1)The question has a base word that is used in the options given below. Choose the option in

which Feel OPTIONS 1) Artimey could feel it in his bones that Aarya was going to become the principal. 2) Jane hasn‘t been feeling like herself since her father passed away. Imran: Why not feel out the other members‘ opinions before we lodge a formal 3) complaint? 4) Joey doesn‘t feel into going out for the party. the usage of the word is awkward.

Solution ‗To feel in one‘s bones‘ means to have an intuition of. ‗To feel like oneself‘ means to be in one's normal frame of mind or state of health. In option 3, ‗feel out‘ means to attempt to ascertain (the nature of a situation, someone‘s attitude, etc.) by indirect or subtle means. In option 4, it would be more appropriate to use ‗feel up to‘ instead of ‗feel into‘. ‗To feel up to‘ means to be fit enough for something or to do something. Hence, the correct answer is option 4.

2)

OPTIONS

1) 2) 3) 4) None of these

Putting in the value, we get 6P =29 Hence, option 2.

3)

Rearrange the sentences to form a coherent paragraph. A. The condition affects 17 to 35 percent of humans. The probable cause is a congenital malfunction in nerve signals in the trigeminal nerve nuclei. B. Another theory suggests that tears leaking into the nose through the nasolacrimal duct are a cause of the photic sneeze reflex; the speed of the reflex seems to favor the first theory, as it happens much too quickly for tears to be generated and drain into the nose. C. Photic sneeze reflex is a genetic autosomal dominant trait, which causes sneezing when exposed suddenly to bright light, possibly many times consecutively. D. Research suggests that some people have an association between this nerve and the nerve that transmits visual impulses to the brain- overstimulation of the optic nerve triggers the trigeminal nerve, and this causes the photic sneeze reflex. E. It is also referred to as photic sneeze response, sun sneezing, photogenic sneezing, the photosternutatory reflex, being photo sensitive, ACHOO syndrome, and "Achooism," with its related backronym Autosomal dominant Compelling Helio-Ophthalmic Outburst syndrome.

OPTIONS 1) ACDBE 2) DCABE 3) CDEBA 4) CEADB 5) CBDAE

Solution

Statement C introduces the theme of the paragraph. Option A with ‗the condition‘ and option D with ‗this nerve‘ have to be preceded by some statement which explains them. Eliminate options 1 and 2. In option 3, statement D mentions ‗this nerve‘ immediately after statement C. There is no indication of it in statement C. Eliminate option 3. Similarly, option 5 can also be eliminated. The only statement that mentions a nerve is statement A. Therefore, D has to follow A. The AD link is present in option 4. Moreover, option 4 has a smooth flow and transition in the presentation of data. Hence, the correct answer is option 4.

4)Tangents are drawn from a point P on x2 + y2 = 4r2 to the circle x2 + y2 = r2. The tangents

touch the smaller circle at points Q and R. The centroid of ΔPQR OPTIONS 1) is at a distance r from chord QR. 2) does not lie on line joining the origin and point P. 2 2 2 3) lies on x + y = r 4) is at a distance 1.5r from P

Solution Let O be the origin and S, the midpoint of QR and C be the centroid of ΔPQR. OP = 2r and OQ = r. ∴ ∠OPQ = 30° and ∠POQ = 60° ∴ In ∆OQR, OS is perpendicular to QR ∴ OS = 0.5r and SP = 1.5r The centroid (C) divides the median (SP) in the ratio 2 : 1. ∴ SC = 0.5r and CP = r Thus, point C is at a distance of r from the origin. Hence, the centroid of ∆PQR lies on x2 + y2 = r2 Hence, option 3.

5)The question below consists of a paragraph in which the first and last sentence has been

identified. Choose from the options the most logical order of the following sentences.

1.

Typically,

steel

is

heat

treated

in

a

multi-step

process.

A. The steel is held at that temperature until the carbon trapped in the martensite diffuses to produce a chemical composition with the potential to create either bainite or pearlite (a crystal structure formed from a mixture of ferrite and cementite). B. The steel is then tempered by heating between the ranges of 150°C-260°C (300°F-500°F) and 370°C-650°C (700°F-1200°F). C. First it is heated to create a solid solution of iron and carbon in a process called austenizing. Austenizing is followed by quenching to produce a martensitic microstructure. D. Tempering in the range of 260°C-370°C (500°F-700°F) is sometimes avoided to reduce temper brittling. 6. Thus the process of steel tempering is carried out and temper brittling is reduced. OPTIONS 1) CDAB 2) CABD 3) CADB 4) DCAB 5) DCBA

Solution The correct order of this passage is C-A-B-D. The passage describes the process of heat treatment to steel. C is the most obvious choice for the first line connecting the opening line of the passage. It describes the first step that goes into the process. The next logical line should be the introductory line to the need of steel being held at a certain temperature. Further lines describe the exact temperatures at which the treatment is carried out. The connecting link between the closing statement and the previous line is the mention of reduction of temper brittling. Hence, the correct answer is option 2.

6)

The integer N is given by N = 2M × 5386, where M is an integer. If N is known to have 388 digits, how many values can M take? OPTIONS 1) 1 2) 2 3) 3 4) 4 5) None of these

Solution

We first note that 2386 × 5386 = 10386, which has 387 digits. Thus, M must be greater than 386. Now, N = 2M × 5386 = 2M − 386(2386 × 5386) = 2M – 386 × 10386 This number has the digits of 2M – 386 followed by 386 zeros. ∴ For N to have 388 digits, 2M – 386 must have 2 digits. The number of positive integral powers of 2 which have two digits is three. These are, respectively, equal to 24 = 16, 25 = 32 and 26 = 64. M can therefore take values 390, 391 and 392. M can take three values. Hence, option 3.

6)

Paleontologist John Ostrom's study of Deinonychus in the late 1960s revolutionized the way scientists thought about dinosaurs, leading to the―dinosaur renaissance‖ and igniting the debate on whether dinosaurs were warm-blooded or cold-blooded. Before this, the popular conception of dinosaurs had been one of plodding, reptilian giants. Ostrom noted the small body, sleek, horizontal posture, ratite-like spine, and especially the enlarged raptorial claws on the feet, which suggested an active, agile predator. What can be inferred about the ―dinosaur renaissance‖? OPTIONS It was a scientific moment of discovery that reshaped the notions about the biological make of dinosaurs. 2) John Ostrom was responsible for it because of his study of the Deinonychus. 1) 3) It busted the notion that dinosaurs were just plodding, reptilian creatures. 4) All of the above 5) None of the above

Solution Option 1 can inferred from the fact that it ingnited the debate. The later description of Ostrom adds to the explanation for ―biological make‖. Option 3 can be inferred from ―Before this, the popular conception of dinosaurs had been one of plodding, reptilian giants.‖ Option 2 can be inferred from ―Paleontologist John Ostrom's study of Deinonychus ... leading to the ―dinosaur renaissance‖.‖

Hence, the correct answer is option 4.

7)

The question below consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from among the options. A. Merely viewing another person's movements activates our own motor cortex, which we normally use for precise control of our actual movements. B. Brain imaging studies have now shown that the human brain contains a similar mirror-neuron system. C. As sports fans, musicians, and students of body language know, watching other people's movements and postures may facilitate the viewer's own motor schemes, sometimes resulting in unintended imitation. D. A monkey's mirror neurons are activated both when he himself is acting, say, taking a raisin from a tray, and when he is viewing another monkey (or the human experimenter) performing the same act. E. Mirror neurons, first discovered in monkeys, may serve help us master basic social skills, providing a common code between the sender and receiver of a nonverbal message.

OPTIONS 1) CDEBA 2) BEDAC 3) ABCED 4) CABED 5) EDBAC

Sol There are two clues that get you two links between the statements. First is the link between statement E and D. The mirror neurons ‗first discovered in monkeys‘ should be placed before statement D in which the ‗monkey‘s mirror neurons‘ are spoken about. Therefore E is placed before D. Secondly, the word ‗similar‘ in statement B refers to the mirror neurons that humans share with the monkeys. Therefore, the monkey‘s neurons have to be mentioned first if they are to be compared to the human‘s brains. Therefore, statement B is placed after statements ED. The importance of the mirror neuron is that when activated it is performing an action or watching someone perform something. Statement A explains this behaviour with reference to human beings – ‗our own motor cortex‘. Statement C functions as an illustration of this activity and is therefore placed at the end of the paragraph.Hence, the correct answer is option 5.

8)

The value of (a1 + a2 + a3 +… + an)(a1−1 + a2−1 + a3−1 +…+ an−1) can be OPTIONS 1) n 2 2) n 3) n2 − 1 2 4) n − n 5) None of these

Solution By AM GM inequality (a1 + a2 + a3 +… + an)n ≥ (n)n(a1a2a3…an) (a1−1 + a2−1 + a3−1 +…+ an−1)n ≥ (n)n(a1a2a3…an) −1 Multiply the two equations and take nth root to get, (a1 + a2 + a3 +… + an)(a1−1 + a2−1 + a3−1 +…+ an−1) ≥ n2 Hence, option 2.

9)Statistics published by the Traffic Control Department show that nearly 80% of all traffic

fatalities occur at speeds of under 50 miles per hour and within 25 miles of home. Therefore, you are safer in a car if you are driving at a speed over 50 miles per hour and not within a 25mile radius of your home. Which of the following, if true, most weakens the conclusion of the argument above? OPTIONS 1) 2) 3) 4) 5) 80% of all persons arrested for driving at a speed over the posted speed limit are intoxicated. 90% of all driving time is registered within the 50-mile radius of the driver‘s home and at speeds less than 25 miles per hour. 80% of the nation‘s annual traffic fatalities occur on six weekends that are considered high-risk weekends because they contain holidays. 90% of all driving time is registered within a 25-mile radius of the driver‘s home and at speeds less than 50 miles per hour. 90% of all driving time is registered outside the 25-mile radius of the driver‘s home and at speeds less than 50 miles per hour.

Solution The conclusion of the argument in the question has a fallacy telling that a person is safer when driving at higher speeds. Moreover, the distance from home does not necessarily make one more or less safe. The real reason there are fewer fatalities at speeds over 50 miles per hour and at a distance greater than 25 miles from home is that less driving time is logged under such conditions, which is given by option 4. Most driving originates at home and is not usually too long and proceeds at speeds set for residential areas. Options 1 and 3 seem to make plausible statements, but they are irrelevant to the claim made in the paragraph. Option 2 with 50-mile radius, 25 miles per hour and option 5 with 'outside' the 25-mile radius change the context of the main data. Hence, the correct answer is option 4.

10)

This question consists of two capitalized words that have a certain relationship. Choose the pair that has words not related to each other in the same way as the capitalized pair. COMSTOCKERY: ENDORSEMENT :: OPTIONS 1) Drawcansir: Bullyragger 2) Hector: Encourage 3) Generous: Alienating 4) Coercive: Voluntary 5) Despot: Democrat

Solution ‗Comstockery‘ means a censorship of literature and other forms of expression and communication because of perceived immorality or obscenity. ‗Endorsement‘ is the antonym. ‗Drawcansir‘ refers to a blustering, bragging bully. ‗Hector‘ means a bully and ‗encourage‘ is the antonym for it. ‗Generous‘ means liberal in sharing, while the antonym for it is ‗alienating‘. ‗Coercive‘ means forcible and the antonym for it is ‗voluntary‘. ‗Despot‘ is a tyrant and ‗democrat‘ is its antonym. ‗Bullyrag‘ is the only synonym to ‗Drawcansir‘. Hence, the correct answer is option 1.

11)

The question below consists of a certain number of sentences or parts of sentences. Some of these sentences or parts of sentences are incorrect or inappropriate due to issues in grammar or spelling. Select the option that indicates the correct and appropriate sentence(s) or parts of sentence(s).

A. B. C. D. E.

Three years back, the Kannada actress Jaimala triggered a major controversy when she said that she had entered the sanctum sanctorium of Sabarimala. This triggered a debate on if women should be allowed to enter Sabarimala. In 1930s, Aliki Diplarakou, who had won the Miss Europe title, dressed up as a man and sneaked in Mt. Athos in Greece generating a similar controversy.

OPTIONS 1) A only 2) A and E 3) A, B, and C 4) B, C, and D 5) C, D, and E

Solution Statement B is incorrect because Sanctum Sanctorum is spelt incorrectly as ―sanctorium‖with an incorrect ―i‖ after the ―r‖. Statement C is incorrect- use ‗whether‘ in the place of ―if.‖ Use "if" to express a condition. You may borrow my car if you are careful with it. Use "whether" to express alternatives. She did not know whether to say yes or no. Statement D is incorrect because the definite article has to be used before 1930s- ‗In the 1930s‘. Statement E is incorrect because the correct idiom would be ‗sneaked into‘ and not ‗sneaked in‘. Hence, the correct answer is option 1.

12)

Since all patients of paralysis I have encountered have failed to recover completely from physical disability, it follows that the paralysis patient who has been admitted today will also be left with some disability. Which of the following most closely parallels the reasoning of the argument? OPTIONS 1) 2) 3) 4) 5) Some birds are incapable of flight; therefore, swans are probably incapable of flight. Every ballet I have attended has failed to interest me; so a theatrical production which fails to interest me must be a ballet. Since all cases of severe depression I have encountered were susceptible to treatment by chlorpromazine, there must be something in the chlorpromazine that adjusts the patient‘s brain chemistry. Because almost all societies have a word for justice, the concept of fair play must be inherent in the biological makeup of the human species. Since no medicine I have tried for my allergy has ever helped, this new product will probably not work either.

Solution The sample argument is a straightforward generalization: All observed P are Q. R is a P. Therefore, R is Q. Option 4 comes a close second, but only option 5 replicates this form. Hence, the correct answer is option 5.

13)There are four sections A, B, C and D in a school. If the pass percentage of sections A, B

and C is 50%, that of sections A, B, D is 55%, that of A, C, D is 60% and that of B, C, D is 65% then which of the following can be the pass percentage of sections A, B, C and D combined together. OPTIONS 1) 56.33 2) 54.67 3) 53.33 4) 52.67

Solution Let the number of students in sections A, B, C and D be a, b, c and d respectively. Total number of students passing from sections A, B and C = (a + b + c) × 0.5 Total number of students passing from sections A, B and D = (a + b + d) × 0.55 Total number of students passing from sections A, C and D = (a + c + d) × 0.60 Total number of students passing from sections B, C and D = (b + c + d) × 0.65 Adding the 4 we get 3 × Total number of students passing from sections A, B, C and D = 1.65(a + b + c + d) + 0.05b + 0.1c + 0.15d ∴ Total number of students passing from sections A, B, C and D

Hence we can see that the minimum value can be 55.

Only option 1 lies in the range. Hence, option 1.

14)

Sakshi: All of the graduates from Seventh Day High School go to Willson College. Anushka: I don‘t know. Some of the students at Willson College come from Ilva High School. Anushka‘s response shows that she has interpreted Sakshi‘s remark to mean that: OPTIONS 1) Most of the students from Seventh Day High School attend Willson College 2) None of the students at Willson College are from Seventh Day High School 3) Only students from Seventh Day High School attend Willson College 4) Seventh Day High School is a better school than Ilva High School 5) Some Ilva High School graduates attend Willson college

Solution The question stem is important here. It asks us to state what meaning Anushka made of Sakshi's statement. The statement that Anushka made in the main data would be appropriate only if Sakshi had said, ―All of the students at Willson college come from Seventh Day High School.‖ Option 5 is a mere repetition of Anushka's statement. Option 4 is irrelevant to the context. Option 2 is contrary as Anushka uses only 'some' for students from Ilva High School. Option 1 is in consonance with what Anushka thinks (not what she understood from Sakshi's statement). Only option 3 clearly states Anushka's assumption or interpretation. Hence, the correct answer is option 3.

15)

Hybrid vehicle drivetrain systems will be extensively allowed with the new regulations, which include kinetic-energy recovery systems (KERS; no push-to-pass systems – KERS in LMP cars must be activated with the accelerator pedal), as well as four-wheel drive (non-hybrid vehicles will remain two-wheel drive, specifically rear-wheel drive). All LMP cars will be weighed at 900 kg (2,000 lb). In addition, LMP bodywork must have a Formula One-style vertical fin on the top of the engine cover to reduce lift tendency and such "flipping" airborne crashes such as the 1999 race with three incidents by the Mercedes-Benz CLR, the most famous is by Peter Dumbreck and the 2008 1000 km of Monza crash by Stéphane Ortelli with the Courage-Oreca LC70. Which of the following most accurately sums up what the passage is talking about?

OPTIONS

1) There are safety regulations that are mandatory to allow LMP cars to race. 2) The most important objective of LMP cars is to ensure that cars are never more than 900 kgs.

3) A vertical fin is necessary to stop cars from flipping and going into airborne crashes. 4) The Mercedes-Benz CLR is the most famous wreck in the history of LMP racing. 5) There are safety regulations that are mandatory to allow hybrid cars to race.

Solution

The passage starts by listing “regulations” and the last line of the passage implies that these regulations are in place to avoid car crashes, and thus are concerned with safety. Options 2, 3 and 4 are incorrect, as they focus on only one aspect of the passage, and not on the summation. Option 5 is incorrect because the passage also talks about non-hybrid cars which fall under the regulations. Hence, the correct answer is option 1.

16)

1 × 31 + 2 × 32 + 3 × 33 + … + n × 3n

What is the value of n? OPTIONS

1) 15 2) 16

3) 17 4) 18 5) 19

Solution

S = 1 × 3 1 + 2 × 3 2 + 3 × 3 3 + … + n × 3n = (31 + 32 + 33 + … + 3n) + (32 + 33 + … + 3n) + (33 + 34 + … + 3n) + … + 3n

Comparing these equations, we get n = 18 Hence, option 4.

17)

The polio vaccine is administered in two ways: IPV is given as a shot in the arm or leg; OPV is given as an oral liquid. OPV is no longer used in the United States, but is still given in other parts of the world where polio is common. The change to an all-IPV schedule in the United States occurred because the few cases of polio that were occurring were caused by the OPV vaccine itself and not the wild virus. The change to IPV protects individuals against paralytic polio, while eliminating the small chance of actually contracting polio from the live oral vaccine. IPV has been used exclusively in the United States since 2000. However, in other countries where wild polio is still a threat, OPV is still used. Which of the following can be inferred from the data given above? OPTIONS 1) Wild polio has been eradicated from the United States. 2) OPV contains live and wild polio virus. 3) IPV is a better form of vaccination against polio. An all-IPV schedule of vaccination eliminates the chances of polio from the wild 4) virus. 5) 1 and 2

Solution

―OPV is no longer used in the United States … because the few cases of polio that were occurring were caused by the OPV vaccine itself and not the wild virus.‖ It can be thus inferred that OPV is used to combat the wild virus. Hence the inference follows that the US has got rid of polio caused by the wild virus. Secondly, the following extract, ―IPV has been used exclusively in the United States since 2000. However, in other countries where wild polio is still a threat, OPV is still used‖ corroborates option 1- that wild polio has been eradicated from the Unites States. Option 2 is incorrect- because it can be inferred that OPV contains live virus but definitely not the ‗wild virus‘. Administering wild virus would be spreading the disease and not vaccination. Option 3- IPV being a better form of vaccination than OPV is too strong an inference to make and cannot be deduced from the passage with any degree of certainty. Option 4 is contrary to the passage. An all-IPV schedule of vaccination eliminates the chances of polio caused by the OPV vaccine itself- not from the wild virus. Hence, the correct answer is option 1.

18)

ADVERTISEMENT: When you enrol with Fly High Business Institute (FHBI), you will have access to our placement counseling service. Last year, 90% of our graduates who asked us to help them find jobs found them. So go to FHBI for your future! The answer to which of the following questions is potentially the LEAST damaging to the claim of the advertisement? OPTIONS

1) How many of your graduates asked FHBI for assistance? 2) How many people graduated from FHBI last year? Did those people who asked for jobs find ones in the areas for which they were 3) trained? Was FHBI responsible for finding the jobs or did graduates find them 4) independently? 5) Was the person doing the advertisement a paid, professional actor?

The advertisement seeks to create an impression that FHBI found jobs for its many graduates and generally does a lot of good for them. But first we should ask how many graduates FHBI had—as finding jobs for a handful of them might have been easy; but if many people enrol at FHBI, they may not have the same success. Further, we might want to know how many people graduated compared with how many enrolled. So option 2 is a valid question. Now, how many of those who graduated came in looking for help in finding a job? Maybe most people had jobs only a few needed help or, perhaps the graduates were so disgusted they did not even seek assistance. So, option 1 is relevant. Option 3 is also important; perhaps FHBI found them very menial jobs —not in business. Finally, maybe the ad is truthful—FHBI graduates found jobs—but maybe they did it on their own. So, option 4 also is a question worth asking. Option 5, however, is the least problematic. Even if it turns out that the ad was done by a paid, professional actor, so what? That‘s what we expect from an advertisement. Hence, the correct answer is option 5.

19)

Gaga has identified fashion as a major influence. She considers Donatella Versace her muse. Gaga has her own creative production team called the Haus of Gaga, which she handles personally. The team creates many of her clothes, stage props, and hairdos. Her love of fashion came from her mother, who she stated was "always very well kept and beautiful.‖ "When I'm writing music, I'm thinking about the clothes I want to wear on stage. It's all about everything altogether—performance art, pop performance art, fashion. For me, it's everything coming together and being a real story that will bring back the super-fan. I want to bring that back. I want the imagery to be so strong that fans will want to eat and taste every part of us." What can we conclude about Gaga from the passage? OPTIONS Gaga is a firm believer in the cult of culture – a society where performance art is at its pinnacle. Gaga‘s mother has a major influence on the kind of personality she assumes on 2) stage. 3) Gaga is a singer and a stage performer. 1) 4) Gaga is a performer-song-writer with a tilt towards elegance and grace.

5)

Gaga creates an identity for each piece of music she writes that becomes larger than the song itself.

solution

The passage states that she keeps in mind the fashion and the performance art pieces while she is writing music – thus it isn‘t just about the music, but the whole package. ―When I'm writing music, I'm thinking about the clothes I want to wear on stage. It's all about everything altogether—performance art, pop performance art, fashion. For me, it's everything coming together and being a real story that will bring back the super-fan.‖ Option 1 is wrong because it‘s too vague. Option 2 is wrong because the passage states that her mother merely inspired her love for fashion. Option 3 is wrong because nowhere does the passage state that she sings. Option 4 is wrong as the passage implies the opposite – that she has a flair for the dramatic – pop performance art et al. Hence, the correct answer is option 5.

