.

Independence of the Election Commission:
The constitution has taken the following steps to ensure independence to the Election Commission.

The members of the Election Commission are appointed by the President as per rules made by the parliament. They hold office during the pleasure of the president. The president can’t remove them unless a resolution to that effect is passed in both houses of parliament by 2/3rds the majority of those present and voting and by a majority membership of each house.

They can only be removed only on grounds of proven misbehavior and in capacity. The members receive a salary as determined by Parliament from time to time and it is charged upon the consolidated fund of India, on which discussion takes place in the parliament During their tenure, their salary and conditions of service can’t be changed to their disadvantage.

The members of the Election Commission enjoy the status of a judge of the Supreme Court and after Retirement, they are not assigned any additional duty. The commission remains politically neutral and above all controversies maintains the dignity of the institution.

Question 3.
Mention the Electoral reforms introduced by the Election Commission of India.
Answer:
During the last sixty years, the history of elections in India indicates that the electoral process is not free from deficiencies. Analysts express doubt about the fairness and impartiality of the Election Commission. To overcome these defects there is a need for electoral reforms.

Reforms Introduced:
The government of India has already introduced certain electoral reforms to bring about the efficiency of the commission. The voting age has been reduced from 21 to 18 in order to encourage young voters. To ensure perfect arrangement for poll staff members now deputed much before by the Election Commission. To avoid the multiplicity of candidates in a constituency number of proposers and seconders has been increased and the amount of the security deposit has been enhanced 20 times.

Electronic voting machines have been used and photo identification cards have been issued to avoid false voting and tender voting and ensure quick counting of votes. If any candidate shows disrespect to the national flag, National Anthem, and to the constitution of India, he shall be disqualified from contesting polls for six years. No candidate can contest from two or more seats simultaneously.

The government prohibits persons from going with arms to polling booths. The sale of liquor during the last 48 hours of the election has been declared illegal. The poll day is declared a paid holiday to enable public servants to cast their votes. The time limit for bye-elections has been reduced to six months. A postal ballot system has been introduced to enable polling officers to cast their votes.

Further, there is a demand for holding simultaneous elections for Parliament and Assemblies. To keep the black money out of elections there is a need for state funding of elections. There is a need for quick disposal of election cases and rotation of reserved seats. To make the election free and fair election expenses must be audited properly.

Question 4.
Explain the powers and functions of the Union Parliament.
Answer:
The Union Legislature in India is called Parliament. It is bicameral in structure. The Upper Upper House is called the Council of States or Rajya Sabha and the Lower House being the popular House it performs most of the functions on behalf of the Parliament and dominates the Upper House.

Powers:
Parliament being the legislative wing, it is responsible for law-making. It also performs other vital functions.

Legislative:
The Union Parliament is a popular body that formulates the laws of the land. It is the Parliament that initiates and approves all legislative proposals. Without the knowledge of the Union Parliament, no law can be enacted.

Executive:
The Union Parliament performs certain executive functions. The ministers sit in the Parliament and remain responsible and answerable to the legislature for all their actions. The Lok Sabha controls the executive by putting various questions to the ministers. It is also the sole authority of the Lok Sabha. To pursue a no-confidence motion against the ministers. There is a responsible, executive in India.

Financial :
The Union Parliament in India enjoys absolute control over financial matters. No single pie will be spent without the knowledge of the Union Parliament. All sorts of financial appropriations are determined and approved by the legislature.

Constitutional :
No Constitution is static. With the development of civilization, and the change in the life of the people the Constitution needs to be
amended. In India, the Union Parliament possesses all powers with regard to the amendment of the Constitution.

Electoral:
The Union Parliament also possesses certain functions with regard to certain elections of the high officials. The Parliament participates in the election of the president and Vice president and another Parliamentary committee.

Judicial :
The Union legislature also possesses some sort of judicial power. The Lok Sabha acts as a judiciary to decide certain cases tike, like the impeachment of the Supreme Court.& High Court Judges, the President, the Vice-President and the no-confidence motion against the Council of Ministers are some of the illustrations of the judicial power of the union legislative

Administrative-Power :
The Union Parliament also possesses some administrative powers. The Parliament has control over the various administrative heads of various departments, The Lok Sabha possesses the power to question to the concerned minister for any administrative commission or commissions.

Miscellaneous Power :
The Union Parliament also enjoys certain miscellaneous powers which include controlling the emergency provisions and issuing ordinances by the President, of India.

Question 5.
Discuss the Legislative Procedure of the Union Parliament.
Answer:
In every constitutional setup, there is a legislature, whose primary responsibility is to formulate the two. There is a fixed procedure principle on the basis of which-the legislative procedure, is being carried out. Similarly, in India, there is a fixed procedure or principle on the basis of which the laws are made. There are two kinds of bills ordinary bill and a money bill. An ordinary bill may be introduced into either House of the Parliament but money bills can only be introduced into the Lok Sabha.

The Procedure of Legislation :
For the passing up of any bill, the legislature in India involves three stages of reading i.e. the first reading, the second reading, and the third reading.

Introduction of the bill:
For legislation, the first step is the introduction of the bill in the House for which a notice will be given one month. The date for the introduction of the bill is fixed by the Speaker or the Chairman of the House concerned and on the due date, the member is asked to present the bill If the majority of members of the House support the introduction of the bill is introduced and is published in the gazette.

First Reading:
After the introduction of the bill, the Chair of the House fixes, the date of its first reading. On the appointed day the member moves the bill. In this stage

• The title of the bill is read.
• The vote is taken

Second Reading:
After the committee has sent the report the bill may be referred for second reading on the fixed date. In the stage of second reading.

• The examination of the Select Committee may be taken into consideration.
• The member may move the bill which will be sent to Select Committee.
• Thirdly the member may move the bill for eliciting public opinion.

Select Committee Stage:
After the second reading, the bill is referred to a select committee. The committee examines the bill thoroughly. There is a detailed discussion of the bill
in this stage. The Select Committee may propose any changes in the bill on the basis of all kinds of information collected.

Report Stage:
After the bill is examined and discussed thoroughly, the Select Committee prepares its report. The suggestions recommended by the Select Committee is taken into account. If the majority of members arrived at a decision, the Chairman of the committee presents the report to the House. If the house agrees to consider the bill as reported by the Select Committee it enters into the second stage of the second reading when the bill is discussed clause by clause and the members are allowed to move their amendments. And the vote is taken.

Third Reading:
In this reading, the discussion is confined to either in support of the bill or rejection of the bill. If the bill is passed by the majority members of the present and voting the bill is passed by the legislature. And the bill is referred to the other House of Parliament. If the bill is passed by the other House then it is referred to the President for his assent. The President may give his assent or return it for reconsideration to the Parliament.

In case of Jhe disagreement of the other House with Regard to the bill, the President may summon a joint sitting of both the Houses of Parliament. If the bill is passed by the majority members in the joint sitting, it will presume that both the Houses of Parliament have passed the bill. After passing by both the Houses of Parliament have passed the bill. After passing by both the Houses of Parliament President gives his assent and the bill becomes an Act.

Question 6.
Analyze the organization and functions of the Lok Sabha.
Answer:
Indian Parliament is bicameral it Council States or Rajya Sabha and the Lower. House is known as the House of People or Lok Sabha, The House of the People-of the Lok Sabha is the direct representatives of the people Ordinarily there are 54 members of the Lok Sabha which consists of two categories of members, 545 members are elected directly by the people and two members are nominated by the President of India from among the Anglo- Indian community. The number of members to be elected to the House is determined on the basis of the ratio of the population of the states.

Term of Office:
The House of People is a temporary House that is ordinarily elected for a period of five years. But before the completion of the term the House may be dissolved and a fresh election may be, ordered. Similarly, the term of the House may also be extended up to a maximum of one year during the time of emergency.
The House meets twice in a year. There shall not be more than six months gap between each interval of the session.

Qualifications of the Members:
The Constitution of India provides tile following qualifications for the members of the House of the People. These are:

• He must be a citizen of India.
• He must have completed 25 years of age
• He must also possess other qualifications prescribed by-the Parliament from time to time.
• The President of India summons prorogues and dissolves the House of People. He also addresses the first session of the House.

Powers and functions of the House of People:
Generally, the Lower House in all Parliamentary forms of Government constitutes the elected representatives of the people. So the House of People in the context of the Indian Parliamentary form of Government occupies the highest position in the administration of the state. The House of People in the context-of-Indian Parliamentary form of Government is the highest authority where the conception of popular sovereignty is reflected. The House of People remains answerable to the people of India.  The various powers and functions of the House of People are discussed below.

Legislative Power:
The House of People or the Lok Sabha enjoys a very dominant position with regard to the legislative power. No bill would be an Act without the knowledge of the House of Parliament but money bills can only be introduced in the Lok Sabha. People Ordinary bills may be introduced in either. House of the Parliament but money bills can only be introduced in the Lok Sabha. But in the case of any other bills, they must be passed by Lok Sabha in order to become an Act.

Administrative Power:
In all types of Parliamentary forms of Government, the Lok Sabha is answerable to the legislature. So there is a responsible executive in all Parliamentary forms of Government. In India, the House of the People is the direct representative of the people, and the Council of ministers of the legislature remains answerable to Lok Sabha for all their actions. The Lok Sabha can control ministers who head various departments through various questions. If the council of ministers does not remain answerable for their actions the legislature may move a no-confidence motion against the ministers.

