Social Science 10th Previous Year Question Paper 2016 (CBSE)

SOCIAL SCIENCE

SET-I

Q.1. Who remarked “when France sneezes the rest of Europe catches cold”.

Answer. Duke Metternich

 Or

Who were called colons in Vietnam?

Answer. French citizens living in Vietnam were known as colons.

 

Q.2. Why should the use of cattle cake as fuel be discouraged?

Answer. Using dung cake or cattle cake as fuel is being discouraged because it consumes most valuable manure which could be used in agriculture.

 

Q.3. Distinguish between pressure groups and political parties by stating any one point of distinction.

Answer. Pressure groups do not aim to directly control or share political power but political parties directly control and share political power.

 

Q.4. Why did India adopt multi-party system?

Answer. India adopted multi-party system because:

  1. India is a large country and has social and geographical diversities.
  2. It is easy to absorb different diversities in a multi-party system.

 

Q.5. Name any two sectional interest groups.

Answer. Trade Unions and Professional bodies like lawyers, teachers etc.

 

Q.6. Why do MNCs set up their offices and factories in those regions where they get cheap labour and other resources?

Answer. MNCs set up offices and factories for products in regions where they can get cheap labour and other resources so that (i) the cost of production is low and (ii) the MNCs can earn greater profits.

 

Q.7. If any damage is done to a consumer by a trader, under which consumer right one can move to consumer court to get compensation?

Answer. Right to seek redressal. The consumers can seek redressal against trade practices of exploitation and have the right to fair settlement of the genuine grievances.

 

.Q.8. Why is the supervision of the functioning of formal sources of loans necessary?

Answer. Supervision of the functioning of formal sources of loans is necessary because banks have to submit information to the RBI on how much they are lending, to whom they are lending and at what interest rate etc.

 

Q.9. “The decade of 1830 had brought great economic hardship in Europe.” Support the statement with arguments.

Answer. The decade of 1830s was known as great economic hardship in Europe because of the following reasons:

  1. Europe had come under the grip of large-scale unemployment. In most of the countries there were more seekers of jobs than employment.
  2.  Cities had become overcrowded and slums had emerged as population from the rural areas migrated to the cities.
  3. Small producers in towns were often faced with stiff competition from imports of cheap machine-made goods from England where industrialization was more advanced specially in the field of textile production.
  4.  In those regions of Europe, where aristocracy still enjoyed power, peasants struggled under the burden of feudal dues and obligations. The rise of food prices and bad harvests added to their hardships.

Or

“The Ho Chi Minh Trail became advantageous to Vietnamese in the war against U.S.” Support the statement with arguments.

Answer. “The Ho-Chi-Minh Trail became advantageous to Vietnamese in the war against U.S.”

  1. The trail symbolizes how the Vietnamese used their limited resources to great advantage.
  2. The trail, an immense network of footpaths and roads was used to transport men and material from North to South.
  3. It was improved in late 1950s and from 1967 about 20,000 North Vietnamese troops came south each month. The trail had support bases and hospitals along the way.
  4. Mostly supplies were carried by women porters on their backs or on their bicycles.
  5. The U.S regularly bombed this trail to disrupt supplies but efforts to destroy this important supply line by intensive bombing failed because they were rebuilt very quickly.

 

Q.10. What type of flag was designed during the ‘Swadeshi Movement’ in Bengal? Explain its main features.

Answer. During the ‘Swadeshi Movement’ in Bengal, a tricolour flag—red, green and yellow was designed. It had eight lotuses representing the eight provinces of British India.

It had a crescent moon, representing Hindus and Muslims.

 

Q.11. “The plantation workers in Assam had their own understanding of Mahatma Gandhi and the notion of Swaraj”. Support the statement with arguments.

Answer. “The plantation workers in Assam had their own understanding of Mahatma Gandhi and the notion of Swaraj”

  1. For plantation workers in Assam, freedom meant the right to move freely in and out of the confined space in which they were enclosed.
  2. Under the Inland Emigration Act of 1859 plantation workers were not permitted to leave the tea gardens without permission.
  3. Swaraj meant retaining a link with the village from which they had come.
  4. When they heard of the Non-cooperation Movement, thousands of workers defied the authorities, left the plantations and headed home.
  5. They believed that Gandhi Raj was coming and everyone would be given land in their own village.

 

Q.12. Classify industries on the basis of source of raw material. How are they different from each other?

Answer. On the basis of sources of raw material industries are classified as:

(i) Agro based industries; (ii) Mineral based industries

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Q.13. ‘Consumption of energy in all forms has been rising all over the country. There is an urgent need to develop a sustainable path of energy development and energy saving.’ Suggest and explain any three measures to solve this binning problem.

Answer. Every sector of the national economy—agriculture, industry, transport, (commercial and domestic), needs greater inputs of energy.

With increasing population and changing lifestyles energy consumption is increasing very fast. We are not self sufficient in energy according to demands. Therefore we have to adopt a cautious approach for the judicious use of our limited resources. Conservation of energy should be done at all levels.

Three measures to reduce consumption of energy in all forms:

  1. We can do our bit by using public transport systems instead of individual vehicles.
  2. Switching off electricity when not in use.
  3. Using power saving devices or using non-conventional sources of energy such as solar energy, wind energy etc.
  4. Checking the power equipments regularly can help in saving of energy.

 

Q.14. Suggest any three steps to minimise the environmental degradation caused by the industrial development in India.

Answer. Steps to minimize the environmental degradation caused by industrial development in India are: –

  1. Minimizing use of water for processing by reusing and recycling in two or more successive stages. Harvesting of rain water to meet water requirements of industries and other domestic purposes.
  2. Treating hot water and effluents before releasing them in rivers and ponds.
  3.  Particulate matter in the air can be reduced by fitting smoke to factories with electrostatic precipitators, fabric filters, scrubbers and inertial separators. Smoke can be reduced by using oil or gas instead of coal in factories.
  4. Machinery and equipment’s can be fitted with silencers to prevent noise pollution.

 

Q.15. What is meant by regional political party? State the conditions required to be recognised as a ‘regional political party’.

Answer. A regional party is a party that is present in only some states. Regional parties or State parties need not be regional in their ideology. They have state identity as they are present only in some states. Some of these parties are all India parties that happen to have succeeded only in states. Example, Samajwadi Party, Rashtriya Janta Dal.

Conditions required for a party to be recognized as a regional political party:

  1. A party that secures at least six percent of the total votes in an election to the legislative assembly of a state.
  2. Wins at least two seats in the legislative assembly.

 

Q.16. What are public interest pressure groups? Describe their functioning.

Answer. Public Interest Groups are those that promote collective rather than selective interests. Their functioning is as follows:

  1. It aims to help groups other than their own members.
  2. They represent some common interest that needs to be defended.
  3. The members of the organization may not benefit from the cause that the organization represents.

For example, a group fighting against bonded labour fights not for itself but for those who are suffering under such bondage. E.g., BAMCEF.

 

Q.17. Which three challenges do you feel are being faced by political parties in India? Give your opinion.

Answer. There are four major areas where the working of political parties faces challenge: 

Lack of internal democracy.

1.All over the world, there is a tendency of political parties towards the concentration of power in one or few leaders at the top.

2.Parties do not keep membership register.

3.They do not conduct internal elections regularly.

4.Ordinary members of the party do not have sufficient information as to what happens inside the party.

No Transparency.

1.Since most political parties do not practice open and transparent procedures for their functioning, these are very few ways for an ordinary worker to rise to the top in a party.

2.Those who happen to be the leaders are in a position of unfair advantage to famous people close to them or even their family member.

3.In many parties, the top positions are always controlled by members of one family.

Money and Muscle Power

1.Since parties are focussed only on winning elections, they tend to use short cuts to win elections.

2.They tend to nominate those candidates who have or can raise a lot of money.

3.Rich people and companies who give funds to the parties tend to have influence on the policies and decisions of the party.

 

Q.18. “Deposits with the banks are beneficial to the depositors as well as to the nation”. Examine the statement.

Answer.

Benefit of deposits to the depositors:

  1. Bank accepts the deposits and pays interest to the depositor.
  2.  Banks help people save their money and keep their money in safe custody of the bank.
  3. People can withdraw the money as and when they require.
  4.  Banks also grant loans to people for a variety of purposes.

Benefit of deposits to the Nation:

  1. Banks use the major proportion of the deposit to extend loans.
  2. There is a huge demand for loans for various economic activities. In times of need, business houses and industries can borrow money from the banks.
  3. Banks mediate between those who have surplus funds and those who are in need of these funds. Thus, it helps in the economic development of the Nation.

 

Q.19. Why had the Indian government put barriers to foreign trade and foreign investments after independence? Analyse the reasons.

Answer. The Indian Government removed these barriers because:

  1. Liberalization of trade and investment policies allows Indian producers to compete with producers around the globe leading to an improvement in performance and quality of products.
  2.  After the barriers on foreign trade and foreign investment were removed to a large
    extent, goods could be imported and exported easily and also foreign companies could set up factories and offices in India. This has led to an increase in trade with different countries.
  3.  Businesses are allowed to make decisions freely about what they wish to import or export due to the liberal policies of the government.
  4.  Doors of investment opened up for MNCs. They have been investing large sums of money in India and have been seeking to earn large profits.

 

Q.20. “Rules and regulations are required for the protection of the consumers in the market place.” Justify the statement with arguments.

Answer. Rules and regulations are required for consumers’ protection because:

1. Sellers usually don’t accept responsibility for the sold products if there is any defect. For example, if a consumer who bought a utensil complains about the defect, then the seller may just ask the consumer to go to another shop.

2. Exploitation of consumers can happen in different ways like use of faulty weights. For example, a trader can weigh less good than what he is supposed to.

3. Consumers can be sold adulterated good purposefully. For example, adding colour to spices and then selling them.

4. If producers are few and consumers are many, producers can exploit lack of competition. For example, big companies can sell the product at any price they want because consumers don’t have a choice.

5. False information can be advertised on media to attract buyers. For example, a company selling baby milk powder advertised for a long time that it was better than mother’s milk.

 

Q.21. “Napoleon had destroyed democracy in France but in the administrative field he had incorporated revolutionary principles in order to make the whole system more rational and efficient.” Analyse the statement with arguments.

Answer.  “Napoleon had destroyed democracy in France but in administrative field he had incorporated revolutionary principles in order to make the whole systems more rational and efficient.”

(a) All privileges based on birth were removed.

(b) Established equality before law.

(c) Right to property was given.

(d) Simplified administrative divisions.

(e) Feudal system was abolished and freed peasants from serfdom and manorial dues.

(f) Guild restrictions were removed.

(g) Transport and communication systems were improved.

Or

“The peace negotiations in Geneva followed the division of Vietnam that set in motion a series of events that turned Vietnam into a battle field.” Analyse the statement with arguments.

Answer. The peace negotiations in Geneva followed the division of Vietnam that set in motion a series of events that turned Vietnam into a battle field.”

  1. In the peace negotiations in Geneva that followed the French defeat, the Vietnamese were persuaded to accept the division of the country, i.e., North and South.
  2. The division set in motion a series of events that turned Vietnam into a battlefield bringing death and destruction to its people as well as the environment.
  3. The Bao Dai regime was soon overthrown by a coup led by Ngo Dinh Diem. Diem built a repressive and authoritarian government.
  4. Anyone who opposed him was called a Communist and was jailed and killed.
  5. With the help of Ho Chi Minh government in North, the NLF fought for the unification of the country. The U.S watched this alliance with fear. Worried about the communist gaining power, it decided to intervene decisively sending in troops and arms.

 

Q.22. Why did Mahatma Gandhiji decide to call off the Civil Disobedience Movement? Explain.

Answer. Mahatma Gandhi decided to call off the Civil Disobedience Movement because:

  1. Worried by the development of Civil Disobedience Movement the colonial government began arresting the Congress leaders one by one.
  2. This led to violent clashes in many places.
  3. When Abdul Ghaffar khan, a devout disciple of Mahatma Gandhi was arrested in April 1930, angry crowds demonstrated in the streets of Peshawar, facing armoured cars and police firing. Many were killed.
  4. A month later, when Mahatma Gandhi was arrested industrial workers in Sholapur attacked the police force, municipal buildings, law courts, railway stations and all other structures that symbolized British rule.
  5. A frightened government responded with the policy of brutal repression. The peaceful satyagrahis were attacked, women and children were beaten and about 1 lakh people were arrested.

 

Q.23. Explain the importance of conservation of minerals. Highlight any three measures to conserve them.

Answer. Reasons for Conservation: 

(i) The strong dependence of industry and agriculture upon minerals. 

(ii) The process of mineral formation is slow. 

(iii) They are non-renewable. 

Methods to conserve: 

(i) Minerals should be used in a planned and sustainable manner. 

(ii) Improved technology needs to be constantly evolved to allow use of low grade ore at low cost. 

(iii) Recycling of metals using scrap metals. 

(iv) Wastage in the mining and processing should be minimised.

 

Q.24. “Roadways still have an edge over railways in India.” Support the statement with arguments.

Answer. Roadways score over railways:

  1. Construction of roads is easier and cheaper as compared to railways.
  2. Roads provide door to door service, thus the cost of loading and unloading is much . lower as compared to railways which generally leave the people and goods at the
    destined railway stations.
  3. Roads can negotiate higher gradients of slope and, as such, can traverse through mountainous terrain. But railways cannot negotiate steep gradients.
  4.  Road transport is economical in transportation of few persons and relatively smaller amount of goods over short distances.
  5. Road transport is also used as a feeder to other modes of transport. They provide links between railway stations, airports and sea ports.
  6. They link agricultural farms with markets and industries, thus linking rural and urban
    areas.

 

Q.25. Describe the popular struggle of Bolivia.

Answer. Popular struggle of Bolivia

  1. People’s struggle against privatisation of water in Bolivia power that struggles are integral part of democracy.
  2. The world Bank pressurised the government to give up its control of municipal water supply. The government sold these rights to a multinational company which increased the price of water by four times. Many people received monthly water bill of ?1,000 in a country where average income is around ?5,000 a month.
  3. In January 2000, a new alliance of labour human rights and community leaders organised a successful gone day strike.
  4. The government agreed to negotiate and the strike was called off.
  5. The police resorted to brutal regression when the agitations started in February followed in April and the government imposed martial law.
  6. But the power of people forced the officials of the MNC to flee the city and made the government concede to all the demand of the protestors.
  7. The contract with MNC was cancelled and the water supply was restored with the municipality at old rates.
    This popular struggle came to be known as ‘Bolivia’s Water Cool’.

 

Q.26. “Political parties are a necessary condition for a democracy”. Analyse the statement with examples.

Answer. “Political parties are a necessary condition for a democracy” in the following ways:

  1. Without political parties democracies cannot exist. If we do not have political parties, every candidate in elections will be independent.
  2. No one will be able to make any promises to the people about any major policy changes.
  3. The government may be formed but its utility will remain uncertain.
  4. Elected representatives will be accountable to their constituency, for what they do in their locality but no one will be responsible for how the country will run.
  5. As societies become large and complex they also needed some agencies to gather different views on various issues and to present these to the government, that’s why political parties are needed.

 

Q.27. How can the formal sector loans be made beneficial for poor farmers and workers? Suggest any five measures.

Answer. Formal sector loans can be made beneficial for poor farmers and workers in the following ways:

  1. Create greater awareness among farmers about formal sector loans.
  2. Process of providing loans should be made easier. It should be simple, fast and timely.
  3. More number of Nationalized Banks/cooperative banks should be opened in. rural sectors. Banks and cooperatives should increase facility of providing loans so that dependence on informal sources of credit reduces.
  4. The benefits of loans should be extended to poor farmers and small scale industries,
  5. While formal sector loans need to expand, it is also necessary that everyone receives these loans. It is important that formal credit is distributed more equally so that the poor can benefit from cheaper loans.

 

Q.28. Describe the impact of globalisation on Indian economy with examples.

Answer. Impact of Globalisation on the Indian Economy:

  1. Greater competition among producers (both local and foreign), has been advantageous to consumers, particularly the well-off section. There is greater choice before the consumers who now enjoy improved quality and lower prices for several products.
  2. Globalisation has led to a higher standard of living especially in urban areas.
  3. MNCs have increased their investments in India in industries such as electronics, automobiles, cellphones, soft drinks, fast food, banking services etc. leading to more job opportunities in these industries and services.
  4.  Globalisation has enabled some large Indian companies to emerge as MNCs themselves like Tata Motors, Infosys, Ranbaxy, Asian Paints, etc.
  5.  Globalisation has also created new opportunities for companies providing services particularly those involving IT (Information Technology). For example, call centres.
  6. Local companies supply raw materials to foreign industries and have prospered. However, for a large number of producers and workers the impact has not been uniform, and globalisation has posed major challenges.

 

Q.29. Three features A, B and C are marked on the given political outline map of India. Identify these features with the help of the following information and write their correct names on the lines marked in the map:

A. The place where cotton mill workers organised Satyagraha.

B. The place related to the calling off the Non-Cooperation Movement.

C. The place where the Indian National Congress Session was held.

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Answer.

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Note: The following questions are for the Visually Impaired Candidates only in lieu of Q.No. 29:

(29.1) Name the city where cotton mill workers organised Satyagraha.

(29.2) Name the place related to the calling off the Non-Cooperation Movement.

(29.3) Where was the Indian Nation Congress Session held in December 1920?

Answer. (29.1) Ahmedabad (29.2) Chauri Chaura (29.3) Nagpur

 

Q.30. On the given political outline map, of India, locate and label the following with appropriate symbols:

A. Oil Field—Digboi

B. Iron and Steel Plant—Bhilai

C. Major Sea Port—Kochi

Answer.

cbse-previous-year-question-papers-class-10-social-science-sa2-outside-delhi-2016-4

Note: The following questions are for the Visually Impaired Candidates only, in lieu of Q.No. 30:

(30.1) In which state is Digboi oil field located?

(30.2) Name the state where Bhilai Iron and Steel Plant is located.

(3Q.3) Name the Southernmost major sea port located on the eastern coast of India.

Answer. (30.1) Assam (30.2) Chattisgarh (30.3) Tuticorin

 

SET II

Q.1. Who was proclaimed German Emperor in a ceremony held at Versailles in January 1871?

Answer. Kaiser William I of Prussia was proclaimed German Emperor in a ceremony held at Versailles in January 1871.

Or

What was the main aim of the Scholar Revolt of 1868?

Answer. The main aim of Scholar Revolt of 1868 was to oppose French control and expansion of Christianity.

 

Q.2. How are ‘Gobar gas plants’ beneficial to the farmers?

Answer. “Gobar Gas Plants” are beneficial to the farmers in the form of energy and improved quality of manure.

 

Q.8. Prove with an argument that there is a great need to expand formal sources of credit in rural India.

Answer. There is great need to expand formal sources of credit in rural India because:

  1. There is no organisation that supervises the credit activities of lenders in the informal sector. They lend at whatever interest rate they choose.
  2. No one can stop rural money-lenders from using unfair means to get their money back.

 

Q.17. “Democracy accommodates social diversities.” Support the statement with examples.

Answer. “Democracy accommodates social diversities” in the following ways:

  1. Democracies develop a procedure to conduct their competition. This reduces the possibility of these tensions becoming explosive or violent.
  2.  No society can fully and permanently resolve conflicts among different groups. But we can certainly learn to respect these differences and can evolve mechanism to negotiate these differences.
    Example, Belgium has successfully negotiated differences among ethnic population. This reduces the possibility of tensions.
  3.  Ability to handle social differences, divisions and conflicts is thus a definite plus point of democratic regimes.

 

Q.18. Explain by giving examples that Multinational Corporations (MNCs) are spreading their productions in different ways.

Answer. 

Multinational Corporations are spreading their productions in different ways :  (i) By setting up partnership with local companies.  (ii) By placing orders with local companies. For example, garments, footwear, sports items, etc.  (iii) By closely competing with the local companies.  (iv) By buying local companies. To take an example, Cargill Foods, a very large American MNC has bought over smaller Indian companies such as Parakh foods. Parakh Food had built a large marketing network in various parts of India, where its brand was well-reputed.

 

Q.19. ‘Credit has its own unique role for development’. Justify the statement with arguments.

Answer. 

1. Credit facilities that are extended to the people indirectly play an important role in the development aspect of the country.The credit facilities extended by formal sources (banks and cooperatives) need to expand and it is also necessary that everyone receives them

2. The high rates of interest charged by the informal sector restrict the income of people and often push them into a state of the debt trap. People in rural areas majorly depend on sources of informal credit for agricultural purposes involving costs on equipment and other resources.

3. Credit at low rates of interest, as opposed to informal sources, would lead to high incomes and increase the financial ability of the people. This would help them in growing crops, do business and set up small-scale industries or trade in goods which would eventually contribute to the healthy development of the country.

NOTE – Credit (loan) refers to the agreement wherein the lender provides the borrower with money or goods and services with a promise of repayment in future.

 

Q.22. Why did Mahatma Gandhi relaunch the Civil Disobedience Movement with great apprehension? Explain.

Answer. Mahatma Gandhi entered into a pact with Irwin on 5 March, 1931.

  1.  By this Gandhi-Irwin Pact, Gandhiji committed to participate in a Round Table Conference in London and the government agreed to release the political prisoners.
  2. In December 1931, Gandhiji went to London for the conference, but the negotiations broke dowrn and he returned disappointed.
  3.  Back in India, he discovered that the government had begun a new cycle of repressive measures.
  4. Abdul Ghaffar Khan and Jawaharlal Nehru were both in jail and the Congress had been declared illegal.
  5.  A series of measures hacj been imposed to prevent meetings, demonstrations and boycotts. Thus, with great apprehension Gandhiji relaunched the Civil Disobedience Movement.

 

Q.23. Explain any five major problems faced by road transport in India.

Answer. Problems faced by road transportation:

  1. The road network is inadequate in proportion to the volume of traffic and passengers.
  2. About half of the roads are unmetalled which makes them useless during rainy season.
  3. The National Highways are inadequate and lack roadside amenities.
  4. The roadways are highly congested in cities.
  5. Most of the bridges and culverts are old and narrow.

 

Q.25. Suggest and explain any five measures to reform political parties.

Answer.

  1. Law to regulate the internal affairs of political parties like maintaining a register of its members, to follow its own constitution, to have independent authority, to act as judge in case of party dispute, to hold open elections to the highest post.
  2.  It should be mandatory for political parties to give one-third tickets to women candidates.
    Also there should be quota for women on the decision-making bodies of the party.
  3.  There should be state funding of elections. The government should give money to parties to support their election expenses in kind (petrol, paper, telephone etc.) or in cash on the basis of votes secured by the party in the previous election.
  4.  People can put pressure on political parties in various ways through petitions, publicity in media and agitations.
  5. Ordinary citizens, pressure groups and movements and the media can play an important role in this. Ordinary citizens can reform politics if they take part directly and join political parties.

SET III

Q.1. Who was proclaimed the King of United Italy in 1861?

Answer. Victor Emmanuel-II

Or

Who led the ‘Scholar Revolt’ in Vietnam in 1868?

Answer. The “Scholar Revolt” in Vietnam in 1868 was led by officials at the imperial court.

 

Q.2. Why has aluminium metal great importance?

Answer. Aluminium metal has great importance because:

  1. It combines the strength of metals such as iron with extreme lightness.
  2. It has good conductivity and great malleability.

 

Q.8. Why are most of the poor households deprived from the formal sector of loans?

Answer. Most of the poor households are deprived from the formal sector loans because of lack of proper documents and absence of collateral.

 

Q.17. Analyse the three components of a political party.

Answer. The three components of a political party are as follows:

  1. The leaders. A political party consists of leaders, who contest elections and if they win the elections, they perform the administrative jobs.
  2.  The active members. They are the ones who work actively for the party. They are the assistants of the leaders and implement the plans and ideologies of the political party. (in) The followers. They are the ardent followers of the parties and their leaders and support them in the elections.

 

Q.18. How are consumers exploited in the market place? Explain.

Answer. Consumers are being exploited in the following manner:

  1. Sale of adulterated goods, i.e. adding something inferior to the product being sold.
  2. Misleading advertisements, i.e. advertisements falsely claiming a product or service to be of superior quality, grade or standard. eloping countries needs mostly takes the form of general, vague and mostly unforceable clauses. The system responds insufficiently to the diverse needs of developing countries which differ enormously regarding their economic power, production structure, and institutional capacity.
  3.  Use of false weights and measures leading to underweight.

