Jmet 2005 Original Paper

JMET 2005 Original Paper SECTION 1: VERBAL COMMUNICATION (1 − 40) Directions: In Questions 1 − 4, select relationship similar to the pair in capitals: 1. GUEST : INVITATION (A) visitor : letter subpoena

the

pair

(B) applicant : application

of

words

that

best

(C) petitioner : plea

expresses

a

(D) witness :

Solution: A guest comes to a place, when he is given an invitation, A witness comes to a court, when he gets a subpoena. Choice (D) 2. SCHOOL : FISH (A) group : deer (B) badge : honor (C) leaf : book (D) mischief : monkeys Solution: School is the collective noun for fish. Mischief is the collective noun for monkeys. Choice (D) 3. FLIMSY : STURDY (A) prognosis : diagnosis (B) gauche : eloquent (C) flippant : earnest (D) drizzle : downpour Solution: The words flimsy and sturdy are antonyms and they are also adjectives. Flippant and earnest bear a similar relationship. Choice (C) 4. GREGARIOUS : OUTGOING (A) groggy : lucid (B) grouchy : irritable sociable

(C) aggressive : extrovert

(D) gritty :

Solution: Gregarious and outgoing are synonymous. Grouchy and irritable is the pair which bears the same relationship. Choice (B) Directions: Questions 5 & 6 relate the paragraphs given below: Number of words in this passage : 236 At the peak of the Battle of Britain, Winston Churchill said in the Commons on August 20, 1940 that “never in the field of human conflict was so much owed by so many to so few”. Little did he then know how a majority of Indians would echo his sentiments, fifty years on, about 1.2 million of their compatriots. The latter have catapulted India into the international hi-tech orbit, lifting the contribution of the services sector in gross domestic product (GDP) to 52% - leaving industry and agriculture jostling for space in the rear. The latest is that software and Information Technology (IT) services are expected to account for 7.7% of GDP by 2008, with software exports of around $ 87 billion. That, in turn, should generate a demand for IT hardware of $ 50 billion. The software industry employs more than 80000 professionals with around 260,000 in software exports, 28,000 in the domestic software market, 280,000 in captive software user organizations, and 245,000 in the ITES-BPO sector. In fact, it has been planned to reach a teledensity of 9 per hundred by 2007 for New Delhi, to attain which 90 million direct exchange lines would be needed! That compares with just 20 million lines in 2000. Even India’s cellular phone market is growing and investments exceeding Rs. 25,000 crore are expected in the next three years, with a subscriber base of 120 million by 2008. 5. According to the author, (A) 1.2 million Indians are significantly influencing the economy of India. (B) Industry and agriculture have contributed to 48% of our GDP.

(C) New Delhi will need Rs. 25,000 crore to invest in 90 million direct exchange lines. (D) 800,000 software professionals are expected to account for 7.7% of GDP by 2008. Explanatory Note: The second sentence supports option A as the answer. All the other options are factually incorrect. Choice (A) 6. The underlined sentence in the first paragraph implies that (A) a large nation was indebted to a small army. (B) the small hi-tech sector in India has helped us go global. (C) quality mass education must be sacrificed at the altar of hi-tech education. (D) the majority should be indebted to the minority. Explanatory Note: The underlined sentence in the first para means a large nation was indebted to a small army which was Churchill’s statement made in the midst of war. Choice (A) Directions: Questions 7 − 12 are based on the passage given below: Number of words in this passage : 332 The guy sitting grimly alone in the corner of the office may not be anti-social. He may, in fact, even be working. That could be one of the inferences drawn from a recent survey conducted by America Online and Salary.com. Socializing with co-workers, spacing out and surfing the Web could, says the survey, cost UScompanies as much as $ 759 billion in salary. The survey of 10,044 employees debunks some popular myths. Men and women were found to have wasted an equal amount of time at work. Older workers were significantly more attentive. As compared to the overall average of two hours a day being wasted, lunch-time not counted, workers over 55 were found to have wasted just 30 minutes. While 33% of the respondents said they wasted time because they didn’t have enough work, 25% said they did so because they were underpaid. However, not all time-wasting activities are detrimental to the organization. Salary.com senior vice-president Bill Coleman felt that personal use of the Internet could even be positive since it could generate new business ideas if not contribute to a happier work environment. “There is such a thing as creative waste. Not all wasted time is bad”, Coleman was quoted by Reuters as saying. A survey on time-wasting in Indian organizations could throw up interesting results. The most irritating waste of time is when those working inside the office are asked for directions by visitors. With receptionists of security staff also doing duty at the switchboard for telephone calls, it is usually the employee nearest the entrance who has to field queries ranging from “Where is so and so?” to “Where is the toilet?”. However, the most formally sanctioned way of wasting time in the Indian organization remains the office-meeting. Organizations are known to hold meetings at the drop of a hat. Even a decision to cut down on meetings would be taken at a meeting! The conference-hall is bigger than the canteen which serves a more useful purpose! 7. Out of the following four options, which is the odd one out? (A) Men and women waste an equal amount of time. (B) Meeting are one of the most common ways to waste time. (C) Younger workers waste less time. (D) Some time-wasting activities are good for organizations. Explanatory Note: Other than option C, which is not true, all the other options contain ideas which can be inferred from the passage. The fourth sentence in the first para backs statement A, the fifth statement in the second para supports option B and the fourth last sentence in the first para implies statement D. So, option C is the odd man out. Choice (C) 8. The passage does NOT deal with: (A) Efficient time management in organizations. (C) Time wasting in Indian organizations. Explanatory Note:

(B) US Workers’ Survey (D) Creative waste

The passage revolves around time-wasting and does not talk about efficient time management. ‘US worker’s survey’ is implied by the 3rd and 4th sentence of the passage. Choice (A) 9. The central idea of the passage relates to: (A) common ways of wasting time in Indian organization. (C) why time is wasted in organizations.

(B) time-wasting in organizations. (D) ill-effects of time-wasting activities.

Explanatory Note: The passage talks about time-wasting in organisations in general and is not restricted to India. It does not touch upon the why of time wasting or its illeffects. Choice (B) 10. The phrase “Creative waste” refers to: (A) Wastage of time that is unproductive. (C) Time wasted during meetings.

(B) Wastage of time that is productive. (D) Answering queries of visitors.

Explanatory Note: The sentence ‘Not all wasted time is bad' means it could sometimes be productive. Refer to the last three sentences in the first para where the term ‘creative waste’ has been used. Choice (B) 11. One of the most common time-wasting activities in Indian organizations is: (A) Answering telephone calls (B) Sitting alone in a corner. (C) Holding meetings (D) Surfing the Web Explanatory Note: Refer to para.

the

sixth

sentence

in the Choice (C)

official

second

12. From the passage, it may be inferred that: (A) More than 5000 respondents admitted to having wasted time at work. (B) The conference hall is a more useful place than the meal canteen. (C) Men waste more time than women at work. (D) On an average, more than two hours of a work day are wasted. Explanatory Note: Option A is the answer. Out of the 10,044 employees who were surveyed, the passage provides facts of 58%(33% + 25%) having admitted to wasting time, which comes to more than 5000 respondents. None of the other statements can be inferred. In option D, note that more than two hours has been mentioned, where as the passage states that two hours are wasted on an average. Choice (A) Directions: In Questions 13 − 17 choose the word which is OPPOSITE in meaning to each of the underlined words: 13. Evidence of his moral turpitude influenced the committee’s decision about his promotion. (A) courage (B) baseness (C) timidity (D) honorableness Solution: ‘Turpitude’, in relation to morals, refers to depravity or wickedness. Its opposite would be ‘honorableness’. Choice (D) 14. Observing his agitation, we tried to propitiate the speaker. (A) provoke (B) placate (C) prohibit (D) facilitate Solution: ‘Propitiate’ means to appease. Its opposite is ‘provoke’ meaning annoy. Choice (A) 15. Muskan’s ubiquitous smile helped to cheer us up in times of misery. (A) small (B) rare (C) common (D) frequent Solution:

deliberately

‘Ubiquitous’ means present everywhere. ‘rare’. Choice (B) 16. His description of the event was rather pejorative. (A) laudatory (B) derogatory (C) predictive

Its

opposite

is

(D) abusive

Solution: ‘Pejorative’ means expressing contempt or disapproval. Its opposite in ‘laudatory’ (expressing praise and commendation). Choice (A) 17. Efforts at managing differences have, till date, been more episodic than otherwise. (A) intermittent (B) eventful (C) continuous (D) half-hearted Solution: ‘Episodic’ means occurring at irregular intervals. Its opposite is continuous. Choice (C) Directions: In Questions 18 − 22 choose the option that is nearly similar in meaning to the capitalized word. 18. INVALIDATE (A) invariable

(B) nullify

(C) naught

(D) intractable

Solution: To make something lose its legal force is to invalidate, which is a synonym of nullify. Choice (B) 19. CONSISTENCY (A) congruity (B) constancy (C) compatibility (D) conformity Solution: When something always happens in a similar way, it is marked by consistency. Repeating itself indicates that there is constancy. Hence, the two are synonymous Choice (B) 20. STUMPED (A) bambozzled (B) subdued (C) subjugated (D) terrorized Solution: One is stumped when one is confused and is unable to answer a question. We are bamboozled or confused when we are tricked or puzzled by a situation. Choice (A) 21. DYSPEPTIC (A) dynamic (B) dwarfish (C) crotchety (D) crafty Solution: Dyspeptic means to be bad-tempered, peevish or irritable, which is the same as being crotchety. Choice (C) 22. MISBEGOTTEN (A) misapprehension

(B) misconception

(C) purloined

(D) delusion

Solution: Something which is illegitimate is misbegotten (not got through fair means) Purloined, which means ill-obtained or stolen is the closest synonym. Note, that all other options contain words in the noun form. Choice (C) Directions: In Statements 23 − 27 only one of the four options is grammatically correct. Identify that correct option. 23. (A) Any organization, large or small, trades with many different people and companies. (B) Any organizations, large or small, trade with many different people and companies. (C) Any organization, large or small, trade with many different people and company. (D) Any organizations, large or small, trade with many different people and companies. Solution:

Option A is right. In B and D ‘organizations’ (plural) cannot go with ‘Any’. In C ‘trade’ does not agree with the subject ‘organization’. Choice (A) 24. (A) Seating arrangements influenced the kind of interaction that takes place. (B) Seating arrangement’s influence the kind of interaction that takes place. (C) Seating arrangements influence the kind of interactions that take place. (D) Seating arrangements influences the kind of interaction that takes place. Solution: In A the tenses are mixed up – ‘influenced’ (past), ‘takes place’ (present). In B the apostrophe makes the sentence wrong. C is right. In D there is no subject-verb agreement [(arrangements (plural) cannot take influences (verb for singular)]. Choice (C) 25. (A) Using too much jargons during communication might obliterate main issue. (B) Using too much jargon during communication might obfuscate main issue. (C) Using too much jargons during communication might obdurate main issue. (D) Using too much jargon’s during communication might obfuscate main issue. Solution: ‘Jargon’ is an uncountable noun and does not take ‘s’. Hence A and C can be ruled out. The apostrophe makes D wrong. Only B is right. Choice (B) 26. (A) In the course of there journey, they were able to absolve a lot of local cultures. (B) In the coarse of their journey, they were able to absorb a lot of local culture. (C) In the course of their journey, they were able to observe a lot of local culture’s. (D) In the course of their journey, they were able to observe a lot of local culture. Solution: ‘There’ in place of ‘their’ makes option A wrong. Use of ‘coarse’ (rough) instead of ‘course’ makes B wrong. The apostrophe makes C wrong. Choice (D) 27. (A) Your advise does not seem to have had any effect. (B) Your advice does not seem to have had any effect. (C) Your advice do not seems to have had any effect. (D) Your advise does not seem to have had any effects. Solution: ‘Advice’ is used as a noun hence ‘se’ (verb form) is wrong (rules out A and D). In C ‘do not’ does not agree with the subject ‘advice’. Choice (B) Directions: Questions 28 − 31 consist of groups of jumbled phrases. Only one of the four options, when unscrambled, can be a grammatically correct sentence. Disregarding punctuation errors, identify the correct option. 28. (A) and the environmental authority / several type of complaints / by area residents / has been lodged with the plant (B) protagonist’s who defeated / great stories portrays / enemy of / there community (C) how to be / the good manager / and a fox / both a hedgehog (D) own priorities / involves sorting / it always / at your Solution: It always involves sorting out your own priorities. Option D, then, makes a grammatically correct sentence. The others do not. Choice (D) 29. (A) a heart-on-heart / I decided to have / talk with him (B) duped by a /I was / fly-in-the-right operator (C) throw my /I decided to / hat in the ring (D) came like / the announcement / a bolt from the heavens

Solution: I decided to throw my hat in the ring. This is a grammatically correct sentence (Option C). Options A, B and D, though they make complete sentences are not the answers as the idiom in them are wrong. In A it should be ‘heart to heart talk’. In B it should be ‘fly-by-night operator’ and D it should be ‘a bolt from the blue’. Choice (C) 30. (A) to the station / I haled a taxi / to take me (B) spend his last few / he preferred to / days in relative anonymity (C) reached to me today / about my appointment / the officious communication (D) get the / pronunciation correct / you can’t never Solution: He preferred to spend his last few days in relative anonymity. Option B makes a complete sentence. In A ‘haled’ is wrong it should be ‘hailed’. [Hale (adj) means strong and healthy while hail (verb) means to call]. In C officious (adj ‘asserting authority or interfering in an annoyingly domineering way’) is used instead of ‘official’ (adj. ‘of or relating to an authority or public body and its activities and responsibilities’). In D we have double negative (can’t never) which is wrong. Choice (B) 31. (A) communication skills as among / business students rank / the most important they have to master (B) as my replacement is / I cannot leave my desk / being late to come (C) still the hot issue’s/this is why / celebrity endorsement are (D) are expected / will attend the summit / MD’s and CEO’s of top companies Solution: Business students rank communication skills as among the most important they have to master. Option A is a grammatically correct sentence. None of the others are. Choice (A) Directions: Statements 32 − 36 consist of four phrases each. One of the phrases (A, B, C or D) is grammatically incorrect. Identify that incorrect phrase. 32. (A) When assertion is used with the win-win approach /(B) and with others who also uses the winwin approach / (C) each party can consider the needs of the other and / (D) move towards a solution that satisfies as many needs as possible. Solution: The error is in B – since the subject in B is ‘others’ the verb should be ‘use’ not ‘uses’. Choice (B) 33. (A) It is always / (B) been hard to change (C) the Indian car buyer’s perception (D) when it comes to designs. Solution: The error is in A – The ‘been’ in B requires that A should be ‘It has always’. Choice (A) 33. (A) It is always / (B) been hard to change (C) the Indian car buyer’s perception (D) when it comes to designs. Solution: The error is in A – The ‘been’ in B requires that A should be ‘It has always’. Choice (A) 34. (A) In a conflict, speak in a pleasant way, / (B) send appropriate non-verbal messages to the other person / (C) and match yours non-verbal behaviour / (D) to the spoken message. Solution: The error is in C – it should be ‘your’ ‘yours’. Choice (C) 35. (A) To live, to love / (B) to serve, and / (C) also admiration are what / (D) I aspire for.

not

Solution: In C it should be ‘admire’ (verb) not admiration (noun) to be parallel to ‘live’, ‘love’, ‘serve’ in the earlier parts of the sentence.

Choice (C) 36. (A) However, the advantages of teamwork can be minimized / (B) and the benefits increased / (C) if members (particularly those who lead them / (D) is aware of the methods for improving performance and making decisions. Solution: The error is in option D since the subject is ‘members’ the verb in D should be ‘are’ not ‘is’. Note: The sentence is illogical A should have ‘disadvantage’ not ‘advantage’. Choice (D) Directions: Read the following passage to answer Questions 37 − 40. Choose the correct option in each of the questions. Number of words in this passage : 299 We define the entrepreneur as an individual who identifies opportunities, and on the basis of his/her ability, desire and confidence, makes judgements and decisions pertaining to the coordination of resources in order to exploit those opportunities for personal gain. Personal gain in this context could be financial, fame, prestige or satisfaction from helping other people. This definition extends the concept beyond the narrow limits of profit maximization. It is important to note that entrepreneurial decision making is distinct from routine managerial / administrative decision making by corporate executives. However, this definition does include innovative venture decisions by executives and others in an already existing organization as legitimate entrepreneurial function. The entrepreneurial function consists of three main elements: recognition of opportunities, judgmental decision and coordination of resources. In terms of organization, the entrepreneur will be involved in risk bearing, autonomous decision making and residual claims. Every person is potentially an entrepreneur. However, the extent of its manifestation in actual entrepreneurial activities, business or otherwise, is a matter of political, social economic, cultural and ideological influences. Put differently, every human being has an innate ability to become an entrepreneur even though this ability is not always translated into action because of a variety of limiting factors. This observation allows us to propose that there are more than 5 billion entrepreneurs in this world, even though this conjecture may not have been fully manifested in the practical world of business. If there are more than 5 billion entrepreneurs in this world, how is it that there is such a dearth of entrepreneurs in the world of business? This is an important question in view of the fact that business communities, academia and policy makers in the public realm have begun to talk about possibilities for fostering entrepreneurial growth in the global economy. 37. Which of the following statements is NOT correct, according to the passage? (A) There are more than 4 billion potential entrepreneurs in this world. (B) Not everybody can become an entrepreneur. (C) Entrepreneurial decision-making is different from managerial decision-making. (D) Executives in organization can be either managers or entrepreneurs, but not both. Explanatory Note: The last sentence in the second para supports statement A. The fourth sentence in the first para backs statement C and the first three sentences of the second para imply that everybody can become an entrepreneur. Hence, statement B which suggests otherwise is the answer. Choice (B) 38. As per the passage, an entrepreneur is one who: (A) takes commercial venture decisions. (C) invites participation in decision-making.

(B) exploits opportunities for personal gain. (D) focuses on maximizing cash profits.

Explanatory Note: The first sentence in the passage provides the answer to the question. It states clearly that an entrepreneur is one who exploits opportunities for personal gains. Choice (B) 39. The passage implies that it is important to understand.

(A) why there are so few entrepreneurs in business. (B) the main functions of an entrepreneur. (C) the factors which inhibit entrepreneurship. (D) the meaning of personal gain for an entrepreneur. Explanatory Note: The key to this question lies in the last para of the passage. The para states that there is dearth of entrepreneurs and we need to understand why it is so. Since the question contains the world implies, we opt for option C as the answer. The implied message is that we need to understand factors which inhibit entrepreneurship. The words 'talk about possibilities for fostering entrepreneurial growth' in the last sentence implies that we are looking at factors inhibiting entrepreneurship. Choice (C) 40. The passage mentions the following functions of an entrepreneur. (A) Risk-taking, decision-making, encouraging creativity. (B) Coordinating resources, recognizing opportunities and leading from the front. (C) Independent decision-making, exploiting opportunities and maximizing profits. (D) Making judgments, innovating and claiming responsibility. Explanatory Note: The last two sentences in the first para (“The entrepreneurial function -------------- claims”) have listed the elements mentioned in statement B as the functions of an entrepreneur. Here, leading from the front is the same as taking judgmental decision. Choice (B) Directions for Questions 41 − 45: Each of these questions has a set of numbered sentences. Each answer option specifies a sequence in which these sentences should appear so that a coherent meaning emerges. Choose that sequences as your answer, which logically yields the most coherent meaning. 41. (i) A company’s market share, revenue and balance sheet are all key elements. (ii) Share prices move up and down according to a bewildering array of factors, only some of which are readily quantifiable or even conventionally discernible by the CPAs and the clients they represent. (iii) Financial markets are neither rational nor efficient, and any investment strategy that ignores this fact is doomed to failure. (iv) But at least equally important are the vagaries of human psychology and behaviour, the conscious and unconscious wishes, conflicts, fears and fantasies that lure people en masse into bad-sometimes catastrophic-decisions. (A) (i) − (iv) − (ii) − (iii) (B) (iii) − (i) − (ii) − (iv) (C) (ii) − (iii) − (i) − (iv) (D) (iii) − (ii) − (i) − (iv) Solution: Statement (iii) is the first sentence since it is a generalisation that is elaborated in the subsequent sentences. We now check options B and D (ii) rather than (i) follows (iii) because from financial markets in (iii) we move to 'share prices' in (ii) to 'a companys' market share’ in (i). Statement (iv) that compares the market to 'human psychology' is apt as the concluding line. Choice (D) 42. (i) In most industries people cost are much higher than the capital costs. (ii) It is no secret that business success today revolves largely around people, not capital. (iii) Even when a company is not people-intensive overall, a people-based business embedded in the company often drives corporate performance. (iv) Many traditional manufacturers are now essentially service businesses. (A) (i) − (ii) − (iii) − (iv) (B) (ii) − (iii) − (i) − (iv) (C) (ii) − (iv) − (i) − (iii) (D) (iv) − (ii) − (i) − (iii) Solution: (ii) is the first sentence as it introduces the idea –importance of people. (iii) follows this – linked by 'Even when a company is not people intensive .... (i) follows carrying the idea forward – the idea being true for 'most industries'. (iv) concludes giving the experience of 'traditional manufacturers'. Choice (B) 43. (i) I have always found that a systematically planned vacation turns out to be more enjoyable.

