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February 3, 2026

TS Inter 1st Year Economics Study Material Chapter 1 Introduction to Economics

Long Answer Questions

Question 1.Examine the wealth and welfare definitions of Economics?

Answer:

Wealth Definition :

Adam Smith was the first person to give a precise definition of Economics and separate this study from other social sciences. Adam Smith is considered as ‘Father of Economics’. He defined it in his famous book Wealth of Nations’, as “An enquiry into the nature and causes of wealth of nations”. Most of the economists in the 19th century held this view.
J.B. Say states that “The aim of political economy is to show the way in which wealth is produced, distributed and consumed”. The other economists who supported this definition are J.B. Say, J.S. Mill, Walker and others.

The main features of Wealth definition :

1.Acquisition of wealth is considered as the main objective of human activity.
2.Wealth means material things.
3.Human beings are guided by self-interest, whose objective is to accumulate more and more wealth.
4.Economics deals with the activities of wealth production, consumption, preservation and increasing.
Criticism :
The Wealth definition was severely criticised by many writers due to its defects.
1.Economists like Carlyle and Ruskin pointed out that economics must discuss ordinary man’s activities. So they called it as a ‘Dismal Science’.
2.In Adam Smith’s definition, wealth was considered to consist of only material things and services are not included. Due to this the scope of economics is limited.
3.Marshall pointed out wealth is only a means to an end but not an end in itself.
4.This definition concentrated mainly on the production side and neglected distribution side.
Welfare definition :
Alfred Marshall tried to remedy the defects of wealth definition in 1890. He shifted emphasis from production of wealth to distribution of wealth.
According to Marshall, “Political Economy or Economics is a study of mankind in the ordinary business of life. It examines that part of individual and social action which is most closely connected with the attainment and with the use of material requisites of well-being. Thus, Economics is on one side, a study of wealth and on the other and more important side, a part of study of man”.
Edwin Cannan defined it as “The aim of political economy is the explanation of the general causes on which the material welfare of human beings depends”.
In the words of Pigou, “The range of enquiry becomes restricted to that part of social welfare that can be brought directly or indirectly into relation with the measuring rod of money”.

The main features of Welfare definition :

1.Economics as a social science is concerned with man’s ordinary business of life.
2.Economics studies only economic aspects of human life and it has no concern with the social, political and religious aspects of human life. It examines that part of individual and social action which is closely connected with acquisition and use of material wealth for promotion of human welfare.
3.According to Marshall, the activities which contribute to material welfare are considered as economic activities.
4.He gave primary importance to man and his welfare and to wealth as means for the promotion of human welfare.

Criticism :

1.Robbins criticised Marshalls economics as a ’social science’ rather than a human science, which includes the study of actions of every human being.
2.Marshalls definition mainly concentrated on the welfare derived from material things only. But non – materialistic goods which are also very important for the well being of the people. Hence, it is incomplete.
3.Critics pointed out that quantitative measurement of welfare is not possible. Welfare is a subjective concept and relative concept and changes according to time, place and persons.
4.According to Marshall, economics deals with those activities which will promote human welfare. But production of alcohol and drugs do not promote human welfare. Hence, the scope of economics is limited.
5.Another important criticism is that it is not concerned with the fundamental problem of scarcity of resources. According to Robbins the economic problem arises due to unlimited wants and limited resources. These factors are ignored in this definition.

Question 2.Critically examine the scarcity definition of economics?

Answer:

Marshall’s Welfare definition until the publication of Lionel Robbins’ book “An Essay on the Nature and Significance of Economic Science” in 1932. Robbins’ definition brought out the logical inconsistencies and inadequacies of the earlier definitions and formulated his own definition of economics. He has given a more scientific definition of economics. In the words of Robbins, “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses”.

I. Main Features:

1) Human Wants are Unlimited :
The fulfillment of one want gives rise to a number of new wants.
2) Means are Scarce :
The means of a person by which his wants may be satisfied are limited. It leads to economic problems as all wants cannot be satisfied by these limited means.
3) Alternative Uses of Scarce Means :
Resources are not only scare but also have multiple uses. For example electricity can be used in homes and also in industries. A piece of land can be used to produce rice or wheat. If a scarce factor is used for the satisfaction of one want, less of it will be available for other wants. Hence, man has to make a decision regarding the alternative uses of resources.
4) Man has therefore to choose between wants. Problem of choice arises.
II. Superiority of Robbins’ Definition :
Robbins’ definition is superior to the earlier definitions in more than one way. The reasons are given below :
1.It is non-classificatory, as it includes all human activities whether they promote human welfare or not.
2.This is a universally accepted definition. It is applicable to all types of societies, because the scarcity of resources is felt by individuals as well as societies.
3.Robbins’ definition of economics is neutral between ends. Being a positive science it does not pass any value judgments regarding ends.
III. Criticism :
Some followers of Marshall like Durban, Fraser, Beveridge and Wootton have criticised Robbins’ definition by saying that it lacks human touch and that it is personal, neutral and devoid of any normative or ethical element. He does not seek to make economics a study of human welfare. Some of them criticized as “barren scholasticism” while others accused him of “behaviourism”.
1.Even though Robbins criticized Marshall’s welfare definition, he has introduced the welfare concept indirectly in his definition. Therefore, the criticism of welfare definition is equally applicable to it.
2.Another criticism of Robbins’ definition is that this definition does not distinguish between ‘ends’ and ‘means’.
3.Scarcity definition has been criticized by economists as to say “economics is neutral between ends”. But economics cannot be neutral between ends.
4.Robbins made economics a positive science. As per Macfie, “economics is fundamentally a normative science, not merely positive science like chemistry”.
5.Robbins’ definition is not applicable to a dynamic society where changes take place and the problem of scarcity of resources can be overcome with the passage of time.
6.Mrs. Joan Robbinson took serious objection to scarcity of resources. How best you utilize them is more important than the idle resources.
7.Robbins’ scarcity definition neglects the more important problems of growth and stability.

Question 3.Explain the nature and scope of Economics?

Answer:

The nature of economics took a definite shape with the writings of Adam Smith, known as Father of Economics, made a beginning in defining economics and its scope with the publication of his famous book on the wealth of nations. Then a number of economists defined economics and its subject matter in different ways.
The scope of any science explains what the science is concerned with. In economics, traditional economic theory is divided into various branches like consmption, production, exchange, distribution, income, employment, planning and development; where as modem economic theory is divided into two branches viz. micro economics and macro economics.

Economics not only explains things as they are, but also elucidates with what it ought to be. For example, economics discuses the existing level of wages, prices and tax rates in the economy and also suggest how they ought to be. Economics is thus, both a positive and normative science.
Traditional economics is basically concerned with consumption, productio, exchange distribution, income, employment, planning and development.

Consumption :
Consumption can be defined as ‘extracting utility from goods and services’. Consumption is the act of using final goods and services to satisfy current wants. Consumption is the basis for production, exchange, distribution.
Production :
In the economics production is the process of conversion of raw materials into final goods by adding form, place and time utility to the raw materials. The factors which participate in production are called factors of production. They are land, labour, capital and organization.
Exchange :
It is concerned with exchange of a good. A good may be exchanged for another good or for money. Before the evolution of money when barter system was in practice, goods were exchanged for goods. There were many problems in barter system. With the introduction of money, value of every good is expressed in terms of money and can be exchanged for money.
Distribution :
Distribution is another important activity in economics. It explains how goods and services are distributed amongst the various factors of production which are responsible for the production. Each factor of production gets its reward. Various theories are there to determine the factor prices.
Income :
Individuals earn income by participating in various economic activities. The activities are related to production of material goods or the services. Income is a continuous flow. Various concepts of national income and the measuring methods of national income are discussed as part of macro economics for analysing economic growth and development.
Employment :
The level of employment in an economy depends on the demand for consumption goods and demand for investment goods. Full employment means employment of all those who are able and willing to work at.the prevailing wage rates.
Planning and Economic Development :
Economic planning is essential for proper and efficient utilization of the available resources. By economic planning we mean achieving the various predetermined targets systematically in a specific period of time. Economic planning is the method by which an optimum allocation of scarce resources amongst the various sectors is made in order to acheive speedy development of the economy and improve the welfare of the people.

Question 4.Explain the concepts and scope of Micro Economics and Macro Economics?

Answer:

Modem economic theory divided it into two branches, namely (i) Micro Economics (ii) Macro Economics. Ragnar Frisch was the first economist to use the words “Micro and Macro” in economic theory in 1930.
Micro Economics :
The term “Micro Economics” is derived from the Greek word MIKROS’ which means small. Thus, micro economics is the theory of small. It was developed by classical economists like Adam Smith, J.B. Say, J.S. Mill, Ricardo, Marshall etc. It studies about individual units or behaviour of that particular units like individual income, price, demand etc. Micro Economics is also known as partial analysis. It mainly,’ concentrates on the determination of prices of commodities and factors of production. It is also known as “Price theory”. According to K.E. Boulding, “Micro Economics is the study of particular firms, particular households, individual prices, wages, incomes individual industries and particular commodities”.
Shapiro says “Micro Economics has got relation with small segments of the society.

Macro Economics :
The term Macro Economics is derived from the Greek word ‘MAKROS’ which means large. Thus, Macro Economics is the study of economic system as a whole. It was developed by J.M. Keynes. It studies aggregates in the economy like national income, total consumption, total saving and total employment etc. It is also known as Income and Employment theory.

According to Boulding “Macro Economics studies national income not individual income, general price level instead of individual prices and national output instead of individual output”. Macro Economics also studies the economic problems like poverty, unemployment, economic growth, development etc. It also deals with the theory of distribution.

The difference between Micro Economics and Macro Economics :
Micro and Macro Economics are interrelated to each other. Inspite of close relationship between the two branches of economics, fundamentally they differ from each other.