 

Q.19. “The consumer movement arose out of dissatisfaction of the consumers”. Justify the statement with arguments.

Answer. The consumer movement actually arose out of dissatisfaction of the consumers:

  1. Many unfair practices were practised by the sellers.
  2. No legal system was available to the consumers to protect them from exploitation in the marketplace.
  3. Moreover, it was presumed that it was the responsibility of consumers to be careful while buying a commodity or service.
  4. A major step taken by the Indian government in this regard was the enactment of the Consumer Protection Act 1986, popularly known as COPRA.

 

Q.22. How did the Civil Disobedience Movement come into force in various parts of the country? Explain with examples.

Answer. Civil Disobedience Movement came into force in various parts of the country:

  1. Gandhiji led the salt march from Sabarmati Ashram to Dandi with his followers starting the Civil Disobedience Movement.
  2.  Thousands in different parts of the country broke the salt law, manufactured salt and demonstrated in front of government salt factories.
  3. In the countryside, the rich Patidars of Gujarat and Jats of Uttar Pradesh were active in the movement. As rich communities were very hard hit by the trade depression and falling prices, they became enthusiastic supporters of the Civil Disobedience Movement.
  4.  As the depression continued and cash invoice dwindled, the small tenants found it difficult to pay the rent. They wanted the unpaid rent to the landlords to be remitted and thus they joined the movement.
  5.  Merchants and industrialists supported the movement by giving financial assistance and also by refusing to buy and sell the imported goods.
  6.  The industrial working class of Nagpur region also participated in the Civil Disobedience Movement. Railway workers, dock workers, mineral of Chota Nagpur etc. participated in protest rallies and boycott campaigns .

 

Q.23. Classify communication services into two categories? Explain main features of each.

Answer. Two types of means of communication are—A. Personal communication,’ B. Mass communication.

A. Features of Personal communication:

  1.  It is the communication between two or more persons at personal level.
  2. The Indian postal network handles parcels as well as personal written communication.
  3.  It includes cards and envelops, posts and telegraph, email etc.
  4. Telephone services like STD, ISD provide easy and comfortable network to a large number of people.

A. Features of Mass communication:

  1.  It is communication through which one can communicate with several people at the same time.
  2. It provides entertainment and creates awareness among people about various National programmes and policies.
  3.  It includes print media like newspapers, magazines, books etc. and electronic media like radio, television etc.

 

Q.25. “Democracy stands much superior in promoting dignity and freedom of the citizens”. Justify the statement.

Answer. Examples to illustrate that dignity and freedom of citizens are best guaranteed in a democracy:

  1. Dignity of women. Democracy recognises dignity of women as a necessary ingredient of society. The one way to ensure that women related problems get adequate attention is’+o have more women as elected representatives. To achieve this, it is legally binding to have a fair proportion of women in the elected bodies. Panchayati Raj in India has reserved one-third seats in local government bodies for women. In March 2010, the Women’s Reservation Bill was passed in the Rajya Sabha ensuring 33% reservation for women in Parliament and State legislative bodies.
  2.  Democracy has strengthened the claims of disadvantaged and discriminated castes. When governments are formed, political parties usually take care that representatives of different castes and tribes find a place in it. Some political parties are known to favour some castes. Democracy provides for equal status and opportunities for all castes.
  3. Democracy transforms people from the status of a subject into that of a citizen. A democracy is concerned with ensuring that people will have the right to choose their rulers and people will have control over the rulers. Whenever possible and necessary, citizens should be able to participate in decision-making that affects them all.
  4. A citizen has the right and the means to examine the process of decision-making. There is transparency in a democracy like India. In October 2005, the Right to Information (RTI) law was passed which ensures all its citizens the right to get all the information about the functions of the government departments. In a democracy, people also have the right to complain about its functioning.

CDS(I) Exam 2019 Maths Previous Year Paper

CDS(I) Exam 2019 

ELEMENTARY MATHEMATICS

प्रश्न 1. जब (1729 + 1929) को 18 से विभाजित किया जाता है, तो शेषफल क्या आता है ?

(a) 6 

(b) 2

(c) 1

(d) 0

 

प्रश्न 2. n का वह सबसे बड़ा मान क्या है कि नीचे दिया गया गुणनफल 10n से विभाजित हो जाए

25 × 33 × 48 × 53 × 67 × 76 × 812 × 99  × 106 × 1512 × 2014 × 2211 × 2515?

(a) 65 

(b) 55 

(c) 50 

(d) 45 

 

प्रश्न 3. संख्या 479865AB में कितने युग्म (A, B) संभव है यदि संख्या 9 द्वारा विभाज्य है और यह दिया हुआ है कि संख्या का अन्तिम अंक विषम है ? 

(a) 5 

(b) 6 

(c) 9

(d) 11

 

प्रश्न 4. दशमलव संकेत पद्धति में गुणनफल 999 × abc = def132 पर विचार कीजिए, जहाँ a, b, c, d, e और f अंक हैं। a, b, c, d, e और f के मान क्रमश: क्या हैं? 

(a) 6, 6, 8, 6, 8, 7 

(b) 8, 6, 8, 6, 7, 8

(c) 6, 8, 8, 7, 8, 6 

(d) 8, 6, 8, 8, 6, 7 

 

प्रश्न 5. तीन गाड़ियाँ A, B और C एक स्थान-बिन्दु से क्रमश: 5 p.m., 6 p.m. और 7 p.m. पर चलना आरम्भ करती हैं और क्रमश: 60 km/hr, 80 km/hr और x km/hr की एकसमान गति से एक ही दिशा में यात्रा करती हैं । यदि यात्रा के दौरान सभी तीनों एक अन्य स्थान-बिन्दु पर एक साथ मिलती हैं, तब x का मान क्या है ? 

(a) 120 

(b) 110 

(c) 105 

(d) 100

 

प्रश्न 6. प्रिया की आयु चार वर्ष पहले 1 से भिन्न किसी पूर्णांक का घन (क्यूब) थी और चार वर्ष बाद किसी पूर्णांक का वर्ग है । उसे कितनी देर तक इंतजार करना चाहिए ताकि उसकी आयु पूर्ववर्ती वर्ष में किसी संख्या का वर्ग और उत्तरवर्ती वर्ष में किसी संख्या का घन (क्यूब) बन जाए? 

(a) 7 वर्ष 

(b) 12 वर्ष 

(c) 14 वर्ष 

(d) 21 वर्ष 

 

प्रश्न 7. निम्नलिखित में से कौन-सा कथन सही नहीं है ? 

(a) 2 से बड़ी दो अभाज्य संख्याओं का अंतर 2 द्वारा विभाज्य है। 

(b) दो भिन्न पूर्णांकों m, n और एक अभाज्य संख्या p के लिए, यदि p गुणनफल m x n को विभाजित करता है, तब p या तो m को या n को विभाजित करता है। 

(c) यदि एक संख्या 6n – 1 के रूप में है (n एक धनपूर्ण संख्या है), तब यह एक अभाज्य संख्या है।

(d) तीन अभाज्य संख्याओं का केवल एक ही ऐसा समुच्चय है जिसमें दो निकटवर्ती अभाज्य संख्याओं में 2 का अंतर है। 

 

प्रश्न 8.  x > 0 के लिए, x + (x+2)/2x का न्यूनतम मान क्या है ?

(a) 1

(b) 2

(c) 2½ 

(d) निर्धारित नहीं किया जा सकता

 

प्रश्न 9. यदि (1+ px)/(1-px) √(1-qx)/(1+qx) = 1 है, तब x के शून्येतर हल क्या हैं ?

(a) ±1/p √(2p-q)/q , 2p ≠ q

(b) ±1/pq √(p-q) , p ≠ q

(c) ±p/q √(p-q) , p ≠ q

(d) ±q/p √(2p-q) , 2p ≠ q

 

प्रश्न 10. एक छात्रावास में प्रति कमरा किराये में 20% की वृद्धि की गई है यदि छात्रावास में कमरों की संख्या में भी 20% की वृद्धि की जाती है और छात्रावास सदैव भरा रहता है, तब कैश काउंटर में कुल संचयन में कितने प्रतिशत बदलाव हुआ ?

(a) 30%

(b) 40%

(c) 44%

(d) 48%

 

प्रश्न 11. राधा और हेमा पड़ोसी हैं और एक ही विद्यालय में पढ़ती हैं । विद्यालय जाने के लिए दोनों ही साइकिल का प्रयोग करती हैं । राधा की गति 8 km/hr है जबकि हेमा की गति 10 km/hr है । विद्यालय पहुँचने के लिए हेमा राधा से 9 मिनट कम लेती है । राधा और हेमा के इलाके से विद्यालय कितना दूर है? 

(a) 5 km 

(b) 5.5 km 

(c) 6 km 

(d) 6.5 km 

 

प्रश्न 12. संख्याओं का निम्नलिखित में से कौन-सा युग्म, समीकरण 3x+2 + 3x = 10 का हल है ? 

(a) 0,2 

(b) 0,-2 

(c) 1,-1 

(d) 1,2

 

प्रश्न 13. यह दिया हुआ है कि log10 2 = 0.301 तथा log10 3 = 0.477 है। (108)10 में कितने अंक हैं ? 

(a) 19 

(b) 20

(c) 21

(d) 22

 

प्रश्न 14. तीन अभाज्य संख्याओं का योगफल 100 है । यदि इनमें से एक किसी दूसरी संख्या से 36 अधिक है, तब इन संख्याओं में से एक संख्या है 

(a) 17 

(b) 29 

(c) 43

(d) उपर्युक्त में से कोई नहीं

 

प्रश्न 15. यदि a, b और c धनात्मक पूर्ण संख्याएँ इस प्रकार हैं कि 

है, तब a, b और का माध्य क्या है ?

(a) 1

(b) 2

(c) 1.33

(d) 2.33

 

अगले तीन (03) प्रश्नांशों के लिए निम्नलिखित पर विचार कीजिए: 

1,00,000 जनसंख्या वाले किसी शहर में तीन प्रकार के समाचार-पत्र (I, II और III) उपलब्ध हैं । इस शहर में इन समाचार-पत्रों को पढ़ने वाले लोगों का प्रतिशत इस प्रकार है :

समाचार-पत्र  पाठकों का अनुपात
I 10%
II 30%
III 5%
दोनों I और II  8%
दोनों II और III 4%
दोनों I और III  2%
सभी तीनों (I, II और III) 1%

प्रश्न 16. केवल एक समाचार-पत्र पढ़ने वाले लोगों की संख्या क्या  है ?

(a) 20,000

(b) 25,000

(c) 30,000

(d) 35,000

 

प्रश्न 17. कम-से-कम दो समाचार-पत्रों को पढ़ने वाले लोगों की संख्या क्या है ? 

(a) 12,000 

(b) 18,000 

(c) 14,000 

(d) 15,000 

 

प्रश्न 18. उन लोगों की संख्या क्या है जो इन तीन समाचार-पत्रों में से कोई भी समाचार-पत्र नहीं पढ़ते हैं ?

(a) 62,000 

(b) 64,000 

(c) 66,000

(d) 68,000 

 

प्रश्न 19.773 के प्रसार में इकाई का अंक क्या है ? 

(a) 1

(b) 3

(c) 7

(d) 9

 

प्रश्न 20. मान लीजिए n इस प्रकार का एक धनात्मक पूर्णांक है कि (n2 + 48) एक पूर्ण वर्ग है । इस प्रकार के n की संख्या क्या है ? 

(a) एक

(b) दो

(c) तीन

(d) चार

 

प्रश्न 21. x =  4/√6 /(√2 + √3) के लिए, (x+2√2)/(x-2√2) + (x+2√3)/(x-2√3) का मान क्या है ? 

(a) 1 

(b) √2 

(c) √3 

(d) 2

 

प्रश्न 22. तीन संख्याओं x, y और z इस प्रकार हैं कि x, z का 30% है और y, z का 40% है । यदि x, y का p% है, तो p का मान क्या है? 

(a) 45

(b) 55

(c) 65

(d) 75

 

प्रश्न 23. एक विमान एक हवाई पत्तन के चारों ओर वृत्ताकार चक्कर लगा रहा है। एक चक्कर पूरा करने में विमान 3 मिनट लेता है । भूमि पर बिन्दु P से समय t सेकण्ड पर और समय (t + 30) सेकण्ड पर विमान के उन्नयन कोण बराबर हैं । समय (t + x) सेकण्ड पर, विमान बिन्दु P के ठीक ऊर्ध्वाधर उड़ता है । x किसके बराबर है ? 

(a) 75 सेकण्ड 

(b) 90 सेकण्ड 

(c) 105 सेकण्ड 

(d) 135 सेकण्ड

 

प्रश्न 24. दो पूर्णांकों p और (दोनों > 1), जो कि सापेक्षतः अभाज्य हैं, के संदर्भ में निम्नलिखित कथनों पर विचार कीजिए : 

1. p और q दोनों अभाज्य संख्याएँ हो सकती हैं। 

2. p और q दोनों भाज्य संख्याएँ हो सकती हैं। 

3. p और q में से एक अभाज्य और दूसरी भाज्य हो सकती है। 

उपर्युक्त में से कौन-से कथन सही हैं? 

(a) केवल 1 और 2

(b) केवल 2 और 3

(c) केवल 1 और 3

(d) 1,2 और 3

 

प्रश्न 25. एक कक्षा में 100 विद्यार्थी हैं, जिनका औसत वज़न 30 kg है । यदि लड़कियों का औसत वज़न 24 kg है और लड़कों का 32 kg है, तो कक्षा में लड़कियों की संख्या कितनी है? 

(a) 25 

(b) 26 

(c) 27 

(d) 28 

 

प्रश्न 26. किन्हीं दो वास्तविक संख्याओं a और b के लिए, √(a-b)2 + √(b-a)2 होगा

(a) हमेशा शून्य 

(b) कभी भी शून्य नहीं 

(c) धनात्मक केवल यदि a≠b 

(d) धनात्मक यदि और केवल यदि a > b 

 

प्रश्न 27. यदि a : b = c : d = 1 : 6 है, तो (a2 + c2)/(b2 +d2) का मान क्या है ?

(a) 1/600 

(b) 1/60 

(c) 1/36 

(d) 1/6

 

प्रश्न 28. किसके बराबर है ? 

 

प्रश्न 29. असमिका 3N– N3 तभी होती है, जब 

(a) N कोई धनपूर्ण संख्या हो 

(b) N, 2 से बड़ी एक धनपूर्ण संख्या हो 

(c) N, 3 से बड़ी एक धनपूर्ण संख्या हो 

(d) N, 3 के अलावा एक धनपूर्ण संख्या हो 

 

प्रश्न 30. निम्नलिखित में से कौन-सी एक अपरिमेय संख्या है ? 

(a) √59049 

(b) 231/ 598 

(c) 0.45454545…… 

(d) 0.12112211122211112222.. 

 

प्रश्न 31. एक दौड़ के तीन हिस्से हैं । अलग-अलग हिस्सों को पूरा करने के लिए एक धावक की आवश्यक गति और उसका समय, निम्नलिखित सारणी में दर्शाए गए हैं :

  भाग I भाग II भाग III
गति (kmph) 9 8 7.5
समय (मिनटों में) 50 80 100

इस धावक की औसत गति क्या है ? 

(a) 8.17 kmph 

(b) 8.00 kmph 

(c) 7.80 kmph 

(d) 7.77 kmph 

 

प्रश्न 32. यदि a/(b + c) = b/(c + a) = c/(a + b) है, तो निम्नलिखित में से कौन-सा कथन सही है ?  

(a) प्रत्येक भिन्न 1 या -1 के बराबर है। 

(b) प्रत्येक भिन्न ½ या 1 के बराबर है।

(c) प्रत्येक भिन्न 1 या -1 के बराबर है । 

(d) प्रत्येक भिन्न केवल ½ के बराबर है। 

 

प्रश्न 33. संख्या 3521 को 8 से विभाजित किया जाता है । शेषफल क्या है ? 

(a) 1 

(b) 3 

(c) 7 

(d) 9 

 

प्रश्न 34. एक अभाज्य संख्या में इकाई के स्थान पर अंक x है। इस प्रकार के कितने अंक x हो सकते हैं ? 

(a) 3 

(b) 4 

(c) 5 

(d) 6

 

प्रश्न 35. यदि एक वस्तु को 6% हानि के बजाय 6% लाभ पर बेचा जाए, तो विक्रेता को रु.6 अधिक प्राप्त होते हैं । वस्तु का क्रय मूल्य क्या है ?

(a) रु. 18

(b) रु. 36 

(c) रु. 42

(d) रु. 50 

 

प्रश्न 36. एक खेत की कटाई 12 पुरुषों अथवा 18 महिलाओं के द्वारा 14 दिनों में की जा सकती है। 8 पुरुष और 16 महिलाएं इस खेत की कटाई कितने दिनों में कर सकते हैं? 

(a) 26 दिन

(b) 24 दिन 

(c) 9 दिन

(d) 8 दिन

 

प्रश्न 37. यदि 3x = 4y = 12z है, तो z किसके बराबर है ? 

(a) xy 

(b) x +y

(c) xy / (x +y)

(d) 4x +3y

 

प्रश्न 38. यदि (4a + 7b) (4c-7d) = (4a – 7b) (4c+ 7d) है, तो निम्नलिखित में से कौन-सा एक सही है? 

(a) a/c = c/d 

(b) a/d = c/b

(c) a/b = d/c

(d) 4a/7b = c/d

 

प्रश्न 39. दिया गया है कि बहुपद (x2 + ax + b)को (x – 1) अथवा (x + 1) से विभाजित करने पर शेषफल समान रहता है। a और b के मान क्रमश: क्या हैं?

(a) 4 और 0 

(b) 0 और 3 

(c) 3 और 0 

(d) और कोई भी पूर्णांक 

 

प्रश्न 40. किसी कार्य को पूरा करने में तुषार को 6 घंटे लगते हैं, जबकि अमर उसी कार्य को 10 घंटों में पूरा करता है । यदि वे दोनों मिलकर काम करें, तो उस कार्य को पूरा करने में कितना समय लगेगा ? 

(a) 3 घंटे 

(b) 3 घंटे 15 मिनट 

(c) 3 घंटे 30 मिनट 

(d) 3 घंटे 45 मिनट 

 

प्रश्न 41. 2 + √[2+{√2 + (√…….. )}] का मान क्या है ? 

(a) 1 

(b) 2 

(c) 3

(d) 4

 

प्रश्न 42. एक परीक्षा में, 52% परीक्षार्थी अंग्रेजी में फेल हुए और 42% गणित में फेल हुए । यदि 17% दोनों विषयों में फेल हुए, तो दोनों विषयों में कितने प्रतिशत परीक्षार्थी पास हुए ? 

(a) 77 

(b) 58 

(c) 48

(d) 23 

 

प्रश्न 43. एक व्यक्ति जिसकी हाल ही में मृत्यु हुई, रु. 3,90,000/ की धनराशि छोड़ गया जिसे उसकी पत्नी, पाँच बेटों और चार बेटियों में बाँटा जाना था । उसने निर्देश दिया था कि जितनी धनराशि प्रत्येक बेटी को मिलती है, प्रत्येक बेटे को उसकी तीन गुना धनराशि मिलनी चाहिए और जितनी धनराशि माँ को मिलती है, प्रत्येक बेटी को उसकी दुगुनी राशि मिलनी चाहिए । पत्नी का हिस्सा कितना था ? 

(a) रु. 14,000

(b) रु. 12,000

(c) रु. 10,000 

(d) रु. 9,000

 

प्रश्न  44. 40% वार्षिक चक्रवृद्धि ब्याज की दर पर रखी गई धनराशि कम-से-कम कितने पूर्ण वर्षों में तिगुनी से ज़्यादा हो जाएगी?

(a) 3

(b) 4

(c) 5

(d) 6

 

प्रश्न 45. एक व्यक्ति ने रु. 17,200 की धनराशि को तीन भागों में  विभाजित कर, उसे 5%, 6% और 9% वार्षिक साधारण ब्याज की दर पर निवेश किया । दो वर्षों की समाप्ति पर, उसे सभी तीनों स्थितियों में एकसमान ब्याज प्राप्त हुआ। 9% ब्याज पर निवेश की गई धनराशि कितनी है

(a) रु.3,200 

(b) रु. 4,000 

(c) रु.4,800 

(d) रु. 5,000 

 

प्रश्न 46. [(x – y)3 + (y – z)3 + (z – x)3] / 3(x – y)(y – z)(z – x) किसके बराबर है?

(a) 1

(b) 0

(c) ⅓ 

(d) 3

 

प्रश्न  47. यदि ax = by = cz और b2 = ac है, तो 1/x + 1/z किसके बराबर है?

(a) 1/y

(b) -1/y

(c) 2/y 

(d) -2/y

 

प्रश्न 48. यदि p और q, समीकरण x2 – 15x + r = 0 के मूल हैं और p – q= 1 है, तो r का मान क्या है ? 

(a) 55

(b) 56

(c) 60

(d) 64 

 

प्रश्न 49. असमिका x2 – 7x + 12 > 0 के लिए, निम्नलिखित में से कौन-सा एक सही है?

(a) 3 < x < 4 

(b) केवल – ∞ <  x  < 3 

(c) केवल 4 < x < ∞

(d) – ∞<  x  < 3 अथवा 4 < x < ∞ 

 

प्रश्न 50. व्यंजक 52n -23n का गुणनखंड है 

(a) 3 

(b) 7 

(c) 17 

(d) उपर्युक्त में से कोई नहीं

 

प्रश्न 51. यदि tan x = 1, 0 < x < 90° है, तो 2 sin x cos x का मान क्या है ? 

(a) ½ 

(b) 1 

(c) √3/2 

(d) √3 

 

प्रश्न 52. sin 46° cos 44° + cos 46° sin 44° का मान क्या है ? 

(a) sin 2° 

(b) 0 

(c) 1 

(d) 2 

 

प्रश्न 53. मान लीजिए 0 < θ < 90° है, तो प्रत्येक θ के लिए, 4 sin2θ + 1 किससे बड़ा अथवा बराबर है ? 

(a) 2 

(b) 4sinθ 

(c) 4 cos θ 

(d) 4tan θ

 

प्रश्न 54. एक समषड्भुज ABCDEF पर विचार कीजिए । B और C पर दो टावर स्थित हैं । A से, B पर स्थित टावर के शीर्ष का उन्नयन कोण 30° है, और C पर स्थित टावर के शीर्ष का उन्नयन कोण 45° है । B और C पर स्थित टावरों की ऊँचाइयों का अनुपात क्या है ? 

(a) 1:√3

(b) 1:3 

(c) 1:2

(d) 1:2√3

 

प्रश्न 55. tan 1° tan 2° tan 3° …… tan 89° का मान क्या है ? 

(a) 0 

(b) 1

(c) 2 

(d) ∞

 

प्रश्न 56. दो समांतर गलियाँ हैं, प्रत्येक गली उत्तर से दक्षिण की ओर दिष्ट है । पहली गली में दक्षिण से उत्तर की ओर जाता हुआ एक व्यक्ति दूसरी गली में जाना चाहता है जो उसके दायीं और है । किसी जगह पर वह दायीं ओर 150° मुड़ता है और 15 मिनट तक 20 km/hr की गति से चलता है। उसके बाद वह 60° बायीं ओर मुड़ता है और 20 मिनट तक 30 km/hr की गति से चलकर दूसरी गली में पहुँच जाता है। दोनों गलियों के बीच की दूरी कितनी है? 

(a) 7.5 km 

(b) 10.5 km 

(c) 12.5 km 

(d) 15 km 

 

प्रश्न 57. यदि 3 tanθ = cot θ जहाँ 0 < θ < π/2 है, तो θ का मान क्या है?

(a) π/6 

(b) π/4 

(c) π/3 

(d) π/2

 

प्रश्न 58. sin2 25° + sin2 65° का मान क्या है ? 

(a) 0 

(b) 1

(c) 2 

(d) 4 

 

प्रश्न 59. sin6 θ + cos6 θ + 3 sin2 θ cos2 θ – 1 का मान क्या है ?