(ii) I decide on a list of possible destinations by carefully browsing the ITDC web-site. (iii) Availability of decent accommodation and not being a popular tourist attraction are the two most important criteria for choosing the venue for any of my vacations. (iv) Then I cross-check against the availability of good hotels near these destinations. (A) (iii) − (ii) − (iv) − (i) (B) (i) − (iv) − (ii) − (iii) (C) (iii) − (i) − (ii) − (iv) (D) (i) − (iii) − (ii) − (iv) Solution: (i) is the first sentence – it opens the topic of 'systematically planned vacation'. (iii) follows – since the first step in planning a vacation is finding accommodation. Then comes finding the destination (ii), (iv) concludes with further verification. Choice (D) 44. (i) The aviation sector is booming in India but many small and medium-sized airlines in the US are on the verge of bankruptcy. (ii) However, US airlines are free to fly any number of flights to India under the latter’s open skies policy with the U.S. (iii) Currently, the domestic aviation policy stipulates a five-year experience before they are allowed to fly abroad. (iv) There are some hot acquisition targets available for the newly floated airlines in India. (v) This model, if successful, will have many takers. (A) (i) − (iv) − (v) − (iii) − (ii) (B) (iv) − (i) − (iii) − (ii) − (v) (C) (iii) − (ii) − (i) − (iv) − (v) (D) (i) − (ii) − (iii) − (iv) − (v) Solution: Sentence (i) is the first sentence since it introduces the aviation sector of India and compares it with that in the US. Since it is booming in India and going bankrupt in the US it seems logical that some companies in India would try to acquire some in the U.S. Hence (iv) follows with this idea. (v) follows (iv) since 'This model' in (v) refers to what is stated in (iv). (ii) follows (iii) since (iii) gives a condition and (ii) shows how that condition can be bypassed. Choice (A) 45. (i) It is this goodwill that really makes sponsorship different from advertising. (ii) For example, sponsorship operates through different cognitive processes than advertising. (iii) In turn, goodwill feeling comes to the company which influences attitude and behaviour toward the brand. (iv) There are several benefits of sponsorship over mass advertising. (v) While advertising changes a consumer’s perception of a specific product, sponsorship changes the perception of a specific sponsor which will rub off on the brand. (vi) It engages the consumer by bestowing benefit on an activity which the consumer has an intense emotional response to. (A) (iv) − (ii) − (vi) − (iii) − (i) − (v) (B) (iv) − (v) − (vi) − (ii) − (i) − (iii) (C) (v) − (iv) − (ii) − (vi) − (i) − (iii) (D) (v) − (vi) − (ii) − (i) − (iii) − (iv) Solution: Sentence (iv) introduces the comparison between sponsorship and mass advertising. (ii) follows pinpointing an advantage of sponsorship. 'Cognitive process' in (ii) leads to 'emotional response' in (vi). This in turn leads to ‘good will’ in (iii) which leads to 'this good will' in (i). (v) concludes the comparison. Choice (A) Directions for Questions 46 − 52: Read each of the short passages and select the right option for the question relating to each passage: 46. Along with the increasing use of Electronic Refrigerators, the demand for ice in the market declined. Formerly, we were buying ice to keep our ice boxes cool and the food stored in the ice box fresh. Now, the ice boxes cool themselves. Similarly, the introduction of web-based eLearning teaching, to be offered simultaneously in different cities, will…. Which of the following best completes the argument left incomplete? (A) Increase the course enrolment. (B) Increase the spread of the course. (C) Reduce the need for class room. (D) Reduce the ineffectiveness in teaching. Solution: The paragraph says that the coming of refrigerators reduced the demand for ice. Earlier ice was used to cool things in an ice box. Now the fridge is the ice box and it cools itself. The analogy is carried to Web-based e-learning since the computer can be used to teach, it becomes the class room and hence the need for class room is reduced. Choice (C)

47. Prosperity will eventually drive out divisive politics. In a prosperous society, there would neither be time nor need for divisive politics. The underlying driver of all forms of divisions is economic. Therefore economic policies favoring rising prosperity would do less harm to society than the “redistribution of poverty” policies. In drawing the above conclusion the author assumes that: Ι . Divisive policy is harmful to the society. Ι Ι . “Redistribution of poverty” policies lead to divisive politics. (A) I only (B) II only (C) Both I and II (D) Neither I nor II. Solution: Since the passage mentions 'harm', one of the underlying assumptions is that divisive policy is harmful to society. As the passage says 'The underlying driver of all forms of division is economic'. We can surmise that II is also assumed. Hence both I and II are assumptions. C hoice (C) 48. It is unfortunate for the country, specially for the poor and women, that whenever any kind of disincentive – even of the mildest nature such as debarring a person with more than two children from contesting any local body election – is introduced to promote family planning, there are always some activists and organizations who unnecessarily oppose the measures without realizing that the voluntary family planning programmes are a miserable flop as clearly highlighted by the national family health surveys. Which of the following, if true, would most strengthen the author’s contention? (A) Percentage of rural women voluntarily seeking family planning services in government health centre facilities has drastically come down over the last decade. (B) One child policy in China, where employees with more than one child are discriminated against, has been very effective in controlling their population. (C) Activists and organization which seem to advocate civil rights issues typically have their own vested interests and hidden agendas. (D) Punitive measures are the best deterrents for refraining people from committing deeds which adversely affect the society at large. Solution: The author talks of 'disincentives' for family planning and says 'activists' 'unnecessarily oppose the measures’. Hence his stand is that disincentives are needed. This can be strengthened by option B which says disincentives worked in China (proof of its success). Choice (B) 49. In a recent study published in the Journal of Family Practice, no significant benefit over a placebo was found from using the antibiotic Amoxicillin among 135 patients with typical indications of a sinus infection. All the patients complained of sinusitis, with pus in the nasal cavity, facial pressure or nasal discharge lasting longer than seven days. A small subgroup of patients receiving the antibiotic became better faster than the others. But the researchers were unable to discern anything about those patients prior to administering Amoxicillin that indicated a bacterial infection, as opposed to a viral one. From the above passage it may be inferred that: (A) Use of an antibiotic is beneficial for sinusitis patients. (B) Antibiotics should be administered to only those sinusitis patients, who have been diagnosed to have a bacterial infection. (C) Antibiotics do not have any effect on sinusitis patients. (D) Use of an antibiotic may be beneficial for a small percentage of sinusitis patients with bacterial infection, but in general antibiotics are useless for sinusitis patients. Solution: The passage says only a small group of patients benefited from the use of Annoxicillin – these were suffering from bacterial infection. Hence D is the right inference. A is negated, B cannot be justified based on the passage. C is sweeping and hence not right. Choice (D) 50. It defies common logic and theory that too little sleep can make one fat. If such findings are made public, I’m afraid lazy people will grab the opportunity to sleep more. But I’m sure this is not the only factor responsible for being overweight. There should be more research on the issue before scientists conclude something so dramatic.

(A) Most of the sleep-deprived people participating in the study which concluded that “too little sleep can make one fat”, had an overweight sister. (B) Most lazy people are fat. (C) Most of the people, participating in the study which concluded that “too little sleep can make one fat”, who got proper sleep also exercised regularly. (D) Most of the sleep-deprived people, participating in the study which concluded that “too little sleep can make one fat”, love pizzas. Solution: The author questions the conclusion that 'too little sleep can make one fat' and calls for more research. This can be strengthened by C which says that 'people who got proper sleep exercised regularly', as it could be that people were of normal weight because they exercised regularly and it may have little to do with sleep. Choice (C) 51. In spite of the economics of direct entry system of recruitment being appreciated and accepted by the merchant navy, our armed forces still seem to be dragging their feet on this issue. If anything, our defence organization appears to be continually augmenting its training establishments by having in its fold professional institutions providing basic university education. There is no death of such institutions in our civil educational system. This results in unnecessary duplication at the expense of the defence budget. From the above paragraph it may be inferred that. (A) Merchant navy used to admit only college graduates in its training programmes. (B) Merchant navy no longer provides basic university education in its training programmes. (C) The nature of the work involved in defense organization and merchant navy are similar. (D) A major part of the defense budget is spent on its training establishments. Solution: The author suggests that the defence establishment adopt the recruitment process adopted by the merchant navy. He then criticisers the defence establishment for duplicating what the civil education system does. Therefore, it can be inferred that the merchant navy does not commit the same error. Choice (B) 52. The smallest of fluctuation in the BSE Sensex sees the doomsayers coming out of the woodwork. One of the popular but misguided insights is: since the market is tanking, run with your money before you are done in. I find this amusing. The same people, when they spot a “Sale” sign in shopping malls or read about a fall in air ticket prices to Sydney or Singapore, try and grab the deal. But when it comes to investing, they live a contradiction. Any fall in the market is a reason to buy. If you are an investor in equities or equity funds, you are there for the long term. Thus, if you were considering equities at Sensex 7500, you should be celebrating at Sensex 6500. The same companies are now cheaper by 13%!. If they fall further, so much the better – doomsayers be dammed! The author in the above paragraph assumes that: (A) Most people sell their equity holding in a falling market. (B) Equity markets are similar in nature to the commodity markets like a supermarket or airline tickets. (C) One should buy equities when the prices are low. (D) Though markets might drop in the short-run, in the long-term they are bound to rise again. Solution: The paragraph contrasts the behaviour of people in relation to shares and commodities. In case of the latter we are eager to buy when price is low whereas when price falls in case of shares, we rush to sell. The author suggests that we buy when share prices are low. The assumption here is that they will appreciate in the long run. Choice (D) 53. Consider the following three pieces of information” Ι . Geeta and Sita are of same age. Ι Ι . Total age of Geeta, Reena and Sita is 88 years. Ι Ι Ι . Reena’s age is same as the sum of Geeta and Sita’s age. Which of the above pieces of information enables you to answer the question, “What is the age of Reena?” (A) Ι and Ι Ι (B) Ι Ι and Ι Ι Ι (C) Ι and Ι Ι Ι (D) Ι , Ι Ι and Ι Ι Ι are not sufficient. Solution: Using Ι and Ι Ι we can get the answer as follows.

Geeta + Sita + Reena = 88 ∴ Reena’s age is 44 years. Choice (B) 54. In a code, South-East becomes West, North-East becomes South and so on. What will West become? (A) South-East (B) North-East (C) East (D) North Solution: The actual directions and the directions as given in the questions can be represented as follows. Actual As given

From the above diagrams it is clear that the directions as given in the question can be obtained by rotating the actual directions by 135° in clockwise direction. Hence, west becomes North – East. Choice (B) 55. If Ms. Q is appointed as the CEO of XYZ corporation then at least one of the following two things will happen. (i) the stock price of XYZ corporation will appreciate. (ii) the employee union will not call a strike. Then the following statement may be deducted: (A) If Ms. Q is appointed as the CEO of XYZ corporation AND the stock price of XYZ corporation appreciates, then the employees union will call a strike. (B) If Ms. Q is appointed as the CEO of XYZ corporation AND the employees union calls a strike, then the stock price of XYZ corporation will appreciate. (C) If Ms. Q is appointed as the CEO of XYZ corporation AND the stock price of XYZ corporation does not appreciate, then employees union will call a strike. (D) If Ms. Q is appointed as the CEO of XYZ corporation AND the employees union does not call a strike, then the stock price of XYZ corporation will not appreciate. Solution: If

Then

p

q

Or

The statement is of the form If p, then q or r. The implications are (i) p ⇒ q or r (ii) p and ~q ⇒ r (iii) p and –r ⇒ q (iv) ~q and –r ⇒ –p Choice (B) is on accordance with implication (iii). Choice (B) 56. In a supply chain, P is a critical supplier in the sense that if P defaults the entire supply chain breaks down, and if the supply chain breaks down production stops. If the supply chain has broken down it may be deducted that (A) P has defaulted and production has stopped. (B) P has defaulted and production might have stopped. (C) P might have defaulted and production has stopped. (D) P might have defaulted and production might have stopped. Solution: Statement 1: p

q

If

,

The statement is of the form, if p then q. The implications are, (i) p ⇒ q (ii) ~q ⇒ ~p Hence, when it is known that q is happening nothing can be said definitely about p. Hence, when the entire supply chain has broken down, it means that night or night not have defaulted Similarly, Statement 2: q r If

,

The statement is of the form, ‘If q, then r’. The implications are, (i) q ⇒ r (ii) –r ⇒ –q Hence, when the supply chain has broken down it means that production has stopped. Choice (C) 57. In a coding language, the letters of the English alphabet are arranged in such a manner that all the vowels are put in the end and the remaining letters are arranged from the first letter onwards. The rearranged alphabets are used to denote the position occupied by letters in the original alphabets. What is the code of “META”? (A) LWPV