Micro Economics	Macro Economics
1. The word micro derived from the Greek word ‘Mikros’ means “small”.	1. The word macro derived from the Greek word ‘Makros’ which means “large”.
2. Micro Economics is the study of individual units of the economy.	2. Macro Economics is the study of economy as a whole.
3. It is known as ‘Price theory’.	3. It is known as ‘Income and Employment theory’.
4. Micro Economics explains price de-termination in both commodity and factor markets.	4. Macro Economics deals with national income, total employment, general price level and economic growth etc.
5. Micro Economics is based on price mechanism which depends on demand and supply.	5. Macro Economics based on aggregate demand and aggregate supply.

Question 5.Explain the different types of goods?

Answer:

Goods are the articles and services which satisfy a human want like books, pens, cell phones etc. Hence, all tangible things that satisfy human wants are called goods. Goods can be divided into two types : free goods and economic goods.

Free Goods :
Goods which are freely supplied by the nature and without prices are known as free goods. The supply of these goods is always abundantly greater than their demand and therefore, do not have any price. Free goods possess only value in use, but no exchange value. Examples are air, water and sunshine. Now-a-days, some of these also became economic goods due to several reasons and these goods are priced.
Economic goods :
An economic good is any physical object, natural or man made or service rendered that can be commanded a price in a market. They always fall short of the demand for them. These economic goods have both value in use and value in exchange such as pens, books, laptops, etc. Economic goods possess three important characteristics i.e., utility, scarcity, and transferability. Economic goods are also divided into three types, i.e. consumer, product, and intermediary.
Consumer Goods :
A consumer good is an economic good or commodity purchased by households for final consumption. Thus, consumer goods are those goods which directly satisfy human wants. For example fruits, milk, pens, clothes, etc.
Producer or Capital Goods :
Goods which are used in the production of other goods are called producer or capital goods. They satisfy human wants indirectly. For example machines, buildings etc. are capital goods. A good can be classified into consumer good or capital good depending on the nature of its use. For example, when paddy is used for food it becomes a consumer good and when used as seed in cultivation, it becomes a capital good.
Intermediary Goods :
Goods which are under the process of production and semi finished goods are known as intermediary goods. Examples are cement, bricks and steel used as intermediary goods in construction work. The goods which are not yet finished and under different stages of production are known as intermediary goods.

Short Answer Questions

Question 1.Examine the welfare definition of economics?

Answer:

Alfred Marshall raised economics to a dignified status by advancing a new definition in 1890. He shifted emphasis from production of wealth to distribution of wealth (welfare). In the words of Marshall, “political economy or economics is a study of mankind in the ordinary business of life; it examines that part of individual and social action which is most closely connected with the attainment and with the use of the material requisites of well – being. Thus, it is on the one side, a study of wealth and on the other and more important side, a part of the study of man”.

I. Important Features of Welfare Definition :

1.Marshall used the term “Economics” for “Political economy” to make it similar to physics. He assumed that economics must be a science even though it deals with the ever changing forces of human nature.
2.Economics studies only economic aspects of human life and it has no concern with the political, social and religious aspects of life. It examines that part of individual and social action which is closely connected with acquisition and use of material wealth which promotes human welfare.
3.Marshall’s definitions considered those human activities which increased welfare.
4.This definition has given importance to man and his welfare and recognised wealth as a mean for the promotion of human welfare.

II. Criticism:

Marshall’s definition is not free from critics. Robbins in his “Essay on the Nature and Significance of Economic Science” finds fault with the welfare definition of economics.
1.Economics is a human science rather than a social science. The fundamental laws of economics apply to all human beings and therefore, economics should be treated as a human science and not as a social science.
2.Lionel Robbins criticized it as classificatory. It distinguishes between materialistic and non materialistic goods and not given any importance to non-materialistic goods which are also very important. Therefore, it is incomplete.
3.Another serious objection is about the quantitative measurement of welfare. Welfare is a subjective concept and changes according to time, place and persons.
4.Marshall includes only those activities which promote human welfare. But the production of alcohol and drugs do not promote human welfare. Yet economics deals with the production and consumption of those goods.
5.Robbins has taken serious objection for not considering ‘scarcity of resources’. According to Robbins’ economic problem arises due to limited resources which are to be used to satisfy unlimited wants.

Question 2.Explain the scarcity definition of economics?

Answer:

Marshall’s welfare definition until the publication of Lionel Robbins’ book “An Essay on the Nature and Significance of Economic Science” in 1932. Robbins’ definition brought out the logical inconsistencies and inadequacies of the earlier definitions and formulated his own definition of economics. He has given a more scientific definition of economics. In the words of Robbins, “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.”

I. Main Features :

Human Wants are Unlimited :
The fulfillment of one want gives rise to a number of new wants.
Means are Scarce :
The means of a person by which his wants may be satisfied are limited. It leads to economic problems as all wants cannot be satisfied by these limited means.
Alternative Uses of Scarce Means :
Resources are not only scarce but also have multiple uses. For example, electricity can be used in homes and also in industries. A piece of land can be used to produce rice or wheat. If a scarce factor is used for the satisfaction of one want, less of it will be available for other wants. Hence, man has to make a decision regarding the alternative uses of resources.
Man has, therefore, to choose between wants. Problem of choice arises.
II. Superiority of Robbins’ Definition :
Robbins’ definition is superior to the earlier definition in more than one way. The reasons are given below :
1.It is non-classificatory, as it includes all human activities whether they promote human welfare or not.
2.This is universally accepted definition. It is applicable to all types of societies, because the scarcity of resources is felt by individuals as well as by societies.
3.Robbins’ definition of economics is neutral between ends. Being a positive science it does not pass any value judgements regarding ends.

Question 3.Explain the growth definition of economics?

Answer:

In the words of Samuelson, “Economics is the study how people and society choose, with or without the use of money, to employ scarce and productive resources which could have alternative uses, to produce various commodities over time and distribute them for consumption, now and in the future, among various people and groups in the society. It analyses the benefits of improving patterns of resource allocation”.

Important Points:
Some of the important points in Samuelsons’ definition are :
1.His definition like Robbins agreed that resources are not only limited but also have several uses.
2.Samuelson’s definition is dynamic in nature as it considers both the present and future consumption, production and distribution.
3.Growth definition deals with the problem of choice in a dynamic society. Hence, this definition broadened the scope of economomics.
4.Samuelson’s definition is superior to that of Robbins’ because he shifted the emphasis from the scarcity of resources to income, output and employment and later to the problems of economic growth.
Samuelson’s definition appears to be the most acceptable at the moment.

Question 4.Explain the fundamental problems of an economy?

Answer:

Fundamental Problems of an Economy
There are certain fundamental problems in any type of economy with which economists are concerned. The following are the basic economic problems. These are interrelated and interdependent.
1.What type of goods are to be produced and in what quantities?
2.How to produce these goods?
3.For whom to produce these goods and services?
4.How efficient the productive resources are in use? Whether available resources are fully utilized?
5.Is the economy growing or static over a period of time?

Question 5.What is Micro Economics? What is its importance?

Answer:

The term ‘Micro Economics’ is derived from the Greek word ‘MIKROS’ which means ‘small’. Thus, Micro Economics deals with individual units like individual demand, price, supply etc. It was popularised by Marshall It is also called as ‘Price Theory’ because it explains pricing in product market as well as factor market.

Importance :
1.Micro Economics provides the basis for understanding the working of the economy as a whole.
2.This study is useful to the government to frame suitable policies to active economic growth and stability.
3.This study is applicable to the field of international trade in the determination of exchange rates.
4.Micro Economics provides an analytical tool for evaluating the economic policies of the government.
5.It can be used to examine the condition of economic welfare and it suggests ways and means to bring about maximum social welfare.

Question 6.Explain the concept of Macro Economics, and its Importance?

Answer:

The term Macro Economics is derived from the Greek word ‘MAKROS’ which means large. It was developed by J.M. Keynes. Macro Economics deals with economic system as a whole like national income, aggregate demand, aggregate supply, general price level etc. It is also known as Income and Employment’ theory.

Importance :
1.Macro Economics study is more useful to the government for formulation and execution of policies for achievement of maximum social benefit.
2.It helps in understanding the problems of unemployment, poverty, inflation etc, and suggests how to solve them.
3.It gives us a picture of the working of the economy as a whole.
4.The study of Macro Economics is helpful in analysing the causes of business cycles and in providing remedies.
5.Macro Economics includes economic growth and suggests how developing countries can use their resources to maximise their growth.
6.Macro Economic study is useful for making international comparisons in terms of average national income.

Question 7.Distinguish between Microeconomics and Macroeconomics?

Answer:

Microeconomics	Macroeconomics
1. The word mikro derived from the Greek word “micros” means “small”.	1. The word makro derived from the Greek word “macros” means “large”.
2. Microeconomics is the study of individual units of the economy.	2. Macroeconomics is the study of economy as a whole.
3. It is known as ‘price theory’.	3. It is known as ‘income and employment theory’.
4. It explains price determination in both commodity and factor markets.	4. It deals with national income, total employment, aggregate savings and investment, general price level and economic development etc.
5. It is based on price mechanism which depends on demand and supply.	5. It is based oh aggregate demand and aggregate supply.
6. It is based on partial equilibrium analysis which explains the equilibrium of an individual unit.	6. It is based on general equilibrium analysis which explains the simultaneous equilibrium in all the sectors of the economy.
7. It is a static analysis without time element.	7. It is a dynamic analysis with time element.

Question 8.Explain the differences between free goods and Economic goods?

Answer:

Differences between Microeconomics and Macroeconomics

Free Goods	Economic Goods
1. free goods are nature’s gift.	1. Economic goods are man made.
2. Their supply is abundant.	2. Supply is always less than their demand.
3. They do not have price.	3. These goods have prices.
4. There is no cost of production.	4. These goods have cost of production.
5. They have value in use and do not have value in exchange.	5. These goods have value in use and also value in exchange.
6. Their values are included in national income.	6. Their values are included in national income.

Question 9.What is utility? What are its types?