(a) 0 

(b) 1

(c) 2 

(d) 4

 

प्रश्न 60. वास्तविक संख्याओं α, β, γ और δ के लिए, निम्नलिखित पर विचार कीजिए : 

1. sec α = 1/4 

2. tan β = 20 

3. cosec γ = 1/2 

4. cos δ =2 

उपर्युक्त में से कितने विवरण संभव नहीं हैं ? 

(a) एक 

(b) दो 

(c) तीन 

(d) चार

 

प्रश्न 61. निम्नलिखित वर्गीकृत बारंबारता बंटन पर विचार कीजिए: 

x f
0 – 10 8
10 – 20 12
20 – 30 10
30 – 40 p
40 – 50 9

यदि उपर्युक्त दत्त का माध्य 25.2 है, तो p का मान क्या है ?

(a) 9 

(b) 10 

(c) 11 

(d) 12

 

प्रश्न 62. निम्नलिखित बारंबारता बटन पर विचार कीजिए : 

x f
8 6
5 4
6 5
10 8
9 9
4 6
7 4

इस बंटन की माध्यिका क्या है ? 

(a) 6 

(b) 7

(c) 8 

(d) 9 

 

प्रश्न 63. 50 क्रमागत धन पूर्णांकों का औसत x है । यदि अगले चार धन पूर्णांकों को भी शामिल कर लिया जाए, तो नया औसत (माध्य) क्या होगा ?

(a) x + 1

(b) x + 2

(c) x + 4

(d) x + (x/54)

 

प्रश्न 64.  दो अंकों वाली ऐसी संख्याओं पर विचार कीजिए जो उनके अंकों का स्थान बदल देने पर भी, वैसी ही बनी रहती हैं । इस प्रकार की दो अंकों की संख्याओं का औसत क्या है?

(a) 33

(b) 44

(c) 55

(d) 66

 

प्रश्न 65. दत्त के आरेखी निरूपण में निम्नलिखित में से क्या-क्या सम्मिलित होते हैं ? 

1. स्तंभ आरेख (बार डाइग्राम) 

2. वृत्तारेख (पाई-डाइग्राम) 

3. चित्रीय आरेख (पिक्टोग्राम) 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए : 

(a) केवल 1 और 2

(b) केवल 2 और 3 

(c) केवल 1 और 

(d) 1,2 और 3

 

प्रश्न 66. निम्नलिखित में से कौन-सी एक विधि से एकत्रित किए गए आँकड़े, प्राथमिक आँकड़े नहीं होते हैं ? 

(a) प्रत्यक्ष व्यक्तिगत साक्षात्कारों द्वारा 

(b) अप्रत्यक्ष व्यक्तिगत साक्षात्कारों द्वारा 

(c) गणनाकारों के माध्यम से भेजी गई सूचियों द्वारा 

(d) प्रकाशित शोध-प्रबंध से 

 

प्रश्न 67. एक व्यक्ति का मासिक व्यय रु.6,000 है । विभिन्न मदों पर व्यय का बंटन निम्नानुसार है : ? 

व्यय की मद राशि (रु. में)
1. खाद्य 2,000
2. वस्त्र 660
3. ईंधन और किराया 1,200
4. शिक्षा  480
5. विविध 1,660

यदि उपर्युक्त आँकड़ों को 15 cm ऊँचाई के एक प्रतिशतता स्तंभ आरेख से निरूपित किया जाए, तो शिक्षा और विविध से संबंधित स्तंभ आरेख के दोनों खंडों की लम्बाइयाँ क्रमश: क्या होंगी?

(a) 1.25 cm और 5 cm

(b) 1.2 cm और 4.15 cm

(c) 1.2 cm और 3.5 cm

(d) 4.15 cm और 6 cm

 

प्रश्न 68. यदि n प्रेक्षणों में से m प्रेक्षणों का माध्य n है और शेष प्रेक्षणों का माध्य m है, तो सभी n प्रेक्षणों का माध्य क्या  है ?

(a) 2m – m2/n

(b) 2m + m2/n

(c) m – m2/n

(d) m + m2/n

 

प्रश्न 69. निम्नलिखित में से कौन-सा एक युग्म सही रूप से सुमेलित है?

(a) माध्यिका – आलेखी स्थिति

(b) माध्य – आलेखी स्थिति

(c) गुणोत्तर माध्य – ओज़ाइव

(d) बहुलक – ओज़ाइव

 

प्रश्न 70. निम्नलिखित युग्म एक असंतत चर के बारंबारता बंटन और उसके बारंबारता बहुभुज से संबंधित हैं । निम्नलिखित में से कौन-सा एक युग्म सही रूप से सुमेलित नहीं है ? 

(a) बहुभुज की आधार रेखा  –  x-अक्ष 

(b) बहुभुज के शीर्षों की कोटियाँ   –   वर्ग बारंबारताएँ

(c) बहुभुज के शीर्षों के भुज – बारंबारता बंटन के वर्ग अंक (क्लास मार्क्स)

(d) बहुभुज का क्षेत्रफल – बंटन की कुल बारंबारता

 

प्रश्न 71. एक आयत में, लम्बाई इसकी चौड़ाई की तीन गुना है । यदि आयत की लम्बाई और चौड़ाई क्रमश: 30% और 10% बढ़ा दी जाएँ, तो इसका परिमाप कितना बढ़ जाएगा ?

(a) 40/3%

(b) 20% 

(c) 25% 

(d) 27% 

 

प्रश्न 72. यदि किसी त्रिभुज की प्रत्येक भुजा को आधा कर दिया जाए, तो उसके क्षेत्रफल में कितने प्रतिशत कमी हो जाएगी? 

(a) 75% 

(b) 50% 

(c) 25% 

(d) कोई परिवर्तन नहीं 

 

प्रश्न 73. एक गोलाकार गुब्बारे का आयतन 700% बढ़ा दिया जाता है । इसके पृष्ठीय क्षेत्रफल में प्रतिशतता वृद्धि कितनी है?

(a) 300%

(b) 400%

(c) 450%

(d) 500%

 

प्रश्न 74. यदि 10 cm त्रिज्या वाले एक वृत्त में दो समानान्तर जीवाओं की लम्बाइयाँ 12 cm और 16 cm हैं, तो इन दो जीवाओं के बीच की दूरी कितनी है ? 

(a) 1 cm अथवा 7 cm 

(b) 2 cm अथवा 14 cm 

(c) 3 cm अथवा 21 cm 

(d) 4 cm अथवा 28 cm

 

प्रश्न 75. ‘a’ भुजा वाले एक वर्ग के दो सम्मुख शीर्षों को केन्द्र मानकर, दो वृत्तीय चाप वर्ग के अंदर इस प्रकार खींचे गए हैं कि वे अन्य दो शीर्षों को जोड़ते हैं, और दो सेक्टर बनाते हैं। इन दोनों सेक्टरों का सर्वनिष्ठ क्षेत्रफल कितना है ? 

(a) a2(π + ½)

(b) a2(π – ½)

(c) a2(π/2  – 1)

(d) a2(π/2  + 1) 

 

प्रश्न 76. ‘a’ भुजा वाले एक वर्ग के कोनों को इस प्रकार काटा गया है कि एक सम अष्टभुज बनता है । अष्टभुज की एक भुजा की लम्बाई कितनी है ?

(a) a(√2 – 1) 

(b) a(√3 – 1)

(c) a/ (√2 + 2) 

(d) a /3 

 

प्रश्न 77. तीन क्रमागत पूर्ण संख्याएँ एक समकोण त्रिभुज की लम्बाइयाँ दर्शाती हैं । इस तरह की तीन क्रमागत पूर्ण संख्याओं के कितने समुच्चय संभव हो सकते हैं? 

(a) केवल एक

(b) केवल दो 

(c) केवल तीन 

(d) अनंतत: अनेक

 

प्रश्न 78. एक ही बिन्दु को केन्द्र मानकर दो वृत्त खींचे गए हैं छोटे वृत्त की परिधि 44 cm है और बड़े वृत्त की परिधि छोटे वृत्त की परिधि की दुगुनी है । इन दोनों वृत्तों के बीच का क्षेत्रफल कितना है ? 

(a) 154 cm2 

(b) 308 cm2 

(c) 462 cm2

(d) 616 cm2

 

प्रश्न 79. एक 6 ft × 12 ft आकार के आयताकार लाल कालीन में 6 इंच चौड़ी गहरे लाल रंग की सीमा पट्टी है । गहरे लाल रंग की सीमा पट्टी का क्षेत्रफल कितना है? 

(a) 9 वर्ग फुट 

(b) 15 वर्ग फुट 

(c) 17 वर्ग फुट 

(d) 18 वर्ग फुट 

 

प्रश्न 80. एक समकोण त्रिभुज का परिमाप उसकी सबसे छोटी भुजा का k गुना है। यदि अन्य भुजा का कर्ण के साथ अनुपात 4:5है, तो k का मान क्या है ? 

(a) 2 

(b) 3 

(c) 4 

(d) 5 

 

प्रश्न 81. एक 12 m लम्बे तार के दो टुकड़े किए गए हैं, इनमें से एक को एक वृत्त के रूप में मोड़ा जाता है और दूसरे को एक वर्ग के रूप में, वृत्त को परिबद्ध करते हुए मोड़ा जाता है। वृत्त की त्रिज्या क्या है? 

(a) 12/ (π + 4) 

(b) 6/ (π + 4) 

(c) 3/ (π + 4) 

(d) 6/ (π + 2√2)

 

प्रश्न 82. एक त्रिभुज के कोण 1 : 1 : 4 के अनुपात में हैं । यदि त्रिभुज की परिमाप उसकी सबसे बड़ी भुजा की k गुना है, तो k का मान क्या है ? 

(a) 1 + 2/√3

(b) 1 – 2/√3

(c) 2 + 2/√3

(d) 2 

 

प्रश्न 83. एक समकोण त्रिभुज का कर्ण 10 cm है और उसका क्षेत्रफल 24cm2 है । यदि उसकी छोटी भुजा को आधा और बड़ी भुजा को दोगुना कर दिया जाता है, तो नया कर्ण कितना हो जाता है ?

(a) √245 cm

(b) √255 cm

(c) √265 cm

(d) √275 cm

 

प्रश्न 84. 8 cm त्रिज्या वाले एक वृत्त में, AB और AC दो जीवाएँ इस प्रकार हैं कि AB = AC = 12 cm है। जीवा BC की लम्बाई कितनी है ? 

(a) 2√6 cm

(b) 3√6 cm

(c) 3√7 cm

(d) 6√7 cm

 

प्रश्न 85. निम्नलिखित कथनों पर विचार कीजिए : 

1. एक समद्विबाहु समलंब हमेशा चक्रीय होता है।

2. कोई भी चक्रीय समांतर चतुर्भुज एक आयत होता है।

उपर्युक्त में से कौन-सा/से कथन सही है/हैं ? 

(a) केवल 1 

(b) केवल-2 

(c) 1 और 2 दोनों 

(d) नतो 1,न ही 2 

 

प्रश्न 86. एक सीढ़ी एक ऊर्ध्वाधर दीवार के सहारे खड़ी हुई है, और इसका तला दीवार से 2.5 m दूर है । यदि यह दीवार पर 0.8 m नीचे की ओर सरक जाती है, तो इसका तला दीवार से 1.4 m और अधिक दूर हो जाता है । सीढ़ी की लम्बाई कितनी है ? 

(a) 6.2 m 

(b) 6. 5m 

(c) 6.8 m 

(d) 7.5m 

 

प्रश्न 87. दो समान वृत्त एक-दूसरे को इस प्रकार प्रतिच्छेद करते हैं कि उनमें से प्रत्येक वृत्त दूसरे वृत्त के केन्द्र से होकर गुज़रता है । यदि दोनों वृत्तों की सर्वनिष्ठ जीवा की 

लम्बाई 10√3 cm है, तो वृत्त का व्यास कितना है? 

(a) 10 cm 

(b) 15 cm 

(c) 20 cm 

(d) 30 cm 

 

प्रश्न 88. निम्नलिखित कथनों पर विचार कीजिए : 

1. तीन असंरेखीय बिन्दुओं से गुज़रकर खींचे जा सकने वाले वृत्तों की संख्या अनंत है। 

2. किसी वृत्त के लघु खण्ड (सेगमेंट) में बनने वाला कोण न्यून कोण होता है।

उपर्युक्त में से कौन-सा/से कथन सही है/हैं?

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों

(d) न तो 1, न ही 2

 

प्रश्न 89. किसी त्रिभुज ABC के संदर्भ में, निम्नलिखित असमिकाओं पर विचार कीजिए :

1. AC – AB < BC

2. BC – AC <AB

3. AB – BC <AC

उपर्युक्त में से कौन-से सही हैं ?

(a) केवल 1 और 2 

(b) केवल 2 और 3

(c) केवल 1 और 3 

(d) 1, 2 और 3

 

प्रश्न 90. निम्नलिखित कथनों पर विचार कीजिए : 

1. किसी त्रिभुज की परिमाप उसकी तीन माध्यिकाओं (मीडियन) के योगफल से बड़ी होती है । 

2. किसी त्रिभुज ABC में, यदि BC पर कोई बिन्दु D है, तो AB + BC + CA>2AD होता है।

उपर्युक्त में से कौन-सा/से कथन सही है/हैं ? 

(a) केवल 1

(b) केवल 2 

(c) 1 और 2 दोनों

(d) न तो 1, न ही 2

 

आगे आने वाले तीन (03) प्रश्नांशों के लिए निम्नलिखित पर विचार कीजिए: 

एक घन किसी गोले के अंतर्गत है । घन के अन्दर एक लंब-वृत्तीय बेलन है जो उसके सभी ऊर्ध्वाधर फलकों को स्पर्श करता है । बेलन के अन्दर एक लंब-वृत्तीय शंकु है । उनकी ऊँचाइयाँ बराबर हैं और शंकु का व्यास बेलन के व्यास के बराबर है। 

प्रश्न 91. गोले के आयतन का शंकु के आयतन से क्या अनुपात हैं ?

(a) 6√3:1 

(b) 7:2 

(c) 3√3 :1 

(d) 5√3:1 

 

प्रश्न 92. घन के आयतन का बेलन के आयतन से क्या अनुपात हैं ?

(a) 4:3 

(b) 21:16 

(c) 14 : 11 

(d) 45: 32 

 

प्रश्न 93. निम्नलिखित कथनों पर विचार कीजिए : 

1. गोले का पृष्ठीय क्षेत्रफल, शंकु के वक्र पृष्ठीय क्षेत्रफल का √5 गुना है। 

2. घन का पृष्ठीय क्षेत्रफल, बेलन के वक्र पृष्ठीय क्षेत्रफल के बराबर है। 

उपर्युक्त में से कौन-सा/से कथन सही है/हैं ?

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1, न ही 2 

 

आगे आने वाले तीन (03) प्रश्नांशों के लिए निम्नलिखित पर विचार कीजिए:

ABCD एक चतुर्भुज है जिसमें AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm और कोण ABC (a) 15 cm एक समकोण है।

प्रश्न 94. त्रिभुज ADC का क्षेत्रफल कितना है? 

(a) 126 cm2 

(b) 124 cm2 

(c) 122 cm2 

(d) 120 cm2

 

प्रश्न 95. चतुर्भुज ABCD का क्षेत्रफल कितना है ?

(a) 300 cm2 

(b) 306 cm2 

(c) 312 cm2 

(d) 316 cm2

 

प्रश्न 96. त्रिभुज ABC के परिमाप और त्रिभुज ADC के परिमाप के बीच कितना अंतर है ?

(a) 4 cm

(b) 5 cm

(c) 6 cm

(d) 7 cm

 

आगे आने वाले दो (02) प्रश्नांशों के लिए निम्नलिखित पर विचार कीजिए : 

एक समबाहु त्रिभुज ABC, 20√3 cm की त्रिज्या वाले एक वृत्त के अंतर्गत है। 

प्रश्न 97. त्रिभुज की भुजा की लम्बाई क्या है ? 

(a) 30 cm 

(b) 40 cm 

(c) 50 cm 

(d) 60 cm

 

प्रश्न 98. त्रिभज ABC का केन्द्रक, शीर्ष A से d दरी पर है। d किसके बराबर है? 

(a) 15 cm 

(b) 20 cm

(c) 20√3 cm

(d) 30√3 cm

 

आगे आने वाले दो (02) प्रश्नांशों के लिए निम्नलिखित पर विचार कीजिए: 

एक लंबकोणिक समांतर षट्फलक की लम्बाई, चौड़ाई और ऊँचाई का योगफल 22 cm है और उसके विकर्ण की लम्बाई 14 cm है। 

प्रश्न 99. लंबकोणीय समांतर षट्फलक का पृष्ठीय क्षेत्रफल कितना है? 

(a) 288 cm2 

(b) 216 cm2 

(c) 144 cm2 

(d) अपर्याप्त दत्त के कारण निर्धारित नहीं किया जा सकता

 

प्रश्न 100. यदि लंबकोणिक समांतर षट्फलक की विमाओं (विस्तार) के घनों (क्यूब) का योगफल S, और उसका आयतन Vहै, तो (S- 3V) किसके बराबर है ?

(a) 572 cm3 

(b) 728 cm3 

(c) 1144 cm3 

(d) उपर्युक्त में से कोई नहीं

CDS(I) Exam 2019 Maths Previous Year Paper

CDS(I) Exam 2019 

ELEMENTARY MATHEMATICS 

Q 1.What is the remainder when (1729 + 1929) is divided by 18? 

(a) 6 

(b) 2

(c) 1 

(d) 0

 

Q 2.What is the largest value of n such that 10n divides the product 25 × 33 × 48 × 53 × 67 × 76 × 812 × 99  × 106 × 1512 × 2014 × 2211 × 2515

(a) 65 

(b) 55

(c) 50 

(d) 45

 

Q 3. How many pairs (A, B) are possible in the number 479865AB if the number is divisible by 9 and it is given that the last digit of the number is odd ? 

(a) 5

(b) 6

(c) 9 

(d) 11

 

Q 4.Consider the multiplication 999 × abc = def132 in decimal notation, where a, b, c, d, e and f are digits. What are the values of a, b, c, d, e and f respectively? 

(a) 6, 6, 8, 6, 8, 7 

(b) 8, 6, 8, 6, 7, 8 

(c) 6, 8, 8, 7, 8,6

(d) 8, 6, 8, 8, 6, 7 

 

Q 5. Three cars A, B and C started from a point at 5 p.m., 6 p.m. and 7 p.m. respectively and travelled at uniform speeds of 60 km/hr, 80 km/hr and x km/hr respectively in the same direction. If all the three met at another point at the same instant during their journey, then what is the value of x ? 

(a) 120

(b) 110

(c) 105

(d) 100 

 

Q 6. Priya’s age was a cube of an integral number (different from 1) four years ago and square of an integral number after four years. How long should she wait so that her age becomes a square of a number in the previous year and a cube of a number in the next year? 

(a) 7 years 

(b) 12 years 

(c) 21 years

(d) 21 years

 

Q 7.Which of the following statements is not true ? 

(a) The difference of two prime numbers, both greater than 2, is divisible by 2. 

(b) For two different integers m, n and a prime number p, if p divides the product m × n, then p divides either m or n.

(c) If a number is of the form 6n – 1 (n being a natural number), then it is a prime number. 

(d) There is only one set of three prime numbers such that there is a gap of 2 between two adjacent prime numbers. 

 

Q 8. For x > 0, what is the minimum value of x + (x+2)/2x ?

(a) 1

(b) 2

(c) 2½ 

(d) Cannot be determined

 

Q 9. If (1+ px)/(1-px) √(1-qx)/(1+qx) = 1, then what are the non-zero solutions of x ?

(a) ±1/p √(2p-q)/q , 2p ≠ q

(b) ±1/pq √(p-q) , p ≠ q

(c) ±p/q √(p-q) , p ≠ q

(d) ±q/p √(2p-q) , 2p ≠ q

 

Q 10. In a hostel the rent per room is increased by 20%. If number of rooms in the hostel is also increased by 20% and the hostel is always full, then what is the percentage change in the total collection at the cash counter ?

(a) 30%

(b) 40% 

(c) 44%

(d) 48%

 

Q 11. Radha and Hema are neighbours and study in the same school. Both of them use bicycles to go to school. Radha’s speed is 8 km/hr whereas Hema’s speed is 10 km/hr. Hema takes 9 minutes less than Radha to reach the school. How far is the school from the locality of Radha and Hema ? 

(a) 5 km 

(b) 5.5 km 

(c) 6 km 

(d) 6.5 km

 

Q 12. Which of the following pair of numbers is the solution of the equation 3x+2 + 3x = 10 

(a) 0,2 

(b) 0,- 2 

(c) 1,-1 

(d) 1,2

 

Q 13. It is given that log10 2 = 0.301 and log10 3 = 0.477. How many digits are there in items : (108)10 ?

(a) 19 

(b) 20

(c) 21

(d) 22

 

Q 14. The sum of three prime numbers is 100. If one of them exceeds another by 36, then one of the numbers is 

(a) 17 

(b) 29 

(c) 43 

(d) None of the above

 

Q 15. If a, b and c are positive integers such that 

then what is the mean of a, b and c?

(a) 1 

(b) 2 

(c) 1.33 

(d) 2.33

 

Consider the following for the next three (03) items:

In a certain town of population size 1,00,000 three types of newspapers (I, II and III) are available. The percentages of the people in the town who read these papers are as follows: 

Newspapers Proportion of Readers
I 10%
II 30%
III 5%
Both I and II  8%
Both II and III 4%
Both I and III  2%
All (I, II and III) 1%

Q 16. What is the number of people who read only one newspaper ? 

(a) 20,000 

(b) 25,000 

(c) 30,000 

(d) 35,000 

 

Q 17.What is the number of people who read at least two newspapers ? 

(a) 12,000 

(b) 13,000 

(c) 14,000 

(d) 15,000

 

Q 18. What is the number of people who do not read any of these three newspapers ? 

(a) 62,000 

(b) 64,000 

(c) 66,000 

(d) 68,000 

 

Q 19. What is the unit place digit in the expansion of 773 ?

(a) 1

(b) 3

(c) 7

(d) 9

 

Q 20. Suppose n is a positive integer such that (n2 + 48) is a perfect square. What is the number of such n

(a) One

(b) Two

(c) Three

(d) Four

 

Q 21. For x =  4/√6 /(√2 + √3), what is the value of (x+2√2)/(x-2√2) + (x+2√3)/(x-2√3)

(a) 1

(b) √2

(c) √3

(d) 2

 

Q 22. x, y and z are three numbers such that x is 30% of z and y is 40% of z. If x is p% of y, then what is the value of p?

(a) 45

(b) 55

(c) 65

(d) 75 

 

Q 23. A plane is going in circles around an airport. The plane takes 3 minutes to complete one round. The angle of elevation of the plane from a point P on the ground at time t seconds is equal to that at time (t + 30) seconds. At time (t + x) seconds, the plane flies vertically above the point P. What is x equal to ? 

(a) 75 seconds 

(b) 90 seconds 

(c) 105 seconds 

(d) 135 seconds

 

Q 24. Consider the following statements in respect of two integers p and q (both > 1) which are relatively prime : 

1. Both p and q may be prime numbers.

2. Both p and may be composite numbers.

3. One of p and q may be prime and the other composite. 

Which of the above statements are correct? 

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3 

 

Q 25. In a class of 100 students, the average weight is 30 kg. If the average weight of the girls is 24 kg and that of the boys is 32 kg, then what is the number of girls in the class ? 

(a) 25 

(b) 26 

(c) 27 

(d) 28

 

Q 26. For any two real numbers a and b, √(a-b)2 + √(b-a)2 is

(a) always zero 

(b) never zero 65 

(c) positive only if a ≠ b 

(d) positive if and only if a >b 

 

Q 27. If a : b=c:d=1:6, then what is the value of (a2 + c2)/(b2 +d2)?

(a) 1/600 

(b) 1/60 

(c) 1/36 

(d) 1/6

 

Q 28. What is equal to ?