Financial Power:
The Lok Sabha possesses absolute control over public finance. No single pie can be expended without the sanction of the Lok Sabha. It is in the Lower House of Parliament the money bill can be introduced in regard to which Rajya Sabha possesses little or no option. The Rajya Sabha can not initiate any financial legislation and it is the financial supremacy of the Lok Sabha to grant finance for the state administration.

Constituent Power:
The union legislature possesses the power to amend the Constitution of India. Though with regard to the amendment of certain provisions of the Constitution the state government’s participation is required yet it is the Union Parliament that possesses more power for a constitutional amendment. The Parliament can initiate all those amendments for which the Lok Sabha plays a decisive role:

Electoral Power:
The Lok Sabha has certain electoral power. Lok Sabha participates in the election of the President of India, and Vice-President of India. Only elected members of the Lok Sabha alone possess the to participate in the election of President and Vice-President.

Judicial:
Lok Sabha also acts as a judiciary to decide certain cases like the impeachment of the President of India. The Vice-President, the Judges of the Supreme Court and High Court, etc. Lok Sabha alone can move and pass a no-confidence motion against the Council Ministers in the Parliament.

Question 7.
Discuss the role and functions of the Speaker of Lok Sabha.
Answer:
The Constitution provides that there shall be a Speaker for Lok Sabha who shall preside over the business of the House. The Speaker is the President of the House who is responsible to ensure the smooth functioning of the Lok Sabha.

Appointment of Speaker:
The Constitution provides that the Speaker should be elected from among the legislatures elected to Lok Sabha. The constitutional status is purely impartial so for which before entering into the office of Speaker he must vacate his membership to ensure impartiality. He may resign from his office for which at least a notice should be given to the House with 15 days in hand.

Functions of the Speaker:
The primary function of the Speaker is to ensure the smooth functioning of the Lok Sabha. It is the Speaker who happens to be responsible for all legislative procedures within Lok- Sabha. He controls the business of the 1 louse. It is the Speaker whose will and wishes prevail over the will and wishes of all other members. There are a lot of functions performed by the Speaker which is discussed below.

The Speaker is the chief authority within Lok Sabha who presides over all legislative proceedings within the Lok Sabha. He conducts the business of the House and every member of the House must address to the dignity of the Speaker in their speech. The Speaker protects the rights of the ruling as well as the opposition members, The Speaker must ensure that the opinions of the opposition members are adequately published.

Every member must be permitted by Speaker before telling anything. The Speaker administers various rules and regulations of the legislative proceeding in Lok Sabha and the ruling of the Speaker is final in this regard. It is the Speaker-who decides the nature and features of various bills introduced in Lok Sabha. Ordinarily, the Speaker does not enjoy the fight to vote but he can cast a vote in case there is a tie-in the vote.

Role and Position of Speaker:
In all Parliamentary forms of government, the Speaker or the Chair Person of the representative House Occupies a very dignitary position. Similarly, in the context of
Indian Parliamentary form of Government the Speaker of Lok Sabha occupies a very dignified position. Since more or less we have inherited the British pattern of office of Speaker where the Speaker does not belong to any political party only to ensure the impartiality of the procedure of the House.

It is the same position with regard to the constitutional status of the office, of Speaker. Though we have not observed the British pattern of practice yet, maximum steps have been taken to ensure the impartiality of the Speaker. In India, the Speaker may be a member of a political party but he ads as a nonparty man after entering into office. The Constitution of India and the convention have assigned dignity to a great extent during the tenure of his office.

So he does not take part in any party affairs during the lifetime of his office. Since he presides over the meetings of the House it is the responsibility of the Speaker to provide adequate opportunity to all members irrespective of party affiliation which will enhance the dignity and the status of the Speaker. The Speaker must not act on the basis of his personal ideology which will strike at the very impartial tradition of the office of the Speaker.

Question 8.
Discuss the composition and powers of the Rajya Sabha and examine its utility in the Indian constitutional setup.
(Or)
Examine the powers and utility of the Council of States in India.
Answer:
Rajya Sabha or Council of States is the second chamber of the Union Parliament. It gives representation to the states and Union Territories on the basis of population. It is a weaker chamber, in comparison to the Lower House, but it plays a vital role in the constitutional setup.

Composition:
The Council of States is the permanent chamber. Its maximum strength is 250-238  members representing the States and Union Territories rest of the 12 members are nominated by the President from persons having excellence either in Arts, Science, Literature, or Social Service. The members of the Rajya Sabha are elected indirectly by the members of respective states and Union Territories through, proportional representation and a single transferable vote system.

Any citizen of India above 30 years of age and possessing all other qualifications can become a member of the House. The term of each member is six years and one-third of them retire every two years. The Vice-President acts as the ex-officio chairman of the House.

Powers and Functions :
The Council of States performs the following functions:

Legislative Functions :
The Rajya Sabha shares equal legislative powers with the Lok Sabha. No ordinary bill can become an Act without its approval, in case of disagreement between the two House on an ordinary, bill, the President can summon a joint sitting and decide the fate of the bill.

Financial Functions:
The House remains subordinate to the Lok Sabha in matters of money bills. No money bill can be introduced into Rajya Sabha. When a bill after approval in the Lok Sabha is sent to the Upper House for approval within a period of 14 days. The House can’t amend the money bills. It merely records its affirmation and the bill is presumed to be passed.

Executive Functions:
The Rajya Sabha cannot exercise effective control over the union government. It can’t pass a no-confidence motion against the ministry nor it can compel the ministry to resign. The ministers remain collectively responsible to the Lok Sabha. It can only raise questions and introduce motions putting the Govt, into trouble.

Amendment of the Constitution:
The Council of States participates in the amendment of the constitution. It can initiate proposals of amendment and without its approval, no portion of the constitution can be amended.

Electoral Power:
The members of the Rajya Sabha do participate in the election of the President & Vice-President of India. They also elect the Deputy Chair Person of the House and Parliamentary committees.

Judicial Powers:
The House shares equal authority with the Lok Sabha in the impeachment of the President. It also approves proposals relating to the removal of Judges of the Supreme Court and High Court.

Special Powers and Utility:
Rajya Sabha is a weaker chamber but It is not powerless. It enjoys certain special powers like;

• Approval of emergency proclamations.
• Initiating proposals for the removal of Vice-President.
• Requesting Parliament under Art-249 to make law on items of state list in the national interest and
• Initiating a proposal for the increase or decrease of posts under the cadre of All India Services.

Utility:
Rajya Sabha is a permanent chamber and it renders useful service to Parliament when Lok Sabha is dissolved. It is a House of elderly statesmen and administrators who contribute their experience toward the promotion of national interests. It relieves the burden of Lok Sabha. It defends the interests of federal units. It represents the diverse interests of the nation.  It plays a vital role as a revisory chamber. It organizes public opinion on important issues interposing delay. Therefore it can’t be considered a superfluous chamber.

Question 9.
Discuss how the Union budget is passed in the Parliament of India.
Answer:
A budget is the annual financial statement of the estimated income and expenditure of a nation. Before, the end of financial year it is the responsibility of the Union Govt. to pass the budget. The Union Finance Ministry prepares the budget and after approval of the ministry, it is introduced into the Lok Sabha with the prior permission of the President.

The Annual Budget is divided into two parts,

• Railway Budget.
• General Budget.

The Railway Minister introduces the railway budget and after 2 to 3 days the Finance Minister presents the General Budget to the Lok Sabha.

Introduction of Budget:
The Finance Minister presents the budget in the last week of February on a fixed date. While introducing the budget, he. makes a budget speech outlining die financial plans and programs of the Govt, for the ensuing year.

Budget Reactions:
After the introduction, each member is given a copy of the budget to go through the details.

General Discussion:
After 3 to 4 days after the introduction, a general1 discussion takes place. The Govt, deferred’s fiscal policies against the criticism of the opposition.

Consideration by Standing Committees:
There are 17 standing committees to review add analyze the details of the general budget. These committees play an active role in the approval of the budget. The recommendation of these committees is put into discussion in the Lok Sabha.

Voting on Demand for Grants:
Just after the general discussion voting on Demand for Grants takes place. The departmental expenditure of different departments is discussed and then put to vote. The Speaker fixes the date and time of such discussion- for each department. If any of the demand is rejected in the House then Govt has to resign.

Passing of Appropriation Bill:
After voting, on Demand for Grants the Appropriation Bill is prepared to assemble the demands passed by the House along with the expenditure charged” upon the Consolidated Fund of India. This Appropriation Bill is presented to the Lok Sabha and it passes the same stages as any other money bill. With the passage of the Appropriation Bill, the demands of expenditure of different departments are sanctioned.

Passing of Finance Bill:
The Finance Bill contains all proposals for taxation and it is presented to the House after the enactment of the Appropriation Bill. It also goes through the same procedure as in the case of a money bill. The Rajya Sabha is given a period of 14 days to approve it. After the passage of the Finance Bill, it is put to the President for signature. It marks the approval of the budget.

Vote on Account:
If for any reason the budget can’t be passed by 31st March the Govt has to seek a Favourable vote from the Parliament to incur necessary expenditures. This adhoc permission is called Vote on Account. The entire budgetary process takes a period of 75 days.

Question 10.
Discuss the organization and functions of the Odisha Legislative Assembly.
Answer:
The State Legislature in Odisha is unicameral and the Lower House is called Legislative Assembly or Vidhan Sabha. It is a representative assembly whose members are elected directly by the citizen voters of the state.

Composition:
The Odisha Legislative Assembly is composed of 147 members elected directly by the citizens on the basis of the universal adult franchise. The Constitution provides that out of seats of the State Legislative Assembly. 34 have been reserved for ST and 22 for SC candidates.