20)

A colour concentrate comes under three varieties viz. A, B and C in which the concentrations of colour are 20%, 30% and 50% respectively. If the per litre prices of A, B and C are Rs. 20, Rs. 30 and Rs. 40 respectively, then what is the minimum cost (approximate) in which one can prepare 10 litres of a 40% colour concentrate using two of the given varieties? OPTIONS

1) Rs. 345 2) Rs. 350 3) Rs. 367 4) Rs. 323 5) Rs. 333

Solution Concentration of the resultant solution is 40%. Mixing 20% and 30% concentrated solution in any proportion will not give a 40% solution. So, 50% solution has to be used.

This can be done in two ways: Case I: 50% and 20% varieties are mixed together. Ratio of 50% variety to the 20% variety in the 10 litre concentrate is:

Case II: 50% and 30% varieties are mixed together. Ratio of 50% variety to the 30% variety in the 10 litre concentrate is:

Total cost = 5 × 40 + 5 × 30 = Rs. 350 Thus the minimum cost in which the required solution can be prepared is Rs. 333 Hence, option 5.

21)

There are 355 grains of sand in bowl A, 555 in bowl B and 1655 in bowl C. They are mixed together and are arranged in groups of 16. How many grains will be left ungrouped? OPTIONS

1) 15 2) 4 3) 8 4) 2 5) 12

Solution

The number of grains that will be left ungrouped is the same as the remainder when (355 + 555 + 1655) is divided by 16. 16 divides 1655. 355 + 555 = (4 – 1)55 + (4 + 1)55 Expand using binomial theorem. All the terms except the penultimate term of each expansion i.e one 4 × 55C54 have powers of 16 in them. ∴ Remainder = 2 × 4 × 55C54 = 440 = (16 × 27) + 8 i.e. equivalent to a remainder of 8. Hence, option 3.

22)

There is no obvious single source for the plot of The Tempest, but researchers have seen parallels in Erasmus's Naufragium, Peter Martyr's De orbo novo, and an eyewitness report by William Strachey of the real-life shipwreck of the Sea Venture on the islands of Bermuda. In addition, one of Gonzalo's speeches is derived from Montaigne's essay Of the Canibales; and much of Prospero's renunciative speech is taken word for word from a speech by Medea in Ovid's poem Metamorphoses. The masque in Act 4 may have been a later addition, possibly in honour of the wedding of Princess Elizabeth of Bohemia and Frederick V, Elector Palatine, in 1613. The play was first published in the First Folio of 1623. Which of the following can’t be concluded about The Tempest from the passage? OPTIONS

1) The Tempest is not a completely original play. 2) Many inspirations shaped the plot of The Tempest. 3) The story of The Tempest revolves around a shipwreck. 4) Montaigne’s essay Of the Canibales was written before The Tempest.

5)

Princess Elizabeth of Bohemia and Frederick V’s wedding had a role to play in shaping up the plot of The Tempest.

Solution We know that a shipwreck is an essential part of the plot – “There is no obvious single source for the plot of The Tempest, but researchers have seen parallels in Erasmus's Naufragium, Peter Martyr's De orbo novo, and an eyewitness report by William Strachey of the real-life shipwreck of the Sea Venture on the islands of Bermuda.” But we don’t know that the plot revolves around a shipwreck. Therefore, option 3 is not a correct conclusion. Options 1 and 2 can be concluded as the essence of the passage itself is that The Tempest has many inspirations/ sources. Option 4 can be concluded since The Tempest was inspired by Montaigne’s essay, which means that it was written before The Tempest. Option 5 can be concluded from “The masque in Act 4 may have been a later addition, possibly in honour of the wedding of Princess Elizabeth of Bohemia and Frederick V, Elector Palatine, in 1613.” Therefore, the wedding did have a role to play in shaping the plot. Hence, the correct answer is option 3.

23)

Either you severely punish a child who is bad or the child will grow up to be a criminal. Your child has just been bad. Therefore, you should punish the child severely. All of the following would be an appropriate objection to the argument except: OPTIONS

1) What do you consider to be a severe punishment? 2) Don’t your first and second premises contradict one another? 3) What do you mean by the term “bad”? 4) In what way has this child been bad? 5) Both 1 and 4

Solution The terms “severely punish” and “bad” are highly ambiguous and subjective. It would be legitimate to ask the speaker just what he considers to be bad behavior (option 3), and severe punishment (option 1). Also, since the speaker has alleged that the child has been “bad,” and since the term is ambiguous, we can also demand clarification on that score (option 4). The one objection that makes no sense to raise is option 2. The premises have the very simple logical structure: If a child is bad (badly behaved, done something wrong) and not punished, then the child becomes a criminal. Child X is bad, hence punish him severely. There is absolutely no inconsistency between those two statements. Hence, the correct answer is option 2. 24) Vishal went to a shop to buy a mobile phone. He chose one and the shopkeeper told him that the basic price of the phone is Rs. 4,200. The shopkeeper also said that he would have to pay VAT at the rate of 12%, tax A at the rate of 6% and tax B at the rate of 7%. The shopkeeper also offered him a discount of 5%. Now, Vishal is puzzled as to in what order should he add the taxes and subtract the discount so that his bill is minimized in the following scenarios? a) The taxes/discount are both applied on the basic price i.e. on Rs. 4,200.

b) The taxes/discount are applied on the price after adding/subtracting the tax/discount till each point. OPTIONS

1)

In a, the order does not matter. In b, first apply 5% discount, then the 6%, 7% and 12% taxes respectively. In a, the order does not matter. In b, first apply the 12%, 7% and 6% tax and finally the 5% discount. In a, apply the discount first and the taxes in any order, later. In b, the order does not matter.

2)

3)

4) The order does not matter in either case. 5) In a, the order does not matter. In b, first apply the 6%, 7% and then 12% tax in that order followed by the 5% discount.

Solution a) The order does not matter because everything is calculated on the base price and then added/subtracted; and addition/subtraction is commutative. b) The order does not matter because the final amount is any case will be 4200 × 0.95 × 1.06 × 1.07 × 1.12; and multiplication is also commutative. Thus, the order is irrelevant in either case. Hence, option 4. 25) The following question consists of a certain number of sentences. Some sentences are grammatically and/or logically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s). A. M.F. Husain, India's foremost modern painter and an internationally recognised artist, passed away on Thursday, he was 97. B. Thirty First Ladies from Africa, Asia, Latin America and the Caribbean joined forces at the United Nations to mobilise support to achieve the goal of zero new HIV infections among children by 2015. C. Usain Bolt set the quickest time in the world this season as he eased to victory in the 200 meters at a Diamond League meet. D. Mitt Romney will skip a key early test for Republican presidential candidates by forgoing the Iowa straw poll. E. A selloff in bonds backed by subprime mortgages has spread through the riskiest segments of the credit markets and ended up rallying in high-yield corporate bonds and commercial real-estate debt.

OPTIONS

1) Only A 2) Only E 3) A and E 4) A and D 5) B, C and E

Solution Sentences B, C and D are correct. Sentence A is incorrect as “he was 97” is an independent clause - it should have been a separate sentence, or it could have been separated from the rest of the sentence by a semi colon, but not by a comma. Sentence E is incorrect as the word “sell off” refers to the sale or disposal of something. The sentence states that the sell off has spread through the riskiest segments and ended up rallying. The sale of something cannot be “rallied”. Moreover, “ended up rallying in high …. debt” is incorrect as it makes no logical sense and is grammatically incorrect. The correct sentence could be “A selloff in bonds backed by subprime mortgages has spread through the riskiest segments of the credit markets, ending the rally in high-yield corporate bonds and commercial real-estate debt.” Hence, the correct answer is option 3. 24)

Find the equation of the straight line which is the image of the line tanθx + y = 2tanθ in the line x + y/√3 = 2. OPTIONS

1) (x – 2) tan(60° + θ) = y 2) (x – 2) tan(60° – θ) = y 3) (x – 2) tan(30° + θ) = y 4) (x – 2) tan(60° + 2θ) = y 5) None of these

Solution x + y/√3 = 2 passes through (2, 0) and makes 120° with the x-axis. tanθx + y = 2tanθ passes through (2, 0) and makes 180° – θ with the x-axis.

∴ the reflection of tanθx + y = 2tanθ will pass through (2, 0) and make (60° + θ) with the x-axis. Hence, option 1.

25)

What

is

the

value

of

OPTIONS 1) −2 2) −1 3) 0 4) 1 5) 2 Get this! Solution We can find the value of the expression by putting x = 487, y = 674 and z = 187, and simplifying the expression

We first simplify the first two terms as

The next two terms can be simplified as

We can see that these add to zero. Thus, the expression will also be equal to zero. Hence, option 3.

26)

Read the sentences and choose the option that best arranges them in a logical order. A. The Organization of Petroleum Exporting Countries' first meeting since the start of prodemocracy movements in the Middle East also turned out to be one of its most turbulent sessions in years. B. It brought to the fore long-simmering divisions between key cartel players Saudi Arabia and Iran and called into question the group's ability to influence oil prices. C. Tensions spilled into the open as solemn-looking delegates filed out of OPEC's modern headquarters and Saudi oil minister Ali Naimi declared it "one of the worst meetings we ever had." D. An acrimonious OPEC meeting failed to produce an agreement to increase oil production despite tight supplies and rising prices.

OPTIONS

1) ABCD 2) ABDC 3) DABC 4) DBAC 5) BCAD

DiscussGet In EmailGet this! Solution To determine the first sentence of the paragraph, we can use certain grammatical cues. Sentence B , beginning with “it” is not appropriate since the sentences which describe “it” would be better starters. Eliminate option 5. Sentence A seems to a good choice glance since it contains the full form of the organization. However, between statement A and statement D, D had to precede A. Grammatically, statement A uses the definite article “the”, which has to follow “an OPEC meeting” in statement D. Similarly, the use of the indefinite article “an” in statement D indicates that the meeting has not been mentioned previously. Logically, D is the perfect introduction to the entire paragraph which then provides the details. Eliminate options 1 and 2. To an extent, statement A restates what has been mentioned earlier in sentence D. Therefore, it cannot come immediately after statement D. Eliminate option 3. Statement B illustrates the effects of this meeting and is maintains a logical flow. Therefore

statement B has to follow D. Statement A with "turbulent sessions" is linked to statement C which describes how “tensions spilled into the open” at the end of the meeting. Hence, the correct answer is option 4.

27)

Select the option which has a similar analogy vis-a-vis the analogy given below. Tediferous: Torch :: OPTIONS

1) Succiniferous: Succour 2) Succiferous: Sap 3) Thuriferous: Thunder 4) Vasiferous: Vase 5) Furciferous: Fruit

Solution

The Latin suffix ‘ferrous’ is taken from ‘ferre’ or ‘gerere’ meaning to bear. Tediferous means to bear a torch. Succiferous means bearing sap. Succiniferous means bearing or producing amber. Thuriferous is incense bearing and vasiferous means to bear a vessel or vas (duct). Furciferous means either bearing a fork or a rascally person by nature. Hence, the correct answer is option 2.

28)

If the equation 2x4 – x3 + 4x2 + ax + b = 0 has real roots A, B, C and D, and the equation 2x4 – 3x3 + 4x2 + cx + d = 0 has real roots A, B, C and E, what is the value of (D + E)? OPTIONS 1) 1 2) 2 3) 3 4) 4

5) Cannot be determined

Observe that the coefficients for x4 and x2 are the same for both the equations. Therefore, subtract the second equation from the first to get 2x3 + (a – c)x + (b – d) = 0 Since this equation is a third order equation, all its roots will satisfy both the equations given. Since the roots satisfy both the equations, the roots of the cubic equation are the common roots of the two equations i.e. A, B and C. For the cubic equation, sum of the roots is equal in magnitude to the coefficient of x2. Since the coefficient of x2 in this equation is zero, the sum of the roots i.e. A + B + C = 0 Now, for the two original equations, sum of the roots = −(coefficient of x3/coefficient of x4) Now, the sum of the roots of the first equation is

Solution

Hence, option 2.

29)

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s). A. With hours before the deadline to submit nominees, the French finance minister has the backing for European Union countries. B. The outgoing head of Hong Kong's securities regulator warned investors against rushing headlong to buy shares in Chinese companies, calling China "the new dotcom" of the investment world. C. Instead of playing cricket with the kids on the alleyway outside, the 4-year-old sweats

in his family's one-room apartment. D. Little progress has been made in negotiations with the Taliban despite several months of contact between western governments and interlocutors for the Islamist group. E. Trading in shares of Hong Kong-listed China Forestry Holdings Ltd. was suspended after its auditors found irregularities in its books.

OPTIONS 1) A and C 2) A, B and C 3) Only B 4) B and E 5) Only C

Solution

Sentences B, D and E are correct. Sentence A is incorrect. The preposition ―for‖ has been incorrectly used instead of the preposition ―of‖ - to have the backing of someone means to have their support. Sentence C is incorrect due to the preposition ―on‖. An ―alleyway‖ means an alley or a narrow street with walls on both sides, therefore, the preposition ―in‖ would be the correct preposition, as ―in‖ indicates within or inside a particular place. Hence, the correct answer is option 1.

30)

Given that a, b and c are in A.P., the straight line ax + by + c = 0 always passes through the point OPTIONS 1) (1, –2) 2) (0, 0) 3) (2, –1) 4) (1, –1) 5) No such point exists

Solution

Since a, b and c are in AP, 2b = a + c. ∴ a – 2b + c = 0 ax + by + c = 0

∴ The line always passes through the point (1, –2). Hence, option 1.

31)

While some of the story lines may pass more directly through one of the two central events than the other, all are either directly or indirectly linked to them both. Through the author's ability to draw the reader into the minds of each of the many and varied protagonists, the reader is given an indepth and multifaceted view of both the heights and the depths of life in New York city for both its ordinary, and its more extraordinary citizens. In subsequent interviews, the author has noted his intention to point out the melodramatic tensions present in all of our lives, whether perched upon a death-defying high wire, or merely trying to live out a more “ordinary” life, “where there is still an invisible tight-rope wire that we all walk, with equally high stakes, only it is hidden to most, and only 1 inch off the ground”. According to the author, melodramatic tensions are: OPTIONS

1) Exclusive to the less-ordinary citizens of New York. 2) Exclusive to those perched upon the death-defying high wires of New York city – both literally and metaphorically.

3) All pervasive, irrespective of the lifestyle you choose. 4) Present in both the heights and depths of New York city and in the minds of all the protagonists.

5) None of the above

Solution

The passage states that “In subsequent interviews, the author has noted his intention to point out the melodramatic tensions present in all of our lives”. Thus the point is that everyone suffers from them. This is described in option 3. Options 1 and 2 are incorrect as they call tensions “exclusive” to a certain category of people. Option 4, though close, is not as appropriate as option 3. Option 5 is wrong as the answer is one of the above. Hence, the correct answer is option 3.

32)

If x, y are distinct integers and belong to the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, how many ratios of the form x/y are non-integral in nature? OPTIONS 1) 83 2) 73 3) 68 4) 78

Solution

Since x and y are distinct integers, this is similar to a case of selecting 2 numbers from 10, where repetition is not allowed. Thus, the denominator can be selected in 10 ways and consequently, the numerator can be selected in 9 ways. Therefore, the total number of ratios that can be formed = 10 × 9 = 90 Now, find the number of ratios of the form x/y which are integral in nature. If y = 1, x can take 9 values (anything from 2 to 10) If y = 2, x can take 4 values (4, 6, 8 and 10) If y = 3, x can take 2 values (6 and 9) If y = 4, x can take 1 value (8) and If y = 5, x can take 1 value (10) For y > 5, the ratio of the form x/y will not be integral in nature. Hence, the number of ratios of the form x/y that are integral = 9 + 4 + 2 + 1 + 1 = 17 Hence, the number of ratios that are non-integral = 90 − 17 = 73 Hence, option 2.

33)

A new clock is designed such that it has only 6 hour markings (from 1 to 6) and minute markings marked from 0 to 30 minutes in between the 6 hour markings. Hence, in one hour, the minute hand completes 2 full rotations while the hour hand completes one 60° rotation

from one hour marking to another. For example, when the hour hand is past five and the minute hand is at 20 minutes, the time can be 5:20 or 5:50 depending upon whether the hour hand is closer to 5-hour mark or to 6-hour mark. What is the angle between the minute hand and the hour hand of the clock at 4:24 PM? OPTIONS 1) 24° 2) 20° 3) 30° 4) 18°

Solution

The hour hand completes one 60° rotation from one hour marking to another in an hour. Thus, the hour hand completes 60° in 60 minutes i.e. 1° per minute. ∴ The angle made by hour hand at 4:24 p.m. = (4 × 60) + (24 × 1) = 264°. The minute hand completes one rotation in 30 minutes. Thus, it covers 360° in 30 minutes i.e 12° per minute. ∴ The angle made by minute hand at 4:24 p.m. = (24 × 12) = 288°. ∴ Angle between the minute hand and the hour hand at 4:24 p.m. = 288 − 264 = 24°. Hence, option 1.

34)

CHOREOMANIA: DANCE OPTIONS 1) Clinomania: Bed 2) Nosomania: Disease 3) Melomania: Music 4) Potomania: Potatoes 5) Polemomania: War

Solution

This question deals with different types of manias or obsessions. Choreomania refers to a dancing mania or frenzy. Clinomania means an excessive desire to stay in bed. Nosomania is a delusion of suffering from a disease. Melomania is a craze for music. Polemomania is a mania for war. Potomania refers to an abnormal desire to drink alcohol and is unrelated to

potatoes. Hence, the correct answer is option 4.

35)

A palindromic number is defined as a positive integer whose value is unchanged when it is read backwards. If N is a palindromic number whose unit‘s digit is 8, and which has an even number of digits, which is the largest number which is definitely a factor of N? OPTIONS 1) 4 2) 8 3) 11 4) 22 5) 44

Solution

We can make the observation that, in any natural palindromic number with an even number of digits, starting from either end, the set of digits in a pair of odd and even places is the same. Hence, the sum of digits in the odd and even places is the same. Thus, any palindromic number with an even number of digits is divisible by 11. Also, if a number has unit‘s digit 8, it must be divisible by 2 (we cannot say conclusively whether it is divisible by higher powers of 2). We can only be sure than N is divisible by 2 and 11. All possible values of N satisfying these conditions will be divisible by 2 × 11 = 22 Hence, option 4.

36)

In planning a clinical trial, the sponsor or investigator first identifies the medication or device to be tested. Usually, one or more pilot experiments are conducted to gain insights for design of the clinical trial to follow. In medical jargon, effectiveness is how well a treatment works in practice and efficacy is how well it works in a clinical trial. In the U.S., the elderly comprise only 14% of the population but they consume over one-third of drugs. Despite this, they are often excluded from trials because their more frequent health issues and drug use produce unreliable data. Women, children, and people with unrelated medical conditions are also frequently excluded. According to the passage, who can clinical trials be held on? OPTIONS 1) Elderly U.S. citizens, because they consume over one-third of the drugs. 2) Women and children and people with unrelated medical conditions. 3) Adult men with related medical conditions that are not part of the elderly.

4) Adult men only. 5) Young adults with related medical conditions.

Solution

We know that they are not held on: the elderly, women, children and people with unrelated medical conditions. Thus we know that the only possible people they can be tested on are adult men that aren‘t the elderly and that they don‘t have unrelated medical conditions. Therefore, options 1 and 2 are wrong and have to be eliminated. Option 4 is too general - adult men includes all adult males, but the elderly males would have to be excluded, making this option incorrect. Similarly, ‗young adults‘ in option 5 may have men and women, which makes it incorrect. Option 3 does not contain any of the people who have to be excluded, making it the correct choice. Hence, the correct answer is option 3.

37)

Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around 5 million, with around 480,000 in England, Scotland and Ireland alone, and just under two million in the United States. The various forms all share moral and metaphysical ideals, which include, in most cases, a constitutional declaration of belief in a Supreme Being. The fraternity is administratively organised into Grand Lodges (or sometimes Orients), each of which governs its own jurisdiction, which consists of subordinate (or constituent) Lodges. Grand Lodges recognise each other through a process of landmarks and regularity. There are also appendant bodies, which are organisations related to the main branch of Freemasonry, but with their own independent administration. What can we conclude about Freemasonry from the passage? OPTIONS 1) Freemasonry is an alternative religion. Freemasonry is probably a boys club only – women weren‘t allowed to be a part 2) of it. Grand Lodges are factions within the Freemasons where people are divided on the 3) basis of societal status. Freemasonry has different sections scattered all over the world, especially the 4) Oriental nations. Appendant bodies are those bodies that allow freemasons to exist freely within 5) themselves.

Solution

We know from the passage that freemasonry is a ―fraternal‖ organisation – which means it‘s a brotherhood, and that implies that women aren‘t allowed. Options 1, 3, 4, and 5 cannot be proved by the passage, therefore they are incorrect. Hence, the correct answer is option 2.

38)

Ram and Shyam start walking on the same road towards each other. If 30 minutes before they meet, they are 5 km away and the speed of Ram is 8 km/hr, find the ratio of the speed of Ram and Shyam? OPTIONS

1) 2: 1 2) 4: 1 3) 4: 3 4) 4: 5 5) 1: 1

Solution

Since Ram and Shyam are 5 kms away from each other 30 minutes before they meet, they together cover 5 km in 30 minutes. ∴ Relative speed of Ram and Shyam together = 5/(30/60) = 10 km/hr Since Ram and Shyam are moving in opposite directions, their relative speed is the sum of their individual speeds. Relative speed = speed of Ram + speed of Shyam ∴ Speed of Shyam = Relative speed – speed of Ram = 10 – 8 = 2 km/hr ∴ Ratio of Speed of Ram to speed of Shyam = 8 : 2 = 4 : 1 Hence option 2.

39)

There are three integers a, b and c such that

Do a, b and c form a geometric progression? A. x, y and z are in A.P. B. x, y and z are in H.P.