 

Q 29. The inequality 3N > N3 holds when 

(a) N is any natural number 

(b) N is a natural number greater than 2 

(c) N is a natural number greater than 3

(d) N is a natural number except 3

 

Q 30. Which one of the following is an irrational number?

(a) √59049 

(b) 231/ 598 

(c) 0.45454545…… 

(d) 0.12112211122211112222.. 

 

Q 31. A race has three parts. The speed and time required to complete the individual parts for a runner is displayed on the following chart: 

# Part I Part II Part III
Speed (kmph) 9 8 7.5
Time (minutes) 50 80 100

What is the average speed of this runner ? 

(a) 8.17 kmph 

(b) 8.00 kmph 

(c) 7.80 kmph 

(d) 7.77 kmph 

 

Q 32. If  a/(b + c) = b/(c + a) = c/(a + b), then which one of the following statements is correct? 

(a) Each fraction is equal to 1 or -1. 

(b) Each fraction is equal to ½  or 1.

(c) Each fraction is equal to ½  or -1.

(d) Each fraction is equal to ½ only.

 

Q 33. The number 3521 is divided by 8. What is the remainder ? 

(a) 1 

(b) 3 

(c) 7 

(d) 9 

 

Q 34. A prime number contains the digit X at unit’s place. How many such digits of X are possible? 

(a) 3 

(b) 4 

(c) 5

(d) 6 

 

Q 35. If an article is sold at a gain of 6% instead of a loss of 6%, the seller gets Rs. 6 more. What is the cost price of the article ?

(a) Rs. 18 

(b) Rs. 36

(c) Rs. 42

(d) Rs. 50

 

Q 36. A field can be reaped by 12 men or 18 women in 14 days. In how many days can 8 men and 16 women reap it? 

(a) 26 days 

(b) 24 days 

(c) 9 days 

(d) 8 days

 

Q 37. If 3x = 4y = 12z, then z is equal to 

(a) xy

(b) x+y

(c) xy/(x+y)

(d) 4x+3y

 

Q 38. If (4a + 7b) (4c-7d) = (4a – 7b) (4c + 7d), then which one of the following is correct ?

(a) a/c = c/d 

(b) a/d = c/b

(c) a/b = d/c

(d) 4a/7b = c/d

 

Q 39. Given that the polynomial (x2 + ax + b) leaves the same remainder when divided by (x – 1) or (x + 1). What are the values of a and b respectively? 

(a) 4 and 0 

(b) 0 and 3 

(c) 3 and 0 

(d) 0 and any integer 

 

Q 40. Tushar takes 6 hours to complete a piece of work, while Amar completes the same work in 10 hours. If both of them work together, then what is the time required to complete the work? 

(a) 3 hours 

(b) 3 hours 15 minutes

(c) 3 hours 30 minutes

(d) 3 hours 45 minutes

 

Q 41. What is the value of 2 + √[2+{√2 + (√……..? )}] 

(a) 1 

(b) 2  

(c) 3 

(d) 4

 

Q 42. In the examination, 52% candidates failed in English and 42% failed in Mathematics. If 17% failed in both the subjects, then what percent passed in both the subjects ? 

(a) 77 

(b) 58 

(c) 48 

(d) 23 

 

Q 43. A man who recently died left a sum of Rs. 3,90,000 to be divided among his wife, five sons and four daughters. He directed that each son should receive 3 times as much as each daughter receives and that each daughter should receive twice as much as their mother receives. What was the wife’s share ? 

(a) Rs. 14,000 

(b) Rs. 12,000 

(c) Rs. 10,000 

(d) Rs. 9,000

 

Q 44. What is the least number of complete years in which a sum of money put out at 40% annual compound interest will be more than trebled ? 

(a) 3

(b) 4

(c) 5 

(d) 6

 

Q 45. A person divided a sum of Rs. 17,200 into three parts and invested at 5%, 6% and 9% per annum simple interest. At the end of two years, he got the same interest on each part of the money. What is the money invested at 9% ? 

(a) Rs. 3,200 

(b) Rs. 4,000 

(c) Rs. 4,800 

(d) Rs. 5,000

 

Q 46. What is [(x – y)3 + (y – z)3 + (z – x)3] / 3(x – y)(y – z)(z – x) equal to ?

(a) 1

(b) 0

(c) ⅓ 

(d) 3

 

Q 47. If a ax = by = cz and b2 = ac, then what is 1/x + 1/z equal to ? 

(a) 1/y

(b) -1/y

(c) 2/y 

(d) -2/y

 

Q 48. If p and q are the roots of the equation x2 – 15x + r = 0 and p – 9 = 1, then what is the value of r? 

(a) 55 

(b) 56 

(c) 60 

(d) 64

 

Q 49. For the inequation x2 – 7x + 12 > 0, which one of the following is correct ? (a) 3 < x 4 

(b) – ∞ < x <3 only 

(c) 4 < x <  ∞ only 

(d)  – ∞ < x < 3 or 4 < x <  ∞

 

Q 50. The expression 52n – 23n has a factor 

(a) 3

(b) 7

(c) 17

(d) None of the above

 

Q 51. If tan x = 1, 0 < x < 90°, then what is the value of 2 sin x cos x ? 

(a) ½ 

(b) 1 

(c) √3/2 

(d) √3  

 

Q 52. What is the value of sin 46° cos 449 + cos 46° sin 44° ? 

(a) sin 2° 

(b) 0 

(c) 1 

(d) 2 

 

Q 53. Suppose 0 < θ < 90°, then for every , 4 sin2 θ + 1 is greater than or equal to 

(a) 2 

(b) 4sinθ 

(c) 4 cos θ 

(d) 4tan θ

 

Q 54. Consider a regular hexagon ABCDEF. Two towers are situated at B and C. The angle of elevation from A to the top of the tower at B is 30°, and the angle of elevation to the top of the tower at C is 45′. What is the ratio of the height of towers at B and C ? 

(a) 1:√3

(b) 1:3 

(c) 1:2

(d) 1:2√3

 

Q 55. What is the value of tan 1° tan 2° tan 3° …… tan 89° ? 

(a) 0 

(b) 1 

(c) 2 

(d) ∞ 

 

Q 56. There are two parallel streets each directed North to South. A person in the first street travelling from South to North wishes to take the second street which is on his right side. At some place, he makes a 150° turn to the right and he travels for 15 minutes at the speed of 20 km/hr. After that he takes a left turn of 60° and travels for 20 minutes at the speed of 30 km/hr in order to meet the second street. What is the distance between the two streets ? 

(a) 7.5 km 

(b) 10.5 km 

(c) 12.5 km 

(d) 15 km

 

Q 57. If 3 tanθ = cot θ where 0 < θ < π/2 then what is the value of θ ?

(a) π/6 

(b) π/4 

(c) π/3 

(d) π/2

 

Q 58. What is the value of sin2 25° + sin2 65° ? 

(a) 0 

(b) 1 

(c) 2 

(d) 4

 

Q 59. What is the value of sin6 θ + cos6 θ + 3 sin2 θ cos2 θ – 1?

(a) 0 

(b) 1 

(c) 2 

(d) 4

 

Q 60. Consider the following for real numbers α, β, γ and δ : 

1. sec α = 1/4 

2. tan β = 20 

3. cosec γ = 1/2 

4. cos δ =2 

How many of the above statements are not possible? 

(a) One 

(b) Two 

(c) Three 

(d) Four

 

Q 61.Consider the following grouped frequency distribution : 

x f
0 – 10 8
10 – 20 12
20 – 30 10
30 – 40 p
40 – 50 9

If the mean of the above data is 25.2, then what is the value of p? 

(a) 9 

(b) 10 

(c) 11 

(d) 12 

 

Q 62. Consider the following frequency distribution: 

x f
8 6
5 4
6 5
10 8
9 9
4 6
7 4

What is the median for the distribution ? 

(a) 6 

(b) 7

(c) 8

(d) 9

 

Q 63. The average of 50 consecutive natural numbers is x. What will be the new average when the next four natural numbers are also included ? 

(a) x + 1 

(b) x + 2 

(c) x + 4 

(d) x + (x/54) 

 

Q 64. Consider two-digit numbers which remain the same when the digits interchange their positions. What is the average of such two-digit numbers ? 

(a) 33 

(b) 44 

(c) 55 

(d) 66 

 

Q 65. Diagrammatic representation of data includes which of the following ? 

1. Bar diagram 

2. Pie-diagram 

3. Pictogram 

Select the correct answer using the code given below : 

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3 

 

Q 66. The data collected from which one of the following methods is not a primary data ? 

(a) By direct personal interviews 

(b) By indirect personal interviews 

(c) By schedules sent through enumerators 

(d) From published thesis

 

Q 67. The monthly expenditure of a person is 36,000. The distribution of expenditure on various items is as follows : 

Item of expenditure Amount (in Rs.)
1. Food 2,000
2. Clothing 660
3. Fuel and Rent 1,200
4. Education 480
5. Miscellaneous 1,600

If the above data is represented by a percentage bar diagram of height 15 cm, then what are the lengths of the two segments of the bar diagram corresponding to education and miscellaneous respectively ?

(a) 1.25 cm and 5 cm

(b) 1.2 cm and 4.15 cm

(c) 1.2 cm and 3.5 cm

(d) 4.15 cm and 6 cm 

 

Q 68. If the mean of m observations out of n observations is n and the mean of remaining observations is m, then what is the mean of all n observations ?

(a) 2m – m2/n

(b) 2m + m2/n

(c) m – m2/n

(d) m + m2/n

 

Q 69. Which one of the following pairs is correctly matched ?

(a) Median – Graphical location

(b) Mean – Graphical location

(c) Geometric mean – Ogive

(d) Mode – Ogive

 

Q 70. The following pairs relate to frequency distribution of a discrete variable and its frequency polygon. Which one of the following pairs is not correctly matched ? 

(a) Base line of the polygon x-axis
(b) Ordinates of the vertices of the polygon Class frequencies
(c) Abscissa of the vertices of the polygon Class marks of the frequency distribution
(d) Area of the polygon Total frequency of the distribution

 

Q 71. In a rectangle, length is three times its breadth. If the length and the breadth of the rectangle are increased by 30% and 10% respectively, then its perimeter increases by 

(a) 40/3%

(b) 20% 

(c) 25% 

(d) 27%

 

Q 72. What is the percentage decrease in the area of a triangle if its each side is halved ? 

(a) 75% 

(b) 50% 

(c) 25% 

(d) No change

 

Q 73. The volume of a spherical balloon is increased by 700%. What is the percentage increase in its surface area?

(a) 300% 

(b) 400%

(c) 450% 

(d) 500%

 

Q 74. If the lengths of two parallel chords in a circle of radius 10 cm are 12 cm and 16 cm, then what is the distance between these two polygon chords? 

(a) 1 cm or 7 cm 

(b) 2 cm or 14 cm 

(c) 3 cm or 21 cm 

(d) 4 cm or 28 cm 

 

Q 75. Considering two opposite vertices of a square of side ‘a’ as centres, two circular arcs are drawn within the square joining the other two vertices, thus forming two sectors. What is the common area in these two sectors?  

(a) a2(π + ½)

(b) a2(π – ½)

(c) a2(π/2  – 1)

(d) a2(π/2  + 1)

 

Q 76. The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon ?

(a) a(√2 – 1) 

(b) a(√3 – 1)

(c) a/ (√2 + 2) 

(d) a /3 

 

Q 77. Three consecutive integers form the lengths of a right-angled triangle. How many sets of such three consecutive integers is/are possible ? 

(a) Only one 

(b) Only two 

(c) Only three 

(d) Infinitely many 

 

Q 78. Two circles are drawn with the same centre. The circumference of the smaller circle is 44 cm and that of the bigger circle is double the smaller one. What is the area between these two circles ? 

(a) 154 square cm 

(b) 308 square cm 

(c) 462 square cm 

(d) 616 square cm

 

Q 79. A rectangular red carpet of size 6 ft × 12 ft has a dark red border 6 inches wide. What is the area of the dark red border ? 

(a) 9 square feet 

(b) 15 square feet 

(c) 17 square feet 

(d) 18 square feet 

 

Q 80. The perimeter of a right-angled triangle is k times the shortest side. If the ratio of the other side to hypotenuse is 4:5, then what is the value of k ? 

(a) 2

(b) 3

(c) 4

(d) 5

 

Q 81. A 12 m long wire is cut into two pieces, one of which is bent into a circle and the other into a square enclosing the circle. What is the radius of the circle ? 

(a) 12/ (π + 4) 

(b) 6/ (π + 4) 

(c) 3/ (π + 4) 

(d) 6/ (π + 2√2)

 

Q 82. The angles of a triangle are in the ratio 1:1: 4. If the perimeter of the triangle is k times its largest side, then what is the value of k? 

(a) 1 + 2/√3

(b) 1 – 2/√3

(c) 2 + 2/√3

(d) 2 

 

Q 83. The hypotenuse of a right-angled triangle is 10 cm and its area is 24 cm2. If the shorter side is halved and the longer side is doubled, the new hypotenuse becomes

(a) √245 cm

(b) √255 cm

(c) √265 cm

(d) √275 cm

 

Q 84. In a circle of radius 8 cm, AB and AC are two chords such that AB = AC = 12 cm. What is the length of chord BC ?

(a) 2√6 cm

(b) 3√6 cm

(c) 3√7 cm

(d) 6√7 cm

 

Q 85. Consider the following statements :

1. An isosceles trapezium is always cyclic. 

2. Any cyclic parallelogram is a rectangle.

Which of the above statements is/are correct ?

(a) l only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 86. A ladder is resting against a vertical wall and its bottom is 2.5 m away from the wall. If it slips 0.8 m down the wall, then its bottom will move away from the wall by 1.4 m. What is the length of the ladder ? 

(a) 6.2 m 

(b) 6.5 m 

(c) 6.8 m 

(d) 7.5 m 

 

Q 87.Two equal circles intersect such that each passes through the centre of the other. If the length of the common chord of the circles is 10√3 cm, then what is the diameter of the circle? 

(a) 10 cm 

(b) 15 cm 

(c) 20 cm 

(d) 30 cm 

 

Q 88. Consider the following statements : 

1. The number of circles that can be drawn through three non-collinear points is infinity. 

2. Angle formed in a minor segment of a circle is acute. 

Which of the above statements is/are correct ? 

(a) l only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2 

 

Q 89. Consider the following inequalities in respect of any triangle ABC:

1. AC – AB < BC

2. BC – AC < AB

3. AB – BC < AC

Which of the above are correct?

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3

 

Q 90. Consider the following statements : 

1. The perimeter of a triangle is greater than the sum of its three medians. 

2. In any triangle ABC, if D is any point on BC, then AB + BC + CA > 2AD.

Which of the above statements is/are correct ?

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Consider the following for the next three (03) items: 

A cube is inscribed in a sphere. A right circular cylinder is within the cube touching all the vertical faces. A right circular cone is inside the cylinder. Their heights are same and the diameter of the cone is equal to that of the cylinder. 

Q 91. What is the ratio of the volume of the sphere to that of the cone? 

(a) 6√3:1 

(b) 7:2 

(c) 3√3 :1 

(d) 5√3:1  

 

Q 92. What is the ratio of the volume of the cube to that of the cylinder ? 

(a) 4:3 

(b) 21:16 

(c) 14:11 

(d) 45:32 

 

Q 93. Consider the following statements : 

1. The surface area of the sphere is √5 times the curved surface area of the cone. 

2. The surface area of the cube is equal to the curved surface area of the cylinder. 

Which of the above statements is/are correct ?

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Consider the following for the next three (03) items : 

ABCD is a quadrilateral with AB = 9 cm, BC = 40 cm, CD = 28 cm, DA = 15 cm and angle ABC is a right-angle. 

Q 94. What is the area of triangle ADC ? 

(a) 126 cm2 

(b) 124 cm2 

(c) 122 cm2 

(d) 120 cm2

 

Q 95. What is the area of quadrilateral ABCD? 

(a) 300 cm2 

(b) 306 cm2 

(c) 312 cm2 

(d) 316 cm2

 

Q 96. What is the difference between perimeter of triangle ABC and perimeter of triangle ADC ?

(a) 4 cm 

(b) 5 cm 

(c) 6 cm 

(d) 7 cm 

 

Consider the following for the next two (02) items:

An equilateral triangle ABC is inscribed in a circle of radius 20√3 cm.

Q 97. What is the length of the side of the triangle ? 

(a) 30 cm 

(b) 40 cm 

(c) 50 cm 

(d) 60 cm 

 

Q 98. The centroid of the triangle ABC is at a distance d from the vertex A. What is d equal to ? 

(a) 15 cm 

(b) 20 cm

(c) 20√3 cm

(d) 30√3 cm

 

Consider the following for the next two (02) items : 

The sum of length, breadth and height of a cuboid is 22 cm and the length of its diagonal is 14 cm. 

Q 99. What is the surface area of the cuboid ? 

(a) 288 cm2 

(b) 216 cm2 

(c) 144 cm2

(d) Cannot be determined insufficient data 

 

Q 100. If S is the sum of the cubes of the dimensions of the cuboid and V is its volume, then what is (S-3V) equal to ?

(a) 572 cm3 

(b) 728 cm3 

(c) 1144 cm3 

(d) None of the above

Social Science 10th Previous Year Question Paper 2015 (CBSE)

SOCIAL SCIENCE

SET-I

Q.  1. What was the main aim of the French revolutionaries?

Answer. The main aim of the French revolutionaries was to create a sense of collective identity amongst the French people. They proclaimed that it was the people who would constitute the nation and shape its  decisions.

Or

What is the meaning of concentration camps?

Answer. Concentration camps are prisons where people are detained and tortured without due process of law.

 

Q.  2. How do minerals occur in sedimentary rocks?

Answer. In sedimentary rocks a numbers of minerals occur in beds or layers. They have been formed as a result of deposition, accumulation and concentration in horizontal strata. For example, coal, iron ore.

 

Q. 3. What was the main aim of the popular movement of April 2006, in Nepal?

Answer. Aim of popular movement of April 2006 in Nepal:

  1. Restoring democracy.
  2. Regaining popular control over the government from the King.

 

Q. 4. How can you say that democracies are based on political equality?

Answer. Democracies are based on political equality as individuals have equal weight in electing representatives.

 

Q. 5. Why do political parties involve partisanship?

Answer. Partisanship is marked by a tendency to take a side and inability to take a balanced view, on an issue. Parties reflect fundamental political divisions in a society. Parties are a part of the society and they involve partisanship.

 

Q. 6. What is meant by double coincidence of wants?

Answer. Double coincidence of wants means when both parties have agreed to sell and buy each other’s commodities.

 

Q. 7. Suppose your parents want to purchase Gold jewellery along with you; then which logo will you look for on the jewellery?

Answer. Hallmark, is the logo to look for while purchasing Gold jewellery.

 

Q. 8. How does money act as a medium of exchange?

Answer. Money acts as a medium of exchange as it acts as an intermediate in the exchange process and transactions. A person holding money can easily exchange it for any commodity or services that he or she might want.

 

Q. 9. How did nationalism develop through culture in Europe? Explain.

Answer. Culture, music, dance and religion played an important role in the growth of nationalism.

  1. Culture. Role of culture was important in creating the idea of the nation. Art, poetry, music etc. helped in developing and expressing nationalist feelings. Romanticism was a cultural movement that led to the development of nationalist sentiment. Romantic artists and poets criticized the glorification of reason and science and instead focussed on emotions and intuition.
  2. Language. Language too played an important role in developing nationalist sentiments. After Russian occupation, the Polish language was forced out of schools and Russian language was imposed everywhere. In 1831, an armed rebellion against Russian rule took place which was ultimately crushed. Following this, many members of the clergy in Poland began to use language as a weapon of national resistance.
  3. Music and Dance. Romantics such as the German philosopher Herder claimed that true German culture was to be discovered among the common people—das volk. It was through folk songs, folk poetry and folk dances that the true spirit of the nation was popularised.

Or

How did Paul Bernard argue in favour of economic development of Vietnam? Explain.

Answer. Paul Bernard was an influential writer and policy-maker who strongly believed that the

purpose of acquiring colonies was to make profits.

  1. According to him, the development of economy will raise the standard of people and people would buy more goods. The market would consequently expand, leading to better profit for French business.
  2. According to Bernard, there were several barriers to economic growth in Vietnam, such as large population, low agricultural productivity and extensive indebtedness amongst the peasants.
  3. To reduce the poverty and increase agricultural productivity, it was necessary to carry out land reforms.
  4. Industrialisation was also essential for creating more jobs as agriculture was not likely to ensure sufficient employment opportunities.

 

Q. 10. Describe the main features of ‘Poona Pact’.

Answer. The Poona Pact:

  1. Dr. B.R. Ambedkar, who organised the dalits into the Depressed Classes Association in 1930 demanded separate electorates for dalits in the Second Round Table Conference organised in London.
  2.  When British accepted this demand in the name of Communal Award, Gandhiji started a fast into death. He believed that separate electorates for dalits would slow down the process of their integration into the society.
  3. Ambedkar and Gandhi came to an agreement with Ambedkar accepting Gandhis position and the result was the Poona Pact of September, 1932.
    — It gave the depressed classes (later to be known as Schedule castes) reserved seats in provincial and central legislative councils.
    — But, they were to be voted in by the general electorate.

 

Q. 11. How did ‘Salt March’ become an effective tool of resistance against colonalism? Explain.

Answer. Mahatma Gandhi found in salt a powerful symbol that could unite the nation.

  1. On 31st January, 1930 he sent a letter to Viceroy Irwin stating eleven demands, one of which was the demand to abolish Salt Tax.
  2. Salt was one of the most essential food items consumed by the rich and poor alike and a tax on it was considered an oppression on the people by the British Government,
  3.  Mahatma Gandhi’s letter was an ultimatum and if his demands were not fulfilled by March 11, he had threatened to launch a civil disobedience campaign.
  4. So, Mahatma Gandhi started his famous Salt March accompanied by 78 of his trusted volunteers. The march was over 240 miles, from Gandhiji’s ashram in Sabarmati to the Gujarati coastal town of Dandi.
  5. On 6th April, he reached Dandi, and ceremonially violated the law, manufacturing salt by boiling sea water. This marked the beginning of the Civil Disobedience Movement.

 

Q. 12. Explain the importance of railways as the principal mode of transportation for freight and passengers in India.

Answer.

  1. Railways are the principal mode of transportation for freight and passengers in India, as they link different parts of the country.
  2.  They carry huge loads and bulky goods to long distances.
  3. Railways make it possible to conduct multiple activities like business, tourism, pilgrimage along with goods transportation over longer distances.
  4. Railways have been a great integrating force for the nation, for more than 150 years now,
  5. They have been helpful in binding the economic life of the country and also promoted cultural fusion.
  6.  They have accelerated the development of the industry and agriculture.

 

Q. 13. Why the ‘Chhotanagpur Plateau Region’ has the maximum concentration of iron and steel industries? Analyse the reasons.

Answer. Chhotanagpur Plateau has the maximum concentration of iron and steel industries because of the relative advantages this region has for the development of this industry like:

  1.  Low cost of iron ore which is mined here.
  2. High grade raw materials in close proximity.
  3. Availability of cheap labour.
  4. Vast growth potential in the home market.
  5. Availability of power because this region has many thermal and hydel power plants.
  6. Liberalisation and FDI have also given boost to the industry with efforts of private enterpreneurs.

 

Q. 14. How can solar energy solve the energy problem to some extent in India? Give your opinion.

Answer. Reasons:

  1. India is a tropical country and gets abundant sunshine.
  2.  It has enormous possibilities of tapping solar energy.
  3. It is an inexhaustible source of energy which is freely available in nature.
  4.  It is a cheaper source of energy and is fast becoming popular in rural and remote areas.
  5.  Photovaltic technology is available which converts sunlight directly into electricity.
  6. Because of its abundant and free availability in all parts of India in addition to its eco friendly nature, solar energy is called the energy of future.

Also use of solar energy will minimise the dependence of rural households on firewood. It will contribute to environmental conservation and reduce pressure on conventional sources of energy.

 

Q. 15. “Dynastic succession is one of the most serious challenges before the political parties.” Analyse the statement.

Answer. Most political parties do not practise open and transparent procedures for their functioning. So there are very few ways for an ordinary worker to rise to the top in a party. Those who happen to be the leaders are in a position of unfair advantage as they favour people close to them or even their family members.