Qualification of the Members:
There are certain qualifications of the members of the State Legislative Assembly, which are as follows:

• He must be a citizen of India.
• He must have completed at least 25 years of age.
• He must not have occupied any other office of profit either under the State Government or the Central Government.

Term:
The term of the Legislative Assembly is five years. But before the completion of the term the House may also be. dissolved by the Governor on account of the failure of the political machinery of the state. Again the term of the House may also be extended another year in the time of emergency.

Functions: The various, functions of the State Legislative Assembly are discussed below.

Legislative Functions:
Formulation of laws is the primary responsibility of the legislature and the legislative assembly is the lower representative House of the citizens exercises relatively greater power in the formulation of laws. No law would be there without the knowledge of the State Legislative Assembly. All the laws relating the finances should alone be introduced in the state Legislative Assembly.

With regard to non-financial matters, the state Legislative Assembly enjoys comparatively a comfortable position. The State Legislature is entitled to formulate laws on the State list concurrent list So the legislative assembly possesses a greater role in the enactment of the laws.

Executive Functions:
The State Legislative Assembly controls the ministry. The executive collectively remains responsible and answerable to the state legislature. The ministers are selected out of the legislature. The Legislative Assembly can put the question to the ministers for their actions and if the legislature loses its faith in the executive it may initiate a no-confidence motion against the Council of Ministers by which the Council of Ministers goes out of office.

Judicial Functions:
The state Legislative Assembly also performs certain judicial functions. Particularly it acts as a judge with regard to the consideration of no-confidence motions and impeachment motions.

Financial Functions:
The Legislative Assembly being the House of popular representatives exercise absolute power over the state treasury. No single paise can be spent without the knowledge of the State Legislative Assembly. The Assembly finalizes the budget, i.e, the annual income and expenditure statement of the revenue administration of the state.

It may pass, reduce, or reject the demands for grants made in the budget. Any legislative proposal for finance must be approved by the state. The State Legislative Assembly must acknowledge all the items of expenditure other than the expenditure raised from the Consolidated Fund of India.

Electoral Function:
The Legislative Assembly also performs certain electoral functions. It participates in the election of the Speaker of the House and elects the representatives to the Council of States. The members of the State Legislative Assembly are also the members of the electoral college which participate in the election of the President of India. So the Legislative Assembly participates in the election of the President of India.

Constituent Function:
Normally the State Legislative Assembly possesses no or little power with regard to the amendment of the Constitution of India. All policy initiatives arc initiated by the Union Parliament and approved by it. But the amendments related to the election of the President of India, High Courts the representation of the States in the Parliament, and Article-368 of the Constitution, all require the ratification of at least one-half of the State, Legislatures.

Question 11.
Discuss the Composition and Functions of the State Legislative Council.
Answer:
In those states where the Legislature is bi-cameral in nature, the Upper House is called the State Legislative council or the Vidhan Parishad the lower house is the Legislative Assembly or the Vidhan Sabha. The State Legislative Council is a permanent House. Unlike the State Legislative Assembly, the members of the State Legislative Council are not directly elected by the people.

Composition:
The members of the State Legislative Council are not directly elected by the people rather its members are elected variously. The Constitution provides that the members of the State Legislative Council should not exceed the l/3rd strength of the legislative assembly. So the maximum strength of the Legislative Council should hot exceed 160 and it must not be less than 40.

There are elected as well as nominated members of the State Legislative Council. There are the following kinds of members in the State Legislative Council what the Constitution provides. One-third of its members shall be elected by the members of various local bodies i.e., Municipalities, District Boards, and other Local Bodies. One-twelfth of its members shall be elected by university graduates of not less than three years standing.

One-twelfth of its members shall be elected by the teachers not less than the standard of secondary schools. One-third of its members shall be elected by the members of the Legislative Assembly. And finally, one-sixth of its members shall be nominated by the Governor from among the persons having knowledge in the field of literature, art, or any other specialized field.

Qualification of the Members:
The Constitution provides that the members of the State Legislative Council should possess the following qualifications. ,

• He must be a citizen of India.
• He must have completed 30 years of age.
• Thirdly, the members should not hold any office of profit either under the State Government or the Central Government. If he holds such an office he must vacate at the time of election.

Tenure:
Ordinarily, the members of the State Legislative Council are elected for a period of six years. But the State Legislative Council is a permanent House and it is not subject to any dissolution. One-third of its members retire in every two years.

Powers and Functions of the Legislative Council:
The legislative Assembly which is the popular House enjoys comparatively more power than the State Legislative Council. However, it would not be assumed that the State Legislative Council doesn’t possess any power.

The following are the various powers and functions of the State Legislative Council.

Legislative Functions:
The State Legislature consists of the Legislative Assembly, the Legislative Council, and the Governor. So the Legislative Council of each and every state, where there is a bicameral legislature, participates in the affairs of formulation of laws. All kinds of bills, except money bill, may be introduced into the State Legislative Council. Again all bills which are introduced and passed by the Legislative Assembly must be sent to the Legislative Council for its assent.

The Legislative Council may or may not give its assent or may return the bill for reconsideration of the bill. But after reconsideration, the council must give its assent. But in case of any bill is rejected by the council for the second time and one month has been completed it would be presumed that the bill has been passed by the Legislative Council.

Executive Functions:
The State Legislative Council also possesses some executive or administrative functions. Unlike the Legislative Assembly, the Legislative Council cannot pursue a no-confidence motion against the Council of Ministry but it can ask questions to the minister regarding the administration of the state. It can pass also resolutions concerning the administration of the state.

Financial Functions:
The State Legislative Council enjoys comparatively less financial power than the Legislative Assembly. The Constitution provides that no financial bill can be introduced in the Legislative Council. All sorts of money bills are first introduced in the State Legislative Assembly and it can be sent to the Council for its assent. The Legislative Council may suggest change but that may or may not be accepted by the legislative assembly. The council may delay the passing of money bills up to maximum 14 days.

From the above discussions, it has become clear that the State Legislative Council enjoys less power in comparison to the State Legislative Assembly: The State Legislative Council is not only the second chamber but also the secondary chamber of the state legislature. It can be termed as the House of elders and its function is to advise and suggestions to the younger who are, strong, active and efficient. The Legislative Assembly can make or unmake everything by taking into confidence the council.

The state Legislative Council is a chamber that has been there with a view to ensuring checks The significance of the State Legislative Assembly is that it is a body of professionals having technical knowledge which represents various functional interests. Its debates are marked by higher intensity, in-depth knowledge and broad political insight. Although it has it’s technical side yet, its hand had been tied with regard to powers in comparison to State Legislative Assembly.

Question 12.
Examine the relationship between the two Houses of the State Legislature.
(Or)
Discuss the relationship between the Legislative Assembly and the Legislative Council of State.
Answer:
The Constitution of India has provided for bicameralism at the state level, though there is bicameralism only in five states. The lower chamber is called the Legislative Assembly of Vidhan Sabha while the upper chamber is known as the Legislative Councilor Vidhan Parishad. The Assembly is the popular chamber that exercises supremacy over the upper chamber.

Organization:
The Assembly has a- membership which is three times that of the membership of the Legislative Council. The Assembly is the Lower House whose members are elected directly for a term of five years. The Legislature Council is a secondary chamber whose members are elected indirectly for a term of six years.

Functions:
Not only in the organization but also in powers and functions the Lower House enjoys a place of primacy.

As regards ordinary bills:
Ordinary bills can be introduced into either House of the. The legislature and unless passed in both of them cannot become an Act. An ordinary bill passed by the Assembly when submitted to the Legislative Council. The latter can reject or approve it within three months. If the period is over even without the approval of the council the bill is supposed to have been passed in the Upper House.

‘If returned it must be’ approved within one month, Thus the Upper House can delay an ordinary bill at best for four months. It cannot prevent any bill from passing in the Assembly. But, if a bill initiated in the upper chamber is opposed by the tower one then the future of the bill is killed.

As regards money bills:
No money bill can be introduced into the Legislative Council. Only when a money bill is passed in the Lower House is submitted to the upper one, the House is given a time of 14 days to give its opinion on the bill. If the period elapses then the bill is supposed to have been passed. The Council can not amend money bills or proposals of taxation.

Control over executive:
The Lower House of the legislature exercises controls over the state council of ministers. The ministers remain accountable to the Assembly and if necessary it can pass a vote of no-confidence and force the ministry to resign, But the Legislative Council has no such control over the executive. It cannot drive the ministers out.

Other Spheres:

• The Assembly participates in the election of the President of India, but the council does not.
• The Assembly can participate in constitutional amendments, but the council can’t.
• The debates and deliberations of the Lower House attract public attention, but no such attention is given to the discussions of the Lower House.
• Therefore, the Legislative Council is considered not only a second chamber but also a secondary one. It does not obstruct the Assembly in its business.

Odisha State Board CHSE Odisha Class 11 Political Science Solutions Unit 4 Constitution at Work-I Objective Questions and Answers.