(B) QGYB

(C) PWLV

(D) TEAM

Solution: The English alphabet and their rearranged order are given below

Original Order

A

B

C

D

E

F

G

H

Rearranged order

B

C

D

F

G

H

J

K

Original Order

I

J

K

L

M

N

O

P

Rearranged order

L

M

N

P

Q

R

S

T

Original Order

Q

Rearranged V order

The code fir META QGYB. Directions for Questions 58 − 64

can

R

S T U V W X Y Z

W X Y Z A E Ι

be

obtained from Choice (B)

O U

the

above

table

as

Each of these problems has two Statements I and II and a question. Use the information provided in Statement I and II to decide whether they are sufficient to answer the question. For each problem, select one of the option (A), (B), (C) or (D) based on the following criteria. (A) Choose option A, if the question can be answered using the information given in just one of the Statements but not the other i.e. choose this option if one of the following condition is met: • Statement I is sufficient to answer the question but Statement II alone is not sufficient. OR • Statement II is sufficient to answer the question but Statement I alone is not sufficient. (B) Choose option B if the question can be answered using the information given in either one of them i.e. choose this option if Statement I alone is sufficient to answer the Question AND Statement II alone is also sufficient to answer the question. (C) Choose option C if the question can be answered using the information given in both Statements I and II together, but cannot be answered individually from I and II. (D) Choose option D if the question cannot be answered even after using the information given in both Statements I and II. 58. X and Y start walking towards each other in a straight line at 9:00 AM. What is the ratio of the distance travelled by X to Y from their respective starting points to the point where they meet each other? Ι . X walks twice as fast as Y. Ι Ι . The distance between the starting points of X and Y is 5 km. Solution: From statement I, as we know the ratio of speeds of X and Y and speeds distance are directly varying, ratio of speeds = ratio of distances. Hence required ratio can be found. Choice (A) 59. What is the remainder when 3m + 1 is divided by 6? Ι . m is even. Ι Ι . m is odd. Solution: Given dividend is 3m + 1 and the divisor is 6. From statement I, we have m as even hence 3m will become a multiple of 6. When 6k + 1 is divided by 6, (where k is a natural number) remainder will be always one.

From statement II, we have m as odd. Let m = 2k + 1 , were k is a whole number. ∴ 3m + 1 changes to 6k + 4. When 6k + 4 is divided by 6, the remainder will be always 4. Choice (B) 60. A spherical iron ball is dropped into a cylindrical tumbler containing such an amount of water that the ball gets completely immersed but water does not overflow out of the tumbler. By how many centimeters does the water level rise in the tumbler? Ι . The radius of the ball is half that of the tumbler. Ι Ι . The tumbler contained 100 cc of water. Solution: When a spherical ball is dropped into a cylindrical tumbler, the volume of the water raised = volume of the spherical ball. Combining both the statements also the question cannot be answered, as there is no information about numerical values of radius of ball or tumbler. Choice (D) 61. What is the exact time? Ι . The time is between 3 PM and 4 PM. Ι Ι . The hour hand and the minute hand are in a straight line. Solution: The question cannot be answered using statement I alone as the position of minute hand is not known. The hour hand and minute hand will be in a straight line on twenty-two occasions in 12 hours. I.e., 11 times when they coincide and 11 times when they are in exactly opposite directions. Hence, II alone is not sufficient. Statements I and II together are not sufficient to answer the question as the hands will coincide one and are in opposite directions once between 3 PM and 4 PM. Choice (D) 62. Will Q take more than 8 hours to complete job X alone. Ι . P works faster than Q. Ι Ι . P and Q can together finish the job in 5 hours. Solution: Statement I alone is not sufficient, as it does not mention anything about the time taken by P or both of them. Statement II alone is not sufficient, as it does not mention anything about the efficiencies of P and Q. Combining both the statements, we can say that Q will take any time more than 10 days. (If Q is equally efficient as P, both will take 10 days but as Q is less efficient, he will take more 10 days). Choice (C) 63. The monthly salary of a Boss is Rs. 40,000. What is the salary of his only subordinate? Ι . The subordinate gets Rs. 10,000 less than the average salary of the Boss and his own salary. Ι Ι . The average salary of the Boss and the subordinate is Rs. 37,000. Solution: Given the salary of the boss is Rs.40,000. Let the subordinate’s salary be Rs. X. From statement I we have

x=

– 10,000

Hence x value can be found. From statement II, we have

= 37,000 Hence found.

x

value

can

be Choice (B)

64. In a written test, Sita, Geeta, Reena and Asha have got their ranks. Who are the first and the last rank holders? Ι . Sita has scored more than Asha but less than Geeta. Ι Ι . Asha has scored more than Reena but less than Geeta and Sita. Solution: Statement Ι alone is not sufficient, as it has no information about Reena. From Ι Ι we get the following information. Geeta, Seeta > Asha > Reena Hence, any one among Geeta and Seeta could be the first ranker and Reena is the last ranker. By using Ι and Ι Ι as Seeta scored less than Geeta, Geeta is the first ranker. Hence, both Ι and Ι Ι are necessary.

Choic e (C)

65. (i) If the monsoon comes in time it rains aplenty in the peninsula. (ii) If it rains aplenty in the peninsula there is no crop failure. (iii) If the fertilizers are not available in the market then there is a crop failure. (iv) If the fertilizers are available in the market that means the shipping line is working smoothly. (v) If there is no crop failure that means fertilizers are not available in the market. (vi) If the shipping line is working smoothly the monsoon does not come in time. (vii) If the fertilizers are not available in the market then it rains aplenty in the peninsula. (A) (i), (ii), (iii), (iv) and (vi) (B) (i), (ii), (iv), (vi) & (vii) (C) (i), (iii), (iv), (vi) & (vii) (D) (ii), (iv), (v), (vi) & (vii) Solution: The given statements can be represented as follows. (i) Monsoon ⇒ rains aplenty (ii) Rains aplenty ⇒ no crop failure. (iii) Fertilizers not available ⇒ crop failure (iv) Fertilizers available ⇒ Shipping line working (v) No crop failure ⇒ fertilizers not available (vi) shippling line working ⇒ monsoon not on time (vii) Fertilizers not available ⇒ rains aplenty. Case (A): From (i) and (ii), Monsoon ⇒ no crop failure From (iii), No crop failure ⇒ fertilizers available. From (iv) fertilizers available ⇒ shipping line working From (vi) shipping line working ⇒ no monsoon But this inconsistent. e (A) 66. (i) All mammals have hair. (ii) Anything which does not have feathers cannot fly. (iii) Anything which has feathers is not a mammal. (iv) Anything which can fly does not have hair. (v) Anything which cannot fly is a mammal. (vi) Anything which has hair does not have feathers. (vii) X is a mammal. (viii) X can fly. (A) (ii), (iv), (vi), (vii) and (viii) (B) (ii), (v), (vi), (vii) & (viii) (viii) (D) (i), (ii), (vi), (vii) & (viii) Solution: The given statements can be represented as follows. (i) mammal ⇒ hair (ii) no feathers ⇒ can not fly (iii) Feathers ⇒ not mammal (iv) can fly ⇒ no hair (v) cannot fly ⇒ mammal (vi) hair ⇒ no feathers (vii) x ⇒ mammal (viii)x ⇒ fly Choice (D):

is Choic

(C) (iii), (iv), (vi), (vii) &

From (viii), x ⇒ fly From (ii), x ⇒ has feathers From (vi), x has no hair From (i), x is not mammal This is inconsistent (viii). 67. (i) Ram always drinks orange juice while watching cricket. (ii) If Ram is with his friends he is not at home. (iii) Ram does not drink orange juice on weekdays. (iv) During weekends, Ram is always with his friends. (v) Ram drinks orange juice only at home. (vi) Ram watches cricket only at home. (vii) Ram is watching cricket. (A) (i), (iii), (iv), (v), (vi) and (vii) (B) (i), (ii), (iv), (v), (vi) & (vii) (C) (i), (ii), (iii), (iv), (v) & (vii) (D) (i), (ii), (iii), (v), (vi) & (vii) Solution: The given statements can be represented as follows. (i) watching cricket ⇒ drink orange juice (ii) With friends ⇒ not at home (iii) Weekdays ⇒ does not drink orange juice (iv) Weekend ⇒ with friends (v) Drinking orange juice ⇒ at home (vi) Watching cricket ⇒ at home (vii) Ram is watching cricket. Choice (C): From (vii) and (i) Ram is drinking orange juice. From (v), Ram is at home From (ii), Ram is not with his friends. From (iv), it is not weekend, i.e weekdays. From (iii), Ram is not drinking orange inconsistent. Choice (C) Questions 68 to 72 are based on the following passage:

Choice (D)

juice.

But

with

this

is

Four students, Promila, Quadir, Rita and Sridhar, each working under the supervision of one of the four Professors Anand, Bose, Chandrasekharan and Deshpande made their final year MBA Project Presentations one by one, one each in the areas of Finance, Marketing, Systems and Human Resource Management (HRM). Each Professor is an expert in only one of the above areas and supervised exactly one of the above students in his own area. The following clues are provided. (i) First presentation was made by Rita. (ii) Prof. Bose works in Finance. (iii) Prof. Deshpande was Promila’s supervisor. (iv) The last presentation was in the Systems area (v) Sridhar’s project was in the HRM area. (vi) Prof. Bose’s student’s presentation followed that of Prof. Chandrasekharan’s students. 68. In which area was Rita’s project? (A) Marketing (B) Finance

(C) Systems

(D) Cannot be determined.

Solution: The given data can be tabulated as follows Finance – Bose – Marketing – Systems –4 HRM Sridhar– From (vi) Prof. Bose’s student's presentation followed that of Prof. Chandrasekharan’s student. ⇒ Bose’s student’s presentation was not the first one. Hence from (i) Rita – Marketing – 1 From (iii), Deshpande – pramila - systems – 4 Thus we get the following arrangement. Finance – Bose –Quadir – 2/3

Marketing -

-– Rita – 1

System – Deshpande – Pramila – 4

HRM –

– Sridhar – 3/2

Rita’s marketing.

project

is

69. What is Prof. Deshpande’s area of expertise? (A) Marketing (B) HRM (C) Systems determined.

Choice (A)

(D) Cannot

be

in

uniquely

Solution: The given data can be tabulated as follows Finance – Bose – Marketing – Systems –4 HRM Sridhar– From (vi) Prof. Bose’s student's presentation followed that of Prof. Chandrasekharan’s student. ⇒ Bose’s student’s presentation was not the first one. Hence from (i) Rita – Marketing – 1 From (iii), Deshpande – pramila - systems – 4 Thus we get the following arrangement. Finance – Bose –Quadir – 2/3

Marketing -

-– Rita – 1

System – Deshpande – Pramila – 4

HRM – Prof. Systems.

– Sridhar – 3/2 Deshpande’s

area

70. In which area was the second presentation? (A) Finance (B) Marketing (C) HRM determined.

of

expertise Choice (C) (D) Cannot

be

is

uniquely

Solution: The given data can be tabulated as follows Finance – Bose – Marketing – Systems –4 HRM Sridhar– From (vi) Prof. Bose’s student's presentation followed that of Prof. Chandrasekharan’s student. ⇒ Bose’s student’s presentation was not the first one. Hence from (i) Rita – Marketing – 1 From (iii), Deshpande – pramila - systems – 4 Thus we get the following arrangement. Finance – Bose –Quadir – 2/3

Marketing -

-– Rita – 1

System – Deshpande – Pramila – 4

HRM – The HRM.

