Plus Two

Kerala Plus Two Political Science Previous Year Question Paper 2011

Question 1.
From the list given below identify the factors that influenced India to frame the foreign policy ideal “peaceful co-existence.” (2)

1. Influence of Buddhism
2. Fear of military strength of neighboring countries.
3. Not to join power blocs.
4. Influence of Gandhian non-violence.

Answer:

1. The influence of Buddhism.
2. Influence Gandhi’s principle of non-violence.

Question 2.
Expand the abbreviations given below: (3)

1. SALT
2. START
3. CTBT

Answer:

1. Strategic Arms Limitation Talks.
2. StrategicArms Reduction Treaty
3. Comprehensive Test Ban Treaty

Question 3.
From the table given below, name the States from which they were carved out. (3)

1. Chhattisgarh – Maharashtra
2. Uttaranchal – Andhra Pradesh
3. Jharkhand – Bihar – Uttar Pradesh – Madya Pradesh

Answer:

1. Chattisgarh – Madhya Pradesh
2. Uttaranchal – Uttar Pradesh
3. Jharkhand – Bihar

Question 4.
If we examine the State Politics in Kerala, Kerala has been practicing Coalition Form of Government successfully since its formation. Find out the factors for the success of a Coalition Government. Do you think that a Coalition is a good Government? Substantiate your arguments. (6)
Answer:
Coalition governments started in Kerala in 1960. In 1957 (CPI) and 1962 (Congress), there were single-party governments. Here are the features of the coalition governments of Kerala:

There is no political party that maintains permanent enmity with any another political party. At one time, Muslim League had worked with Communist groups. Kerala Congress is a regional party. It has many groups and all of them have aligned themselves with both the Left and Right Fronts. It was the Achutha Menon Ministry that completed its fuil term for the first time. Even when some highly useful bills are enacted some parties create problems Tor the majority ruling party making the government collapse. In the 1960s and 70s, there were Ton- political, but influential organizations like the SNDP and NSS trying to help bring stability in the governments. The golden period of Kerala’s coalition governments is the Achutha Menon Ministry of 1970. The various political parties of Kerala do not have a stable and fixed ideological base. The best example of this instable ideological base is the Kerala Congress Groups which come in and go out of Ministries, both Left and Right. Sometimes they are here and sometimes they are there.

Question 5.
“A new balance between environmental concern and industrial needs is needed.”
“Sustainable development is not possible without protecting the environment.”
In light of the above statements, state your arguments for sustainable development without compromising environmental protection. (4)
Answer:
In modern times, ‘development’ should be seen as sustainable development. The traditional concepts of development were based on the growth of industries,, in the statistics about per capita income. But in the 1992 Rio Summit, the UN presented before the world “Agenda-21 ” which is a different development mode!. It is sustainable development Let us see how sustainable development is possible without harming our environment.

a. Give priority to non-traditional energy sources. Here we give stress to wind, waves and solar power to produce energy.
b. Avoid plastic waste and things like plastic bags. Make use of things that can be used again and again.
c. if deforestation is done for the development of roads and industries, plant trees in more places to compensate for the deforested land.
d. Ensure that the marshes and watersheds are maintained and protected.
e. Make sure that common resources of the world like; air and water are not polluted. Enforce anti-pollution laws.

People must realize that this earth belongs to future generations also and therefore steps must be taken to insure that it is not polluted. There should- be awareness programs on the part of the governments.

Question 6.
After the Second World War, nations are grouped under two power blocs – one under USA and other under USSR. List out the factors responsible for this Bipolarity. (4)
Answer:
After the Second World War, nations joined either the Soviet Bloc or the American Bloc. Beyond an ideological grouping, this polarization could be seen as a means of strengthening the economic and military power of the Superpowers, Let us see in which areas they tried to make their supremacy felt:

(a) Taking control of the natural resources: America and Soviet Union competed among themselves to keep developing countries with oil, natural gas, rare minerals and other resources in their group.

(b) The Superpowers wanted venues to store their arms and strategic spots from which they could use them against enemy countries.

(c) The Superpowers wanted friendly countries around from which they could spy on the movements of their enemies.

(d) In a war-like atmosphere, the Superpowers wanted to make huge profits by selling the destructive weapons they manufactured to various countries. All these were the reasons for the polarization,

Question 7.
From the list given below, find out the institutions which are not the principal organs of U.N.O (3)
(1) General Assembly
(2) World Health Organisation
(3) Security Council
(4) Economic and Social Council
(5) United Nations Educational Scientific and Cultural Organization (UNESCO)
(6) United Nations International Children’s Emergency Fund (UNICEF)
Answer:
(a) World Health Organization.
(b) United Nations Educational, Scientific and Cultural Organization
(c) United Nations International Children’s Emergency Fund

Question 8.
Interstate relations in the Post-Cold War era have been subjected to many changes in power relations. Examine them on the basis of the hints below. (4)
(1) Imperialism
(2) Disintegration of Communist Bloc
(3) American Hegemony
(4) Weak ness of Non-Alignment Movement
Answer:
With the end of the Cold War, the dangerous power struggle between the Superpowers ended. Both Paper March – 2011 America and Soviet Union desisted from their desire to bring third-world nations under their control. An internal economic crisis rocked the Soviet Union, In his efforts to find solutions to the pressing problem, Gorbachev tried some reforms known as Glasnost and Perestroika. In fact, these policies led to the disintegration of the Soviet Union and the isolation of Russia as an economic power. The disintegration of the USSR began in March 1885 and by 1991, it was complete. Now it is the American hegemony. Estonia, Latvia and Lithuania came out of the Soviet Union and joined NATO. America has been eyeing at the rich hydrocarbon resources of some Asian countries and it is trying to build its army bases in some of these countries on a lease basis.

America now has three kinds of hegemony or dominance:
1. Dominance as a military power: American military presence is felt almost everywhere In the world and they sell military hardware to many developing nations.

2. Structural dominance: America has its omnipresence in the world through the Internet, the Breton Woods system that controls global economy and non-traditional educational disciplines like MBA and Fashion Technology. 15% of the world trade is done by America.

3. Dominance as a Soft Power: Ideological and cultural dominance is what is meant by soft power. America has been able to westernize consumerism in many countries. Today’s generation that prefers coca-cola to tender coconut water is in the grip of this Western soft power. With the collapse of the Soviet Union many people doubt the relevance of the NAM (Non- Aligned Movement) which was formed under the leadership of Nehru. Tito and Nasser. Today NAM is trying hard to become an economic power, it can make positive contributions in areas like global warming, production of carbon, poverty in Africa, proper utilization of international resources, terrorism and so on.

Question 9.
Identify the Commission which was appointed by the Government to enquire into Emergency Excess in 1977. (1)
Answer:
Shah Commission

Question 10.
Match the Country with the Leaders who are associated with Non-Alignment Movement. (2)
A – B
Ghana – Nehru
India – Nassar
Egypt – Nkrumah
Yugoslavia – Tito, Sukarno
Answer:
1. Ghana – Nkrumah
2. India – Nehru.
3. Egypt – Nasser
4. Yugoslavia – Tito

Question 11.
Independent India faced many challenges in nation-building process. Do you think that we have overcome ail these challenges? You can use the following hints to develop your answer. (7)
(1) Ensure the accommodation of Diversity
(2) Ensure Democracy
(3) Ensure Equality
(4) Ensure Development
Answer:
independent India faced three kinds of challenges.
(a) Integrating India
(b) Ensuring the welfare of the people and development
(c) Establish the democratic system

(a) Integrating India: When India got freedom, it had more than 500 Princely States. The rulers of these places wanted to get back their sovereignty when the British left. The government approached the Princely States keeping three things in mind.

• The majority of people of the Princely States wanted to join Indian Union.
• Giving some kind of self-rule to some Princely States.
• In the background of the division, we needed States with precision.

Integration:
Except for Junagarh, Hyderabad. Kashmir and Manipur, all the Princely States signed in the Instrument of Accession and joined the Indian Union. Then through a referendum, Junagarh joined Indian Union. Because of popular uprising in Hyderabad against the Nizam, the Indian army took some action and got Hyderabad also into the Union. The Congress Group in Manipur wanted to join the Union, but other parties objected. However, the Manipur king was persuaded and he too joined the Union. Kashmir King also signed the Instruction of Accession to save himself from the attacks of Pakistan and thus Kashmirtoo became part of India.

The division of the country into States on linguistic basis showed that it could accommodate all the diversities. The people can accept the diversities and live in unity. This is the strength of a country. The Telangana protest and the martyrdom of Potti Sriramuiu should be remembered here.

Ensuring the welfare of people:
India was a poor country. The country has included provisions in the Constitution to ensure protection to the socially backward people, to religious and cultural minorities and to give all the people equality. Through Directive Principles, the Constitution shows us the way to eradicate poverty and to make the marginalized people come into mainstream society.

Five Year Plans:
The country has a development model based on socialist principles. We have adopted a mixed economy accommodating both public and private sector enterprises.

Establishing democratic system:
Democracy was a discovery of foreigners. But the big thing was that we chose democracy in spite of the fact that India is a poor country and there are many illiterates here. The first election was called the greatest gamble in history by foreign media. A British member of the Civil Service said that the future generations would condemn this democratic process as a foolish enterprise. The first Election Commission was formed with Dr. SukumarSen as the Commissioner. Illiterate Indians were supposed to think in terms of caste and creed. But by making a voters’ list based on our secular system and equality, we succeeded in conducting a fair election and we were successful in our democratic experiment Even after 70 years of Independence, we still face some challenges to our democracy. There are new demands for regional autonomy. There is the Maoist threat. There is intolerance, following the integration of Manipur. There is the Kashmir problem. In spite of all these we have been able to maintain our democratic tradition. After the 1975 Emergency, our rulers have been able to maintain democratic order without any interruption.

Question 12.
Ban Ki-Moon is the present Secretary-General of the United Nations. Identify the nation to which he belongs. (1)
(1) America
(2) South Korea
(3) Japan
(4) North Korea
Answer:
South Korea

Question 13.
From the list given below, find out the ultimate aim of the United Nations Organization. (1)

1. Ensure international peace and security
2. To avoid armament race
3. Ensure economic stability

Answer:

1. Ensuring international peace and security.

Question 14.
Nations face security threats. They may be traditional and non-traditional. Find out any five major security threats and prepare a brief note. (5)
Answer:
The concept of global security came in the 1990s. Based on this idea, the challenges countries and people face are called non-traditional treats. First, let us see the most important traditional threats:
a. Military attacks and annexations.
b. The presence of nuclear weapons, their testing and possible misuse.
c. Colonialism.

Non-traditional threats challenge even the existence of mankind and their living. Here are some of the important threats of this kind:
a. terrorism
b. contagious diseases
c. human rights violations
d. global warming
e. challenges that global resources face.

Question 15.
“History makes man wise”. Based on the above statement, bring out the lessons we learn from the National Emergency of 1975.
Answer:
The historical events help us to get greater insights. India got her freedom after constant agitations and sacrifices. Our Constitution stresses human rights. But we saw during the Emergency of 1975 that there were some provisions in the Constitution that could make the rights null and void. It was in this period that the people thought of the challenges to democracy and the precautions we should take to preserve our rights.

Question 16.
Match the following. (4)
A                 –            B
1. Chipko Movement – Agrarian struggles
2. Dalit Movement – Social Justice
3. Kissah Movement – Gender equality
4. Women Movement – Environmental Issues, Educational Issues
Answer:
a. Chipko Movement – Environmental Problems
b. Dalit Movement – social justice
c. Kisan Movement – agriculture protests
d. Women Movement – Gender equality

Question 17.
We have experienced several agitations for social justice by the marginalized sections. Do you think these agitations can ensure social justice? Express your opinion. (4)
Answer:
The protests of the marginalized people become relevant in light of the demands they make. Problems that are not
high lighted or rejected by the mainstream political organizations are often brought up by organizations of the marginalized people. Overcoming the narrow vote-bank politics, there have been some movements working for various needs of the people. These organizations work for environmental protection (Chipko Movement), for ensuring social justice (Dalit Panthers) and for gender equality (Women Movements). There was the Plachimada Protest (against exploitation of water resources). The Chengara Protest was against the situation in which people had to live on their own land as aliens.

All the above movements were for common public interests. Long before the Rio Summit took place for Environmental Protection, the illiterate women in the Himalayan villages had organized the Chipko Movement for the protection of their environment. It shows the importance of such movements.

It is not protests and movements that should bring social justice, but the government. The protests by various groups have highlighted the problems and governments have been made aware of their significance forcing them to make laws to ensure social justice.

Question 18.
In a class-room discussion, teacher pointed out that new forms of regionalism are emerging in India. Do you agree with this comment? Substantiate your arguments with suitable examples. (3)
Answer:

India, some new kinds of regionalism are coming up. In the name of “Son of the soil some movements have come up in Maharashtra and Coorg (Kutak) area. The statement of Sachin Tendulkar that Mumbai is the city of all Indians should be taken as a fitting reply to all such region-minded people.

The regional demands that took place in Punjab and the North-Eastern States sometimes degenerated into armed struggle and revolts. The Operation Blue Star of June 1984 and the consequent assassination of Indira Gandhi by her Sikh bodyguards can be pointed out in this context.

The long-standing satyagraha protest by Irom Urmila for recalling the soldiers from Manipur is also a proof of regional demands. (Very recently she stopped her satyagraha)

Question 19.
What can we do for the preservation of beautiful Earth for future generations? Suggest measures. (3)
Answer:
We should know that this beautiful earth belongs to future generations, too. The following suggestions may help:
a. Don’t overuse water. Protect the water sources from pollution.
b. Governments should stress sustainable development for prosperity.
c. Create the awareness that social justice is applicable to the environment also.
d. Let the intelligent man realize that just like him the flora and fauna of this earth have a right to survive here. .
e. Never forget that the earth’s resources will one day finish up. This awareness should come to those who exploit them and those who consume them.

Question 20.
After the disintegration of USSR, America became a power to dominate world politics. Examine the reasons for American Hegemony. (3)
Answer:
The most important points that helped American hegemony are:
a. Disintegration of the USSR and the rise of the Baltic countries.
b: The global interests and power of the Breton Woods system.
c. The military moves and attacks America makes to counter-terrorism.

Question 21.
Given below are certain regional groupings. State the purpose for which they are established. (4)
(1) NATO
(2) ASEAN
(3) SEATO
(4) European Union
Answer:
NATO: It is a military alliance that America formed to reduce the power of the Soviet Union and to prevent the spread of Communism.