OPTIONS 1) The question can be answered by one of the statements, but not by the other. The question can be answered by using either statement, independently of the 2) other. The question can be answered by using both statements together, but not by either 3) statement alone. 4) The question cannot be answered by either of the statements. DiscussGet In EmailGet this! Solution If a, b and c form a geometric progression, b2 = ac Using statement A alone a(1/x) = b(1/y) = c(1/z) = Constant

where k is the log of the constant mentioned above. Hence,

x, y and z are in A.P.

∴ b² = a × c Thus, a, b and c are in G.P. Hence, the question can be answered using statement A alone. Using Statement B alone x, y and z are in H.P. y is the harmonic mean of x and z.

This equation does not yield a meaningful relationship to establish if a, b and c are in G.P. For example, if a = c = 10, then b = 10, and hence a, b and c forms an GP. Similarly, if a = 10 and c = 100, then b = 104/3. Hence, a, b and c do not form an GP. Hence, the question cannot be answered using statement B alone. Hence, the question can be answered using statement A alone but not by using statement B alone. Hence, the question can be answered using one of the statements but not by using the other. Hence, option 1.

40)

The question is followed by two statements, A and B. Select the correct option based on the following instructions: Mark (1) if the question can be answered by one of the statements, but not by the other. Mark (2) if the question can be answered by using either statement, independently of the other.

Mark (3) if the question can be answered by using both statements together, but not by either statement alone. Mark (4) if the question cannot be answered by either of the statements. What is the length of side AB of triangle ABC? A. AB ≤ AC = 4 and area of triangle ABC = 8 B. Exactly two sides have integer lengths

OPTIONS

1) 1 2) 2 3) 3 4) 4

Solution

Using Statement A alone: AC = 4 and AB ≤ AC Thus, AB ≤ 4 Area of triangle ABC = 8 Now, in any triangle, Area = (1/2) × Product of two adjacent sides × Sin(angle between the two sides) Hence, in triangle ABC, A (∆ABC) = (1/2) × AB × AC × Sin A ∴ 8 = (1/2) × AB × 4 × Sin A ∴ AB × Sin A = 4

Now, AB ≤ 4. Also, the sine of any angle can have a maximum value of +1 and a minimum value of −1. Since AB is positive, sin A ≤ 1 Hence, for the above equation to hold, AB has to be equal to 4. Hence, AB = 4 Thus, the question can be answered using statement A alone. Using Statement B alone: This statement does not provide any information that can help find the value of AB. Thus, the question cannot be answered using statement B alone. Thus, the question can be answered using statement A alone but not by using statement B alone. Thus, the question can be answered by one statement but not by the other. Hence, option 1.

41)

Researchers debate about whether psychopathy/sociopathy are incorrectly put together under ASPD. These clinicians and researchers who believe that it was incorrect to label the two in the same category are upset that an important distinction has been lost between these two disorders. In other words, the DSM-IV-TR considers ASPD and psychopathy to be the same, or similar. However, they are not the same since antisocial personality disorder is diagnosed via behavior and social deviance, whereas psychopathy also includes affective and interpersonal personality factors. Other criticisms of ASPD are that it is essentially synonymous with criminality. Nearly 80%– 95% of felons will meet criteria for ASPD — thus ASPD predicts nothing in criminal justice populations, whereas psychopathy (using the Hare Psychopathy Checklist-Revised (PCL-R)) is found in only roughly 20% of inmates and PCL-R is considered one of the best predictors of violent recidivism. What are researchers upset about, according to this paragraph? OPTIONS

1) 2) 3) 4) 5)

That ASPD doesn‘t take into consideration the percentage of incarcerated people who suffer from ASPD. That ASPD and the DSM-IV-TR are considered to be the same. That ASPD is the only sure-fire way to diagnose antisocial symptoms amongst future criminals. That the DSM-IV-TR doesn‘t take into account ASPD‘s association with criminals. That psychopathy and sociopathy aren‘t supposed to be thrown together as they are in ASPD.

solution

The passage states that ―Researchers debate about whether psychopathy/sociopathy are incorrectly put together under ASPD. These clinicians and researchers who believe that it was incorrect to label the two in the same category are upset that an important distinction has been lost between these two disorders.‖ Option 1 is wrong as the passage doesn‘t talk about percentage of criminals actually suffering from ASPD – it talks about percentage of criminals who will meet the criteria for it. Option 2 is wrong as they aren‘t considered to be the same. Options 3 and 4 have no basis in the passage. Hence, the correct answer is option 5.

42)

The question below contains a number of sentences. Each sentence has pairs of word(s)/phrases that are highlighted. From the highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one. 1. The sudden torrent [A] / deluge [B] doused the flames and contained the wildfire before any real damage was done. 2. The poor farmers had no choice but to truckle [A] / buckle [B] to the landlord‘s demands in order to save their land. 3. The theorem posits [A] / emplaces [B] a deep knowledge of Bayer‘s theory of relativity for accurate results. 4. After the overthrow of the Pope, there was a sudden interest in heterodox [A] / conservative [B] theories regarding the importance of the Cross in the Christian religion. 5. His new book has claimed that social networking sites are actively used to subvert [A] / change [B] the morals of teenagers.

OPTIONS 1) ABBBA 2) BABAA

3) BAAAB 4) BAAAA 5) ABABA

Solution

Truckle means to act in a subservient manner. Buckle under is a phrase that means to succumb or give in. In this case, the preposition ‗under‘ is absent. This eliminates options 1 and 5. Posit means to assume or put forward as fact or the factual basis for an argument. Emplace means to put in place or position. Logically posit fits in the blank. This eliminates option 2. Subvert means to corrupt. Therefore, it is the apt word contextually. This eliminates option 3 Hence the correct answer is option 4.

43)

FIFA has organized a charity tournament such that 4 matches will be played in 4 different countries namely England, France, Italy and Germany. For these 4 matches, 2 football clubs from each of the 4 mentioned countries are selected. The matches are scheduled in such a way that none of the clubs will play their matches on home soil and the clubs from the same country won‘t face each other. If none of the clubs from Italy play in England and none of the clubs from England play in France then clubs from which countries will participate in a match in Italy? OPTIONS 1) England and Germany 2) England and France 3) Germany and France 4) Either 1 or 2 5) Both 1 and 2

Solution

No club plays in its own country. Also, it is known that clubs from Italy do not play in England and clubs from England do not play in France. Since clubs from Italy and England will not play in England, 1 club each from France and Germany will play their match in England. Similarly, 1 club each from Germany and Italy will play their match in France. Now, clubs from England, Germany or France should play in Italy. Note that both the clubs from Germany have already played in England and France. Hence, teams from England and France will play their match in Italy. Hence, option 2.

44)

Let α, β be positive real numbers such that α + β = 1, then find the maximum possible value of [(α3 + β3) − (β4 + α4)] OPTIONS 1) 2) 3) 4) 5)

T = α3 − α4 + β3 − β4 =α3(1 − α) + β3(1 − β) = α3β + β3α = αβ(α2 + β2 ) = αβ(1 − 2αβ) … [As α + β = 1]

Solution

Hence, option 3.

45)

Fill in the blanks with the most appropriate set of words from the options: Sellers might agree to sell at a common ___ price; buy the product from a supplier at a specified maximum price; ___ to a price book or list price; engage in cooperative price advertising; ___ financial credit terms offered to purchasers; use uniform trade-in allowances; limit discounts; ___ a free service or fix the price of one component of an overall service; adhere uniformly to previously-

announced prices and terms of sale; establish uniform costs and markups; ___ mandatory surcharges; purposefully reduce output or sales in order to charge higher prices; or purposefully share or pool markets, territories, or customers. OPTIONS

1) Spot, cohere, assimilate, interrupt, foist 2) Target, adhere, standardise, discontinue, impose 3) Mean, obey, standardise, discontinue, inflict 4) Base, practice, amend, interpose, enforce 5) Target, adhere, allocate, withdraw, cancel

Solution

A selling price has to be the target that is to be achieved by the seller. Base price means the initial price without additional incurred expenses. Therefore, option 4 can be eliminated. Cohere, obey, and practice are not grammatical in the second blank. This eliminates options 1, 3 and 4. Cancel does not fit into the fifth blank. Hence, option 5 is eliminated. Hence, the correct answer is option 2.

46)

The best means is to avoid any questionable foods or beverages. Other measures include good hygiene, specific vaccines, and in certain situations, prophylactic medications. Studies show a decrease in the incidence of TD with use of bismuth subsalicylate and with use of antimicrobial chemoprophylaxis. Bismuth subsalicylate (two tablets or two ounces four times daily) will reduce the likelihood of travelers' diarrhoea, but few travelers adhere to a four-times-per-day regimen because it is inconvenient. Side effects may include black tongue, black stools, nausea, constipation, and ringing in the ears (tinnitus). Bismuth subsalicylate should not be taken by those with aspirin allergy, kidney disease, or gout, nor concurrently with certain antibiotics, and should not be taken for more than three weeks. Which of the following is the passage most likely to be talking about? OPTIONS 1) How to treat Traveller‘s diarrhoea

2) Precautions to take while travelling 3) Prevention is better than cure 4) The many useful benefits of consuming Bismuth subsalicyclate 5) Ways to prevent Traveller‘s diarrhoea

Solution

The passage lists various ways to prevent (we know prevent because it uses the term ―prophylactic‖) traveller‘s diarrhoea - ―The best means is to avoid any questionable foods or beverages. Other measures include good hygiene, specific vaccines, and in certain situations, prophylactic medications. Studies show a decrease in the incidence of TD with use of bismuth subsalicylate and with use of antimicrobial chemoprophylaxis.‖ This is encapsulated by option 5. Option 1 is incorrect because the focus is on preventing, not treating. Option 2 and 3 is not specific enough with regard to Traveller‘s diarrhoea. Option 4 is incorrect as the passage does not focus on ‗many useful benefits of consuming Bismuth subsalicyclate‘; in fact, it lists the many side effects and warnings of the tablet. Hence, the correct answer is option 5.

47)

A reagent is a “substance or compound that is added to a system in order to bring about a chemical reaction or is added to see if a reaction occurs.” Although the terms reactant and reagent are often used interchangeably, a reactant is less specifically a “substance that is consumed in the course of a chemical reaction”. Solvents and catalysts, although they are involved in the reaction, are usually not referred to as reactants. In organic chemistry, reagents are compounds or mixtures, usually composed of inorganic or small organic molecules that are used to affect a transformation on an organic substrate. Examples of organic reagents include the Collins reagent, Fenton's reagent, and Grignard reagent. There are also analytical reagents which are used to confirm the presence of another substance. Examples of these are Fehling's reagent, Millon's reagent and Tollens' reagent. According to the passage, what does a reagent do? OPTIONS 1) A reagent speeds up a chemical reaction so that the effect can be observed quickly. 2) A reagent is a substance that gets used up during a reaction. 3) 4) 5) A reagent is a compound that is added to a system in order to bring about a physical reaction. A reagent is a substance composed of inorganic or small organic molecules that are added to a system that enables the reactant to dissolve. A reagent is a substance/ compound/ mixture that brings about a chemical reaction or a transformation on an organic substrate.

solution

The passage clearly states two things – “A reagent is a "substance or compound that is added to a system in order to bring about a chemical reaction or is added to see if a reaction occurs."” And that “In organic chemistry, reagents are compounds or mixtures, usually composed of inorganic or small organic molecules that are used to affect a transformation on an organic substrate.” The only option that combines both definitions is option 5, and hence it is the right answer. Option 1 is wrong as that is not what a reagent does.

Option 2 is wrong as it focuses only on one aspect of the definition of a reagent – that it gets consumed during a reaction. Option 3 is wrong as the reaction is chemical, not physical. Option 4 is wrong as it focuses only on one aspect. Hence, the correct answer is option 5.

48)

a and b are natural numbers. Let f(a, b) be the number of cells that the line joining (a, b) to (0, 0) cuts in the region 0 ≤ x ≤ a and 0 ≤ y ≤ b. For example f(1, 1) is 1 because the line joining (1, 1) and (0, 0) cuts just one cell. Similarly f(2, 1) is 2 and f(3, 2) = 4. Find f(343, 56). OPTIONS 1) 390 2) 392 3) 399 4) 397 5) 395

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Solution Let d the GCD of a and b, x = a/d and y = b/d and L be the line joining (0, 0) to (x, y). Then, the line joining (0, 0) and (x, y) repeated d times forms the line joining (0, 0) and (a, b). For calculating the number of cells cut by L, note that the line L has to cut x cells along the x-axis and y cells along the y-axis. But one of these cells is common. ∴ The number of cells cut by L is (x + y – 1).

∴ The number of cells cut by the line joining (a, b) to (0, 0) = (x + y – 1) × d = (xd) + (yd) − d = [a + b – GCD(a, b)]. ∴ f(343, GCD(343, ∴ f(343, 56) = f(a, 56) b) = = [343 56) 343 + 56 (a + + 56 b – = − 7 = – GCD(a, GCD(343, b)) 56)] 7 392.

Hence, option 2.

49)

A triangle which has zero area is called a degenerate triangle. Any triangle which is not a degenerate triangle is a called a non-degenerate triangle. A non-degenerate triangle ABC has integer sides. BD bisects the angle ABC. If AD = 3 and DC = 6, then among the following which is the smallest possible value of the perimeter of the triangle? OPTIONS

1) 25 2) 26 3) 27 4) 28 5) 30

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Solution

By angle bisector theorem

AB

and

BC

are

integers

hence

3k

should

be

a

positive

integer.

Hence For Hence, For Hence,

the the

perimeter triangle m

=

AB

+

BC to 4, we

+

CA

= m

9

+

m

+ be and

2m

=

3(3

+ than

2m) 3. on. 27. 3.

inequality =

satisfy, 5, get option

should 6 the

greater so as

m

=

6,

perimeter

Alternatively, By angle bisector theorem

AB

and

BC

are

integers

hence

3k

should

be

a

positive

integer.

Hence

the

perimeter

=

AB

+

BC

+

CA

=

9

+

m

+

2m

=

3(3

+

2m)

Hence, the perimeter should be a multiple of 3, and among the options 27 is the smallest multiple of 3. Hence, option 3.

50)

How many positive integral solutions exist for: ab + cd = a + b + c + d if 1 ≤ a ≤ b ≤ c ≤ d ? OPTIONS

1) One 2) Two 3) Three 4) Four 5) No positive integral solution

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Solution ab ∴ ∴ 1 ∴ For (a – 1) 0 ≤ [ab (a ≤ (a – + − – cd a 1)(b a 1) ≤ − = b – + 1) ≤ (b – integral is 0 or a 1] + b 1) ≤ + + (c [cd – ≤ (c – b −c 1)(d c 1) ≤ + −d – c + 1) ≤ (d – 1] + = = d 2 2 d 1)

solutions, 1.

Because if it is 2, then (b – 1), (c – 1), (d – 1) are all greater than or equal to 2 and hence the expression takes value greater than 8. If (a Thus, Hence, option 3. (a – – 1) 1) = = 0 ⇒ 1 there a ⇒ = 1, a b = can 2, are 3 be b 1 = or 2, 2, c c= = 2 2, and d d = = 3 2

integral

solutions.

51)

America‟s car thieves show clear preferences in the vehicles they steal. Size, speed and luxury are all important factors when it comes to selecting a target. And the country's car thieves are, at least, patriotic. If America's car making giants have struggled in recent years to build vehicles that match the public taste, they are keeping car thieves happy. Only two of the top ten stolen cars in Americameasured in terms of cash paid out by insurers- come from a foreign manufacturer. America's car criminals are more suspicious of Japanese or European models and are reluctant to be seen in smaller cars. Which of the following, if true, most seriously undermines the credibility of the argument above? OPTIONS

1) American cars are bigger, faster and more luxurious compared to foreign made ones.

2) American cars cost more, are poorly designed, and easier to steal.

3) Car thefts and patriotism are not related. The primary reason to steal a car is to part it out and take advantage of the demand for used parts.

4)

5) America‟s car thieves have horrible choices.

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Solution

The argument that we have to weaken is that size, speed and luxury are the reasons for more American cars being stolen. Option 2 advances another reason- they are costlier (lucrative to a thief) and poorly designed (making them) easier to steal. Therefore, option 2 undermines the credibility of the argument that car thieves steal American cars because of size, speed and luxury. Option 1 is an inference. Furthermore, it does not undermine the credibility of the argument in any way. Option 3 does not address the argument. Option 4 does not weaken the argument about why more American cars are stolen. It has not been implied in the passage that the „used parts‟ of non-American cars have more demand (or fetch a better price) than that of American cars. Option 5 is loose and does not attack the argument. Hence, the correct answer is option 2.

52)

Find the remainder when [(2 × 4 × 6 × 8 × 10 ×…× 200) – (1 × 3 × 5 × 7 × 9 ×…× 199)] is divided by 201. OPTIONS 1) 1 2) 100 3) 200 4) 0 5) 2

Solution

(2 × 4 × 6 × 8 × 10 ×…× 200)

=

(201

–

199)(201

–

197)(201

–

195)…(201

–

3)(201

–

1)

Now, each term of this product will have 201 multiplied with it; except for the last term which will be ± (199 × 197 × 195 ×…× 3 × 1) Since the total number of terms in the original bracket is even (100 terms), the sign preceding (199 × 197 × 195 ×…× 3 × 1) will be „+‟. So, (2 × 4 × 6 × 8 × 10 ×…× 200) changes to the form (201 × n) + (199 × 197 × 195 ×…× 3 × 1) ∴ (2 × 4 × 6 × 8 × 10 ×…× 200) – (1 × 3 × 5 × 7 × 9 ×…× 199)

= (201 × n) + (199 × 197 × 195 ×…× 3 × 1) – (1 × 3 × 5 × 7 × 9 ×…× 199) = Since 201 divides (201 this number, the × remainder is n) 0.

Hence, option 4.

53)

The question below contains a number of sentences. Each sentence has pairs of word(s)/phrases that are highlighted. From the highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one. 1. The new car was tested [A] / examined [B] by the Pollution Control Board to verify that it met the Euro 4 norms. 2. The Judge ruled [A] / resolved [B] in favour of the plaintiff. 3. The King rose from the throne to indicate that the matter had been certified [A] / settled [B]. 4. He was assigned the chore [A] / job [B] of maintaining the records of the King‟s expeditions. OPTIONS 1) ABAA 2) BABA 3) AABB 4) BAAB 5) AABA

Solution Test means to put to the test, as for its quality, and examine means to observe carefully or critically. It is implied that tests would be conducted to ascertain conformity. Therefore, the correct answer would be tested. Ruled means that the decision is handed down by someone in authority. Resolve on the other hand means one exercises a choice to make a decision In the context of a judge, the decision is handed down; therefore, the correct answer would be ruled. Certify means to guarantee as meeting a standard. Settle implies finality in the matter. Chore is a routine or minor duty while a job is a regular activity in exchange for payment. Maintaining records would be a regular duty. Hence, the correct answer is job. Hence, the correct answer is option 3.

54)

Read the sentences and choose the option that best arranges them in a logical order. A. Most of the philosophers commonly counted "great" have not been sceptics, of course, they are usually quite straightforward with their claims, not only to know, but to know what knowledge is, and often have given reasons supporting their view. B. Even the extreme sceptic must come dangerously close, for him, to knowing what knowledge is, if his claims are to be at all intelligible and interesting, since a person who does not know what he is denying the possibility or actuality of would have little claim to be taken seriously. C. Accordingly, each sceptical philosopher has articulated, more or less, a conception of knowledge which he regards as reasonable to accept. D. From its earliest phases up to the present, philosophical inquiry has taken the nature of knowledge to be a central concern. E. Still, no philosophical positions have been more contested than those on the nature of knowledge, and this remains so up to today.

OPTIONS

1) EDCAB

2) DBCEA

3) DBCAE

4) ABCDE

5) ABDCE

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Solution

The first sentence can be either sentence A or D, as the other sentences are clearly a continuation of some preceding sentence. Sentence D introduces the concept of philosophical inquiry and knowledge, therefore it will be appropriate only as the introductory sentence and not as any later sentence. Options 1, 4 and 5 can be eliminated. The DBC link is already provided in both the remaining options. The only choice that remains is between AE or EA. Sentence E presents the concluding statement which includes what the author feels about the topic i.e. it can be seen that a conclusion has been drawn. Therefore, it is most appropriate as a conclusion to the paragraph. Sentence A is simply a continuation of the opinion that the author has been expressing and not what he has inferred. Therefore, the correct sequence is DBC followed by AE. Hence, the correct answer is option 3.

55)

Find the sum 1 – 3 + 3 – 3 + 3 +...∞ OPTIONS 1) 0.25 2) –0.25 3) 0.75 4) –0.75 5) None of these

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2 3 4

Solution The given expression can be expressed as a difference of 2 GPs such that both the GPs have a 2 common ratio r = 3 = 9 Since r > 1, the formula for infinite sum of a G.P. does not hold and the sum does not converge. Hence, option 5.

56)

Fill in the blanks with the most appropriate pair of words from among the given options. It now seems clear to anyone with eyes that the invasion of Afghanistan was built upon a great miscalculation; that Afghanistan can be _________ invaded; throughout history, such undertakings have always _________. OPTIONS 1) easily, exacerbated 2) successfully, floundered 3) effectively, intensified 4) profitably, profited 5) fully, defeated

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Solution The word „miscalculation‟ and „invaded‟ control the first blank. The comparison of options makes „fully‟, „profitably‟ and „effectively‟ inferior to „easily‟ and „successfully‟. Therefore, we can eliminate options 3, 4 and 5. If it was a “miscalculation” history will provide proof of its failure rather than its success; Therefore, „floundered‟ fits best in the second blank in contrast to „exacerbated‟ which is logically and grammatically inconsistent. Hence, the correct answer is option 2.