Answer:

The want satisfying capacity of a commodity at a point of time is known as utility. Types of Utility:
1) Form Utility :
Form utilities are created by changing the shape, size and colour etc., of a commodity so as to increase its want satisfying power.
Ex : Conversion of a wooden log into a chair.
2) Place Utility :
By changing the place some goods acquire utility.
Ex : Sand on the sea shore has no utility. If it is brought out and transported to market, it gains utility. This is place utility.
3) Time Utility :
Time utilities are created by storage facility.
Ex : Business men store food grains in the stock points in the off season and releases them to markets to meet high demand and obtain super normal profits.
4) Service Utility :
Services also have the capacity to satisfy human wants.
Ex: Services of Lawyer, Teacher, Doctor etc. These services directly satisfy human wants. Hence, they are called as service utilities.

Question 10.Analyse the characteristics of wants. [Mar. 17]

Answer:

Human wants are starting point of all economic activities. They depend on social and economic conditions of individuals.
Characteristic features of wants :
1) Unlimited wants :
Human wants are unlimited. There is no end to human wants. When one want is satisfied another want takes its place. Wants differ from person to person, time to time and place to place.
2) A Particular Want is Satiable :
Although a man cannnot satisfy all his wants, a particular want can be satisfied completely in a period of time.
Ex : If a person is thirsty he can satisfy it by drinking a glass of water.
3) Competition :
Human wants are unlimited. But the means to satisfy therr are limited of scarce. Therefore, they complete with each other in priority of satisfaction.
4) Complementary :
To satisfy a particular want we need a group of commodities at the same time.
Ex : Writing need is satisfied only when we have pen, ink and paper together.
5) Substitution :
Most of our wants can be satisfied by different ways.
Ex : If we feel hungry, we can eat rice or fruits satisfy this want.
6) Recurring :
Many wants appear again and again though they are satisfied at one point of time.
7) Habits :
Wants change into habits, which cannnot be given up easily.
Ex : Smoking cigarettes for joke results into a habit if it is not controlled.
8) Wants vary with time, place and person :
Wants go on changing with the passage of time. They are changing from time to time, place to place and person to person. Human wants are divided into
1.Necessities,
2.Comforts and
3.Luxuries.

Very Short Answer Questions
Question 1.
Explain the wealth definition.
Answer:
Wealth means stock of assets held by an individual or institution that yields has the potential for yielding income in some form. Wwalth includes money, shares of companies, land etc. Wealth has three properties. 1. Utility 2. scarcity 3. Transferability.

Question 2.
What is Micro Economics?
Answer:
The word Micro’ is derived from Greek word ‘Mikros’ which means ‘small’. It was devel-oped by Marshall. It is the study of the individual units like individual demand, price, supply etc.
Question 3.
What is Macro Economics?
Answer:
The word Macro’ is derived from Greek work ‘Makros’ which means ‘Large’. It was developed by J.M. Keynes. It studies aggregates or economy as a whole like national income, employment, general price level etc. It is also called “Income and Employment” theory.
Question 4.
What is Positive Economics?
Answer:
A positive science is defined as a body of systematised knowledge concerning ‘what it is’. The classical school economists were of the opinion that economics is purely a positive science which had no right to comment upon the rightness or wrongness of economic policy. Here, economists cannot give any final judgement on any matter.
Question 5.
What is Normative Economics?
Answer:
Normative economics may be defined as a body of systematised knowledge relating to the object of “what ought to be’ and concerned with the ideal as distinguished from the actual. Historical school of Germany has introduced this in Economics.
Question 6.
What are Free goods?
Answer:
Anything which satisfy human want is known as good. Goods which are freely supplied by the nature and without prices are known as free goods. The supply of these goods is always abundantly greater thatn their demand. Hence, they do not command price. Free goods possess only value-in-use, no value-in-exchage. For example, air, water, sunshine.
Question 7.
Explain Economic goods.
nswer:
Economic goods are man made, they have cost of production and price. They are limited in supply. They have both value in use and value in exchange. Ex : Pen, Book etc.

Question 8.Explain the Consumer Goods?

Answer:

Consumer good is an economic good or commodity purchased by households for final consumption. Thus, consumer goods are those goods which directly satisfy human wants. For Ex : Fruits, Milk, Pen, Clothes etc. Consumer goods are divided into two types.
a) Perishable goods – Which loose their value in single use, Ex : Milk, fruits etc.
b) Durable goods – Which yields service over time. Ex : TVs & Computers.

Question 9.Explain the Capital Goods?

Answer:

Goods which are used in the production of other goods are called producer or capital goods. They satisfy human wants indirectly. Ex : Machines, tools, buildings etc.

Question 10.What are single use and durable use goods?

Answer:

Single use capital Goods :
There goods are used only once in the production process. For Example : Raw materials coal and Electricity.
Durable use capital Goods :
These goods are used for long time in the process of production. Machines, tools etc., are the durable capital Goods.

Question 11.

What is Wealth?

Answer:

Wealth means stock of assets held by an individual or institution that has the potential for yielding income in some form. Wealth includes money, shares of companies, land etc. Wealth has three properties. 1. Utility 2. Scarcity 3. Transferability.

TS Inter 1st Year Political Science Study Material Chapter 12 Forms of Governments

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February 2, 2026

TS Inter 1st Year Political Science Study Material Chapter 12 Forms of Governments

Long Answer Questions

Question 1.What is Unitary form of Government? Explain its features?

Answer:

In the Unitary Government the entire power of the government is vesed with the central government only.
A.V Dicey :
‘Unitary government is one in which the central power habitually exercises the supreme Legislature authority’.
Herman Finer :
Unitary government is one in which all powers and authorities are lodged with a centre whose will and agents are legally omnipotent over the whole area’.
J.W. Gamer :
Unitary government is one in which the whole power of the government is conferred by the constitution upon a single central organ from which the local governments derive their authority7′.
Features of Unitary Government:
a) Centralization of powers :
In unitary system, all powers are centralized in the hands of the central government and only centre is the reservoir of all state powers.
b) Provincial governments :
In unitary states, local/provincial governments are created and given power by the central governments. A provincial government directs their powers always derived from the central government. Ex. England.
c) Flexible constitution :
The central government alone has the power to amend the constitution and in this sense the constitution of a unitary state is always flexible like England.
d) Simple uniform administration :
The existence of an all-powerful government exercising power over all the people and places leads to the existence of simple, state and strong administration or the whole state.
e) Single citizenship :
In a unitary government, there is only single citizenship – the citizenship of the whole country. No provincial citizenship is given to its people.

Question 2.What is Federal Government? Examine its Characteristics?

Answer:

The term, federation is derived from Latin word ’Foedus’ meaning treaty or agreement. A federal polity comes into existence, either as a result of centripetal or centrifugal forces. The instrument by which a federation is brought about by the nature of a treaty or agreement between independent states and the new units of government, national or central which they agree to create. A new federal state is thus created to which sovereign states surrender their sovereignty and agree to become its component parts, for example, United States of America, Australia, India, Canada, etc.

Definitions of Federal Government :
Several political scholars have defined federation in different ways. Some definitions are the following.
Montesquieu :
Federation is a convention by which several parties agree to become members of larger on which they intend to establish’.
Herman Finer :
‘Federal states are one in which part of the authority and powers are vested in the local areas while another part is vested in a central institution deliberately constituted by an association of the local areas’.
A.V. Dicey :
‘A federal state is a political set-up intended to reconcile national unity and powers with the maintenance of state sights’.
J. W. Gamer :
‘Federal government is a system in which the totally of government power is divided and distributed between the centre and the states by the national constitution’.
K. C. Wheare :
A Federal government is a method of dividing power. So that the regional and central government independent’.
Features of Federal Government:
a) Written Constitution :
For a federal government the constitution must almost necessarily be a written constitution which determines the relation between the central and provincial/regional governments.
b) Rigid Constitution :
The natural corollary of the supremacy of the constitution and it being a written document, is that it should not be altered either by the central Legislatures.or by Regional Legislatures under their ordinary law-making procedure.
c) Division of powers :
In a federal political system, there is an essential feature of distribution of powers between central and regional governments under the constitution. Major sectors are vested with union/central and National and Provincial important things are vested with regional governments. For example, external affairs, exports and ports and education, agriculture health are exercised by union and state governments respectively.
d) Bicameralism :
Bicameralism is another important character of the federal government. In federal government, there should be Two-Chambers, representing people and states such as House of people and House states respectively.
e) Dual citizenship :
In a federal political system, constitution provides for dual citizenship to the citizens. Accordingly, the citizens have membership in both the centre and states simultaneously.
f) Independent Judiciary :
In a federal political system, independence of judiciary and intensity of judicial system is another important feature. Independence of judiciary will safeguard the minimum rights of people against the acts of Legislature and administrative authorities.

Question 3.What is presidential form of Government? Discuss its features?

Answer:

Under the presidential system, the Legislature and executive are two distinct departments of the government. There is more or less a separation between the two. The head of the state, the president, is real executive both as a Matter of law and fact and such power is the result of a direct grant from the constituent authority effected through express promises of the constitution.

Features of the Presidential Government :
a) President as Head of the state and government :
In a presidential government, president serves as the head of the state and government. He enjoys all the executive powers in practice. He implements the decisions and programmes of the government with the help of secretaries.
b) Separation of Legislature from the Executive :
In this form of government executive and Legislature are separate and independent of each other and do not interfere in the jurisdiction of each other.
c) Election/Head of the state and government :
Presidential executive, is not hereditary or nominated by the Legislature, but is elected by the people.
d) Impeachment of the President :
The removal by the impeachment is provided according to constitution, in case he is held guilty of violating, the oath of office. Usually, the power of impeachment is given to the legislature.
e) Checks and balances :
In a presidential government, there is another important feature that is, the principle of ‘checks and balances’. In presidential system, every organ enjoys autonomy and exercise powers independently. At the same time, every organ acts as a check against the excessive authority of the other organ. The legislature must give its consent to all decisions of the president and president must give his approval to the all decisions of the legislature. At the same time, judiciary reviews all constitutional cases and interprets them.