ASEAN: This is a fellowship of the South East Asian nations. It started with the declaration in Bangkok in 1967. The members of ASEAN are: Indonesia, Malaysia, Philippines, Singapore, Thailand, Myanmar, Cambodia, Vietnam, Lao PDR and Brunei. The aims of ASEAN are: trying to bring about quick economic growth among member countries, progress in social and cultural matters, peace and stability in the region and making opportunities for the members to solve their mutual problems in an amicable manner.

CEATO: This was started in 1954 under the leadership of America with the intention of preventing Communism from spreading. Its headquarters were in Bangkok. On 31 June 1977, this organization was dispersed. Its members were France. Britain, Australia, New Zealand, Pakistan, Philippines and Thailand.

European Union: After the disintegration of the Soviet Union, this organization was started through the Maastricht Treaty. There are 27 members in it. It is considered as an effort to unify the economic and political matters of Europe. It has common currency, common flag, European Commission and European Central Bank, It thus becomes the biggest economic power in the world.

Question 22.
Though there are many regional groupings in the world, European Union is the most powerful one.’ Do you agree with this statement? Substantiate your arguments. (3)
Answer:
It is true that the strongest regional group in the world is the European Union (EU). Here are the reasons:
a. It is the biggest economic power in the world. It has a greater GDP than America. Euro is more valuable in the international currency than the US dollar.
b. Two of the EU members have veto power in the UN Security Council.
c. Britain and France are nuclear powers. After the USA, EU spends the maximum amount of money for defense. At one these countries were in enmity, leading to even World Wars, but now they are on the path of unity and growth.

Question 23.
Globalisation has reached every nook and corner of our society. We are experiencing its merits and demerits. Identify any three evil effects of globalization. (3)
Answer:
Globalization has mainly 3 demerits:

1. It weakens the traditional concept of sovereignty of nations. The governments that ought to work for social justice withdraw from their responsibilities and this is a defect of globalization.
2. As soft power, we see how Western Culture is making inroads into traditional cultures of nations. There is a tendency for consumerism to grow and the poor and marginalized people continue to remain so.
3. The MNCs are ready to trade anything for the growing market. The resources of the earth are mindlessly exploited. As result global warming and the excessive melting of glaciers threaten the very existence of mankind.

Question 24.
Observe the following statements on South East Asia and prepare a seminar paper on ‘Politics of South East Asia’ (4)
(1) Influence of military is very high. Hence the soil of many nations is fertile for military coup.
(2) Economic backwardness of people is not suitable for the success of democracy.
(3) Ethnic issue makes the problem’more complex.
(4) The lack of charismatic leaders accelerates the threat to democracy.
Answer:
South-Eastern Asia has always been a venue of political polarization. This area includes Bangladesh, Bhutan, India, Maldives, Nepal, Pakistan and Sri Lanka.

In Pakistan and Bangladesh democracy comes and goes. Often, there democracy has led to military rule. Ganeral Yahya Khan, Zia-ul-Haq and Parvez Musharaf were military leaders who overthrew democracy and assumed power. Lack of stable political parties and parties working only for selfish interests are the main reasons for the lack of stable democracy in these countries. The 18 constitutions Amend Act was signed by President Asif Ali Zardari on 19 April 2014. It is hoped that the reduction of Presidential power, the increased powers of the PM and the Parliament might make democracy more stable in Pakistan. on Paper March – 2011 The problems in the Sind and Punjab provinces of Pakistan and the question of survival by the Tamils in Sri Lanka have made South East Asia have turmoil. People think it is the lack of leaders like Nehru that brings troubles to democracy in other countries.

The situation in Bangladesh is not different. It has a Constitution upholding secularism and democracy. The bad days for democracy here started in 1975 with the restructuring of its Constitution. From Parliamentary democracy, it went to Presidential rule. This change helped Sheikh Mujibur Rehman to rule the country in an undemocratic manner. In 1975 itself he was killed. Later Zia-ur-Rehman formed the Bangladesh National Party which won the election in 1979. He was also killed. Then the military leader General Ershad came to power. Later he was elected President. The military rulers of Bangladesh used political parties as a camouflage for their military dictatorship. They were afraid of the democratic rights and desires of the people.

In Nepal, we see the dominance of Maoists organizations. The Maldives is slowly coming towards democracy. Rajapakse of Sri Lanka thinks that the racial problem there could be solved with the fall of the LTTE. Economic backwardness does not become a reason for the collapse of democracy. When India got its freedom it was a very poor country. But it has not adversely affected our democracy.

The problems in the Sind and Punjab provinces of Pakistan and the question of survival by the Tamils in Sri Lanka have made South East Asia to have turmoil. People think it is the lack of leaders like Nehru that brings troubles to democracy in other countries.

Plus Two Political Science Previous Year Question Papers and Answers

Kerala Plus Two Political Science Previous Year Question Paper 2014

Question 1.
“The first Five Year Plan concentrated on the agrarian sector of our country” whether this step made any benefit on our economy? Express your view on this. (2)
Answer:
The first Five Year Plan aimed at improving agriculture. Here, stress was given to dams and irrigation. The land distribution was quite defective and so in the first Plan, stress was given to land reforms to rectify the situation.

Question 2.
Match the following : (2)
Sant Harchand – Mizo National Front
Singh Longowal
Indira Gandhi – Prime MinisterofKashmir
Lai Denga – Akali Dal
SheikAbdullah – Operation Bluestar
Answer:
Sant Harchand Singh Longoval – Akali Dal Indira Gandhi – Operation Blue Star
Lai Denga – Mizo National Front Sheikh Abdullah – Kashmir Prime Minister

Question 3.
Explain the Punjab issue in the light of Ananthapur Sahib Resolution. How the issue resolved? (4)
Answer:
The Indo-Pakistan division and the formation of Haryana and Himachal Pradesh caused the social situation in Punjab change. Punjab State came into existence in 1966 on linguistic basis. Akali Dal propa gated an idea called ‘Punjabi Suba’ and Indira Gandhi approved this demand. Thus Punjab was divided into Punjab and Haryana. Harýana was for the Hindi- speaking people and Punjab for the Punjabi speak ers. Even in the 1967 election, Akali Dal came to power in Punjab by making agreements first with Jan Sangh and later with Janta Party.

Because of certain reasons, the situation became bad for Akali Dal and before completing the term, the government was dismissed by the Centre. The Akali Dal could not get the support of the Hindus. The Sikh Com munityitself was divided on tribal and caste lines. The Dalits supported Congress. In 1970, a group of Akalis demanded political autonomy. They also said that there should be rethinking about Centre State relationship. In 1973, in Anandapur, they passed a resolution supporting this idea. They de manded a Sikh Kaum (Sikh Nation) through this resolution.

This resolution made only the Sikh community happy. In 1980 the Akali Government was dismissed. The Akali Dal leaders tried to prevent the sharing of river water. Some religious leaders also demanded freedom for the Sikh nation. The worst was the demand for an independent Khalistan.

Question 4.
Pakistan is not a stable democratic state. What are reasons for the failure of Pakistan in building a stable democracy? (2)
Answer:
Because of the following reasons Pakistan does not have a stable democracy:
a. Interference by the army, priests and landlords in the administration.
b. Because of the dispute between India and Pakistan, the Pakistani army acquired great power.
c. Lack of international support for the democratic governments often helped the military to come to power.
d. America and some other Western countries prefer a military government in Pakistan. They are afraid that democracy there would make Muslim extremism grow and the extremists might get control over the nuclear weapons in the possession of Pakistan. They think military rule is better for the safety of the Western and Southern Asian regions.

Question 5.
Name the member nations of SAARC. (2)
Answer:

• Nepal
• Sri Lanka
• Pakistan
• India
• Maldives
• Bangladesh
• Bhutan
• Afghanistan

Question 6.
Name the common currency of European Union. (1)
Answer:
Euro

Question 7.
ASEAN is developing as an alternative centre of power in the present-day world. Explain the objectives of ASEAN. (3)
Answer:
ASEAN is an organization of South East Asian Nations. It was formed after the declaration made at Bangkok. Indonesia, Malaysia, Philippines, Singapore, Thailand, Myanmar, Cambodia, Vietnam, Laos and Brunei are the embers of ASEAN. Its objectives are: quick progress in the economic condition of the member nations, social and cultural progress, protecting peace and stability in the region and settling disputes amicably among member countries.

Question 8.
‘On 25th June 1975 emergency declared throughout the country.’ Explain the circumstances which led to the declaration of emergency in the country. (4)
Answer:
By June 1975, the enmity between the ruling party and the opposition became very strong. Jay Prakash Narayan demanded the resignation of Mrs. Gandhi. On 25 June 1975 there was a big protest on the Ramlila Ground in Delhi. There also he demanded

Mrs Gandhi’s’ resignation. He declared he would start a satyagraha. He asked the police and government employees not to obey any rule that was not normal. Government felt it could not continue working. Many people were against Congress As a reaction to all this, on 25 June 1975, Indira Gandhi declared an Emergency saying that there was threat to the internal security of the country.

Question 9.
‘Anti Arrack Movement in Andhra Pradesh was not a mere strike against the liquor mafia of the region, but it had wider perspectives’. How did the Anti-Arrack Movement contribute a great deal in increasing social awareness on women’s questions? (4)
Answer:
In the 1990s, many women in Nellur in Andhra became literate. In the class, women spoke about the drinking habits of their men-folk. Drinking alcohol causes both physical and mental harm. It also adversely affects the economic situation of the family. Men do not go to work. The manufacturers of various kinds of alcoholic beverages make money by using all sorts of illegal means. It is the women that suffer because of the drinking habit of men. The women in Nellur protested against alcoholism and forced a wine shop to close down. This news spread like wild fire into some 5000 villages. They held meetings and passed resolutions and sent them to the Collectors. The arrack auction in Nellur had to be postponed 17 times. The protest in Nellur spread to the rest of the State.

Question 10.
Name the political leader who raised the popular slogan ‘Garibi Hatao’? (1)
Answer:
Medha Patkar

Question 11.
Enumerate the strategies adopted by Mrs. Indira Gandhi to increase her popular support and to win the 1971 Lok Sabha elections. (4)
Answer:
Raised the slogan “Garibi Hatao’.
Gave a boost to land reform measures.
Nationalized some major banks.
Got support from the regional parties striving for their development.

Question 12.
Match the following leaders listed in A with the parties in list B. (2)
A                       –              B
Acharya Narendra Dey – Bharatiya Jan Sang h
EMS Namboodinpad – Swathantratha Party
C. Rajagopalachary – Communist Party
Syamaprasad Mukherjee – Socialist Party
Answer:
Acharya Narendra Dev – Socialist Party E.JVI.S. Namboodiripad – Communist Party C. Rajagopalachari – Swat’antra Party Shyamaprasad Mukherjee- Bhartiya Jan Sangh

Question 13.
USA is often symbolized as the ‘World Police’. This term is used to indicate the hegemony of America in world politics. Explain the different dimensions of American hegemony in international politics? (6)
Answer:
World nations try to gain and maintain dominance over others by using military, economic and cultural power. During the Cold War the fight was between the Soviet Union and America. With the disintegration of the Soviet, Union America remains the only Superpower. Dominance or hegemony is attained through three things:

• Hard Power
• Structural Power
• Soft Power

Hard Power: This includes military power and the relations between nations. Today America is in the forefront of military power. There is nobody to challenge its military might. It has the capacity to reach any corner of the world any moment. They spend a major part of their budget to maintain this position. They spend huge sums of money for research and technological developments. It is technology that keeps America in the forefront. With their military might they are even ready to police the world, and punish the culprits.

Structural Power: This dominance is based on the economic structure. The1 global economic system relies on America. If America helps the global economic system, it is mainly for their benefits and profits. But America does a lot of good things for the world. For example, communication channels through the oceans. Merchant ships travel through sea routes and America has much authority on the water transport system. It is the American navy that keeps the sea-routes safe for ships.

The next is the Internet. In fact it was an American military project. It was started in 1950. Today the global network functions using satellites. Most of them belong to America. 28% of the world economy is controlled by America. 15% of the international trade is also done by them. In any economic sector, at least one of out of three biggest companies will be American. The world economic structure follows the Breton Woods style of America. The World Bank,
I. M.F. and World Trade Organization etc. are examples of American supremacy in world business and finance.

Now comes another example – the MBA degree. It was America that made this course and the degree so popular. It was Americans who discovered that business is a profession that could be taught. The first Business School was established in Pennsylvania in 1881. Its name was Wharton School. Today in all countries MBA has become a prestigious degree.

Soft Power: This is the ideological and cultural dominance. America has become the model for all other nations and they try to copy America. In weak countries, America is able to make the people like its culture.
We all speak highly of the American life style and personal success. America is number one in the world. By using ‘soft power, and not force, America is able to achieve this dominance over the world.

Question 14.
Gorbachev tried to democratise USSR. He implemented economic and political reforms in the country. Read the above indicators and explain the role of Gorbachev to disintegrate USSR. (4)
Answer:
The control exercised by the Soviet government on its citizens made their life difficult.

• There was ho freedom of expression or democracy.
• Many institutions needed reforms. But the Communist Party strictly controlled them and reforms were not possible.
• The Party refused to give people their rights. The Soviet Union wds a Union of 15 Republics. They had their own cultures and problems.
• Although on paper there were 15 Republics, only Russia was allowed to exercise control. Russia other republics were either ignored or suppressed.
• Although the Soviet Union was able to maintain its equality with the US in arms race, it was very costly for them. Western technology was better than the Russian technology. The political and economic needs of the Soviet people were not taken, care of by the Soviet government.
• Soviet Union used most of its resources to develop atomic weapons, to make arms, to increase military facilities and to develop its satellite East European countries.
• The go-slow policy, refusal to correct mistakes and the closed door policy quickened the country’s downfall.

Question 15.
At the time of Independence India faced many challenges. Identify three important challenges faced by our country during independence and describe briefly on each of them. (4)
Answer:
Independent India faced three kinds of challenges.
a. Integrating India
b. Ensuring the welfare of the people and development
c. Establish a democratic system
a. Integrating India: When India got freedom, it had more than 500 Princely States. The rulers of these places wanted to get back their sovereignty when the British left. The government approached the Princely States keeping three things in mind.

a. The majority of people of the Princely States wanted to join the Indian Union.
b. Giving some kind of self-rule to some Princely States.
c. In the background of the division, we needed States with precision.