57)

Fill in the blanks with the most appropriate pair of words from among the given options. This turn towards authoritarianism bodes ill for the Turkish economy, _________ its strong fundamentals; it will have corrosive effects on the quality of policymaking, as well as _________ Turkey‟s claim to global economic standing. OPTIONS

1) notwithstanding, strengthen

2) albeit, arraign

3) despite, undermine

4) notwithstanding, vindicate

5) in spite of, dissipate

Solution

For the first blank, all the words in the options make logical sense. “Bodes ill” and “strong fundamentals” require contrasting words such as „notwithstanding‟, „albeit‟, „despite‟ and „in spite of‟. For the second blank „strengthen‟,„arraign‟ and „vindicate‟ can be eliminated because they do not combine well with “corrosive effects”. „Dissipate‟ is an incorrect word to use contextually. It means „to disperse or squander (as in money etc)‟. „Undermine‟ is our answer choice since it combines well with “corrosive effects”. Hence, the correct answer is option 3.

58)

Ajay purchased 2 kg apples, Bijay purchased 3kg mangoes and Celine purchased 12 dozens of bananas. The total cost of the purchase was exactly 180 rupees. If the prices of 1kg mango, 1 kg apple and 1 dozen bananas are all positive integer rupees, then how many different combinations of prices can be there? OPTIONS 1) 435 2) 225 3) 196 4) 210 Solution Let the price of 1 kg apples, 1 kg mangoes and 1 dozen bananas be x, y, z respectively.

Hence,

2x

+

3y

+

12z

=

180

As all of them are positive integers, x has to be a multiple of 3 and y has to be even. Hence, And x' Maximum + value of z y' = 14, + gives one 2z solution (x', y' = ) = (1, 30 1) x = 3x', y = 2y'

For z = 13, we get 3 solutions (x', y' ) = (1, 3), (2, 2), (3, 1) . . . Similarly Hence a for z total = of 1 we 1 + get 3 27 + solutions 5 +…+ (x', 27 y' = )=(1, 14

2

27), =

(2, 196

26)…(27,1) solutions.

Hence, option 3.

59)

19

C0 × C4 + C 1 × C3 +

7

19

7

19

C 2 × C2 + C3 × C1 + C4 × C 0 =

7

19

7

19

7

OPTIONS

1)

19

C7 × C5

7

2)

19

C7

3)

26

C4

4)

26

C7

7

5)

26

C4 × C4

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Solution

Consider a 26-element set partitioned into a 19-element subset A and a 7-element subset B.

Note that Ci × C4 – i is the number of ways in which you can select i things out of 19 and 4 – i things out of 7 to get 4 things out of 26. Thus, either you could select (zero things from A and 4 from B) or (1 from A and 3 from B) or (2 from A and 2 from B) or (3 from A and 1 from B) or (4 from A and none from B). Thus, can ∴

19 19

19

7

C7 × C4 + C 6 × C4 + select ×

19 7

7

19

6

19

C5 × C4 + 4 ×

6

5

19

C4 × C4 represents the number of ways in which you things out of 26.

19

4

C7

C4

7

+

19

19

C6

7

C4

7

+

C5

×

7

5

C4

19

+

7

19

C4

×

4

C4

=

4

26

C4

Equivalently + ∴

19

C0 × C4 +

C1 × C3 + 19 x) (1

7

19

C2 × C 2 +

19

C 3 × C1 +

C4 × C0 is the coefficient of x in (1 7 + x) .

7

C0 ×

7

C4 +

19

C1 ×

C3 +

19

C2 ×

7

C2 +

19

C3 ×

C1 +

19

C4 ×

7

C0

=

26

C4

Hence, option 3.

60)

There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n. OPTIONS

1) 8

2) 10

3) 9

4) 7

Solution

We can easily see that 8 is possible. For example if students are numbered 1 to 8, and student i knows student j if and only if |i − j| ≢ 1, 4 (mod 8) and student 1 doesn't know 8(and vice versa), meaning student 1, knows 3, 4, 6, 7 (and vice versa). Student 2 knows 4, 5, 7, 8 and vice versa and so on. We will prove that no n > 8 is possible

Let us suppose n = 9 is possible. Then no student may know 6 others as among those 6, either 3

don‟t know each other or 3 know each other. So together with the original student there exist 4 who know each other. Hence, this is not possible. Similarly it is not possible that a student doesn‟t know 4 others.

Hence, each student knows exactly 5 others. But this is not possible as 9 × 5 = 45 is odd. Hence, Hence, option 1.

Question Of the D

required

n

=

8

61)

Find the product of the real roots of the equation:

x101 – 3x100 + 2x99 + x98 – 3x97 + 2x96 +…+ x2 – 3x + 2x0 = 0 OPTIONS 1) –1 2) 1 3) 2 4) –2 5) 3

Solution S = x101 – = x99(x2 – = = = ∴ The Product (x –

3x100 + 3x + (x2 – (x2 – 2)

2x99 + x98 – + x96(x2 – 3x + 3x + 1)(x – 2)(x102 – are x =

3x97 + 3x +

2x96 +…+ x2 – 2) +…+ x0(x2 –

3x + 3x +

2x0 2)

2)(x99 + x96 + x93 +…+ x3 + x0) 2)(x102 – 1)/(x3 – 1)(x2 + x + 1) 1 and = 1) 1) 0 –1. –2

2)(x102 –

1)/(x –

(x – roots

1)/(x2 + x + 2, =

Hence, option 4.

62)

The ten largest broadband service providers in the world gained over 23m subscribers in the year to the end of March. Together they have 191m subscribers, or almost 40% of the world‘s 492m broadband customers, according to TeleGeography, a research firm. The lion's share is taken by China Telecom and China Unicom, which together account for a fifth of all global broadband subscribers. Ranked 2nd and 3rd, USA & Germany together account for a sixth of all global broadband subscribers. Both China Telecom and China Unicom gained around 9m more subscribers over the past year, equivalent to the entire broadband subscriber base of Verizon. Which of the following can be validly concluded from the above? OPTIONS 1) China has the largest number of broadband subscribers in the world. 2) The government's censorship of the internet in China has helped increase the broadband subscriber base in China. 3) China and the Western world have around the same number of internet users. 4) The number of broadband subscribers in Verizon has declined. 5) Broadband access in China is subsidised by the government.

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Solution Option 2 contradicts itself. Therefore, it can be negated. Options 3, 4 and 5 cannot be concluded from the passage. If the 2nd and 3rd ranked countries, USA and Germany, account for a sixth of all broadband subscribers, then we can definitely conclude that China, with a share of one-fifth of all global broadband subscribers, has the largest number of broadband subscribers in the world. Hence, the correct answer is option 1.

63)

Given below is the figure of a regular 7-pointed star. Determine the measure of the angle(in radians) shown as a in the figure.

OPTIONS

1) 2) 3) 4)

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Solution

The sum triangle,

of

the

angles

of

a

Triangle

is

π,

hence

in

the

small

Hence, option 2.

64)

Thus another approach is to incorporate the notion of suffering into the definition. The

definition offered by the Oxford English Dictionary incorporates suffering as a necessary condition, with "the painless killing of a patient suffering from an incurable and painful disease or in an irreversible coma", and this approach can be seen as a part of other works, such as Marvin Khol and Paul Kurtz's "a mode or act of inducing or permitting death painlessly as a relief from suffering". However, focusing on this approach to defining euthanasia may also lead to counterexamples: such definitions may encompass killing a person suffering from an incurable disease for personal gain (such as to claim an inheritance), and commentators such as Tom Beauchamp & Arnold Davidson have argued that doing such would constitute "murder simpliciter" rather than euthanasia. Which of the following accurately defines euthanasia, as per the passage? OPTIONS 1) Assisting in the painless death of a person willing to die. 2) Killing someone to end their mental suffering. 3) Killing someone to end their physical and mental suffering. 4) Killing someone painlessly to end their suffering 5) Killing someone with a painful or irreversible disease painlessly.

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Solution The key words to focus on are ―irreversible and painful disease‖ and ―painless death‖. Even though this definition of euthanasia is argued by the passage, since it doesn‘t offer any alternatives, that is the best one there is. Option 5 encapsulates these points. Option 1 doesn‘t talk about irreversible disease. Option 2 talks about mental suffering which is not mentioned in the passage. Options 3 and 4 don‘t mention what the ―suffering‖ is – physical and mental suffering are too vague to constitute anything definite, as they do not bring out the ―incurable‖ aspect. Hence, the correct answer is option 5.

65)

n

C0 – nC1 + nC2 – nC3 + nC4 +…+ (–1)n–1 nCn–1 + (–1)n nCn = ? OPTIONS 1) 0 2) (–1)n + 1 3) 1 4) 2n

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Solution (1 Put a = 0 –1

+ a)n = nC0 + nC1 × a + nC2 × a2 + nC3 × a3 +…+ nCn–1 × an–1 + nCn × an in the above equation (–1)n–1 nCn–1 + to get (–1)n nCn

= nC0 – nC1 + nC2 – nC3 + nC4 +…+

Hence, option 1.

66)

In the question, a word/phrase has been used in sentences in five different ways. Choose the option corresponding to the sentence in which the usage of the word/phrase is incorrect or inappropriate. BEAR OPTIONS

1) It must be inspiring to see the Americans bear so well. 2) The wooden roof cannot bear the strain of Samantha's weight. 3) The Iraqi ambassador's claim doesn't bear close examination. 4) It doesn't bear repeating. 5) During spring, the tree will bear.

Solution “Bear” has the following meanings in the context of the given sentences: To hold or remain firm under a loadas in option 2. To hold up to scrutinyas in option 3. To be fit or worthy ofas in option 4. To produce by natural growthas in option 5. In option 1, the usage of the word “bear” is inappropriate. The correct sentence will be: It must be inspiring to see the Americans bearing up so well OR It must be inspiring to see the Americans bear up so well.

In this context, “bearing up” or “bear up” would mean to endure or face hardship bravely. Hence, the correct answer is option 1.

67)

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s).

A. When I was first contacted about contributing to this session, the thought expressed to me was that it might be good to do something to promote dialogue between Continental and Analytic temperaments within the Society of Christian Philosophers. B. European Central Bank President Jean-Claude Trichet rejected any direct ECB participation in a second bailout for Greece, escalating a clash within governments as they rush to craft a solution involving investors. C. External Affairs Minister Pranab Mukherjee registered India's strong disapproval at Presidentelect Barack Obama's plan to appoint a special envoy for the India-Pakistan-Afghanistan region. D. There are many varieties and grades of paper materials, and whilst it is fairly easy to spot the varieties, it is far more difficult to spot the grades. E. A city that looks like a cramped row of shiny, tall matchboxes in places, Mumbai is finally going to get some respite.

OPTIONS 1) A and E 2) A and C 3) C and D 4) E and B 5) B and C

Solution Sentences A, D and E are correct. Sentence B is incorrect. ―... escalating a clash within governments‖ is incorrect as the word ―within‖ is used in case of something happening within one entity or within a single structure. In this case however the clash is ‗with‘ governments, that is, between the bank and the governments. Sentence C is incorrect as the word ―disapproval‖ is to be followed by the preposition ―of‖ and not the preposition ―at‖ one disapproves ―of‖ something. Hence, the correct answer is option 5.

68)

A ring of radius 2 cm rolls on the outer circumference of the ring x2 + y2 – 2x + 4y – 4 = 0.

Find the equation of the curve traced by its centre. OPTIONS 1) (x – 1)2 + (y + 2)2 = 25 2) (x – 1)2 + (y + 2)2 = 5 3) (x – 1)2 + (y + 2)2 = 1 4) None of these

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Solution x2 + y2 – ∴ (x −

2x + 1)2 +

4y – (y +

4

= 2)2 =

0. 32

Now, the ring that is rolling will have the same centre as the original ring. Because it is rolling on the outer circumference of the original ring, its radius (2 cm) will get added to the radius of the original ring (3 cm). So, its locus is a circle with the same centre as the original circle and radius = 5 cm Hence, its equation is (x – 1)2 + (y + 2)2 = 25

Hence, option 1.

Danish randomly picks 3 distinct integers from the set {1, 2, 3, 4, 5, 6, 7} and arranges them in descending order to form a 3-digit number. Kavitha randomly picks 3 distinct integers from the set {1, 2, 3, 4, 5, 6} and also arranges them in descending order to form a 3-digit number. What is the probability that the number formed by Danish is greater than that of Kavitha? OPTIONS 1) 2) 3) 4) 5)

Solution There Case 1:

are Danish

two Picks a

cases: 7

In this case, the number formed by Danish will always be greater than that of Kavitha

Case

2:

Danish

does

not

pick

a

7

Now if Danish does not pick a 7, he has to pick all 3 digits from {1, 2, 3, 4, 5, 6}. Since, Kavitha is picking from the same set, the probability that Danish‘s number is larger is same as Kavitha‘s number is larger.

Hence, option 4.

69)

A ring of radius 2 cm rolls on the outer circumference of the ring x2 + y2 – 2x + 4y – 4 = 0. Find the equation of the curve traced by its centre. OPTIONS 1) (x – 1)2 + (y + 2)2 = 25 2) (x – 1)2 + (y + 2)2 = 5

3) (x – 1)2 + (y + 2)2 = 1 4) None of these

Solution x2 + y2 – ∴ (x −

2x + 1)2 +

4y – (y +

4

= 2)2 =

0. 32

Now, the ring that is rolling will have the same centre as the original ring. Because it is rolling on the outer circumference of the original ring, its radius (2 cm) will get added to the radius of the original ring (3 cm). So, its locus is a circle with the same centre as the original circle and radius = 5 cm Hence, its equation is (x – 1)2 + (y + 2)2 = 25

Hence, option 1.

70)

The question below consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from among the options.

A. The Process has its critics, who point out that diamonds from the huge Marange mine in Zimbabwe have just been cleared for sale, despite much evidence of government-sponsored violence there. B. Charles Taylor, the former dictator of Liberia, who is on trial for war crimes in neighbouring Sierra Leone, is accused of giving Ms Campbell a “blood diamond” in 1997. C. Amid much media interest, Naomi Campbell, a model, gave evidence at the special court for Sierra Leone in The Hague. D. Ms Campbell admitted receiving a gift of “dirty looking stones”. E. Since 2000, the governments of over 75 countries have signed up to the Kimberley Process, which certifies that diamonds produced for foreign markets have not helped to fund violence.

OPTIONS 1) CBDEA 2) CDBAE 3) DEACB 4) DAEBC

5) BDEAC

Solution EA is a clear link. E mentions ―the Kimberley Process‖ and A expands upon it by mentioning that ―the Process has its critics‖. We can eliminate options 2 and 4. Out of the remaining options B looks possible as a starting statement but C at the end of BDEA is illogical. We can eliminate option 5. DEACB in option 3 is also illogical. D must come after B since in D Ms Campbell admits to receiving the diamond gifted to her by Charles Taylor (as mentioned in B). Therefore, we can eliminate option 3. Hence, the correct answer is option 1.

71)

Glee is set in Lima, Ohio. Murphy chose a Midwest setting as he himself grew up in Indiana, and recalled childhood visits to Ohio to the Kings Island theme park. Although set in Lima, the show is filmed at Paramount Studios in Hollywood. Murphy has said that he has never seen a High School Musical film, to which Glee has been compared, and that his interest lay in creating a "postmodern musical," rather than "doing a show where people burst into song," drawing more heavily on the format of Chicago. Murphy intended the show to be a form of escapism. "There's so much on the air right now about people with guns, or sci-fi, or lawyers running around. This is a different genre, there's nothing like it on the air at the networks and cable. Everything's so dark in the world right now, that's why Idol worked. It's pure escapism," he said. Murphy intended to make a family show to appeal to adults as well as children, with adult characters starring equally alongside the teenage leads. Murphy has mapped out plans for the series covering three years of broadcast. Which of the following didn‘t Murphy have in mind when he constructed the show? OPTIONS 1) Murphy wanted Glee to be different from High School Musical, to which it has been compared. 2) Murphy wanted a format of the show that looks like its been filmed in the city of Chicago, rather than Lima, Ohio. 3) Murphy wanted a show that promised pure escapism – to get away from other dark content on air currently. 4) Murphy wanted a family show that appealed to adults as well as kids. 5) Murphy had planned a future for the show.

Solution Since Glee is a musical, we can assume that the ―Chicago‖ that Murphy was referring to is a musical as well, especially since he has compared the two. Thus it can‘t be a city. Thus, option 2 is something he didn‘t have in mind.

All other options can be deduced from the passage, and are thus wrong. Option 1 can be concluded from ―Murphy has said that he has never seen a High School Musical film, to which Glee has been compared, and that his interest lay in creating a "postmodern musical," rather than "doing a show where people burst into song."‖ Options 3 and 4 are explicitly stated in the passage. Option 5 can be concluded from ―Murphy has mapped out plans for the series covering three years of broadcast.‖ Hence, the correct answer is option 2.

72)

How many values can the positive integer x take if 4(xn + 1) is a perfect cube for every natural number n? OPTIONS

1) 0 2) 1 3) 2 4) More than 2

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Solution Obviously x = Lets assume 1 is we even a solution. We will that odd. 1)n + 1) prove for x ≠ Let x = that 1, there we 2a + is no other 4(xn + 2b, solution. 1) = y3 then 1)=(2b)3 = b3

have

a y such

have 1, y =

Clearly y is 4((2a +

hence, x is

∴(2(n-1) an + n.2(n-2) a(n-1) +…+an +

Clearly if n is odd, we will get a successive loop similar to above. Hence we cannot find anx ≠1 which will give an integral y.

Hence, Hence, option 2.

there

is

only

one

value

of x.

73)

How many pairs (a, b) such that both a and b are non-zero exist if a and b are the roots of x2 +ax + b = 0 OPTIONS 1) 1 2) 2 3) 3 4) 4 5) None

Solution a and b are ∴ a2 + a2 + b = ∴b= ∴ ∴ ∴ ∴a= (2a +

the 0 –2a2 and b =

roots

of x2 + ax + b = and b2 + ab + b =

0 0 0 1

–(a + 2a2 = a +

1)

since b ≠

2a2 − a − 1 1)(a – –0.5 –0.5 pairs are (–0.5, 1)

= = or or –0.5) and (1,

0 0 1 –2. –2)

Correspondingly b equals ∴ The two non-zero

Hence, option 2.

74)

The following question has a paragraph from which the last sentence has been deleted. From

the given options, choose the one that completes the paragraph in the most appropriate way. In size, animals are outdone on land by plants, among whose foliage they may often hide. In contrast, the photosynthetic algae, which feed the open oceans, are usually too small to be seen, but marine animals range to the size of whales. Diversity of form, in contrast to size, only impinges peripherally on human awareness of life and thus is less noticed. ___. OPTIONS 1) Nevertheless, animals represent three-quarters or more of the species on Earth. 2) Nevertheless, the diversity reflects the flexibility in feeding, defense, reproduction and mobility. 3) Nevertheless, animals follow virtually every known mode of living for the creatures of Earth. 4) Nevertheless, humans study animals to learn about themselves. 5) Nevertheless, animals dominate human conceptions of life on Earth.

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Solution The last sentence takes off immediately from ―Diversity of form, in contrast to size, only impinges peripherally on human awareness of life and thus is less noticed‖ - it means human awareness of animals is more centred on their size than ―diversity‖. The closing sentence (because of the constant ‗nevertheless‘) will reinforce that ‗diversity‘ is important. ―... animals represent three quarters or more of the species‖ reinforces this train of thought logically, since diversity in form will result in the animals being classified as different species. Thus option 1 completes the paragraph appropriately. Option 2 is logically disconnected with the penultimate sentence. The closing sentence should answer the question of how diverse the animals on earth are. Option 2 fails to do this and instead answers the question of what is the diversity between different species of animals. Options 3 and 4 are unrelated to the paragraph - neither ‗size‘ nor ‗diversity‘ is being discussed. Option 5 also follows the thread of neither ‗size‘ nor ‗diversity‘ - to state that ‗animals dominate human conception of life on earth‘ is too abrupt and unrelated. Hence, the correct answer is option 1.

75)

Read the sentences and choose the option that best arranges them in a logical order.

A. A person of good moral character is one who, from the deeper and more pervasive dimensions of the self, is intent upon advancing the various goods of human life with which they are effectively in contact. B. Character is expressed in what one does without thinking, as well as to what one does after acting without thinking. C. “Character” refers to the settled dispositions to act in certain ways, given the relevant circumstances. D. The actions which come from character will usually persist when the individual is unobserved, as

well as when the consequences of the action are not what one would prefer.

OPTIONS 1) BCAD 2) DABC 3) ADCB 4) CBDA 5) CABD

Solution Sentence C is the most appropriate sentence which can begin the paragraph as it introduces the subject of ―character‖ and gives the basic idea or the basic meaning of the word ―character‖. This eliminates options 1, 2 and 3. Between sentence A and sentence B, sentence B further elaborates on the concept of ―character‖, while statement A puts forth an example of a person with good character - an example or an illustration is to be portrayed after the concept has been fully dealt with, hence sentence B will follow sentence C. Eliminate option 5. Since B states that character is expressed in what one ―does‖, it should be followed by sentence D, which further elaborates on these ―actions‖. Therefore, the correct sequence is CBDA. Hence, the correct answer is option 4.

76)

Let x1, x2, x3, … be a sequence of integers which has infinitely many positive integers as well as infinitely many negative integers. If for every positive integer n, the remainders of x1, x2,x3, …, xn upon divisions by n are all distinct, then, choose the most correct statement about the sequence. OPTIONS

1) Every integer appears at most once in the sequence 2) Every integer appears at least once in the sequence 3) Every integer appears exactly once in the sequence

4) None of the above

Solution Assume that there are positive integers i, j such that i > j and xi = xj. Then for n > i xi ≡xj (mod n), which is a contradiction. Hence, any number can appear at most once in the sequence. Next, Then, ∴ t ≥ n ≥ l, k and xl ≡ xk (mod n) which is a 1 for every positive integer n, let Sn = {x1, x2, x3…, xn }, max Sn = xl and min Sn = xk

if t = xl − xk ≥ n contradiction.

Hence,

max Sn –

min Sn = xl − xk ≤ n −

Now Sn ⊆ [min Sn, max Sn] both of which contain n integers. So the n numbers in Sn are then consecutive integers from min Sn to max Sn. Thus each integer appears exactly once in the sequence.

Hence, option 3.

which Feel OPTIONS 1) Artimey could feel it in his bones that Aarya was going to become the principal. 2) Jane hasn‘t been feeling like herself since her father passed away. Imran: Why not feel out the other members‘ opinions before we lodge a formal 3) complaint? 4) Joey doesn‘t feel into going out for the party. the usage of the word is awkward.