– Sridhar – 3/2 second

presentation

could

be

in the Choice (D)

71. Which student’s project did Prof. Bose supervise? (A) Quadir (B) Rita (C) Sridhar above

area

of

Finance

or

(D) Can’t be determined from

Solution: The given data can be tabulated as follows Finance – Bose – Marketing – Systems –4 HRM Sridhar– From (vi) Prof. Bose’s student's presentation followed that of Prof. Chandrasekharan’s student. ⇒ Bose’s student’s presentation was not the first one. Hence from (i) Rita – Marketing – 1 From (iii), Deshpande – pramila - systems – 4 Thus we get the following arrangement. Finance – Bose –Quadir – 2/3

Marketing -

-– Rita – 1

System – Deshpande – Pramila – 4

HRM – Prof. project.

– Sridhar – 3/2 Bose

72. What is Prof. Anand’s area of expertise? I. HRM II. Systems III. Marketing (A) Either I or II (B) Either I or III

supervised

Quadir’s Choice (A)

(C) Either II or III

(D) Neither I, nor II, nor III

Solution: The given data can be tabulated as follows Finance – Bose – Marketing – Systems –4 HRM Sridhar– From (vi) Prof. Bose’s student's presentation followed that of Prof. Chandrasekharan’s student. ⇒ Bose’s student’s presentation was not the first one. Hence from (i) Rita – Marketing – 1 From (iii), Deshpande – pramila - systems – 4 Thus we get the following arrangement. Finance – Bose –Quadir – 2/3

Marketing -

-– Rita – 1

System – Deshpande – Pramila – 4

HRM –

– Sridhar – 3/2

Prof. Anand’s area Marketing. Directions for Questions 73 − 75

of

expertise

could Choice (B)

be

HRM

or

Each Question consists of a set of numbered Statements. Among them there is only one Statement which logically follows from the rest. Choose this “conclusion” Statement from the given options. Example: With the four statements. (i) None of the paper setters can do logic. (ii) Insane people are not fit to serve in a jury. (iii) None of the paper setters are fit to be in a jury. (iv) Anyone who is sane can do logic; the correct answer is (iii), which is a logical consequences of the rest. 73. (i) No soup, that is cold, has Croutons in it. (ii) The soup in the cup is hot. (iii) No soup that does not have Croutons in it is fit for drinking. (iv) The soup in the cup is fit for drinking. (A) (i) (B) (ii) (C) (iii) (D) (iv) Solution: From (iv), the soup in the cup is fit drinking. By comparing the above with (iii), it can be concluded that the soup in the cup has croutons in it. By comparing the above with (i), it can be concluded that the soup in the cup is not cold i.e the soup in the cup is hot, which is statement (ii) Choice (B) 74. (i) All the papers presented in the conference that fail to get a prize, are rejected for journal publication. (ii) All the papers, which are rejected for journal publication, are to appear in the proceedings. (iii) None of the papers, appearing in the proceedings, has any real data set. (iv) All the papers without any real data set have an extensive simulation study. (v) My paper has an extensive simulation study. (vi) My paper did not get a prize in the conference. (A) (iii) (B) (iv) (C) (v) (D) (vi) Solution: From (vi), my paper did not get a prize in the conference. By comparing the above with (i), it can be concluded that my paper is rejected for publication. By comparing the above with (ii), it can be concluded that my paper has to appear in the proceedings. By comparing the above with (iii), it can be drawn that my paper does not have real data. By comparing the above with (iv), it can be concluded that my paper has an extensive simulation study which is same as (V). Choice (D) 75. (i) Rainy days are always cloudy. (ii) Everybody caries an umbrella when it is raining. (iii) When people carry umbrellas the day never turns out fine. (iv) The only days when I have a fight with my wife are cloudy days. (v) I call no day unlucky when I do not have a fight with my wife. (vi) My lucky days always turn out fine.

(A) (i)

(B) (iii)

(C) (iv)

(D) (vi)

Solution: From (ii) on all rainy days people carry umbrella. By comparing the above with (iii) it can be said that rainy days are not fine. By comparing the above with (vi) it can be concluded that rainy days are my unlucky days. By comparing the above with (v), it can be concluded that I have fight with my wife on all rainy days. By comparing the above with (iv), it can be concluded that rainy days are always cloudy, which is (i). Choice (A) Questions 76 − 80 are based on the following paragraph.

A business School with six Professors L, M, N, O, P and Q, has decided to implement a new scheme of course management. Each Professor has to coordinate one course and support another course. This semester, O’s support course is Finance, while three others have it in coordinator’s role. P and Q have marketing as one of their subjects. Q coordinates Operations, which is a support course for both N and P. Finance and IT are L’s subjects. Both L and O have same subjects. Strategy is a support course for only one of the Professors.

76. Who coordinates the Strategy course? (A) M

(B) N

(C) O

(D) None of the six

Solution: The given date can be tabulated as follows.

Support

Coordinate

L M N

Operations

O

Finance

P

Operations

Q

Operations

L’s subjects are Finance and IT which are also the subjects of O. ⇒ O coordinates IT. P and Q have marketing as one of their subjects. ⇒ P coordinates marketing and Q supports it. Three lectures have Finance as their coordinating subjects. ⇒ L, M and N are the professors who coordinate finance. Only one professor supports strategy. It has to be M. L and O have same subjects.

∴ L supports IT. Hence, the final arrangement is as follows:

Support

Coordinate

L

IT

Finance

M

Strategy

Finance

N

Operations

Finance

O

Finance

IT

P

Operations

Marketing

Q

Marketing

Operations

No course.

one

coordinates

strategy Choice (D)

77. Which course is supported by M? (A) Finance

(B) Strategy

(C) IT

(D) Operations

Solution: The given date can be tabulated as follows.

Support

Coordinate

L M N

Operations

O

Finance

P

Operations

Q

Operations

L’s subjects are Finance and IT which are also the subjects of O. ⇒ O coordinates IT. P and Q have marketing as one of their subjects. ⇒ P coordinates marketing and Q supports it. Three lectures have Finance as their coordinating subjects.

⇒ L, M and N are the professors who coordinate finance. Only one professor supports strategy. It has to be M. L and O have same subjects. ∴ L supports IT. Hence, the final arrangement is as follows:

Support

Coordinate

L

IT

Finance

M

Strategy

Finance

N

Operations

Finance

O

Finance

IT

P

Operations

Marketing

Q

Marketing

Operations

M strategy. (B)

supports Choice

78. Who coordinates the IT course? (A) L

(B) N

(C) O

(D) None of the six

Solution: The given date can be tabulated as follows.

Support

Coordinate

L M N

Operations

O

Finance

P

Operations

Q

Operations

L’s subjects are Finance and IT which are also the subjects of O. ⇒ O coordinates IT. P and Q have marketing as one of their subjects.

⇒ P coordinates marketing and Q supports it. Three lectures have Finance as their coordinating subjects. ⇒ L, M and N are the professors who coordinate finance. Only one professor supports strategy. It has to be M. L and O have same subjects. ∴ L supports IT. Hence, the final arrangement is as follows:

Support

Coordinate

L

IT

Finance

M

Strategy

Finance

N

Operations

Finance

O

Finance

IT

P

Operations

Marketing

Q

Marketing

Operations

O

coordinates Choice

IT. (C)

79. Who all are coordinating the Finance course? (A) L, M and N

(B) M, N and O

(C) N and O

Solution: The given date can be tabulated as follows.

Support

Coordinate

L M N

Operations

O

Finance

P

Operations

Q

Operations

(D) L and N

L’s subjects are Finance and IT which are also the subjects of O. ⇒ O coordinates IT. P and Q have marketing as one of their subjects. ⇒ P coordinates marketing and Q supports it. Three lectures have Finance as their coordinating subjects. ⇒ L, M and N are the professors who coordinate finance. Only one professor supports strategy. It has to be M. L and O have same subjects. ∴ L supports IT. Hence, the final arrangement is as follows:

Support

Coordinate

L

IT

Finance

M

Strategy

Finance

N

Operations

Finance

O

Finance

IT

P

Operations

Marketing

Q

Marketing

Operations

L, Finance

M

and

N

80. Which course has only one coordinator and only one support Professor? (A) Marketing

(B) Operations

(C) Finance

Solution: The given date can be tabulated as follows.

Support

Coordinate

L M N

Operations

O

Finance

P

Operations

Q

Operations

(D) Strategy

coordinate Choice (A)

L’s subjects are Finance and IT which are also the subjects of O. ⇒ O coordinates IT. P and Q have marketing as one of their subjects. ⇒ P coordinates marketing and Q supports it. Three lectures have Finance as their coordinating subjects. ⇒ L, M and N are the professors who coordinate finance. Only one professor supports strategy. It has to be M. L and O have same subjects. ∴ L supports IT. Hence, the final arrangement is as follows:

Support

Coordinate

L

IT

Finance

M

Strategy

Finance

N

Operations

Finance

O

Finance

IT

P

Operations

Marketing

Q

Marketing

Operations

Marketing professor.

course

has

only

one

coordinator Choice (A)

and

only

one

support

SECTION 3: QUANTITATIVE ABILITY (81 − 120) 81. If a = 3150 × 576 × 7140, b = 3148 × 576 × 7141, c = 3148 × 580 × 7139, d = 3151 × 580 × 7142 then the order of a, b, c, d from largest to smallest is: (A) d, a, c, b (B) c, d, b, a (C) c, d, a, b (D) d, c, a, b Solution: Given a = 3150 × 576 × 7140

b = 3148 × 576 × 7141 =

∴ b= c = 3148 × 580 × 7139 d = 3151 × 580 × 7142 d = c × 33 × 73

c=

, d > c, a > b, c > a

Only choice D satisfies all these conditions. Choice (D) 82. If A, B and C are the angles of a triangle and eiA, eiB and eiC are in Arithmetic Progression, then the triangle is: (A) Right angled but not isosceles. (B) Isosceles but not right angled. (C) Equilateral (D) Right angled isosceles Solution: eiA = cosA + isinA; eiB = cosB + isinB; eiC = cosC + isinC Given (cosA + isinA) + (cosC + isinC) = 2(cosB + isinB) Equating real and imaginary parts, cosA + cosC = 2 cosB –––––– (1) sinA + sinC = 2 sinB ––––––– (2) It is also given that A, B, C are angles of a triangle. ∴ A + B + C = 180° The given condition (1) and (2) are satisfied only when A = B = C = 60°, ∴ the triangle is equilateral. Choice (C)

83. A polynomial f(x) with real coefficients satisfies the functional equation f(x). f(2) = 9, then f(4) is: (A) 82

(B) 17

(C) 65

= f(x) +

. If

(D) None of the above

Solution: By considering a general nth degree polynomial and writing the given equation, it can be proved by comparing the co-efficients of xn, xn–1, xn–2, . . . . that f(x) either takes the form xn + 1 or –xn + 1. If f(2) = 2n + 1 = 9, we get n = 3 But f(2) = 2n + 1 = 9 would imply 2n = –8 which not possible. Hence, f(x) = x3 + 1 So f(4) = 43 + 1 = 65. Choice (C) 84. MTNL has a waiting list of 5005 applicants for its recently launched mobile phone scheme. The list shows that there are at least 5 males between any two females. The largest possible number of females in the waiting list is: (A) 920 (B) 835 (C) 721 (D) 1005 Solution: The list would have the largest number of females if the 1st, 7th, 13th etc are females. As 5005 = 6(834) + 1, there are at the most 1+ 834 i.e., 835 females. Choice (B) 85. A mixture comprises two chemicals A and B. The price of A is Rs.100/- per litre and that of B is Rs.200/- per litre. We can spend a maximum of Rs.600/- for making the mixture. The densities of A and B are 10 kgs / litre and 12 kgs / litre respectively. The mixture must contain each of the chemicals to the extent of at least 25% by weight. The maximum weight of the mixture that can be made is closest to: (A) 60 kg (B) 51 kg (C) 54 kg (D) 48 kg Solution: These are two constraints that the volumes of chemicals A and B have to notify, cost and weight. Let the volume be a lt and b lt respectively. The cost is 100a + 200b, which has to be less than as equal to Rs.600. ∴ a + 2b ≤ 6. To obtain the maximum weight, we need to use all the money at our disposal. i.e. a + 2b = 6. The weight is 10a + 12b

= 10a + 12

= 10a + (36 – 6a)

= 4a + 36 (1) As each chemical constraints at that 25% of the weight.

and i.e. 4a + 36 ≤ 40a and 4a + 36 ≤ 144 – 24a

∴ 1 ≤ a and a ≤ The weight is maximum when a is maximum (from 1)

∴ The maximum weight is

=

= Choice (B)

86.

is equal to

(A) Solution:

Let

A2 =

A3 =

=

(B)

(C)

(D)

Each entry in the matrix is a polynomial in 1/n. So each entry in without a constant term.