Question 4.What is Parliamentary form of government?

Answer:

In a parliamentary system a clear distinction is made between the head of the state and the head of the Government here, the head of the state King or Queen in Britain or President of India, possesses nominal or titular authority whereas real authority rests with the government of which Prime Minister is the head. Example : Australia, Canada, Japan etc.
Parliamentary form of government as a system in which the real executive, the cabinet, is immediately and legally responsible to the Legislature for its political policies and acts, ultimately responsible to the electorate.

Features of Parliamentary Governments :
a) Nominal and Real executives :
In parliamentary form of government there should be two kinds Of executive in the Political system one of them, National Executive is the Head of the state and other one is real executive, Head of the government is president and Head of the government is the Prime Ministers.
b) Co-ordination between the Legislature and executive :
Another important feature among, is that, there is a close relationship and co-ordination between legislature and executive bodies of the government. The executive members are selected from the Legislature and so executive remained as responsible for the Legislature for all its acts.
c) Significant role of the prime minister :
In parliamentary form of government, the prime minister holds the real executive authority. He holds the government as comer stone. He has the authority to from the council of ministers and also has right to reshuffle and dissolve the government.
d) Collective responsibility :
The most important feature of the parliamentary government works on the principle of collective responsibility. It means the ministers enjoy the office only as long as they have confidence of the parliament.
e) Individual responsibility :
In a parliamentary government, every minister is individually responsible to the Legislature for the efficient conduct of his department or office. In case there is any lapse in the administration, the ministers are personal answerable to parliament.
f) Dissolution of Lower House :
The head of the state can dissolve the lower house on the recommendation of the prime minister. If deadlock rises between cabinet and Legislature they can appeal to the electorate through elections.
g) Effective opposition :
In a parliamentary form of government opposition party is considered as soul of the democracy. If the ruling party loses its confidence in the Legislature, opposition party is the alternative to form a government and it works against ruling party through questioning the acts.

Short Answer Questions

Question 1.Write a note on merits and demerits of Unitary form of Government?

Answer:

Merits of Unitary Government:
a) Powerful Administration :
In unitary government, all the powers of the government are vested in the hands of central government. It helps to take decisions fast and work timely and to maintain internal peace, laws and order.
b) Simple and less Expressive :
The unitary system of government easy and less in expressive for administration.
c) Flexible in Administration :
The administration of a unitary state is flexible and can easily adapt itself to the changing social needs and environment. Because it can amend the constitution as and when required.
d) Suitable for small states :
unitary form of government as it is simple and less expressive suitable for smalls states.
e) Quick decisions :
It can be very useful in meeting emergencies. Being a unitary governments, is provincial in nature and can take all necessary decisions quickly and implement with full force.
f) National integration :
In unitary government, there is a simple citizenship which shows no discrimination among its people and helps to national unity integrity and solidarity among its people.

Demerits of the Unitary Government:
a) Fascist Powers :
In unitary government, all powers are vested with single government and there is a scope for Fascist or dictatorial attitude.
b) Centralization of administration :
In unitary government, all powers are concen-trated with the single government and no scope for distribution of powers between union and provincial government and it leads to more burden on the central government to manage whole nation.
c) Unsuitable for Larger States :
unitary governments are suitable for smaller states whereas it is not suitable for larger state which has vast land larger population. Because such states have multi religions, racial and cultural people and unitary government cannot tackle with such society.
d) Neglect of local initiatives :
In unitary governments with centralization of powers and with sanctioning of limited powers to provincial governments, it discourages local governments from making their own policies.
e) Scope for growth of inefficiency :
In unitary government, with centralization of powers, each and every aspect of the society should be administered by the single administrative unit and it leads to inefficiency in providing provisions for its people.

Question 2.Explain the merits and demerits of Parliamentary form of Government?

Answer:

Merits of Parliamentary Government:
a) Harmony and co-ordination between Legislature and executive :
In a parliamentary government, it secures co-operation and co-ordination from the Legislature because it was formed with the single majority party from Legislature. It enacts laws and implementing laws through taking confidence of legislators.
b) A Scrub on Autocracy :
Parliamentary government effectively checks the despotic attitude of the majority party in the lower house of the Legislature. Legislators prevent the government from the making mistakes against public interest through its questioning and a vote of no-confidence in the other motions.
c) Governmentally Able and Experienced :
In a parliamentary government, Government should be consisted with the top leaders of the majority party. Able and experienced people from the party have a hold on the party and government.
d) Responsible Government :
In a parliamentary from a government, council of ministers along with prime minister hold the offices and enjoys the powers and acts on the collective responsibility to the Legislature. In a parliamentary system, opposition party controls the ruling party through its vigilance in the outside of the Legislature.
e) Flexible Government :
Flexibility is another merit of the parliamentary from of a government, according to Bagehot, under this government; the people can choose a ruler for the occasion who may be especially qualified to successfully pilot the ship of the state through motional crisis.
f) Alternative to Government :
Parliamentary system is in the real sense a government by criticism. The majority from the government the majority continues the opposition. The opposition must criticises the government. The lapses of the government are its opportunities and ruling party lost confidence opposition party is ready to hold the office.

Demerits of the Parliamentary Government:
a) Unstable Government :
The government has no fixed life. It remains in office only so long as it can retain parliamentary majority which is sentient to the vagaries of the represent actives.
b) Violation of the theory of separation of powers :
In a parliamentary of government, there is a combination of executive and Legislature functions in the same set of individuals lead to tramp while the same men may be at one members of the Legislature and the executive, their functions in the two roles are distinct but in political experience, they worked in no distinction.
c) Executive becomes Autocratic / tyranny of majority :
When the executive is confident of support by majority members in the Legislation, at is likely to become autocratic. The opposition feels helpless in correcting the erratic behaviour of the government because all decisions taken on the basis of voting.
d) Unsuitable for emergencies :
A national crisis cannot meet with promptness in parliamentary government because much of tis time wasted in discussions. Get emergency needs prompt action, while taking decisions, be fear of the opposition and the masses at large.
e) Bureaucratic Dictatorship :
In a parliamentary government, bureaucracy becomes unduly important. The ministers being amateurs heavily rely on bureaucratise for everything.
f) National Interests ignored :
In a parliamentary government, political parties often gnore the interests of the nation for the sake of interest of the party in power. All national aspects are divided in the interest of the party only.
Despite all there defects, parliamentary government is very popular. It is considered more democratic and a true reflection of the public opinion.

Question 3.Discuss the merits and demerits of Federal form of Government?

Answer:

a) Scope for unity in diversity :
The federal government, there is scope for achieving unity in diversity. It is very essential to the multireligions, multicultural and multilinguistic societies.
b) Against Dictatorship :
In the federal political system, there is a scope for preventing the rise of a single despotism, check the growth of bureaucratic authority and conserves the political liberties of people.
c) Less-burden on the centre :
In federal political system, there is distribution of powers between centre and state governments, according to the constitution and each discharges its duties accordingly. So, it decreases the burden upon the central govemment while executing its functions.
d) Scope for New Political experiments :
In a federal political system, regional gov-ernments will introduce new policies / and programmes and make experiments for the development of socio-economic spheres of the society.
e) Suitable for larger states :
Federation is said to be the only form of government which is suitable for vast or larger area states. Larger states can be administered with the constitutional distribution of powers between central and state governments.
f) Leads to efficient Administration :
In a federal form of governments, powers and functions are transferred to the local / state governments. As a result, with the limited subjects, centre can work efficiently and it has scope for concentrating on all important national interests.

Demerits of Federal Government:

a) Weak central government :
Federal government is a weak government due to dis-tribution of powers between the centre and state governments. Regional or provincial governments demand the centre for their regional cause.
b) Lack of uniform laws :
In a federal government, there is a chance to adopt different laws by federal and state governments. Laws passed by the various provincial governments are complex in nature. It leads to controversy between federal and state governments, or among state governments.
c) Controversies and dispute :
In federal political system, there is a distribution of subjects between centre and state governments. When it comes to the concurrent list, centre and state governments try to escape from their duties and subjects remain unimplemented or unfulfilled.
d) Expensive mechanism :
In federal political system, there are two sets of govern-ments, i.e., federal government at centre level and provincial government at regional level. It is more expensive to establish infrastructure of administrative units and re-cruitment and maintenance of bureaucracy.
e) Fear of Disintegration :
In federal political system, federal state itself is formed through treaty of federation or confederation. There is no certainity of sustainability of federation which stands upon the willingness of the provinces / states. For examples U.S.A. experienced such fear in 1882, USSR disintegrated and several states like Latin America, Balkan states faced such problems.

Question 4.Distinguish between unitary and Federal form of Government?

Answer:

Distinction between Unitary and Federal Governments :

Unitary Government	Federal Government
1. May or may not be written constitution.	1. There will be written constitution.
2. It has Flexible constitution.	2. It has rigid constitution.
3. There is only one Government for the entire country.	3. There will be two types of governments, i.e., union level and provincial level.
4. Centralization of powers.	4. Decentralization of powers between centre and state governments.
5. Government is not as much Democratic form of government.	5. It is purely Democratic government which all governments take their part in Decision-making.

TS Intermediate 1st Year Political Science Study Material: Telangana Inter I Yr Textbook Solutions at manabadi.co.in

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January 31, 2026

TS Intermediate 1st Year Political Science Study Material: Telangana Inter I Yr Textbook Solutions at manabadi.co.in

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TS Inter 1st Year Political Science Study Material – Telangana Board Textbook Solutions

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TS Inter 1st Year Political Science Study Material in English Medium

TS Inter 1st Year Political Science Study Material Chapter 11 Organs of Government

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January 31, 2026

TS Inter 1st Year Political Science Study Material Chapter 11 Organs of Government

Long Answer Questions

Question 1.Explain the structure of Bicameralism and the functions of the Legislature?