Solution ‗To feel in one‘s bones‘ means to have an intuition of. ‗To feel like oneself‘ means to be in one's normal frame of mind or state of health. In option 3, ‗feel out‘ means to attempt to ascertain (the nature of a situation, someone‘s attitude, etc.) by indirect or subtle means. In option 4, it would be more appropriate to use ‗feel up to‘ instead of ‗feel into‘. ‗To feel up to‘ means to be fit enough for something or to do something. Hence, the correct answer is option 4.

2)

OPTIONS

1) 2) 3) 4) None of these

Putting in the value, we get 6P =29 Hence, option 2.

3)

Rearrange the sentences to form a coherent paragraph. A. The condition affects 17 to 35 percent of humans. The probable cause is a congenital malfunction in nerve signals in the trigeminal nerve nuclei. B. Another theory suggests that tears leaking into the nose through the nasolacrimal duct are a cause of the photic sneeze reflex; the speed of the reflex seems to favor the first theory, as it happens much too quickly for tears to be generated and drain into the nose. C. Photic sneeze reflex is a genetic autosomal dominant trait, which causes sneezing when exposed suddenly to bright light, possibly many times consecutively. D. Research suggests that some people have an association between this nerve and the nerve that transmits visual impulses to the brain- overstimulation of the optic nerve triggers the trigeminal nerve, and this causes the photic sneeze reflex. E. It is also referred to as photic sneeze response, sun sneezing, photogenic sneezing, the photosternutatory reflex, being photo sensitive, ACHOO syndrome, and "Achooism," with its related backronym Autosomal dominant Compelling Helio-Ophthalmic Outburst syndrome.

OPTIONS 1) ACDBE 2) DCABE 3) CDEBA 4) CEADB 5) CBDAE

Solution

Statement C introduces the theme of the paragraph. Option A with ‗the condition‘ and option D with ‗this nerve‘ have to be preceded by some statement which explains them. Eliminate options 1 and 2. In option 3, statement D mentions ‗this nerve‘ immediately after statement C. There is no indication of it in statement C. Eliminate option 3. Similarly, option 5 can also be eliminated. The only statement that mentions a nerve is statement A. Therefore, D has to follow A. The AD link is present in option 4. Moreover, option 4 has a smooth flow and transition in the presentation of data. Hence, the correct answer is option 4.

4)Tangents are drawn from a point P on x2 + y2 = 4r2 to the circle x2 + y2 = r2. The tangents

touch the smaller circle at points Q and R. The centroid of ΔPQR OPTIONS 1) is at a distance r from chord QR. 2) does not lie on line joining the origin and point P. 2 2 2 3) lies on x + y = r 4) is at a distance 1.5r from P

Solution Let O be the origin and S, the midpoint of QR and C be the centroid of ΔPQR. OP = 2r and OQ = r. ∴ ∠OPQ = 30° and ∠POQ = 60° ∴ In ∆OQR, OS is perpendicular to QR ∴ OS = 0.5r and SP = 1.5r The centroid (C) divides the median (SP) in the ratio 2 : 1. ∴ SC = 0.5r and CP = r Thus, point C is at a distance of r from the origin. Hence, the centroid of ∆PQR lies on x2 + y2 = r2 Hence, option 3.

5)The question below consists of a paragraph in which the first and last sentence has been

identified. Choose from the options the most logical order of the following sentences.

1.

Typically,

steel

is

heat

treated

in

a

multi-step

process.

A. The steel is held at that temperature until the carbon trapped in the martensite diffuses to produce a chemical composition with the potential to create either bainite or pearlite (a crystal structure formed from a mixture of ferrite and cementite). B. The steel is then tempered by heating between the ranges of 150°C-260°C (300°F-500°F) and 370°C-650°C (700°F-1200°F). C. First it is heated to create a solid solution of iron and carbon in a process called austenizing. Austenizing is followed by quenching to produce a martensitic microstructure. D. Tempering in the range of 260°C-370°C (500°F-700°F) is sometimes avoided to reduce temper brittling. 6. Thus the process of steel tempering is carried out and temper brittling is reduced. OPTIONS 1) CDAB 2) CABD 3) CADB 4) DCAB 5) DCBA

Solution The correct order of this passage is C-A-B-D. The passage describes the process of heat treatment to steel. C is the most obvious choice for the first line connecting the opening line of the passage. It describes the first step that goes into the process. The next logical line should be the introductory line to the need of steel being held at a certain temperature. Further lines describe the exact temperatures at which the treatment is carried out. The connecting link between the closing statement and the previous line is the mention of reduction of temper brittling. Hence, the correct answer is option 2.

6)

The integer N is given by N = 2M × 5386, where M is an integer. If N is known to have 388 digits, how many values can M take? OPTIONS 1) 1 2) 2 3) 3 4) 4 5) None of these

Solution

We first note that 2386 × 5386 = 10386, which has 387 digits. Thus, M must be greater than 386. Now, N = 2M × 5386 = 2M − 386(2386 × 5386) = 2M – 386 × 10386 This number has the digits of 2M – 386 followed by 386 zeros. ∴ For N to have 388 digits, 2M – 386 must have 2 digits. The number of positive integral powers of 2 which have two digits is three. These are, respectively, equal to 24 = 16, 25 = 32 and 26 = 64. M can therefore take values 390, 391 and 392. M can take three values. Hence, option 3.

6)

Paleontologist John Ostrom's study of Deinonychus in the late 1960s revolutionized the way scientists thought about dinosaurs, leading to the―dinosaur renaissance‖ and igniting the debate on whether dinosaurs were warm-blooded or cold-blooded. Before this, the popular conception of dinosaurs had been one of plodding, reptilian giants. Ostrom noted the small body, sleek, horizontal posture, ratite-like spine, and especially the enlarged raptorial claws on the feet, which suggested an active, agile predator. What can be inferred about the ―dinosaur renaissance‖? OPTIONS It was a scientific moment of discovery that reshaped the notions about the biological make of dinosaurs. 2) John Ostrom was responsible for it because of his study of the Deinonychus. 1) 3) It busted the notion that dinosaurs were just plodding, reptilian creatures. 4) All of the above 5) None of the above

Solution Option 1 can inferred from the fact that it ingnited the debate. The later description of Ostrom adds to the explanation for ―biological make‖. Option 3 can be inferred from ―Before this, the popular conception of dinosaurs had been one of plodding, reptilian giants.‖ Option 2 can be inferred from ―Paleontologist John Ostrom's study of Deinonychus ... leading to the ―dinosaur renaissance‖.‖

Hence, the correct answer is option 4.

7)

The question below consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from among the options. A. Merely viewing another person's movements activates our own motor cortex, which we normally use for precise control of our actual movements. B. Brain imaging studies have now shown that the human brain contains a similar mirror-neuron system. C. As sports fans, musicians, and students of body language know, watching other people's movements and postures may facilitate the viewer's own motor schemes, sometimes resulting in unintended imitation. D. A monkey's mirror neurons are activated both when he himself is acting, say, taking a raisin from a tray, and when he is viewing another monkey (or the human experimenter) performing the same act. E. Mirror neurons, first discovered in monkeys, may serve help us master basic social skills, providing a common code between the sender and receiver of a nonverbal message.

OPTIONS 1) CDEBA 2) BEDAC 3) ABCED 4) CABED 5) EDBAC

Sol There are two clues that get you two links between the statements. First is the link between statement E and D. The mirror neurons ‗first discovered in monkeys‘ should be placed before statement D in which the ‗monkey‘s mirror neurons‘ are spoken about. Therefore E is placed before D. Secondly, the word ‗similar‘ in statement B refers to the mirror neurons that humans share with the monkeys. Therefore, the monkey‘s neurons have to be mentioned first if they are to be compared to the human‘s brains. Therefore, statement B is placed after statements ED. The importance of the mirror neuron is that when activated it is performing an action or watching someone perform something. Statement A explains this behaviour with reference to human beings – ‗our own motor cortex‘. Statement C functions as an illustration of this activity and is therefore placed at the end of the paragraph.Hence, the correct answer is option 5.

8)

The value of (a1 + a2 + a3 +… + an)(a1−1 + a2−1 + a3−1 +…+ an−1) can be OPTIONS 1) n 2 2) n 3) n2 − 1 2 4) n − n 5) None of these

Solution By AM GM inequality (a1 + a2 + a3 +… + an)n ≥ (n)n(a1a2a3…an) (a1−1 + a2−1 + a3−1 +…+ an−1)n ≥ (n)n(a1a2a3…an) −1 Multiply the two equations and take nth root to get, (a1 + a2 + a3 +… + an)(a1−1 + a2−1 + a3−1 +…+ an−1) ≥ n2 Hence, option 2.

9)Statistics published by the Traffic Control Department show that nearly 80% of all traffic

fatalities occur at speeds of under 50 miles per hour and within 25 miles of home. Therefore, you are safer in a car if you are driving at a speed over 50 miles per hour and not within a 25mile radius of your home. Which of the following, if true, most weakens the conclusion of the argument above? OPTIONS 1) 2) 3) 4) 5) 80% of all persons arrested for driving at a speed over the posted speed limit are intoxicated. 90% of all driving time is registered within the 50-mile radius of the driver‘s home and at speeds less than 25 miles per hour. 80% of the nation‘s annual traffic fatalities occur on six weekends that are considered high-risk weekends because they contain holidays. 90% of all driving time is registered within a 25-mile radius of the driver‘s home and at speeds less than 50 miles per hour. 90% of all driving time is registered outside the 25-mile radius of the driver‘s home and at speeds less than 50 miles per hour.

Solution The conclusion of the argument in the question has a fallacy telling that a person is safer when driving at higher speeds. Moreover, the distance from home does not necessarily make one more or less safe. The real reason there are fewer fatalities at speeds over 50 miles per hour and at a distance greater than 25 miles from home is that less driving time is logged under such conditions, which is given by option 4. Most driving originates at home and is not usually too long and proceeds at speeds set for residential areas. Options 1 and 3 seem to make plausible statements, but they are irrelevant to the claim made in the paragraph. Option 2 with 50-mile radius, 25 miles per hour and option 5 with 'outside' the 25-mile radius change the context of the main data. Hence, the correct answer is option 4.

10)

This question consists of two capitalized words that have a certain relationship. Choose the pair that has words not related to each other in the same way as the capitalized pair. COMSTOCKERY: ENDORSEMENT :: OPTIONS 1) Drawcansir: Bullyragger 2) Hector: Encourage 3) Generous: Alienating 4) Coercive: Voluntary 5) Despot: Democrat

Solution ‗Comstockery‘ means a censorship of literature and other forms of expression and communication because of perceived immorality or obscenity. ‗Endorsement‘ is the antonym. ‗Drawcansir‘ refers to a blustering, bragging bully. ‗Hector‘ means a bully and ‗encourage‘ is the antonym for it. ‗Generous‘ means liberal in sharing, while the antonym for it is ‗alienating‘. ‗Coercive‘ means forcible and the antonym for it is ‗voluntary‘. ‗Despot‘ is a tyrant and ‗democrat‘ is its antonym. ‗Bullyrag‘ is the only synonym to ‗Drawcansir‘. Hence, the correct answer is option 1.

11)

The question below consists of a certain number of sentences or parts of sentences. Some of these sentences or parts of sentences are incorrect or inappropriate due to issues in grammar or spelling. Select the option that indicates the correct and appropriate sentence(s) or parts of sentence(s).

A. B. C. D. E.

Three years back, the Kannada actress Jaimala triggered a major controversy when she said that she had entered the sanctum sanctorium of Sabarimala. This triggered a debate on if women should be allowed to enter Sabarimala. In 1930s, Aliki Diplarakou, who had won the Miss Europe title, dressed up as a man and sneaked in Mt. Athos in Greece generating a similar controversy.

OPTIONS 1) A only 2) A and E 3) A, B, and C 4) B, C, and D 5) C, D, and E

Solution Statement B is incorrect because Sanctum Sanctorum is spelt incorrectly as ―sanctorium‖with an incorrect ―i‖ after the ―r‖. Statement C is incorrect- use ‗whether‘ in the place of ―if.‖ Use "if" to express a condition. You may borrow my car if you are careful with it. Use "whether" to express alternatives. She did not know whether to say yes or no. Statement D is incorrect because the definite article has to be used before 1930s- ‗In the 1930s‘. Statement E is incorrect because the correct idiom would be ‗sneaked into‘ and not ‗sneaked in‘. Hence, the correct answer is option 1.

12)

Since all patients of paralysis I have encountered have failed to recover completely from physical disability, it follows that the paralysis patient who has been admitted today will also be left with some disability. Which of the following most closely parallels the reasoning of the argument? OPTIONS 1) 2) 3) 4) 5) Some birds are incapable of flight; therefore, swans are probably incapable of flight. Every ballet I have attended has failed to interest me; so a theatrical production which fails to interest me must be a ballet. Since all cases of severe depression I have encountered were susceptible to treatment by chlorpromazine, there must be something in the chlorpromazine that adjusts the patient‘s brain chemistry. Because almost all societies have a word for justice, the concept of fair play must be inherent in the biological makeup of the human species. Since no medicine I have tried for my allergy has ever helped, this new product will probably not work either.

Solution The sample argument is a straightforward generalization: All observed P are Q. R is a P. Therefore, R is Q. Option 4 comes a close second, but only option 5 replicates this form. Hence, the correct answer is option 5.

13)There are four sections A, B, C and D in a school. If the pass percentage of sections A, B

and C is 50%, that of sections A, B, D is 55%, that of A, C, D is 60% and that of B, C, D is 65% then which of the following can be the pass percentage of sections A, B, C and D combined together. OPTIONS 1) 56.33 2) 54.67 3) 53.33 4) 52.67

Solution Let the number of students in sections A, B, C and D be a, b, c and d respectively. Total number of students passing from sections A, B and C = (a + b + c) × 0.5 Total number of students passing from sections A, B and D = (a + b + d) × 0.55 Total number of students passing from sections A, C and D = (a + c + d) × 0.60 Total number of students passing from sections B, C and D = (b + c + d) × 0.65 Adding the 4 we get 3 × Total number of students passing from sections A, B, C and D = 1.65(a + b + c + d) + 0.05b + 0.1c + 0.15d ∴ Total number of students passing from sections A, B, C and D

Hence we can see that the minimum value can be 55.

Only option 1 lies in the range. Hence, option 1.

14)

Sakshi: All of the graduates from Seventh Day High School go to Willson College. Anushka: I don‘t know. Some of the students at Willson College come from Ilva High School. Anushka‘s response shows that she has interpreted Sakshi‘s remark to mean that: OPTIONS 1) Most of the students from Seventh Day High School attend Willson College 2) None of the students at Willson College are from Seventh Day High School 3) Only students from Seventh Day High School attend Willson College 4) Seventh Day High School is a better school than Ilva High School 5) Some Ilva High School graduates attend Willson college

Solution The question stem is important here. It asks us to state what meaning Anushka made of Sakshi's statement. The statement that Anushka made in the main data would be appropriate only if Sakshi had said, ―All of the students at Willson college come from Seventh Day High School.‖ Option 5 is a mere repetition of Anushka's statement. Option 4 is irrelevant to the context. Option 2 is contrary as Anushka uses only 'some' for students from Ilva High School. Option 1 is in consonance with what Anushka thinks (not what she understood from Sakshi's statement). Only option 3 clearly states Anushka's assumption or interpretation. Hence, the correct answer is option 3.

15)

Hybrid vehicle drivetrain systems will be extensively allowed with the new regulations, which include kinetic-energy recovery systems (KERS; no push-to-pass systems – KERS in LMP cars must be activated with the accelerator pedal), as well as four-wheel drive (non-hybrid vehicles will remain two-wheel drive, specifically rear-wheel drive). All LMP cars will be weighed at 900 kg (2,000 lb). In addition, LMP bodywork must have a Formula One-style vertical fin on the top of the engine cover to reduce lift tendency and such "flipping" airborne crashes such as the 1999 race with three incidents by the Mercedes-Benz CLR, the most famous is by Peter Dumbreck and the 2008 1000 km of Monza crash by Stéphane Ortelli with the Courage-Oreca LC70. Which of the following most accurately sums up what the passage is talking about?

OPTIONS

1) There are safety regulations that are mandatory to allow LMP cars to race. 2) The most important objective of LMP cars is to ensure that cars are never more than 900 kgs.

3) A vertical fin is necessary to stop cars from flipping and going into airborne crashes. 4) The Mercedes-Benz CLR is the most famous wreck in the history of LMP racing. 5) There are safety regulations that are mandatory to allow hybrid cars to race.

Solution

The passage starts by listing “regulations” and the last line of the passage implies that these regulations are in place to avoid car crashes, and thus are concerned with safety. Options 2, 3 and 4 are incorrect, as they focus on only one aspect of the passage, and not on the summation. Option 5 is incorrect because the passage also talks about non-hybrid cars which fall under the regulations. Hence, the correct answer is option 1.

16)

1 × 31 + 2 × 32 + 3 × 33 + … + n × 3n

What is the value of n? OPTIONS

1) 15 2) 16

3) 17 4) 18 5) 19

Solution

S = 1 × 3 1 + 2 × 3 2 + 3 × 3 3 + … + n × 3n = (31 + 32 + 33 + … + 3n) + (32 + 33 + … + 3n) + (33 + 34 + … + 3n) + … + 3n

Comparing these equations, we get n = 18 Hence, option 4.

17)

The polio vaccine is administered in two ways: IPV is given as a shot in the arm or leg; OPV is given as an oral liquid. OPV is no longer used in the United States, but is still given in other parts of the world where polio is common. The change to an all-IPV schedule in the United States occurred because the few cases of polio that were occurring were caused by the OPV vaccine itself and not the wild virus. The change to IPV protects individuals against paralytic polio, while eliminating the small chance of actually contracting polio from the live oral vaccine. IPV has been used exclusively in the United States since 2000. However, in other countries where wild polio is still a threat, OPV is still used. Which of the following can be inferred from the data given above? OPTIONS 1) Wild polio has been eradicated from the United States. 2) OPV contains live and wild polio virus. 3) IPV is a better form of vaccination against polio. An all-IPV schedule of vaccination eliminates the chances of polio from the wild 4) virus. 5) 1 and 2

Solution

―OPV is no longer used in the United States … because the few cases of polio that were occurring were caused by the OPV vaccine itself and not the wild virus.‖ It can be thus inferred that OPV is used to combat the wild virus. Hence the inference follows that the US has got rid of polio caused by the wild virus. Secondly, the following extract, ―IPV has been used exclusively in the United States since 2000. However, in other countries where wild polio is still a threat, OPV is still used‖ corroborates option 1- that wild polio has been eradicated from the Unites States. Option 2 is incorrect- because it can be inferred that OPV contains live virus but definitely not the ‗wild virus‘. Administering wild virus would be spreading the disease and not vaccination. Option 3- IPV being a better form of vaccination than OPV is too strong an inference to make and cannot be deduced from the passage with any degree of certainty. Option 4 is contrary to the passage. An all-IPV schedule of vaccination eliminates the chances of polio caused by the OPV vaccine itself- not from the wild virus. Hence, the correct answer is option 1.

18)

ADVERTISEMENT: When you enrol with Fly High Business Institute (FHBI), you will have access to our placement counseling service. Last year, 90% of our graduates who asked us to help them find jobs found them. So go to FHBI for your future! The answer to which of the following questions is potentially the LEAST damaging to the claim of the advertisement? OPTIONS

1) How many of your graduates asked FHBI for assistance? 2) How many people graduated from FHBI last year? Did those people who asked for jobs find ones in the areas for which they were 3) trained? Was FHBI responsible for finding the jobs or did graduates find them 4) independently? 5) Was the person doing the advertisement a paid, professional actor?

The advertisement seeks to create an impression that FHBI found jobs for its many graduates and generally does a lot of good for them. But first we should ask how many graduates FHBI had—as finding jobs for a handful of them might have been easy; but if many people enrol at FHBI, they may not have the same success. Further, we might want to know how many people graduated compared with how many enrolled. So option 2 is a valid question. Now, how many of those who graduated came in looking for help in finding a job? Maybe most people had jobs only a few needed help or, perhaps the graduates were so disgusted they did not even seek assistance. So, option 1 is relevant. Option 3 is also important; perhaps FHBI found them very menial jobs —not in business. Finally, maybe the ad is truthful—FHBI graduates found jobs—but maybe they did it on their own. So, option 4 also is a question worth asking. Option 5, however, is the least problematic. Even if it turns out that the ad was done by a paid, professional actor, so what? That‘s what we expect from an advertisement. Hence, the correct answer is option 5.

19)

Gaga has identified fashion as a major influence. She considers Donatella Versace her muse. Gaga has her own creative production team called the Haus of Gaga, which she handles personally. The team creates many of her clothes, stage props, and hairdos. Her love of fashion came from her mother, who she stated was "always very well kept and beautiful.‖ "When I'm writing music, I'm thinking about the clothes I want to wear on stage. It's all about everything altogether—performance art, pop performance art, fashion. For me, it's everything coming together and being a real story that will bring back the super-fan. I want to bring that back. I want the imagery to be so strong that fans will want to eat and taste every part of us." What can we conclude about Gaga from the passage? OPTIONS Gaga is a firm believer in the cult of culture – a society where performance art is at its pinnacle. Gaga‘s mother has a major influence on the kind of personality she assumes on 2) stage. 3) Gaga is a singer and a stage performer. 1) 4) Gaga is a performer-song-writer with a tilt towards elegance and grace.

5)

Gaga creates an identity for each piece of music she writes that becomes larger than the song itself.

solution

The passage states that she keeps in mind the fashion and the performance art pieces while she is writing music – thus it isn‘t just about the music, but the whole package. ―When I'm writing music, I'm thinking about the clothes I want to wear on stage. It's all about everything altogether—performance art, pop performance art, fashion. For me, it's everything coming together and being a real story that will bring back the super-fan.‖ Option 1 is wrong because it‘s too vague. Option 2 is wrong because the passage states that her mother merely inspired her love for fashion. Option 3 is wrong because nowhere does the passage state that she sings. Option 4 is wrong as the passage implies the opposite – that she has a flair for the dramatic – pop performance art et al. Hence, the correct answer is option 5.