CHSE Odisha 11th Class Political Science Unit 4 Constitution at Work-I Objective Questions

Multiple Choice Questions With Answers

Question 1.
How many members are there in the election commission of India?
(a) one
(b) Two
(c) Three
(d) Five
Answer:
(c) Three

Question 2.
Which article of the constitutions of India deals with Election Commission?
(a) Art. 248
(b) Art. 268
(c) Art. 348
(d) Art. 324
Answer:
(d) Art. 324

Question 3.
How many members were there in the Election Commission of India where the Indian Constitution came into force?
(a) one
(b) two
(c) three
(d) four
Answer:
(a) one

Question 4.
In which year did membership of the election commission increase?
(a) 1977
(b) 1981
(c) 1985
(d) 1989
Answer:
(d) 1989

Question 5.
Who appoints the members of the Election commission?
(a) President of India
(b) Prime minister of India
(c) Parliament of India
(d) Council ministers
Answer:
(a) President of India

Question 6.
When the members of the election commission retire from service?
(a) At the age of 60 years
(b) At the age of 65 years
(c) At the age of 62 years
(d) At the age of 70 years
Answer:
(b) At the age of 65 years

Question 7.
Which type of representation is never seen in a democracy?
(a) Propositional Representation
(b) Universal suffrage
(c) Minority representation
(d) Communal representation
Answer:
(d) Communal representation

Question 8.
To which of the following offices the Election Commission does not conduct polls?
(a) President & Vice President
(b) Loksabha & Rajya Sabha
(c) Legislative Assembly Members
(d) Members of Municipality
Answer:
(d) Members of Municipality

Question 9.
From which year electronic voting. machine (EVM) was introduced in General Election?
(a) January 15, 1990
(b) March 15, 1989
(c) April 15, 1996
(d) February 15, 1998
Answer:
(b) March 15, 1989

Question 10.
When the campaigning for election ends?
(a) 24 hours before the poll
(b) 48 hours before the poll
(c) 24 hours before the end of the poll
(d) 48 hours before the end of the poll
Answer:
(d) 48 hours before the end of the poll

Question 11.
What percentage of vote does a candidate need to secure so that his security deposit will not be forfeited?
(a) One third
(b) One fourth
(c) One fifth
(d) One-sixth of the valid votes.
Answer:
(d) One-sixth of the valid votes.

Question 12.
Who among the following is a supporter of universal suffrage?
(a) J.S. Mill
(b) II.J. Laski
(c) Sir Henry Maine
(d) Blantschli
Ans.
(b) II.J. Laski

Question 13.
Electoral reforms have been introduced on the recommendation of which commission?
(a) Savalwal Committee
(b) Sindhi Committee
(c) Dinesh Goswamy Committee
(d) Virappa moilee Committee
Answer:
(c) Dinesh Goswamy Committee

Question 14.
On whose name the bills are introduced into the Parliament?
(a) President of India
(b) Prime Minister
(c) Speaker
(d) Departmental Minister
Ans.
(a) President of India

Question 15.
What is the tenure of Lok Sabha?
(a) five years
(b) four years
(c) six years
(d) none of these
Answer:
(a) five years

Question 16.
Who nominates the 12 members of Rajyasabha
(a) President of India
(b) Chairman of Rajya Sabha
(c) Members of Rajya Sabha
(d) Prime Minister
Answer:
(a) President of India

Question 17.
Who initiates money bill in the Lok Sabha?
(a) President of India
(b) Prime Minister
(c) Finance Minister of India
(d) Speaker of Lok Sabha
Answer:
(c) Finance Minister of India

Question 18.
How many seats are reserved for SC and ST in the Lok Sabha?
(a) 79 and 40
(b) 75 and 51
(c) 34 and 22
(d) 85 and 47
Answer:
(a) 79 and 40

Question 19.
What is the term of office of a Member of the Rajya Sabha?
(a) 5 years
(b) 6 years
(c) 4 years
(d) permanent
Answer:
(b) 6 years

Question 20.
Through which motion the President can be removed from office?
(a) No – confidence motion
(b) Censure motion
(c) Impeachment
(d) Exit motion
Answer:
(c) Impeachment

Question 21.
What is the minimum age qualification for membership of LokSabha?
(a) 25 years
(b) 30 years
(c) 35 years
(d) 21 years
Answer:
(a) 25 years

Question 22.
How many states of India have bicameral legislature?
(a) five
(b) six
(c) ten
(d) seven
Answer:
(a) five

Question 23.
Which one is not a function of the legislature?
(a) Enactment of Law
(b) Amendment of the Constitution
(c) Preparation of budget
(d) Ventilation of public grievances
Answer:
(c) Preparation of budget

Question 24.
How the Legislature controls the executive?
(a) By passing a no-confidence motion
(b) By putting questions to the ministers
(c) By initiation cut motion
(d) All the above
Answer:
(d) All the above

Question 25:
Which is the most powerful organ of Govt, in India?
(a) Executive
(b) Parliament
(c) Supreme Court
(d) Bureaucracy
Answer:
(b) Parliament

Question 26.
Which is the exclusive power of Rajya Sabha?
(a) To initiate money bills
(b) To initiate proposals for the removal of the President
(c) To initiate proposals for the removal of the Vice President
(d) To initiate proposals for the removal of the comptroller Auditor-General
Answer:
(c) To initiate proposals for the removal of the Vice President

Question 27.
On whose recommendation posts under All India Services can be increased or decreased?
(a) Lok Sabha
(b) Rajya Sabha
(c) Supreme Court
(d) Cabinet Sub-Committee
Answer:
(b) Rajya Sabha

Question 28.
What constitutes the Quorum of the LokSabha?
(a) l/5th of the total membership
(b) l/6th of the total membership
(c) l/10thof-total membership
(d) l/20th of the total membership
Answer:
(c) l/10thof-total membership

Question 29.
Who presides over the joint sitting of the Parliament?
(a) President of India
(b) Prime Minister of India
(c) Vice President
(d) Speaker of Lok Sabha
Answer:
(d) Speaker of Lok Sabha

Question 30.
What is the maximum strength of a Legislative Assembly?
(a) 485
(b) 450
(c) 500
(d) 600
Answer:
(c) 500

Question 31.
The Union Council of Ministers is responsible to
(a) Lok Sabha
(b) Rajya Sabha
(c) Union Parliament .
(d) President of India
Answer:
(a) Lok Sabha

Question 32.
Who prorogues the session of Parliament?
(a) Speaker of Lok Sabhas
(b) Prime Minister
(c) President
(d) Vice President
Answer:
(c) President

Question 33.
A money bill is introduced into?
(a) The Lok Sabha
(b) The Rajya Sabha
(c) Into either House of Parliament
(d) Union Cabinet
Answer:
(a) The Lok Sabha

Question 34.
Which House can initiate proposals of amendment?
(a) Lok Sabha
(b) Rajya Sabha
(c) Either Lok Sabha or Rajya Sabha
(d) State Legislative Assembly
Answer:
(c) Either Lok Sabha or Rajya Sabha

Question 35.
The Rajya Sabha is
(a) The Second Chamber of Parliament
(b) The Upper House of Parliament
(c) A Permanent Chamber
(d) All the above
Answer:
(d) All the above

Question 36.
Who acts as a link between the President and Union Parliament?
(a) Prime Minister
(b) Vice President
(c) Home Minister
(d) Speaker of Lok Sabha
Answer:
(d) Speaker of Lok Sabha

Question 37.
Who protects the privileges of members of Parliament?
(a) President
(b) Vice President
(c) Prime Minister
(d) Speaker
Answer:
(d) Speaker

Question 38.
Which is not a duty of the Speaker of Lok Sabha?
(a) To maintain discipline
(b) To interpret the rules of business of the House.
(c) To introduce bills
(d) To certify the money bills
Answer:
(c) To introduce bills

Question 39.
On whose recommendation the Governor dissolves the State Legislative Assembly?
(a) Prime Minister
(b) chief minister
(c) President
(d) State Council of Minister
Answer:
(c) President

Question 40.
On which items the State Legislature can make law?
(a) State List
(b) State List & Concurrent List
(c) Union List and State List
(d) State List and residuary matters
Answer:
(d) State List and residuary matters

Question 41.
How many S.C. and S.T. members are there in the Odisha Legislative Assembly?
(a) 22 and 34
(b) 34 and 22
(c) 32 and 24
(d) 24 and 32
Answer:
(a) 22 and 34

Question 42.
What is the strength of Odisha Vidhan Sabha?
(a) 155
(b) 165
(c) 149
(d) 147
Answer:
(d) 147

Question 43.
How many members represent Odisha in the Lok Sabha?
(a) Ten
(b) Twenty
(c) Twenty one
(d) Twenty-five
Answer:
(c) Twenty one

Question 44.
What is the term of the Legislative Assembly?
(a) five years
(b) six years
(c) one year
(d) four years
Answer:
(a) five years

Question 45.
Out of the 21 seats how many seats are reserved for SC and ST candidates representing Odisha in the Lok Sabha?
(a) 3 and 4
(b) 3 and 5
(c) 4 and 5
(d) 5 and 7
Answer:
(b) 3 and 5

Question 46.
When does the question hour start?
(a) 10 AM to 11 AM
(b) 11 AM to 12 Noon
(c) 12 Noon to 1 PM
(d) 4 PM to 5 PM
Answer:
(d) 4 PM to 5 PM

Question 47.
When the zero-hour starts?
(a) 9AMto 10 AM
(b) 10 AM to 11 AM
(c) 11 AM to 12 Noon
(d) 12 Noon to 1 PM
Answer:
(d) 12 Noon to 1 PM

Question 48.
Out of 147 members in Odisha Vidhan Sabha how many seats are reserved for SC and ST candidates?
(a) 23 and 27
(b) 21 and 25
(c) 23 and 34
(d) 27 and 39
Answer:
(c) 23 and 34

Question 49.
Who presides over the meeting of the Rajya Sabha?
(a) President of India
(b) Vice President
(c) Speaker
(d) Home Minister
Answer:
(b) Vice President

Question 50.
What is the maximum strength of Lok Sabha?
(a) 547
(b) 545
(c) 550
(d) 552
Answer:
(d) 552

Question 51.
When does the financial year start?
(a) January 1st
(b) March 1st
(c) April 1st
(d) June 1st
Answer:
(c) April 1st

Question 52.
Who certifies whether a bill is a money bill or not?
(a) President of India
(b) Speaker of Loksabha
(c) Finance Minister
(d) Prime Minister
Answer:
(b) Speaker of Loksabha

Question 53.
Who convinces the sessions of Parliament?
(a) President of India
(b) Prime Minister
(c) Speaker
(d) Secretary of Loksabha
Answer:
(a) President of India

Question 54.
In which part of the constitution there is mention of the election commission?
(a) Part-VIII
(b) Part – XI
(c) Part – XIV
(d) Part-XV
Answer:
(d) Part-XV

Question 55.
By which amendment Act the voting age of voters is reduced from 21 to 18 years?
(a) 59th
(b) 60th
(c) 61st
(d) 62nd
Answer:
(c) 61st

Answer the following questions in one word or digit

Question 1.
Who was the first Chief Election Commissioner of India?
Answer:
Sukumar Sen

Question 2.
Who is responsible for conducting a free and fair pool in India?
Answer:
Election Commission of India.