Integration: Except Junagarh, Hyderabad. Kashrnir and Manipur, all the Princely States signed in the Instrument of Accession and joined the Indian Union. Then through a referendum, Junagarh joined Indian Union. Because of popular uprising in Hyderabad against the Nizam, the Indian army took some action and got Hyderabad also into the Union The Congress Group in Manipurwanted to join thp Union, but other parties objected. However, the Manipur king was persuaded and he too joined the Union. Kashmir King also signed the Instruction of Accession to save himself from the attacks of Pakistan and thus Kashmirtoo became part of India.

The division of the country into States on linguistic basis showed that it could accommodate all the diversities. The people cart accept the diversities and live in unity. This is the strength of a country. The Telangana protest and the martyrdom of Potti Sriramulu should be remembered he? Ensuring the welfare of people: India Was a poor country. The country has included provisions in the Constitution to ensure protection to the socially backward people, to religious and cultural minorities and to give ail the people equality. Through Directive Principles, the Constitution shows us the way to eradicate poverty and to make the marginalized people come into mainstream society.

Five Year Plans: The country has a development model based on socialist principles. We have adopted a mixed economy accommodating both public and private sector enterprises.

Establishing democratic system: Democracy was a discovery of foreigners. But the big thing was that we chose democracy in spite of the fact that India is a poor country and there are many illiterates here. The first election was called the greatest gamble in history by foreign media. A British member of the Civil Service said that the future generations would condemn this democratic process as a foolish enterprise. The first Election Commission was formed with Dr. Sukumar Sen as the Commissioner. Illiterate Indians were supposed to think in terms of caste and creed. But by making a voters’ list based on our secular system and equality, we succeeded in conducting a fair election and we were successful in our democratic experiment Even after 70 years of independence, we still face some challenges to our democracy. There are new demands for regional autonomy. There is the Maoist threat. There is intolerance, following the integration of Manipur. There is the Kashmir problem. In spite of all these we have been able to maintain our democratic tradition. After the 1975 Emergency, our rulers have been able to maintain democratic order without any interruption.

Question 16.
Give a brief note on the Green Revolution and its contribution to the food security of our country. (3)
Answer:
Green Revolution is the name given to the policies of the government which aimed at maximum production in the minimum period in the agricultural sector. In the 1960s, the agricultural sector was in a very bad shape. Between 1965 and 67 there were huge droughts in many parts of India. This reduced food production and in many areas there was famine like condition.

To overcome this crisis, India was forced to seek assistance from countries like America. Following the American policies, we too started some new economic policies. The government wanted self-sufficiency in food and therefore a new agricultural policy was implemented. This policy included farming all lands where irrigation was available, using high yield varieties of seeds and fertilizing the land. Subsidies were given for irrigation and insecticides. It was also decided that the government would purchase the produce at a minimum price. All these changes together paved the way for what is known as the Green Revolution.

The Green Revolution brought some positive changes in agricultural growth. Food stuff was easily available. Of course, it was the rich merchants and large farm- owners that were the prime beneficiaries. There was a polarization of the rich and poor. This helped the Left Parties to bring together the poor farmers and the masses. As a result, there arose a powerful Leftleaning lobby of middle-class farmers.

Question 17.
Identify the person who is popularly known as the ‘Milkman of India’. (1)
Answer:
Varghese Kurian.

Question 18.
“Indo-China war of 1962 made many impacts in our domestic and in international politics”. On the light of the above statement briefly describe India-China relations. (7)
Answer:
Nehru had an open-hearted approach to China. But people like Pate! thought China was not a country to be believed. Nehru never expected any attack from China. But in 1962, China did attack India.

Two things spoiled tne relations between India and China. One was the Tibetan issue and the other was border disputes. Even in the 1950s when they were friends, India and China had border disputes. China was not ready to accept our suggestions regarding the border. China claimed Ladakh in Kashmir and some areas of Arunachal Pradesh to be theirs. During the period of 1957-59, they also took Aksai Chin sector and built the Karakoram Highway. The second issue was Tibet. In 1950, China annexed Tibet, it was a breach of faith. In the beginning India kept quiet. But the Chinese started imposing their culture on the Tibetans. In 1959, the Tibetan Spiritual leader, Dalai Lama, sought refuge in India. China then accused India saying that India was acting against the interest of China, in October 1962 China infiltrated into Indian territories which it claimed to be hers. The first attack lasted a week Chinese army occupied some place in Arunachal Pradesh. The next attack came a month iaier. But the Indian army stopped the Chinese in the western part of Ladakh. China declared a unilateral ceasefire and retreated from the places it had taken.

Results of the india-China War: During the war, Russia kept her neutrality. India had to seek support from America and Britain. The war was shameful to the country. But it strengthened national feeling Nehru’s close friend and the then defense minister V.K. Krishna Menon had o resign. Nehru was criticized for blinding believing China for his lack of military preparation to prevent the attack. A no-confidence motion was brought against his government. In Lok Sabha there were a lot of discussions. In many bye-elections Congress lost. The Opposition was also affected by the war. In 1964 Communist Part was divided into two – Pro-Chinese and Pro-Russia. One was CPI (M) and the other was CPI.

The War awakened the nation. The North-Eastern region was backward. The Chinese war prompted the nation to keep its unity and to embark upon developmental projects.

Question 19.
During the Cold War period the super powers made alliances with comparatively weaker states. Identify the significance of such alliances. (2)
Answer:
During the Cold War period, the Superpowers competed among themselves to assist the smaller powers. It was because the Superpowers needed the smaller
powers for the following:

• To get oil and essential minerals.
• To get areas to make military camps.
• To spy on other countries.
• Some of the expenses for the military would be borne by the smaller nations.

Question 20.
After 1989, India is witnessing a politics of coalition. Analyse the merits and demerits of coalition politics practiced in India. (3)
Answer:
Merits:
a. It is more democratic.
b. Local or regional problems could be handled more efficiently.
c. Makes the administration more transparent.
d. Gives continuity to governments.

Demerits:
a. Stability is not ensured.
b. Less efficient
c. It would be difficult bold and strategic decisions,

Question 21.
“Ayodhya issue created far-reaching consequences” on the light of the above statement, explain how the Ayodhya issue reflected in Indian politics after 1990’s. (3)
Answer:
a. Political parties could not get majority and ensure stable government.
b. There was criminalization of politics.
c. Religious fundamentalism came into politics.

Question 22.
UN is the world organization constituted after the Second World War for the promotion of international peace and security. After completing 65 years, UN needs basic reforms. Explain in your view about the restructuring of UN. What should be the position of India, in the restructured UN? (6)
Answer:
There is a need to reform UNO as per the need of the time. The circumstances today are different from those existing at the time of the formation of the UNO. There should be objective solutions to the problems of the world. No country should assume the role of world police.

There should be a structural change in the UN to enable it to eradicate terrorism. There should be proper representation of the developing nations in the UN. The demand of India to have permanent membership in the Security Council is a logical and just demand. India wants permanent membership because of the following reasons:

• It has the world’s second-largest population.
• It is the largest democracy in the world.
• India has participated in the UN activities since its inception.
• It has long relations with the UN Peacekeeping force. India’s economic situation is improving.
• India gives regularly to the UN budget.
• It has never defaulted on any payment.

The above reasons are good enough for India to get a permanent membership in the UN Security Council. Permanent membership has its own significance. India’s importance will increase in world matters. Our foreign policy will influence others.

Question 23.
Modern world faces new security threats. Identify four among them and give brief explanation to each of them. (4)
Answer:
a. Terrorism: Political attacks make the life of ordinary citizens difficult. The terrorists want the political circumstances to change. They try to bring about changes by threats or armed attacks. By unleashing violence, they make the people restless. They try to make the dislike and discontentment of the people their weapon against governments. Their activities include hijacking planes and bombing trains and markets and other places where people assemble. They attacked and destroyed the World Trade Centre in New York on 11 September 2001. The government and the people are more cautious now against terrorists.

b. Human Rights Violations: We see that throughout the world there are human right violations. There is no unified thinking in any country about how to protect human rights. Recent incidents of human right violations are the annexation of Kuwait by Iraq, the ethnic cleansing in Ruanda and the mass killings of the people of Eastern Timor by the Indonesian army. All these prompted world leaders to have a talk. The talk was about whether the UN should interfere in such matters. The matter is still unresolved.

c. Global Poverty: This is another factor of security threat. It is believed that the population in the underdeveloped countries will triple in 50 years. In countries where the population is low, the per capita income will be high. Therefore the economically advanced countries will prosper further whereas the poor countries will grow poorer. The gap between countries of the North and South will increase. People from the South countries immigrate to the North countries for better life and earning. This also creates a threat forthe security of mankind.

d. Contagious Diseases: Contagious diseases are another threat to mankind. AIDS, bird flu, SARS (Severe Acute Respiratory Syndrome) etc. are dangerous contagious diseases. These spread quickly from one country to another. A country’s success or failure in controlling these diseases affects other countries also. Recently swine-flu spread all over the world. It is when a problem becomes a threat to a nation and its people that it becomes an international security threat.

Question 24.
Globalization has its cultural consequences. Globalization imposes Western Culture on the rest of the World. On the basis of the above statements explain the cultural consequences of globalization. (3)
Answer:
Globalization is the exchange of ideas, materials and human resources. Now this exchange is possible among nations without much control. Looked at this way, it assumes different levels of political, economic and cultural meanings. In his sense it has merits and demerits. Some societies may be affected only very little, but some may be affected much more.

Let us see how it works. Politically speaking, the authority of the government gets weaker. It will have to reduce its welfare schemes. Instead of social welfare, the stress is on the market. With the coming MNCs (Multi-National Corporations), it becomes difficult for the governments to take independent decisions.

Globalization has influenced the economic sphere greatly. World Bank, IMF, WTO etc. play big roles.

All these are controlled mainly by America and its allies. The world economy itself has come under their influence. In this, a re-thinking is necessary. It is high time that we found out who the beneficiaries of globalization are.

The effects of globalization are not limited to political and economic spheres. It affects our home, food, dress and even thoughts. There is a fear that it would lead to a single world culture. There is the dominance of Western Culture in globalization. There is a danger to traditional cultures. But some people say that culture is not something that sands still. Every culture accepts things from other cultures.

Question 25.
Protection of global commons is important for the existence of life in our Planet. Explain global commons and the efforts to preserve them. (3) .
Answer:
The earth’s atmosphere, Oceans, Antarctica, Space etc. are global commons. For the survival of mankind these have to be protected. There are many steps taken at global level for their protection.

The following are some of them:
Kyoto Protocol
Earth Summit
Rio Summit
Schemes for Sustainable Development.

Plus Two Political Science Previous Year Question Papers and Answers

Kerala Plus Two Political Science Chapter Wise Questions and Answers Chapter 4 India’s External Relations

Question 1.
Write true’ or ‘false’ against each of these statements.
a) Non- alignment allowed India to gain assistance both from USA and USSR.
b) India’s relationship with her neighbours has been strained from the beginning.
c) The cold war has affected the relationship between India and Pakistan.
d) The treaty to peace and Friendship in 1971 was the result of India’s closeness to USA.
Answer:
a. true b. false c. true d. false

Question 2.
Match the following.

A	The goal of India’s foreign policy in the period 1950 -1964	i	Tibetan spiritual leader who crossed over to India
B	Panchsheel	ii	Preservation of territorial integrity, sovereignty and economic development
C	Bandung Conference	iii	Five principles of peaceful coexistence
D	Dalai Lama	iv	Led to the establishment of NAM

Answer:
a – ii
b – iii
c – iv
d – i

Question 3.
One Article in the Indian constitution gives it an international character. It declares our commitment to protect international peace and security. Identify the Article.
a) Article 32
b) Article 21
c) Article 51
d) Article 72
Answer:
c) Article 51

Question 4.
The first Non-Aligned summit was held in 1961 at (Bandung, Belgrade, Beijing)
Answer:
Belgrade

Question 5.
We had signed some important treaties with China and Pakistan. Arrange the data provided in the following table.

Treaty	Leader of India	Leader of Pakistan / China
Panchseel	Indira Gandhi	Ayub Khan
Tashkent Agreement	Jawaharlal Nehru	Zulphikar Ali Bhutto
Shimla Agreement	Lai Bahadur Sastri	Chou En Lai

Answer:

Treaty	Leader of India	Leader of Pakistan / China
Panchseel	Jawaharlal Nehru	Chou En Lai
Tashkent Agreement	Lai Bahadur Sastri	Ayub Khan
Shimla Agreement	Indira Gandhi	Zulphikar Ali Bhutto

Question 6.
The friendship among three international personalities led to the formation of NAM. Identify them.

Answer:
Egypt – Nasser
Yugoslavia-Tito

Question 7.
The five legs of the following star represent ‘Big Five’ countries. Try to fill the blanks

Answer:
China, France, England

Question 8.
In 1957 the Tibetan spiritual leader crossed the Chinese border and came to India. It was a landmark in the Indo Sino relation. Identify the Person.
Answer:
Dalai Lama

Question 9.
The following are the major revolutions that took place in different countries of the world. Chronologically arrange them.

a	1688	1	Chinese Revolution
b	1773	2	American Revolution
c	1789	3	Glorious Revolution
d	1917	4	Russian Revolution
e	1949	5	French Revolution

Answer:
a. Glorious Revolution
b. American Revolution
c. French Revolution
d. Russian Revolution
e. Chinese Revolution

Question 10.
After colonial administration, India was divided into India and Pakistan. In 1971 Pakistan was further divided into Pakistan and Bangladesh. These three countries consider three persons as the fathers of these countries. Identify them.
Answer:
India – Mahatma Gandi
Pakistan – Muhammad Ali Jinnah
Bangladesh – Mujibur Rehman

Question 11.
India conducted two nuclear explosions during 1974 and 1998. identify the code names given to these explosions.

Year	Code Name
1974
1998

Answer:
1974-Buddha Laughs
1998 – Operation Shakti

Question 12.
Two personalities are associated with the concept of cold war. One person is Bernard Baruch, and then who is the other person?
Answer:
Walter Lippmann

Question 13.
The boundary line between India and Pakistan is . ‘Radcliffe Line’. Identify the boundary line between India and China?
a) Durand Line.
b) 17th Parallel
c) Mac Mohan Line
d) Demarcation Line
Answer:
c) Mac Mohan Line

Question 14
Match the columns.