(A)n is also a polynomial in 1/n

In the limiting case each entry equals zero and hence we get a null matrix.

∴

Choice (A)

87. A, B and C are assigned a piece of work which they can complete by working together in 15 days. Their efficiencies (measured in terms of rate of doing work) are in the ratio 1 : 2 : 3. After 1/3 of the work is completed, one of them has to be withdrawn due to budget constraint. Their wages per day are in the ratio 3 : 5 : 6. The number of days in which the remaining two persons can complete the work (at optimal cost) is: (A) 18

(B) 20

(C) 15

(D) 12

Solution: The efficiencies (work /unit time), wages and work/wage far A, B, C are tabulated below.

A

B

C

ABC

Efficiency

1

2

3

6

Wages

3

5

6

14

Work/wage

1/3

2/5

3/6

If one of the 3 workers has to be withdrawn it should be A (Who does the least work per rupee) The total work = (1 + 2 + 3)15 = 90 unit days. After one third of the work in over, 60 unit days of work remain. B and C take 60/(2 + 3) or 12 days to complete that work. Choice (D) 88. An investor desires to invest a certain sum of money in two securities A and B. The risk and return of A and B are: A B Risk (β ) 3.00 6.00 Return in %(R) 9.00 12.00 Measures of both risk and return are additive. i.e. β p = XA β A + XB β B , RP = XA RA + XB RB , where XA, XB are the proportions of the money invested in the securities A & B in the portfolio P. The investor has a maximum risk tolerance of 4.00. The return that he can earn (in percent) is: (A) 9 (B) 12 (C) 10 (D) 16 Solution: As the risk factors of securities A and B are 3 and 6 respectively, and the maximum risk tolerance is 4, we have

3XA + 6XB = 4 and xA + XB = 1

Solving the above equations, we get XA =

and XB =

As return in portfolio is given by

RP = XA. RA + XBRB, we have RP =

(9)+

(12) = 10

∴ The maximum return from the portfolio is 10% Choice (C) 89. If you have 3 tickets to a lottery for which 10 tickets were sold and 5 prizes are to be given, the probability that you will win at least one prize is:

(A)

(B)

(C)

(D)

Solution: Probability of winning at least one price = 1 – probability of wining no prizes. Out of the 10 tickets 5 have a prize associated with them and 5 do not have any prize associated with them. If you have 3 tickets with you, the possible number of cases that you may not get any prize is by choosing 3 tickets out of the no prize tickets = 5C3

∴ Probability of not winning even a single prize =

∴ Probability

of

winning

.

al

least are prize = 1 – = Choice (D) 90. Statistics show that 20% of smokers get lung cancer and 80% of lung cancer patients are smokers. If 30% of the population smokes, then the percentage of population having lung cancer is (A) 4 (B) 3 (C) 8 (D) 7.5 Solution: The following figure represents the data and calculation.

30% of the population are smokers of these 20% (i.e 6%of total population) have lung cancer. These represent only 80% if the cancer patients. Therefore 1/4 of these, i.e 1.5% of the total population are the non-smoking cancer patients. The percentage of population having by cancer in (6 + 1.5) or 7.5%. Choice (D) 91. The adjacent sides AB, BC of a square ABCD of side ‘a’ units are tangent to a circle. The vertex D of the square lies on the circumference of the circle. The radius of the circle could be

(A) a(2 −

)

(B) a(

− 1)

(C)

(D) a(

+ 1)

Solution: In the given figure, let ABCD be the square AB and BC are tangents to the circle. Vertex P lies on the circle, whose centre in O.

Let T, U be the points of contact of the circle with AB, BC. ∴ OT = TB = BU = OU = radius of the circle (OTBU is a square) extending UO and TO to meet AD and PC at Q & P respectively. OQ = AB – TB. OP = BC – BU Since AB = BC & TB = BU ∴ OP = OQ. ∴ OPDQ is also a square. OD the diagonal of OPDQ = radius of circle.

∴ OQ =

=

. Similarly

OU + OQ = radius + ∴ OU + OQ = UQ =AB = a.

r+

r

=a

=

).

92.

is equal to

=

a(2 Choice (A)

–

(A)

(B) tan-1

(C) π

(D)

Solution:

= (tan−1 3 − tan−1 1) + (tan−15 − tan−13) +…[tan−1(2n + 1) − tan−1(2n − 1)]

=

Choice (A)

93. Semicircle C1 is drawn with a line segment PQ as its diameter with centre at R. Semicircles C 2 & C3 are drawn with PR & QR as diameters respectively, both C 2 & C3 lying inside C1. A full circle C4 is drawn in such a way that it is tangent to all the three semicircles C1, C2 & C3, C4 lies inside C1 and outside C2 & C3. The radius of C4 is:

(A)

(B)

(C)

(D)

Solution: Let the radius of C1 be 2x. ∴ the radii of C2 and C3 is x. let the radius of C4 be y and the centres C2, C3, C4 be A,B,C respectively.

AC2 = CR2 + RA2 ∴ (2x –y)2 + x2 = (x + y)2 ⇒ 4x2 – 4xy + y2 + x2 = x2 + 2xy + y2 ⇒ 4x2 = 6xy ⇒y = PQ/6.

1/6

(4x)

Choice (B)

=

94. We define the modulus of a m × n matrix by |A| =

< θ ≤ π /2), for which the matrix

(A)

(B)

. The angle, θ , (0

will have the maximum possible modulus is:

(C)

(D) None of the above

Solution: Given,

 A =

Here, A =

∴  A =Max = Max (cosθ + sinθ , sinθ + cosθ , 1)

= max (cosθ + sinθ ),

0≤ θ ≤

=

[∵ sinθ +

cosθ is

95. If 5 log27(y) + 2log9(81y) then y is equal to (A) 81 (B) 2187 (C) 729 Solution: We first try to get every term in the form log3y. 5 log27y + 2 log981y = 20 ⇒

= 20

⇒

log3y + 4 + log3y = 20

⇒

log3y = 16 ⇒ log3y = 6

maximum Choice (D) (D) 59049

when θ = π /4)

=

729 (C)

⇒y

=

96. We define f : R by f(x) = (A) 0 and −1

36 = Choice

. Then the function f(f(f(x))) is discontinuous at:

(B) −1 and 1

(C) −1

(D) None of the above

Solution: Given, f : R–{1} → R is defined

as, f(x) = (i) Clearly, f(x) is not defined when x = 1 ⇒ f(x) is discontinuous at x = 1. ⇒ f(f(f(x))) is discontinuous at x = 1. (ii) f(0) = 1 ⇒ f(f(0)) is undefined. ⇒ f(f(f(x))) is discontinuous at x = 0 Hence, choice (D) is the right option. Choice (D) 97. A toy consists of a base that is the section of a sphere and a conical top. The volume of the conical top is 30π sq. units and its height is 10 units. The total height of the toy is 19 units. The volume of the sphere (in cubic units) from which the base has been extracted is

(A)

(B)

(C)

(D)

Solution:

The following figure shows a cross sectional view of a cone mounted on a section of a sphere.

ABC is the conical part AD is the height of the cone, BD is the radius of the base of the cone. Given height of cone = 10 units

Volume of cone = = 30π ⇒ BD2 = 9 ⇒ BD = 3

Consider the spherical part

Height of the toy = height of conical part + DA. ∴ 19 = 10 + DA DA = 9. OA is the radius of the sphere OA = OB = R (say) BD = 3 cm OD = AD – AO = 9 – R Since OBD is right angled, OB2 = OD2 + DB2 ⇒ R2 = (9 – R)2 + 32 ⇒ R2 = 81 – 18R + R2 + 9 ⇒ 18R = 90 R=5

∴ Volume of sphere =

=

× 5× 5× 5

= Choi ce (D) 98. A man 6 feet tall standing 50 feet away from the base of a tower observes that the angle subtended by the tower at his eye level is tan−12. A flagstaff atop the tower subtends an angle of tan−10.1 at the same point. The height (in feet) of the flagstaff is closest to: (A) 18 (B) 20 (C) 25 (D) 22

Solution:

Let AD be the height of the person, BE be the tower and EF be the flagstaff. Then, AD = 6ft, AB = DC = 50ft

From ∆ DCE, tan

⇒

=

⇒ y = 75 (approximately)

From ∆ DCF,

tan

⇒ tan

⇒

⇒x =

=

= x + 75

–75

= 95 – 75 = 20 (approximately) Hence, height of the flagstaff is 20ft. Choice (B) 99. An employee joined a company on 1.4.2004 in the salary grade 8000 − 500 − 9500 − 750 − 12500 with a basic salary of 9000. He is due to retire on 31.3.2007. He contributes 10% of his basic salary to an EPF scheme. His employer contributes an equal amount, If on retirement, he gets full amount of his share of EPF and 50% of the employer’s share, the amount of EPF received by him, ignoring any interest earned on the deposits, will be

(A) 34500

(B) 17250

(C) 43500

(D) 51750

Solution: From April 04 to March 05, he gets 9000 p.a From April 05 to March 06, he gets 9500 p.a From April 06 to March 07, he gets 10,250 p.a ∴ His contribution = 12(900 + 950 + 1025) = 12(2875) = 34,500. ∴ He also gets 50% of the employers. Contribution, i.e.17,250. He Rs.51,750.

get

a

total

100. Operator A has the matrix representation A =

in conventional

representation in the basis of its eigenvectors (eigenbasis)

(A)

(B)

(C)

of Choice (D)

basis. Its

is :

(D)

Solution: We have (x, y) = x (1, 0) + y(0,1) So T(x, y) = xT(1, 0) + yT(0,1) = x(0, – 1) + y (1,0) = (y, –x) Hence the linear transformation of A is T(x, y) = T(y, –x). Now we have the eigen values of A as λ = i and λ = – i The eigen vectors can be taken as (1, i) and (1, – i). Now T(1, i) = (i, – 1) and T(1, – i) = (– i, – 1) Now (i, –1) = i(1, i) + o (1, – i) and (– i, –1) = o(1, i) + (– i) (1, – i).