Question 3.
From which year EVMs are being used in Elections?
Answer:
14th March 1989

Question 4.
How many proposers and seconders sign the presidential nomination?
Answer:
50 and 50

Question 5.
For which posts direct election is held in India?
Answer:
Membership of Loksabha and Vidhansabha

Question 6.
For which posts indirect election is held?
Answer:
President, Vice-President’ & Rajya Sabha members.

Question 7.
From which date the voting age of voters is reduced from 21 to 18 years?
Answer:
21st March 1989.

Question 8.
What is the tenure of office of the members of the Election Commission?
Answer:
6 yrs or attaining 65 yrs which is earlier.

Question 9.
Which chamber of the legislature safeguards the interests of a federation?
Answer:
Upper Chamber

Question 10.
Which one is the primary organ of government?
Answer:
Legislature

Question 11.
The council Ministers in a parliamentary system remain answerable to which house of the legislature?
Answer:
Lower

Question 12.
From which word has the term Parliament has been derived?
Answer:
Latin word ‘Parle’

Question 13.
How many nominated members are there in the Rajya Sabha?
Answer:
12

Question 14.
How many members of Loksabha represent the Union Territories?
Answer:
13

Question 15.
Besides the Union List on which list can, the Parliament make law during normalcy?
Answer:
Concurrent List

Question 16.
By which power, the President can return an ordinary bill back to the Parliament for reconsideration?
Answer:
Suspensive Veto

Question 17.
Who gives the certificate to a money bill?
Answer:
Speaker

Question 18.
Who presides over the Rajya Sabha?
Answer:
Vice President

Question 19.
Who elects the members of the Rajya Sabha?
Answer:
Members of Vidhan Sabha

Question 20.
When was the first election to the Parliament in India held?
Answer:
1952

Question 21.
Who reads out the Oath of office and secrecy to the members of the Rajya Sabha?
Answer:
Chairman or Vice Chairman of the house

Question 22.
Which house of parliament can initiate proposals for the removal of the Vice President?
Answer:
Upper House

Question 23.
Which house of parliament initiates A confidence motion against the union council ministers
Answer:
LokSabha

Question 24:
For how many days can the Rajya Sabha detain a money bill?
Answer:
14 days.

Question 25.
Who acts is the leader of Lok Sabha?
Answer:
Prime Minister

Question 26.
Who acts as a link between the Parliament and President?
Answer:
Speaker

Question 27.
Who introduces the Annual Budget into the Lok Sabha?
Answer:
Finance Minister of India

Question 28.
For how many days the Rajya Sabha can delay an ordinary bill?
Answer:
Six Months

Question 29.
What is the hour just after the question hour is called?
Answer:
Zero hour

Question 30.
Who exercises casting vote in case of a tie?
Answer:
Speaker

Question 31.
Can there be a joint sitting for a constitutional amendment bill?
Answer:
No

Question 32.
Which constitutional authority can enhance the jurisdiction of the Supreme Court?
Answer:
Parliament

Question 33.
When the Lok Sabha is dissolved who approves the emergency proclamations?
Answer:
Rajya Sabha

Question 34.
Who Presides over the Lok Sabha during the absence of the Speaker?
Answer:
Deputy Speaker

Question 35.
What is the maximum limit of expenditure of a member of Lok Sabha during elections?
Answer:
25 lakhs

Question 36.
What is the maximum election expenditure limit of a member of Vidhan Sabha?
Answer:
15 lakhs

Question 37.
In which court of law the electoral disputes between the President and Vice President are settled?
Answer:
Supreme Court of India

Question 38.
In which court of law the electoral disputes of MPs and MLAs are settled?
Answer:
High Court

Question 39.
What is the amount of security deposit a presidential candidate must pledge?
Answer:
Rs. 15,000/

Question 40.
Who reads the oath of office of the member of parliament?
Answer:
President of India or his representative

Question 41.
What is the amount of the MP LAD fund?
Answer:
Rs.5 crores

Question 42.
What is the amount of the MLA LAD fund?
Answer:
One crore

Question 43.
How many members are there in the Rajya Sabha?
Answer:
233+12 = 245

Question 44.
When does the financial year start?
Answer:
April 1st

Question 45.
By which motion, the Union Council of ministry can be removed?
Answer:
No confidence motion.

Question 46.
Who casts the casting vote in case of a tie in the Loksabha?
Answer:
Speaker of Loksabha

Question 47.
What is the monthly salary of the Vice President?
Answer:
Rs. 1,25,000

Question 48.
What is the constitutional name of the budget?
Answer:
Annual Financial Statement

Fill in the blanks

1. Free and fair elections are indispensable for a ____ state.
Answer: Democracy.

2.The Indian constitution under Art._____ provides for an election commission.
Answer: Art. 324.

3. The membership of the election commission has increased to three from _____ general election.
Answer: Xth.

4. The tenure of office of the election commission is ____ years.
Answer: Six.

5. The members of the election commission retire at the age of ______ years.
Answer: 65.

6. The Chief Election Commissioner can be removed from office on the ground of _____.
Answer: Proved misbehavior and incapacity.

7._____ removes the members of the Election Commission?
Answer: President.

8. Seats have been reserved for the SC and STs in the Loksabha under Art. ______
Answer: Art. 330.

9. Under Art. _____ spats have been reserved for SC and ST candidates in the Vidhansabha.
Answer: Art. 332.

10. The president nominates two members from Anglo Indian Community to the Loksabha under Art._______
Answer: Art. 331.

11.______ Allots symbols to different political parties.
Answer: Election Commission.

12. Art. _____ provides for a joint sitting of the parliament.
Answer: Art. 108.

13. The Legislative Council can be created or abolished under Art. ______ of the constitution?
Answer: Art. 169.

14.Art._____ provides for consolidated fund of India.
Answer: Art. 266.

15. The constitution under Art. ______ provides for the emergency funds of India.
Answer: Art. 267.

16.______ sanctions fund out of the contingency fund of India.
Answer: President of India.

17. The parliament consists of the Loksabha. The Rajyasabha and the _____.
Answer: President of India.

18. Odisha sends ____ members to Rajyasabha.
Answer: 10.

19. The maximum strength, of Loksabha, is ____.
Answer: 552.

20. The maximum strength of the Rajya Sabha is _____.
Answer: 250.

21._____ members from Odisha represent the Parliament.
Answer: 31.

22. The members of Rajya Sabha are ____ elected.
Answer: Indirectly.

23. The minimum age of a member of Lok Sabha is _____ years.
Answer: 25 years.

24. A member of the Rajya Sabha must be above _____ years of age.
Answer: 30.

25. One-third members of the Rajya Sabha retire every ____ years
Answer: Two.

26. Rajya Sabha can detain an ordinary bill for not more than ______.
Answer: Six months.

27. Money bills are introduced into the ______.
Answer: Lok Sabha.

28.No Money Bill can be introduced into the Parliament without ______.
Answer: Prior permission of the President.

29.The Lok Sabha represents ___SC and ___ST candidates.
Answer: 79 & 40.

30. ______ is the Presiding Officer of the Lok Sabha.
Answer: Speaker.

31. The Lok Sabha is summoned for at least a ____ year.
Answer: Twice.

32. The ______ casts his vote in case of a tie.
Answer: Speaker.

33. So far National Emergency has been declared in India for _____ times.
Answer: Three.

34. The Lok Sabha can be dissolved by the _____ on the advice, of the-Prime Minister.
Answer: President.

35. The _____ can initiate proposals for the removal of the Vice-President.
Answer: Rajya Sabha.

36.No confidence motion is introduced only in the ______ house of parliament.
Answer: Lower.

37. Indian Parliament is ______.
Answer: Bicameral.

38._____ is the federal chamber of the Union Parliament.
Answer: Rajya Sabha.

39. The last National Emergency in India is declared on the ground of ______.
Answer: Internal disturbance.

40.______ is the final authority to decide on the disqualification of a member.
Answer: Speaker.

41. The President nominates ______ members from the Anglo-Indian Community to the Lok Sabha if the said community has not been adequately represented in the House.
Answer: Two.

42. The Indian President exercises only _____ veto power.
Answer: Suspensive.

43. The Quorum of the Lok Sabha is ______ of the total membership.
Answer: One-tenth.

44._____ was the only Prime Minister of India who never faced the Parliament.
Answer: Charan Singh.

45._____ members of the Rajya Sabha are elected.
Answer: 238.

