This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
whats similes dose romeo use to convey juliets beauty |
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Answer» William Shakespeare is known for his deft use of language in his works. In “Romeo and Juliet” through the character of Romeo we come to know how effectively similes are used to convey the message. Romeo in his speech uses two similes to describe the beauty of Juliet. First simile compares her beauty to a rich jewel worn by an Ethiopian. The comparison here is so effective that the jewel shines brighter against the dark skin background. Such a beauty is very expensive and rare to be seen on earth. The second simile is used to compare Juliet’s beauty to a snowy dove which stands out as it troops with crows referring to her companions. They are outshone by her heavenly beauty. This is how Romeo conveys Juliet’s beauty. Romeo glorifies the beauty of Juliet. She teaches the torches to burn bright. Shelooks like a rich jewel hanging in an Ethiope’s ear. Her beauty is too rich and too dear. She dances like a snowy dove among crows. After the dance, Romeo wants to touch the hand of Juliet. So that, his rude hand would be blessed. He swears that he had never seen true beauty till that night. Romeo praises Juliet's beauty with many similes. He compares her beauty to a rich jewel in an Ethiope's ear. Her beauty is too rich for use and expensive on earth. Then he compares her as white as snowy dove which differs from the crows. In the opening lines, he exaggerates that Juliet's beauty surpasses the brightness of light. His comparison shows his passion and excess possessiveness towards Juliet. |
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| 2. |
Two coins are tossed simultaneously. Find the probability of getting at least one head. |
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Answer» Given that two coins are tossed simultaneously. Hence the possible outcomes are {(H, H), (H, T), (T, H), (T, T)} which are equally likely. Hence, total possible outcomes = n(S) = 4. Let the event E be getting at least one head. Therefore E = {(H, H), (H, T), (T, H)}, Hence the number of outcomes favourable to E is n(E) = 3. \(\therefore\) P(E) = \(\frac{n(E)}{n(S)} = \frac{3}{4}\). Hence, the probability of getting at least one head is \(\frac{3}{4}\). |
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| 3. |
Which of these is a RATIONAL number?A. 3π B. 5√5 C. 0.3466666... D. 0.345210651372849... |
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Answer» Correct option is: C. 0.3466666... |
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| 4. |
Which of these is the polynomial whose zeroes are 1/3 and (-3/4)?A. 12x2 + 5x − 3B. 12x2 − 5x − 3C. 12x2 + 13 + 3D. 12x2 − 13x − 3 |
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Answer» Correct option is: A. 12x2 + 5x − 3 |
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| 5. |
Using ruler and compass how will you construct ∆ABC, if AB=3.5, BC=6 and angle ABC=60^o?(a) Draw line BC=6 cm and an angle CBA=600. Cut off AB=3.5. Join AC, triangle ABC is the required triangle(b) Draw line BC=6 cm and AB= 3.5 and then angle ABC=60o, ABC is the required triangle(c) Draw line AB= 3.5cm and cut off AB = 6 cm at any point and make angle CBA=600(d) Draw angle CBA= 600 and make |
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Answer» The correct choice is (a) Draw line BC=6 cm and an angle CBA=600. Cut off AB=3.5. Join AC, triangle ABC is the required triangle To explain I would say: Figure below shows the construction:- Draw line BC=6 cm with a ruler and an angle CBA=600 with the compass. Cut off AB=3.5 by compass. Join AC, triangle ABC is the required triangle. |
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| 6. |
Which of these numbers can be expressed as a product of two or more prime numbers? i) 15 ii) 34568 iii) (15 × 13)A. only (ii) B. only (iii) C. only (i) and (ii) D. all - (i), (ii) and (iii) |
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Answer» Correct option is: D. all - (i), (ii) and (iii) |
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| 7. |
1245 is a factor of the numbers p and q.Which of the following will ALWAYS have 1245 as a factor? (i) p + q (ii) p × q (iii) p ÷ qA. only (ii) B. only (i) and (ii) C. only (ii) and (iii) D. all - (i), (ii) and (iii) |
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Answer» Correct option is: B. only (i) and (ii) |
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| 8. |