Answer:

Legislature may be Bicameral or Unicameral. In Bicameralism there are two houses, namely, lower and upper house or first chamber and second chamber. The lower house represents the will of the people. The upper house represents the interests of the states.
Ex’s in India Rajyasabha is the upper house and Loksabha is the lower house.
The members of the upper house are elected from the component states. These members represent their respective states in the central government. The people directly elect the members of the lower house .through universal adult franchise.

Functions of the legislature :

The basic function of the legislature is to enact laws as per the will of the people. The legislature in modern times is discharging certain administrative and judicial duties besides forming the laws. The functions of the legislature also depend upon the form of the government. The role of the legislature is limited ina presidential form of government. But, it has an extensive role in the parliamentary government. The functions fo the legislature can be analysed under different heads like : Legislative functions, Executive functions, Financial functions, Judicial functions, Constitutional functions and other functions.

Legislative functions :
To frame the laws is the basic function of the legislature. It is the important duty of the legislature to pass laws as per the will of the people. The legislature has powers to frame new laws and also to change, revise or cancel the laws which are outdated. The legislature not only makes laws but also conducts detailed discussions and consultations on different subjects. The legislature discusses extensively every bill before it becomes law.
Functions to control executive :
In the parliamentary government, the council of ministers is responsible to the legislature. The legislature exercises control on the council of ministers in dealing with the problems cropping up in the country, and their solutions through different resolutions and questions. It can also pull down the government through a no confidence motion if such a need arises.
Financial functions :
The financial functions of the legislature are of much importance in democratic countries. The legislature has to approve the income and expenditure under different heads shown in the budget. The legislature can decide the amount of expenditure under different heads. Levying new taxes or abolishing already existing taxes can be taken up with the consent of the legislature only.
Judicial functions :
The legislature, especially the upper house performs some judicial functions. The House of Lords in England functions as the highest court of justice. In U.S.A. and India, the legislature has to try impeachment cases against the president or the Justices of Supreme Court and High Courts. Some times the legislature conducts enquiry through separate committees on the allegations against the government. The legislature has the authority to punish anybody who commits breach of privileges of members and those who violate the rules of the house.
Constitutional functions :
The legislature has the right to amend the constitution besides framing the laws. It can amend the constitution as per the needs and requirements of the country which change from time to time.
Other functions :
Besides the above functions, the legislature has some more functions like, accepting or rejecting the ordinances declared by the government; electing the speaker, appointing necessary committees to enquire into the lapses of the government and to formulate rules and procedures of the legislative business.

Question 2.What is Executive? What are its functions?

Answer:

Of the three organs of government, the Executive occupies the most important place. Very often it is referred to as the government. It refers to that branch of government which executes or enforces the laws of the state those are framed by the legislature that is why the executive is identified with government in modem times. Broadly

speaking, the executive has three parts :

1.The Head of the state
2.The Council of ministers and
3.The Employees.

Functions of the Executive :
Defence and Foreign affairs :
The executive takes suitable decisions and implements them in case of any threat to the national independence and sovereignty and protects the country from foreign aggression. The duties of the executive include establishing embassies in others countries, recognising newly formed states and concluding treaties and alliances with the foreign countries.
Administrative functions :
The entire administration is carried on in the name of the executive. In this context, its functions include appointment of the officers in highest ranks allotting their duties, providing training, giving directions to different administrative departments, changing the rules and regulations from time to time, to protect law and order, to appoint and advise the council of ministers in parliamentary system, to create new departments or reorganise the existing ones or abolish them altogether as deemed necessary.
Legislative functions :
The executive prepares the draft bills to be presented to the legislature and gets them enacted. In the parliamentary government as the members are directly associated with the legislature the ministers present the draft bills to the legislature and get its acceptance. After acceptance by the legislature, the draft bills can become acts with the assent of the chief executive. In the presidential government, the president sends to the legislature for its acceptance certain messages embodying the various legislative measures considered necessary by him. All the bills passed by the legislature can become acts only with the assent of the president. When the legislature does not meet, the executive can issue ordinances.
Financial functions :
It is the duty of the executive to prepare the annual budget containing income and expenditure of the government and gets the approval of the legislature. The legislature cannot levy new taxes without the consent of the executive. Levy or abolition of taxes, provision of capital funds, reduction of prices etc. come under the domain of executive responsibility.
Judicial functions :
The executive has the certain functions like : To implement the judgements of the courts of law, to reduce or cancel the punishment, to appoint the Judges, to appoint special courts for the enquiry of certain special problems etc. In some of the democratic countries the chief executive appoints judges of the highest courts of justice.
Welfare functions :
It is the Prime duty of the executive in the modern times to undertake welfare measures. The executive has to work for the planned development and contribute for the improvement of the standards of living.

Question 3.Discuss Judiciary and its Functions?

Answer:

The Judiciary is the third important organ of the government. Legislature enacts the laws. The executive implements them. But it is the judiciary which decides the constitutional validity of these laws both in theory and practice. The judiciary keeps the democratic government within the constitutional limits. The judiciary also has to protect the law abiding citizens and punish the criminals. It consists of the judges and magistrates charged with the duty of administering justice. In brief, it is the branch of the government which settles disputes and administers justice.

Functions of the Judiciary :
Dispensing Justice :

It has to solve the disputes between the citizens, the citizens and the government and different governments. It punishes the criminals after due trial.
Protection of Civil rights :
The courts of law protect the fundamental rights given to the citizens by the constitution. The citizens can approach the court of law when their fundamental rights are violated. The courts issue writs for enforcement of these rights. The citizens can obtain stay orders from courts in advance when they apprehend violation of their rights. In order to protect the rights of the individuals, the courts of law can issue writs like Habeas Corpus, Mandamus, Prohibition etc.
Constitutional protection :
The Judiciary safeguards the constitution in the democratic countries. The Judiciary annuls the unconstitutional decisions of the legislature and the executive. By interpreting the constitution and laws it reviews the laws of the legislature and the actions of the executive and strikes down unconstitutional measures. This authority of the judiciary is called as ‘Judicial Review’.
Protection of equilibrium in federal system :
Judiciary plays a key role in the federal system. The courts of law solve the disputes between the provinces and the central government and also between one province and another. It supervises to see that neither the disputes between the central and provincial governments that arise due to matters relating to the division and distribution of powers.
Advisory functions :
The highest court of justice provides advice to the head of the State on request. For instance in India, the President takes the advice of the Supreme Court on certain problems of constitutional applications. Appellate Jurisdiction: The highest court of justice has to provide justice on the appeals made against the judgements of the lower courts. At times, it ratifies the judgements given in the lower courts and some other times, such judgements are reversed.
Protection of records :
The judiciary has to preserve all the cases along with their judgements. These records will help lawyers and judges in the trial of similar cases in future.
Providing service regulations :
The courts of justice prescribe service regulations of employees working in courts of law.
Functioning as the Head of State :
In some countries and under certain conditions, as identified in India, the Chief Justice of the Supreme Court can function as acting Head of the State when there is no Vice-President in office.

Short Answer Questions

Question 1.What are the reasons for the decline of the significance of legislature?

Answer:

The political thinkers opine that the legislature, which has wide powers theoretically, is losing its significance gradually in the democratic countries. There are many reasons for this.
1.The executive acquired a lot of constitutional and legal powers to achieve comprehensive Socio-economic development.
2.The legislature has to depend on the executive as it does not possess even the fundamental capacity to understand the novel measures introduced in the administrative system due to advancement of science and technology.
3.Since the highest political offices are filled in through direct elections, the government gained importance by directly influencing the people. It could develop direct relations with the people lessening the importance of the legislature.
4.Another reason for the reduction of the importance of the legislature is delegated legislation. The legislature, passess a law in a skeleton form and delegates power to the executive to fill in the details of it in the shape of rules and regulations. This is called ‘delegated legislation’. This power is used by the executive to implement plans and welfare schemes.
5.Other reasons the political thinkers are worried about the fact that the significance of the legislature is further reduced due to certain reasons like lack of a powerful opposition, less duration of the sessions of the parliament, the irresponsible behaviour of the ruling party and also the misbehaviour of the legislators.

Question 2.Discuss the reasons for the growth of importance of the Executive?

Answer:

In recent years, several factors have led to a steady increase in the powers, functions, prominence and prestige of the Executive organ all over the world. The factors are as follows :

Concept of welfare state :
As a result of the advent of the concept of welfare state, the functions of the modem state are gradually increasing. The present state is called upon to look after multifarious activities like labour welfare, education, social security, health, production, distribution etc., which promote the welfare of the people. Hence, the executive requires vast powers to cope with the problems of the modern welfare state.
Delegated legislation :
Today the legislative organ is overburdened with work. As a result, it passes laws in a skeleton farm only and empowers the executive to make detailed bye-laws, rules and regulations. This is known as delegated legislation. This has led to the growth of executive importance.
Party system :
The present representative system is under the control of the political parties. Parties have provided leadership to the executive and reduced the legislatures to the level of registering bodies. Now, it is the executive organ which performs most of the legislative functions by extra constitutional methods.
Economic planning :
For the planned economic development, the government interferes in’ all economic, aspects. As a result the executive branch is becoming more prominent.

Question 3.Discuss Judicial Review?

Answer:

Judicial Review means reviewing the laws made by the legislatures. The laws of the legislatures (parliament, assemblies, Councils, Parishades etc.,) must not be unconstitutional. The courts of law can nullify all laws which are unconstitutional. This is the Judicial Review. The Judicial Review is not limited only to laws. It is applicable to all the activities of the executive at different levels of central, state and local government institutions. Every State will have a constitution. It is its basic law and all the laws must be within the limits of the constitution. The constitution provides the courts of law with the right to see that all laws and activities conform to the constitution. Judicial Review is not found in all the countries.

