Class 11

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 Solutions CHSE Odisha Chapter 11 Straight Lines Ex 11(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 11 Straight Lines Exercise 11(a)

Question 1.
Find the distance between the following pairs of points.
(i) (3, 4), (-2, 1);
Solution:
Distance between points (3, 4) and (-2, 1) is
\(\sqrt{(3+2)^2+(4-1)^2}=\sqrt{25+9}=\sqrt{34}\)

(ii) (-1, 0), (5, 3)
Solution:
The distance between the points (-1, 0) and (5, 3) is
\(\sqrt{(-1-5)^2+(0-3)^2}\)
= \(\sqrt{36+9}=\sqrt{45}=3 \sqrt{5}\)

Question 2.
If the distance between points (3, a) and (6, 1) is 5, find the value of a.
Solution:
Distance between the points. (3, a) and (6, 1) is
\(\sqrt{(3-6)^2+(a-1)^2}=\sqrt{9+(a-1)^2}\)
∴ \(\sqrt{9+(a-1)^2}=5\)
or, 9 + (a – 1)² = 25
or, (a – 1)² = 16
or, a – 1 = ± 4
a = 1 ± 4 = 5 or, – 3

Question 3.
Find the coordinate of the points which divides the line segment joining the points A (4, 6), B (-3, 1) in the ratio 2: 3 internally. Find also the coordinates of the point which divides \(\overline{\mathbf{A B}}\) in the same ratio externally.
Solution:

Question 4.
Find the coordinates of the mid-point of the following pairs of points.
(i) (-7, 3), (8, -4);
Solution:
Mid-point of the line segment joining the points (-7, 3) and (8, -4) are \(\left(\frac{-7+8}{2}, \frac{3-4}{2}\right)=\left(\frac{1}{2},-\frac{1}{2}\right)\)

(ii) (\(\frac{3}{4}\), -2), (\(\frac{-5}{2}\), 1)
Solution:
Mid-point of the line segment joining the points. (\(\frac{3}{4}\), -2) and (\(\frac{-5}{2}\), 1) is,
\(\left(\frac{\frac{3}{4}-\frac{5}{2}}{2}, \frac{-2+1}{2}\right)=\left(\frac{-7}{8}, \frac{-1}{2}\right)\)

Question 5.
Find the area of the triangle whose vertices are (1, 2), (3, 4) (\(\frac{1}{2}\), \(\frac{1}{4}\))
Solution:
Area of the triangle whose vertices are (1, 2), (3, 4) and (\(\frac{1}{2}\), \(\frac{1}{4}\)) is

Question 6.
If the area of the triangle with vertices (0, 0), (1, 0), (0, a) is 10 units, find the value of a.
Solution:
Area of the triangle with vertices (0, 0),(1,0), (0, a), is \(\frac{1}{2}\) × 1 × a = \(\frac{a}{2}\)
∴ \(\frac{a}{2}\) = 10 or a = 20

Question 7.
Find the value of a so that the points (1, 4), (2, 7), (3, a) are collinear.
Solution:
As points (1, 4), (2, 7), (3, a) are collinear, we have the area of the triangle with vertices (1, 4), (2, 7), and (3, a) is zero.
∴ \(\frac{1}{2}\) {1(7 – a) + 2(a – 4) + 3 (4 – 7)} = 0
or, 7 – a + 2a – 8 + 12 – 21 =0
⇒ a = 10

Question 8.
Find the slope of the lines whose inclinations are given.
(i) 30°
Solution:
The slope of the line whose inclination is 30°.
tan 30° = \(\frac{1}{\sqrt{3}}\)

(ii) 45°
Solution:
Slope = tan 45° = +1

(iii) 60°
Solution:
Slope = tan 60° = √3

(iv) 135°
Solution:
Slope = tan 135° = – 1

Question 9.
Find the inclination of the lines whose slopes are given below.
(i) \(\frac{1}{\sqrt{3}}\)
Solution:
The slope of the line is \(\frac{1}{\sqrt{3}}\)
∴ tan θ = \(\frac{1}{\sqrt{3}}\) or, θ = 30°
∴ The inclination of the line is 30°

(ii) 1
Solution:
Slope = 1 = tan 45°
∴ The inclination of the line is 45°.