Hence

the

matrix

is Choice (C)

101.

is equal to: (A) 7e Solution:

=

(B) 7

(C) 2e

(D) 2

=7⋅

7

=

7 ⋅ (1

+

0)0 Choice (B)

102. If z ∈ C lies on the circle whose equation is |z − 3i| = 3

(A)

(B) tan−13

(C) tan−13

, then the argument of

=

is:

(D)

Solution:

⇒ x2 + (y – 3)2 = 18 We note that (3, 6) or 3 + 6i is a point in the locus.

Now = i(1– i) = 1 + i

The

argument

is

tan–11 Choice (A)

=

Note: As all the options are constants, for every point on the locus of , the argument must be constant. 103. A complex number z lies on the curve |z + 6| = 3. The largest magnitude of |z + 3| will be (A) 6 (B) 3 (C) 36 (D) 12 Solution:  z + 6 = 3. The possible values of z are – 3 and – 9. for largest magnitude of  z + 3  is attained at z = – 9 and equals  – 9 + 3 = 6. Choi ce (A) 104. Two vessels A and B of equal capacities contain mixtures of milk and water in the ratios 4 : 1 and 3 : 1, respectively. 25% of the mixture from A is taken out and added to B. After mixing it thoroughly, an equal amount is taken out from B and added back to A. The ratio of milk to water in vessel A after the second operation is (A) 79 : 21 (B) 83 : 17 (C) 77 : 23 (D) 81 : 19 Solution: The composition of the mixtures in the two vessels at different stages in given below. A Initial

B

M

W

M

W

4

1

3

1

Or After 1sttransfer

16

4

Or 15

5

12

3

19

6

After 2ndtransfer 12 +

3+

∴ The ratio of milk and water in A after the 2 transfers in Choice (A) 105. Two circles C1 and C2 having the same radius of 2 cm and the centres at P and Q respectively intersect each other such that the line of centres PQ intersects C1 and C2 at F and E respectively. EF = 1 cm. The whole assembly is enclosed in a rectangle of minimum area. The perimeter of rectangle is (A) 20 units (B) 22 units (C) 24 units (D) 26 units Solution: Length of the rectangle = 2 + 1 + 1 + 1 + 2 = 7 Breadth of the rectangle = 2 + 2 = 4 Perimeter

=

22 (B)

Choice

106.

is equal to:

(A) 0

(B)

(C) 2

(D)

Solution:

= = (–cosx + sinx)

+ (cosx – sinx)

=

+

=

2 Choic

e (C) 107. If each permutation of the digits 1, 2, 3, 4, 5, 6 is listed in increasing order of magnitude, the 289th term will be (A) 326541

(B) 341256

(C) 356241

(D) 314256

Solution: This question is similar to finding the rank of a word, in alphabetical order. When arranged in ascending order, we need to find the 289th term. All the numbers, of the form 1 _ _ _ _ _ , will occupy the places 1 to 120 (5! terms) of the form 2 _ _ _ _ _, will occupy the places 121 to 240 (5! terms), of the form 31 _ _ _ _ _ will occupy places 241 to 264 (4! terms) and the number of the form 32 _ _ _ _ will occupy (4! terms) places 265 to 288. Since we need the 289th term, it will be 34 1 2 5 6 . Choice (B)

108. For ∅ π /2 , let a = (A) 1 .

;b=

, then the value of α

(C) −1

(B) i

-1

+β

-1

will be :

(D) 0

Solution: Given,

α =

= (1 + sin2φ + sin4φ + . . . )

= sec2φ

=

(As 0 < φ < π /2, 0 < sinφ < 1)

and similarly β =

= 1 + cos2φ + cos4φ + . . .

= cosec2φ

(0 < cosφ < 1) =

109. Define

, then the value of

is:

(A)

(B)

(C)

(D)

Solution: Given, φ (x) = (x – xi) = (x – x1) (x – x2) . . . . (x – xn) φ ' (x) = (x – 2) (x – 3) . . . . . (x – n) + (x – 1) (x – 3) . . . (x – n) + . . . . . . so on. (in the first term (x – 1) is missing, in the second term (x – 2) is missing and so on)

Consider,

=x⋅

=

=x⋅

x⋅

=

–

n

= Choice (D) 110. The relationship between the price of gasoline y (in Rupees) and its weekly supply, x (in

hundreds of gallons) is y = 0.37 + . If the weekly supply decreases at a rate of 50 gallons per week when the supply is 600 gallons, the price of gasoline will be changing at the rate of: (A) Rs.0.625 × 10-4 (B) Rs.0.625 × 10-3 0.625 × 10-1

(C) Rs.0.625 × 10-2

Solution: Given, price of Gasoline.

y = 0.37 + differentiating with respect to time

. when x = 600 gallons.

then,

(or rate of change of price)

=

=

Choice (A)

(D) Rs.

111. A line makes equal intercepts of length ‘a’ on the coordinate axes, intersecting the X axis and Y axis at A and B respectively. A circle is circumscribed about the triangle OAB, where O is the origin of the coordinate system. A tangent is drawn to this circle at the point O. The sum of the perpendicular distances of the vertices A, B and O from this tangent is:

(A) 2a

(B)

(C)

(D) a

Solution:

From the figure, it is clear that the sum of the perpendicular distances of A, B, and O from the tangent to the circle at O in AP + BQ = twice the perpendicular distance from O On AB = length of the hypotenuse AB = a. Choice (D) 112. Point P has coordinates (3, 2) with reference to a rectangular frame in two dimensional space. This coordinate frame is rotated in the clockwise direction though an angle of 30º (π /6 radians). The coordinates of P with reference to the rotated frame are:

(A)

(B)

(C)

(D

) Solution: If the reference frame in rotated through θ in the anticlockwise direction the coordinates x1, y1 in the rotated frame are given by x1 = x cos θ + y sinθ y1 = –x sinθ + y cosθ Setting θ = –30°

x1 =

and

y1 =

x1 =

as (x, y) = (3, 2)

and y1 = Choice (A)

113.

is equal to (where i = (A) 1

(B) −1

)

(C) −i

(D) i

Solution: Put l = 2,

= = [0 – i (–1)] = I Choice (D) 114. An equilateral triangle is inscribed in a circle such that its vertices lie on the circumference of the circle. A point is selected at random from within the circle. The probability of finding the point inside the triangle is

(A)

(B)

(C)

(D)

Solution: We assume that the probability of selecting c point from a region of a certain area in proportional to the area. The required probability P is given by

P = = . Choice (B) 115. Set A consists of n elements. A subset X 1 ⊆ A is constituted. Elements of X1 are replaced in A and a second subset X2 ⊆ A is constituted. This process is repeated to form m subsets X 1, X2, …

Xn of A. The number of ways in which we can form X1, X2, ... Xm such that (A) (2n − 1)m (B) 2mn − 1 (C) (2m − 1)n (D) n! m! − 1

are:

Solution: Let A = {a1, a2, a3 . . . .an} X1 X2 X3 . . . xm are subsets of A. The first element 'a' should be in at least one of the subsets. This can be done in 2m – 1. Similarly the remaining (n – 1) elements should be in at least one of the subsets. This can be done in (2 m – 1)n – 1

∴ Total number of ways in which we can form X 1, X2, X3, . . . . Xm such that 1)n. Choice (C)

= A are (2m –

116. Let [x] represent the greatest integer ≤ x. Define f : R → R by f(x) = [x] + [−x]. At any integral value of x, the function f(x) is: (A) Continuous (B) Discontinuous but has a unique limit (C) Does not have a limit (D) Has only left hand limit Solution: Let a be an integer = a + (– a – 1) = –1 = (a – 1) + (–a) = –1 However f(a) = 0. Thus limit exists and f is discontinuous. Choice (B) 117. The position vector of the mirror image of the point represented by the position vector

across the plane mirror x + y = 0 is

(A)

(B)

(C)

(D)

Solution: We transform this situation in Cartesian coordinates. The image (x, y, z) of a point P(x, y, z) with respect to a plane ax + by + cz + d = 0 is given by

= Accordingly x = –3, y = –2 and z = 4 Choice (A) 118. Let (x) and [x] represent the fractional and integral components of x ∈ R. We define f : R → R; g : R → R by f(x) = (x) ; g(x) = sin[x]π . The range of g o f is: (A) (−1, 1) (B) {0} (C) [1, 1] (D) ∅ Solution: The integral part of a fractional part of any real number is 0. So [(x)] = 0 for all x Now gο f(x) = sin[(x)] π = 0. Choice (B) Directions Q Nos. 119 and 120 are based on the following information: A 300 room motel can rent all its rooms at Rs. 150 per room per day. For every one rupee increase in tariff, the occupancy falls by 2 rooms. Normal maintenance, independent of occupancy is Rs.120 per room per day. Occupancy entails additional costs of Rs.16 per room per day on the units occupied. 119. The optimal tariff (in Rupees) to maximize annual profits. (A) 150 (B) 162 (C) 158 (D) 160 Solution: The given question can be answered from the Choices. When the tariff is Rs.150, The revenue = 150 × 300 = Rs.45000 The normal maintenance expenditure = 300 × 120 = Rs.36000 Additional expenditure = 300 × 16 = Rs.4800

Total expenditure = Rs.40800 Profit = 45000 – 40800 = Rs.4200 When the tariff is Rs.162, occupancy = 300 – 2 × 12 = 276 Revenue = 162 × 276 = Rs.44712 Total expenditure = 36,000 + 276 (16) = Rs.40416 Profit = 44712 – 40416 = Rs.4296 When the tariff is Rs.158, occupancy = 300 – 2 × 8 = 284 Revenue = 158 × 284 = Rs.44872 Total expenditure = 36,000 + 284 × 16 = Rs.40544 ∴ Profit = 44,872 – 40544 = Rs.4328 When the tariff is Rs.160, occupancy = 300 – 2 × 10 = 280 Revenue = 160 × 280 = Rs.44,800 Total expenditure = 36,000 + 280 × 16 = Rs.40,480 ∴ Profit = 44,800 – 40, 480 = Rs.4320 ∴ Optimum tariff Rs.158.

is Choice (C)

120. Now, suppose that rooms of the motel can be permanently shut down in blocks of 5, if desired, resulting in savings of normal maintenance of Rs.120 per room per day. The optimal tariff (in Rupees) to maximize annual profits in this case would be. (A) 158 (B) 160 (C) 162 (D) 156 Solution: Trying from the choices, we have the following: When the tariff is Rs.158 Revenue = 158 × 284 = Rs.44872 Expenditure = 285 × 120 + 284 × 16 = Rs.38,744 (As 16 rooms are unoccupied, in the blocks of 5, 15 can be shutdown) Hence profit = 44872 – 38,744 = Rs.6128. When the tariff is Rs.160 Revenue = 160 × 280 = Rs.44,800 Expenditure = 280 × 120 + 280 × 16 = Rs.38,080 (All the 20 rooms can be shut down) Hence profit = Rs.6,720 When the tariff is Rs.162 Revenue = 162 × 276 = Rs.44,712 Expenditure = 280 × 120 + 276 × 16 = Rs.38016 (20 rooms, can be shut down in the blocks of 5) Profit = 44712 – 38016 = Rs.6,696. When the tariff is Rs.156 Revenue = 156 × 288 = Rs.44,928 Expenditure = 290 × 120 + 288 × 16 = Rs.39408 (10 rooms in the blocks of 5 can be shut down) Hence profit = Rs.5520 ∴ Optimum tariff Rs.160.