The Judicial Review first originated in United States of America in the context of the judgement given by the Supreme Court in the Marbury-Madison dispute in the beginning of the nineteenth century. The courts of law follow different theories, principles and views in reviewing the constitutional viability of the laws. The Judicial Review is based on the following theories which can be studied in detail in higher classes.

1.Theory of the efficiency of law.
2.Theory of separation of powers.
3.Theory of constitutional dynamism.
4.Theory of activity.
5.Theory of decision by experience.
6.Theory of constitutional development.

Question 4.Write brief note on Rule of Law?

Answer:

Rule of law is a unique feature of British constitution. It at first originated in England later many states like India and the United States have adopted this feature. Rule of law is purely based on the principle of common law. It denotes that law should be general in form. It should be uniformly applicable to all the citizens living in a state. There should not be different types of law for various sections of the community. In other words the government must treat all the citizens equally as per the law.

The governance and administration in a particular state should be carried on in accordance with the laws. A.V Dicey in his “Law of the constitutions” (1885) gave a precise explanation of the rule of law. According to him, rule of law stands for equality before the law. This implies equal subjection of all classes including the officials or common man. Law makes no discrimination between individuals. A.V Dicey says that “Every official from Prime Minister to the attender, all are equal before the law”.

Therefore, Rule of law is helpful to all the citizens in protecting their responsibilities in a more effective manner. The constitution of India too recognizes the Rule of law as a basic feature of India constitution. The Supreme Court of India time and again declared Rule of law as a basic Structure of Indian Constitution. Articles 14 to 21 of the Indian Constitution have incorporated the spirit of this concept. However, the scope of this concept is gradually shrinking owing to the over burdening of legislative work with enormous functions. On the whole, the cardinal virtue of Rule of law is that “All are equal before law and no one must arbitrarily be punished” constitutes the core value of any democratic system in the world.

Question 5.What is Judicial Activism?

Answer:

According to the idea of judicial activism judges should use their powers to correct injustices, especially when the other branches a Government do not act to do so. The courts play an active role in shaping social policy on such issues as civil rights, political unfairness protection of individual rights and public morality.
Judicial activism is policy making function of judiciary in competition with poilcy making by the legislative and executive. This element is associated with the doctrine of judicial review. The essence of true judicial activism lies in rendering decisions by the judiciary which are in tune with the temper and tempo of the times.

Behind every judicial decision, judicial activism and judicial restraint are the two aspects that describe the philosophy and motivation. The concept of judicial activism is the polar opposite of judicial restraint. Judicial activism refers to a theory of judgement that takes into account the spirit of the law and the changing times, whereas judicial restraint relies on a strict interpretation of the law and the importance of legal precedent.
Judicial activism is a dynamic process of judicial outlook in a changing society. Arthur Schlesinger jr. introduced the term ‘Judicial activism’ in 1947. According to Black’s Law Dictionary, “Judicial activism is a judicial philosophy which motivates judges to depart from traditional precedents in favour of progressive and new social policies”.

Very Short Answer Questions

Question 1.How many organs of government are there? What are they?

Answer:

The powers of Government are separated among these three organs – legislature, executive and judiciary. They are inter-related and sometimes independent of each other. Political philosophers like Cicero, Jean Bodin and John Locke wrote treatises on the inter-relationship of three organs of government.

Question 2.What is meant by the theory of separation of powers?

Answer:

Montesquieu stated that concentration of powers in one person or a body of persons would result in despotism and negate individual liberty. He suggested separation of powers among the three organs of government in a balanced manner. Every organ must check the misuse of powers of other organs. Then only individuals enjoy their liberties without fear from the governmental interference.

Question 3.What is meant by Plural Executive?

Answer:

Among various types of Executive, Plural Executive is one. If the executive powers are exercised by a body of persons having co-equal authority, it is called “Plural Executive”. The Swiss Federal Council and the President in the former U.S.S.R. are the examples of Plural Executives. This Plural Executive combines the merits of both the parliamentary and the presidential executives, avoiding their defects.

Question 4.What is independence of the Judiciary?

Answer:

Independence of judiciary implies an opportunity to the judges to perform their duties without fear or favour and act impartially. The judges should have no relation with the legislature and the executive. Both the organs should not interfere in the functioning of the judiciary. It should be protected from political pressure and influence. Otherwise, the very purpose of judiciary stands defeated.

Question 5.What is Judicial Review?

Answer:

It is the power of a court to enquire whether a law passed by legislature or executive order or other official action is in accordance with the constitution or not If a law, or order or action is against the constitution then the court declares it as “Unconstitutional” and “Invalid”. The Judicial Review power originated in the USA in 1803. The American Supreme God Court and the Indian Supreme Court are some of the courts having this power.

Question 6.Senate?

Answer:

Senate is the Upper House of United States Congress, which is a small group of elected people who decide the laws of the country. It consists of 100 members. Every U.S. state elects two people to represent them in the U.S. Senate. These people are called senators.

Question 7.

Council of States?

Answer:

Council of States is the Upper House of Indian Parliament. It is also known as the Rajya Sabha. It consists of 250 members out of them 238 members are elected by the members of state legislative assemblies through the system of proportional representation by means of single transferable vote. The remaining 12 members are nominated by the President of India from the fields of Arts, Literature, Social Service, Cooperative Movement, Science and Technology. It is a permanent house and it can never be dissolved. Each member shall remain in office for a period of 6 years. For every 2 years 1/3 of its members shall retire.

Question 8.House of lords?

Answer:

The House of Lords, also known as The House of peers, is the upper House of the parliament of the United Kingdom. Membership is granted by appointment or else by heredity. Like the House of common, it meets in the palace of West Minister. Currently, there are 300 members in the House of Lords members of whom 240 are Elected members and 60 appointed. Independent members upto 12 Church of England Bishops may sit in the House as ex officio Lords spiritual. Elected members will serve a single non-renewable term of 15 years.

Question 9.

Independent Judiciary?

Answer:

Independence of Judiciary implies an opportunity to the Judges to perform their duties without fear or favour and act impartially. The Judges should have no relation with the Legislature and the Executive. Both the organs should not interfere in the functioning of the Judiciary. It should be protected from political pressure and influence. Otherwise the very purpose of Judiciary stands defeated.

Question 10.Parliamentary Executive?

Answer:

A parliamentary System of government means that the Executive branch of government has the direct or indirect support of the parliament. This support is usually shown by a vote of confidence. The Relationship between the executive and the Legislature in a parliamentary system is called Responsible government. According to this system, there is a President who is the formal Head of the State, and the Prime Minister and the council of ministers, which run the government.

Question 11.What is Uni-bicameralism?

Answer:

In government, the first organ is the Legislature, it may be unicameral or Bicameral. Unicameralism is derived from two Latin words namely uni, which means one, and camera, which means, the chamber is the practice of having one Legislative or parliamentary chamber. Thus, a unicameral parliament of the unicameral legislature is a legislature that consists of one chamber or house.
Ex.: Armenia, Bulgaria, Denmark, Sweden etc.

Question 12.What is Bi-bicameralism?

Answer:

‘Bi’ means two and Cameral means house or chamber. If a Legislature consists of two houses or chambers, it is called a Bi-cameral legislature, and such an arrangement is called Bi-cameralism. The bi-cameral legislature is necessary for a federal government as the second chamber gives representation to the states. In the Bi-cameral setup, the upper house is less powerful than the lower house.
Ex.: Rajya Sabha and Lok Sabha in India, Senate and House of Representatives in America.

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions Exercise 6(d)

Other

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January 31, 2026

I.
Question 1.
Simplify
(i) $\frac{\sin 2 \theta}{1+\cos 2 \theta}$

Answer:

(ii) $\frac{3 \cos \theta+\cos 3 \theta}{3 \sin \theta-\sin 3 \theta}$
Answer:

Question 2.
Evaluate the following
(i) 6sin 20° – 8 sin³ 20°

Answer:
2(3 sin 20° – 4sin³ 20°) (Formula)
= 2.sin (3 × 20°) = 2 sin 60°
= $\frac{2 \sqrt{3}}{-2}$ = √3

(ii) cos²72° – sin²54°
Answer:
cos²72° – sin²54°
= sin²18° – cos²36°

(iii) sin²42° – sin²12°
Answer:
sin²42° – sin²12° (Formula)
sin (42° + 12°) sin (42° – 12°)
= sin 54° sin 30°
= $\left(\frac{\sqrt{5}+1}{4}\right) \frac{1}{2}=\frac{\sqrt{5}+1}{8}$

Question 3.
(i) Express $\frac{\sin 4 \theta}{\sin \theta}$ in terms of cos3 θ and cos θ.