Two statements are given below - one labelled Assertion (A) and the other labelled Reason (R). Read the statements carefully and choose the option that correctly describes statements (A) and (R).Assertion (A): 9 x + 12 y - 7 = 0 and 6 x + 8 y - 14 = 0 form a consistent pair of linear equations.Reason (R): A pair of linear equations, px + qy + r = 0 and fx + gy + h = 0, has no solution if \(\frac{p}{f}=\frac{q}{g}≠\frac{r}{h}.\)A. Both (A) and (R) are true and (R) is the correct explanation of the (A). B. Both (A) and (R) are true but (R) is not the correct explanation of the (A). C. (A) is true but (R) is false. D. (A) is false but (R) is true. |
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Answer» D. (A) is false but (R) is true. |
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| 9. |
Match the items in List-I with items in List-II and select the correct answer from the codes given belowList - IList – IIA. TaxationI. M. Govinda RaoB. AgricultureII. C. RangarajanC. Monetary PolicyIII. Arvind PangarihaD. Indian Economy, Planningand State Level ReformsIV. Ashok GulatiE. Fiscal PolicyV. Parthasarthy ShomeCodes:1. A - II, B - IV, C - I, D - III, E - V2. A - I, B - IV, C - III, D - II, E - V3. A - V, B - IV, C - II, D - III, E - I4. A - V, B - IV, C - III, D - II, E - I |
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Answer» Correct Answer - Option 3 : A - V, B - IV, C - II, D - III, E - I The correct answer is A - V, B - IV, C - II, D - III, E - I.
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| 10. |
Gondwana coalfields are found in (a) Assam (b) Madhya Pradesh (c) Meghalaya (d) Jammu and Kashmir |
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Answer» Gondwana coalfields are found in Madhya Pradesh. |
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| 11. |
India has eight coastal states but more than half the sea salt is made along the Gujarat coast because (a) Gandhiji started the salt movement in Gujarat (b) Low rainfall and relative humidity are ideal for the production of salt through evaporation of sea water (c) Kandla port exports salt (d) The salinity of sea water is very high near the Gujarat coast |
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Answer» (b) Low rainfall and relative humidity are ideal for the production of salt through evaporation of sea water |
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| 12. |
Examine the relations between liberty and equality |
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Answer» There is an inseparable relation between liberty and equality. Liberty and equality are like the two sides of a coin. Equality without liberty is meaningless. Here are their relations: a. Somebody who takes the words in their bare meaning, he may argue that they are contradictory. b. Full liberty will deny it to many people and thus destroy equality. c. A certain amount of control on a person’s liberty comes in full equality. d. The concept of full liberty and full equality can only be a myth. e. It is in practical situations that liberty and equality are practiced. It is not in an imaginary situation. Only in a stable society, they can be practiced. f. Liberty on a large scale will ensure that everybody gets it. g. Equality on a large scale is inevitable for the continued existence of liberty., h. Therefore liberty and equality are complementary and not contradictory |
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| 13. |
Match column B & C with Column A.ABCNatural equalityEqual social statusAll can enter common pubic placesCivil equalityBom equal and freeEquality for allPolitical equalityEqual opprotunities to earn and saveEqual pay for equal workSocial equalityAll have equal rightsAll are before the lawEconomic equalityEqual chances to get positions of powerVoting right |
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| 14. |
Explain Natural and Economic equalities. |
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Answer» Equality is of different kinds. Two of them are Natural Equality and Economic equality. Natural equality is what Nature has given us as a gift. It is our natural right. The three natural equalities are: Freedom to live, freedom to have rights and, freedom to own property. Only in a society where there is economic equality, other forms of equality can have any meaningful existence. The relation between Natural Equality and Economic equality is shown below: Natural Equality: This idea came up connecting it to natural law. It. says that nature created everyone equal. The spokespersons of natural equality say that inequalities are human creations and society should be freed from them. Natural Equality is a mere ideal. Even the concept that nature created all as equals itself is untrue. Economic equality means the resources of the nation should be enjoyed equally by all. It talks about the eradication of poverty. Although complete equality is impossible, at least a person’s basic needs should be fulfilled. It does not want resources to be monopolized in a few hands. Everyone should have the right to work, to get reasonable wages and also rest. Ideologies like Socialism stress economic equality. |
