CAT 2021 Slot 1 Question Paper with Solutions

VARC

The passage below is accompanied by a set of questions. Choose the best answer to each question.

For the Maya of the Classic period, who lived in Southern Mexico and Central America between 250 and 900 CE, the category of ‘persons’ was not coincident with human beings, as it is for us. That is, human beings were persons – but other, nonhuman entities could be persons, too. In order to explore the slippage of categories between ‘humans’ and ‘persons’, I examined a very specific category of ancient Maya images, found painted in scenes on ceramic vessels. I sought out instances in which faces (some combination of eyes, nose, and mouth) are shown on inanimate objects. Consider my iPhone, which needs to be fed with electricity every night, swaddled in a protective bumper, and enjoys communicating with other fellow-phone-beings. Does it have personhood (if at all) because it is connected to me, drawing this resource from me as an owner or source? For the Maya (who did have plenty of other communicating objects, if not smartphones), the answer was no. Nonhuman persons were not tethered to specific humans, and they did not derive their personhood from a connection with a human. It’s a profoundly democratising way of understanding the world. Humans are not more important persons – we are just one of many kinds of persons who inhabit this world.

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The Maya saw personhood as ‘activated’ by experiencing certain bodily needs and through participation in certain social activities. For example, among the faced objects that I examined, persons are marked by personal requirements (such as hunger, tiredness, physical closeness), and by community obligations (communication, interaction, ritual observance). In the images I examined, we see, for instance, faced objects being cradled in humans’ arms; we also see them speaking to humans. These core elements of personhood are both turned inward, what the body or self of a person requires, and outward, what a community expects of the persons who are a part of it, underlining the reciprocal nature of community membership.

Personhood was a nonbinary proposition for the Maya. Entities were able to be persons while also being something else. The faced objects I looked at indicate that they continue to be functional, doing what objects do (a stone implement continues to chop, an incense burner continues to do its smoky work). Furthermore, the Maya visually depicted many objects in ways that indicated the material category to which they belonged – drawings of the stone implement show that a person-tool is still made of stone. One additional complexity: the incense burner (which would have been made of clay, and decorated with spiky appliques representing the sacred ceiba tree found in this region) is categorised as a person – but also as a tree. With these Maya examples, we are challenged to discard the person/nonperson binary that constitutes our basic ontological outlook. The porousness of boundaries that we have seen in the Maya world points towards the possibility of living with a certain uncategorisability of the world.

Q1. Which one of the following best explains the “additional complexity” that the example of the incense burner illustrates regarding personhood for the Classic Maya?

1. The example adds a new layer to the nonbinary understanding of personhood by bringing in a third category that shares a similar relation with the previous
2. The example provides an exception to the nonbinary understanding of personhood that the passage had hitherto
3. The example adds a new layer to the nonbinary understanding of personhood by bringing in a third category that shares a dissimilar relation with the previous
4. The example complicates the nonbinary understanding of personhood by bringing in the sacred, establishing the porosity of the divine and the

Sol: In addition to being categorised as a person, the incense burner was also categorised as a tree as it was decorated with spiky appliques representing the sacred ceiba tree. The third categorisation as a tree is similar to the other two categorisations; the same object is a tree and a person-tool. So, option A is the correct answer.

Q2. Which one of the following, if true about the Classic Maya, would invalidate the purpose of the iPhone example in the passage?

1. Classic Maya songs represent both humans and non-living objects as characters, talking and interacting with each
2. The clay incense burner with spiky appliques was categorised only as a person and not as a tree by the Classic
3. Unlike modern societies equipped with mobile phones, the Classic Maya did not have any communicating objects.
4. The personhood of the incense burner and the stone chopper was a function of their usefulness to humans.

Sol: The Maya would not have regarded the iphone as a nonhuman person. They saw personhood as ‘activated’ by experiencing certain bodily needs and through participation in certain social activities.

If option A were true “if the incense burner and stone chopper were regarded as persons just because of their usefulness to humans “, then the purpose of the iPhone example would be invalidated.

Q3. Which one of the following, if true, would not undermine the democratising potential of the Classic Maya worldview?

1. They understood the stone implement and the incense burner in a purely human
2. They depicted their human healers with physical attributes of local medicinal
3. While they believed in the personhood of objects and plants, they did not believe in the personhood of rivers and
4. They believed that animals like cats and dogs that live in proximity to humans have a more clearly articulated personhood.