Answer:
sin4θ = sin (3θ + θ) = sin 3θ cos θ +cos 3θ sin θ
= (3 sin θ – i sin 3θ) cos θ + (4 cos 3θ – 3 cos θ) sin θ
= 3 sin θ cos θ – 4 sin 3θ cos θ + 4 cos 3θ sin θ – 3 cos θ sin θ
= 4 cos 3θ sin θ – 4 sin 3θ cos θ
= sin θ(1 cos 3θ – 4 sin 2θ cos θ)
= sin θ [4 cos 3θ – 4 sin 2θ cos θ]
∴ $\frac{\sin 4 \theta}{\sin \theta}=\frac{\sin \theta\left(4 \cos ^3 \theta-4 \sin ^2 \theta \cos \theta\right)}{\sin \theta}$
= 4 cos 3θ – 4 sin 2θ cos θ
= 4 cos 3θ – 4 (1- cos 2θ) cos θ
= 8 cos 3θ – 4 cos θ

(ii) Express cos⁶ A + sin⁶ A in terms of sin 2A.
Answer:
cos⁶A + sin⁶A = (cos²A + sin²A)³
= (cos²A + sin²A)³ – 3 cos²A sin²A (cos²A + sin² A)
= 1 – 3 cos²A sin²A ……………(1)
= 1 – $\frac{3}{4}$ (4 cos² A sin² A)
= 1 – $\frac{3}{4}$ sin²2A

(iii) Express $\frac{1-\cos \theta+\sin \theta}{1+\cos \theta+\sin \theta}$ in terms of tan $\frac{\theta}{2}$
Answer:

Question 4.
(i) If sin α = $\frac{3}{5}$ , where $\frac{\pi}{2}$ < α < π, evaluate cos 3α and tan 2α. (March 2015-T.S)

Answer:
since $\frac{\pi}{2}$ < α < π, a lies in second quadrant and given sin α = $\frac{3}{5}$ we have cos α = – $\frac{4}{5}$
cos 3α = 4 cos³ α – 3 cos α

(ii) If cos A = $\frac{7}{25}$ and $\frac{3 \pi}{2}$ < A < 2π, then find the value of cot $\frac{A}{2}$ .
Answer:

(iii) If 0 < θ < $\frac{\pi}{8}$ , show that $\sqrt{2+\sqrt{2+\sqrt{2+2 \cos 4 \theta}}}$ = 2cos(θ/2)
Answer:

Question 5.
Find the extreme values of
(i) cos 2x + cos2x

Answer:
cos 2x + cos2x = 2 cos² x – 1 + cos² x
= 3 cos² x – 1
and 0 ≤ cos² x ≤ 1
⇒ 0 ≤ 3 cos² x ≤ 3
⇒ -1 ≤ 3 cos² x – 1 ≤ 2
Maximum value = 2
and minimum value = -1
(or) cos 2x + cos² x = cos 2x + $\left(\frac{1+\cos 2 x}{2}\right)$
We have -1 < cos 2x ≤ 1
⇒ -3 ≤ 3 cos 2x ≤ 3
⇒ -2 ≤ 3 cos 2x + 1 ≤ 4
⇒ -1 ≤ $\frac{3 \cos 2 x+1}{2}$ ≤ 2
Maximum value = 2
Minimum value = -1

(ii) 3sin²x + 5 cos²x
Answer:
3sin²x + 5 cos²x

Question 7.
Find the periods for the following functions
(i) cos⁴x

Answer:

(ii) 2sin $\left(\frac{\pi \mathbf{x}}{\mathrm{4}}\right)$ + 3cos $\left(\frac{\pi x}{3}\right)$
Answer:

(iii) sin²x + 2 cos²x
Answer:
Let f(x) = sin²x + 2cos²x

(iv) 2sin( $\frac{\pi}{4}$ + x)cos x
Answer:

Period of f(x) is LCM of [π, π] = π

(v) $\frac{5 \sin x+3 \cos x}{4 \sin 2 x+5 \cos x}$
Answer:

II.
Question 1.
(i) If 0 < A < $\left(\frac{\pi}{4}\right)$ , and cos A = $\frac{4}{5}$ , find the values of sin 2A and cos 2A.

Answer:

(ii) For what values of A in the first quadrant, the expression $\frac{\cot ^3 A-3 \cot A}{3 \cot ^2 A-1}$ is positive?
Answer:
$\frac{\cot ^3 A-3 \cot A}{3 \cot ^2 A-1}$ > 0
⇒ cot³A – 3 cot A > 0
⇒ cot A (cot² A – 3) > 0
⇒ cot A > 0 or cot² A > 3
⇒ cot A > √3

(iii) Prove that $\frac{\cos 3 A+\sin 3 A}{\cos A-\sin A}$ = 1 + 2 sin 2A
Answer:

Question 2.
(i) Prove that cot( $\frac{\pi}{4}$ – θ) = $\frac{\cos 2 \theta}{1-\sin 2 \theta}$ and hence find the value of cot 15°.

Answer:

(ii) If θ lies in third quadrant and sin θ = – $\frac{4}{5}$ , find the values of cosec $\left(\frac{\theta}{2}\right)$ and tan $\left(\frac{\theta}{2}\right)$ .
Answer:
Given θ lies in third quadrant.

(iii) If 450° < θ < 540° and sin θ = $\frac{12}{13}$ , then calculate sin $\left(\frac{\theta}{2}\right)$ and cos $\left(\frac{\theta}{2}\right)$ .
Answer:

(iv) Prove that $\frac{1}{\cos 290^{\circ}}+\frac{1}{\sqrt{3} \sin 250^{\circ}}=\frac{4}{\sqrt{3}}$
Answer:

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions Exercise 6(b)

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January 30, 2026

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions Exercise 6(b)

I.
Question 1.
Find the periods for the given 1 – 5 functions.
(i) cos (3x + 5) + 7

Answer:
Let f(x) = cos (3x + 5) + 7
We have period of cos x is 2π ∀ x ∈ R
∴ f (x) is periodic and period of f is = $\frac{2 \pi}{|3|}=\frac{2 \pi}{3}$
(or) f (x + p) = f(x)
⇒ cos (3x + 3p + 5) + 7 = cos (2π+ 3x + 5) + 7
3x + 3p + 5 = 2π + 3x + 5
⇒ 3x = 2π
⇒ x = $\frac{2 \pi}{3}$

Question 2.
tan x

Answer:
The function tan x is periodic with period π
∴ f(x) = tan 5x is periodic and its period is
$\frac{\pi}{|5|}=\frac{\pi}{5}$

Question 3.
cos $\left(\frac{4 x+9}{5}\right)$ (Mar. ’14)

Answer:
The function f(x) = cos x ∀ x ∈ R has the period 2π
∴ f(x) = cos $\left(\frac{4 x+9}{5}\right)$ is periodic and period of f is $\frac{2 \pi}{\frac{4}{5}}=\frac{5 \pi}{2}$

Question 4.
|sin x|

Question 5.
tan (x + 4x + 9x + …. + n²x) (n any positive integer) (March 2015-A.P&T.S)

Answer:
tan [1 + 2² + 3² + ……… + n²) x
= tan $\left[\frac{\mathrm{n}(\mathrm{n}+1)(2 \mathrm{n}+1)}{6}\right]$ x
Period = $\frac{6 \pi}{n(n+1)(2 n+1)}$

Question 6.
Find a sine function whose period is $\frac{2}{3}$ .

Answer:
$\frac{2 \pi}{\mathrm{k}}=\frac{2}{3}$ ⇒ 3π = |k| ∴ sin kx = sin (3n x)

Question 7.
Find a cosine function whose period is 7. (March 2013)

Answer:
f(x) = cos[ $\frac{2 \pi}{7}$ .x] ( $\frac{2 \pi}{k}$ = 7 ⇒ $\frac{2 \pi}{7}$ = k)

II. Sketch the graph of the following functions
Question 1.
tan x between 0 and $\frac{\pi}{4}$ .

Answer:

Question 2.
cos 2x in the interval [0, π]

Answer:

Question 3.
sin 2x in the interval (0, π).

Answer:

Question 4.
sin x in the interval [-π, +π]. (May 2014)

Answer:

Question 5.
cos²x in [0, π].

Answer:

Question 6.
Sketch the region enclosed by y = sin x, y = cos x and X – axis in the interval [0, π].

Answer:
y = sin x

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions Exercise 6(a)

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January 30, 2026

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions Exercise 6(a)

I.
Question 1.
Convert the following into simplest form
(i) tan (θ – 14π)

Answer:
tan (θ – 14π) = tan [- (14π – θ)]
= – tan (14π – θ)
= – tan [ 2(7π) – θ)
= – tan (-θ) = tan θ

(ii) cot ( $\frac{21 \pi}{2}$ – θ)
Answer:
cot ( $\frac{21 \pi}{2}$ – θ) = cot[10π + ( $\frac{\pi}{2}$ – θ)]
= cot ( $\frac{\pi}{2}$ – θ) = tan θ

(iii) cosec (5π + θ)
Answer:
cosec (5π + θ) = cosec [4π + (π + θ)]
= cosec(π + θ) = – cosec θ

(iv) sec (4π – θ)
Answer:
sec (4π – θ) = sec [2(2π) – θ]
= sec (- θ) = sec θ

Question 2.
Find the values of each of the following
(i) sin (-405°)

Answer:
sin (-405°) = -sin 405° = -sin (360°+45°)
= – sin 45° = $-\frac{1}{\sqrt{2}}$

(ii) cos $\left(-\frac{7 \pi}{2}\right)$
Answer:
cos $\left(-\frac{7 \pi}{2}\right)$ = cos $\frac{7 \pi}{2}$ = cos (630°)
= cos (360 + 270°) = cos 270°
= cos (180 + 90) = -cos 90 = 0
(or) cos $\left(-\frac{7 \pi}{2}\right)$ = 0 (∵ cos(2n + 1) $\frac{\pi}{2}$ = 0)

(iii) sec (2100°)
Sol. sec (2100°) = sec [5 × 360° + 300°]
= sec 300° = sec (360° – 60°)
= sec 60° = 2

(iv) cot (-315°)
Answer:
cot (-315°) = – cot 315° = – cot (270 + 45°)
= cot 45° = 1

Question 3.
Evaluate
(i) cos² 45° + cos² 135° + cos² 225° + cos² 315°

Answer:
cos 45° = $\frac{1}{\sqrt{2}}$ , cos 135° = cos (180 – 45°)
= – cos 45° = $-\frac{1}{\sqrt{2}}$

cos 225° = cos (180 + 45°)
= – cos 45° = – $\frac{1}{\sqrt{2}}$

cos 315° = cos(360 – 45°)
= cos 45° = $\frac{1}{\sqrt{2}}$

∴ cos² 45° + cos² 135° + cos² 225° + cos² 315°
= $\frac{1}{2}+\frac{1}{2}+\frac{1}{2}+\frac{1}{2}$ = 2

(ii) sin² $\frac{2 \pi}{3}$ + cos² $\frac{5 \pi}{6}$ – tan² $\frac{3 \pi}{4}$

Answer:

(iii) cos 225° – sin 225° + tan 495° – cot 495°
Answer:
cot (180 + 45) – sIn (180 + 45) + tan (360 + 135) – cot (360 + 135)
= – cot 45° + sin 45° + tan 135 – cot 135°
= – cos 45° + sin 45° +tan(180 – 45) – cot(180 – 45)
= – cos 45° + sin 45° – tan 45° + cot 45°
= $-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}$ – 1 + 1 = 0

(iv) (cos θ – sin θ) if
(a) θ = $\frac{7 \pi}{4}$
(b) θ = $\frac{11 \pi}{4}$
Answer:

Question 4.
(i) If sin θ = – $\frac{1}{3}$ and 0 does not lie in the third 3 quadrant, find the values of (a) cos θ and (b) cot θ. (March 2013)

Answer:
sin θ = – $\frac{1}{3}$ and sin θ is negative and does not lie in third quadrant,
⇒ θ lies in fourth quadrant. In IVth quadrant cos θ is positive and cot θ is negative.
a) cos θ = $\sqrt{1-\sin ^2 \theta}=\sqrt{1-\frac{1}{9}}=\frac{2 \sqrt{2}}{3}$
b) cot θ = $\frac{\cos \theta}{\sin \theta}$ = -2√2

(ii) If cos θ = t (0 < t < 1) and θ does not lie in the first quadrant, find the values of a) sin θ b) tan θ
Answer:
cos θ = t, (0 < t < 1)
⇒ cos θ is positive and 0 does not lie in first quadrant
⇒ θ lies in IVth quadrant
a) sin θ = $-\sqrt{1-\cos ^2 \theta}=-\sqrt{1-t^2}$
b) tan θ = $\frac{\sin \theta}{\cos \theta}=-\frac{\sqrt{1-t^2}}{t}$

(iii) Find the value of sin 330°. cos 120° + cos 210°. sin 300°
Answer:
sin 330° cos 120° + cos 210° sin 300°
= sin (360 – 30) cos (180 – 60) + cos ( 180 + 30) sin (360 – 60)
= (-sin 30°) (-cos 60°) + (-cos 30°) (- sin 60°)
= sin 30 cos 60 + cos 30 sin 60 = sin (30 + 60)
= sin 90° = 1

(iv) If cosec θ + cot θ = $\frac{1}{3}$ , find cos θ and determine the quadrant in which θ lies.
Answer:
we have coses²θ – cot² θ = 1
⇒ (cosec θ + cot θ) (cosec θ – cot θ) = 1

∴ sin θ is positive and cos θ is negative,
⇒ θ lies in IInd quadrant.

Question 5.
(i) If sin α + cosec α= 2, find the value of sinⁿ α + cosecⁿ α; n ∈ Z.

Answer:
Given sin α + cosec α = 2
Squaring both sides
sin² α = cosec² α + 2 = 4
⇒ sin α + cosec α = 2
cubing on both sides
sin³ α + cosec³ α + 3 sin α cosec α (sin α + cosec α) = 8
sin³ α + cosec³ α + 3 (2) = 8
⇒ sin³ α + cosec³ α = 2
In the same way sinⁿ α + cosecⁿ α = 2 (n ∈ z)

(ii) If sec θ + tan θ = 5, find the quadrant in which θ lies and find the value of sin θ
Answer:
We have sec² θ – tan² θ = 1
⇒ (sec θ + tan θ) (sec θ – tan θ) = 1
Also given sec θ + tan θ = 5 ………….(2)

Adding (1) and (2)

tan θ is +ve, sec θ is + ve
⇒ θ lies is first quadrant.

II.
Question 1.
Prove that
(i) $\frac{\cos (\pi-A) \cot \left(\frac{\pi}{2}+A\right) \cos (-A)}{\tan (\pi+A) \tan \left(\frac{3 \pi}{2}+A\right) \sin (2 \pi-A)}$ = cos A

Answer:

(ii) $\frac{\sin (3 \pi-A) \cos \left(A-\frac{\pi}{2}\right) \tan \left(\frac{3 \pi}{2}-A\right)}{{cosec}\left(\frac{13 \pi}{2}+A\right) \sec (3 \pi+A) \cot \left(A-\frac{\pi}{2}\right)}$
Answer:

(iii) sin 780°. sin 480° + cos 240°. cos 300° = $\frac{1}{2}$
Answer:
sin [2 × 360 + 60] sin [360 + 120] + cos [180 + 60] cos [360-60]
= sin 60 sin 120 – cos 60 cos 60
= sin 60 sin 60 – cos 60. cos 60
= $\frac{\sqrt{3}}{2} \frac{\sqrt{3}}{2}-\frac{1}{2} \cdot \frac{1}{2}=\frac{3}{4}-\frac{1}{4}=\frac{1}{2}$

(iv) $\frac{\sin 150^{\circ}-5 \cos 300^{\circ}+7 \tan 225^{\circ}}{\tan 135^{\circ}+3 \sin 210^{\circ}}$ = -2
Answer:

(v) cot $\left(\frac{\pi}{20}\right)$ . cot $\left(\frac{3 \pi}{20}\right)$ . cot $\left(\frac{5 \pi}{20}\right)$ . cot $\left(\frac{7 \pi}{20}\right)$ . cot $\left(\frac{9 \pi}{20}\right)$ = 1
Answer:
cot $\left(\frac{\pi}{20}\right)$ . cot $\left(\frac{3 \pi}{20}\right)$ . cot $\left(\frac{5 \pi}{20}\right)$ . cot $\left(\frac{7 \pi}{20}\right)$ . cot $\left(\frac{9 \pi}{20}\right)$
= cot 9°. cot 27°. cot 45°. cot 63°. cot 81°
= cot 9°. cot 27°. 1.cot (90 – 27) . cot (90 -9)
= cot 9°. cot 27°. 1. tan 27°. tan 9°
= 1

Question 2.
(i) Simplify $\frac{\sin \left(-\frac{11 \pi}{3}\right) \tan \left(\frac{35 \pi}{6}\right) \sec \left(-\frac{7 \pi}{3}\right)}{\cot \left(\frac{5 \pi}{4}\right) {cosec}\left(\frac{7 \pi}{4}\right) \cos \left(\frac{17 \pi}{6}\right)}$

Answer:

(ii) If tan 20 ° = p, prove that
$\frac{\tan 610^{\circ}+\tan 700^{\circ}}{\tan 560^{\circ}-\tan 470^{\circ}}=\frac{1-p^2}{1+p^2}$
Answer:
Given that tan 20° = p then

(iii) If α, β are complementary angles such that b sin α = a, then find the value of (sin α cos β – cos α sin β)
Answer:
Given α, β are complementary angles α + β = 90°
⇒ β = 90° – α
∴ sin α cos β – cos α sin β
= sin (α – β)
= sin[α – (90 – α)]
= sin [2α – 90°]
= -sin[90 – 2α]
= -cos 2α
= -(1 – 2sin²α) = -1 + 2sin²α
= -1 + 2 $\left(\frac{a^2}{b^2}\right)$
= $\frac{2 a^2-b^2}{b^2}$

Question 3.
(i) If cos A = cos B = – $\frac{1}{2}$ , A does not lie in the second quadrant and B does not lie in third quadrant, then find the value of $\frac{4 \sin B-3 \tan A}{\tan B+\sin A}$

Answer:
cos A = – $\frac{1}{2}$ and A does not lie in second quadrant
⇒ A lies in third quadrant
cos B = – $\frac{1}{2}$ and B does not lie in third quadrant
⇒ B lies in second quadrant
cos A = – $\frac{1}{2}$ and A lie in third quadrant
⇒ A = 240°
cos B = – $\frac{1}{2}$ and B lies in second quadrant.
⇒ B = 120°

(ii) If 8 tan A = -15 and 25 sin B = -7 and neither A nor B is in the fourth quadrant, then show that sin A cos B + cos A sin B = $\frac{-304}{425}$
Answer:
8 tan A = -15 25 sin B = -7
⇒ tan A = $\frac{-15}{8}$ ⇒ sin B = $\frac{-7}{25}$
Given neither A nor B is in the fourth quadrant, clearly A is in second quadrant and B is in third quadrant,
sin A cos B + cos A sin B

TS Inter 1st Year Maths 1A Study Material Pdf Download | TS Intermediate Maths 1A Solutions

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January 30, 2026

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Chapter 3 Matrices Ex 3(f)
Chapter 3 Matrices Ex 3(g)
Chapter 3 Matrices Ex 3(h)
Chapter 3 Matrices Ex 3(i)

TS Inter 1st Year Maths 1A Study Material Pdf Download | TS Intermediate Maths 1A Solutions

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TS Inter 1st Year Maths 1A Addition of Vectors Solutions

Chapter 4 Addition of Vectors Ex 4(a)
Chapter 4 Addition of Vectors Ex 4(b)

TS Inter 1st Year Maths 1A Products of Vectors Solutions

TS Inter 1st Year Maths 1A Trigonometric Ratios upto Transformations Solutions

Chapter 6 Trigonometric Ratios upto Transformations Ex 6(a)
Chapter 6 Trigonometric Ratios upto Transformations Ex 6(b)
Chapter 6 Trigonometric Ratios upto Transformations Ex 6(c)
Chapter 6 Trigonometric Ratios upto Transformations Ex 6(d)
Chapter 6 Trigonometric Ratios upto Transformations Ex 6(e)
Chapter 6 Trigonometric Ratios upto Transformations Ex 6(f)

TS Inter 1st Year Maths 1A Trigonometric Equations Solutions

Chapter 7 Trigonometric Equations Ex 7(a)

TS Inter 1st Year Maths 1A Inverse Trigonometric Functions Solutions

Chapter 8 Inverse Trigonometric Functions Ex 8(a)

TS Inter 1st Year Maths 1A Hyperbolic Functions Solutions

Chapter 9 Hyperbolic Functions Ex 9(a)

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Chapter 10 Properties of Triangles Ex 10(a)
Chapter 10 Properties of Triangles Ex 10(b)

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January 29, 2026