A	B	C
Bharathiya Kisan union	Caste system	Mahendra Singh Tilkayat
Chipko movement	Sardar Sarovar project	Maharastra
Narmada Bhachao Andolan	Meerut Agitation	Sundar Lai Bhahuguna
Dalit Panthers	Uttarakhand	Medha Patkar

Answer:

A	B	C
Bharathiya Kisan union	Meerut Agitation	Mahendra Singh Tilkayat
Chipko movement	Uttarakhand	Sundar Lai Bhahuguna
Narmada Bhachao Andolan	Sardar Sarovar project	Medha Patkar
Dalit Panthers	Caste system	Maharastra

Question 15.
“Foreign policy means the policy which a nation fol-lows while maintaining her relation with other nations”. So the foreign policy of any country is influenced by international environment. India’s foreign policy was also influenced by the international environment in which India got independence. Can you identify the international conditions in which we evolved our foreign policy?
Answer:
The world was going through very difficult circumstances when India got her freedom. This situation has influenced our foreign policy. Five factors have influenced our foreign policy in a greater measure.

• The II World War and the rebuilding after that.
• The efforts to form an international organization.
• The emergence of many small nations at the end of colonialism.
• The challenges the new Nations faced for democracy and welfare.
• The Cold War between America and Russia because of ideological differences.

Question 16.
The Directive Principles of State Policy provided Indian constitution an international character. As a student who learned Directive Principles of State Policy, can you mention the provisions of Directive Principles of State policies that gave our constitution an inter-national character.
Answer:
Article 51 of our Constitution gives importance to international peace and security. It states that India Government:

• will encourage international peace and security.
• will maintain cordial relations between nations.
• will respect all the international laws, treaties and organizations.
• will try to solve international disputes through mediation.

Question 17.
Jawaharlal Nehru is the architect of India’s foreign policy. He played a major role in fostering Afro Asian unity. Find out the important contributions of India to Afro-Asian Unity.
Answer:
Nehru was a chief spokesperson of Afro-Asian unity. Under his leadership, in March 1947, there was an Asian Relations Conference. It supported the freedom struggle of Indonesia. India made great efforts to free Indonesia from the hands of the Dutch. For this purpose in 1949 an international conference was summoned.

India was also against the apartheid policy of South Africa. The Conference that held in the Indonesian city of Bandung, is known as the Bandung Conference. The intervention of India helped many African and Asian nations to get their freedom from their colonial masters. This Conference later proved to be the starting point of the Non-Aligned Policy.

Question 18.
“A country without material, men or money-the three means of power is now fast coming to be recognized as the biggest moral power in the civilized world…. Her word is listened to with respect in the councils of the great’. So India is developed as a major power in international politics. Can you give a brief note about the development of India’s foreign policy?
Answer:
The Indian National Movement was a protest against colonialism and imperialism. It helped other Asian and African nations to fight for their freedom and against colonialism and imperialism. Our leaders got into contact with the leaders of other Afro-Asian nations and together they formulated a policy against colonial rule.

The foreign policy of a country depends on the internal and external factors prevalent in the country. The ideas and goals of the Freedom Movement have influenced our foreign policy. India got freedom when the Cold War was going on between Russia and America at the political, economic and military levels. It was around this time that the United Nations was born. The use of atomic weapons began just a little before this period. Therefore it was necessary to formulate a foreign policy in keeping with the interests of the nation. The following 3 things were important in formulating such a policy.

a. The role of Nehru:
Nehru was the Prime Minister and Foreign Minister of India from 1946 to 1964. He had a big role in the formulation of our foreign policies. He followed a policy which was conducive to the maintenance of our sovereignty, protection of our boundaries, our unity and our economic growth. It was with all these in his mind, he became one of the chief architects of the Non-Aligned Policy.

b. Keeping equidistance from both the superpowers. As the Cold War was going between the superpowers, we wanted world peace. For that we:

• continued with our non-aligned policy.
• tried to reduce the tension of the Cold War.
• supplied manpower for the peaceful missions of the United Nations.

As a newly independent country, India could not claim any big political power. Therefore India decided to keep away from the on-going Cold War between the superpowers. The Non-Aligned Policy helped us to do that It was difficult for India to maintain this non-aligned stance always. When the British attacked Egypt and Russia attacked Hungary, we could not stick with our non-aligned stand. But in many international problems India maintained an independent stand. India received help both from the USA and also Russia on different occasions.

c. Afro-Asian Unity:
Another factor that influenced the foreign policy of India was Afro-Asian Unity. Nehru maintained good relations with different Asian and African leaders. In March’1947, the Asian Relations Conference was summoned. Through this, India raised her voice against colonialism and apartheid. The Bandung Conference paved the way for the formulation of the Non-Aligned Movement. Indo-China Relations: In the beginning the relations between India and China were cordial. There is a

historical and cultural background.to that. Nehru played a big role in maintaining the good relationship. India was the first country to recognize China after the Chinese Revolution. Nehru did his best to help China to come out of the Western shadow. He helped China in many international matters. Because of the cordial relations, on the borders between India and China only paramilitary personnel, not army, were deployed.

The Panchsheel Agreement (25 April 1954) between the PMs of India and China were a big landmark. The PMs exchanged visits and received the love and respect from the people. Nehru had cordial relations with China. But people like Vallabhbhai Patel were not sure if the Chinese could be trusted so much. But Nehru never thought the Chinese would attack India. But in 1962, Nehru was proved wrong when the Chinese attacked us.

Chinese Attack in 1962:
Two things spoiled the good relationship between India and China. One was the Tibetan Issue and the other was boundary dispute. Even in the 1950s, when India had good relations with China the boundary disputes existed. China was not ready to accept our views and suggestions regarding the boundaries. The main dispute was about the boundary in the West and East. China claimed the Ladakh Region of Jammu and Kashmir and many areas of Arunachal Pradesh.

Between 1957-59, the Chinese occupied the Aksai-Chin sector and built the Karakoram Highway. There were letters between leaders, but nothing positive happened. The second issue was Tibet. In 1950, China annexed Tibet. It was a breach of trust. In the beginning India did not object to it. But it could not continue to maintain its silence as the Chinese tried to impose their culture on the Tibetans. In 1959, the Dalai Lama, the spiritual leader of the Tibetans, sought refuge in India. Then the Chinese started accusing us of anti Chinese activities. In October 1962, the Chinese army infiltrated into areas of dispute.

The attacks lasted a week. The Chinese army occupied some important places in Arunachal Pradesh. The next series of attacks came the following month. But the Indian Army stopped the Chinese on the western side of Ladakh. But in the East they were able to come up to4he Assam Plain. Then they announced a unilateral ceasefire and retreated from the occupied lands.

After-effects of the Indo-Chinese war:
During The War, Russia kept neutrality. So India had to seek military help from the USA and Britain. The war was a shame to the country. But it fortified our national feeling. After the war, many top military officers resigned. Nehru’s close friend and the then Defence Minister V.K Krishna Menon, had to resign. Nehru was criticized for his blind faith in China and for not being militarily ready to counter the attacks.

A No Confidence Motion was brought against him. Many discussions took place in the Parliament. Congress was defeated in many by elections to the Lok Sabha The War affected even the Opposition. In 1964, the Communist Party split as Pro-Chinese and Pro- Russian. The group that leaned towards Congress was CPI and the group with the Pro-China stand was CPI(M).

The War brought caution among the leaders The north Eastern areas were backward. The War forced the country to embark upon projects to protect its unity and also to make economic progress in the country.

Indo-Pak Relations:
It can be said that Pakistan is the closest, and at the same time, the farthest neighbour of India. Pakistan is close to India historically, geographically and culturally. But when it comes to democracy, outlook on religion, and mutual understanding, Pakistan is the farthest neighbour.

The good aspects of Indo-Pak Relations:
Both countries worked together to rehabilitate the women kidnapped during the division of the country. An understanding was negotiated through the mediation of the World Bank for sharing river water. The leaders of both countries cooperated in the Agra Summit. Although it proved to be a failure in the end, it gave some hope for the future.The cricket diplomacy reduced the tension between the two countries.

During the time of Atal Bihari Bajpai in India and Musharaf in Pakistan, there were bus and train services between the two countries. Although the above things are good, for quite some time serious disputes have been going on between the two neighbours. The first dispute is in the case of Kashmir. Even in 1947 itself there was a clash between Indian and Pakistani soldiers.

Since was Impugn wefore the United Nations, it did not develop into a full-scale war. With that Pakistan became a decisive factor in our relations with America and China.In 1965, Pakistan madean armed attack in the Rann of Kutch in Gujarat. Later in August arid September, Pakistani army attacked Kashmir.

The Pakistan government expected the Kashmiri people to support them but it did not happen. Then Lai BhadurSastri ordered the Indian army to attack Pakistan from the Punjab border. The army came close to Lahore. Then, there was a treaty between India and Pakistan, signed by Satri of India and Ayub Khan of Pakistan. This was the Tashkent Agreement. For Pakistan this war caused a huge military loss. Our financial situation also went bad.

In 1970, Pakistan faced a lot of internal problems. During the first election in West Pakistan the Party of Zulfikar AN Bhutto got the majority. But in East Pakistan, the Awami League led by MujiburRehman got the majority. The East Pakistanis wanted to be free from West Pakistan. They thought that they were treated as second class citizens. The rulers of West Pakistan were not willing to recognize the Awami League or respect the verdict of the people.

In 1971, the West Pakistani army arrested Mujibur Rehman and threatened the people of East Pakistan. The people there wanted their own separate country called Bangladesh. Because of the repressive measures by the Pakistani government, India had to accommodate some 80 lakh refugees. India . supported the demand for Bangladesh. Pakistan accused India of aiding East Pakistan.

In the circumstances, America and China supported . Pakistan and thus the three countries were against India. In 1971, India signed a Peace arid Friendship Treaty for 20 years with the Soviet Union. According to this Treaty, if India was attacked by any country , Russia would come to her assistance.

In 1971 Pakistan attacked Punjab, Rajasthan and Jammu-Kashmir. Indians attacked Pakistan from the East and West simultaneously. With popular support, the Indian army surrounded Dhaka from three sides. In 10 days the Pakistani army surrendered. With the freedom of Bangladesh, India declared a unilateral ceasefire. The war ended. Indira Gandhi and Zulfikar AN Bhutto signed the Shimia Agreement on 3 July 1972.

Another big problem was the Kargil Issue. The Indian army reported that many parts of the Line of Control were occupied by Mujahidins, India felt that Pakistan had a hand in this and it also started behaving in that manner. This resulted in a controversy between the two countries. On 26 July 1999, India recaptured some of the places occupied by the Mujahidins. As both the countries had atomic weapons, this issue captured world attention. But the dispute limited itself to the Kargil area. General Musharaf recalled the Pakistani army from there.

There are still many disputes between India and Pakistan. One of them is regarding terrorist attacks. The attacks on the Parliament and Mumbai worsened the relations between the two countries. Recently Pakistan made some moves against the terrorists there. It is hoped that such actions will bring peace to the Asian mainland.

Question 19.
India is always against armament race particularly nuclear armament race. But at the very same time India refused to sign NPT or CTBT Is it found contradictory? Mention your opinion about India’s Nuclear policy.
Answer:
India supports non-proliferation of atomic weapons. It believes that atomic power should be used only for peaceful purposes. In 1974, India tested its first atomic device.Nehru believed that what modern India wanted was scientific and technological growth, in 1940, under Homi. J. Bhabha India embarked on an atomic scheme. India wants atomic power only for peaceful purposes. Nehru was against atomic weapons. Therefore he requested the big powers to disarm.

But the collection of atomic weapons was increasing. In 1968, the five major atomic powers tried to bring a treaty which prohibited the use of atomic weapons. It is called the Non-Proliferation Treaty (NPT). But India refused to sign it saying that it was discriminatory in nature. When India tested its first atomic device, its intention was peaceful. India asserts that atomic power should be used only for peaceful purposes. whereas it denies non-atomic powers to make any tests, thus preventing them from developing atomic power even for peaceful purposes.

Additional Question

Question 1.
What is Kargil war? What were its consequences?
Answer:
in the early years of the 1990s, a group calling itself Mujahidins forcefully occupied many parts of the Line of Control. The areas they ocupied included Dras, Kaksara and Batalik. In India it was believed that this occupation was with the knowledge of the Pakistani authorities. So India reacted and this brought about the Kargil War.

This happened in May-June 1999. By 26 July, 1999, the Indian Army was ableto take control of ail the illegally occupied places by the Mujahidin. Following this war, the Pak Commander-in-Chief of the Army, General Parvez Musharaf, staged a coup d’etat and became the ruler of Pakistan.

Question 2
Describe the difference between Neutrality and Non Alignment.
Answer:
There are some major differences between Neutrality and
Non-Alignment.

• Neutrality is relevant only when there is a war. But Non-Alignment is relevant both in the times of war and also peace.
• Neutrality is used in international laws. But the term Non-Alignment is used in the mutual relations between countries. Neutrality would mean keeping away. But Non-Alignment does not mean keeping away from something. There is inclusion in Non-Alignment.

Question 3.
India conducted first nuclear explosion in
Answer:
May 1974

Question 4.
Write a short note on India’s Nuclear Policy.
Answer:
India is against testing of atomic weapons for war like purposes. India stands for complete disarmament within the framework of the United Nations. Even then India refuses to sign the NPT. It is so because India thinks NPT is discriminatory. It allows the atomic powers to make further tests.

Plus Two Political Science Chapter Wise Questions and Answers

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 8 Application of Integrals.

Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 8 Application of Integrals

Plus Two Maths Application of Integrals 4 Marks Important Questions

Question 1.
(i) The area bounded by the curve y = f(x) x-axis and the line x= a and x= b is……
(ii) Find the area enclosed between the Parabola y = x² and the straight line 2x – y + 3 = 0 (March – 2010)
Answer:

Question 2.
Find the area enclosed between the curve x² = 4y and the line x = 4y – 2 (March -2011)
Answer:

Question 3.
(i) Area of the shaded portion in the figure is equal to

(ii) Consider the curves y = x², x = 0, y = 1, y = 4.
Draw a rough sketch and shade the region bounded by these curves, Find area of the shaded region.
Answer:

Question 4.
Consider the following figure:

(i) Find the point of Intersection P of the circle x² + y² = 32 and the line y = x.
(ii) Find the area of the shaded region. (EDUCATE – 2017; March – 2013; March – 2014)
Answer:

Question 5.
(a) The area bounded by the curve, above the x-axis, between x = a and x = b is

(b) Find the area of the circle x² + y² = 4 using integration. (March – 2016)
Answer:

Question 6.
(i) The area bounded by y = 2cosx , the x-axis from x = 0 to x = \(\frac{\pi}{2}\) is
(a) 0
(b) 1
(c) 2
(d) -1
(ii) Find the area of the region bounded by the y² = 4ax and x² = 4ay, a > 0 (March – 2017)
Answer:

When x = 4a, y = 4a and x = 0, y = 0.
Therefore the point is (0, 0) and (4a, 4a).