Sol: The option that is line with the Mayan worldview will be the answer. Human healers being given the physical attributes of local medicinal plants suggests that these plants are equal in status to humans.

The Maya thought entities could be persons while also being something else. So, option A would undermine the ‘democratising’ potential of the Maya worldview.

Options C and D have an essence of superiority which is against the Mayan worldview. Hence, B is correct.

Q4. On the basis of the passage, which one of the following worldviews can be inferred to be closest to that of the Classic Maya?

1. A tribe that perceives its hunting weapons as sacred person-artefacts because of their significance to its
2. A futuristic society that perceives robots to be persons as well as robots because of their similarity to humans
3. A tribe that perceives its utensils as person-utensils in light of their functionality and bodily needs
4. A tribe that perceives plants as person-plants because they form an ecosystem and are marked by needs of

Sol: The Maya saw personhood as ‘activated’ by experiencing certain bodily needs and through participation in certain social activities. Personhood was not based on the usefulness of nonpersons to humans or their similarity to humans. Option D touches upon the point of social participation (forming an ecosystem)

The passage below is accompanied by a set of questions. Choose the best answer to each question.

We cannot travel outside our neighbourhood without passports. We must wear the same plain clothes. We must exchange our houses every ten years. We cannot avoid labour. We all go to bed at the same time. We have religious freedom, but we cannot deny that the soul dies with the body, since ‘but for the fear of punishment, they would have nothing but contempt for the laws and customs of society’. In More’s time, for much of the population, given the plenty and security on offer, such restraints would not have seemed overly unreasonable. For modern readers, however, Utopia appears to rely upon relentless transparency, the repression of variety, and the curtailment of privacy. Utopia provides security: but at what price? In both its external and internal relations, indeed, it seems perilously dystopian.

Such a conclusion might be fortified by examining selectively the tradition which follows More on these points. This often portrays societies where ‘it would be almost impossible for man to be depraved, or wicked’. This is achieved both through institutions and mores, which underpin the common life. The passions are regulated and inequalities of wealth and distinction are minimized. Needs, vanity, and emulation are restrained, often by prizing equality and holding riches in contempt. The desire for public power is curbed. Marriage and sexual intercourse are often controlled: in Tommaso Campanella’s The City of the Sun (1623), the first great literary utopia after More’s, relations are forbidden to men before the age of twenty-one and women before nineteen. Communal child-rearing is normal; for Campanella this commences at age two. Greater simplicity of life, ‘living according to nature’, is often a result: the desire for simplicity and purity are closely related. People become more alike in appearance, opinion, and outlook than they often have been. Unity, order, and homogeneity thus prevail at the cost of individuality and diversity. This model, as J. C. Davis demonstrates, dominated early modern utopianism. And utopian homogeneity remains a familiar theme well into the twentieth century.

Given these considerations, it is not unreasonable to take as our starting point here the hypothesis that utopia and dystopia evidently share more in common than is often supposed. Indeed, they might be twins, the progeny of the same parents. Insofar as this proves to be the case, my linkage of both here will be uncomfortably close for some readers. Yet we should not mistake this argument for the assertion that all utopias are, or tend to produce, dystopias. Those who defend this proposition will find that their association here is not nearly close enough. For we have only to acknowledge the existence of thousands of successful intentional communities in which a cooperative ethos predominates and where harmony without coercion is the rule to set aside such an assertion. Here the individual’s submersion in the group is consensual (though this concept is not unproblematic). It results not in enslavement but voluntary submission to group norms. Harmony is achieved without harming others.

Q5. All of the following arguments are made in the passage EXCEPT that:

1. in early modern utopianism, the stability of utopian societies was seen to be achieved only with individuals surrendering their sense of
2. there have been thousands of communities where homogeneity and stability have been achieved through choice, rather than by
3. in More’s time, there was plenty and security, so people did not need restraints that could appear unreasonable
4. the tradition of utopian literature has often shown societies in which it would be nearly impossible for anyone to be sinful or

Sol: The passage states that ‘in More’s time, for much of the population, given the plenty and security on offer, such restraints would not have seemed overly unreasonable‘.

On the other hand, option C says that people did not need restraints. This is not the same. Hence, C is the answer.

Q6. Following from the passage, which one of the following may be seen as a characteristic of a utopian society?

1. Institutional surveillance of every individual to ensure his/her security and
2. A society without any laws to restrain one’s
3. The regulation of homogeneity through promoting competitive heterogeneity
4. A society where public power is earned through merit rather than through

Sol: ‘Utopia appears to rely upon relentless transparency, the repression of variety, and the curtailment of privacy. Utopia provides security: but at what price? In both its external and internal relations, indeed, it seems perilously dystopian.’