(iii) √3
Solution:
Slope = √3 = tan 60°  ∴ θ = 60°
∴ Inclination = 60°

(iv) – 1
Solution:
Slope = – 1 = tan 135°
∴ Inclination = 135°

Question 10.
Find the angle between the pair of lines whose slopes are ;
(i) \(\frac{1}{\sqrt{3}}\), 1
Solution:

(ii) √3, -1
Solution:

Question 11.
(a) Show that the points (0, -1), (-2, 3), (6, 7), and (8, 3) are vertices of a rectangle.
Solution:


∴ The opposite sides are equal and two consecutive sides are perpendicular. So it is a rectangle.

(b) Show that the points (1, 1), (-1, -1), and (-√3, √3) are the vertices of an equilateral triangle.
Solution:

Question 12.
Find the coordinates of the point P(x, y) which is equidistant from (0, 0), (32, 10), and (42, 0).
Solution:

Question 13.
If the points (x, y) are equidistant from the points (a + b, b – a) and (a – b, a + b), prove that bx = ay.

Question 14.
The coordinate of the vertices of a triangle are (α₁, β₁), (α₂, β₂), and (α₃, β₃). Prove that the coordinates of its centroid is \(\left(\frac{\alpha_1+\alpha_2+\alpha_3}{3}, \frac{\beta_1+\beta_2+\beta_3}{3}\right)\)
Solution:

Question 15.
Two vertices of a triangle are (0, -4) and  (6, 0). If the medians meet at the point (2, 0), find the coordinates of the third vertex.
Solution:

∴ \(\frac{6+x}{3}\) = 2, \(\frac{-4+y}{3}\) = 0
⇒ x = 0, y = 4
∴ The coordinates of the 3rd vertex are (0, 4).

Question 16.
If the point (0, 4) divides the line segment joining(-4, 10) and (2, 1) internally, find the point which divides it externally in these same ratios.
Solution:

Question 17.
Find the ratios in which the line segment joining (-2, -3) arid (5, 4) is divided by the coordinate axes and hence find the coordinates of these points.
Solution:

Question 18.
In a triangle, one of the vertices is at (2, 5) and the centroid of the triangle is at (-1, 1). Find the coordinates of the midpoint of the side opposite to the given angular point.
Solution:

Question 19.
Find the coordinates of the vertices of a triangle whose sides have midpoints at (2, 1), (-1, 3), and (-2, 5).
Solution:

∴ x₂ + x₃ – 4 or, x₂ – 4 – 3 = 1
∴ x₁ = – 4 – x₂ = -4 – 1 = -5
Similarly y₁ + y₂ + y₃ = 5 + 1 + 3 = 9
As y₁ + y₂ = 10
we have y₃ = 9 – 10 = – 1
Again y₁ + y₃ = 6
or, y₁ = 6 – y₃ = 6 + 1 = 7
and y₂ = 10 – y₁ = 10 – 7 = 3
∴ The coordinates of A, B, and C are (-5, 7), (1, 3), and (3, -1).

Question 20.
If the vertices of a triangle have their coordinates given by rational numbers, prove that the triangle cannot be equilateral.
Solution:
Let us choose the contradiction method. Let the triangle is equilateral if the co¬ ordinate of the vertices is rational numbers.
Let ABC be an equilateral triangle with vertices A (a, 0), B (a, 0), and C (b, c) where a, b, c are rational.

⇒ a² = b² + c² = \(\frac{a^2}{4}\) + c²
⇒ c² =  a² – \(\frac{a^2}{4}\) = \(\frac{3a^2}{4}\) ⇒ c = \(\frac{\sqrt{3}}{2}\) a     ….(2)
Now b = \(\frac{a}{2}\), c = \(\frac{\sqrt{3}}{2}\) a
If a is rational then b is rational but c is irrational, i.e., the coordinates of the vertices are not rational, which contradicts the assumption.
Hence assumption is wrong.
So the triangle cannot be equilateral if the coordinate of the vertices is rational numbers.

Question 21.
Prove that the area of any triangle is equal to four times the area of the triangle formed by joining the midpoints of its sides.
Solution:

∴ The area of triangle ABC is four times the area of triangle DEF. (Proved)

Question 22.
Find the condition that the point (x, y) may lie on the line joining (1, 2) and (5, -3).
Solution:

∴ As points A, B, and C are collinear, we have the area of the triangle ABC as 0.
∴ \(\frac{1}{2}\) {1(-3 – y) + 5(y – 2) + x(2 + 3)} = 0
or, – 3 – y + 5y – 10 + 5x = 0
or, 5x + 4y = 13

Question 23.
Show that the three distinct points (a², a), (b², b), and (c², c) can never be collinear.
Solution:
Area of the triangle with vertices (a², a), (b², b) , and (c², c) is
\(\frac{1}{2}\) {a²(b – c) + b²(c – a) c²(a – b)}
= (a – b)(b – c)(a – c)
which is never equal to zero except when a = b = c, hence the points are not collinear.