46. The Union Territories represent ______ members to the Upper House.
Answer: Six.

47. Proposals of the constitutional amendment are initiated by _______ house of parliament.
Answer:
Either.

48. Under Art _____the Rajya Sabha can pass a resolution and empower the Parliament to create or abolish All India Services.
Answer: 249.

49. A legislative proposal before final approval is known as _______.
Answer: Bill.

50. All money bills are _______ bills.
Answer: Public.

51. The President of India can not withhold assent to a ______bill.
Answer: Money.

52. There is a bicameral legislature in ______ states of India.
Answer: Five.

53. The state legislature in Orissa is ______.
Answer: Unicameral.

54. The second chamber of the State Legislature in India is known as _____.
Answer: Vidhan Parishad.

55. The Presiding officer of the state legislative council is known as ______.
Answer: Chairman.

56. A member of the Legislative Council must be above years of age.
Answer: 30.

57. The legislative Council can delay an ordinary bill for a maximum period of ______.
Answer: Four months.

58. A member of the State Legislative Assembly must be not less than _____ years of age.
Answer: 25.

59. The Speaker of the Legislative Assembly determines the agenda in consultation with the ______.
Answer: Chief Minister.

60. The maximum strength of the Odisha Legislative Assembly is ______.
Answer:147.

61.Out of 147 members _____ seats have been reserved for the SC and ______seats for ST candidates.
Answer:23 and 34.

62. Provision for the creation of abolition of the Legislative Council has been mentioned under Art. ______ of the Constitution.
Answer:169.

63. The members of the State Legislative Council are ______ elected.
Answer: Indirectly.

64. The second chamber of the state legislature can retain money bills for ______ days.
Answer:14 days.

65._____ legislature is suitable for a small & poor country.
Answer: Unicameral.

66. The term of the Indian Parliament is ______.
Answer:5 years.

67. There are ______ Scheduled Caste and Scheduled Tribe members in the Lok Sabha from Odisha.
Answer:3 and 5.

68. There ____ SC and _____ ST members in the Lok Sabha.
Answer:79 and 40.

69. The Speaker of Lok sabha gets a monthly salary of _____ rupees.
Answer:55,000.

70. Odisha Vidhansabha is _____ in structure.
Answer: Unicameral.

71. The second chamber of the state legislature is called ______.
Answer: Vidhan Parishad

72. A _______ legislature is useful for a federal state.
Answer: Bicameral.

73. Under Art. ______ the Rajya Sabha can recommend the creation of posts for All India Services.
Answer:312.

74. The Legislative Council should not have less than _____ members.
Answer:40.

75. Money bills are introduced into the Lok Sabha as per Art. ______.
Answer:109 .

76. Railway budget is being introduced separately from the year_______.
Answer:1925.

77. Art. ______ provides for a vote on Account.
Answer:116.

78.Art._____ of the constitution deals with state legislature.
Answer:168.

79. The minimum age required for membership in Vidhansabha is _____.
Answer:25 yrs.

80. Universal franchise is extended under Art. ______.
Answer: Art. 326.

81. Anybody contesting for membership in Lok Sabha has to deposit _______ rupees as a security deposit.
Answer:10,000.

82. Anybody contesting for a seat in the Vidhan Sabha has to deposit Rs. _______ as security.
Answer:5000.

Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Ex 3(b) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 3 Relations And Functions Exercise 3(b)

Question 1.
Let A = {a, b, c }, |B| = {1, 2}
(a) Determine all the relations from A to B and determine the domain, range, and inverse of each relation.
(b) Determine all the relations from B to A.
(c) Is there any relationship that is both a relation from A to B and B to A? How many?
(d) Of all the relations from A to B, identify which relations are many ones, one-many, and one-one and represent this diagrammatically.
Solution:
(a) A = {a, b, c}, B = {1, 2}
∴ A × B = {(a, 1), (a, 2), (b, 1), (b, 2), (c, 1), (c, 2)}
∴ |A × B| = 6
∴ |P(A × B)| = 2⁶ = 64
∴ There are 64 relations from A to B as any subset of A × B. The domain of these relations is any subset of A. The inverse of these relations is any subset of B × A.
(b) There are 64 relations from B to A as any sub-set of B x A is a relation from B to A.
(c) Φ is the only relation that is from A to B and from B to A.
(d) Some many-one relations are {(a, 1), (b, 1), (c, 1), (b, 2) (c, 2)}, {(a, 2), (b, 2), (c, 2)}.

Question 2.
Are the following sets related?
(i) Φ from A to B.
(ii) A × B from A to B.
(iii) A × Φ from A to Φ.
(iv) Φ × B from Φ to B.
(v) Φ × Φ from Φ to Φ.
(vi) Φ × C from A to B.
(vii) Φ × Φ from A to B.
Determine the domain range and inverse of each of the relations mentioned above
Solution :
(i) Φ from A to B is a relation.
(ii) A × B from A to B is a relation.
(iii) A × Φ from A to Φ is a relation.
(iv) Φ × B from Φ to B is a relation.
(v) Φ × Φ from Φ to Φ is a relation.
(vi) Φ × C from A to B is a relation.
(vii) Φ × Φ from A to B is a relation.
∴ Domain of Φ i.e. D_Φ = Φ
Range of Φ i.e., R_Φ = Φ
Similarly, D_{A × B} = A, R_{A × B} = β
D_{A × Φ} = Φ, R_{A × Φ} = Φ
D _{Φ × B} = Φ = Φ, R _{Φ × B} = Φ
D _{Φ × Φ} = Φ, R _{Φ × C} = Φ
D _{Φ × C} = Φ, R _{Φ × C} = Φ
D _{Φ × Φ} = Φ, R _{Φ × Φ} = Φ
The inverse of the above relations is Φ, B × A, Φ × A, B × Φ, Φ × Φ, C ×  Φ, and Φ × Φ respectively.

Question 3.
Express the following relations on A to B in each case in tabular form :
(i) A = {n ∈ N : n ≤ 10}, B = N
f = {(x, y) ∈ A × B : y = x²}
Solution:
A = {n ∈ N : n ≤ 10}
= {1, 2, 3,…..10}, B = N
∴ B = {1, 2, 3}
∴ f ={(x, y) ∈ A × B : y = x²}
= {(1, 1), (2, 4), (3, 9)…..(10, 100)}

(ii) A = B = R
∴ f = {(x, y) : x² + y² = 1 and |x – y| = 1}
Solution:
A = B = R
∴ f = {(x, y) : x² + y² = 1 and |x – y| = 1}
={(0, 1) (1, 0), (-1, 0), (0, -1)}

(iii) (1, 2, 3, 4), B = {1, 2, 3, 4, 5}
f = {x, y) : 2 divides 3x+y}
Solution:
A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5}
∴ f = {(x, y) : 2 divides 3x+y}
={(1, 1), (1, 3), (1, 5), (2, 2), (2, 4), (3, 1), (3, 3), (3,5), (4, 2), (4, 4)}

Question 4.
A and B are non-empty sets such that |A| = m, |B| = n. How many relations can be defined from A to B ? (Remember that the number of relations is the number of subsets of (A × B).
Solution:
|A| = m, |B| = n
⇒ |A × B| = mn
A relation is a subset of A to B
∴ Number of relations from A to B
= Number of subsets of A × B
= 2^mn (∴ |A × B| = mn)

Question 5.
Give an example of a relation f such that
(i) dom f – rng f (ii) dom f ⊂ rng f
(iii) dom f ⊃ rng f
(iv) f ∪ f^-1 = Φ
(v) f = f^-1
(vi) f ∪ f^-1 ≠ Φ
Solution:
Let A = { 1, 2, 3} = B
(i) Let f = {(x, y) ∈ A × B : x = y}
∴ Dom f = {1, 2, 3} = Range f

(ii) Let f = {(1, 1), (1, 2), (2, 3)}
on A = (1, 2, 3}
∴ Dom f = {1, 2} ⊂ { 1, 2, 3} = Range f

(iii) Do yourself

(iv) Let f = Φ
∴ f^-1 = Φ = f ∪ f^-1 = Φ

(v) Let f = {(x, y) ∈ A × B; x² + y² = 1}, where A = B = {1, – 1, 0}
= {(1, 0), (0, 1), (-1, 0), (0, -1)}
f^-1 = {(0, 1) (1, 0), (0, -1), (-1, 0)}
=f

(vi) Let f = {(1, 3), (3, 1)} on A = { 1, 2, 3}
∴ f^-1 = {3, 1), (1, 3)},
so that f ∩ f^-1 = Φ.

Question 6.
Let R = {(a, a³) I a is a prime number less than 10}
Fine (i) R, (ii) dom R, (iii) rng R (iv) R^-1 (v) dom R^-1 (vi) rng R^-1
Solution:
R = {(a, a³)} a is a prime number less than 10}
(i) R = {(2, 8), (3, 27), (5, 125), (7, 343)}
(ii) dom R = {2, 3, 5, 7}
(iii) rng R = {8, 27, 125, 343}
(iv) R^-1 = {(8, 2), (27, 3), (125, 5), (343, 7)}
(v) Dom R^-1 = {8, 27, 125, 343} = rng R
(vi) rng R^-1 = {2, 3, 5, 7} = dom R

Question 7.
Let A = {1, 2, 3, 4, 5, 6} and Let R be a relation on A defined by R = {(a, b)} a divides b
Find (i) R, (ii) dom R, (iii) rng R (iv) R^-1, (v) Dom R^-1 (vi) rng R^-1
Solution:
A = {1, 2, 3, 4, 6}
R on A is defined by
R = {(a, b) | a divides b}
(i) R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 6) (2, 2), (2, 4), (2, 6), (3, 3), (3, 6), (4, 4), (6, 6)}
(ii) dom R = {1,2, 3, 4, 6} = A
(iii) rng R = {1, 2, 3, 4, 6} = A
(iv) R^-1 = {(1, 1), (2, 1), (3, 1), (4, 1), (6, 1), (2, 2) (4, 2), (6, 2), (3, 3), (6, 3), (4, 4), (6, 6)}
(v) dom R^-1 = {1, 2, 3, 4, 6} = A
(vi) rng R^-1 = {l, 2, 3, 4, 6} = A

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 4 Trigonometric Functions Ex 4(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 4 Trigonometric Functions Exercise 4(a)

Question 1.
State which of the following is positive.
(i) cos 271°
Solution:
cos 271° is + ve as 271° lies in 4th quadrant.