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| 15. |
Prepare a seminar report on three different types of equality such as political equality, economic equality and social equality. |
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Answer» The Political Science students of Class XI of Kozhikode Government Higher Secondary School conducted a seminar on the topic “Three Different Types of Equality”. The students of the Class were divided into 3 groups and they discussed the relevant portions of the Text. The leaders of each group presented their views a) Political Equality: To ensure political equality in a society, people should have the opportunities to take part in active politics. Only if they have the right to play their role in the affairs the nation, there will be political equality there. They should have following rights: i) To participate in the election of the government. ii) To contest in the elections. iii) The right to hold public office. iv) The right to creatively criticize the government through the print and electronic media and through speeches. The right to criticize the government using any legal medium. vi) The right to form political parties. b) Economic Equality: The meaning of Economic Equality is that all citizens must be able to enjoy the nation’s resources equally. This is important for the eradication of poverty. To achieve Economic Equality, the following should be ensured: i) Make circumstances so that all citizens can earn their livelihood. ii) All citizens should have enough income to meet their needs. iii) There should be no gross inequality in wealth in the society. iv) There should be no economic exploitation of man by man. The distribution of the means of production and wealth should be controlled, aiming at the welfare of all in the society. c) Social Equality: This means that all in the society have equal social status. Nobody should have special rights. All should have opportunities to develop their personality. In short, nobody should be given any special consideration in name of caste, religion, race or riches. The Human Rights Declaration by the UN is good for ensuring social equality. To ensure social equality, equal opportunities should be provided to all. There should no divisions on the basis of caste, religion, race, riches, and gender. There should be Rule of law which ensures that all are equal before the law. Casteism must be abolished completely. The government and the society should do all they can to uplift the marginalized communities and bring them into the mainstream society. Conclusion: After the presentation, a meaningful discussion followed. The teacher added more points. It was a good seminar. |
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| 16. |
What is Bailadila famous for? (a) Bauxite (b) Iron ore (c) Copper (d) Coal |
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Answer» Iron ore is Bailadila famous for. |
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| 17. |
What kind of equality is the right to vote? |
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Answer» Political equality is equality is the right to vote. |
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| 18. |
……….. inequality is the inequality that results from the differences in abilities and features that come by birth. |
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Answer» Natural inequality is the inequality that results from the differences in abilities and features that come by birth. |
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| 19. |
What do you mean absolute equality? |
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Answer» Absolute or complete equality is an impossible concept. Man, even by nature, is not equal in physical and mental abilities. There are differences among people in body structure, capabilities, attitudes, likings, etc. Lasky felt that since people’s needs and capabilities are different, it is impossible to behave with them equally. The needs and capabilities of a mathematician are not the same as a brick-maker. Therefore it is not possible to see or consider them equally. |
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| 20. |
Write the meaning of term infotainment. |
| Answer» Infotainment refers to the type of media, usually television, which provides a combination of information and entertainment both. | |
| 21. |