Plus Two Maths Application of Integrals 6 Marks Important Questions

Question 1.
Consider the circle x² + y² = 16 and the straight line \(y=\sqrt{3} x\) as shown ¡n the figure

(i) Find the points A and B as shown in the figure.
(ii) Find the area of the shaded region in the figure using definite integral. (May -2010)
Answer:
(i) The point of intersection of x² + y² = l6 and

Question 2.
(i) Draw the rough sketch of \(\frac{x^{2}}{4}+\frac{y^{2}}{9}=1\)
(ii) Find the area bounded by the above curve using integration. (May – 2011)
Answer:
(i) The curve is an ellipse.

Question 3.
(i) Find the area enclosed between the curve y² = x, x = 1, x = 4 and x-axis.
(ii) Using ntegration, find the area of the region bounded by the triangle whose vertices are (1, 0), (2, 2) and (3, 1). (March-2012)
Answer:

Required area ΔABC = Area ΔAB2
+ Area 2BC3 – Area ΔAC3
Equation AC is y = 2(x – 1)
Equation BC is y = 4 – x
Equation AB is y = 1/2 (x – 1)

Question 4.

Using the above figure
Find the equation of AB.
Findthe point P.
Find the area of the shaded region by integration. (May – 2013)
Answer:
(i) The equation of a line passing through (0,2)

Question 5.
Consider the ellipse \(\frac{x^{2}}{9}+\frac{y^{2}}{4}=1\) and the line \(\frac{x}{3}+\frac{y}{2}=1\).
(a) Find the points where the line intersects the ellipse?
(b) Shade the smaller region bounded by the ellipse and the line.
(c) Find the area of the shaded region. (May – 2014)
Answer:

Question 6.
Consider the function f(x) = |x| + 1; g(x) = 1 – |x|
(a) Sketch the graph and shade the enclosed region between them.
(b) Find the area of the shaded region. (March – 2015)
Answer:

(b) The equation of the line through AB is

Question 7.
Using the given figure answer the following questions.

Define the equation of the given curve.
Find the area of the enclosed region.
Find the area when a = lo and b = 5. (March – 2011; May – 2015; March – 2017)
Answer:
(i) The figure represents an ellipse with equation

Ellipse is symmetric w.r.t coordinate axles. Therefore the area of the enclosed region is same as four times area enclosed by the curve in first quadrant.

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 7 Integrals.

Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 7 Integrals

Plus Two Maths Application of Derivatives 3 Marks Important Questions

Question 1.
Find the following integrals. (May -2011)
\(\begin{array}{l}
\text { (i) } \int x^{2} e^{2 x} d x \\
\text { (ii) } \int e^{x} \sin x d x
\end{array}\)
Answer:

Question 2.
(i) \(\int e^{x} \sec x(1+\tan x) d x=\ldots \ldots\)
(a) ex cosx + c (b) ex sec x + c
(C) ex tanx + c (d) ex sin x + c
(ii) Find \(\int \sin 2 x \cos 3 x d x\) (March – 2014)
Answer:

Question 3.
Find the following integrals.
(i) \(\begin{array}{l}
\text { (i) } \int \frac{1}{(x+1)(x+2)} d x \\
\text { (ii) } \int \frac{2 x-1}{(x-1)(x+2)^{2}} d x
\end{array}\) (March – 2014)
Answer:

Plus Two Maths Application of Derivatives 4 Marks Important Questions

Question 1.
Consider the integral \(I=\int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x\)
(i) Express \(I=\frac{\pi}{2} \int_{0}^{\pi} \frac{\sin x}{1+\cos ^{2} x} d x\)
(ii) Show that \(I=\frac{\pi^{2}}{4}\) (March – 2012)
Answer:

Question 2.
(i) Evaluate: \(\int_{2}^{3} \frac{x}{x^{2}+1} d x\)
(ii) Evaluate: \(\int_{0}^{\pi} \frac{x}{1+\sin x} d x\) (March – 2014)
Answer:

Question 3.
(a) What is the value of \(\int_{0}^{1} x(1-x)^{9} d x\) If the
\(\begin{array}{llll}
\text { (i) } \frac{1}{10} & \text { (ii) } \frac{1}{11} & \text { (iii) } \frac{1}{90} & \text { (iv) } \frac{1}{110}
\end{array}\)
(b) Find \(\int_{0}^{1}(2 x+3) d x\) of a sum. (March – 2015)
Answer:

Question 4.
Evaluate \(\int_{0}^{x} \log (1+\cos x) d x\)
Answer:

Question 5.
Find \(\int_{0}^{5}(x+1) d x \text { as limit of a sum. }\)
Answer:

Question 6.
Evaluate \(\int_{0}^{4} x^{2} d x\) as the limit of a sum. (March – 2017)
Answer:

Plus Two Maths Application of Derivatives 6 Marks Important Questions

Question 1.
(i) Fill in the blanks; \(\int \frac{1}{x} d x=\)_____
(ii) Evaluate \(\int \frac{5 x+1}{x^{2}-2 x-35} d x\)
(iii) Integrate with respect to x. \(\sqrt{x^{2}+4 x+8}\) (March – 2010)
Answer:

Question 2.
(i) Evaluate \(\int-\frac{\cos e c^{2} x}{\sqrt{\cot ^{2} x+9}} d x\)
(ii) Evaluate \(\int\left(\cos ^{-1} x\right)^{2} d x\) (May -2010)
Answer:

Question 3.
(i) Evaluate \(\int_{0}^{\pi} \frac{x \sin x}{1+\cos ^{2} x} d x\)
(ii) Evaluate \(\int_{0}^{2} e^{x} d x \text { as limit of a sum. }\) (May -2010)
Answer:

Question 4.
(i) Fill in the blanks \(\int \cot x d x=\)_____
(ii) Evaluate the integrals
\(\begin{array}{l}
\text { (a) } \int \sin 2 x \cos 4 x d x \\
\text { (b) } \int \frac{x}{(x+1)(x+2)} d x
\end{array}\) (March -2011)
Answer:

Question 5.
(i) Evaluate \(\int_{0}^{1} x d x\) as the limit of a sum.
(ii) Evaluate \(\int_{0}^{1} x(1-x)^{n} d x\) (March – 2011)
Answer:

Question 6.
(i) Evaluate \(\int_{1}^{2} \frac{1}{x(1+\log x)^{2}} d x\)
(ii) Evaluate \(\int_{0}^{3}\left(2 x^{2}+3\right) d x\) as the limit of a sum. (May – 2011)
Answer:

Question 7.
(i) What is \(\int \frac{1}{9+x^{2}} d x=?\)
(ii) Evaluate the integrals \(\int \frac{1}{1+x+x^{2}+x^{3}} d x\) (May – 2012)
Answer:

Question 8.
(i) Evaluate \(\int_{0}^{3} f(x) d x\)
where \(f(x)=\left\{\begin{array}{ll}
x+3, & 0 \leq x \leq 2 \\
3 x, & 2 \leq x \leq 3
\end{array}\right.\)

(ii) Prove that \(\int_{0}^{1} \log \left(\frac{x}{1-x}\right) d x=\int_{0}^{1} \log \left(\frac{1-x}{x}\right) d x\) Find the value of \(\int_{0}^{1} \log \left(\frac{x}{1-x}\right) d x\) (May – 2012)
Answer:

Question 9.
(i) Find \(\int \cot x d x=\ldots \ldots\)
(ii) Find \(\int x \log x d x\)
(iii) Find \(\int \frac{x-1}{(x-2)(x-3)} d x\) (March – 2013)
Answer:

Question 10.
Evaluate
\(\text { (i) } \int \frac{x+3}{\sqrt{5-4 x-x^{2}}} d x\)
\(\text { (ii) } \int_{\pi / 6}^{\pi / 3} \frac{d x}{1+\sqrt{\tan x}}\) (May – 2013)
Answer:

Question 11.
Evaluate
\(\begin{array}{l}
\text { (i) } \int x^{2} \tan ^{-1} x d x \\
\text { (ii) } \int_{-1}^{2} x^{3}-x d x
\end{array}\) (May – 2013)
Answer:

Question 12.
Evaluate \(\int_{0}^{\pi / 4} \log (1+\tan x) d x\) (March – 2013)
Answer:

Question 13.
(a) The value of \(\int_{\frac{-\pi}{2}}^{\frac{\pi}{2}} \cos x d x\) (May – 2014)
(b) Prove that \(\int_{0}^{\pi} \frac{x}{a^{2} \cos ^{2} x+b^{2} \sin ^{2} x} d x=\frac{\pi^{2}}{2 a b}\)
Answer:

Question 14.
(a) \(\int \frac{1}{x^{2}+a^{2}} d x=\)
(b) Find \(\int \frac{1}{9 x^{2}+6 x+5} d x\)
(c) Find \(\int \frac{x}{(x-1)^{2}(x+2)} d x\) (May – 2014)
Answer:

Question 15.
Integrate the following
\(\begin{array}{l}
\text { (a) } \frac{x-1}{x+1} \\
\text { (b) } \frac{\sin x}{\sin (x-a)} \\
\text { (c) } \frac{1}{\sqrt{3-2 x-x^{2}}}
\end{array}\) (March – 2015)
Answer:

Question 16.
(a) Prove that \(\int \cos ^{2} x d x=\frac{x}{2}+\frac{\sin 2 x}{4}+c\)
(b)Find \(\int \frac{1}{\sqrt{2 x-x^{2}}} d x\)
(c) Find \(\int x \cos x d x\) (May – 2015)
Answer:

Question 17.
Find the following:
\(\begin{array}{l}
\text { (i) } \int \frac{1}{x\left(x^{7}+1\right)} d x \\
\text { (ii) } \int_{1}^{4}|x-2| d x
\end{array}\)
Answer:

Question 18.
Find \(\int_{0}^{\frac{\pi}{2}} \log \sin x d x\)
Answer:

Question 19.
Find the following: \(\begin{array}{l}
\text { (i) } \int \cot x \log (\sin x) d x \\
\text { (ii) } \int \frac{1}{x^{2}+2 x+2} d x \\
\text { (iii) } \int x e^{9 x} d x
\end{array}\) (May – 2017)
Answer:

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 6 Application of Derivatives.

Kerala Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 6 Application of Derivatives

Plus Two Maths Application of Derivatives 4 Marks Important Questions

Question 1.
(a) Find the equation of the tangent to the curve \(x^{\frac{2}{3}}+y^{\frac{2}{3}}=2\) at (1,1).
(b) Find two positive numbers whose sum is 15 and the sum of whose squares is minimum. (May – 2015)
Answer:

Question 2.
(a) The slope of the tangent to the curve given
\(x=1-\cos \theta, y=\theta-\sin \theta \text { by at } \theta=\frac{\pi}{2}\)
(i) 0
(ii) – 1
(iii) 1
(iv) Not defined.

(b) Find the intervals in which the function f(x) = x² – 4x + 6 is strictly decreasing.
(C) Find the minimum and maximum value, if any, of the function f(x) = (2x – 1)² + 3 (March – 2016)
Answer:
(a) (iii) 1
(b) Given; f(x) = x² – 4x + 6 ⇒ f’(x) = 2x – 4
For turning points; f’(x) = 2x – 4 0 ⇒ x = 2
So volurn.,e is niaxirnum when h = 2r
The intervals are (- ∞, 2); (2, ∞)
f’(0) = 2 x 0 – 4 = -4
Therefore f(x) is decreasing in (- ∞, 2)
(c) f(x) = (2 x 1)² + 3
⇒ f’(x) 2(2x – 1) x 2 f”(x) = 8
For tuming points; f’(x) = 8x – 4 = 0 ⇒ x = 1/2
f(x) has minimum value at x = 1/2 minimum value is \(f\left(\frac{1}{2}\right)=3\)
2)

Question 3.
(a) Which of the following function has neither local maxima nor local minima?
(i) f(x) = x² + x
(ii) f(x) = logx
(iii) f(x) = x³ – 3x + 3
(iv) f(x) = 3 + |x|
(b) Find the equation of the tangent to the curve y = 3x² at (1,1). (March – 2016)
Answer:

Question 4.
(i) The slope of the normal to the curve, y = x³ – x² at (1, -1) is
(a) 1
(b) – 1
(c) 2
(d)0

(ii) Find the intervals in which the function f(x) = 2x³ – 24x + 25 is increasing or decreasing. (May – 2016)
Answer:
(i) (b) – 1
(ii) f(x) = 2x³ – 24x + 25
f’(x) = 6x² – 24
f’(x) = O
⇒ 6x² – 24 = 0 ⇒ x² = 4 ⇒ x = – 2,2
Therefore the intervals are (-∞, -2); (-2, 2); (2, ∞)
f(x) is increasing in the intervals (-∞, -2); (2, ∞)
f(x) is decreasing in the intervals (-2, 2)

Question 5.
(i) The slope of the normal to the curve, y² – 4x at (1,2) is
(a) 1
(b) 1/2
(c) 2
(d) – 1

(ii) Find the intervals in which the function 2x³ + 9x² + 12x – 1 is strictly increasing. (March – 2017)
Answer:
(i) (b) – 1
(ii) f(x) = 2x³ + 9x² + 12x – 1
f’(x) = 6x² + 18x + 12
= 6(x² + 3x + 2) = 6(x + 1) (x + 2)
f’(x) = O
⇒ 6(x + 1)(x + 2) = 0 ⇒ x = – 1 – 2
Therefore the intervals are
(- ∞, – 2); (- 2, – 1); (- 1, ∞)
In the ¡nterval (- ∞, – 2)
f’( – 3) = 6(- 3 + 1) (- 3 + 2) > 0
Therefore increasing In the interval (- 2, – 1)
f’(- 1.5) = 6(- 1.5 + 1)(- 1.5 + 2) < 0
Therefore decreasing In the interval (- 1, ∞)
f’(0) = 6(0 + 1)(0 + 2) > 0
Therefore increasing

Question 6.
Find two positive numbers whose sum is 16 and sum of whose cubes is minimum. (March – 2017)
Answer:
Let the numbers be x and 16 – x. Then,
S = x³ + (16 – x)³
= S’ = 3x² + 3(16 – x)²(- 1)
⇒ S” = 6x + 6(16 – x)………..(1)
For turning points S’ = 0 ⇒ 3 x² – 3(16 – x)² = 0
⇒ x² – 16 + 32x – x² =0
⇒ – 16² + 32x = 0 = x² = \(\frac{16 \times 16}{32}\) =8
(1) ⇒ S” = 6(8) + 6(16 – 8) > 0
TherefocemrnimumM x = 8
Thusthe numbers are8 and 16 – 8 = 8

Plus Two Maths Application of Derivatives 6 Marks Important Questions

Question 1.
(i) Show that the function x³ – 6x² + 15x + 4 is strictly increasing in R.
(ii) Find the approximate change in volume of a cube of side x meters caused by an increase in the side by 3%.
(iii) Find the equation of the tangent and normal at the point (1,2) on the parabola y² = 4x. (March – 2010)
Answer:
(i) Given; f(x) = x³ – 6x² + 15x + 4
f’(x) = 3x² – 12x + 15 = 3(x² – 4x +5)
= 3(x² – 4x + 4 + 1) = 3(x – 2)² + 1) > 0
For any value of x, f(x) is a strKly ¡ncreasing.