Question 24.
If A, B, and C are points (-1, 2), (3, 1), and (-2, -3) respectively, then show that the points which divide BC, CA, and AB in the ratios (1: 3), (4: 3) and (-9: 4) respectively are collinear.
Solution:
Let the points P, Q, and R divides \(\overline{\mathrm{BC}}\), \(\overline{\mathrm{CA}}\), in \(\overline{\mathrm{AB}}\) the ratio 1: 3, 4: 3 and -9: 4

Question 25.
Prove analytically :
(a) The line segment joining the midpoints of two sides of a triangle is parallel to the third and half of its length.

Solution:
Let the coordinates of the triangle ABC be (x₁, y₁), (x₂, y₂) and (x₃, y₃)
The points D and E are the midpoints of the sides \(\overline{\mathrm{AB}}\) and \(\overline{\mathrm{AC}}\)

(b) The altitudes of a triangle are concurrent.
Solution:

(c) The perpendicular bisectors of the sides of a triangle are concurrent.
Solution:

(d) An angle in a semicircle is a right angle.
Solution:

∴ The angle in a semicircle is a right angle. (Proved)

Odisha State Board Elements of Mathematics Class 11 CHSE Odisha Solutions Chapter 10 Sequences and Series Ex 10(a) Textbook Exercise Questions and Answers.

CHSE Odisha Class 11 Math Solutions Chapter 10 Sequences and Series Exercise 10(a)

Question 1.
Which of the following in a sequence?
(i) f(x) = [x], x ∈ R
(ii) f(x) = |x|, x ∈ R
(iii) f(x) = \(\sqrt[n]{\pi}\) ,n∈ N
Solution:
(iii) f(x) = \(\sqrt[n]{\pi}\) ,n∈ N is a sequence f(n) : N → X, X ⊂ R.

Question 2.
Determine if (t_n) is an arithmetic sequence if :
(i) t_n = an² + bn
Solution:
t_n = an² + bn
⇒ t_n+1 = a(n + 1)² + b(n – 1)
⇒ t_n+1 – t_n = a{(n + 1)² – n²} + b{n + 1 – n}
= a(2n + 1) + b
Which is not independent of n.
∴ (t_n) is not an A.P.

(ii) t_n = an + b
Solution:
t_n = an + b
⇒ t_n+1 = a(n + 1) + b
Now t_n+1 – t_n
= {a(n + 1) + b} – {an + b}
= a (constant)
∴ (t_n) is an arithmetic sequence.

(iii) t_n = an² + b
Solution:
t_n = an² + b
⇒ t_n+1 = a(n + 1)² + b
∴ t_n+1 – t_n = a[(n + 1)² – n²] + b – b
= a(2n + 1)
(does not independent of n)
∴ (t_n) is not an arithmetic sequence.

Question 3.
If a geometric series converges which of the following is true about its common ratio r?
(i) r > 1
(ii) -1 < r < 1
(iii) r > 0
Solution:
(ii) -1 < r < 1

Question 4.
If an arithmetic series ∑tn converges, which of the following is true about t_n?
(i) t_n < 1
(ii) |t_n| < 1
(iii) t_n = 0
(iv) t_n → 0
Solution:
(iii) t_n = 0

Question 5.
Which of the following is an arithmetic-geometric series?
(i) 1 + 3x + 7x² + 15x³+ ….
(ii) x + \(\frac{1}{2}\)x + \(\frac{1}{3}\)x² + ….
(iii) x + (1 + 2)x² + (1 + 2 + 3)x³ +…
(iv) x + 3x² + 5x³ + 7x⁴ + …
Solution:
(iv) x + 3x² + 5x³ + 7x⁴ + … is an arithmetic geometric series with a = 1, d = 2, r = x.