Why coastal cities were favoured by the colonial rulers |
| Answer» The coartal cites were favoured hy the colonial rulers as primary commodities could be easily txported and manufactured goods could be cheaply imported. | |
| 22. |
What changes have been brought by the technology in newspaper industry? |
| Answer» The use of internet and LAN has made the process of newspaper production fully automatic. Moreo rer, use of newsmaking softwares has helped in givi ig customised look to the newspapers. In this auomatic chain, the use of paper is completely eliminated. | |
| 23. |
What role does pressure groups play in Indian democracy? |
| Answer» Pressure groups play a vital role in the process of government. A pressure group is an interest group that operates to promote the interest of its members through lobbying and external inducement of pressure. It is generally an association of pewple with a common economic interest who try to influence government action in legislation, admin strative procedures or judicial decisions. | |
| 24. |
“The exact balance of power between the Central and the State government varies from one federation to another”. Discuss it. |
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Answer» The exact balance of power between the central and the state government varies from one federation to another due to the nature of route adopted by the country like: |
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| 25. |
“Political parties are controlled by the rich.” Do you agree with this statement? |
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Answer» Yes, I do. The fact that more than 100 members of the Indian Parliament are billionaires justifies this statement. |
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| 26. |
Derive an expression for the self inductance of a long solenoid of N number of turns containing a medium of relative permeability |
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Answer» We know that, \(B = \mu_0ni\) \(\because n = \frac Nl\) \(B = \frac{\mu_0Ni}l\) \(\phi = NB.A\) \(\phi = \frac{\mu_0N^2iA}{l}\) \(\because \phi = Li\) \(Li = \frac{\mu_0N^2 iA}l\) \(L = \frac{\mu_0AN^2}l\) |
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| 27. |
Give an assessment of democratic movements in Afghanistan. |
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Answer» Afghanistan is a landlocked country in the mountains of South Central Asia, sharing borders with Pakistan to the South East and Iran to the West. The Government of Mohamed Daoud was overthrown and he was assassinated by a group of Nur Mohamed Taraki, Babrak Karmol and Amin Taha in a miliary coup in April 1978. Mohamed Taraki became the President, Prime Minister and General Secreatry of People’s Democratic Party of Afghanistan (PDPA) in 1978 and the country was renamed as Democratic Republic of Afghanisthan(DRA). As per Peshawar Accord, Democratic Republic of Afghanistan (DRA) became Islamic State of Afghanistan (ISA) and an Interim government was set up for the purpose of transition. In the meanwhile Taliban the Islamic fundamentalist group bombed Kabul in 1995. The UN interactions with the Afghan delegation lead to Bonn Agreement of 2001. It was intended for a broad based, gender sensitive, multi-ethnic and fully representative government. The 11th September 2001, attack on World Trade Organisation (WTO) by Taliban led by A1 -Qaeda leader Osama Bin laden attracted the attention of the whole world. As a result, the North Atlantic Treaty Organisation (NATO) alliances rushed towards Afghanisthan to hunt for Talibanis with the support of the US Government. The democratic process began with the adoption of new constitution in 2004 and later Presidential elections were held. In 2005 election was held to Paliament and provinces. The New National assembly was inaugurated in December 2005. The NATO allies were able to prevent the Al- Qaeda and Talibanis to come to power and strengthened democracy within the framework of Islamic Republic. As a result of these developments, in 2009 elections, Dr Hamid Karzai became the President. Afghanistan is continuing ‘ the democratic process. |
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| 28. |
Explain the structure of State Administration. |