SECTION 4: DATA INTERPRETATION (121 − 150)

Questions 121 to 129 are based on the following charts.

Choice (B)

is

121. Current reserves and annual consumption of India is 5.58 and 0.72 billion barrels. If the expected annual growth rate of consumption for India is 2%, the oil reserves of India (in billion barrels) after five years would be (A) 1.74

(B) 1.76

(C) 1.78

(D) cannot say

Solution: As the given pie charts show information about production, consumption and reserves, but nothing about India’s imports and exports of oil, the question cannot be answered. Choice (D)

122. How many days of India’s oil consumption is equivalent to daily consumption of the USA? (A) 8

Solution:

(B) 10

(C) 11

(D) insufficient data

India’s oil consumption is 5.13% of the total consumption and that of USA’s it is 51.28% of the total consumption. Hence 10 days of India’s consumption is equal to that of USA’s daily consumption

as

Choice (B)

123. If estimated global reserves of oil is 1146.49 billion barrels, the level of reserves located in the USA in billion barrels would be approximately. (A) 29

(B) 34

(C) 36

(D) 98

Solution: Reserves of oil in USA = 2.53% of 1146.4 ≅ 29

billion

barrels.

Choice (A)

124. Daily production and consumption of the USA is 8.84 and 20 million barrels respectively. Assuming that these levels remain constant, how long would the oil reserves in the USA last? (year = 360 days, global reserves = 1146.49 billion barrels) (A) 4 years

(B) 6 years

(C) 8 years

(D) 9 years

Solution: USA’s oil reserves = 29 billion barrels. (from Q.No.127) USA’s daily production = 8.84 million barrels. At the rate of 8.84 million barrels a day for 360 days, it is 360 × 8.84 a year.

≅ 9.2 years

Hence oil reserves of USA will last for = i.e., years. Choice (D)

9

125. Which of the charts truly represent the global position? (A) All the charts

(B) Two of the charts

(C) One of the charts (D) Cannot say

Solution: Only position

chart

1

(Global

reserves

of oil) Choice (C)

represent

global

126. Daily production and consumption figures of India are 0.6 and 2.2 million barrels. For which of the following countries the difference between consumption and production is the lowest? (A) Iran

(B) India

(C) Saudi Arabia

(D) Russia

Solution: Difference between India’s production and consumption = 2.2 – 0.66 = 1.54 million barrels. Difference between Russia’s production and consumption.

= 3.29 – 3.99 = 0.69 million barrels. (For Iran and Saudi Arabia, as there is no information about their respective shares in oil consumption, It is the lowest forRussia.) Choice (D)

127. Reserves and annual production figures for India are 5.58 and 0.24 billion barrels respectively. Which country has the lowest ratio of annual production to reserve? (A) USA

(B) Iran

(C) Saudi Arabia

(D) India

Solution: The ratio of Annual production to reserves for the four countries can be directly obtained from the two graphs

India:

USA:

Saudi Arabia:

and Iran:

It for Iran (B)

is

lowest Choice

128. The reserves located in Libya as percentage of reserves located in Russia is (A) 50

(B) 52

(C) 54

(D) 56

Solution:

Required

percentage

= Choice (B)

129. Which of the following is true? (A) Saudi Arabia and USA are the highest consumer and producer respectively. (B) Saudi Arabia and USA are the higher produce and consumer respectively. (C) Russia is the lowest producer and consumer. (D) None of the above.

Solution: From the given pie charts of production and consumption, we observe that Saudi Arabia is the highest producer and USA is the greater consumer respectively. Choice (B) Questions 130 to 133 are based on the following table.

All India installed capacity (in MW) of power Region Sector Total HYDRO THERMAL NUCLEAR Northern State 17898

6401

11491

0

Region Central 13642

3810

8652

1180

State 19611

4180

15405

0

Central 7387

875

5752

760

8318

0

0

6340

780

7915

2256

5656

0

Central 8552

204

8348

0

North State 1098 Eastern Region Central 1235

274

824

0

860

375

0

41692

0

29467

2720

Western Region Southern Region Eastern Region

State 18744 10395 Central 7120 State

State 65265 23505 All India Central 37936

5749

130. What is the percentage of Nuclear Power in total installed capacity in the country? (A) 2.74

(B) 2.81

(C) 2.51

(D) 2.63

Solution: Installed capacity in Nuclear Power = 2720 Total installed capacity in all the three sources = 65265 + 37936 = 103201

Required Percentage =

≅ Choice (D)

131. Hydro power is the major source of energy in (A) Northern and Southern Regions.

(B) Eastern and Western Regions.

(C) Southern and North Eastern Region

(D) None of the above.

Solution: In Northern Region, the contribution from thermal source (20143) is more than that of Hydel source (10211). ∴ Thermal power is the major source in Northern Region. Similarly, in every

other region the contribution from Therma power is more than Hydel Power. So, Hyder Power is not the major source in any of the regions. Choice (D)

132. In any sector, across the regions, the highest contribution from any one of the three sources to the total installed capacity is (A) 79%

(B) 78%

(C) 89%

(D) 98%

Solution: The highest contribution is by Thermal source in central sector in Eastern Region i.e.,

Choice (D)

133. Which region has the highest installed capacity by the Central sector as compared to the State sector. (A) Northern Region (B) Southern Region

(C) Eastern Region

(D) North Eastern Region

Solution: We have to find out the region in which ratio of central to state installed capacity is highest. Of the four regions given in the choices, only Eastern Region and North Eastern region have this ratio more than 1.

Now, for Eastern Region,

North Eastern Region =

∴ It

is

the

highest

Region. Questions 134 to 140 are based on then following Charts:

for

North Choice (D)

Eastern

134. Trend of stock and index futures contracts diverged in the month of (I) March to April (II) April to May (III) May to June (A) I and II (B) II and III (C) I and III (D) I, II and III Solution: The Number of Stock futures contracts decreased from March to April, but the Number of Index futures contracts increased from March to April. Similarly,

From May to June, the % increase in one of them is very less but the percentage increase in the other one is very high. ∴ This happened in both the cases from March to April and also from May to June. Choice (C) 135. Difference in the growth or decline rates between number and turnover of futures contact in any given month is the highest for (I) Stock futures (II) Index Futures (A) I only (B) II only (C) I and II (D) Insufficient Data Solution: The difference is the highest from March to April for number of Index futures (approximately 75% increase) and Turnover of Index futures (approximately 25% decrease) i.e., a total difference of 100 percentage points. Choice (B) 136. The highest monthly percentage growth or decline occurred in the case of (A) Number of Stock Futures Contracts. (B) Number of Index Futures Contracts. (C) Turnover of Stock Futures Contracts. (D) Turnover of Index Futures Contracts. Solution: The required percentage for Number of Index futures contracts from March to April is more than 50%. For each of the other, it is less than 50%. Cho ice (B) 137. Value of a contract is defined as the ratio of turnover to number of contracts. The value of the contract was highest for both stock and index futures occurred in (A) January (B) February and March (C) Only March (D) Insufficient Data Solution: For stock futures contract, the values that must be observed are for February and March,

Now for February =

for March =

(approximately )

( approximately)

By comparing the above values,

Similarly for stock futures contracts, for

February =

March = The required value is highest for March; ∴ For both stock futures contract and Index futures contracts it is the highest in March. Choice (C) 138. The highest growth rate between January and June occurred in then case of (A) Number of Stock Futures contracts (B) Number of index Futures contracts. (C) Turnover of Stock Futures contracts (D) Turnover of index Futures contracts.

Solution: The growth for each of the four values are as follows. Number of Stock futures: 460 → 580 Number of Index futures: 200 → 360 Turnover of Stock futures: 16 → 16 Turnover of Index futures: 7.8 → 7.8 ∴ It is the highest for Number of contracts. Choice (B) 139. Consistent growth pattern is observed for (A) Number of Stock Futures contracts (C) Both Stock and Index Future Contracts Solution: For none June.

of

the

four

given,

index

futures

(B) Number of Index Futures contracts (D) None of the above

there is a Choice (D)

consistent

growth

from

January

to

140. Which of the following is true? (A) Number and Turnover of Stock futures follow a similar pattern. (B) Number and Turnover of Index futures follow a similar pattern.’ (C) Number of Stock futures and Turnover of index futures follow a similar pattern. (D) Number of index futures and Turnover of Stock futures follow a similar pattern. Solution: In the given case, both number and Turnover of Stock Futures followed the same pattern. Choice (A) is true. But in the Choices, Choice (C) is also true as Number of Stock Futures and Turnover of Index Futures followed the same pattern. Hence any of (A) and (C) is true. Choice (A, C) Questions 141 to 145 are based on the following charts:

141. FII flows recorded negative growth rates in (A) One years

year (D) Four years

(B) Two

years

(C) Three

Solution: FII flows recorded negative growth rate from 1994-95 to 1995-96 and from 1996-97 to 1997-98 i.e., a total of two years. Choice (B)

142. Difference between FII and FDI flows is maximum in the year. (A) 1992-93 95-96

(B) 1993-94

(C) 1994-95

(D) 19

Solution: By

observation,

difference

is

the

94.

maximum

in

1993-

Choice (B)

143. FDI flows recorded highest growth between 96

(A) 1992-93 and 1993-94 (D) 1995-96 and 1996-97

(B) 1993-94

and

1994-95

(C) 1994-95

and

1995-

Solution: The 96

growth

is

the

highest

from 1994-95 Choice (C)

to

1995-

144. FDI flows were greater than FII flows in (A) 1992-93 and 1993-94 1997−98 (D) 1992-93 and 1997-98

(B) 1996-97

and

1997-98

(C) 1993-94

and

Solution: FDI 98.

flows

were

greater

than

FII

flows in Choice (D)

1992-93

and

1997-

145. Over the years which of the following flows are highly volatile. (A) FII flows

flows (D) both FII and Total

(B) FDI

flows

(C) Total

Solution: Of the given three, FDI following the consistent pattern in every year and it is increasing in every year. But FII and total flows are not following the consistent pattern. Choice (D) Questions 146 to 150 are based on the following charts:

146. The ratio of interest earned to total income shows (A) Increasing Trend (B) Decreasing Trend trend

(C) Erratic

(D) No particular

Solution: The required ratio, i.e., interest earned to total Income decreased in the first two years and then remained same for the next two years. Hence, Choice (D) is the correct Choice. Choice (D) 147. Total income and interest earned reported similar decline between (A) 2001 and 2002 (B) 2002 and 2003 (C) 2003 and 2004 Solution: They 2004.

showed

decrease

from

(D) 2004 and 2005

Choice (C)

2003

to

148. The difference between total income and total expenditure is maximum in the year. (A) 2002 (B) 2003 (C) 2004 (D) 2005 .

Solution: The 2005.

difference

is

the

highest

in the Choice (D)

year

149. Which of the following statements in correct? (A) Total income and total expenditure follow similar trend. (B) Total income and interest paid follow similar trend. (C) Total income and total expenditure do not follow similar trend. (D) Other expenses and Interest paid follow similar trend. Solution: Of the given options, (A) is true as total income and total expenditure followed a similar trend. Choice (A) 150. The ratio of total interest paid to expenditure is minimum in the year (A) 2002 (B) 2003 (C) 2004 Solution: The required ratio i.e., Interest paid to 2002

total

expenditure

is the Choice (A)

minimum

(D) 2005

in

the

year