(ii) We have; V = x³ and Δx = 3% of x = 0.03x
\(d V=\frac{d V}{d x} \Delta x=3 x^{2} \Delta x\)
= 3x² x 0.03x = 0.09x³ = 0.09V
\(\Rightarrow \frac{d V}{V}=0.09\)

Therefore 9% is the approximate increase In volume.

(iii) Given; y²….4x ⇒ 2y \(\frac{d y}{d x}\) = 4 ⇒ \(\frac{d y}{d x}=\frac{2}{y}\)
Slope at (1,2) = \(\frac{2}{2}\) = 1
Equation of tangent at (1,2) is; y – 2 = 1(x – 1)
⇒ x – y + 1 = 0
Equation of normal at (1,2) is; y – 2 = – 1(x – 1)
⇒ x + y – 3 = 0

Question 2.
Consider the parametric forms
x = 1 + \(\frac{1}{t}\) – and y = t – \(\frac{1}{t}\) ofa curve
(i) Find \(\frac{d y}{d x}\)
(ii) Find the equation of the tangent at t = 2.
(iii) Find the equation of the normal at t = 2. (May – 2010)
Answer:

Question 3.
(i) The radius of a circle is increasing at the rate of 2cmls. Find the rate at which area of the circle is increasing when radius is
6cm.
(ii) Prove that the function f(x) = log sin x is strictly increasing in \(\left(0, \frac{\pi}{2}\right)\) and strictly decreasing in \(\left(\frac{\pi}{2}, \pi\right)\)
(iii) Find the maximum and minimum value of the function f(x) = x³ – 6x² + 9x + 15. (March – 2011)
Answer:

Question 4.
(i) Find the approximate value of (82)^1/4 up to three places of decimals using differentiation.
(ii) Find two positive numbers such that Their sum is 8 and the sum of their squares is minimum. (May – 2011)
Answer:

(ii) Let the numbers be x and 8 – x. Then,
S = x² + (8 – x)²
⇒ S’ = 2x + 2(8 – x)( – 1)
⇒ S” = 2 + 2 = 4 ………..(1)
For turning points S’ = 0 = 2x – 2(8 – x) = 0
⇒ 4x – 16 = 0 ⇒ x = 4
(1) ⇒ S” = 4 > 0
Therefore minimum at x = 4
Thus the numbers are 4 and 8 – 4 = 4.

Question 5.
(i) The slope of the tangent to the curve y = x³ – 1 at x = 2 is ……….
(ii) Use differentiation to approximate \(\sqrt{36.6}\)
(iii) Find two numbers whose sum is 24 and whose product as large as possible. (March – 2012, March – 2016)
Answer:

Therefore minimum at x =12
Thus the numbers are 12 and 24 – 12 = 12.

Question 6.
(i) Show that the function x³ – 3x² + 6x – 5 is strictly increasing on R.
(ii) Find the interval in which the function f(x) = sin x + cosx; 0 < x < 2π is strictly increasing or strictly decreasing. (May – 2012)
Answer:
(i) Given; f(x) = x³ – 3x² + 6x – 5
f’(x) = 3x² – 6x + 6 = 3(x² – 2x +2)
= 3(x² – 2x + 1 + 1) 3(x – 1)² + 1) > 0
For any value cit x, f(x) is a strictly increasing.

Question 7.
(i) Find the slope of the normal to the curve y = sinθ at θ = π/4
(ii) Show that the function f(x) = x³ – 6x² + 15x + 4 is strictly increasing in R.
(iii) Show that all rectangles with a given perimeter, the square has the maximum area. (March – 2013)
Answer:

(ii) f(x) = x³ – 6x² + 15x + 4
Differentiating w.r.t x;
f(x) = 3x² – 12x + 15 = 3(x² – 4x + 5)
= 3 (x² – 4x + 4 + 1)
= 3 ((x – 2)² + 1) > 0, ∀x∈R
Therefore fis strictly increasing in R.

(iii) Let x and ybe the length and breadth of a rectangle with area A and perimeter P.

Question 8.
A right circular cylinder is inscribed in a given cone of radius R cm and height H cm as shown in the figure.

(i) Find the Surface Area S of the circular cylinder as a function of x.
(ii) Find a relation connecting x and R when S is a maximum. (May – 2013)
Answer:
(i) There are two similar triangles ΔDJB and ΔDHF

Question 9.
(i) Which of the following function is Increasing for all values of x in its domain?
(a) sin x
(b) log x
(c) x²
(d) |x|

(ii) Find a point on the curve y = (x – 2)² at which the tangent is parallel to the chord joining the points (2,0) and (4,4).
(iii) Find the maximum profit that a company can make, if the profit function is given by p(x) = 41 – 24x – 6x². (March – 2014)
Answer:
(i) (b) log x
(ii) Given; y = (x – 2)² ⇒ \(\frac{d y}{d x}\) = 2(x – 2)
Slope of the chord = \(\frac{4-0}{4-2}=2\)
\(\Rightarrow 2=2(x-2) \Rightarrow x=3 \Rightarrow y=(3-2)^{2}=1\)
Therefore the required point is (3, 1)

(iii) Given; p(x) = 41 – 24x – 6x²
p’(x) = – 24 – 12x
p”(x) = – 12
For turning points p’(x) = – 24 – 12x = 0
⇒ x = -2
Since p”(x) = – 12 always maximum Therefore maximum value p(- 2) = 41 – 24(- 2) 6(- 2)² = 65

Question 10.
(a) Find the slope of the tangent to the parabola y² = 4ax at (at², 2at).
(b) Find the intervals in which the function x² – 2x + 5 is strictly increasing.
(c) A spherical bubble volume at the rate of which the diminishing when the is decreasing in 2cm³/sec. Find the surface area is radius is 3cm. (May – 2014)
Answer:

Question 11.
(a) Which of the following function is always increasing?
(i) x + sin 2x
(ii) x – sin 2x
(ill) 2x + sin 3x
(iv) 2x – sin 2x
(b) The radius of a cylinder is increasing at a rate of 1cm/s and its height decreasing at a rate of 1cm/s. Find the rate of change of its volume when the radius is 5cm and the height is 5cm.
(c) Write the equation of tangent at (1,1) on the curve 2x² + 3y² = 5. (March – 2015)
Answer:

HSE Kerala Board Syllabus HSSLive Plus Two Computer Application Chapter Wise Previous Questions and Answers Pdf Free Download in both English Medium and Malayalam Medium are part of SCERT Kerala Plus Two Chapter Wise Previous Questions and Answers. Here HSSLive.Guru have given Higher Secondary Kerala Plus Two Computer Application Chapter Wise Previous Year Important Questions and Answers based on CBSE NCERT syllabus.

Board	SCERT, Kerala
Text Book	NCERT Based
Class	Plus Two
Subject	Computer Application
Chapter	All Chapters
Category	Kerala Plus Two

Kerala Plus Two Computer Application Chapter Wise Previous Year Questions and Answers

• Chapter 1 Review of C++ Programming
• Chapter 2 Arrays
• Chapter 3 Functions
• Chapter 4 Web Technology
• Chapter 5 Web Designing Using HTML
• Chapter 6 Client-Side Scripting Using Java Script
• Chapter 7 Web Hosting
• Chapter 8 Database Management System
• Chapter 9 Structured Query Language
• Chapter 10 Enterprise Resource Planning
• Chapter 11 Trends and Issues in ICT

We hope the given HSE Kerala Board Syllabus HSSLive Plus Two Computer Application Chapter Wise Previous Questions and Answers Pdf Free Download in both English Medium and Malayalam Medium will help you. If you have any query regarding Higher Secondary Kerala Plus Two Computer Application Chapter Wise Previous Year Important Questions and Answers based on CBSE NCERT syllabus, drop a comment below and we will get back to you at the earliest.

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 5 Continuity and Differentiability.

Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 5 Continuity and Differentiability

Plus Two Maths Continuity and Differentiability 3 Marks Important Questions

Question 1.
Consider \(f(x)=\left\{\begin{array}{ll}
\frac{x^{2}-x-6}{x+2}, & x \neq-2 \\
-5, & x=-2
\end{array}\right.\)

(i) Find f(-2)
(ii) Check whether the function f(x) is continuous at x= -2. (March – 2009)
Answer:

Question 2.
If f(x) = sin(Log x), prove that x² y₂ + xy₁ + y = 0 (May -2009)
Answer:
Given; y sin(Iogx)
Differentiating with respect to X;
\(y_{1}=\cos (\log x) \frac{1}{x} \Rightarrow x y_{1}=\cos (\log x)\)
Again differentiating with respect to x
\(\begin{array}{l}
\Rightarrow x y_{2}+y_{1}=-\sin (\log x) \frac{1}{x} \\
\Rightarrow x^{2} y_{2}+x y_{1}=-y \Rightarrow x^{2} y_{2}+x y_{1}+y=0
\end{array}\)

Question 3.
(i) Establish that g(x) =1 – x + |x| is continuous at origin.
(ii) Check whether h(x) = |l – x + |x|| is continuous at origin. (March – 2010)
Answer:
(i) Given; g(x) = 1 – x + |x| ⇒ g(x) (1 – x) + |x|
Here g(x) is the sum of two functions continuous functions hence continuous.
(ii) We have;
\(\begin{array}{l}
f o g(x)=f(g(x)) \\
=\quad f(1-x+|x|)=|1-x+| x \mid=h(x)
\end{array}\)
The composition of two continuous functions is again continuous. Therefore h(x) continuous.

Question 4.
Find \(\frac{d y}{d x}\) of the following
\(\begin{array}{l}
\text { (i) } x=\sqrt{a^{\sin ^{4} 4}} \quad y=\sqrt{a^{\cos ^{-1} t}} \\
\text { (ii) } y=\cos ^{-1} \frac{\left(1-x^{2}\right)}{\left(1+x^{2}\right)}, 0<x<1 \\
\text { (iii) } y=\sin ^{-1} 2 x \sqrt{1-x^{2}}, y_{\sqrt{2}}<x<y_{\sqrt{2}}
\end{array}\)
Answer:

Question 5.
Find \(\frac{d y}{d x} \text { if } x^{3}+2 x^{2} y+3 x y^{2}+4 y^{3}=5\) (March – 2015)
Answer:

Question 6.
Find all points of discontinuity of f where f is defined by \(f(x)=\left\{\begin{array}{ll}
2 x+3, & x \leq 2 \\
2 x-3, & x>2
\end{array}\right.\) (March – 2016)
Answer:
In both the intervals x \(\leq[latex] 2 and x > 2 the function f(x) is a polynomial so continuous. So we havetocheckthe continuity at x = 2.

Question 7.
If e^x-y = x^y, then prove that [latex]\frac{d y}{d x}=\frac{\log x}{[\log \operatorname{ex}]}\) (May – 2014; March – 2016)
Answer:

Plus Two Maths Continuity and Differentiability 4 Marks Important Questions

Question 1.
Find \(\frac{d y}{d x}\) of the following (March – 2009)
\(\begin{array}{l}
\text { (i) } y=\sin ^{-1}\left(3 x-4 x^{3}\right)+\cos ^{-1}\left(4 x^{3}-3 x\right) \\
\text { (ii) } y=\tan ^{-1}\left(\sqrt{\frac{1-\cos x}{1+\cos x}}\right)
\end{array}\)
Answer:

Question 2.
Consider the function f(x) = |x| x ∈ R
(i) Draw the graph of f(x) =|x|
(ii) Show that the function is continuous at x = 0. (March – 2010)
Answer:

f(0^–) f(0^–) = 0. therefore continuous at x = 0.
AIso from the figure we can see that the graph does not have a break or jump.

Question 3.
(i) Find the derivative of y = x^a + a^x with respect to x.
(ii) If e^y (x + 1) = 1 , showthat \(\frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}\) (May – 2011)
Answer:

Question 4.
(i) Check the continuity of the function given by f(x) \(f(x)=\left\{\begin{array}{ll}
x \sin \frac{1}{x}, & x \neq 0 \\
1, & x=0
\end{array}\right.\)

(ii) Verify Mean Value Theorem for the function f(x) = x + 1/x in the interval [1,3]. (May – 2011)
Answer:


Hence Mean Value Theorem ¡s verified.

Question 5.
(i) Determine the value of k so that the function (May – 2012)

Answer:

Question 6.
Consider a fUnction f: R → R defined by
\(f(x)=\left\{\begin{array}{cc}
a+x, & x \leq 2 \\
b-x, & x>2
\end{array}\right.\)

(i) Find a relation between a and b if f is continuous at x = 2.
(ii) Find a and b, if f is continuous at x2 and a + b = 2. (May – 2013)
Answer:
(i) Since fis continuous at x = 2, we have;

(ii) Given a = 2 …(2) Solving (1) and (2) we have;
⇒ 2a = – 2 ⇒ a = – 1
⇒ b = 2 – a = 2 + 1 = 3

Question 7.
(i) Find if x = a(t – sin t) y = a(1 + cos t)
(ii) Verify Rolles theorem for the function f(x) = x2 + 2 in the interval [-2, 2] (March – 2014)
Answer:

Question 8.
(a) Find the relationship between a and b so that the function f defined by
\(f(x)=\left\{\begin{array}{ll}
a x^{2}-1, & x \leq 2 \\
b x+3, & x>2
\end{array}\right.\) is continuous.