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Answer» The State Administration consists of the Governor, the Chief Minister, the Council of Ministers and Secretaries to these offices. State Secretariat: For the sake of administrative convenience, the structure of the government of the state is divided into many departments, A ministry may consist of two or more Departments and a Minister is in charge of all of them. The Minister is the political head of the Department whose administrative head is the Principal Secretary, a career civil servant. The Secretariat is located in the state capitals and consists of offices of Ministers, Secretaries, Departments and Sections. The Secretariat is the Highest office of the government. It is the Principle Executive instrument as well. The Secretariat ensures ‘Objectivity, continuity and constituency’ in the administration. If is the main authority to frame rules and principles of procedure for the functioning of the government. The primary responsibility of the Secretariat is to assist the ministers in the following matters. 1. Formulating and modifying legislation from time to time. 2. Planning and budget formulation. 3. Co-ordinating with the centre and other states. 4. Promoting organizational competency. 5. Answering questions in the Assembly. The Secretariat is divided into a number of administrative departments. It consists of Principal Secretary, Secretary, Joint Secretary, Deputy Secretary and Under Secretary. The number of Secretariat departments differ from state to state. Departments common to most of the states, the following are : 1. Departments of Personnel and Administrative Reforms (DPAR) 2. Home and Transport. 3. Finance and Planning. 4. Education. 5. Revenue and Excise. 6. Public Works Department (PWD) 7. Forests. 8. Agriculture 9. Energy 10. Co-operation 11. Labour and Employment. 12. Food and Civil Supplies. 13. Rural Development and Panchayat Raj (RDPR) 14. Law and Parliamentary affairs. 15. Social Welfare etc, |
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| 29. |
When was Tashkent Agreement reached between India and Pakistan?(a) 1975 (b) 1971 (c) 1962 (d) 1965 |
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Answer» In 1965 Tashkent Agreement reached between India and Pakistan. |
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| 30. |
What is the general meaning of globlisation? (A) Nationdisation(B) Internationalisation(C) Polarisation(D) Unification |
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Answer» Unification is the general meaning of globlisation. |
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| 31. |
Globlisation included of which area.(a) Economic(b) Social(c) Culture (d) Political |
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Answer» Globlisation included of Economic area. |
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| 32. |
Which has been mostly affected by Globalisation?(a) Poor(b) Industrialist(c) Capilalist (d) None of these |
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Answer» Poor has been mostly affected by Globalisation. |
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| 33. |
Who is most affected from Globlisation(a) Poor(b) Capitalist(c) Industrialist (d) No Body |
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Answer» Poor is most affected from Globlisation. |
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| 34. |
Compare any three Micro minerals on the basis of their sources and benefits. |
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Answer» Iron: Part of a molecule (hemoglobin) found in red blood cells that carries oxygen in the body; needed for energy metabolism Organ meats; red meats; fish; poultry; shellfish (especially clams); egg yolks; legumes; dried fruits; dark, leafy greens; iron-enriched breads and cereals; and fortified cereals Zinc: Part of many enzymes; needed for making protein and genetic material; has a function in taste perception, wound healing, normal fetal development, production of sperm, normal growth and sexual maturation, immune system health Meats, fish, poultry, leavened whole grains, vegetables Iodine: Found in thyroid hormone, which helps regulate growth, development, and metabolism Seafood, foods grown in iodine-rich soil, iodized salt, bread, dairy products |
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| 35. |
Common people’s life was thoroughly depicted through the Subaltern history. Give your opinions. |
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Answer» Common people’s life was thoroughly depicted through the Subaltern history. Points • begining in Marxist historiography • role of Antonio Gramsci • contribution of Ranjit Guha • Indian thinkers - Mahatma Phule ‘Gulamgiri’, Dr Ambedkar ‘Who Were the Shudras’. |
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| 36. |
Which fields are included in Applied Art? |
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Answer» Points: Industrial sector, adverisement sector, back drop, technology essential for television, editing, computer graphics, ornaments etc |
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| 37. |