In many parties in India, we see a trend of dynastic succession. The top positions are always controlled by members of a particular family, which is unfair to other members of the party, and bad for democracy. This is so because people who do not have adequate experience or popular support come to occupy positions of power.

More than loyalty to party principles and policies, personal loyalty to the leader becomes more important. This tendency is seen all over the world, even in older democracies.

 

Q. 16. How is democracy accountable and responsive to the needs and expectations of the citizens? Analyse.

Answer. A democracy is concerned with ensuring that people have the right to choose their rulers and have control over the rulers.

— Whenever possible and necessary, citizens should be able to participate in decision making in a democracy.

— Democracy ensures that decision-making is based on norms and procedures. A citizen has the right anti the means to examine the process of decision-making. Thus democracy entails transparency.

— For a democracy to produce an accountable, responsive and legitimate government, it must ensure the following:

  1. Regular, free and fair elections.
  2. Open public debate on major policies and legislations. .
  3. Citizens’ right to be informed about government policies.
  4.  A government free from corruption.

 

Q. 17. “A challenge is an opportunity for progress.” Support the statement with your arguments.

Answer. A challenge is not just any problem. Only those difficulties are a ‘challenge’ which are significant and can be overcome and therefore carry within them an opportunity for progress. Democracy is the dominant form of government in the contemporary world. It does not face a particular challenger, but the promise of democracy is far from realised anywhere in the world. Democracy as a whole faces certain challenges.

Legal constitutional changes by themselves cannot help to overcome challenges to democracy—like economic inequality, unemployment, illiteracy, caste, gender discrimination. Democratic reforms can be carried out by political activities, parties, movements and politically conscious citizens, in order to realise the opportunity in a challenge, in order to overcome it an go up to a higher level.

 

Q. 18. Why is modern currency accepted as a medium of exchange without any use of its own? Find out the reason.

Answer. Modem forms of money currency in India include paper notes and coins which are known as Rupees and Paise.

  1. It is accepted as a medium of exchange because the currency is authorised by the Government of India.
  2. In India, the Reserve Bank of India issues currency notes on behalf of the Central Government. As per Indian law, no other individual or organisation is allowed to issue currency.
  3.  The law legalises the use of the rupee as a medium of payment that cannot be refused in settling transactions in India.
  4. No individual in India can legally refuse a payment made in rupees.
    Therefore, the rupee is widely accepted as a medium of exchange.

 

Q. 19. “Foreign trade integrates the markets in different countries.” Support the statement with arguments.

Answer. 

  1.  Foreign trade creates opportunities for producers to reach beyond domestic markets.
    Producers can compete in markets located in other countries of the world. Similarly for the buyers, import of goods from another country leads to expanding choice of goods beyond what is domestically produced. Buyers can thus choose from a wide range of products to suit their individual tastes.
  1. With the opening of trade, goods travel from one market to another. Choice of goods in the market rises. Prices of similar goods in two markets tend to become equal, and producers in the two countries now closely compete against each other even though they are separated by thousands of miles.
    Foreign trade, thus, results in connecting the markets or integration of markets in different countries.
    For example., There are endless number of footwear brands available in the Indian market. A consumer who is aware of international trends can choose between a local brand like Bata, Lakhani and international brands like Adidas, Nike, Reebok etc.

 

Q. 20. Explain with an example how you can use the right to seek redressal.

Answer. Right to seek redressal:

  1. The consumers can seek redressal against trade practices of exploitation and have the right to fair settlement of the genuine grievances.
  2.  He has a right to get compensation from a manufacturer/trader if he is harmed. The consumer can seek redressal through Consumer Courts functioning at district, state and national levels.
    Example: Mahesh sent a money order to his village for his mother’s medical treatment. The money did not reach his mother at the time when she needed it and reached months later. Mahesh, thus filed a case in the district level consumer court to seek redressal.

Q. 21. Describe any five steps taken by the French Revolutionaries to create a sense of collective identity among the French people.

Answer. The first clear-cut expression of nationalism came with the French Revolution in 1789. In 1789, France was under the rule of an absolute monarch.

When the revolutionaries came to power in France, they were determined to create a new sense of unity and nationhood. For this, they emphasized the concept of France being the father land (La Patrie) for all French people, who were from now on addressed as citizens (citoyen). They were given the tricolour flag, the three colours representing liberty*; equality and fraternity.

French revolutionaries introduced various other measures such as:

  1. The Estate General was elected by the body of active citizens and renamed the National Assembly.
  2.  New hymns were composed, oaths taken and martyrs commemorated all in the name of the nation.
  3.  A centralized administrative system was put in place and it formulated uniform laws for all citizens within its territory.
  4.  Internal customs, duties and dues were abolished and a uniform system of weights and measures was adopted.
  5.  Regional dialects were discouraged and French, as it was spoken and written in Paris, became the common language of the nation. .
  6. They further declared that it was the mission and the destiny of the French nation to liberate the people of Europe from despotism and help them to become nations.

Or

Describe any five steps taken by the French for the development of the ‘Mekong Delta Region’.

Answer. Steps taken by the French for the development of the ‘Mekong Delta Region’:

  1. Colonies were considered essential to supply natural resources and other essential goods. Like other western nations, France also thought that it was the mission of the advanced’ European countries to bring benefits of civilization to backward people.
  2. The colonial economy in Vietnam was primarily based on rice cultivation and rubber
    plantations owned by the French and a small Vietnamese elite. The French built canals and drained lands in the Mekong Delta to increase rice cultivation. A vast system of irrigation was built which led to great expansion in rice production and gradually Vietnam became the third largest exporter of rice in the world.
  3. Rail and port facilities were set up to support and service this sector.
  4.  Indentured Vietnamese labour was widely used in the rubber plantations, French did little to industrialise the economy.
  5. in the rural areas landlordism spread and standard of living declined.

 

Q. 22. Explain the attitude of the Indian merchants and the industrialists towards the ‘Civil Disobedience Movement’.

Answer. Role of merchants and the industrialists in the Civil Disobedience Movement:

  1. Merchants reacted against colonial policies that restricted business activities.
  2. They wanted protection against import of foreign goods and wanted a rupee-sterling foreign exchange ratio that would discourage imports.
  3. Industrialsits formed the Indian Industrial and Commercial Congress in 1920.
  4.  They formed the Federation of the Indian Chamber of Commerce and Industries ‘ (FJCCl) in 1927.
  5.  Thev refused to sell or buy imported goods. They gave financial assistance and supported the Civil Disobedience Movement.
  6.  Industrialists like G.D. Birla and Pursnottamdas Thakurdas attacked colonial control over the Indian economy.

 

Q. 23. What is the manufacturing sector? Why is it considered the backbone of development? Interpret the reason.

Answer. Production of goods in large quantities after processing from raw materials to more valuable products is called manufacturing.

Manufacturing belongs to the secondary’ sector in which the primary’ materials are processed and converted into finished goods. The economic strength of a country is measured by the development of manufacturing industries.

Importance of manufacturing industries for development in India:

  1. It helps in modernising agriculture, which is the base of our economy.
  2.  It reduces heavy dependence on agricultural income by providing jobs in non- agricultural sectors.
  3.  Industrial development is necessary for eradication of poverty and unemployment because people get jobs and generate more income.
  4.  Export of manufactured goods expands trade and brings in much needed foreign exchange.
  5. Industries bring riches faster to a nation because manufacturing changes raw materials into finished goods of a higher value, so industrial development brings prosperity to the country.

 

Q. 24. Which is the most abundantly available fossil fuel in India? Assess the importance of its different forms. 

Answer. Coal is the most abundantly available fossil fuel in India.

Four types of coal and their characteristics:

(a) Anthracite. 1. It is the highest quality hard coal;

2. It contains more than 80% carbon content. It gives less smoke.

(b) Bituminous. 1. It is the most popular coal in commercial use and has 60-80% carbon content;

2. Metallurgical coal is high grade bituminous coal and is of special value for smelting iron in blast furnaces.

(c) Lignite. 1. IHs a low grade brown coal;

2. It is soft with high moisture content. The main lignite reserve is Neyveli in Tamil Nadu.

(d) Peat. 1. It has a low carbon and high moisture content;

2. It has low heating capacity and gives lot of smoke on burning.

 

Q. 25. What is meant by a political party? Describe the three components of a political party.

Answer. Political party is a group of people who come together to contest elections and to hold power in the government. They agree on some policies to promote collective good. They seek to implement those policies by winning popular support through elections. Thus political parties tend to fill political offices and exercise political power.

Answer. Components of a political party are: (1) The leaders, (2) active members and (3) the followers.

  1. The leaders are recruited and trained by parties. They are made ministers to run the government. The big policy decisions are taken by the political executives that come from the political parties.
  2.  Parties have lakhs of members and activists spread over the country. Many of the pressure groups are the extensions of political parties among different sections of society. But since most of the members belong to a party, they go by the direction of the party leadership, irrespective of their personal opinion.
  3. The followers are the ordinary citizens, who believe in the policies of their respective party and give popular support through elections. Often the opinions of the followers crystallise on the lines parties take.

 

Q. 26. Suggest any five effective measures to reform political parties.

Answer. See Q. 26, 2011 (I Delhi).

 

Q. 27. How do banks play an important role in the economy of India? Explain.

Answer.

  1. Banks help people to save their money and keep their money in safe custody. To ensure safety of their money, people deposit their money with banks. Banks accept deposits and pay interest on deposits. People have the provision to withdraw their money as and when they require.
  2. Banks also grant loans to people for a variety of purposes. In times of need individuals, business houses and industries can borrow money from the banks.
  3. Credit provided by banks is crucial for the country’s growth and economic
    development. Credit is needed for all kinds of economic activities, to set up business, buy cars, houses, etc.
  4. Banks also help people in obtaining cheap and affordable loans. This can help people to grow crops, do business, set up small-scale industries or trade in goods and also help indirectly in the country’s development. They should do so, so that relatively poor people do not have to depend on informal sources of credit (money-lenders).

 

Q. 28. “Globalisation and greater competition among producers has been advantageous consumers.” Support the statement with examples.

Answer.

  1.  Greater competition among producers (both local and foreign) has been advantageous to consumers, particularly the well-off section. Rich people enjoy improved quality and lower prices for several products and enjoy a higher standard of living.
  2. MNCs have increased their investments in India over the past 20 years in industries such as cell phones, automobiles, electronics, soft drinks, fast food and services such as banking thereby providing consumers with a vast variety of products.
  3. New jobs have been created in all these industries and services, thereby increasing purchasing power of individuals.
  4. Top Indian companies have benefitted from the increased competition. They have invested in newer technology and production methods indirectly benefitting the consumers.
  5.  Consumers today, enjoy much higher standards of living than was possible earlier.

 

Q. 29. Three features A, B and C are marked on the given political outline map of India.

Identify these features with the help of the following information and write their correct names on the lines marked in the map:

A. The place where the Indian National Congress Session was held.

B. The place associated with the Peasant’s Satyagraha.

C. The place related to calling off the Non-Cooperation Movement.

cbse-previous-year-question-papers-class-10-social-science-sa2-outside-delhi-2015-1

Answer.

cbse-previous-year-question-papers-class-10-social-science-sa2-outside-delhi-2015-2

Note: The following questions are for the Visually Impaired Candidates only, in lieu of Q.  No. 29.

(29.1) Name the place where the Indian National Congress Session was held in Dec., 1920.

(29.2) Name the place associated with the movement of Indigo Planters.

(29.3) Name the place related to the Satyagraha of peasants in Gujarat.

Answer. (29.1) Nagpur (29.2) Champaran (29.3) Kheda

 

Q. 30 (30.1) Two features A and B are marked on the given political outline map of India.

Identify these features with the help of the following information and write their correct names on the lines marked in the map:

A. Iron-orb mines B. Terminal Station of East-West Corridor

(30.2) On the same political outline map of India, locate and label the following:

(i) Vishakhapatnam—Software Technology Park

cbse-previous-year-question-papers-class-10-social-science-sa2-outside-delhi-2015-3

Answer.

cbse-previous-year-question-papers-class-10-social-science-sa2-outside-delhi-2015-4

Note: Tite foil Giving questions are for the VISUALLY IMPAIRED CANDIDATES only, in lieu of Q.  No. 30.

(30.1) In which state are Bailadila Iron-ore mines located?

(30.2) Name the Western Terminal Station of East-West Corridor.

(30.3) Name the well known Software Technology Park located in Karnataka State.

Answer. (30.1) Chhattisgarh (30.2) Porbandar (30.3) Bangalore or Mysore

 

SET II

Q. 2. Why has the ‘National Manufacturing Competitiveness Council’ been set up?

Answer. The trend of growth rate in the manufacturing sector over the last decade has been around 7% per annum. The desired growth rate over the next decade is 12%. The NMCC has been set up to improve productivity with government policy intervention and efforts by Industry.

 

Q. 3. What is the guiding philosophy of Bhartiya Janata Party?

Answer. The source of inspiration of Bharatiya Janata Party is the ancient Indian culture and values. Cultural nationalism (Hindutva) is an important element in its conception of Indian nationhood and politics.

 

Q. 6. What is meant by trade barrier?

Answer. Barriers or restrictions that are imposed by the government on free import and export activities are called trade barriers. Tax on imports is an example of a trade barrier because it increases the price of imported commodities. The government can use a trade barrier like ‘tax’ to increase or decrease (regulate) foreign trade and to decide what kind of goods and how much of what should come into the country.

 

Q. 10. Describe the spread of Non-Cooperation Movement in the countryside.

Answer. The Non-cooperation movement spread to the countryside also.

It drew into the struggles of peasants and tribals from different parts of India.

  1. In Awadh, the peasants’ movement ied by Baba Ramchandra was against talukdars and landlords who demanded extremely high rents and a variety of other cesses from the peasants. Peasants were forced to work in landlords’ farms without any payment (begar). Peasants had no security of tenure, thus being regularly evicted so that they could acquire no right over the leased land. The demands of the peasants were— reduction of revenue, abolition of begar and social boycott of oppressive landlords.
  2. In the Gudem Hills of Andhra Pradesh a militant guerrilla movement spread in the early 1920s against the closure of forest areas by the colonial government, preventing people from entering the forests to graze their cattle, or to collect fuelwood and fruits. They felt that their traditional rights were being denied.
  3. For plantation workers in Assam, freedom meant the right to move freely in and out of the confined space in which they were enclosed. It meant retaining a link with the village from which they had come.

Under the Inland Emigration Act of 1859, plantation workers were not permitted to leave tea gardens without permission. In fact the permission was hardly granted. When they heard of the Non-Cooperation Movement, thousands of workers defied the authorities and left for their homes.

 

Q. 12. Describe any three features of waterways in India,

Answer.

  1. Waterways are the cheapest means of transport.
  2.  Waterways are a fuel efficient and environment friendly mode of transport.
  3. They are most suitable for carrying heavy and bulky goods.
  4.  India’s trade with foreign countries if carried from the ports located along the coast, and more than 95% of the’country’s trade volume is moved by the sea.

 

Q. 15. How do money and muscle power play an important role in elections?

Answer. Political parties need to face and overcome the growing challenge of Money and Muscle power during elections in order to remain effective instruments of democracy.
Since parties are focussed only on winning elections, they tend to use shortcuts to win elections, for example, like booth-rigging, distribution of food, money, alcohol, etc. to the poor voters to get their votes. Political parties tend to nominate those candidates who have or can raise lots of money. Rich people and companies who give funds to the parties tend to have influence on the policies and decisions of the party. These days, parties are supporting criminals who can win elections. This is a major cause of concern to the democrats all over the world who are worried about the increasing role of rich people and big companies in democratic politics.

 

Q. 22. Explain any five major problems posed by the First World War in India.

Answer. The outbreak of the First World War had created a new economic and political situation in India:

  1. Tire increased defence expenditure was financed by war loans and by raising tax rates, custom duties, etc. There was tremendous price rise during the war years. Between 1913 and 1918, the prices had almost doubled. People, particularly common people, were lacing extreme hardships.
  2. Forced recruitment in the army caused widespread anger in the villages. .
  3. The failure of crops in many parts of India had created food shortages, leading to the added misery of the people.
  4. In addition to this, there was the outbreak of the great influenza epidemic. Millions of people perished due to influenza and starvation.
  5. The nationalist movement grew stronger during the war years. A large number of Muslims were drawn into the anti-British struggle during the war. The defence of the ‘Caliphate’ (Khilafat) became an important question for Muslims. Peasant movements during war period also had helped the nationalist movement to grow stronger.

 

Q. 23. Why was the cotton textile industry concentrated in the cotton growing belt in the early years? Explain.

Answer. In the early years, the cotton growing belt was primarily concentrated in Maharashtra and Gujarat.

  1. Availability of raw cotton was abundant and cheap here because these are the traditional cotton growing states.
  2. Moist climate in these coastal states also helped in the development of cotton textile industry because humid conditions are required for weaving the cloth, else the yam breaks.
  3. Well developed transportation system and accessible port facilities in Maharashtra and Gujarat led to their concentration there.
  4. Proximity to the market was yet another factor as cotton clothes were ideal and comfortable to wear in these warm and humid states.
  5. Cheap labour was also abundantly available.

 

Q. 26. “The democracy has been evolved through struggles and movements all over the world.” Support the statement with examples.

Answer.

  1. Democracy has evolved through struggles and movements all over the world. The struggles in Poland, Nepal and Bolivia all relate to establishing and restoring democracy. The struggled in these countries is a reminder that popular struggles are integral to the working of democracy.
  2. The role of popular struggle does not come to an end with the establishment of democracy. Democracy involves conflict of interests and viewpoints. These views are expressed in organised ways through which ordinary citizens can play a role in democracy.
  3. In a democracy, several different kinds of organisations work behind any big struggle. These organisations influence the decisions in a democracy either by creating parties, contesting elections and forming government. They promote the interest and viewpoints of citizens in a democracy through interest groups or pressure groups.
  4. Democracy evolves through popular struggle. Some major decisions may take place through consensus. But some decisions involve conflict between the groups who have exercised power and those who aspire to share power. Here the popular struggle helps in the expansion of democracy.

SET III

Q. 2. Why was the Haldia sea-port set up?

Answer. Haldia sea-port was set up as a subsidiary port, in order to relieve growing pressure on the Kolkata port.

 

Q. 3. What is meant by ‘transparency’?

Answer. In a democracy, every citizen has the right and means to examine the process of decision making. This is known as transparency.

 

Q. 6. Why was the Consumer Protection Act enacted by the Indian Parliament?

Answer. The Consumer Protection Act was enacted by the Indian parliament in 1986 to protect the consumers from unfair trade practices and retain interest of consumers.

 

Q. 10. Describe any three major problems faced by the peasants of Awadh in the days of Non-Cooperation Movement.

Answer. The movement of Awadh peasants was led by:

  1. The peasants’ movement Baba Ramchandra was against talukdars and landlords who demanded extremely high rents and a variety of other cesses from the peasants.
  2. Peasants were forced to work in landlords’ farms without any payment (begar). Peasants had no security of tenure, thus being regularly evicted so that they could acquire no right over the leased land.
  3. The demands of the peasants were: reduction of revenue, abolition of begar and social boycott of oppressive landlords.

 

Q. 12. Describe the significance of tourism as a trade in India.

Answer.

  1. With increase in the number of foreign tourists visiting India, we earned foreign exchange worth ?21,828 crore in 2004 which is further increasing year by year making tourism an important trade.
  2. Over 2.6 million foreign tourists visit India every year for appreciating our heritage, our culture, for medical purposes or for business purposes, etc.
  3. Over 15 million people are directly engaged in the tourism industry.
  4. Tourism promotes national integration, provides support to local handicrafts and cultural pursuits.
  5. Tourism also helps in the development of international understanding about our culture and heritage.
  6.  Rajasthan, Goa, Jammu & Kashmir and temple towns of south India are the most popular tourist destinations. These states earn huge sums of money from tourism trade.

 

Q. 15. “There is an overwhelming support for the idea of democracy all over the world.” Support the statement.

Answer. Over a hundred countries of the world today claim and practice some kind of democratic politics.

— They have formal constitutions, hold elections, have parties and they guarantee rights of citizens. Thus, in most countries, the democracy produces a government that is accountable to the citizens and responsive to the needs and expectations of the citizens.

— No society7 can fully and permanently resolve conflict among different groups. But we can learn to respect these differences and evolve mechanisms to negotiate them. Democracy is best suited as it develops a procedure to conduct competitions. Belgium is a successful example of negotiating difference among ethnic population.

— Passion for respect and freedom is the basis of democracy and has been achieved in various degrees in various democracies.

— The support for democracy is overwhelming all over the world and is evident from South Asia, where the support exists in countries with democratic as well as undemocratic regimes.

— People wish to be ruled by representatives elected by them, as a democratic government is people’s own government and makes them believe that it is suitable for their country as it is a legitimate government.

 

Q. 22. How did the ‘Non-Cooperation Movement’ spread in cities across the country? Explain its effects on the economic front.

Answer. In the cities, the Non-Cooperation Movement started with middle class participation.

  1. Thousands of students left government-controlled schools and colleges. Headmasters and teachers resigned and. lawyers gave up their legal practices.
  2.  The Council elections were boycotted in most provinces except Madras.
  3. Foreign goods and foreign cloth was boycotted. Traders and merchants also refused to trade in foreign goods.

The economic sphere was affected by the Non-Cooperation Movement.

  1. Foreign goods were boycotted, liquor shops were picketed and foreign doth was burnt. The import of foreign cloth halved between 1921-1922. Its value dropped from Rs 102 crores to Rs 57 erores.
  2. Many merchants and traders refused to trade in foreign goods or finance foreign trade. (Hi) People began discarding imported clothes and wearing Indian ones.
  3. The production of Indian textile mills and handlooms went up. Use of khadi was popularised.

 

Q. 23. Explain the pro-active approach adopted by the National Thermal Power Corporation (NTPC) for preserving the natural environment and resources.

Answer. NTPC is taking the following measures in places where it is setting up power plants to preserve natural environment and resources:

  1. Optimum utilization of equipment by adopting latest techniques and upgrading existing equipment.
  2. Minimizing waste generation by maximizing ash utilization.
  3.  Providing green belts for nurturing ecological balance. .
  4. Reducing environmental pollution through ash pond management, ash water recycling system and liquid waste management.
  5. Ecological monitoring,, reviews and online data base management for all its power stations.

 

Q. 26. Why do we feel that democracy is a better form of government than any other form? Explain.

Answer. Democracy is a better form of government than any other form because:

  1. It is based on the idea of deliberation and negotiation. Thus the necessary delay in implementation.
  2. Decisions are acceptable to people and are more effective.
  3. A citizen has the right and the means to examine the process of decision-making. There is transparency in a democracy.
  4.  Democratic government is a legitimate government, people’s own government.
  5. Ability to handle differences, decisions and conflicts is a positive point of democratic regimes.
  6. Democracy has strengthened the claims of the disadvantaged and discriminated castes for equal status and equal opportunity.

CDS(I) Exam 2016 Maths Previous Year Paper

CDS(I) Exam 2016 

ELEMENTARY MATHEMATICS

प्रश्न 1. यदि समीकरण lx2 + mx + m = 0 के मूल p:q के अनुपात में हैं, तो √(p/q) +  √(q/p) +√(m/l) किसके बराबर है? 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

प्रश्न  2. यदि के मूल α और β हैं, तो αβ का मान क्या है? 

(a) -15 

(b) -5 

(c) 0 

(d) 5

 

प्रश्न  3. यदि p/x + q/y = m और q/x + p/y = n हैं, तो x/y किसके बराबर है? 

(a) (np + mq)/(mp + nq)

(b) (np + mq)/(mp – nq

(c) (np – mq)/(mp – nq

(d) (np – mq)/(mp + nq)

प्रश्न  4. यदि a2 – by – cz = 0, ax – b2+cz = 0 और ax + by – c2 = 0, हैं, तो का मान क्या होगा? 

(a) a+b+c 

(c) 1 

(b) 3 

(d) 0 

 

प्रश्न  5. यदि समीकरण x2px + q = 0 और x2 + qxp = 0 का एक उभयनिष्ठ मूल है, तो निम्नलिखित में से कौन-सा एक सही है? 