(b) Verify mean value theorem for the function f(x) = x2 – 4x -3 ¡n the interval [1, 4]. (May – 2014)
Answer:
(a) Since fis continuous

Hence mean value theorem satisfies for the funcion.

Question 9.
(a) Find ‘a’ and ‘b’ if the function
\(f(x)=\left\{\begin{array}{ll}
\frac{\sin x}{x}, & -2 \leq x \leq 0 \\
a \times 2^{x}, & 0 \leq x \leq 1 \\
b+x, & 1<x \leq 2
\end{array}\right.\) is continous on [-2, 2]

(b) How many of the functions
f(x) = |x|, g(x) = |x|², h(x) = |x|³ are not differentiable at x = 0?
(i) 0
(ii) 1
(iii) 2
(iv) 3 (March – 2015)
Answer:
(a) Since f(x) is continuous on [-2, 2]

Question 10.
(a) Find the relation between ‘a’ and ‘b’ if the function f defined by
\(f(x)=\left\{\begin{array}{l}
a x+1, x \leq 3 \\
b x+3, x>3
\end{array}\right.\) is continuous.
lbx+3.x>3
(b) If e^y (x + 1) = 1, show thats \(\frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}\) (May -2015)
Answer:

Question 11.
Find the value of a and b such that the function \(f(x)=\left\{\begin{array}{cc}
5 a & x \leq 0 \\
a \sin x+\cos x & 0<x<\frac{\pi}{2} \\
b-\frac{\pi}{2} & x \geq \frac{\pi}{2}
\end{array}\right.\) is continuous. (March – 2010)
Answer:

Question 12.
(i) Find \(\frac{d y}{d x}, \text { if } x=a \cos ^{2} \theta ; y=b \sin ^{2} \theta\)
(ii) Find the second derivative of the function y = e^x sinx. (May – 2017)
Answer:

Question 13.
Find \(\frac{d y}{d x}\) of the following (4 score each)
(i) y^x = x^y (May – 2015)
(ii) (COSx)^y = (cosy)^x (March – 2017)
Answer:

Plus Two Maths Continuity and Differentiability 6 Marks Important Questions

Question 1.
Find \(\frac{d y}{d x}\) if
(i) sinx + cosy = xy
(ii) x = acos³t, y = asin³t
(iii) y = x^x + (logx)^x (May -2009; May -2011; March -2015)
Answer:
(i) Given; sinx + cosy = xy
Differentiating with respect to x;

Question 2.
(i) Let y =3 cos(log x) + 4 sin (log x)
(a) Find \(\frac{d y}{d x}\)
(b) Prove that x² y₂ + xy₁ + y = 0

(ii) (a) Find the derivative of y = e^2x+logx
(b) Find \(\frac{d y}{d x}\)
if x = a (θ – sinθ), y = a(1 – cosθ) (March – 2009)
Answer:

Question 3.
(i) Show that the function f (x) defined by f(x) = sin (cosx) is a continuous function.
(ii) If \(\frac{d y}{d x}=\frac{1}{\frac{d x}{d y}}\), Show that \(\frac{d^{2} y}{d x^{2}}=\frac{-\frac{d^{2} x}{d y^{2}}}{\left(\frac{d x}{d y}\right)^{3}}\) (May -2010)
Answer:
Given; f(x) = sin(cos x)
Let g(x) = sin(x) and h(x) = cos x
Both these function are trigonometric functions hence continuous.
goh(x) = g(h(x)) = g(cos x) = sin(cos x) = f(x)

Since f(x) is the composition of two continuous functions, hence continuous.

Question 4.
(i) Let y = x^{sin x} + (sinx)^x. Find \(\frac{d y}{d x}\)
(ii) Given; \(y=\sqrt{\tan ^{-1} x}\)
(a) \(2\left(1+x^{2}\right) y \frac{d y}{d x}=1\)
(b) \(\left(1+x^{2}\right) y \frac{d^{2} y}{d x^{2}}+\left(1+x^{2}\right)\left(\frac{d y}{d x}\right)^{2}+2 x y \frac{d y}{d x}=0\) (May – 2010; Onam – 2017)
Answer:

Question 5.
(i) The function \(f(x)=\left\{\begin{array}{ll}
5, & x \leq 2 \\
a x+b, 2< & x<10 \text { is } \\
21, & x \geq 10
\end{array}\right.\) continuous. Find a and b
(ii) Find \(\frac{d y}{d x}\) (a) if y = Sin (xsinx)
(iii) If y = ae” + be’; show that \(\frac{d^{2} y}{d x^{2}}-(m+n) \frac{d y}{d x}+m n y=0\) (March – 2011)
Answer:

Question 6.
(i) Match the following.

(ii) If y = sin^-1 x, prove that (1 – x²) y₂ – xy₁ = 0 (March – 2012; May -2017)
Answer:

Question 7.
(i) Consider \(f(x)=\left\{\begin{array}{ll}
3 x-8, & x \leq 5 \\
2 k, & x>5
\end{array}\right.\) Find the value of k if f(x) is continuous at x = 5.
(ii) Find \(\frac{d y}{d x}, \text { if } y=(\sin x)^{\log x}, \sin x>0\)
(iii) If y = (sin-1 x)2, then show that \(\left(1-x^{2}\right) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}=2\). (March -2013)
Answer:

Question 8.
(i) Find, if y = 1ogx, x>0
(ii) Is f(x) = |x| differentiable at x = 0?
(iii) Find if x = sin θ – cos θ and y= sinθ + cosθ (May – 2013)
Answer:

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 4 Determinants.

Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 4 Determinants

Plus Two Maths Determinants 3 Marks Important Questions

Question 1.
Prove that \(\begin{array}{|lll|}
1 ! & 2 ! & 3 ! \\
2 ! & 3 ! & 4 ! \\
3 ! & 4 ! & 5 !
\end{array}\) (March – 2015)
Answer:

Question 2.
Using properties of determinants prove the following. (March – 2010; Christmas -2017)
Answer:

Plus Two Maths Determinants 4 Marks Important Questions

Question 1.
Consider the matrix \(A=\left[\begin{array}{ll}
2 & 5 \\
3 & 2
\end{array}\right]\)

(i) Find adj (A)
(ii) Find A1
(iii) Using A^-1 solve the system of linear equations 2x + 5y = 13x + 2y = 7 (March – 2010)
Answer:

Plus Two Maths Determinants 6 Marks Important Questions

Question 1.
Consider the matrix \(A=\left[\begin{array}{lll}
a & b & c \\
b & c & a \\
c & a & b
\end{array}\right]\)

(i) Using the column operat,on
C₁ → C₁ + C₂ + C₃,
show that \(|A|=(a+b+c)\left|\begin{array}{ccc}
1 & b & c \\
1 & c & a \\
1 & a & b
\end{array}\right|\)
(ii) Show that |A| = – (a3 + b3 + e3 — 3abc)
(iii) Find A x adj(A) if a = 1,b = 10,c = 100 (May – 2010)
Answer:

Question 2.
(i) (a) If \(A=\left[\begin{array}{ccc}
1 & 1 & 5 \\
0 & 1 & 3 \\
0 & -1 & -2
\end{array}\right]\)

What is the value of |3A|?
(b) Find the equation of the line joining the points (1,2) and (-3,-2) using determinants.
(ii) Show that \(\left|\begin{array}{lll}
1 & a & a^{2} \\
1 & b & b^{2} \\
1 & c & c^{2}
\end{array}\right|=(a-b)(b-c)(c-a)\)
Answer:

(b) Let (x,y) be the coordinate of any point on The line, then (1,2), (-3, -2) and (x, y) are collinear.

Hence the area formed will be zero.

Question 3.
Consider the following system of linear equations; x + y + z = 6, x – y + z = 2, 2x + y + z = 1
(i) Express this system of equations in the Standard form AXB
(ii) Prove that A is non-singular.
(iii) Find the value of x, y and z satisfying the above equation. (May – 2011)
Answer:

Question 4.
(i) lf \(\left|\begin{array}{ll}
x & 3 \\
5 & 2
\end{array}\right|=5\), then x = ………..
(ii) Prove that
\(\left|\begin{array}{ccc}
y+k & y & y \\
y & y+k & y \\
y & y & y+k
\end{array}\right|=k^{2}(3 y+k)\)
(iii) Solve the following system of linear Equations, using matrix method; 5x + 2y = 3, 3x + 2y = 5 (March – 2012)
Answer:

Question 5.
(i) Let B is a square matrix of order 5, then |kB| is equal to ………..
(a) |B|
(b) k|B|
(c) k⁵|B|
(d) 5|B|

(ii) Prove that \(\left|\begin{array}{lll}
1 & x & x^{2} \\
1 & y & y^{2} \\
1 & z & z^{2}
\end{array}\right|=(x-y)(y-z)(z-x)\)
(iii) Check the consistency of the following equations; 2x + 3y + z = 6, x + 2y – z = 2, 7x + y + 2z =10 (May – 2012)
Answer:

Therefore the system is consistent and has unique solutions.

Question 6.
(i) Find the values of x in which \(\left|\begin{array}{ll}
3 & x \\
x & 1
\end{array}\right|=\left|\begin{array}{ll}
3 & 2 \\
4 & 1
\end{array}\right|\)

(ii) Using the property of determinants, show that the points A(a,b + c), B(b,c + a), C(c,a + b) are collinear.
(iii) Examine the consistency of system of following equations: 5x – 6y + 4z = 15, 7x + y – 3z = 19, 2x + y + 6z = 46 (EDUMATE – 2017; March – 2013)
Answer:

Since, the system is consistent and has unique solutions.

Question 7.
Consider a system of linear equations which is given below;
\(\begin{array}{l}
\frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4 ; \frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1 \\
\frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2
\end{array}\)

(i) Express the above equation in the matrix form AX = B.
(ii) Find A^-1, the inverse of A.
(iii) Find x,y and z. (May – 2013)
Answer:

Question 8.
Consider the matrices \(A=\left[\begin{array}{ll}
2 & 3 \\
4 & 5
\end{array}\right]\)

(i) Find A² – 7A – 21 = 0
(ii) Hence find A-1
(iii) Solve the following system of equations using matrix method 2x + 3y = 4; 4x + 5y = 6 (March – 2014)
Answer:

(iii) The given system of equations can be converted into matrix form AX = B

Question 9.
(i) Let A be a square matrix of order 2 x 2 then |KA| is equal to
(a) K|A|
(b) K²|A|
(c) K³|A|
(d) 2K|A|

(ii) Prove that
\(\left|\begin{array}{ccc}
\mathbf{a}-\mathbf{b}-\mathbf{c} & \mathbf{2 a} & 2 \mathbf{a} \\
2 \mathrm{~b} & \mathrm{~b}-\mathrm{c}-\mathrm{a} & 2 \mathrm{~b} \\
2 \mathrm{c} & 2 \mathrm{c} & \mathrm{c}-\mathrm{a}-\mathrm{b}
\end{array}\right|=(\mathrm{a}+\mathrm{b}+\mathrm{c})^{3}\)

(iii) Examine the consistency of the system of Equations. 5x + 3y = 5; 2x + 6y = 8 (May- 2014)
Answer:

(iii) The given system of equation can be written in matrix form as

solution exist and hence it is consistent.

Question 10.
(a) Choose the correct statement related to the matnces \(A=\left[\begin{array}{ll}
1 & 0 \\
0 & 1
\end{array}\right], B=\left[\begin{array}{ll}
0 & 1 \\
1 & 0
\end{array}\right]\)
\(\begin{array}{l}
\text { (i) } A^{3}=A, B^{3} \neq B \\
\text { (ii) } A^{3} \neq A, B^{3}=B \\
\text { (iii) } A^{3}=A, B^{3}=B \\
\text { (iv) } A^{3} \neq A, B^{3} \neq B
\end{array}\)

(b) lf \(M=\left[\begin{array}{ll}
7 & 5 \\
2 & 3
\end{array}\right]\) then verity the equation M² – 10M + 11 I₂ = O

(c) Inverse of the matrix \(\left[\begin{array}{lll}
0 & 1 & 2 \\
0 & 1 & 1 \\
1 & 0 & 2
\end{array}\right]\) (March – 2015)
Answer:

Question 11.
Solve the system of Linear equations x + 2y + z = 8; 2x + y – z = 1; x – y + z = 2 (March – 2015)
Answer:

Question 12.
(a) If \(\left|\begin{array}{ll}
x & 1 \\
1 & x
\end{array}\right|=15\) then find the value of X.

(b)Solve the following system of equations 3x – 2y + 3z = ?, 2x + y – z = 1 4x – 3y + 2z = 4 (May – 2015)
Answer:

Question 13.
(i)The value of the determinant \(\left|\begin{array}{ccc}
1 & 1 & 1 \\
1 & -1 & -1 \\
1 & 1 & -1
\end{array}\right|\) is
(a) -4
(b) 0
(c) 1
(d) 4

(ii) Using matrix method, solve the system of linear equations x + y + 2z = 4; 2x – y + 3z = 9; 3x – y – z = 2 (May – 2016)
Answer:
(i) (d) 4
(ii) Express the given equation in the matrix form as AX = B

Question 14.
(i) If \(A=\left[\begin{array}{ll}
a & 1 \\
1 & 0
\end{array}\right]\) is such that A² = I then a equals
(a) 1
(b) -1
(c) 0
(d) 2

(ii)Solve the system of equations x – y + z = 4; 2x + y – 3z = 0; x + y + z = 2 Using matrix method. (March – 2017)
Answer:

Question 15.
(i) IfA is a 2 x 2 matrix with |A| = 5, then |adjA| is
(a) 5
(b) 25
(c) 1/5
(d) 1/25

(ii) Solve the system of equations using matrix method.
x + y + z = 1; 2x + 3y – z = 6; x – y + z = -1 (May – 2017)
Answer:
(i) (a) 5
(ii) LetA X=B,

Kerala State Board New Syllabus Plus Two Maths Chapter Wise Previous Questions and Answers Chapter 12 Linear Programming.