(ii) sec 73°
Solution:
sec 73° is + ve as sec +ve in the 1st quadrant.

(iii) sin 302°
Solution:
sin 302° is- ve as sin is -ve in the 4th quadrant

(iv) cosec 159°
Solution:
cosec 159° is + ve as 159° lies in 2nd quadrant and cosec is +ve there.

(v) sec 199°
Solution:
sec 199° is – ve as 199° lies in the 3rd quadrant and sec is -ve there.

(vi) cosec 126°
Solution:
cosec 126° is + ve as cosec is +ve in 2nd quadrant.

(vii) cos 315°
Solution:
cos 315° is +ve as 315° lies in 4th quadrant and cos is +ve there.

(viii) cot 375°
Solution:
cot 375° is +ve as 375° lies in 1st quadrant.

Question 2.
Express the following as trigonometric ratios of some acute angles.
(i) sin 1185°
Solution:
sin 1185° = sin\(\left(13 \frac{\pi}{2}+15^{\circ}\right)\)
=(- 1) ^{\(\frac{13-1}{2}\)} cos 15° = cos 15°

(ii) tan 235°
Solution:
tan 235° = tan (180° + 45°) = tan 45°

(iii) sin (- 3333°)
Solution:
sin (-3333°) – -sin 3333°
= – sin\(\left(37 \frac{\pi}{2}+3^{\circ}\right)\)
= – (- 1) ^{\(\frac{27-1}{2}\)} cos 3° =- cos 3°

(iv) cot (- 3888°)
Solution:
cot (-3888°) = – cot 3888°
= – cot\(\left(43 \frac{\pi}{2}+18^{\circ}\right)\)
= – (- tan 18°) = tan 18°

(v) tan 458°
Solution:
tan 458° = tan\(\left(5 \frac{\pi}{2}+8^{\circ}\right)\) = – cot 8°

(vi) cosec (- 60°)
Solution:
cosec (- 60°) = – cosec 60°

(vii) cos 500°
Solution:
cos 500° = cos\(\left(5 \frac{\pi}{2}+50^{\circ}\right)\)
= – (-1) ^{\(\frac{5+1}{2}\)} sin 55° – sin 50°

(viii)sec 380°
Solution:
sec 380° = sec (360° + 20°)
= sec 20°

Question 3.
Find the domain of tangent and cotangent functions.
Solution:
Domain of tan x is R – \(\left\{\frac{(2 n+1) \pi}{2}, n \in Z\right\}\) as tangent is not defined for
x = \(\frac{(2 n+1) \pi}{2}\)
The domain of cot x is R – {nπ, n ∈ Z} as cotangent is not defined for x = nπ.

Question 4.
Determine the ranges of sine and cosine functions.
Solution:
The maximum and minimum values of sine and cosine are 1 and -1, respectively.
∴ Ranges of sine and cosine are [-1, 1].

Question 5.
Find a value of A when cos 2A = sin 3A
Solution:
cos 2A = sin 3A = cos (90° – 3A)
or, 2A = 90° – 3A
or, 5A = 90° or, A = 18°

Question 6.
Find the value of
cos 1°. cos 2° …..cos 100°
Solution:
cos 1° cos 2° …..cos 100°
= 0 as cos 90° is there which is zero.

Question 7.
Find the value of
cos 24° + cos 5° + cos 175° + cos 204° + cos 300°
Solution:
cos 24° + cos 5° + cos 175° + cos 204° + cos 300°
= cos 24° + cos 5° + cos (180° – 5°) + cos (180° + 24°) + cos (360°- 60°)
= cos 24° + cos 5° – cos 5° – cos 24° + cos 60° = cos 60° = 1/2

Question 8.
Evaluate
tan\(\frac{\pi}{20}\).tan\(\frac{3 \pi}{20}\).tan\(\frac{5 \pi}{20}\).tan\(\frac{7 \pi}{20}\).tan\(\frac{9 \pi}{20}\)
Solution:
tan\(\frac{\pi}{20}\).tan\(\frac{3 \pi}{20}\).tan\(\frac{5 \pi}{20}\).tan\(\frac{7 \pi}{20}\).tan\(\frac{9 \pi}{20}\)
= tan 9° tan 27° tan 45° tan 63° tan 81°
= tan 9°. tan 27°. 1 tan (90° – 27°). tan (90° – 9°)
= tan 9° tan 27° cot 27° cot 9°
= (tan 9°. cot 9°) x (tan 27°. cot 27°)
=1 × 1=1

Question 9.
Show that
\(\frac{\sin ^3\left(180^{\circ}+\mathbf{A}\right) \cdot \tan \left(360^{\circ}-\mathbf{A}\right) \sec ^2\left(180^{\circ}-\mathbf{A}\right)}{\cos ^2\left(90^{\circ}+\mathbf{A}\right){cosec}^2 A \cdot \sin \left(180^{\circ}-A\right)}\) = tan³ A
Solution:
L.H.S

= tan³A      (R.H.S)

Question 10.
If A = cos² θ + sin⁴ θ then prove that for all values of θ, 3/4 ≤ A ≤ 1.
Solution:
A = cos² θ + sin⁴ θ =1 – sin² θ sin⁴ θ
or, sin⁴ θ – sin² θ + (1 – A) = 0 …(1)
Eqn. (I) is quadratic in sin² θ.
∴ sin² θ = \(\frac{-b \pm \sqrt{b^2-4 a c}}{2 a}\)
\(=\frac{1 \pm \sqrt{1-4(1-\mathrm{A})}}{2 \times 1}\)
Where a=1, b = – 1, c = 1 – A
∴ sin² θ = \(\frac{1 \pm \sqrt{4 A-3}}{2}\)
We know that sin20 is not negative and lies in [0, 1]
So, \(\sqrt{4 \mathrm{~A}-3}\) ≤ 1
⇒ 4A – 3 ≤ 1 ⇒ 4A ≤ 4 ⇒ A ≤ 1  …(2)
Again, since sin² θ is real,
b² – 4ac must be +ve
i.e., 4A – 3 ≥ 0 ⇒ A ≥ 3/4
∴ From (2) and (3),
We have 3/4 ≤ A ≤ 1          (Proved)

Odisha State Board CHSE Odisha Class 11 Math Solutions Chapter 6 Complex Numbers and Quadratic Equations Ex 6(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 6 Complex Numbers and Quadratic Equations Exercise 6(a)

Question 1.
Multiply (2√-3 + 3√-2) by (4√-3 – 5√-2)
Solution:
(2√-3 + 3√-2) by (4√-3 – 5√-2)
= (2√3i + 3√2i) (4√3i – 5√2i)
= i² (2√3 + 3√2) (4√3 – 5√2)
= – 1(24 – 10√6 + 12√6 – 30)
= – 1(- 6 + 2√6) = 6 – 2√6

Question 2.
Multiply (3√-7 – 5√-2) (3√-2 + 5√-2)
Solution:
(3√-7 – 5√-2) (3√-2 + 5√-2)
= (3√7i – 5√-2i) (3√2i + 5√2i)
= i² (3√7- 5√2) (3√2 + 5√2)
= (- 1)8√2(3√7 – 5√2 )
= – 24√14 + 80

Question 3.
Multiply (√-1 +√-1) (a – b√-1)
Solution:
(√-1 +√-1) (a – b√-1)
= (i + i) (a – bi) = 2i(a – bi)
= 2ai – 2bi² = 2ai + 2b

Question 4.
Multiply (x – \(\frac{1+\sqrt{-3}}{2}\)) (x – \(\frac{1-\sqrt{3}}{2}\))
Solution:
(x – \(\frac{1+\sqrt{-3}}{2}\)) (x – \(\frac{1-\sqrt{3}}{2}\))
= (x + \(\frac{-1-i \sqrt{3}}{2}\)) (x + \(\frac{-1+i \sqrt{3}}{2}\))
= (x + ω) (x + ω²) = x² + ω²x + ωx + ω³
= x² + x (ω ² + ω) + 1 = x² –  x + 1

Question 5.
Express with rational denominator. \(\frac{1}{3-\sqrt{-2}}\)
Solution:
\(\begin{aligned}
& \frac{1}{3-\sqrt{-2}}=\frac{1}{3-\sqrt{2} \mathrm{i}}=\frac{3+\sqrt{2} \mathrm{i}}{(3-\sqrt{2} \mathrm{i})(3+\sqrt{2} \mathrm{i})} \\
& =\frac{3+\sqrt{2} \mathrm{i}}{9-2 \mathrm{i}^2}=\frac{3+\sqrt{2} \mathrm{i}}{9+2}=\frac{3+\mathrm{i} \sqrt{2}}{11}
\end{aligned}\)