Question 6.
For an arithmetic sequence (t_n) t_p = q, t_q = p, (p ≠ q), find t_n.
Solution:
t_p = q ⇒ a + (p – 1)d = q    ……(1)
t_q = p ⇒ a + (q – 1)d = p    ……(2)
From (1) and (2) we have (p – q)d = q – p
⇒ d = (-1)
Putting d = (-1) in (1)
we have a = p + q – 1
∴ t_n = a + (n – 1)d
= (P + q – 1) + (n – 1) (-1)
= p + q – n

Question 7.
For an arithmetic series, ∑a_n S_p = q and S_q = p (p ≠ q) find S_p+q
Solution:
S_p = q and S_q = p

Question 8.
The sum of a geometric series is 3. The series of squares of its terms have a sum of 18. Find the series.
Solution:

Question 9.
The sum of a geometric series is 14, and the series of cubes of its terms have a sum of 392 find the series.
Solution:


∴ The series is \(\sum_{n=1}^{\infty} \frac{7}{2^{n-1}}\)

Question 10.
Find the sum as directed
(i) 1 + 2a + 3a² + 4a³ + …..(first n terms(a ≠ 1))
Solution:

(ii) 1 + (1 + x)y + (1 + x + x²)y² + …..(to infinity)
Solution:
Let S_∞ = 1 + (1 + x)y + (1x + x²)y² + …
⇒ S_n = 1 + (1 + 1 + x)y + (1 + x + x²)y² + ……+(1 + x + …. x^n-1)y^n-1

(iii) 1 + \(\frac{3}{5}\) + \(\frac{7}{25}\) + \(\frac{15}{125}\) + \(\frac{31}{625}\) + …..(to infinity)
Solution:

(iv) 1 + 4x + 8x² + 13x³ + 19x⁴ + …..(to infinity). Assuming that the series has a sum for |x| < 1.
Solution:

(v) 3.2 + 5.2² + 7.2³ + …..(first n terms)
Solution:
Sn = 3.2 + 5.22 + 7.3 + ….n terms = 2[3 + 5.2 + 7.22 + ….n terms]

Question 11.
Find the sum of the infinite series.
(i) \(\frac{1}{1 \cdot 2}+\frac{1}{2 \cdot 3}+\frac{1}{3 \cdot 4}+\ldots\)
Solution:

= 1 – \(\frac{1}{n+1}\)
∴ \(S_{\infty}=\lim _{n \rightarrow \infty} S_n=1\)

(ii) \(\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+\frac{1}{3 \cdot 4 \cdot 5}+\ldots\)
Solution:
\(\frac{1}{1 \cdot 2 \cdot 3}+\frac{1}{2 \cdot 3 \cdot 4}+\frac{1}{3 \cdot 4 \cdot 5}+\ldots\)

(iii) \(\frac{1}{2 \cdot 5 \cdot 8}+\frac{1}{5 \cdot 8 \cdot 11}+\frac{1}{8 \cdot 11 \cdot 14}+\ldots\)
Solution:
Here t_n = \(\frac{1}{(3 n-1)(3 n+2)(3 n+5)}\)
The denominator of t_n is the product of 3 consecutive terms of A.P. Now multiplying and dividing by (3n + 5) – (3n – 1) we have
\(t_n=\frac{(3 n+5)-(3 n-1)}{6(3 n-1)(3 n+2)(3 n+5)}\)

(iv) \(\frac{3}{1^2 \cdot 2^2}+\frac{5}{2^2 \cdot 3^2}+\frac{7}{3^2 \cdot 4^2}+\ldots\) [Hint : take t_n = \(\frac{2 n+1}{n^2(n+1)^2}=\frac{(n+1)^2-n^2}{n^2(n+1)^2}\)]
Solution:

(v) \(\frac{1}{1 \cdot 5}+\frac{1}{3 \cdot 7}+\frac{1}{5 \cdot 9}+\ldots .\)
Solution:

Question 12.
Find S_n for the series.
(i) 1.2 + 2.3 + 3.4 + ….
Solution:

(ii) 1.2.3 + 2.3.4 + 3.4.5 + …
Solution:

(iii) 2.5.8 + 5.8.11 + 8.11.14 +…
Solution:

(iv) 1.2.3.4 + 2.3.4.5 + 3.4.5.6 + …
[Hint : t_n = (3n – 1) (3n + 2)(3n + 5)]
Solution:

(v) 1.5 + 2.6 + 3.7 + …
[Hint: t_n = n(n + 4) is not a product of two successive terms of an A.P. for the term following n should be n+1, not n+4. So the method of previous exercises is not applicable. Instead, write t_n = n² + 4n and find S_n = \(\sum_{k=1}^n k^2+4 \sum_{k=1}^n k\) applying formulae]
Solution:

(vi) 2.3 + 3.6 + 4.11 + …
[Hint : Take t_n = (n + 1) (n² + 2)]
Solution:

(vii) 1.3² + 2.5² + 3.7² + ….
Solution:

Question 13.
Find the sum of the first n terms of the series:
(i) 5 + 6 + 8 + 12 + 20 + …
Solution:

(ii) 4 + 5 + 8 + 13 + 20 + …
Solution:

Question 14.
(i) Find the sum of the product of 1,2,3….20 taken two at a time. [Hint: Required sum = \(\frac{1}{2}\left\{\left(\sum_{k=1}^{20} k\right)^2-\sum_{k=1}^{20} k^2\right\}\)]
Solution:
We know that
(x₁ + x₂ + x₃ + …. + x_n)²
= (x²₁ + xⁿ₂ + … + x²_n) + 2 (Sum of all possible Products taken two at a time)
∴ 2 (Sum of products of 1. 2, 3,…… 20 taken two at a time)
= (1 + 2 + 3 + … 20)² – (1² + 2² + … + 20²)
\(=\left(\frac{20 \times 21}{2}\right)^2-\frac{20(20+1)(40+1)}{6}\)
= (210)² – 70 × 41
= 44100 – 2870 = 41230
∴ The required sum = \(\frac{41230}{2}\) = 20615

(ii) Do the same for 1, 3, 5, 7,….19.
Solution:
Here the required sum

Question 15.
If a = 1 + x + x² + ….. and b = 1 + y + y² + ….|x| <  1 and |y| <  1, then prove that 1 – xy + x²y² + x³y³ + ….. =  \(\frac{a b}{a+b-1}\)
Solution:

Question 16.
If a, b, c are respectively the pth, qth, rth terms of an A.P., then prove that a(q – r) + b(r – p) + c(p – q) = 0
Solution:
Let the first term of an A.P. = A and the common difference = D.
According to the question
t_P = a, t_q = b, t_r = c
⇒ A + (p – q)D = a      …..(1)
A + (q – 1)D = b           …..(2)
A + (r – 1)D = c            …..(3)
L.H.S = a(q – r) + b (r – p) + c (p – q)
= (A + (p – 1)D) (q – r) + (A + (q – 1)D)
(r- p) + (A + (r – 1)D) (p – q)
= A (q – r + r – p + p – q) + D [(p – 1)
(q – r) + (q – 1) (r – p) + (r – 1) (p – q)]
= D (pq – pr + qr – pq + pr – qr) – D (q – r + r – p + p – q) = 0

Question 17.
If \(\frac{1}{a}, \frac{1}{b}, \frac{1}{c}\) are in A.P. and a + b + c ≠ 0, prove that \(\frac{\mathbf{b}+\mathbf{c}}{\mathbf{a}}, \frac{\mathbf{c}+\mathbf{a}}{\mathbf{b}}, \frac{\mathbf{a}+\mathbf{b}}{\mathbf{c}}\) are in A.P.
Solution:

Question 18.
If a², b², c² are in A.P. Prove that \(\frac{1}{b+c}, \frac{1}{c+a}, \frac{1}{a+b}\) are in A.P.
Solution:

Question 19.
If \(\frac{b+c}{a}, \frac{c+a}{b}, \frac{\mathbf{a}+\mathbf{b}}{c}\) are in A.P.,prove that \(\frac{\mathbf{1}}{\mathbf{a}}, \frac{\mathbf{1}}{\mathbf{b}}, \frac{\mathbf{1}}{\mathbf{c}}\) are inA.P.given a + b + c ≠ 0
Solution:

Question 20.
If (b – c)², (c – a)², (a – b)² are in A.P., prove that \(\frac{1}{b-c}, \frac{1}{c-a}, \frac{1}{a-b}\) are in A.P.
Solution:

Question 21.
If a, b, c are respectively the sum of p, q, r terms of an A.P., prove that \(\frac{a}{p}(q-r)+\frac{b}{q}(r-p)+\frac{c}{r}(p-q)\) = 0
Solution:

Question 22.
If a, b, c,d are in G.P., prove that (a² + b² + c²)(b² + c² + d²) = (ab + bc + cd)².
Solution:
Let a, b, c, and d are in G.P.
Let the common ratio = r
⇒ b = ar, c = ar², d = ar³
LHS = (a² + b² + c²) (b² + c² + d²)
= (a² + a²r² + a²r⁴) (a²r² + a²r⁴ + a²r⁶)
= a⁴r² (1 + r² + r⁴)²
= (a²r + a²r³ + a²r⁵)²
= (a.ar + ar.ar² + ar².ar³)²
= (ab + bc + cd)² = R.H.S. (proved)