(a) p-q= 0 

(b) p+q-2 = 0 

(c) p+q-1 = 0 

(d) p-q- 1 = 0 

 

प्रश्न 6. यदि x = 23+2-3 है, तो 2x3 – 6x – 5 का मान किसके बराबर है? 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

प्रश्न  7. दो व्यंजकों का जोड़ और अंतर क्रमशः 5x2 x – 4 और x2 + 9x – 10 है। उन दो व्यंजकों का म०स० (HCF) क्या होगा? 

(a) (x + 1) 

(b) (x – 1) 

(c) (3x +7) 

(d) (2x – 3) 

प्रश्न  8. यदि (s-a) + (s – b) + (s – c) = s है, तो का मान क्या होगा? 

(a) 3 

(b) 1 

(c) 0 

(d) -1 

 

प्रश्न  9. यदि बहुपद x6 + px5 + qx4x2x – 3, (x4 – 1) से विभाज्य है, तो p2+q2 का मान क्या है? 

(a) 1 

(b) 9 

(c) 10 

(d) 13 

 

प्रश्न  10. मान लीजिए p और q शून्येतर पूर्णांक हैं। बहुपद A(x) = x2 + px +q पर विचार कीजिए। यह दिया गया है कि (x -m) और (x – km), A(x) के सरल गुणनखंड हैं, जहां m एक शून्येतर पूर्णांक है, k एक धनात्मक पूर्णांक और k ≥ 22 है। निम्नलिखित में से कौन-सा एक सही है? 

(a) (k + 1)2 p2 = kq 

(b) (k + 1)2q = kp2 

(c) k2q = (k + 1)p2 

(d) k2p2 = (k + 1)2q

 

प्रश्न  11. मान लीजिए m एक शून्येतर पूर्णांक और n एक धनात्मक पूर्णांक है। मान लीजिए R, बहुपद xn +mn को (x – m) से विभाजित करने पर प्राप्त शेषफल है। तब 

(a) R एक शून्येतर सम पूर्णांक है 

(b) R विषम है, यदि m विषम है 

(c) किसी पूर्णांक s के लिए R = S2 है, यदि n सम है 

(d) किसी पूर्णांक t के लिए R = t3 है, यदि 3, n को विभाजित करता है 

 

प्रश्न  12. यदि 4x2y = 128 और 33x32y – 9xy = 0 हैं, तो x+ y का मान किसके बराबर हो सकता है? 

(a) 7 

(b) 5 

(c) 3 

(d) 1 

 

प्रश्न  13. यदि ax2 – (a2 + 1)x + a के रैखिक गुणनखंड p और q हैं, तो p+q किसके बराबर है? 

(a) (x – 1)(a + 1) 

(b) (x + 1) (a + 1) 

(c) (x – 1)(a-1) 

(d) (x + 1)(a-1) 

 

प्रश्न  14. यदि है, तो bx2ax + b किसके बराबर है? (दिया गया है कि b ≠ 0.) 

(a) 0 

(b) 1 

(c) ab 

(d) 2ab

 

प्रश्न  15. यदि a3 = 117 + b3 और a = 3+ b हैं, तो a+b का मान क्या है? (दिया गया है कि a > 0 और b> 0.) 

(a) 7 

(b) 9 

(c) 11 

(d) 13 

 

प्रश्न  16. यदि ax2 + bx + c = 0 के मूलों का जोड़, उनके व्युत्क्रमों के वर्गों के जोड़ के बराबर है, तो निम्नलिखित संबंधों में से कौन-सा एक सही है? 

(a) ab2+ bc2 = 2a2

(b) ac2 + bc2 = 2b2

(c) ab2 + bc2 = a

(d) a2 + b2 + c2 = 1 

 

प्रश्न  17. व्यंजक , जहाँ n एक पूर्णांक है, के बारे में निम्नलिखित कथनों पर विचार कीजिए : 

1. n के यथातथ्य दो मान हैं, जिनके लिए Sn = 861 है। 

2. Sn = S-(n+1) है और इस प्रकार किसी पूर्णांक m के लिए हमारे पास n के दो मान हैं, जिनके लिए Sn = m है। उपर्युक्त कथनों में से कौन-सा/से सही है/हैं? 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2  

 

प्रश्न  18. दो विभिन्न शून्येतर पूर्णांकों p और 4 के बारे में निम्नलिखित कथनों पर विचार कीजिए : 

1. (p+q) के (p-q) से कम होने के लिए ऋणात्मक होना ही चाहिए। 

2. (p+q) के (p-q) से अधिक होने के लिए p और q दोनों धनात्मक होने ही चाहिए। 

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं? 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2 

 

प्रश्न  19. यदि a/b = b/c = c/a है, तो निम्नलिखित में से कौन-सा/से सही है/हैं? 

1. (b3 + c3 + d3)/(a3 + b3 + c3) = d/a

2. (a2 + b2 + c2)/(b2 + c2 + d2) = a/d

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2 

 

प्रश्न  20. 710 – 510 किससे विभाज्य है? 

(a) 5 

(b) 7 

(c) 10 

(d) 11 

 

प्रश्न  21. मान लीजिए दो अंको की एक संख्या अपने अंकों के योगफल की k गुना है। यदि संख्या के अंकों को आपस में बदलने से बनी संख्या अपने अंको के योगफल की m गुना है, तो m का मान क्या है? 

(a) 9-k 

(b) 10-k 

(c) 11-k 

(d) k-1 

 

प्रश्न  22. एक आदमी ने 5 कि० मी०/घंटा की चाल से चलते हुए देखा कि विपरीत दिशा से आती हुई 225 मी० लंबी एक रेलगाड़ी उसे 9 सेकंड में पार करती है। रेलगाड़ी की चाल क्या है? (a) 75 कि० मी०/घंटा 

(b) 80 कि० मी०/घंटा 

(c) 85 कि० मी०/घंटा 

(d) 90 कि० मी०/घंटा 

 

प्रश्न  23. (sin 35°/ cos 55°)2 – (cos 55°/ sin 35° )2 + 2 sin 30° किसके बराबर है?

(a) -l 

(b) 0

(c) 1 

(d) 2 

 

प्रश्न  24. एक साइकिल चालक A से B तक 14 कि० मी० की दूरी बिना रुके एक निश्चित औसत चाल से तय करता है। यदि उसकी औसत चाल 1 कि० मी० प्रति घंटा कम होती है, तो वह उसी दूरी को पूरा करने के लिए 20 मिनट अधिक लेता है। उस साइकिल चालक की प्रारंभिक औसत चाल क्या है? 

(a) 5 कि० मी०/घंटा 

(b) 6 कि० मी०/घंटा 

(c) 7 कि० मी०/घंटा 

(d) उपर्युक्त में से कोई नहीं

 

प्रश्न  25. यदि कोई धनराशि साधारण ब्याज की किसी निश्चित वार्षिक दर से 5 वर्ष में दो गुनी हो जाती है और साधारण ब्याज की किसी अन्य वार्षिक दर से 12 वर्ष में तीन गुनी हो जाती है, तो साधारण ब्याज की उन दोनों वार्षिक दरों में क्या अंतर है? 

(a) 2% 

(b) 3% 

(c) 33% 

(d) 43% 

 

प्रश्न  26. मान लीजिए ABC और A’B’C’ दो त्रिभुज हैं, जिनमें AB> A’B’, BC> BC’ और CA> CA’ हैं।  मान लीजिए D, E और F क्रमशः भुजाओं BC, CA और AB के मध्य-बिंदु हैं। मान लीजिए D’, E’ और F‘ क्रमशः भुजाओं BC’, CA’ और A’B’ के मध्य-बिंदु हैं। निम्नलिखित कथनों पर विचार कीजिए : 

कथन I : 

AD > A’D‘, BE > B‘E’ और CF > C’F’ हमेशा सत्य हैं।

कथन II : 

(AB2 + BC2 + CA2)/(AD2 + BE2 +CF2) = (A‘B’2+ B’C2+ C’A2 )/(A’D2+ B’E 2 + C’F 2 )

उपर्युक्त कथनों के लिए निम्नलिखित में से कौन-सा एक सही है? 

(a) कथन I और कथन II दोनों सत्य हैं तथा कथन II, कथन I की सही व्याख्या है 

(b) कथन I और कथन II दोनों सत्य हैं लेकिन कथन II, कथन I की सही व्याख्या नहीं है 

(c) कथन I सत्य है लेकिन कथन II असत्य है 

(d) कथन I असत्य है लेकिन कथन II सत्य है

 

प्रश्न  27. दो व्यक्तियों की वार्षिक आय 9 : 7 के अनुपात में हैं और उनके व्यय 4 : 3 के अनुपात में हैं। यदि उनमें से प्रत्येक व्यक्ति रुपये 2,000 प्रति वर्ष बचाता है, तो उनकी वार्षिक आय में क्या अंतर है? 

(a) रु. 4,000 

(b) रु. 4,500 

(c) रु. 5,000 

(d) रु. 5,500 

 

प्रश्न  28. मान लीजिए S पहले चौदह धन पूर्णांकों का एक समुच्चय है। युग्मों (a, b) की संभावित संख्या क्या है, जहाँ a, b ∊ S और a b इस प्रकार कि ab को 15 से विभाजित करने पर शेषफल 1 रहता है? 

(a) 3 

(b) 5 

(c) 6 

(d) उपर्युक्त में से कोई नहीं 

 

प्रश्न  29. एक घड़ी 1 बजने पर एक बार बजती है, 2 बजने पर दो बार बजती है, 3 बजने पर तीन बार बजती है और इसी क्रम में बजती रहती है। यदि 5 बजे यह बजने में 8 सेकंड लेती है, तो 10 बजे उसे बजने में कितना समय लगता है? 

(a) 14 सेकंड

(b) 16 सेकंड 

(c) 18 सेकंड 

(d) उपर्युक्त में से कोई नहीं 

 

प्रश्न  30. 2 इकाई त्रिज्या वाले एक वृत्त में व्यास AB, 2 इकाई लंबी जीवा को P पर अनुलंब प्रतिच्छेदित करता है। यदि AP > BP, तो AP किसके बराबर है? 

(a) (2 + √5) इकाई 

(b) (2 + √3) इकाई 

(c) (2 + √2) इकाई 

(d) 3 इकाई

 

प्रश्न  31. समीकरण x2 + px +q= 0 के एक मूल को दूसरे मूल का वर्ग होने के लिए p और q किस प्रतिबंध के अधीन होंगे? 

(a) 1 + q + q2 = 3pq 

(b) 1 + p + p2 = 3pq 

(c) p3 + q + q2 = 3pq 

(d) q3+ p + p2 = 3pq

 

प्रश्न  32. यदि संख्या N = 90 × 42 × 324 × 55, 3m से विभाज्य है, तो m का अधिकतम मान क्या है? उपर्युक्त कथनों में से कौन-से सही हैं?

(a) 8 

(b) 7 

(c) 6 

(d) 5 

 

प्रश्न  33. एक मोटरसाइकिल को 25-50 कि० मी०/घंटा के परिसर में किसी चाल से चलाए जाने पर 20 मि. लि. पेट्रोल प्रति किलोमीटर की खपत होती है और किसी अन्य चाल से चलाए जाने पर 40 मि० लि. पेट्रोल प्रति किलोमीटर की खपत होती है। यदि मोटरसाइकिल पहले 10 कि० मी० में 40 कि० मी०/घंटा की चाल से, अगले 30 कि० मी० में 60 कि. मी./घंटा की चाल से और अंतिम 10 कि० मी० में 30 कि० मी०/ घंटा की चाल से चलाई जाती है, तो मोटरसाइकिल द्वारा 50 कि० मी० की दूरी तय करने में कितने पेट्रोल की खपत होगी? 

(a) 1 लि० 

(b) 1.2 लि० 

(c) 1.4 लि० 

(d) 1.6 लि.

 

प्रश्न  34. निम्नलिखित कथनों पर विचार कीजिए : 

1. प्रत्येक धन पूर्णांक एक वास्तविक संख्या होती है। 

2. प्रत्येक वास्तविक संख्या एक परिमेय संख्या होती है।

3. प्रत्येक पूर्णांक एक वास्तविक संख्या होती है। 

4. प्रत्येक परिमेय संख्या एक वास्तविक संख्या होती 

(a) 1, 2 और 3 

(b) 1, 3 और 4 

(c) केवल 2 और 3 

(d) केवल 3 और 4 

 

प्रश्न  35. k के किस मान के लिए (x + 1),  x3 + kx2 x + 2 का एक गुणनखंड है? 

(a) 4 

(b) 3 

(c) 1 

(d) -2

 

प्रश्न  36. निम्नलिखित कथनों पर विचार कीजिए : 

1. एक धनात्मक वास्तविक संख्या m का अस्तित्व इस प्रकार है कि cos x = 2m+1 है। 

2. mn ≥ m +n, जहाँ सभी m, n धन पूर्णांकों के समुच्चय के सदस्य हैं। 

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं? 

(a) केवल 1 

(b) केवल 2

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2 

 

प्रश्न  37. असमिका 1 + 1/x – 1/x2 0 का हल क्या है? (दिया गया है कि x ≠ 0.) 

(a) x > 0 

(b) x < 0 

(c) (-1-√5)/2 ≤  x ≤ (-1+√5/2)

(d) x ≤ (-1-√5)/2 or x ≥ (-1+√5/2)

 

प्रश्न  38. बिंदुओं P(5, – 1), Q(3, – 2) और R(1, 1) में से कौन-से बिंदु असमिका निकाय x + y ≤ 4 और x – y ≥ 2 के हल में मौजूद हैं? 

(a) केवल Q और R 

(b) केवल P और R 

(c) केवल P और 0 

(d) P, Q और R 

 

प्रश्न  39. एक यात्री रेलगाड़ी 120 कि० मी० यात्रा के लिए 1 घंटा कम समय लेती है, यदि इसकी चाल सामान्य चाल से 10 कि० मी०/घंटा बढ़ाई जाती है। इसकी सामान्य चाल क्या है? 

(a) 50 कि० मी० /घंटा 

(b) 40 कि० मी०/घंटा 

(c) 35 कि० मी०/घंटा 

(d) 30 कि० मी०/घंटा 

 

प्रश्न  40. k का वह मान, जिसके लिए समीकरण निकाय 3xky-20 = 0 और 6x – 10y+40 = 0 का कोई हल नहीं है, क्या है? 

(a) 10 

(b) 6 

(c) 5 

(d) 3 

 

प्रश्न  41. धन पूर्णांकों a, b और c के लिए निम्नलिखित पर विचार कीजिए : 

1. LCM (ab, ac) = a LCM (b, c

2. HCF (ab, ac) = a HCF (b, c

3. HCF (a, b) < LCM (a, b

4. HCF (a, b), LCM (a, b) को विभाजित करता है। 

उपर्युक्त में से कौन-से सही हैं? 

(a) केवल 1 और 2 

(b) केवल 3 और 4 

(c) केवल 1, 2 और 4 

(d) 1, 2, 3 और 4

 

प्रश्न  42. तीन भाई हैं। किसी समय पर उनमें से दो की आयु का योगफल 4 वर्ष, 6 वर्ष और 8 वर्ष है। सबसे बड़े और सबसे छोटे की आयु का अंतर क्या है? 

(a) 3 वर्ष 

(b) 4 वर्ष 

(c) 5 वर्ष 

(d) 6 वर्ष 

 

प्रश्न  43. एक व्यक्ति सायं 4 बजे से सायं 5 बजे के बीच बाजार जाता है। जब वह वापस आता है, तब वह पाता है कि घड़ी में घंटे की सुई और मिनट की सुई की स्थिति को आपस में बदल गई हैं। वह कितने समय (लगभग) के लिए घर से बाहर था? 

(a) 55.38 मिनट 

(b) 55.48 मिनट 

(c) 55.57 मिनट 

(d) 55.67 मिनट 

 

प्रश्न  44. 100 व्यक्तियों का एक समूह है। उनमें से 70 व्यक्ति हिन्दी बोल सकते हैं, 60 व्यक्ति अंग्रेजी बोल सकते हैं और 30 व्यक्ति फ्रेंच बोल सकते हैं। इसके साथ ही, उनमें से 30 व्यक्ति हिन्दी और अंग्रेजी दोनों बोल सकते हैं तथा 20 व्यक्ति हिन्दी और फ्रेंच दोनों बोल सकते हैं। यदि x उन व्यक्तियों की संख्या है जो अंग्रेजी और फ्रेंच दोनों बोल सकते हैं, तो निम्नलिखित में से कौन-सा एक सही है? (मान लीजिए कि प्रत्येक व्यक्ति तीनों भाषाओं में से कम-से-कम एक भाषा बोल सकता है।) 

(a) 9 <  x  < 30 

(b) 0< x <8 

(c) x = 9

(d) x = 8 

 

प्रश्न  45. एक कपड़े का व्यापारी बुनकर से कपड़ा खरीदता है और सामान्य मीटर मापनी से 10 से० मी० लंबी मापनी का प्रयोग कर बुनकर को धोखा देता है। वह अपने ग्राहकों को लागत मूल्य पर कपड़ा बेचने का दावा करता है, लेकिन बेचते समय जिस मापनी का प्रयोग करता है वह सामान्य मीटर मापनी से 10 से० मी० छोटी है। उसका लाभ क्या है? 

(a) 20% 

(b) 21% 

(c) 22²/₉%

(d) 23⅓ % 

 

प्रश्न  46. दो नल A और B किसी टंकी को क्रमशः 60 मिनट और 75 मिनट में भर सकते हैं। एक निकास C भी है। यदि A, B और C एकसाथ खोल दिए जाएँ, तो टंकी 50 मिनट में भरती है। भरी टंकी को C द्वारा खाली करने में कितना समय लगेगा? 

(a) 100 मिनट 

(b) 110 मिनट 

(c) 120 मिनट 

(d) 125 मिनट 

 

प्रश्न  47. 1000 मी० लंबी एक दौड़ में A, B को 100 मी० या 10 सेकंड से हराता है। यदि वे एक ही स्थल से 1000 मी० की दौड़ एकसाथ आरंभ करते हैं और यदि B दौड़ की लंबाई के आधे से 50 मी० कम तक दौड़ने के पश्चात् घायल हो जाता है, जिसके कारण उसकी चाल आधी हो जाती है, तो A, B को कितने समय से हराएगा? 

(a) 65 सेकंड 

(b) 60 सेकंड 

(c) 50 सेकंड 

(d) 45 सेकंड  

 

प्रश्न  48. एक व्यक्ति के वेतन में मूल वेतन की 10% वृद्धि कर दी गई। लेकिन वेतन वृद्धि के बाद भी उसे वेतन की उतनी ही राशि प्राप्त हुई। उसे अपने वेतन की कितनी प्रतिशत राशि प्राप्त नहीं हुई? 

(a) 11% 

(b) 10% 

(c) (100/11)%

(d) (90/11)% 

 

प्रश्न  49. एक ट्रक वृत्तीय पथ पर चलते हुए केंद्र पर 36° अनुरेखित करने पर 100 मी० की दूरी तय करता है। वृत्त की त्रिज्या किसके बराबर है?

(a) 100/π  मी० 

(b) 250/π  मी० 

(c)500/π  मी० 

(d) 600π  मी० 

 

प्रश्न  50. दो खंभे एक सड़क के दोनों किनारों पर P और पर इस प्रकार लगाए जाते हैं कि P और Q को मिलाने वाली रेखा सड़क की लंबाई पर लंब होती है। एक व्यक्ति सड़क के समांतर P से x मीटर दूर चलता है और एक अन्य खम्भा R पर लगाता है। उसके बाद वह व्यक्ति उसी दिशा में x मीटर बढ़कर मुड़ जाता है और सड़क के अनुलंब y मीटर की दूरी तय करता है; जहाँ वह पाता है कि वह स्वयं, Q और R एक ही रेखा पर हैं। P और Q के बीच की दूरी (अर्थात् सड़क की चौड़ाई) मीटर में क्या है? 

(a)  x 

(b) x/2

(c)  Y

(d) 2y 

 

प्रश्न  51. मान लीजिए एक वृत्त की जीवाएँ AB और CD वृत्त के अंदर बिंदु P पर प्रतिच्छेद करती हैं। दो समकोण त्रिभुज A’P’B’ और C’Q’D’ नीचे दिए चित्रों के अनुसार इस प्रकार बनती हैं कि A’P’ = AP, B’P’ = BP, C’Q’ = CP, D’O’ = DP BTT LA‘P‘B’ = 90° = ZC’Q’D’ हैं : 

निम्नलिखित कथनों में से कौन-से सही नहीं हैं?

1. A’P’B’ और CQ’D’ समरूप त्रिभुज हैंआवश्यक नहीं कि सर्वांगसम हों। 

2. A’P’B’ और C’Q’D’ सर्वांगसम त्रिभुज हैं। 

3. A’P’B‘ और CQ’D’ समान क्षेत्रफल के . त्रिभुज हैं। 

4. A’P’B‘ और COD’ समान परिमाप के त्रिभुज 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 2 और 3 

(b) केवल 1 और 3 

(c) केवल 1, 2 और 4 

(d) 1, 2, 3 और 4 

 

प्रश्न  52. मान लीजिए कि ABC एक त्रिभुज है, जिसमें AB की एक इकाई है। D और E क्रमशः AB और AC पर इस प्रकार स्थित बिंदुएँ हैं कि BC और DE समांतर हैं। यदि त्रिभुज ABC का क्षेत्रफल, त्रिभुज ADE के क्षेत्रफल का दो गुना है, तो AD की लंबाई क्या है? 

(a) 1 इकाई

(b) ⅓  इकाई

(c) 1/√2 इकाई

(d) 1/√3 इकाई

 

प्रश्न  53. एक आयत की भुजाओं के मध्य-बिंदुओं को एक उपयुक्त क्रम में जोड़कर एक समचतुर्भुज बनाया जाता है। यदि समचतुर्भुज का क्षेत्रफल 2 वर्ग इकाई है, तो आयत का क्षेत्रफल क्या है?

(a) 2√2 वर्ग इकाई 

(b) 4 वर्ग इकाई 

(c) 4√2 वर्ग इकाई 

(d) 8 वर्ग इकाई 

 

प्रश्न  54. यदि एक सम बहुभुज का प्रत्येक अंतःकोण 140° है, तो बहुभुज के शीर्षों की संख्या किसके बराबर है? 

(a) 10

(b) 9

(c) 8

(d) 7

 

प्रश्न  55. मान लीजिए कि त्रिभुज ABC और त्रिभुज DEF इस ABC = ∠DEF, और ACB = ∠DFE और BAC = ∠EDF हैं। मान लीजिए L, BC का मध्य-बिंदु है और M, EF का मध्य-बिंदु है। निम्नलिखित कथनों पर विचार कीजिए : 

कथन I : त्रिभुज ABL और त्रिभुज DEM समरूप हैं। 

कथन II : त्रिभुज ALC, त्रिभुज DMF के सर्वांगसम है, तब भी, जब AC DF है। 

उपर्युक्त कथनों के लिए निम्नलिखित में से कौन-सा एक सही है? 

(a) कथन I और कथन II दोनों सत्य हैं कथन II, कथन I की सही व्याख्या है 

(b) कथन I और कथन II दोनों सत्य हैं लेकिन कथन II, कथन I की सही व्याख्या नहीं है 

(c) कथन I सत्य है लेकिन कथन II असत्य है 

(d) कथन I असत्य है लेकिन कथन II सत्य है 

 

प्रश्न  56. 7/11 मीटर व्यास के एक पहिए द्वारा 4 कि० मी० की दूरी तय करने में लगाए गए चक्करों की संख्या क्या होगी? 

(a)  500

(b) 1000

(c)  1700

(d) 2000

 

प्रश्न  57. किसी समद्विबाहु त्रिभुज का आधार 300 इकाई है। इसकी समान भुजाओं में से प्रत्येक की लंबाई 170 इकाई है। त्रिभुज का क्षेत्रफल क्या है? 