20)

A colour concentrate comes under three varieties viz. A, B and C in which the concentrations of colour are 20%, 30% and 50% respectively. If the per litre prices of A, B and C are Rs. 20, Rs. 30 and Rs. 40 respectively, then what is the minimum cost (approximate) in which one can prepare 10 litres of a 40% colour concentrate using two of the given varieties? OPTIONS

1) Rs. 345 2) Rs. 350 3) Rs. 367 4) Rs. 323 5) Rs. 333

Solution Concentration of the resultant solution is 40%. Mixing 20% and 30% concentrated solution in any proportion will not give a 40% solution. So, 50% solution has to be used.

This can be done in two ways: Case I: 50% and 20% varieties are mixed together. Ratio of 50% variety to the 20% variety in the 10 litre concentrate is:

Case II: 50% and 30% varieties are mixed together. Ratio of 50% variety to the 30% variety in the 10 litre concentrate is:

Total cost = 5 × 40 + 5 × 30 = Rs. 350 Thus the minimum cost in which the required solution can be prepared is Rs. 333 Hence, option 5.

21)

There are 355 grains of sand in bowl A, 555 in bowl B and 1655 in bowl C. They are mixed together and are arranged in groups of 16. How many grains will be left ungrouped? OPTIONS

1) 15 2) 4 3) 8 4) 2 5) 12

Solution

The number of grains that will be left ungrouped is the same as the remainder when (355 + 555 + 1655) is divided by 16. 16 divides 1655. 355 + 555 = (4 – 1)55 + (4 + 1)55 Expand using binomial theorem. All the terms except the penultimate term of each expansion i.e one 4 × 55C54 have powers of 16 in them. ∴ Remainder = 2 × 4 × 55C54 = 440 = (16 × 27) + 8 i.e. equivalent to a remainder of 8. Hence, option 3.

22)

There is no obvious single source for the plot of The Tempest, but researchers have seen parallels in Erasmus's Naufragium, Peter Martyr's De orbo novo, and an eyewitness report by William Strachey of the real-life shipwreck of the Sea Venture on the islands of Bermuda. In addition, one of Gonzalo's speeches is derived from Montaigne's essay Of the Canibales; and much of Prospero's renunciative speech is taken word for word from a speech by Medea in Ovid's poem Metamorphoses. The masque in Act 4 may have been a later addition, possibly in honour of the wedding of Princess Elizabeth of Bohemia and Frederick V, Elector Palatine, in 1613. The play was first published in the First Folio of 1623. Which of the following can’t be concluded about The Tempest from the passage? OPTIONS

1) The Tempest is not a completely original play. 2) Many inspirations shaped the plot of The Tempest. 3) The story of The Tempest revolves around a shipwreck. 4) Montaigne’s essay Of the Canibales was written before The Tempest.

5)

Princess Elizabeth of Bohemia and Frederick V’s wedding had a role to play in shaping up the plot of The Tempest.

Solution We know that a shipwreck is an essential part of the plot – “There is no obvious single source for the plot of The Tempest, but researchers have seen parallels in Erasmus's Naufragium, Peter Martyr's De orbo novo, and an eyewitness report by William Strachey of the real-life shipwreck of the Sea Venture on the islands of Bermuda.” But we don’t know that the plot revolves around a shipwreck. Therefore, option 3 is not a correct conclusion. Options 1 and 2 can be concluded as the essence of the passage itself is that The Tempest has many inspirations/ sources. Option 4 can be concluded since The Tempest was inspired by Montaigne’s essay, which means that it was written before The Tempest. Option 5 can be concluded from “The masque in Act 4 may have been a later addition, possibly in honour of the wedding of Princess Elizabeth of Bohemia and Frederick V, Elector Palatine, in 1613.” Therefore, the wedding did have a role to play in shaping the plot. Hence, the correct answer is option 3.

23)

Either you severely punish a child who is bad or the child will grow up to be a criminal. Your child has just been bad. Therefore, you should punish the child severely. All of the following would be an appropriate objection to the argument except: OPTIONS

1) What do you consider to be a severe punishment? 2) Don’t your first and second premises contradict one another? 3) What do you mean by the term “bad”? 4) In what way has this child been bad? 5) Both 1 and 4

Solution The terms “severely punish” and “bad” are highly ambiguous and subjective. It would be legitimate to ask the speaker just what he considers to be bad behavior (option 3), and severe punishment (option 1). Also, since the speaker has alleged that the child has been “bad,” and since the term is ambiguous, we can also demand clarification on that score (option 4). The one objection that makes no sense to raise is option 2. The premises have the very simple logical structure: If a child is bad (badly behaved, done something wrong) and not punished, then the child becomes a criminal. Child X is bad, hence punish him severely. There is absolutely no inconsistency between those two statements. Hence, the correct answer is option 2. 24) Vishal went to a shop to buy a mobile phone. He chose one and the shopkeeper told him that the basic price of the phone is Rs. 4,200. The shopkeeper also said that he would have to pay VAT at the rate of 12%, tax A at the rate of 6% and tax B at the rate of 7%. The shopkeeper also offered him a discount of 5%. Now, Vishal is puzzled as to in what order should he add the taxes and subtract the discount so that his bill is minimized in the following scenarios? a) The taxes/discount are both applied on the basic price i.e. on Rs. 4,200.

b) The taxes/discount are applied on the price after adding/subtracting the tax/discount till each point. OPTIONS

1)

In a, the order does not matter. In b, first apply 5% discount, then the 6%, 7% and 12% taxes respectively. In a, the order does not matter. In b, first apply the 12%, 7% and 6% tax and finally the 5% discount. In a, apply the discount first and the taxes in any order, later. In b, the order does not matter.

2)

3)

4) The order does not matter in either case. 5) In a, the order does not matter. In b, first apply the 6%, 7% and then 12% tax in that order followed by the 5% discount.

Solution a) The order does not matter because everything is calculated on the base price and then added/subtracted; and addition/subtraction is commutative. b) The order does not matter because the final amount is any case will be 4200 × 0.95 × 1.06 × 1.07 × 1.12; and multiplication is also commutative. Thus, the order is irrelevant in either case. Hence, option 4. 25) The following question consists of a certain number of sentences. Some sentences are grammatically and/or logically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s). A. M.F. Husain, India's foremost modern painter and an internationally recognised artist, passed away on Thursday, he was 97. B. Thirty First Ladies from Africa, Asia, Latin America and the Caribbean joined forces at the United Nations to mobilise support to achieve the goal of zero new HIV infections among children by 2015. C. Usain Bolt set the quickest time in the world this season as he eased to victory in the 200 meters at a Diamond League meet. D. Mitt Romney will skip a key early test for Republican presidential candidates by forgoing the Iowa straw poll. E. A selloff in bonds backed by subprime mortgages has spread through the riskiest segments of the credit markets and ended up rallying in high-yield corporate bonds and commercial real-estate debt.

OPTIONS

1) Only A 2) Only E 3) A and E 4) A and D 5) B, C and E

Solution Sentences B, C and D are correct. Sentence A is incorrect as “he was 97” is an independent clause - it should have been a separate sentence, or it could have been separated from the rest of the sentence by a semi colon, but not by a comma. Sentence E is incorrect as the word “sell off” refers to the sale or disposal of something. The sentence states that the sell off has spread through the riskiest segments and ended up rallying. The sale of something cannot be “rallied”. Moreover, “ended up rallying in high …. debt” is incorrect as it makes no logical sense and is grammatically incorrect. The correct sentence could be “A selloff in bonds backed by subprime mortgages has spread through the riskiest segments of the credit markets, ending the rally in high-yield corporate bonds and commercial real-estate debt.” Hence, the correct answer is option 3. 24)

Find the equation of the straight line which is the image of the line tanθx + y = 2tanθ in the line x + y/√3 = 2. OPTIONS

1) (x – 2) tan(60° + θ) = y 2) (x – 2) tan(60° – θ) = y 3) (x – 2) tan(30° + θ) = y 4) (x – 2) tan(60° + 2θ) = y 5) None of these

Solution x + y/√3 = 2 passes through (2, 0) and makes 120° with the x-axis. tanθx + y = 2tanθ passes through (2, 0) and makes 180° – θ with the x-axis.

∴ the reflection of tanθx + y = 2tanθ will pass through (2, 0) and make (60° + θ) with the x-axis. Hence, option 1.

25)

What

is

the

value

of

OPTIONS 1) −2 2) −1 3) 0 4) 1 5) 2 Get this! Solution We can find the value of the expression by putting x = 487, y = 674 and z = 187, and simplifying the expression

We first simplify the first two terms as

The next two terms can be simplified as

We can see that these add to zero. Thus, the expression will also be equal to zero. Hence, option 3.

26)

Read the sentences and choose the option that best arranges them in a logical order. A. The Organization of Petroleum Exporting Countries' first meeting since the start of prodemocracy movements in the Middle East also turned out to be one of its most turbulent sessions in years. B. It brought to the fore long-simmering divisions between key cartel players Saudi Arabia and Iran and called into question the group's ability to influence oil prices. C. Tensions spilled into the open as solemn-looking delegates filed out of OPEC's modern headquarters and Saudi oil minister Ali Naimi declared it "one of the worst meetings we ever had." D. An acrimonious OPEC meeting failed to produce an agreement to increase oil production despite tight supplies and rising prices.

OPTIONS

1) ABCD 2) ABDC 3) DABC 4) DBAC 5) BCAD

DiscussGet In EmailGet this! Solution To determine the first sentence of the paragraph, we can use certain grammatical cues. Sentence B , beginning with “it” is not appropriate since the sentences which describe “it” would be better starters. Eliminate option 5. Sentence A seems to a good choice glance since it contains the full form of the organization. However, between statement A and statement D, D had to precede A. Grammatically, statement A uses the definite article “the”, which has to follow “an OPEC meeting” in statement D. Similarly, the use of the indefinite article “an” in statement D indicates that the meeting has not been mentioned previously. Logically, D is the perfect introduction to the entire paragraph which then provides the details. Eliminate options 1 and 2. To an extent, statement A restates what has been mentioned earlier in sentence D. Therefore, it cannot come immediately after statement D. Eliminate option 3. Statement B illustrates the effects of this meeting and is maintains a logical flow. Therefore

statement B has to follow D. Statement A with "turbulent sessions" is linked to statement C which describes how “tensions spilled into the open” at the end of the meeting. Hence, the correct answer is option 4.

27)

Select the option which has a similar analogy vis-a-vis the analogy given below. Tediferous: Torch :: OPTIONS

1) Succiniferous: Succour 2) Succiferous: Sap 3) Thuriferous: Thunder 4) Vasiferous: Vase 5) Furciferous: Fruit

Solution

The Latin suffix ‘ferrous’ is taken from ‘ferre’ or ‘gerere’ meaning to bear. Tediferous means to bear a torch. Succiferous means bearing sap. Succiniferous means bearing or producing amber. Thuriferous is incense bearing and vasiferous means to bear a vessel or vas (duct). Furciferous means either bearing a fork or a rascally person by nature. Hence, the correct answer is option 2.

28)

If the equation 2x4 – x3 + 4x2 + ax + b = 0 has real roots A, B, C and D, and the equation 2x4 – 3x3 + 4x2 + cx + d = 0 has real roots A, B, C and E, what is the value of (D + E)? OPTIONS 1) 1 2) 2 3) 3 4) 4

5) Cannot be determined

Observe that the coefficients for x4 and x2 are the same for both the equations. Therefore, subtract the second equation from the first to get 2x3 + (a – c)x + (b – d) = 0 Since this equation is a third order equation, all its roots will satisfy both the equations given. Since the roots satisfy both the equations, the roots of the cubic equation are the common roots of the two equations i.e. A, B and C. For the cubic equation, sum of the roots is equal in magnitude to the coefficient of x2. Since the coefficient of x2 in this equation is zero, the sum of the roots i.e. A + B + C = 0 Now, for the two original equations, sum of the roots = −(coefficient of x3/coefficient of x4) Now, the sum of the roots of the first equation is

Solution

Hence, option 2.

29)

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s). A. With hours before the deadline to submit nominees, the French finance minister has the backing for European Union countries. B. The outgoing head of Hong Kong's securities regulator warned investors against rushing headlong to buy shares in Chinese companies, calling China "the new dotcom" of the investment world. C. Instead of playing cricket with the kids on the alleyway outside, the 4-year-old sweats

in his family's one-room apartment. D. Little progress has been made in negotiations with the Taliban despite several months of contact between western governments and interlocutors for the Islamist group. E. Trading in shares of Hong Kong-listed China Forestry Holdings Ltd. was suspended after its auditors found irregularities in its books.

OPTIONS 1) A and C 2) A, B and C 3) Only B 4) B and E 5) Only C

Solution

Sentences B, D and E are correct. Sentence A is incorrect. The preposition ―for‖ has been incorrectly used instead of the preposition ―of‖ - to have the backing of someone means to have their support. Sentence C is incorrect due to the preposition ―on‖. An ―alleyway‖ means an alley or a narrow street with walls on both sides, therefore, the preposition ―in‖ would be the correct preposition, as ―in‖ indicates within or inside a particular place. Hence, the correct answer is option 1.

30)

Given that a, b and c are in A.P., the straight line ax + by + c = 0 always passes through the point OPTIONS 1) (1, –2) 2) (0, 0) 3) (2, –1) 4) (1, –1) 5) No such point exists

Solution

Since a, b and c are in AP, 2b = a + c. ∴ a – 2b + c = 0 ax + by + c = 0

∴ The line always passes through the point (1, –2). Hence, option 1.

31)

While some of the story lines may pass more directly through one of the two central events than the other, all are either directly or indirectly linked to them both. Through the author's ability to draw the reader into the minds of each of the many and varied protagonists, the reader is given an indepth and multifaceted view of both the heights and the depths of life in New York city for both its ordinary, and its more extraordinary citizens. In subsequent interviews, the author has noted his intention to point out the melodramatic tensions present in all of our lives, whether perched upon a death-defying high wire, or merely trying to live out a more “ordinary” life, “where there is still an invisible tight-rope wire that we all walk, with equally high stakes, only it is hidden to most, and only 1 inch off the ground”. According to the author, melodramatic tensions are: OPTIONS

1) Exclusive to the less-ordinary citizens of New York. 2) Exclusive to those perched upon the death-defying high wires of New York city – both literally and metaphorically.

3) All pervasive, irrespective of the lifestyle you choose. 4) Present in both the heights and depths of New York city and in the minds of all the protagonists.

5) None of the above

Solution

The passage states that “In subsequent interviews, the author has noted his intention to point out the melodramatic tensions present in all of our lives”. Thus the point is that everyone suffers from them. This is described in option 3. Options 1 and 2 are incorrect as they call tensions “exclusive” to a certain category of people. Option 4, though close, is not as appropriate as option 3. Option 5 is wrong as the answer is one of the above. Hence, the correct answer is option 3.

32)

If x, y are distinct integers and belong to the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, how many ratios of the form x/y are non-integral in nature? OPTIONS 1) 83 2) 73 3) 68 4) 78

Solution

Since x and y are distinct integers, this is similar to a case of selecting 2 numbers from 10, where repetition is not allowed. Thus, the denominator can be selected in 10 ways and consequently, the numerator can be selected in 9 ways. Therefore, the total number of ratios that can be formed = 10 × 9 = 90 Now, find the number of ratios of the form x/y which are integral in nature. If y = 1, x can take 9 values (anything from 2 to 10) If y = 2, x can take 4 values (4, 6, 8 and 10) If y = 3, x can take 2 values (6 and 9) If y = 4, x can take 1 value (8) and If y = 5, x can take 1 value (10) For y > 5, the ratio of the form x/y will not be integral in nature. Hence, the number of ratios of the form x/y that are integral = 9 + 4 + 2 + 1 + 1 = 17 Hence, the number of ratios that are non-integral = 90 − 17 = 73 Hence, option 2.

33)

A new clock is designed such that it has only 6 hour markings (from 1 to 6) and minute markings marked from 0 to 30 minutes in between the 6 hour markings. Hence, in one hour, the minute hand completes 2 full rotations while the hour hand completes one 60° rotation

from one hour marking to another. For example, when the hour hand is past five and the minute hand is at 20 minutes, the time can be 5:20 or 5:50 depending upon whether the hour hand is closer to 5-hour mark or to 6-hour mark. What is the angle between the minute hand and the hour hand of the clock at 4:24 PM? OPTIONS 1) 24° 2) 20° 3) 30° 4) 18°

Solution

The hour hand completes one 60° rotation from one hour marking to another in an hour. Thus, the hour hand completes 60° in 60 minutes i.e. 1° per minute. ∴ The angle made by hour hand at 4:24 p.m. = (4 × 60) + (24 × 1) = 264°. The minute hand completes one rotation in 30 minutes. Thus, it covers 360° in 30 minutes i.e 12° per minute. ∴ The angle made by minute hand at 4:24 p.m. = (24 × 12) = 288°. ∴ Angle between the minute hand and the hour hand at 4:24 p.m. = 288 − 264 = 24°. Hence, option 1.

34)

CHOREOMANIA: DANCE OPTIONS 1) Clinomania: Bed 2) Nosomania: Disease 3) Melomania: Music 4) Potomania: Potatoes 5) Polemomania: War

Solution

This question deals with different types of manias or obsessions. Choreomania refers to a dancing mania or frenzy. Clinomania means an excessive desire to stay in bed. Nosomania is a delusion of suffering from a disease. Melomania is a craze for music. Polemomania is a mania for war. Potomania refers to an abnormal desire to drink alcohol and is unrelated to

potatoes. Hence, the correct answer is option 4.

35)

A palindromic number is defined as a positive integer whose value is unchanged when it is read backwards. If N is a palindromic number whose unit‘s digit is 8, and which has an even number of digits, which is the largest number which is definitely a factor of N? OPTIONS 1) 4 2) 8 3) 11 4) 22 5) 44

Solution

We can make the observation that, in any natural palindromic number with an even number of digits, starting from either end, the set of digits in a pair of odd and even places is the same. Hence, the sum of digits in the odd and even places is the same. Thus, any palindromic number with an even number of digits is divisible by 11. Also, if a number has unit‘s digit 8, it must be divisible by 2 (we cannot say conclusively whether it is divisible by higher powers of 2). We can only be sure than N is divisible by 2 and 11. All possible values of N satisfying these conditions will be divisible by 2 × 11 = 22 Hence, option 4.

36)

In planning a clinical trial, the sponsor or investigator first identifies the medication or device to be tested. Usually, one or more pilot experiments are conducted to gain insights for design of the clinical trial to follow. In medical jargon, effectiveness is how well a treatment works in practice and efficacy is how well it works in a clinical trial. In the U.S., the elderly comprise only 14% of the population but they consume over one-third of drugs. Despite this, they are often excluded from trials because their more frequent health issues and drug use produce unreliable data. Women, children, and people with unrelated medical conditions are also frequently excluded. According to the passage, who can clinical trials be held on? OPTIONS 1) Elderly U.S. citizens, because they consume over one-third of the drugs. 2) Women and children and people with unrelated medical conditions. 3) Adult men with related medical conditions that are not part of the elderly.

4) Adult men only. 5) Young adults with related medical conditions.

Solution

We know that they are not held on: the elderly, women, children and people with unrelated medical conditions. Thus we know that the only possible people they can be tested on are adult men that aren‘t the elderly and that they don‘t have unrelated medical conditions. Therefore, options 1 and 2 are wrong and have to be eliminated. Option 4 is too general - adult men includes all adult males, but the elderly males would have to be excluded, making this option incorrect. Similarly, ‗young adults‘ in option 5 may have men and women, which makes it incorrect. Option 3 does not contain any of the people who have to be excluded, making it the correct choice. Hence, the correct answer is option 3.

37)

Freemasonry is a fraternal organisation that arose from obscure origins in the late 16th to early 17th century. Freemasonry now exists in various forms all over the world, with a membership estimated at around 5 million, with around 480,000 in England, Scotland and Ireland alone, and just under two million in the United States. The various forms all share moral and metaphysical ideals, which include, in most cases, a constitutional declaration of belief in a Supreme Being. The fraternity is administratively organised into Grand Lodges (or sometimes Orients), each of which governs its own jurisdiction, which consists of subordinate (or constituent) Lodges. Grand Lodges recognise each other through a process of landmarks and regularity. There are also appendant bodies, which are organisations related to the main branch of Freemasonry, but with their own independent administration. What can we conclude about Freemasonry from the passage? OPTIONS 1) Freemasonry is an alternative religion. Freemasonry is probably a boys club only – women weren‘t allowed to be a part 2) of it. Grand Lodges are factions within the Freemasons where people are divided on the 3) basis of societal status. Freemasonry has different sections scattered all over the world, especially the 4) Oriental nations. Appendant bodies are those bodies that allow freemasons to exist freely within 5) themselves.

Solution

We know from the passage that freemasonry is a ―fraternal‖ organisation – which means it‘s a brotherhood, and that implies that women aren‘t allowed. Options 1, 3, 4, and 5 cannot be proved by the passage, therefore they are incorrect. Hence, the correct answer is option 2.

38)

Ram and Shyam start walking on the same road towards each other. If 30 minutes before they meet, they are 5 km away and the speed of Ram is 8 km/hr, find the ratio of the speed of Ram and Shyam? OPTIONS

1) 2: 1 2) 4: 1 3) 4: 3 4) 4: 5 5) 1: 1

Solution

Since Ram and Shyam are 5 kms away from each other 30 minutes before they meet, they together cover 5 km in 30 minutes. ∴ Relative speed of Ram and Shyam together = 5/(30/60) = 10 km/hr Since Ram and Shyam are moving in opposite directions, their relative speed is the sum of their individual speeds. Relative speed = speed of Ram + speed of Shyam ∴ Speed of Shyam = Relative speed – speed of Ram = 10 – 8 = 2 km/hr ∴ Ratio of Speed of Ram to speed of Shyam = 8 : 2 = 4 : 1 Hence option 2.

39)

There are three integers a, b and c such that

Do a, b and c form a geometric progression? A. x, y and z are in A.P. B. x, y and z are in H.P.