Question 6.
\(\frac{3 \sqrt{-2}+2(-5)}{3 \sqrt{-2}-2 \sqrt{-2}}\)
Solution:

Question 7.
\(\frac{3+2 \sqrt{-1}}{2-5 \sqrt{-1}}+\frac{3-2 \sqrt{-1}}{2+5 \sqrt{-1}}\)
Solution:

Question 8.
\(\frac{a+x \sqrt{-1}}{a-x \sqrt{-1}}-\frac{a-x \sqrt{-1}}{a+x \sqrt{-1}}\)
Solution:

Question 9.
\(\frac{(x+\sqrt{-1})^2}{x-\sqrt{-1}}-\frac{\left(x-\sqrt{-1^2}\right)}{x+\sqrt{-1}}\)
Solution:

Question 10.
\(\frac{(a+\sqrt{-1})^3-(a-\sqrt{-1})^3}{(a+\sqrt{-1})^2-(a-\sqrt{-1})^2}\)
Solution:

Question 11.
Find the value of (- i)⁴ⁿ⁺³; when n is positive.
Solution:
(- i)⁴ⁿ⁺³
= (-i⁴ⁿ) (-i)³ = 1(- i³) = – (-i) = i

Question 12.
Find the square root of (a + 40i) + \(\sqrt{9-40 \sqrt{-i}}\)
Solution:

Question 13.
Express in the form of a + ib:
(i) \(\frac{3+5 i}{2-3 i}\)
Solution:

(ii) \(\frac{\sqrt{3}-i \sqrt{2}}{2 \sqrt{3}-i \sqrt{3}}\)
Solution

(iii) \(\frac{(\mathrm{I}+\mathrm{i})^2}{3-\mathrm{i}}\)
Solution:

(iv) \(\frac{(a+i b)^3}{a-i b}-\frac{(a-i b)^3}{a+i b}\)
Solution:

(v) \(\frac{1+i}{1-i}\)
Solution:
\(\frac{1+i}{1-i}\) = \(\frac{(1+i)^2}{2}=\frac{1-1+2 i}{2}\)
= i = 0 + i

Question 14.
Express the following points geometrically in the Argand plane.
(i) 1
Solution:
1 = 1 + i0 = (1, 0)

(ii) 3i
Solution:
3i = 0 + 3i = (0, 3)

(iii) – 2
Solution:
– 2 = – 2 + i0 = (- 2, 0)

(iv) 3 + 2i
Solution:
3 + 2i = (3, 2)

(v) – 3 + i
Solution:
– 3 + i = (- 3, 1)

(vi) 1-i
Solution:
1 – i = (1, – 1)

Question 15.
Show that the following numbers are equidistant from the origin:
√2 +i, 1 + i√2, i√3
Solution:
|√2 + i| = \(\sqrt{(\sqrt{2})^2+1^2}\) = √3
|1 + i√2| = \(\sqrt{1^2+(\sqrt{2})^2}\) = √3
and |i√3| = √3
∴ The points are equidistant from the origin.

Question 16.
Express each of the above complex numbers in the polar form.
Solution:

Question 17.
If 1, ω, ω² are the three cube roots of unity, prove that (1 + ω²)⁴ = ω
Solution:
L.H.S. = (1 + ω²)⁴ = (- ω)⁴ = ω⁴
= ω³ .ω = 1. ω = ω
= R.H.S. (Proved)

Question 18.
(1 – ω+ ω² ) (1 + ω – ω² ) = 4
Solution:
L.H.S. = (1 – ω+ ω² ) (1 + ω – ω² )
= (- ω – ω )(- ω² – ω² ) (∴ 1 + ω + ω² = 0)
= (- 2ω² – 2ω²) = 4ω³ = 4 = R.H.S.

Question 19.
(1 – ω) (1 – ω)² (1 – ω⁴) (1 – ω⁵) = 9
Solution:
L.H.S. =
(1 – ω) (1 – ω)² (1 – ω⁴) (1 – ω⁵)
= (1 – ω) (1 – ω²) (1 – ω) (1 – ω²)
= (1 – ω)² (1 – ω²)²
= {(1 – ω) (1 – ω²)}²
= (1 – ω² – ω + ω³)²
= {3 – (ω² + ω + 1)}²
= (3)² = 9 = R.H.S.

Question 20.
(2 + 5ω + 2ω² )⁶ = (2 + 2ω + 5ω² )⁶ =729
Solution:
L.H.S. = (2 + 5ω + 2ω² )⁶
(2 + 2ω² + 5ω)⁶ = {2(1 + ω² ) + 5ω}⁶
(- 2ω + 5ω)⁶ = (3ω)⁶ = 729ω⁶ = 729
Again, (2 + 2ω + 5ω² )⁶
= {2(1 + ω) + 5ω² )⁶
= (- 2ω² + 5ω² )⁶ = (3ω²)⁶
= 729ω¹² =729
∴ (2 + 5ω + 2ω² )⁶ = (2 + 2ω + 5ω² )⁶ =729

Question 21.
(1 – ω + ω² ) (1 – ω² + ω⁴) (1 – ω⁴ +ω²)  ….to 2n factors = 2²ⁿ
Solution:
L.H.S. = (1 – ω + ω² ) (1 – ω² + ω⁴) (1 – ω⁴ +ω²)  ….to 2n factors = 2²ⁿ
= (- ω – ω) (1 – ω² + ω) (1 – ω + ω² )  ….to 2n factors = 2²ⁿ
= (- 2ω) (- ω² – ω² ) (- ω – ω)  ….to 2n factors = 2²ⁿ
= [(- 2ω)(- 2ω) … to n factors] × [(- 2ω²)(- 2ω²) …. to n factors]
= (- 2ω)ⁿ × (- 2ω²)ⁿ = (4ω³)ⁿ = 4ⁿ = 2²ⁿ
R.H.S. (Proved)

Question 22.
Prove that x³ + y³ + z³– 3xyz
= (x + y + z) (x + ωy + ω²z) (x + yω² + zω)
Solution:
R.H.S. = (x + y + z) (x + ωy + ω²z) (x + yω² + zω)
= (x + y + z) (x + xyω² + zxω + xyω + y²ω³+ yz ω2 + zxω² + yzω⁴ + z²ω³)
= (x + y + z) [x² + y² + z² + xy (ω² + ω) +yz (ω² + ω) + zx(ω² + ω)]
= (x + y + z) (x² + y² + z² – xy – yz – zx)
= x³ + y³ + z³ – 3xyz = L.H.S. (Proved)

Question 23.
If x = a + b, y = aω + b ω², z = aω² + bω show that
(1) xyz = a³ + b³
Solution:
L.H.S. = xyz
= (a + b) (a ω + b ω²) (a ω² + b ω)
= (a + b) (a² ω³ + ab ω² + ab ω⁴ + b² ω³)
= (a + b) {a² + b² + ab(ω² + ω)}
= (a + b) (a² – ab + b²) = a³ + b³ = R.H.S. (Proved)

(2) x² + y² + z² = 6ab
Solution:
L.H.S. = x² + y² + z²
= (a + b)² + (a ω + b ω²)² (a ω² + b ω)²
= a² + b² + 2ab + a² ω² + b² ω⁴ + 2ab ω³ + a² ω⁴ + b² ω² + 2ab ω³
= a² + a² ω² + a² ω + b² + b² ω + b² ω² + 2ab + 2ab + 2ab
= a²(1 + ω² + ω) + b² (1 + ω + ω²) + 6ab
= 0 + 0 + 6ab = 6ab = R.H.S. (Proved)

(3) x³ + y³ + z³ = 3(a³ + b³)
Solution:
L.H.S. = x³ + y³ + z³
= (a + b)³ + (a ω + b ω²)³ + (aω² + b²)³
= a³ + 3a²b + 3ab² + b³ + a³ ω³ + 3a²b² bω² + 3a ωb² ω⁴ + b³ ω⁶ + a³ ω⁶ + 3a² ω⁴bω + 3a ω²b² ω² + b³ ω³
= a³ + a³ + a³ + b³ + b³ + b³ + 3a²b(1 + ω⁴ + ω⁵) + 3ab² (1 + ω⁵ + ω⁴)
= 3a³ + 3b³ + 0 + 0 = 3 (a³ + b³) = R.H.S. (Proved)

Question 24.
If ax + by + cz = X, cx + by + az = Y, bx + ay + cz = Z
show that (a² + b² + c² – ab – bc- ca) (x² +y² + z² – xy – yz – zx) = X² + Y² + Z² – YZ – ZX – XY
Solution:
L.H.S.
= (a² + b² + c² – ab – bc – ca) (x² + y² + z² – xy – yz – zx)
= (a + b ω + cω²) (a + bω² + cω) (x + yω + zω)² (x + yω² + z ω) (Refer Q.No.22)
= {(a + bω + cω²) (x + yω + zω²)} {(a + bω² + cω) (x + yω² + zω)}
= (ax + ayω + azω² + bx ω + byω² + bzω³ + cxω² + cyω³ + czω⁴) × (ax + ay ω² + azω + bxω² + byω⁴ + bzω³ + cxω + cyω³ + czω²)
= {(ax + cy + bz) + (cx + by + az) ω + (bx + ay + cz) ω²} x (ax + cy + bz) + (cx + by + az) ω + (bx + ay + cz) ω²}
= (X + Yω² + Zω) (X + Yω + Zω²)
= X² + Y² + Z² – XY – YZ – ZX (Refer Q. No. 22)
(Where X = ax + cy + bz.
Y = cx + by + az.
Z = bx + ay + cz).