(a) 9600 वर्ग इकाई 

(b) 10000 वर्ग इकाई 

(c) 12000 वर्ग इकाई 

(d) उपर्युक्त में से कोई नहीं 

 

प्रश्न  58. चार समान चक्रिकाओं को इस प्रकार रखा जाता है कि प्रत्येक चक्रिका दो अन्य चक्रिकाओं को स्पर्श करती है। यदि उनके द्वारा परिबद्ध रिक्त स्थान का क्षेत्रफल 150/847 वर्ग से० मी० है, तो प्रत्येक चक्रिका की त्रिज्या किसके बराबर है? 

(a) 7/6 से० मी० 

(b) 5/6 से० मी० 

(c) 1/2 से० मी० 

(d) 5/11 से० मी०

 

प्रश्न  59. ABC और DEF समरूप त्रिभुज हैं। यदि भुजा AB और भुजा DE का अनुपात (√2 + 1) : √3 है, तो त्रिभुज ABC के क्षेत्रफल का त्रिभुज DEF के क्षेत्रफल से क्या अनुपात है?

 (a) (3-2√2): 3 

(b) (9-6√2): 2 

(c) 1:(9-6√2)

 (d) (3+2√2):2 

 

प्रश्न  60. 3 इकाई की त्रिज्या के एक वृत्त के बिंदु P पर एक बाह्य बिंदु ० से एक स्पर्श-रेखा इस प्रकार खींची जाती है कि OP = 4 इकाई है। यदि वृत्त का केंद्र C है, तो कोण COP का sine क्या है? 

(a) ⅘  

(b) ¾  

(c)

 (d) ½  

 

प्रश्न  61. p और q भुजाओं वाले एक समकोण त्रिभुज में एक अंतःवर्ग खींचा जाता है। त्रिभुज का समकोण, वर्ग का समकोण भी है। वर्ग का विकर्ण किसके बराबर है? 

(a) pq/(p+2q)

(b) pq/ (2p+q)

(c) √2pq/(p+q) 

(d) 2pa /(p+q) 

 

प्रश्न  62. यदि x/a – y/b tanθ = 1 और x/a tanθ + y/b = 1 हैं, तो x2/a2 – y2/b2  का मान क्या है? 

(a) 2sec2θ 

(b) sec2θ 

(c) cos2θ 

(d) 2cos2θ 

 

प्रश्न  63. निम्नलिखित पर विचार कीजिए : 

उपर्युक्त में से कौन-सी सर्वसमिका/सर्वसमिकाएँ है/हैं? 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d)  न तो 1 और न ही 2 

 

प्रश्न  64. यदि p = cotθ + tanθ  और q = secθ – cosθ हैं, तो (p2q)^⅔ – (q2p)^⅔ किसके बराबर है? 

(a) 0 

(b) 1 

(c) 2

(d) 3 

 

प्रश्न  65. दो प्रेक्षक एक मीनार (x मीटर ऊँची) के ठीक उत्तर में एक-दूसरे से मीटर की दूरी पर उपस्थित हैं। उन दोनों द्वारा प्रेषित मीनार के उन्नयन कोण क्रमशः 30° और 45° हैं। तो x/y किसके बराबर है? 

(a)  (√2 – 1)/ 2

(b)  (√3 – 1)/ 2

(c)  (√3 + 1)/ 2

(d) 1

 

प्रश्न  66. यदि (cos2θ – 3cosθ + 2)/ sin2θ = 1 जबकि 0 < θ < π/2 है, तो निम्नलिखित कथनों में से कौन-सा/से सही है/हैं?

 1. उपर्युक्त समीकरण को संतुष्ट करने वाले, θ के दो मान हैं।

 2. θ = 60° उपर्युक्त समीकरण से संतुष्ट है।

 नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए।

 (a) केवल 1

 (b) केवल 2 

 (c) 1 और 2 दोनों

 (d) न तो 1 और न ही 2

 

प्रश्न  67. एक त्रिभुज ABC में यदि A – B = π/2 है, तो C+2B किसके बराबर है? 

(a) 2π/3

(b) 3π/4

(c)  π 

(d) π/2

 

प्रश्न  68. निम्नलिखित में से कौन-सा, समीकरण 3-tan2θ = α(1-3 tan2θ) के बारे में सही है? (दिया गया है कि एक वास्तविक संख्या है।) 

(a) α ∊ [⅓ + 1] 

(b) α ∊ [-∞, ⅓]∪[3, ∞] 

(c) α ∊ [∞, ⅓]∪[3, ∞] 

(d) उपर्युक्त में से कोई नहीं 

 

प्रश्न  69. एक समतल में पाँच रेखाएँ हैं, जिनमें से कोई भी दो समांतर नहीं हैं। उन बिंदुओं की, जिन पर ये प्रतिच्छेद कर सकती हैं, अधिकतम संख्या क्या है? 

(a) 4 

(b) 6 

(c) 10

(d) उपर्युक्त में से कोई नहीं 

 

प्रश्न  70. केंद्र 0 और 7 से० मी० त्रिज्या के एक वृत्त पर विचार कीजिए। मान लीजिए QR, 2 से० मी० लम्बी एक जीवा है और मान लीजिए P, QR का मध्य-बिंदु है। मान लीजिए CD इसी वृत्त की, P से गुजरने वाली, एक अन्य जीवा इस प्रकार है कि CPQ न्यूनकोण है। यदि M, CD का मध्य-बिंदु है और MP = 24 से० मी० है, तो निम्नलिखित कथनों में से कौन-से सही हैं? 

1. ∠QPD = 1350 

2. यदि CP = m से० मी० और PD = n से० मी० __ हैं, तो m और n द्विघात समीकरण x2– 10x + 1 = 0 के मूल हैं। 

3. त्रिभुज OPR के क्षेत्रफल का त्रिभुज OMP के क्षेत्रफल से अनुपात 1: 22 है। 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 और 2 

(b) केवल 2 और 3

(c) केवल 1 और 3 

(d) 1, 2 और 3 

 

प्रश्न  71. मान लीजिए ABC एक त्रिभुज है, जिसमें AB = AC है। मान लीजिए बिंदुओं X का, जो कि त्रिभुज के अंदर या त्रिभुज पर इस प्रकार हैं कि BX = CX है, बिंदुपथ L है। निम्नलिखित कथनों में से कौन-से सही हैं? 

1. L, A से गुजरने वाली एक सरल रेखा है और त्रिभुज ABC का अंतः केंद्र L पर है।

2. L, A से गुजरने वाली एक सरल रेखा है और त्रिभुज ABC का लम्ब केंद्र L पर एक बिंदु है। 

3. L, A से गुजरने वाली एक सरल रेखा है और त्रिभुज ABC का केन्द्रक L पर एक बिंदु है।

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 और 2 

(b) केवल 2 और 3 

(c) केवल 1 और 3 

(d) 1, 2 और 3 

 

प्रश्न  72. केंद्र C वाले एक वृत्त पर विचार कीजिए। मान लीजिए OP, OQ क्रमशः वृत्त के बाह्य बिंदु 0 से वृत्त पर खींची गई स्पर्श-रेखाएँ हैं। मान लीजिए R, OP पर एक बिंदु और S, OQ पर एक बिंदु इस प्रकार है कि OR × SQ = OS × RP है। निम्नलिखित कथनों में से कौन-सा/से सही है/हैं? 

1. यदि X, केंद्र 0 और त्रिज्या OR का वृत्त है तथा Y, केंद्र 0 और त्रिज्या OS का वृत्त है, तो X = Y है।

2. POC + QCO = 90° नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2

 

प्रश्न  73. यदि m और n भिन्न धन पूर्णांक हैं, तो निम्नलिखित में से कौन-सा/से पूर्णांक है/हैं?

1. m/n + п/т 

2. mn(m/n + п/т)(m2 +n2)-1 

3. mn / (m2 + n2)  

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) 1 और 2 

(b) केवल 2 

(c) 2 और 3 

(d) केवल 3 

 

प्रश्न  74. सभा कक्ष के बाहर एक व्यक्ति ने मधुकर को बताया कि प्रत्येक बैठक 13/4 घंटों के बाद होती है। पिछली बैठक ठीक 45 मिनट पहले ही समाप्त हुई है और अगली बैठक अपराह्न 2 बजे होगी। मधुकर को यह सूचना किस समय प्राप्त हुई? 

(a) 10:20 पूर्वाह्न

(b) 11:30 पूर्वाह्न 

(c) 11:40 पूर्वाह्न

(d) 11:50 पूर्वाह्न 

 

प्रश्न  75. एक घर का किसी विशेष महीने का व्यय रु. 20,000 है, जिसमें से शिक्षा पर रु. 8,000, खाने पर रु. 5,900, खरीदारी पर रु. 2,800 और शेष व्यक्तिगत देखभाल पर व्यय हुए हैं। कुल व्यय का कितना प्रतिशत व्यय व्यक्तिगत देखभाल पर हुआ 

(a) 12% 

(b) 16.5% 

(c) 18% 

(d) 21.8%

 

प्रश्न  76. यदि 

जहाँ x, y और 2 धन पूर्णांक हैं, तो z किसके बराबर हैं?

(a) 1

(b) 2 

(c) 3 

(d) 4  

 

प्रश्न  77. एक वृत्तीय पथ दो संकेंद्री वृत्तीय वलयों से इस प्रकार बना है कि जब छोटे वलय को बड़े वलय की परिधि पर घुमाया जाता है, तो वह पूरे तीन परिक्रमण करता है। यदि मार्ग का क्षेत्रफल, छोटे वलय के क्षेत्रफल का n गुना है, तो n किसके बराबर है? 

(a) 4 

(b) 6 

(c) 8 

(d) 10 

 

प्रश्न  78. निम्नलिखित कथनों पर विचार कीजिए : 

1. यदि n 3 और m 3 भिन्न धनात्मक पूर्णांक हैं, तो m भुजाओं वाले एक सम बहुभुज के बहिष्कोणो का योगफल, n भुजाओं वाले एक सम बहुभुज के बहिष्कोणों के योगफल से भिन्न है? 

2. मान लीजिए m, n पूर्णांक इस प्रकार हैं कि m> n> 3 तो m भुजाओं वाले एक सम बहुभुज के अन्तः कोणों का योगफल, n भुजाओं वाले एक सम बहुभुज के अन्तः कोणों के योगफल से अधिक है और उनका योगफल (m +n)π/2 

उपर्युक्त कथनों में से कौन-सा/से सही है/हैं? 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2

 

प्रश्न  79. निम्नलिखित कथनों पर विचार कीजिए : 

1. एक सम बहुभुज का, जिसका बहिष्कोण 70° है, अस्तित्व है। 

2. मान लीजिए n ≥25 है। तो किसी भी n भुजाओं वाले सम बहुभुज का बहिष्कोण न्यून है। उपर्युक्त कथनों में से कौन-सा/से सही है/हैं? 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2 

 

प्रश्न  80. किसी त्रिभुज PQR में बिंदु X, PQ पर और बिंदु Y, PR पर इस प्रकार हैं कि XP = 1.5 इकाई, XQ= 6 इकाई, PY = 2 इकाई तथा YR = 8 इकाई हैं। निम्नलिखित में से कौन-से सही हैं? 

1. QR = 5XY 

2. QR, XY के समांतर है। 

3. त्रिभुज PYX, त्रिभुज PRQ के समरूप है। 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 और 2 

(b) केवल 2 और 3 

(c) केवल 1 और 3 

(d) 1, 2 और 3 

 

प्रश्न  81. यदि एक तिर्यक रेखा चार समांतर सरल रेखाओं का प्रतिच्छेद करती है, तो इस प्रकार बने कोणों के भिन्न मानों की संख्या क्या होगी? 

(a) 2 

(b) 4 

(c) 8 

(d) 16

 

प्रश्न  82. एक व्यक्ति पूर्व की ओर 7 कि० मी० चलता है, फिर दायें मुड़ता है तथा 3 कि० मी० चलता है, और फिर दाएँ मुड़ता है एवं 13 कि० मी० चलता है। उस व्यक्ति के प्रारम्भिक बिंदु से उसकी वर्तमान स्थिति की न्यूनतम दूरी कितनी है? 

(a) 6 कि० मी० 

(b) 3√5 कि० मी० 

(c) 7 कि० मी० 

(d) 4√5 कि० मी०

 

प्रश्न  83. ABC एक त्रिभुज है, जिसमें D, BC का मध्य-बिंदु है और E, AD का मध्य-बिंदु है। निम्नलिखित कथनों में से कौन-सा/से सही है/हैं? 

1. त्रिभुज ABC का क्षेत्रफल, त्रिभुज BED के क्षेत्रफल का चार गुना है। 

2. त्रिभुज ADC का क्षेत्रफल, त्रिभुज BED के क्षेत्रफल का दो गुना है। 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 

(b) केवल 2 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2 

 

प्रश्न  84. जैसा कि ऊपर अंकित चित्र में दर्शाया गया है, 3 मी० त्रिज्या के एक वृत्त को 1 मी० और 2 मी० त्रिज्या के अर्धवृत्त से तीन क्षेत्रों में विभाजित किया गया है। तीनों क्षेत्रों A, B और C का अनुपात क्या होगा?

(a) 2: 3:2 

(b) 1: 1: 1 

(c) 4: 3:4 

(d) 1:2 : 1 

 

प्रश्न  85. यदि √(x/y) = 10/3 – √(y/x) और x – y = 8 हैं, तो xy का मान किसके बराबर है? 

(a) 36 

(b) 24 

(c) 16 

(d)  9 

 

प्रश्न  86. ABC एक त्रिभुज है, जिसमें C समकोण है, जैसा कि ऊपर अंकित चित्र में दर्शाया गया है। 

निम्नलिखित में से कौन-सा एक सही है?

(a) AQ2 + AB2 = BP2 + PQ2

(b) AQ2 + PQ2 = AB2 + BP2 

(c) AQ2 + BP2 = AB2 + PQ2

(d) AQ2 + AP2 = BK2 + KQ2 

 

प्रश्न  87. ऊपर अंकित चित्र में AD = CD = BC है। 

∠CDB का मान क्या है? 

(a) 32° 

(b) 64° 

(c) 78° 

(d) अपर्याप्त आँकड़ों के कारण निर्धारित नहीं किया जा सकता 

 

प्रश्न  88. ABC एक समबाहु त्रिभुज है और बिंदुएँ X, Y एवं z क्रमशः BC, CA तथा AB पर इस प्रकार हैं कि BX = CY = AZ है। निम्नलिखित में से कौन-सा/से सही है/हैं? 

1. XYZ एक समबाहु त्रिभुज है। 

2. त्रिभुज XYZ, त्रिभुज ABC के समरूप है। 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) केवल 1 

(b) केवल 2 AR 

(c) 1 और 2 दोनों 

(d) न तो 1 और न ही 2

 

प्रश्न  89. 

ऊपर अंकित चित्र में p और q समांतर रेखाएँ हैं। कोण x, y और 2 के मान क्या हैं? 

(a) x = 80°, y= 40°, 2 = 100° 

(b) x = 80°, y= 50°, Z = 105° 

(c) x = 70°, y= 40°, 2 = 110° 

(d) x = 60°, y= 20°, 2 = 120° 

 

प्रश्न  90.

वे रैखिक असमिकाएँ, जिनके लिए हल समुच्चय छायित क्षेत्र द्वारा ऊपर अंकित चित्र में दर्शाया गया है, हैं 

(a) 2x+6y ≤ 21, 5x – 2y ≤ 10 

(b) 2x+6y 21, 5x – 2y ≥ 10 

(c) 2x + 6y ≥ 21, 5x – 2y ≤ 10 

(d) 2x + 6y ≥ 21, 5x – 2y ≥ 10

 

प्रश्न  91. एक चुनाव का, जिसमें छह दलों ने भाग लिया, परिणाम वृत्तारेख (पाई चार्ट) द्वारा दर्शाया गया। इस वृत्तारेख में दल A का कोण 135° था। यदि इसे 21960 मत मिले, तो कुल कितने वैध मत डाले गए थे? 

(a) 51240 

(b) 58560 

(c) 78320 

(d) 87840 

 

प्रश्न  92. 5 प्रेक्षणों के माध्य और माध्यिका क्रमशः 9 और 8 हैं। यदि प्रत्येक प्रेक्षण से 1 घटाया जाए, तो नया माध्य और नई माध्यिका होंगे, क्रमशः 

(a) 8 और 7 

(b) 9 और 7 

(c) 8 और 9 

(d) अपर्याप्त आँकड़ों के कारण निर्धारित नहीं किए जा सकते 

 

प्रश्न  93. 40 बच्चों की आयु का बंटन निम्नलिखित है :

Age (in years) 5-6 6-7 7-8 8-9 9-10 10-11
No. of Children 4 7 9 12 6 2

उपर्युक्त बारंबारता बंटन के बारे में निम्नलिखित कथनों पर विचार कीजिए : 

1. आयु बंटन की माध्यिका 7 वर्ष है। 

2. 70% बच्चे 6–9 वर्ष के आयु वर्ग में हैं। 

3. बच्चों की बहुलक आयु 8 वर्ष है। 

उपर्युक्त कथनों में से कौन-से सही हैं? 

(a) केवल 1 और 2 

(b) केवल 2 और 3 

(c) केवल 1 और 3 

(d) 1, 2 और 3 

 

प्रश्न  94. मान लीजिए 0 < i <10 के लिए xi = λi  है, जहाँ λ > 1 है। निम्नलिखित में से कौन-सा एक सही है? 

(a) AM < माध्यिका 

(b) GM < माध्यिका 

(c) GM = माध्यिका 

(d) AM = माध्यिका 

 

प्रश्न  95. मान लीजिए i = 1, 2, 3, …, 11 के लिए xi = 1/i है। निम्नलिखित में से कौन-सा एक सही नहीं है? 

(a) AM > 1/6 

(b) GM > 1/6 

(c) HM > 1/6 

(d) माध्यिका = HM

 

प्रश्न  96. ⅕ log10 3125 – 4 log10 2 +log10 32 का मान क्या है? 

(a) 0 

(b) 1 

(c) 2 

(d) 3

 

प्रश्न  97. यदि tanθ + cotθ = 4/√3 है, जहाँ 0 < θ < π/2, तो sinθ + cosθ किसके बराबर है? 

(a) 1 

(b) (√3-1) /2

(c) (√3+1) /2 

(d) √2 

 

प्रश्न  98. व्यंजक [(243 +647)2 + (243 – 647)2 ] / [243 × 243 + 647 × 647] का मान किसके बराबर है? 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

प्रश्न  99. यदि a और b ऋणात्मक वास्तविक संख्याएँ हैं और c एक धनात्मक वास्तविक संख्या है, तो निम्नलिखित में से कौन-सा/से सही है/हैं? 

1. a – b < a – c 

2. यदि a < b, तो a/c  < b/c 

3. 1/b  < 1/c 

नीचे दिए गए कूट का प्रयोग कर सही उत्तर चुनिए। 

(a) 1 

(b) केवल 2 

(c) केवल 3 

(d) 2 और 3 

 

प्रश्न  100. 

जैसा कि ऊपर अंकित चित्र में दर्शाया गया है, AD एक वृत्त का व्यास है, वृत्त का क्षेत्रफल 707 वर्ग मी० है और AB = BC = CD है। वृत्त के अंदर सभी वक्र अर्धवृत्त हैं, जिनके व्यास AD पर हैं। रु. 63 प्रति वर्ग मी० की दर से छायित क्षेत्र को सपाट करने की लागत क्या है? 

(a) रु. 29,700 

(b) रु. 22,400 

(c) रु. 14,847 

(d) उपर्युक्त में से कोई नहीं

CDS(I) Exam 2016 Maths Previous Year Paper

CDS(I) Exam 2016 

ELEMENTARY MATHEMATICS 

Q 1. If the roots of the equation lx2 + mx + m = 0 are in the ratio p:q, then

√(p/q) +  √(q/p) +√(m/l)  is equal to 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

Q 2. If has α and β as its roots, then the value of αβ is 

(a) -15 

(b) -5 

(c) O 

(d) 5 

 

Q 3. If p/x + q/y = m and q/x + p/y = n, then what is х/у equal to? 

(a) (np + mq)/(mp + nq)

(b) (np + mq)/(mp – nq

(c) (np – mq)/(mp – nq

(d) (np – mq)/(mp + nq)

 

Q 4. If a2 – by – cz = 0, ax – b2+cz = 0 and ax + by – c2 = 0, then the value of 

will be 

(a) a+b+c 

(b) 3 

(c) 1 

(d) 0 

 

Q 5. If the equations x2px + q = 0 and x2 + qxp = 0 have a common root, then which one of the following is correct? 

(a) p-q=0 

(b) p+q-2 = 0 

(c) p+q-1=0 

(d) p-q-1 = 0 

 

Q 6. If x = 2^(⅓)+2^(-⅓), then the value of 2x3 – 6x – 5 is equal to 

(a) 0

(b) 1 

(c) 2 

(d) 3 

 

Q 7. The sum and difference of two expressions are 5x2 x – 4 and x2 + 9x – 10 respectively. The HCF of the two expressions will be 

(a) (x + 1) 

(b) (x – 1) 

(c) (3x + 7) 

(d) (2x – 3) 

Q 8. If (s-a) +(s-b)+(s -c) = s, then the value of will be 

(a) 3 

(b) 1 

(c) 0 

(d) -1 

 

Q 9. If the polynomial x6 + px5 + qx4x2x – 3 is divisible by (x4 – 1), then the value of p2 +q2 is 

(a) 1 

(b) 9 

(c) 10 

(d) 13 

 

Q 10. Let p and q be non-zero integers. Consider the polynomial 

A(x) = x2 + px +

It is given that (xm) and (x – km) are simple factors of A(x), where m is a non-zero integer and k is a positive integer, k > 2. Which one of the following is correct? 

(a) (k + 1)2 p2 = kq 

(b) (k + 1)2q = kp2 

(c) k2q = (k + 1)p2 

(d) k2p2 = (k + 1)2

 

Q 11. Let m be a non-zero integer and n be a positive integer. Let R be the remainder obtained on dividing the polynomial xn + mn by (x-m). Then 

(a) Ris a non-zero even integer 

(b) Ris odd, if m is odd 

(c) R= s2 for some integer s, if n is even 

(d) R = t3 for some integer t, if 3 divides

 

Q 12. If 4x2y = 128 and 33x32y – 9xy = 0, then the value of x + y can be equal to 

(a) 7 

(b) 5 

(c) 3 

(d) 1 

 

Q 13. If the linear factors of ax2 – (a2 +1)x+ a are p and q, then p+q is equal to 

(a) (x – 1)(a + 1) 

(b) (x + 1)(a + 1) 

(c) (x – 1)(a – 1) 

(d) (x + 1)(a – 1)

 

Q 14. If then bx2 – ax + b is equal to (given that b ≠ 0) 

(a) o 

(b) 1 

(c) ab 

(d) 2ab

 

Q 15. If a3 = 117 + b3 and a = 3+b, then the value of a+b is (given that a>0 and b>0) (a) 7 

(b) 9 

(c) 11 

(d) 13 

 

Q 16. If the sum of the roots of ax2 + bx + c = 0 is equal to the sum of the squares of their reciprocals, then which one of the following relations is correct? 

(a) ab2+ bc2 = 2a2

(b) ac2 + bc2 = 2b2

(c) ab2 + bc2 = a

(d) a2 + b2 + c2 = 1 

 

Q 17. Consider the following statements in respect of the expression 

where n is an integer : 

1. There are exactly two values of n for which Sn = 861. 

2. Sn = S-(n+1) and hence for any integer m, we have two values of n for which Sn = m. 

Which of the above statements is/are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 18. Consider the following statements in respect of two different non-zero integers p and q

1. For (p+q) to be less than (p-q), q must be negative. 

2. For (p+q) to be greater than (P-9), both p and q must be positive. 

Which of the above statements is/are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2 

 

Q 19. If a/b = b/c = c/a then which of the following is/are correct?

1. (b3 + c3 + d3)/(a3 + b3 + c3) = d/a

2. (a2 + b2 + c2)/(b2 + c2 + d2) = a/d

Select the correct answer using the code given below. 