Which of the following was not a common social reform attempted by all the Hindu social reformers of the 19th century (a) emancipation of women (b) monogamy (c) female education (d) untouchability |
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Answer» (d) untouchability |
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| 38. |
As a young citizen of Sri Lanka, what measures would you have suggested to your government at that time, if given a chance? |
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Answer» As a citizen of Sri Lanka I would have suggested the following to the government : - 1. Tamils in Sri Lanka shouldn't be discriminated as it results in riots. 2. Tamils should be given a independent territory out of some part of Sri lanka . 3. Sinhalas should not be favoured in universities and government jobs. 4. There should be equal political rights given to both ethnic groups (Tamils & Sinhalas) |
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| 39. |
State the world cultural heritage sites located in Maharashtra and give information about any one of them. |
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Answer» World heritage sites in Maharashtra. Points: • Ajintha caves • Verul caves • Gharapuri / Elephanta caves • Chhatrapati Shivaji Terminus Railway Station, Mumbai • Information about any one monument - Where that monument is located, architecture, historical importance needs of conservation etc. |
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| 40. |
What are the Economic consequences of migration in India ? |
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Answer» A major benefit for the source region is the remittance sent by migrants. Remittances from the international migrants are one of the major sources of foreign exchange. Punjab, Kerala and Tamil Nadu receive very significant amount from their international migrants. The amount of remittance sent by the internal migrants is very meagre as compared to the international migrants, but it plays an important role in the growth of economy of the source area. Remittances are mainly used for food, repayment of debts, treatment, marriages, children’s education, agricultural inputs, construction of houses, etc. Thousands of poor villages of Bihar, Uttar Pradesh, Odisha, Andhra Pradesh, Himachal Pradesh, etc. remittance works as a lifeline for their economy. Migration from the rural areas of eastern Uttar Pradesh, Bihar, Madhya Pradesh and Odisha to the rural areas of Punjab, Haryana and western Uttar Pradesh accounted for the success of their Green Revolution strategy for agricultural development. Besides this, unregulated migration to the metropolitan cities of India has caused overcrowding. Development of slums in industrially developed states such as Maharashtra, Gujarat, Karnataka, Tamil Nadu and Delhi is a negative consequence of unregulated migration within the country. |
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| 41. |
Critically analyse the Socio economic benefits that are being experienced by the implementation of Integrated Tribal Development Project in Bharmaur district of Himachal Pradesh. |
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Answer» Under the fifth five-year plan, the tribal sub-plan was introduced in 1974and Bharmaur was designated as one of the five Integrated Tribal Development Projects (ITDP) in Himachal Pradesh. This project drastically improved the life of the Gaddis and narrowed the gap in the level of development between Bharmaur and other areas of Himachal Pradesh. A lot of development was made in the field of transport and communication, agriculture and allied activities and social and community services. The most significant contribution of the ITDP -in the region is the development of infrastructure in terms of schools, healthcare facilities, potable water, roads, electricity and communication network. The villages located along river Ravi in Holi and Khani areas are the main beneficiaries of infrastructural development. The social benefits from ITDP are the tremendous increase in literacy rate, improvement in sex-ratio and decline in child marriages. The cultivation of pulses and other cash crops has increased in Bharmaur region. In addition to this, now only ten percent of the total households practice transhumance. |
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| 42. |
Assertion: The Cold War was neither a war or an armed military conflict nor a condition of peace. It was rather a state of uneasy peace. Reason: The Cold War was not being fought by clever moves, propagandist activities and diplomatic conflicts. a) Both the Assertion and the Reason are correct and the Reason is the correct explanation of the Assertion. b) Both the Assertion and the Reason are correct but the Reason is not the correct explanation of the Assertion. c) The Assertion is incorrect but the Reason is correct. d) The Assertion is correct but the Reason is incorrect. |