Kerala Plus Two Maths Chapter Wise Previous Questions Chapter 12 Linear Programming

Plus Two Maths Linear Programming 4 Marks Important Questions

Question 1.
Consider the linear programming problem;
Maximise; Z = x +y , 2x + y – 3< 0, x – 2y + 1 < 0, y < 3, x < 0, y < 0
(i) Draw its feasible region.
(ii) Find the corner points of the feasible region.
(iii) Find the corner at which Z attains its maximum. (March – 2012)
Answer:

(ii) In the figure the shaded region ABC is the feasible region. Here the region is bounded. The corner points are A(1, 1), B(5, 3), C(O, 3).
(iii) Given; Z = x + y

Corner points	Value of Z
A	Z = (l)+(1) = 2
B	Z = (5)+(3) = 8
C	Z = (0)+(3) = 3

Since maximum value of Z occurs at B, the soluion is Z = (5) + (3) = 8.

Question 2.
Consider the LPP Minimise; Z = 200 k + 500y, x + 2y > 10, 3x + 4y < 24, x > 0, y > 0
(i) Draw the feasible region.
(ii) Find the co-ordinates of the comer points of the feasible region.
(iii) Solve the LPP. (May – 2012)
Answer:

(ii) In the figure the shaded region ABC is the feasible region. Here the region is bounded. The corner points are 4(4, 3), 5(0, 6), C(0, 5)
(iii) Given; Z = 200x + 500y

Corner points	Value of Z
A	Z = 200(4)+500(3) = 2300
B	Z = 200(0)+500(6) = 3000
C	Z = 200(0)+500(5) = 2500

Since minimum value of Z occurs at A, the soluion is Z = 200(4) + 500(3) = 2300.

Question 3.
Consider the LPP
Maximise; Z = 5x + 3y
Subject to; 3x + 5y < 15, 5x + 2y < 10x, y > 0
(i) Draw the feasible region.
(ii) Find the corner points of the feasible region.
(iii) Find the corner at which Z attains its maximum. (March – 2013)
Answer:
In the figure, the shaded region OABC is the feasible region. Here the region is bounded.
The corner points are

Given; Z = 5x + 3y

Corner points	Value of Z
O	Z = 0
A	Z = 5(2)+3(0) = 10
B	\(Z=5\left(\frac{20}{19}\right)+3\left(\frac{45}{19}\right)=\frac{235}{19}\)
C	Z = 5(0)+3(3) = 9

Since maximum value of Z occurs at B, the soluion is Z =

Question 4.
Consider the linear programming problem: Minimize Z = 3x + 9y Subject to the constraints: x + 3y < 60 x + y > 10, x < y, x > 0, y > 0
(i) Draw its feasible region.
(ii) Find the vertices of the feasible region
(iii) Find the minimum value of Z subject to the given constraints. (March-2014, SAY-2016)
Answer:

(ii) The feasible region is ABCD.
Solving x + y = 10, x = y we get B(5, 5)
Solving x + 3y = 60, x = y we get C(15, 15)
Hence the comer points are A(0, 10) , B(5, 5), C(15, 15), D(0, 20)
(iii) Given; Z = 3x + 9y

Corner points	Value of Z
A	Z = 3(0)+9(10) = 90
B	Z = 3(5)+9(5) = 60
C	Z = 3(15)+ 9(15) = 190
D	Z = 3(0)+9(20) = 180

Form the table, minumum value of Z is 6 O at B(5, 5).

Question 5.
Consider the linear inequalities 2x + 3y < 6; 2x + y < 4; x, y < 0
(a) Mark the feasible region.
(b) Maximise the function z = 4x + 5y subject to the given constraints. (March – 2014)
Answer:

(b) 15.2x + 3y = 6

X	0	2
Y	4	0

2x + y = 4

X	0	3
Y	2	0

Corner points	z = 4x + 5y
0(0, 0)	z = 0
A(2, 0)	8 + 0 = 8
B(1.5, 1)	6 + 5 = 11
C(0, 2)	0 + 10 = 10

Maximum at x = 1.5, y = 1
Maximum value is Z = 11

Question 6.
Consider the linear programming problem: Minimise Z = 4x + 4y Subject to x + 2y < 8; 3x + 2y < 12x, y < 0
(a) Mark its feasible region.
(b) Find the comer points of the feasible region.
(c) Find the corner at which Z attains its minimum. (May – 2014)
Answer:
(a) x + 2y = 8,

X	0	8
y	4	0

3x + 12y = 12

X	0	4
y	6	0

The comer points are 0(0, 0), A(4, 0), B(2, 3), C(0, 4)

(c)

Corner point	Z = -3x + 4y
0 (0, 0)	Z = 0 + 0 = 0
A (4, 0)	Z = -12 + 0 = -12
B (2, 3)	Z = -6 + 12 = 6
C (0, 4)	Z = 0 + 16 = 16

Z attains minimum at (4, 0).

Question 7.
Consider the linear programming problem: Maximum z = 4x + y
Subject to constraints: x + y < 50, 3x + y < 9x, y < 0
(a) Draw the feasible region
(b) Find the corner points of the feasible region
(c) Find the corner at which ‘z’ attains its maximum value. (May – 2015)
Answer:
(a) x + y = 50,

X	0	50
y	50	0

3x + y = 90

X	0	30
y	90	0

(b) Solving the equations we get the points as
O(0, 0) A(30, 0); B(20, 30); C(0, 50)

(c)

Vertices	Z
0(0,0)	0
A(30,0)	120 maximum
B(20,30)	110
C(0,50)	50

Z attains maximum at A(30, 0)

Question 8.
Consider the LPP
Maximise z = 3x + 2y
Subject to the constraints: x + 2y < 10, 3x + y < 15; x, y < 0
(a) Draw its feasible region
(b) Find the corner points of the feasible region
(c) Find the maximum value of Z. (March – 2016)
Answer:

(b) The corner points 0(0,0), A(5,0), B(4,3), C(0, 5)
Z is maximum at B(4, 3), z = 18.

(c)

o	(0,0)	Z = 3(0)+ 2(0) = 0
A	(5,0),	Z= 3(5)+ 2(0) = 15
B	(4,3),	Z= 3(4)+ 2(3) = 18
C	(0,5)	Z= 3(0) + 2(5) = 10

Question 9.
Consider the linear programming problem: Maximum z = 50x + 40y
Subject to constraints:
x + 2y < 10; 3x + 4y < 24; x, y < 0
(i) Draw the feasible region
(ii) Find the comer points of the feasible region
(iii) Find the maximum value of z. (March – 2017)
Answer:

(ii) In the figure the shaded region ABC is the feasible region. Here the region is bounded. The corner points are A(4, 3), B(0, 6), C(0, 5)
(iii) Given; Z = 50x + 40y

Corner points	Value of Z
A	Z = 50(4)+ 40(3) = 320
B	Z= 50(0)+ 40(6) = 240.
C	Z= 50(0)+ 40(5) = 200

Since minimum value of Z occurs at A, the soluion is Z = 50(4) + 4(3) = 320.

Plus Two Maths Linear Programming 6 Marks Important Questions

Question 1.
A furniture dealer sells only tables and chairs. He has Rs. 12,000 to invest and a space to store 90 pieces. A table costs him Rs. 400 and a chair Rs. 100. He can sell a table at a profit of Rs. 75 and a chair at a profit of Rs. 25. Assume that he can sell all the items. The dealer wants to get maximum profit.
(i) By defining suitable variables, write the objective function.
(ii) Write the constraints.
(iii) Maximise the objective function graphically. (March – 2010)
Answer:
(i) Let x be the number of Tables and y be the number of Chairs. Then; Maximise; z = 75x + 25y
(ii) Furniture constraints x + y < 90
Investment constraint 400x + 100y < 12000
Therefore;Maximise; Z = 75x + 25y, x + y < 90, 4x + y < 120, x<0, y<0
(iii) In the figure the shaded region OABC is the feasible region. Here the region is bounded. The corner points are O(0, 0), A(30, 0) B(10, 80), C(0, 90).

Given; Z = 75x + 25y

Corner points	Value of Z
O	Z =75(0) +25(0) = 0
A	Z= 75(30)+ 25(0) = 2250
B	Z= 75(10)+ 25(80) = 2750
C	Z= 75(0)+ 25(90) = 2250

Since minimum value of Z occurs at B, the soluion is Z = 2750.

Question 2.
A company produces two types of cricket balls A and B. The production time of one ball of type B is double type A (time in units). The company has the time to produce a maximum of 2000 balls per day. The supply of raw materials is sufficient for the production of 1500 balls (both A and B) per day. The company wants to make maximum profit by making a profit of Rs. 3 from a ball of type A and Rs. 5 from type B.

Then,
(i) By defining suitable variables write the objective function.
(ii) Write the constraints.
(iii) How many balls should be produced in each type per day in order to get maximum profit? (May – 2010)
Answer:
(i) Let x be the number of balls of type A and y be the number of balls of type B. Then Maximise profit is Z = 3x + 5y
(ii) Balls constraints 2x + y < 2000 investment constraint x + y < 1500
Therefore; Maximise; Z = 3x + 5y, 2x + y < 2000, x + y < 1500, x < 0, y < 0

(iii) In the figure the shaded region OABC is the fesible region. Here the region ¡s bounded. The corner points are O(0, 0), A(1000, 0) B(500, 1000), C(0, 1500). Given; Z = 3x + 5y

Comer points	Value of Z
O	Z = 3(0)+ 5(0) = 0
A	Z = 3(1000) + 5(0) = 3000
B	Z= 3(500) + 5(1000) = 6500
C	Z= 3(0) + 5(1500) = 7500

Since maximum value of Z occurs at C, the soluion is Z = 3(0) + 5(1500) = 7500.

Question 3.
The graph of a linear programming problem is given below. The shaded region is the feasible region. The objective function is Maximise; Z = px + qy

(i) What are the co-ordinates of the corners of the feasible region?
(ii) Write the constraints.
(iii) If the Max. Z occurs at A and B, what ¡s the relation between p and q?
(iv) If q = 1, write the objective function.
(v) Find Max. Z. (March – 2011)
Answer:
(i) From the figure the feasible region is OABC.
Then the comer points are;
A is (5, 0), B is (3, 4), C is (0, 5) and O (0, 0)
(ii) The constraints are 2x + y < 10, x + 3y < 15, x < 0, y < 0
(iii) Given; Z = px + qy

Corner points	Value of Z
O	Z=p(0)+q(0) = 0
A	Z = p(5) + q(Q) = 5p
B	Z = p( 3)+g(4) = 3p+4q
C	Z = p(0)+q(5) = 5q

Since maximum at A and B we have;
⇒ 3p + 4q = 5p ⇒ 2p = 4q ⇒ p = 2q
(iv) When q = 1, then p ⇒ 2q ⇒ p = 2
Objective function is; Z = 2x + y
(v) We have; Z px + qy at B Z has maximum ⇒ Z = 2(3) + 4 = 10

Question 4.
A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and I hour on machine B to produce a package of bolts. He earns a profit of Rs. 17.50 per package on nuts and Rs. 7.00 per package on bolts. How many packages of each should be produced each day so as to maximise his profit, if he produced each day so as to maximise the profit if he operates his machines for at the most 12 hours a day?
(i) By suitable defining the variables write the objective function of the problem.
(ii) Formulate the problem as a linear programming problem(LPP)
(iii) Solve the LPP graphically and find the number of packages of nuts and bolts to be manufactured. (May -2011)
Answer:
(i) Let x be the number of packages of nuts produced and y be the number of packages of bolts produced. Then;
Maximise profit is; Z = 17. 5x + 7y
(ii) Time constraint for Machine A; x + 3y < 12
Time constraint for Machine B; 3x + y < 12
Therefore; Maximise; Z = 17.5x + 7y, x + 3y < 12, 3x + y < 12, x < 0, y < 0
(iii) In the figure the shaded region OABC is the visible region. Here the region is bounded. The corner points are 0(0,0), A (4, 0) B(3, 3), C(0, 4).

Given; Z = 17.5x + 7y

Comer points	Value of Z
O	Z =17.5(0) +7(0) = 0
A	Z =17.5(4)+ 7(0) = 70
B	Z= 17.5(3)+ 7(3) = 73.5
C	Z= 17.5(0)+7(4) = 28

Since maximum value of Z occurs at B, the soluion is Z = 17.5(3) + 7(3) = 73.5.

Question 5.
A bakery owner makes two types of cakes A and B. Three machines are needed for this purpose. The time (in minutes) required for making each type of cakes in each machine is given below;

Machine	Types of cakes
1	12	6
II	18	0
III	6	9

Each machine is available for almost 6 hours per day. Assume that all cakes will be sold out every day. The bakery owner wants to make a maximum profit per day by making Rs. 7.5 from type A and Rs. 5 from type B.
(i) Write the objective function by defining suitable variables.
(ii) Write the constraints.
(iii) Find the maximum profit graphically. (May- 2013, EDUMATE – 2017)
Answer:
(i) Number of cake of type A: x
Number of cake of type B: y
Then profit function is Maximise: Z = 75x + 5y

(ii) 12x + 6y < 360; 18x + 0y < 360
6x + 9y < 360; x > 0, y > 0
Simplifying we get;
2x – i – y < 60………..(1)
x < 20………..(2)
2x + 3y < 120………..(3)
x > 0, y > 0

The feasible region is OABCDO
Solving (1) and (2) we get the point B- (2020)
Solving (1) and (3) we get the point C- (15,30)
A-(20,0), O-(0,0), D-(0,40)
Given; Z = x + y

Corner points	Value of Z
O	Z = 7.5(0) +5(0) = 0
A	Z =150
B	Z = 250
C	Z =112.5
D	Z = 200

Since maximum value of Z occurs at B, the soluion is Z = 250 (20, 20).

Question 6.
In a factory, there are two machines A and B producing toys. They respectively produce 60 and 80 units in one hour. A can run a maximum of 10 hours and B a maximum of 7 hours a day. The cost of their running per hour respectively amounts to 2,000 and 2,500 rupees. The total duration of working these machines cannot exceed 12 hours a day. If the total cost cannot exceed Rs. 25,000 per day and the total daily production is at least 800 units, then formulate the problem mathematically. (March – 2014)
Answer:
Let x be the running time for machine A and y be the running time for machine B.
Since machines cannot work more than 12 hours x + y < 12
Since maximum production of two machines is 800 units.
60x + 80y < 800
Maximum cost of production is 25000, 2000x + 2500y < 25000
0 < x < 10, 0 < y < 7