OPTIONS 1) The question can be answered by one of the statements, but not by the other. The question can be answered by using either statement, independently of the 2) other. The question can be answered by using both statements together, but not by either 3) statement alone. 4) The question cannot be answered by either of the statements. DiscussGet In EmailGet this! Solution If a, b and c form a geometric progression, b2 = ac Using statement A alone a(1/x) = b(1/y) = c(1/z) = Constant

where k is the log of the constant mentioned above. Hence,

x, y and z are in A.P.

∴ b² = a × c Thus, a, b and c are in G.P. Hence, the question can be answered using statement A alone. Using Statement B alone x, y and z are in H.P. y is the harmonic mean of x and z.

This equation does not yield a meaningful relationship to establish if a, b and c are in G.P. For example, if a = c = 10, then b = 10, and hence a, b and c forms an GP. Similarly, if a = 10 and c = 100, then b = 104/3. Hence, a, b and c do not form an GP. Hence, the question cannot be answered using statement B alone. Hence, the question can be answered using statement A alone but not by using statement B alone. Hence, the question can be answered using one of the statements but not by using the other. Hence, option 1.

40)

The question is followed by two statements, A and B. Select the correct option based on the following instructions: Mark (1) if the question can be answered by one of the statements, but not by the other. Mark (2) if the question can be answered by using either statement, independently of the other.

Mark (3) if the question can be answered by using both statements together, but not by either statement alone. Mark (4) if the question cannot be answered by either of the statements. What is the length of side AB of triangle ABC? A. AB ≤ AC = 4 and area of triangle ABC = 8 B. Exactly two sides have integer lengths

OPTIONS

1) 1 2) 2 3) 3 4) 4

Solution

Using Statement A alone: AC = 4 and AB ≤ AC Thus, AB ≤ 4 Area of triangle ABC = 8 Now, in any triangle, Area = (1/2) × Product of two adjacent sides × Sin(angle between the two sides) Hence, in triangle ABC, A (∆ABC) = (1/2) × AB × AC × Sin A ∴ 8 = (1/2) × AB × 4 × Sin A ∴ AB × Sin A = 4

Now, AB ≤ 4. Also, the sine of any angle can have a maximum value of +1 and a minimum value of −1. Since AB is positive, sin A ≤ 1 Hence, for the above equation to hold, AB has to be equal to 4. Hence, AB = 4 Thus, the question can be answered using statement A alone. Using Statement B alone: This statement does not provide any information that can help find the value of AB. Thus, the question cannot be answered using statement B alone. Thus, the question can be answered using statement A alone but not by using statement B alone. Thus, the question can be answered by one statement but not by the other. Hence, option 1.

41)

Researchers debate about whether psychopathy/sociopathy are incorrectly put together under ASPD. These clinicians and researchers who believe that it was incorrect to label the two in the same category are upset that an important distinction has been lost between these two disorders. In other words, the DSM-IV-TR considers ASPD and psychopathy to be the same, or similar. However, they are not the same since antisocial personality disorder is diagnosed via behavior and social deviance, whereas psychopathy also includes affective and interpersonal personality factors. Other criticisms of ASPD are that it is essentially synonymous with criminality. Nearly 80%– 95% of felons will meet criteria for ASPD — thus ASPD predicts nothing in criminal justice populations, whereas psychopathy (using the Hare Psychopathy Checklist-Revised (PCL-R)) is found in only roughly 20% of inmates and PCL-R is considered one of the best predictors of violent recidivism. What are researchers upset about, according to this paragraph? OPTIONS

1) 2) 3) 4) 5)

That ASPD doesn‘t take into consideration the percentage of incarcerated people who suffer from ASPD. That ASPD and the DSM-IV-TR are considered to be the same. That ASPD is the only sure-fire way to diagnose antisocial symptoms amongst future criminals. That the DSM-IV-TR doesn‘t take into account ASPD‘s association with criminals. That psychopathy and sociopathy aren‘t supposed to be thrown together as they are in ASPD.

solution

The passage states that ―Researchers debate about whether psychopathy/sociopathy are incorrectly put together under ASPD. These clinicians and researchers who believe that it was incorrect to label the two in the same category are upset that an important distinction has been lost between these two disorders.‖ Option 1 is wrong as the passage doesn‘t talk about percentage of criminals actually suffering from ASPD – it talks about percentage of criminals who will meet the criteria for it. Option 2 is wrong as they aren‘t considered to be the same. Options 3 and 4 have no basis in the passage. Hence, the correct answer is option 5.

42)

The question below contains a number of sentences. Each sentence has pairs of word(s)/phrases that are highlighted. From the highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one. 1. The sudden torrent [A] / deluge [B] doused the flames and contained the wildfire before any real damage was done. 2. The poor farmers had no choice but to truckle [A] / buckle [B] to the landlord‘s demands in order to save their land. 3. The theorem posits [A] / emplaces [B] a deep knowledge of Bayer‘s theory of relativity for accurate results. 4. After the overthrow of the Pope, there was a sudden interest in heterodox [A] / conservative [B] theories regarding the importance of the Cross in the Christian religion. 5. His new book has claimed that social networking sites are actively used to subvert [A] / change [B] the morals of teenagers.

OPTIONS 1) ABBBA 2) BABAA

3) BAAAB 4) BAAAA 5) ABABA

Solution

Truckle means to act in a subservient manner. Buckle under is a phrase that means to succumb or give in. In this case, the preposition ‗under‘ is absent. This eliminates options 1 and 5. Posit means to assume or put forward as fact or the factual basis for an argument. Emplace means to put in place or position. Logically posit fits in the blank. This eliminates option 2. Subvert means to corrupt. Therefore, it is the apt word contextually. This eliminates option 3 Hence the correct answer is option 4.

43)

FIFA has organized a charity tournament such that 4 matches will be played in 4 different countries namely England, France, Italy and Germany. For these 4 matches, 2 football clubs from each of the 4 mentioned countries are selected. The matches are scheduled in such a way that none of the clubs will play their matches on home soil and the clubs from the same country won‘t face each other. If none of the clubs from Italy play in England and none of the clubs from England play in France then clubs from which countries will participate in a match in Italy? OPTIONS 1) England and Germany 2) England and France 3) Germany and France 4) Either 1 or 2 5) Both 1 and 2

Solution

No club plays in its own country. Also, it is known that clubs from Italy do not play in England and clubs from England do not play in France. Since clubs from Italy and England will not play in England, 1 club each from France and Germany will play their match in England. Similarly, 1 club each from Germany and Italy will play their match in France. Now, clubs from England, Germany or France should play in Italy. Note that both the clubs from Germany have already played in England and France. Hence, teams from England and France will play their match in Italy. Hence, option 2.

44)

Let α, β be positive real numbers such that α + β = 1, then find the maximum possible value of [(α3 + β3) − (β4 + α4)] OPTIONS 1) 2) 3) 4) 5)

T = α3 − α4 + β3 − β4 =α3(1 − α) + β3(1 − β) = α3β + β3α = αβ(α2 + β2 ) = αβ(1 − 2αβ) … [As α + β = 1]

Solution

Hence, option 3.

45)

Fill in the blanks with the most appropriate set of words from the options: Sellers might agree to sell at a common ___ price; buy the product from a supplier at a specified maximum price; ___ to a price book or list price; engage in cooperative price advertising; ___ financial credit terms offered to purchasers; use uniform trade-in allowances; limit discounts; ___ a free service or fix the price of one component of an overall service; adhere uniformly to previously-

announced prices and terms of sale; establish uniform costs and markups; ___ mandatory surcharges; purposefully reduce output or sales in order to charge higher prices; or purposefully share or pool markets, territories, or customers. OPTIONS

1) Spot, cohere, assimilate, interrupt, foist 2) Target, adhere, standardise, discontinue, impose 3) Mean, obey, standardise, discontinue, inflict 4) Base, practice, amend, interpose, enforce 5) Target, adhere, allocate, withdraw, cancel

Solution

A selling price has to be the target that is to be achieved by the seller. Base price means the initial price without additional incurred expenses. Therefore, option 4 can be eliminated. Cohere, obey, and practice are not grammatical in the second blank. This eliminates options 1, 3 and 4. Cancel does not fit into the fifth blank. Hence, option 5 is eliminated. Hence, the correct answer is option 2.

46)

The best means is to avoid any questionable foods or beverages. Other measures include good hygiene, specific vaccines, and in certain situations, prophylactic medications. Studies show a decrease in the incidence of TD with use of bismuth subsalicylate and with use of antimicrobial chemoprophylaxis. Bismuth subsalicylate (two tablets or two ounces four times daily) will reduce the likelihood of travelers' diarrhoea, but few travelers adhere to a four-times-per-day regimen because it is inconvenient. Side effects may include black tongue, black stools, nausea, constipation, and ringing in the ears (tinnitus). Bismuth subsalicylate should not be taken by those with aspirin allergy, kidney disease, or gout, nor concurrently with certain antibiotics, and should not be taken for more than three weeks. Which of the following is the passage most likely to be talking about? OPTIONS 1) How to treat Traveller‘s diarrhoea

2) Precautions to take while travelling 3) Prevention is better than cure 4) The many useful benefits of consuming Bismuth subsalicyclate 5) Ways to prevent Traveller‘s diarrhoea

Solution

The passage lists various ways to prevent (we know prevent because it uses the term ―prophylactic‖) traveller‘s diarrhoea - ―The best means is to avoid any questionable foods or beverages. Other measures include good hygiene, specific vaccines, and in certain situations, prophylactic medications. Studies show a decrease in the incidence of TD with use of bismuth subsalicylate and with use of antimicrobial chemoprophylaxis.‖ This is encapsulated by option 5. Option 1 is incorrect because the focus is on preventing, not treating. Option 2 and 3 is not specific enough with regard to Traveller‘s diarrhoea. Option 4 is incorrect as the passage does not focus on ‗many useful benefits of consuming Bismuth subsalicyclate‘; in fact, it lists the many side effects and warnings of the tablet. Hence, the correct answer is option 5.

47)

A reagent is a “substance or compound that is added to a system in order to bring about a chemical reaction or is added to see if a reaction occurs.” Although the terms reactant and reagent are often used interchangeably, a reactant is less specifically a “substance that is consumed in the course of a chemical reaction”. Solvents and catalysts, although they are involved in the reaction, are usually not referred to as reactants. In organic chemistry, reagents are compounds or mixtures, usually composed of inorganic or small organic molecules that are used to affect a transformation on an organic substrate. Examples of organic reagents include the Collins reagent, Fenton's reagent, and Grignard reagent. There are also analytical reagents which are used to confirm the presence of another substance. Examples of these are Fehling's reagent, Millon's reagent and Tollens' reagent. According to the passage, what does a reagent do? OPTIONS 1) A reagent speeds up a chemical reaction so that the effect can be observed quickly. 2) A reagent is a substance that gets used up during a reaction. 3) 4) 5) A reagent is a compound that is added to a system in order to bring about a physical reaction. A reagent is a substance composed of inorganic or small organic molecules that are added to a system that enables the reactant to dissolve. A reagent is a substance/ compound/ mixture that brings about a chemical reaction or a transformation on an organic substrate.

solution

The passage clearly states two things – “A reagent is a "substance or compound that is added to a system in order to bring about a chemical reaction or is added to see if a reaction occurs."” And that “In organic chemistry, reagents are compounds or mixtures, usually composed of inorganic or small organic molecules that are used to affect a transformation on an organic substrate.” The only option that combines both definitions is option 5, and hence it is the right answer. Option 1 is wrong as that is not what a reagent does.

Option 2 is wrong as it focuses only on one aspect of the definition of a reagent – that it gets consumed during a reaction. Option 3 is wrong as the reaction is chemical, not physical. Option 4 is wrong as it focuses only on one aspect. Hence, the correct answer is option 5.

48)

a and b are natural numbers. Let f(a, b) be the number of cells that the line joining (a, b) to (0, 0) cuts in the region 0 ≤ x ≤ a and 0 ≤ y ≤ b. For example f(1, 1) is 1 because the line joining (1, 1) and (0, 0) cuts just one cell. Similarly f(2, 1) is 2 and f(3, 2) = 4. Find f(343, 56). OPTIONS 1) 390 2) 392 3) 399 4) 397 5) 395

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Solution Let d the GCD of a and b, x = a/d and y = b/d and L be the line joining (0, 0) to (x, y). Then, the line joining (0, 0) and (x, y) repeated d times forms the line joining (0, 0) and (a, b). For calculating the number of cells cut by L, note that the line L has to cut x cells along the x-axis and y cells along the y-axis. But one of these cells is common. ∴ The number of cells cut by L is (x + y – 1).

∴ The number of cells cut by the line joining (a, b) to (0, 0) = (x + y – 1) × d = (xd) + (yd) − d = [a + b – GCD(a, b)]. ∴ f(343, GCD(343, ∴ f(343, 56) = f(a, 56) b) = = [343 56) 343 + 56 (a + + 56 b – = − 7 = – GCD(a, GCD(343, b)) 56)] 7 392.

Hence, option 2.

49)

A triangle which has zero area is called a degenerate triangle. Any triangle which is not a degenerate triangle is a called a non-degenerate triangle. A non-degenerate triangle ABC has integer sides. BD bisects the angle ABC. If AD = 3 and DC = 6, then among the following which is the smallest possible value of the perimeter of the triangle? OPTIONS

1) 25 2) 26 3) 27 4) 28 5) 30

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Solution

By angle bisector theorem

AB

and

BC

are

integers

hence

3k

should

be

a

positive

integer.

Hence For Hence, For Hence,

the the

perimeter triangle m

=

AB

+

BC to 4, we

+

CA

= m

9

+

m

+ be and

2m

=

3(3

+ than

2m) 3. on. 27. 3.

inequality =

satisfy, 5, get option

should 6 the

greater so as

m

=

6,

perimeter

Alternatively, By angle bisector theorem

AB

and

BC

are

integers

hence

3k

should

be

a

positive

integer.

Hence

the

perimeter

=

AB

+

BC

+

CA

=

9

+

m

+

2m

=

3(3

+

2m)

Hence, the perimeter should be a multiple of 3, and among the options 27 is the smallest multiple of 3. Hence, option 3.

50)

How many positive integral solutions exist for: ab + cd = a + b + c + d if 1 ≤ a ≤ b ≤ c ≤ d ? OPTIONS

1) One 2) Two 3) Three 4) Four 5) No positive integral solution

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Solution ab ∴ ∴ 1 ∴ For (a – 1) 0 ≤ [ab (a ≤ (a – + − – cd a 1)(b a 1) ≤ − = b – + 1) ≤ (b – integral is 0 or a 1] + b 1) ≤ + + (c [cd – ≤ (c – b −c 1)(d c 1) ≤ + −d – c + 1) ≤ (d – 1] + = = d 2 2 d 1)

solutions, 1.

Because if it is 2, then (b – 1), (c – 1), (d – 1) are all greater than or equal to 2 and hence the expression takes value greater than 8. If (a Thus, Hence, option 3. (a – – 1) 1) = = 0 ⇒ 1 there a ⇒ = 1, a b = can 2, are 3 be b 1 = or 2, 2, c c= = 2 2, and d d = = 3 2

integral

solutions.

51)

America‟s car thieves show clear preferences in the vehicles they steal. Size, speed and luxury are all important factors when it comes to selecting a target. And the country's car thieves are, at least, patriotic. If America's car making giants have struggled in recent years to build vehicles that match the public taste, they are keeping car thieves happy. Only two of the top ten stolen cars in Americameasured in terms of cash paid out by insurers- come from a foreign manufacturer. America's car criminals are more suspicious of Japanese or European models and are reluctant to be seen in smaller cars. Which of the following, if true, most seriously undermines the credibility of the argument above? OPTIONS

1) American cars are bigger, faster and more luxurious compared to foreign made ones.

2) American cars cost more, are poorly designed, and easier to steal.

3) Car thefts and patriotism are not related. The primary reason to steal a car is to part it out and take advantage of the demand for used parts.

4)

5) America‟s car thieves have horrible choices.

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Solution

The argument that we have to weaken is that size, speed and luxury are the reasons for more American cars being stolen. Option 2 advances another reason- they are costlier (lucrative to a thief) and poorly designed (making them) easier to steal. Therefore, option 2 undermines the credibility of the argument that car thieves steal American cars because of size, speed and luxury. Option 1 is an inference. Furthermore, it does not undermine the credibility of the argument in any way. Option 3 does not address the argument. Option 4 does not weaken the argument about why more American cars are stolen. It has not been implied in the passage that the „used parts‟ of non-American cars have more demand (or fetch a better price) than that of American cars. Option 5 is loose and does not attack the argument. Hence, the correct answer is option 2.

52)

Find the remainder when [(2 × 4 × 6 × 8 × 10 ×…× 200) – (1 × 3 × 5 × 7 × 9 ×…× 199)] is divided by 201. OPTIONS 1) 1 2) 100 3) 200 4) 0 5) 2

Solution

(2 × 4 × 6 × 8 × 10 ×…× 200)

=

(201

–

199)(201

–

197)(201

–

195)…(201

–

3)(201

–

1)

Now, each term of this product will have 201 multiplied with it; except for the last term which will be ± (199 × 197 × 195 ×…× 3 × 1) Since the total number of terms in the original bracket is even (100 terms), the sign preceding (199 × 197 × 195 ×…× 3 × 1) will be „+‟. So, (2 × 4 × 6 × 8 × 10 ×…× 200) changes to the form (201 × n) + (199 × 197 × 195 ×…× 3 × 1) ∴ (2 × 4 × 6 × 8 × 10 ×…× 200) – (1 × 3 × 5 × 7 × 9 ×…× 199)

= (201 × n) + (199 × 197 × 195 ×…× 3 × 1) – (1 × 3 × 5 × 7 × 9 ×…× 199) = Since 201 divides (201 this number, the × remainder is n) 0.

Hence, option 4.

53)

The question below contains a number of sentences. Each sentence has pairs of word(s)/phrases that are highlighted. From the highlighted word(s)/phrase(s), select the most appropriate word(s)/phrase(s) to form correct sentences. Then, from the options given, choose the best one. 1. The new car was tested [A] / examined [B] by the Pollution Control Board to verify that it met the Euro 4 norms. 2. The Judge ruled [A] / resolved [B] in favour of the plaintiff. 3. The King rose from the throne to indicate that the matter had been certified [A] / settled [B]. 4. He was assigned the chore [A] / job [B] of maintaining the records of the King‟s expeditions. OPTIONS 1) ABAA 2) BABA 3) AABB 4) BAAB 5) AABA

Solution Test means to put to the test, as for its quality, and examine means to observe carefully or critically. It is implied that tests would be conducted to ascertain conformity. Therefore, the correct answer would be tested. Ruled means that the decision is handed down by someone in authority. Resolve on the other hand means one exercises a choice to make a decision In the context of a judge, the decision is handed down; therefore, the correct answer would be ruled. Certify means to guarantee as meeting a standard. Settle implies finality in the matter. Chore is a routine or minor duty while a job is a regular activity in exchange for payment. Maintaining records would be a regular duty. Hence, the correct answer is job. Hence, the correct answer is option 3.

54)

Read the sentences and choose the option that best arranges them in a logical order. A. Most of the philosophers commonly counted "great" have not been sceptics, of course, they are usually quite straightforward with their claims, not only to know, but to know what knowledge is, and often have given reasons supporting their view. B. Even the extreme sceptic must come dangerously close, for him, to knowing what knowledge is, if his claims are to be at all intelligible and interesting, since a person who does not know what he is denying the possibility or actuality of would have little claim to be taken seriously. C. Accordingly, each sceptical philosopher has articulated, more or less, a conception of knowledge which he regards as reasonable to accept. D. From its earliest phases up to the present, philosophical inquiry has taken the nature of knowledge to be a central concern. E. Still, no philosophical positions have been more contested than those on the nature of knowledge, and this remains so up to today.

OPTIONS

1) EDCAB

2) DBCEA

3) DBCAE

4) ABCDE

5) ABDCE

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Solution

The first sentence can be either sentence A or D, as the other sentences are clearly a continuation of some preceding sentence. Sentence D introduces the concept of philosophical inquiry and knowledge, therefore it will be appropriate only as the introductory sentence and not as any later sentence. Options 1, 4 and 5 can be eliminated. The DBC link is already provided in both the remaining options. The only choice that remains is between AE or EA. Sentence E presents the concluding statement which includes what the author feels about the topic i.e. it can be seen that a conclusion has been drawn. Therefore, it is most appropriate as a conclusion to the paragraph. Sentence A is simply a continuation of the opinion that the author has been expressing and not what he has inferred. Therefore, the correct sequence is DBC followed by AE. Hence, the correct answer is option 3.

55)

Find the sum 1 – 3 + 3 – 3 + 3 +...∞ OPTIONS 1) 0.25 2) –0.25 3) 0.75 4) –0.75 5) None of these

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2 3 4

Solution The given expression can be expressed as a difference of 2 GPs such that both the GPs have a 2 common ratio r = 3 = 9 Since r > 1, the formula for infinite sum of a G.P. does not hold and the sum does not converge. Hence, option 5.

56)

Fill in the blanks with the most appropriate pair of words from among the given options. It now seems clear to anyone with eyes that the invasion of Afghanistan was built upon a great miscalculation; that Afghanistan can be _________ invaded; throughout history, such undertakings have always _________. OPTIONS 1) easily, exacerbated 2) successfully, floundered 3) effectively, intensified 4) profitably, profited 5) fully, defeated

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Solution The word „miscalculation‟ and „invaded‟ control the first blank. The comparison of options makes „fully‟, „profitably‟ and „effectively‟ inferior to „easily‟ and „successfully‟. Therefore, we can eliminate options 3, 4 and 5. If it was a “miscalculation” history will provide proof of its failure rather than its success; Therefore, „floundered‟ fits best in the second blank in contrast to „exacerbated‟ which is logically and grammatically inconsistent. Hence, the correct answer is option 2.

57)

Fill in the blanks with the most appropriate pair of words from among the given options. This turn towards authoritarianism bodes ill for the Turkish economy, _________ its strong fundamentals; it will have corrosive effects on the quality of policymaking, as well as _________ Turkey‟s claim to global economic standing. OPTIONS

1) notwithstanding, strengthen

2) albeit, arraign

3) despite, undermine

4) notwithstanding, vindicate

5) in spite of, dissipate

Solution

For the first blank, all the words in the options make logical sense. “Bodes ill” and “strong fundamentals” require contrasting words such as „notwithstanding‟, „albeit‟, „despite‟ and „in spite of‟. For the second blank „strengthen‟,„arraign‟ and „vindicate‟ can be eliminated because they do not combine well with “corrosive effects”. „Dissipate‟ is an incorrect word to use contextually. It means „to disperse or squander (as in money etc)‟. „Undermine‟ is our answer choice since it combines well with “corrosive effects”. Hence, the correct answer is option 3.