(a) l only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 20. 710 – 510 is divisible by 

(a) 5 

(b) 7 

(c) 10 

(d) 11

 

Q 21. Let a two-digit number be k times the sum of its digits. If the number formed by interchanging the digits is m times the sum of the digits, then the value of m is 

(a) 9 – k 

(b) 10 – k 

(c) 11 – k 

(d) k – 1

 

Q 22. A man walking at 5 km/hour noticed that a 225 m long train coming in the opposite direction crossed him in 9 seconds. The speed of the train is 

(a) 75 km/hour 

(b) 80 km/hour 

(c) 85 km/hour 

(d) 90 km/hour 

 

Q 23. (sin 35°/ cos 55°)2 – (cos 55°/ sin 35° )2 + 2 sin 30° is equal  to

(a) -l 

(b) 0

(c) 1 

(d) 2

 

Q 24. A cyclist moves non-stop from A to B, a distance of 14 km, at a certain average speed. If his average speed reduces by 1 km per hour, he takes 20 minutes more to cover the same distance. The original average speed of the cyclist is 

(a) 5 km/hour 

(b) 6 km/hour 

(c) 7 km/hour 

(d) None of the above

 

Q 25. If a sum of money at a certain rate of simple interest per year doubles in 5 years and at a different rate of simple interest per year becomes three times in 12 years, then the difference in the two rates of simple interest per year is 

(a) 2% 

(b) 3% 

(c) 31% 

(d) 44% 

 

Q 26. Let ABC and A‘B‘C’ be two triangles in which AB > A‘B’, BC> B’C‘ and CA > C’A’. Let D, E and F be the mid points of the sides BC, CA and AB respectively. Let D’, E’ and F be the midpoints of the sides B’C’, C’A’ and A‘B‘ respectively. Consider the following statements : 

Statement I : 

AD > A‘D’, BE > B’E’ and CF > C’F’ are always true. 

Statement II : 

(AB2 + BC2 + CA2)/(AD2 + BE2 +CF2) = (A‘B’2+ B’C2+ C’A2 )/(A’D2+ B’E 2 + C’F 2 )

Which one of the following is correct in respect of the above statements?

(a) Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I 

(b) Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I 

(c) Statement I is true but Statement II is false 

(d) Statement I is false but Statement II is true

 

Q 27. The annual incomes of two persons are in the ratio of 9:7 and their expenses are in the ratio of 4:3. If each of them saves 2,000 per year, what is the difference in their annual incomes? 

(a) 4,000 

(b) 4,500 

(c) 5,000 

(d) 5,500 

 

Q 28. Let S be a set of first fourteen natural numbers. The possible number of pairs (a, b), where a, b S and a ≠ b such that ab leaves remainder 1 when divided by 15, is 

(a) 3 

(b) 5 

(c) 6

(d) None of the above 

 

Q 29. A clock strikes once at 1 o’clock, twice at 2 o’clock and thrice at 3 o’clock, and so on. If it takes 8 seconds to strike at 5 o’clock, the time taken by it to strike at 10 o’clock is 

(a) 14 seconds 

(b) 16 seconds 

(c) 18 seconds 

(d) None of the above 

 

Q 30. In a circle of radius 2 units, a diameter AB intersects a chord of length 2 units perpendicularly at P. If AP > BP, then AP is equal to 

(a) (2+√5) units 

(b) (2 +√3) units 

(c) (2+ √2) units 

(d) 3 units 

 

Q 31. Under what condition on p and q, one of the roots of the equation x2 + px +q = 0 is the square of the other? 

(a) 1 + q + q2 = 3pq 

(b) 1 + p + p2 = 3pq 

(c) p3 + q + q2 = 3pq 

(d) q3+ p + p2 = 3pq

 

Q 32. What is the maximum value of m, if the number N = 90 × 42 × 324 × 55 is divisible by 3m

(a) 8 

(b) 3 

(c) 6 

(d) 5

 

Q 33. A bike consumes 20 mL of petrol per kilometre, if it is driven at a speed in the range of 25-50 km/hour and consumes 40 ml of petrol per kilometre at any other speed. How much petrol is consumed by the bike in travelling a distance of 50 km, if the bike is driven at a speed of 40 km/hour for the first 10 km, at a speed of 60 km/hour for the next 30 km and at a speed of 30 km/hour for the last 10 km? 

(a) 1 L 

(b) 1.2 L 

(c) 1.4 L 

(d) 1.6 L

 

Q 34. Consider the following statements : 

1. Every natural number is a real number. 

2. Every real number is a rational number. 

3. Every integer is a real number. 

4. Every rational number is a real number. 

Which of the above statements are correct? 

(a) 1, 2 and 3 

(b) 1, 3 and 4 

(c) 2 and 3 only 

(d) 3 and 4 only 

 

Q 35. For what value of k is (x + 1) a factor of x3+ kx2x + 2? 

(a) 4 

(b) 3 

(c) 1 

(d) -2 

 

Q 36. Consider the following statements : 

1. There exists a positive real number m such that cos x = 2m+1

2. mn ≥ m +n for all m, n belonging to a set of natural numbers. 

Which of the above statements is/are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 37. The solution of the inequation 1 + 1/x – 1/x2 0 is (given that x ≠ 0) 

(a) x > 0 

(b) x < 0 

(c) (-1-√5)/2 ≤  x ≤ (-1+√5/2)

(d) x ≤ (-1-√5)/2 or x ≥ (-1+√5/2)

 

Q 38. Which of the points P(5, -1), Q(3, -2) and R(1, 1) lie in the solution of the system of inequalities x + y ≤ 4 and x-y ≥ 2 ? 

(a) Q and R only 

(b) P and R only 

(c) P and Q only 

(d) P, Q and R 

 

Q 39. A passenger train takes 1 hour less for a journey of 120 km, if its speed is increased by 10 km/hour from its usual speed. What is its usual speed? 

(a) 50 km/hour 

(b) 40 km/hour 

(c) 35 km/hour 

(d) 30 km/hour

 

Q 40. The value of k, for which the system of equations 3x – ky – 20 = 0 and 6x – 10y + 40 = 0 has no solution, is 

(a) 10 

(b) 6 

(c) 5 

(d) 3

 

Q 41. Consider the following in respect of natural numbers a, b and c: 

1. LCM (ab, ac) = a LCM(b, c) 

2. HCF(ab, ac) = a HCF(b, c) 

3. HCF(a, b) < LCM(a, b) 

4. HCF(a, b) divides LCM(a, b). 

Which of the above are correct? 

(a) 1 and 2 only 

(b) 3 and 4 only 

(c) 1, 2 and 4 only 

(d) 1, 2, 3 and 4 

 

Q 42. There are three brothers. The sums of ages of two of them at a time are 4 years, 6 years and 8 years. The age difference between the eldest and the youngest is 

(a) 3 years 

(b) 4 years 

(c) 5 years 

(d) 6 years 

 

Q 43. A person goes to a market between 4 p.m. and 5 p.m. When he comes back, he finds that the hour hand and the minute hand of the clock have interchanged their positions. For how much time (approximately) was he out of his house? 

(a) 55.38 minutes 

(b) 55.48 minutes 

(c) 55.57 minutes 

(d) 55-67 minutes

 

Q 44. In a gathering of 100 people, 70 of them can speak Hindi, 60 can speak English and 30 can speak French. Further, 30 of them can speak both Hindi and English, 20 can speak both Hindi and French. If x is the number of people who can speak both English and French, then which one of the following is correct? (Assume that everyone can speak at least one of the three languages.) 

(a) 9 < x < 30

(b) 0 ≤ x < 8

(c) x = 9 

(d) x = 8

 

Q 45. A cloth merchant buys cloth from a weaver and cheats him by using a scale which is 10 cm longer than a normal metre scale. He claims to sell cloth at the cost price to his customers, but while selling uses a scale which is 10 cm shorter than a normal metre scale. What is his gain? 

(a) 20% 

(b) 21% 

(c) 22²/₉%

(d) 23⅓ % 

 

Q 46. Two pipes A and B can fill a tank in 60 minutes and 75 minutes respectively. There is also an outlet C. If A, B and C are opened together, the tank is full in 50 minutes. How much time will be taken by C to empty the full tank? 

(a) 100 minutes 

(b) 110 minutes 

(c) 120 minutes 

(d) 125 minutes 

 

Q 47. In a race of 1000 m, A beats B by 100 m or 10 seconds. If they start a race of 1000 m simultaneously from the same point and if B gets injured after running 50 m less than half the race length and due to which his speed gets halved, then by how much time will A beat B

(a) 65 seconds 

(b) 60 seconds 

(c) 50 seconds 

(d) 45 seconds

 

Q 48. The salary of a person is increased by 10% of his original salary. But he received the same amount even after the increment. What is the percentage of his salary he did not receive? 

(a) 11% 

(b) 10% 

(c) (100 /11)% 

(d) (90 /11)% 

 

Q 49.  A truck moves along a circular path and describes 100 m when it has traced out 36° at the centre. The radius of the circle is equal to 

(a) 100/π m

(b) 250/π m

(c)500/π m

(d) 600π m

 

Q 50. Two poles are placed at P and on either side of a road such that the line joining P and Q is perpendicular to the length of the road. A person moves x metre away from P parallel to the road and places another pole at R. Then the person moves further x metre in the same direction and turns and moves a distance y metre away from the road perpendicularly, where he finds himself, Q and R on the same line. The distance between P and Q (i.e., the width of the road) in metre is 

(a)  x 

(b) x/2

(c)  Y

(d) 2y 

 

Q 51. Suppose chords AB and CD of a circle intersect at a point P inside the circle. Two right-angled triangles A’P’B‘ and C’O’D’ are formed as shown in the figures below such that A‘P’ = AP, B’P’ = BP, C’Q’ = CP, D’Q’ = DP and LA‘P’B’ = 90° = ZC’O’D’:  Which of the following statements are not correct?

1. A’P’B’ and C’O’D’ are similar triangles, but need not be congruent. 

2 A‘P’B‘ and C’Q’D‘ are congruent triangles. 

3. A‘P’B’ and C’O‘D’ are triangles of the same area. 

4. A‘P’B’ and C‘Q’D’ are triangles of the same perimeter. 

Select the correct answer using the code given below. 

(a) 2 and 3 only 

(b) 1 and 3 only 

(c) 1, 2 and 4 only 

(d) 1, 2, 3 and 4 

 

Q 52. Suppose ABC is a triangle with AB of unit length. D and E are the points lying on AB and AC respectively such that BC and DE are parallel. If the area of triangle ABC is twice the area of triangle ADE, then the length of AD is 

(a) ½ unit 

(b) ⅓ unit

(c) 1/√2 unit

(d) 1/√3 unit

 

Q 53. A rhombus is formed by joining midpoints of the sides of a rectangle in the suitable order. If the area of the rhombus is 2 square units, then the area of the rectangle is 

(a) 2√2 square units 

(b) 4 square units 

(c) 4√2 square units 

(d) 8 square units 

 

Q 54. If each interior angle of a regular polygon is 140°, then the number of vertices of the polygon is equal to 

(a)  10

(b)  9

(c)  8

(d) 7

 

Q 55. Let the triangles ABC and DEF be such that ∠ABC = ∠DEF, ∠ACB = ∠DFE and ∠BAC = ∠EDF. Let L be the midpoint of BC and M be the midpoint of EF. Consider the following statements : 

Statement I : 

Triangles ABL and DEM are similar.

Statement II : 

Triangle ALC is congruent to triangle DMF even if AC ≠ DF. 

Which one of the following is correct in respect of the above statements?

(a) Both Statement I and Statement II are true and Statement II is the correct explanation of Statement I 

(b) Both Statement I and Statement II are true but Statement II is not the correct explanation of Statement I

(c) Statement I is true but Statement II is false 

(d) Statement I is true but statement II is true 

 

Q 56. The number of rounds that a wheel of diameter 7/11 metre will make in traversing 4 km will be 

(a) 500 

(b) 1000 

(c) 1700 

(d) 2000 

 

Q 57. The base of an isosceles triangle is 300 units and each of its equal sides is 170 units. Then the area of the triangle is 

(a) 9600 square units

(b) 10000 square units 

(c) 12000 square units 

(d) None of the above 

 

Q 58. Four equal discs are placed such that each one touches two others. If the area of empty space enclosed by them is 150/847 square centimetre, then the radius of each disc is equal to

(a) 7/6 cm

(b) 5/6 cm

(c) 1/2 cm 

(d) 5/11 cm 

 

Q 59. ABC and DEF are similar triangles. If the ratio of side AB to side DE is (2+1): √3, then the ratio of area of triangle ABC to that of triangle DEF is 

(a) (3-2√2):3 

(b) (9-6√2):2

(c) 1:(9-6√2) 

(d) (3+2√2):2 

 

Q 60. A tangent is drawn from an external point o to a circle of radius 3 units at P such that OP = 4 units. If C is the centre of the circle, then the sine of the angle COP is 

(a) ⅘  

(b) ¾  

(c) ⅗ 

(d) ½  

 

Q 61. A square is inscribed in a right-angled triangle with legs p and q, and has a common right angle with the triangle. The diagonal of the square is given by 

(a) pq/(p+2q)

(b) pq/ (2p+q)

(c) √2pq/(p+q) 

(d)2pa /(p+q)

 

Q 62. If x/a – y/b tanθ = 1 and x/a tanθ + y/b = 1, then the value of x2/a2 – y2/b2  is 

(a) 2sec2θ 

(b) sec2θ 

(c) cos2θ 

(d) 2cos2θ 

 

Q 63. Consider the following: 

Which of the above is/are identity/ identities? 

(a) 1 only 

(b) 2 only

(c) Both 1 and 2

(d) Neither 1 nor 2 

 

Q 64. If p = cotθ + tanθ and q = secθ – cosθ, then (p2q)^⅔ – (q2p)^⅔ is equal to

(a) o 

(b) 1 

(c) 2

(d) 3 

 

Q 65. Two observers are stationed due north of a tower (of height x metre) at a distance y metre from each other. The angles of elevation of the tower observed by them are 30° and 45° respectively. Then x/y is equal to 

(a)  (√2 – 1)/ 2

(b)  (√3 – 1)/ 2

(c)  (√3 + 1)/ 2

(d) 1

 

Q 66. If (cos2θ – 3cosθ + 2)/ sin2θ = 1 where 0 < θ < π/2 then which of the following statements is/are correct? 

1. There are two values of θ satisfying the above equation. 

2. θ = 60° is satisfied by the above equation.

 Select the correct answer using the code given below. 

(a) 1 only

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2 

 

Q 67. In a triangle ABC if A-B= π/2 then C+2B is equal to 

(a) 2π/3

(b) 3π/4

(c)  π

(d) π/2

 

Q 68. Which of the following is correct in respect of the equation 3-tan2θ = α(1-3 tan2θ) (Given that a is a real number.) 

(a) α ∊ [⅓ + 1] 

(b) α ∊ [-∞, ⅓]∪[3, ∞] 

(c) α ∊ [∞, ⅓]∪[3, ∞] 

(d) None of the above 

 

Q 69. There are five lines in a plane, no two of which are parallel. The maximum number of points in which they can intersect is 

(a) 4 

(b) 6 

(c) 10 

(d) None of the above 

 

Q 70. Consider a circle with centre at O and radius 7 cm. Let QR be a chord of length 2 cm and let P be the midpoint of QR. Let CD be another chord of this circle passing through P such that ∠CPQ is acute. IfM is the midpoint of CD and MP = √24 cm, then which of the following statements are correct? 

1. ∠OPD = 135° 

2. If CP = m cm and PD = n cm, then m and n are the roots of the quadratic equation x2 – 10x + 1 = 0.

3. The ratio of the area of triangle OPR to the area of triangle OMP is 1:2√2. 

Select the correct answer using the code given below.

(a) 1 and 2 only

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3 

 

Q 71. Let ABC be a triangle in which AB = AC. Let L be the locus of points X inside or on the triangle such that BX = CX. 

Which of the following statements are correct? 

1. L is a straight line passing through A and in-centre of triangle ABC is on L. 

2. L is a straight line passing through A and orthocentre of triangle ABC is a point on L. 

3. L is a straight line passing through A and the centroid of triangle ABC is a point on L. 

Select the correct answer using the code given below. 

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3

 

Q 72. Consider a circle with centre at C. Let OP, OQ denote respectively the tangents to the circle drawn from a point o outside the circle. Let R be a point on OP and S be a point on OQ such that OR × SQ = OS × RP. Which of the following statements is/are correct? 

1. If X is the circle with centre at O and radius OR, and Y is the circle with centre at O and radius OS, then X = Y. 

2. ∠ POC+ QCO = 9Select the correct answer using the code given below. 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 73. If m and n are distinct natural numbers, then which of the following is/are integer/integers? 

1. m/n + п/т 

2. mn(m/n + п/т)(m2 +n2)-1 

3. mn / (m2 + n2

Select the correct answer using the code given below. 

(a) 1 and 2 

(b) 2 only 

(c) 2 and 3 

(d) 3 only 

 

Q 74. Outside the meeting room, Madhukar was told by a person that each meeting takes place after 13/4 hours. The last meeting has been over just 45 minutes ago and the next meeting will take place at 2 p.m. At what time did Madhukar receive this information? 

(a) 10:20 a.m. 

(b) 11:30 a.m. 

(c) 11:40 a.m. 

(d) 11:50 a.m.

 

Q 75. The expenditure of a household for a certain month is Rs. 20,000, out of which Rs. 8,000 is spent on education, Rs. 5,900 on food, Rs. 2,800 on shopping and the rest on personal care. What percentage of expenditure is spent on personal care? 

(a) 12% 

(b) 16.5% 

(c) 18% 

(d) 21.8% 

 

Q 76. If 

where x, y and z are natural numbers, then what is z equal to? 

(a) 1 

(b) 2 

(c) 3 

(d) 4 

 

Q 77. A circular path is made from two concentric circular rings in such a way that the smaller ring when allowed to roll over the circumference of the bigger ring, it takes three full revolutions. If the area of the pathway is equal to n times the area of the smaller ring, then n is equal to 

(a) 4 

(b) 6 

(c) 8 

(d) 10 

 

Q 78. Consider the following statements : 

1. If n ≥ 3 and m 3 are distinct positive integers, then the sum of the exterior angles of a regular polygon of m sides is different from the sum of the exterior angles of a  regular polygon of n sides. 

2. Let m, n be integers such that m > n > 3. Then the sum of the interior angles of a regular polygon of m sides is greater than the sum of the interior angles of a regular polygon of n sides, and their sum is (m + n)π/2

Which of the above statements is/are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 79. Consider the following statements : 

1. There exists a regular polygon whose exterior angle is 70°. 

2. Let n ≥ 5. Then the exterior angle of any regular polygon of n sides is acute. 

Which of the above statements is/are correct? 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2

 

Q 80. In a triangle PQR, point X is on PQ and point Y is on PR such that XP = 1.5 units, XQ = 6 units, PY = 2 units and YR = 8 units. Which of the following are correct? 

1. QR = 5XY 

2. QR is parallel to XY. 

3. Triangle PYX is similar to triangle PRO.

Select the correct answer using the code given below. 

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3 

 

Q 81. If a transversal intersects four parallel straight lines, then the number of distinct values of the angles formed will be

(a) 2 

(b) 4

(c) 8 

(d) 16

 

Q 82. A person travels 7 km eastwards and then turns right and travels 3 km and further turns right and travels 13 km. What is the shortest distance of the present position of the person from his starting point? 

(a) 6 km 

(b) 3√5 km 

(c) 7 km 

(d) 4√5 km 

 

Q 83. ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Which of the following statements is/are correct? 

1. The area of triangle ABC is equal to four times the area of triangle BED. 

2. The area of triangle ADC is twice the area of triangle BED. 

Select the correct answer using the code given below. 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2 

 

Q 84. A circle of 3 m radius is divided into three areas by semicircles of radii 1 m and 2 m as shown in the figure above. The ratio of the three areas A, B and C will be 

(a) 2:3:2 

(b) 1:1:1 

(c) 4:3:4 

(d) 1:2:1 

 

Q 85. If √(x/y) = 10/3 – √(y/x) and x – y = 8, then the value of xy is equal to 

(a) 36 

(b) 24 

(c) 16 

(d) 9

 

Q 86. ABC is an equilateral triangle and X, Y and Z are the points on BC, CA and AB respectively such that BX = CY = AZ. 

Which of the following is/are correct?

(a) AQ2 + AB2 = BP2 + PQ2

(b) AQ2 + PQ2 = AB2 + BP2 

(c) AQ2 + BP2 = AB2 + PQ2

(d) AQ2 + AP2 = BK2 + KQ2 

 

Q 87. In the figure given above, AD = CD = BC. 

What is the value of ∠CDB?

(a) 32° 

(b) 64° 

(c) 78° 

(d) Cannot be determined due to insufficient data

 

Q 88. ABC is a triangle right angled at C as shown in the figure above. 

Which one of the following is correct? 

1. XYZ is an equilateral triangle. 

2. Triangle XYZ is similar to triangle ABC. 

Select the correct answer using the code given below. 

(a) 1 only 

(b) 2 only 

(c) Both 1 and 2 

(d) Neither 1 nor 2 

 

Q 89. In the figure given above, p and q are parallel lines. What are the values of the angles x, y and z? 

(a) x = 800, y = 40°, z = 100° 

(b) x = 80°, y = 50°, z = 105° 

(c) x = 70°, y = 40, z = 110° 

(d) x = 60°, y=20, z = 120° 

 

Q 90. The linear inequations, for which the shaded area in the figure given above is the solution set, are 

(a) 2x+6y ≤ 21, 5x – 2y ≤ 10 

(b) 2x+6y 21, 5x – 2y ≥ 10 

(c) 2x + 6y ≥ 21, 5x – 2y ≤ 10 

(d) 2x + 6y ≥ 21, 5x – 2y ≥ 10 

 

Q 91. The election result in which six parties contested was depicted by a pie chart. Party A had an angle 135° on this pie chart. If it secured 21960 votes, how many valid votes in total were cast? 

(a) 51240 

(b) 58560 

(c) 78320 

(d) 87840 

 

Q 92. The mean and median of 5 observations are 9 and 8 respectively. If 1 is subtracted from each observation, then the new mean and the new median will respectively be 

(a) 8 and 7 

(b) 9 and 7 

(c) 8 and 9 

(d) Cannot be determined due to insufficient data 

 

Q 93. The age distribution of 40 children is as follows :

Age (in years) 5-6 6-7 7-8 8-9 9-10 10-11
No. of Children 4 7 9 12 6 2

Consider the following statements in respect of the above frequency distribution : 

1. The median of the age distribution is 7 years. 

2. 70% of the children are in the age group 6-9 years. 

3. The modal age of the children is 8 years. 

Which of the above statements are correct? 

(a) 1 and 2 only 

(b) 2 and 3 only 

(c) 1 and 3 only 

(d) 1, 2 and 3

 

Q 94. Suppose xi = λi for 0 ≤ i ≤ 10, where λ > 1. 

Which one of the following is correct? 

(a) AM < Median 

(b) GM < Median 

(c) GM = Median 

(d) AM = Median 

 

Q 95. Suppose xi  =1/ i= for i = 1, 2, 3, …, 11. 

Which one of the following is not correct? 

(a) AM  > 1/6 

(b) GM > 1/6 

(c) HM > 1/6 

(d) Median = HM 

 

Q 96. The value of  ⅕ log10 3125 – 4 log10 2 +log10 32 is 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

Q 97. If tanθ + cotθ = 4/√3, where 0 < θ < π/2, then sinθ + cosθ is equal to 

(a) 1 

(b) (√3-1) /2

(c) (√3+1) /2 

(d) √2 

 

Q 98. The value of the expression [(243 +647)2 + (243 – 647)2 ] / [243 × 243 + 647 × 647] is equal to 

(a) 0 

(b) 1 

(c) 2 

(d) 3 

 

Q 99. If a and b are negative real numbers and c s a positive real number, then which of the following is/are correct? 

1. a-b < a

2. If a < b, then a/c  < b/c

3. 1/b  < 1/c

Select the correct answer using the code given below. 

(a) 1 

(b) 2 only 

(c) 3 only 

(d) 2 and 3

 

Q 100. 

AD is the diameter of a circle with area 707 m2 and AB = BC = CD as shown in the figure above. All curves inside the circle are semicircles with their diameters on AD. What is the cost of levelling the shaded region at the rate of Rs. 63 per square metre? (a) 29,700 

(b) 22,400 

(c) 14,847 

(d) None of the above

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