Option A deals with providing security but at the cost of privacy.

Q7. All of the following statements can be inferred from the passage EXCEPT that:

1. utopian societies exist in a long tradition of literature dealing with imaginary people practising imaginary customs, in imaginary
2. many conceptions of utopian societies emphasise the importance of social uniformity and cultural homogeneity
3. utopian and dystopian societies are twins, the progeny of the same
4. it is possible to see utopias as dystopias, with a change in perspective, because one person’s utopia could be seen as another’s

Sol: The author says that since utopia and dystopia share a lot in common, it may not be unreasonable to start with the hypothesis that they are ‘twins’. But then he also adds that while the two are ‘uncomfortably close’, ‘we should not mistake this argument for the assertion that all utopias are, or tend to produce, dystopias. Hence, option C cannot be inferred from the passage.

Q8. Which sequence of words below best captures the narrative of the passage?

1. Relentless transparency – Homogeneity – Utopia –
2. Curtailment of privacy – Dystopia – Utopia – Intentional
3. Utopia – Security – Homogeneity – Intentional
4. Utopia – Security – Dystopia –

Sol: Intentional community is an important point. A and D miss out on that.

Between B and C, B can be ruled out as it doesn’t talk about homogeneity which is discussed in paragraph 2.

Hence, C is the correct option.

The passage below is accompanied by a set of questions. Choose the best answer to each question.

The sleights of hand that conflate consumption with virtue are a central theme in A Thirst for Empire, a sweeping and richly detailed history of tea by the historian Erika Rappaport. How did tea evolve from an obscure “China drink” to a universal beverage imbued with civilising properties? The answer,

in brief, revolves around this conflation, not only by profit-motivated marketers but by a wide variety of interest groups. While abundant historical records have allowed the study of how tea itself moved from east to west, Rappaport is focused on the movement of the idea of tea to suit particular purposes.

Beginning in the 1700s, the temperance movement advocated for tea as a pleasure that cheered but did not inebriate, and industrialists soon borrowed this moral argument in advancing their case for free trade in tea (and hence more open markets for their textiles). Factory owners joined in, compelled by the cause of a sober workforce, while Christian missionaries discovered that tea “would soothe any colonial encounter”. During the Second World War, tea service was presented as a social and patriotic activity that uplifted soldiers and calmed refugees.

But it was tea’s consumer-directed marketing by importers and retailers – and later by brands – that most closely portends current trade debates. An early version of the “farm to table” movement was sparked by anti-Chinese sentiment and concerns over trade deficits, as well as by the reality and threat of adulterated tea containing dirt and hedge clippings. Lipton was soon advertising “from the Garden to Tea Cup” supply chains originating in British India and supervised by “educated Englishmen”. While tea marketing always presented direct consumer benefits (health, energy, relaxation), tea drinkers were also assured that they were participating in a larger noble project that advanced the causes of family, nation and civilization.

Rappaport’s treatment of her subject is refreshingly apolitical. Indeed, it is a virtue that readers will be unable to guess her political orientation: both the miracle of markets and capitalism’s dark underbelly are evident in tea’s complex story, as are the complicated effects of British colonialism. Commodity histories are now themselves commodities: recent works investigate cotton, salt, cod, sugar, chocolate, paper and milk. And morality marketing is now a commodity as well, applied to food, “fair trade” apparel and eco-tourism. Yet tea is, Rappaport makes clear, a world apart – an astonishing success story in which tea marketers not only succeeded in conveying a sense of moral elevation to the consumer but also arguably did advance the cause of civilisation and community.

I have been offered tea at a British garden party, a Bedouin campfire, a Turkish carpet shop and a Japanese chashitsu, to name a few settings. In each case the offering was more an idea – friendship, community, respect – than a drink, and in each case the idea then created a reality. It is not a stretch to say that tea marketers have advanced the particularly noble cause of human dialogue and friendship.

Q9. This book review argues that, according to Rappaport, tea is unlike other “morality” products because it:

1. had an actual beneficial effect on social interaction and society in
2. was marketed by a wide range of interest groups
3. was actively encouraged by interest groups in the government
4. appealed to a universal group and not just to a niche section of people

Sol: The answer lies in the last line of the penultimate paragraph. – ‘Yet tea is, Rappaport makes clear, a world apart “an astonishing success story in which tea marketers not only succeeded in conveying a sense of moral elevation to the consumer but also arguably did advance the cause of civilisation and community.’