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Answer» (d) The Assertion is correct but the Reason is incorrect |
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| 43. |
The term 'the largest garage sale in history' is associated with:- a) Cuban Missile Crisis b) Gulf War c) Bolshevik Revolution d) Shock Therapy |
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Answer» (d) Shock Therapy |
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| 44. |
Show that the product of three positive integers is divisible by 6. |
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Answer» Let n be any positive integer. Since any positive integer is of the form 6q or 6q + 1 or 6q + 2 or 6q + 3 or 6q + 4, 6q + 5. If n = 6q, n (n + 1) (n + 2) = 6q (6q + 1) (6q + 2), which is divisible by 6 If n = 6q + 1 n (n + 1) (n + 2) = (6q + 1) (6q + 2) (6q + 3) n (n + 1) (n + 2) = 6 (6q + 1) (3q + 1) (2q + 1) Which is divisible by 6 If n = 6q + 2 n (n + 1) (n + 2) = (6q + 2) (6q + 3) (6q + 4) n (n + 1) (n + 2) = 12 (3q + 1) (2q + 1) (2q + 3), Which is divisible by 6. Similarly we can prove others. Hence it is proved that the product of three consecutive positive integers is divisible by 6. |
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| 45. |
A straight line passing through a point on a circle is |
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Answer» A straight line which passes through two points on a circle is a secant. |
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| 46. |
The decimal expansion of 49/40 will terminate after how many places of decimal? |
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Answer» \(\frac{49}{40}\) = \(\frac{49}{4×10}\) = \(\frac{\frac{49}{4}}{10}\) = \(\frac{12.25}{10}\) = 1.225. The decimal expansion of 49/40 is 1.225 which is terminating after 3 places of decimal. |
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| 47. |
The decimal expansion of 141/120 will terminate after how many places of decimal. |
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Answer» 141/120=1.175 hence it terminate after 3 decimal places |
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| 48. |
Write the algebra of the following sequences and its sum of n terms 1.5, 10, 15, 20, ……….. 2. 6, 11, 16, 21, ……… 3. 4, 9,14,19, ………. 4. 3, 8, 13, 18, ………….. |
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Answer» 1. 5, 10, 15, 20, First term f = 5 Common difference = d = 10 – 5 = 5 General form xn = dn + (f – d) = 5n + (5 – 5) = 5n xn = 5n Sum = \(\frac{1}{2}\)n(x1 + xn) = \(\frac{1}{2}\)n(5 + 5n) = \(\frac{5}{2}\)n(n + 1) 2. 6, 11, 16,21, ………….. First term f = 6 Common difference d = 11 - 6 = 5 General form xn = dn + (f - d) = 5n + (6 - 5) = 5n xn = 5n + 1 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(6 + 5n + 1) = \(\frac{n}{2}\)(5n + 7) 3. 4, 9, 14, 19, …………. First term f = 4 Common difference d = 9 - 4 = 5 f - d = 4 - 5 = -1 General form xn = dn + (f - d) xn = 5n - 1 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(4 + 5n - 1) = \(\frac{n}{2}\)(5n + 3) 4. 3, 8, 13, 18, ………… First term f = 3 Common difference d = 8 - 3 = 5 f - d = 3 - 5 = -2 General form xn = dn + (f - d) xn = 5n - 2 Sum = \(\frac{n}{2}\)(x1 + xn) = \(\frac{n}{2}\)(3 + 5n - 2) = \(\frac{n}{2}\)(5n + 1) |
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| 49. |
The angles of a quadrilateral are in an arithmetic sequence. The largest angle is 150°. Find other angles. |
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Answer» Sum of four angles of a quadrilateral = 360° Angles are in arithmetic sequence, so first angle + 3 x common difference (d) = 150° i.e., f + 3d = 150 The four angles are f, f + d, f + 2d, f + 3d. f + f + d + f + 2d + f + 3d = 360° f + f + d + f + 2d + 150 = 360° 3f + 3d = 360° - 150 = 210 3(f + d) = 210 f + d = \(\frac{210}{3}=70\) The four angles are f, 70, f + 2d, 150 . f + 2d = \(\frac{150+70}{2}=110\) Common difference = 110 – 70 = 40 First angle = 70 – 40 = 30 So, the four angles are 30, 70, 110, 150 |
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| 50. |
Write the sequence of numbers which leaves the remainder 3 on dividing by 5 and 10. |
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Answer» The number which can be divided by 5 and 10 must be divisible by 10. ∴ The sequence of numbers which leaves the remainder 3 on dividing by 5 and 10 is 3, 13, 23, 43,……… |
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