58)

Ajay purchased 2 kg apples, Bijay purchased 3kg mangoes and Celine purchased 12 dozens of bananas. The total cost of the purchase was exactly 180 rupees. If the prices of 1kg mango, 1 kg apple and 1 dozen bananas are all positive integer rupees, then how many different combinations of prices can be there? OPTIONS 1) 435 2) 225 3) 196 4) 210 Solution Let the price of 1 kg apples, 1 kg mangoes and 1 dozen bananas be x, y, z respectively.

Hence,

2x

+

3y

+

12z

=

180

As all of them are positive integers, x has to be a multiple of 3 and y has to be even. Hence, And x' Maximum + value of z y' = 14, + gives one 2z solution (x', y' = ) = (1, 30 1) x = 3x', y = 2y'

For z = 13, we get 3 solutions (x', y' ) = (1, 3), (2, 2), (3, 1) . . . Similarly Hence a for z total = of 1 we 1 + get 3 27 + solutions 5 +…+ (x', 27 y' = )=(1, 14

2

27), =

(2, 196

26)…(27,1) solutions.

Hence, option 3.

59)

19

C0 × C4 + C 1 × C3 +

7

19

7

19

C 2 × C2 + C3 × C1 + C4 × C 0 =

7

19

7

19

7

OPTIONS

1)

19

C7 × C5

7

2)

19

C7

3)

26

C4

4)

26

C7

7

5)

26

C4 × C4

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Solution

Consider a 26-element set partitioned into a 19-element subset A and a 7-element subset B.

Note that Ci × C4 – i is the number of ways in which you can select i things out of 19 and 4 – i things out of 7 to get 4 things out of 26. Thus, either you could select (zero things from A and 4 from B) or (1 from A and 3 from B) or (2 from A and 2 from B) or (3 from A and 1 from B) or (4 from A and none from B). Thus, can ∴

19 19

19

7

C7 × C4 + C 6 × C4 + select ×

19 7

7

19

6

19

C5 × C4 + 4 ×

6

5

19

C4 × C4 represents the number of ways in which you things out of 26.

19

4

C7

C4

7

+

19

19

C6

7

C4

7

+

C5

×

7

5

C4

19

+

7

19

C4

×

4

C4

=

4

26

C4

Equivalently + ∴

19

C0 × C4 +

C1 × C3 + 19 x) (1

7

19

C2 × C 2 +

19

C 3 × C1 +

C4 × C0 is the coefficient of x in (1 7 + x) .

7

C0 ×

7

C4 +

19

C1 ×

C3 +

19

C2 ×

7

C2 +

19

C3 ×

C1 +

19

C4 ×

7

C0

=

26

C4

Hence, option 3.

60)

There are n new students in a class. Among any three of them, there exist two who know each other and among any four of them, there exist two who do not know each other. Find the greatest possible value of n. OPTIONS

1) 8

2) 10

3) 9

4) 7

Solution

We can easily see that 8 is possible. For example if students are numbered 1 to 8, and student i knows student j if and only if |i − j| ≢ 1, 4 (mod 8) and student 1 doesn't know 8(and vice versa), meaning student 1, knows 3, 4, 6, 7 (and vice versa). Student 2 knows 4, 5, 7, 8 and vice versa and so on. We will prove that no n > 8 is possible

Let us suppose n = 9 is possible. Then no student may know 6 others as among those 6, either 3

don‟t know each other or 3 know each other. So together with the original student there exist 4 who know each other. Hence, this is not possible. Similarly it is not possible that a student doesn‟t know 4 others.

Hence, each student knows exactly 5 others. But this is not possible as 9 × 5 = 45 is odd. Hence, Hence, option 1.

Question Of the D

required

n

=

8

61)

Find the product of the real roots of the equation:

x101 – 3x100 + 2x99 + x98 – 3x97 + 2x96 +…+ x2 – 3x + 2x0 = 0 OPTIONS 1) –1 2) 1 3) 2 4) –2 5) 3

Solution S = x101 – = x99(x2 – = = = ∴ The Product (x –

3x100 + 3x + (x2 – (x2 – 2)

2x99 + x98 – + x96(x2 – 3x + 3x + 1)(x – 2)(x102 – are x =

3x97 + 3x +

2x96 +…+ x2 – 2) +…+ x0(x2 –

3x + 3x +

2x0 2)

2)(x99 + x96 + x93 +…+ x3 + x0) 2)(x102 – 1)/(x3 – 1)(x2 + x + 1) 1 and = 1) 1) 0 –1. –2

2)(x102 –

1)/(x –

(x – roots

1)/(x2 + x + 2, =

Hence, option 4.

62)

The ten largest broadband service providers in the world gained over 23m subscribers in the year to the end of March. Together they have 191m subscribers, or almost 40% of the world‘s 492m broadband customers, according to TeleGeography, a research firm. The lion's share is taken by China Telecom and China Unicom, which together account for a fifth of all global broadband subscribers. Ranked 2nd and 3rd, USA & Germany together account for a sixth of all global broadband subscribers. Both China Telecom and China Unicom gained around 9m more subscribers over the past year, equivalent to the entire broadband subscriber base of Verizon. Which of the following can be validly concluded from the above? OPTIONS 1) China has the largest number of broadband subscribers in the world. 2) The government's censorship of the internet in China has helped increase the broadband subscriber base in China. 3) China and the Western world have around the same number of internet users. 4) The number of broadband subscribers in Verizon has declined. 5) Broadband access in China is subsidised by the government.

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Solution Option 2 contradicts itself. Therefore, it can be negated. Options 3, 4 and 5 cannot be concluded from the passage. If the 2nd and 3rd ranked countries, USA and Germany, account for a sixth of all broadband subscribers, then we can definitely conclude that China, with a share of one-fifth of all global broadband subscribers, has the largest number of broadband subscribers in the world. Hence, the correct answer is option 1.

63)

Given below is the figure of a regular 7-pointed star. Determine the measure of the angle(in radians) shown as a in the figure.

OPTIONS

1) 2) 3) 4)

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Solution

The sum triangle,

of

the

angles

of

a

Triangle

is

π,

hence

in

the

small

Hence, option 2.

64)

Thus another approach is to incorporate the notion of suffering into the definition. The

definition offered by the Oxford English Dictionary incorporates suffering as a necessary condition, with "the painless killing of a patient suffering from an incurable and painful disease or in an irreversible coma", and this approach can be seen as a part of other works, such as Marvin Khol and Paul Kurtz's "a mode or act of inducing or permitting death painlessly as a relief from suffering". However, focusing on this approach to defining euthanasia may also lead to counterexamples: such definitions may encompass killing a person suffering from an incurable disease for personal gain (such as to claim an inheritance), and commentators such as Tom Beauchamp & Arnold Davidson have argued that doing such would constitute "murder simpliciter" rather than euthanasia. Which of the following accurately defines euthanasia, as per the passage? OPTIONS 1) Assisting in the painless death of a person willing to die. 2) Killing someone to end their mental suffering. 3) Killing someone to end their physical and mental suffering. 4) Killing someone painlessly to end their suffering 5) Killing someone with a painful or irreversible disease painlessly.

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Solution The key words to focus on are ―irreversible and painful disease‖ and ―painless death‖. Even though this definition of euthanasia is argued by the passage, since it doesn‘t offer any alternatives, that is the best one there is. Option 5 encapsulates these points. Option 1 doesn‘t talk about irreversible disease. Option 2 talks about mental suffering which is not mentioned in the passage. Options 3 and 4 don‘t mention what the ―suffering‖ is – physical and mental suffering are too vague to constitute anything definite, as they do not bring out the ―incurable‖ aspect. Hence, the correct answer is option 5.

65)

n

C0 – nC1 + nC2 – nC3 + nC4 +…+ (–1)n–1 nCn–1 + (–1)n nCn = ? OPTIONS 1) 0 2) (–1)n + 1 3) 1 4) 2n

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Solution (1 Put a = 0 –1

+ a)n = nC0 + nC1 × a + nC2 × a2 + nC3 × a3 +…+ nCn–1 × an–1 + nCn × an in the above equation (–1)n–1 nCn–1 + to get (–1)n nCn

= nC0 – nC1 + nC2 – nC3 + nC4 +…+

Hence, option 1.

66)

In the question, a word/phrase has been used in sentences in five different ways. Choose the option corresponding to the sentence in which the usage of the word/phrase is incorrect or inappropriate. BEAR OPTIONS

1) It must be inspiring to see the Americans bear so well. 2) The wooden roof cannot bear the strain of Samantha's weight. 3) The Iraqi ambassador's claim doesn't bear close examination. 4) It doesn't bear repeating. 5) During spring, the tree will bear.

Solution “Bear” has the following meanings in the context of the given sentences: To hold or remain firm under a loadas in option 2. To hold up to scrutinyas in option 3. To be fit or worthy ofas in option 4. To produce by natural growthas in option 5. In option 1, the usage of the word “bear” is inappropriate. The correct sentence will be: It must be inspiring to see the Americans bearing up so well OR It must be inspiring to see the Americans bear up so well.

In this context, “bearing up” or “bear up” would mean to endure or face hardship bravely. Hence, the correct answer is option 1.

67)

The following question consists of a certain number of sentences. Some sentences are grammatically incorrect or inappropriate. Select the option that indicates the grammatically incorrect and inappropriate sentence(s).

A. When I was first contacted about contributing to this session, the thought expressed to me was that it might be good to do something to promote dialogue between Continental and Analytic temperaments within the Society of Christian Philosophers. B. European Central Bank President Jean-Claude Trichet rejected any direct ECB participation in a second bailout for Greece, escalating a clash within governments as they rush to craft a solution involving investors. C. External Affairs Minister Pranab Mukherjee registered India's strong disapproval at Presidentelect Barack Obama's plan to appoint a special envoy for the India-Pakistan-Afghanistan region. D. There are many varieties and grades of paper materials, and whilst it is fairly easy to spot the varieties, it is far more difficult to spot the grades. E. A city that looks like a cramped row of shiny, tall matchboxes in places, Mumbai is finally going to get some respite.

OPTIONS 1) A and E 2) A and C 3) C and D 4) E and B 5) B and C

Solution Sentences A, D and E are correct. Sentence B is incorrect. ―... escalating a clash within governments‖ is incorrect as the word ―within‖ is used in case of something happening within one entity or within a single structure. In this case however the clash is ‗with‘ governments, that is, between the bank and the governments. Sentence C is incorrect as the word ―disapproval‖ is to be followed by the preposition ―of‖ and not the preposition ―at‖ one disapproves ―of‖ something. Hence, the correct answer is option 5.

68)

A ring of radius 2 cm rolls on the outer circumference of the ring x2 + y2 – 2x + 4y – 4 = 0.

Find the equation of the curve traced by its centre. OPTIONS 1) (x – 1)2 + (y + 2)2 = 25 2) (x – 1)2 + (y + 2)2 = 5 3) (x – 1)2 + (y + 2)2 = 1 4) None of these

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Solution x2 + y2 – ∴ (x −

2x + 1)2 +

4y – (y +

4

= 2)2 =

0. 32

Now, the ring that is rolling will have the same centre as the original ring. Because it is rolling on the outer circumference of the original ring, its radius (2 cm) will get added to the radius of the original ring (3 cm). So, its locus is a circle with the same centre as the original circle and radius = 5 cm Hence, its equation is (x – 1)2 + (y + 2)2 = 25

Hence, option 1.

Danish randomly picks 3 distinct integers from the set {1, 2, 3, 4, 5, 6, 7} and arranges them in descending order to form a 3-digit number. Kavitha randomly picks 3 distinct integers from the set {1, 2, 3, 4, 5, 6} and also arranges them in descending order to form a 3-digit number. What is the probability that the number formed by Danish is greater than that of Kavitha? OPTIONS 1) 2) 3) 4) 5)

Solution There Case 1:

are Danish

two Picks a

cases: 7

In this case, the number formed by Danish will always be greater than that of Kavitha

Case

2:

Danish

does

not

pick

a

7

Now if Danish does not pick a 7, he has to pick all 3 digits from {1, 2, 3, 4, 5, 6}. Since, Kavitha is picking from the same set, the probability that Danish‘s number is larger is same as Kavitha‘s number is larger.

Hence, option 4.

69)

A ring of radius 2 cm rolls on the outer circumference of the ring x2 + y2 – 2x + 4y – 4 = 0. Find the equation of the curve traced by its centre. OPTIONS 1) (x – 1)2 + (y + 2)2 = 25 2) (x – 1)2 + (y + 2)2 = 5

3) (x – 1)2 + (y + 2)2 = 1 4) None of these

Solution x2 + y2 – ∴ (x −

2x + 1)2 +

4y – (y +

4

= 2)2 =

0. 32

Now, the ring that is rolling will have the same centre as the original ring. Because it is rolling on the outer circumference of the original ring, its radius (2 cm) will get added to the radius of the original ring (3 cm). So, its locus is a circle with the same centre as the original circle and radius = 5 cm Hence, its equation is (x – 1)2 + (y + 2)2 = 25

Hence, option 1.

70)

The question below consists of a set of labelled sentences. These sentences, when properly sequenced, form a coherent paragraph. Choose the most logical order of sentences from among the options.

A. The Process has its critics, who point out that diamonds from the huge Marange mine in Zimbabwe have just been cleared for sale, despite much evidence of government-sponsored violence there. B. Charles Taylor, the former dictator of Liberia, who is on trial for war crimes in neighbouring Sierra Leone, is accused of giving Ms Campbell a “blood diamond” in 1997. C. Amid much media interest, Naomi Campbell, a model, gave evidence at the special court for Sierra Leone in The Hague. D. Ms Campbell admitted receiving a gift of “dirty looking stones”. E. Since 2000, the governments of over 75 countries have signed up to the Kimberley Process, which certifies that diamonds produced for foreign markets have not helped to fund violence.

OPTIONS 1) CBDEA 2) CDBAE 3) DEACB 4) DAEBC

5) BDEAC

Solution EA is a clear link. E mentions ―the Kimberley Process‖ and A expands upon it by mentioning that ―the Process has its critics‖. We can eliminate options 2 and 4. Out of the remaining options B looks possible as a starting statement but C at the end of BDEA is illogical. We can eliminate option 5. DEACB in option 3 is also illogical. D must come after B since in D Ms Campbell admits to receiving the diamond gifted to her by Charles Taylor (as mentioned in B). Therefore, we can eliminate option 3. Hence, the correct answer is option 1.

71)

Glee is set in Lima, Ohio. Murphy chose a Midwest setting as he himself grew up in Indiana, and recalled childhood visits to Ohio to the Kings Island theme park. Although set in Lima, the show is filmed at Paramount Studios in Hollywood. Murphy has said that he has never seen a High School Musical film, to which Glee has been compared, and that his interest lay in creating a "postmodern musical," rather than "doing a show where people burst into song," drawing more heavily on the format of Chicago. Murphy intended the show to be a form of escapism. "There's so much on the air right now about people with guns, or sci-fi, or lawyers running around. This is a different genre, there's nothing like it on the air at the networks and cable. Everything's so dark in the world right now, that's why Idol worked. It's pure escapism," he said. Murphy intended to make a family show to appeal to adults as well as children, with adult characters starring equally alongside the teenage leads. Murphy has mapped out plans for the series covering three years of broadcast. Which of the following didn‘t Murphy have in mind when he constructed the show? OPTIONS 1) Murphy wanted Glee to be different from High School Musical, to which it has been compared. 2) Murphy wanted a format of the show that looks like its been filmed in the city of Chicago, rather than Lima, Ohio. 3) Murphy wanted a show that promised pure escapism – to get away from other dark content on air currently. 4) Murphy wanted a family show that appealed to adults as well as kids. 5) Murphy had planned a future for the show.

Solution Since Glee is a musical, we can assume that the ―Chicago‖ that Murphy was referring to is a musical as well, especially since he has compared the two. Thus it can‘t be a city. Thus, option 2 is something he didn‘t have in mind.

All other options can be deduced from the passage, and are thus wrong. Option 1 can be concluded from ―Murphy has said that he has never seen a High School Musical film, to which Glee has been compared, and that his interest lay in creating a "postmodern musical," rather than "doing a show where people burst into song."‖ Options 3 and 4 are explicitly stated in the passage. Option 5 can be concluded from ―Murphy has mapped out plans for the series covering three years of broadcast.‖ Hence, the correct answer is option 2.

72)

How many values can the positive integer x take if 4(xn + 1) is a perfect cube for every natural number n? OPTIONS

1) 0 2) 1 3) 2 4) More than 2

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Solution Obviously x = Lets assume 1 is we even a solution. We will that odd. 1)n + 1) prove for x ≠ Let x = that 1, there we 2a + is no other 4(xn + 2b, solution. 1) = y3 then 1)=(2b)3 = b3

have

a y such

have 1, y =

Clearly y is 4((2a +

hence, x is

∴(2(n-1) an + n.2(n-2) a(n-1) +…+an +

Clearly if n is odd, we will get a successive loop similar to above. Hence we cannot find anx ≠1 which will give an integral y.

Hence, Hence, option 2.

there

is

only

one

value

of x.

73)

How many pairs (a, b) such that both a and b are non-zero exist if a and b are the roots of x2 +ax + b = 0 OPTIONS 1) 1 2) 2 3) 3 4) 4 5) None

Solution a and b are ∴ a2 + a2 + b = ∴b= ∴ ∴ ∴ ∴a= (2a +

the 0 –2a2 and b =

roots

of x2 + ax + b = and b2 + ab + b =

0 0 0 1

–(a + 2a2 = a +

1)

since b ≠

2a2 − a − 1 1)(a – –0.5 –0.5 pairs are (–0.5, 1)

= = or or –0.5) and (1,

0 0 1 –2. –2)

Correspondingly b equals ∴ The two non-zero

Hence, option 2.

74)

The following question has a paragraph from which the last sentence has been deleted. From

the given options, choose the one that completes the paragraph in the most appropriate way. In size, animals are outdone on land by plants, among whose foliage they may often hide. In contrast, the photosynthetic algae, which feed the open oceans, are usually too small to be seen, but marine animals range to the size of whales. Diversity of form, in contrast to size, only impinges peripherally on human awareness of life and thus is less noticed. ___. OPTIONS 1) Nevertheless, animals represent three-quarters or more of the species on Earth. 2) Nevertheless, the diversity reflects the flexibility in feeding, defense, reproduction and mobility. 3) Nevertheless, animals follow virtually every known mode of living for the creatures of Earth. 4) Nevertheless, humans study animals to learn about themselves. 5) Nevertheless, animals dominate human conceptions of life on Earth.

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Solution The last sentence takes off immediately from ―Diversity of form, in contrast to size, only impinges peripherally on human awareness of life and thus is less noticed‖ - it means human awareness of animals is more centred on their size than ―diversity‖. The closing sentence (because of the constant ‗nevertheless‘) will reinforce that ‗diversity‘ is important. ―... animals represent three quarters or more of the species‖ reinforces this train of thought logically, since diversity in form will result in the animals being classified as different species. Thus option 1 completes the paragraph appropriately. Option 2 is logically disconnected with the penultimate sentence. The closing sentence should answer the question of how diverse the animals on earth are. Option 2 fails to do this and instead answers the question of what is the diversity between different species of animals. Options 3 and 4 are unrelated to the paragraph - neither ‗size‘ nor ‗diversity‘ is being discussed. Option 5 also follows the thread of neither ‗size‘ nor ‗diversity‘ - to state that ‗animals dominate human conception of life on earth‘ is too abrupt and unrelated. Hence, the correct answer is option 1.

75)

Read the sentences and choose the option that best arranges them in a logical order.

A. A person of good moral character is one who, from the deeper and more pervasive dimensions of the self, is intent upon advancing the various goods of human life with which they are effectively in contact. B. Character is expressed in what one does without thinking, as well as to what one does after acting without thinking. C. “Character” refers to the settled dispositions to act in certain ways, given the relevant circumstances. D. The actions which come from character will usually persist when the individual is unobserved, as

well as when the consequences of the action are not what one would prefer.

OPTIONS 1) BCAD 2) DABC 3) ADCB 4) CBDA 5) CABD

Solution Sentence C is the most appropriate sentence which can begin the paragraph as it introduces the subject of ―character‖ and gives the basic idea or the basic meaning of the word ―character‖. This eliminates options 1, 2 and 3. Between sentence A and sentence B, sentence B further elaborates on the concept of ―character‖, while statement A puts forth an example of a person with good character - an example or an illustration is to be portrayed after the concept has been fully dealt with, hence sentence B will follow sentence C. Eliminate option 5. Since B states that character is expressed in what one ―does‖, it should be followed by sentence D, which further elaborates on these ―actions‖. Therefore, the correct sequence is CBDA. Hence, the correct answer is option 4.

76)

Let x1, x2, x3, … be a sequence of integers which has infinitely many positive integers as well as infinitely many negative integers. If for every positive integer n, the remainders of x1, x2,x3, …, xn upon divisions by n are all distinct, then, choose the most correct statement about the sequence. OPTIONS

1) Every integer appears at most once in the sequence 2) Every integer appears at least once in the sequence 3) Every integer appears exactly once in the sequence

4) None of the above

Solution Assume that there are positive integers i, j such that i > j and xi = xj. Then for n > i xi ≡xj (mod n), which is a contradiction. Hence, any number can appear at most once in the sequence. Next, Then, ∴ t ≥ n ≥ l, k and xl ≡ xk (mod n) which is a 1 for every positive integer n, let Sn = {x1, x2, x3…, xn }, max Sn = xl and min Sn = xk

if t = xl − xk ≥ n contradiction.

Hence,

max Sn –

min Sn = xl − xk ≤ n −

Now Sn ⊆ [min Sn, max Sn] both of which contain n integers. So the n numbers in Sn are then consecutive integers from min Sn to max Sn. Thus each integer appears exactly once in the sequence.

Hence, option 3.