Hence, option A is correct.

Q10. The author of this book review is LEAST likely to support the view that:

1. the ritual of drinking tea promotes congeniality and
2. tea became the leading drink in Britain in the nineteenth
3. tea drinking has become a social ritual
4. tea drinking was sometimes promoted as a patriotic

Sol: ‘I have been offered tea at a British garden party, a Bedouin campfire, a Turkish carpet shop and a Japanese chashitsu, to name a few settings (Option C is true). In each case the offering was more an idea “friendship, community, respect” than a drink (Option A is true), and in each case the idea then created a reality.’ From these lines, we know options A and C are true.

‘During the Second World War, tea service was presented as a social and patriotic activity that uplifted soldiers and calmed refugees’. (Option D is true)

Hence, answer is option B.

Q11. Today, “conflating consumption with virtue” can be seen in the marketing of:

1. ergonomically designed products.
2. sustainably farmed foods.
3. natural health
4. travel to pristine

Sol: Conflating consumption with virtue means promoting consumption of something as virtuous. The consumption of sustainably farmed foods is marketed as the right thing to do, whereas it is actually not good. Hence, option B is the correct answer.

Q12. According to this book review, A Thirst for Empire says that, in addition to “profit motivated marketers”, tea drinking was promoted in Britain by all of the following EXCEPT:

1. tea drinkers lobbying for product
2. the anti-alcohol lobby as a substitute for the consumption of
3. manufacturers who were pressing for duty-free
4. factories to instil sobriety in their

Sol: Read the following lines – ‘Beginning in the 1700s, the temperance movement advocated for tea as a pleasure that cheered but did not inebriate, and industrialists soon borrowed this moral argument in advancing their case for free trade in tea (and hence more open markets for their textiles) (option C). Factory owners joined in, compelled by the cause of a sober workforce (option D), while Christian missionaries discovered that tea “would soothe any colonial encounter” (option B).’

So, option A is the answer.

The passage below is accompanied by a set of questions. Choose the best answer to each question.

Cuttlefish are full of personality, as behavioral ecologist Alexandra Schnell found out while researching the cephalopod’s potential to display self-control…. “Self-control is thought to be the cornerstone of intelligence, as it is an important prerequisite for complex decision-making and planning for the future,” says Schnell.

Schnell’s study used a modified version of the “marshmallow test”. During the original marshmallow test, psychologist Walter Mischel presented children between age four and six with one marshmallow. He told them that if they waited 15 minutes and didn’t eat it, he would give them a second marshmallow. A long-term follow-up study showed that the children who waited for the second marshmallow had more success later in life. The cuttlefish version of the experiment looked a lot different. The researchers worked with six cuttlefish under nine months old and presented them with seafood instead of sweets. (Preliminary experiments showed that cuttlefishes’ favorite food is live grass shrimp, while raw prawns are so-so and Asian shore crab is nearly unacceptable.) Since the researchers couldn’t explain to the cuttlefish that they would need to wait for their shrimp, they trained them to recognize certain shapes that indicated when a food item would become available. The symbols were pasted on transparent drawers so that the cuttlefish could see the food that was stored

inside. One drawer, labeled with a circle to mean “immediate,” held raw king prawn. Another drawer, labeled with a triangle to mean “delayed,” held live grass shrimp. During a control experiment, square labels meant “never.”

“If their self-control is flexible and I hadn’t just trained them to wait in any context, you would expect the cuttlefish to take the immediate reward in the control, even if it’s their second preference,” says Schnell and that’s what they did. That showed the researchers that cuttlefish wouldn’t reject the prawns if it was the only food available. In the experimental trials, the cuttlefish didn’t jump on the prawns if the live grass shrimp were labeled with a triangle— many waited for the shrimp drawer to open up. Each time the cuttlefish showed it could wait, the researchers tacked another ten seconds on to the next round of waiting before releasing the shrimp. The longest that a cuttlefish waited was 130 seconds.

Schnell [says] that the cuttlefish usually sat at the bottom of the tank and looked at the two food items while they waited, but sometimes, they would turn away from the king prawn “as if to distract themselves from the temptation of the immediate reward.” In past studies, humans, chimpanzees, parrots and dogs also tried to distract themselves while waiting for a reward.

Not every species can use self-control, but most of the animals that can share another trait in common: long, social lives. Cuttlefish, on the other hand, are solitary creatures that don’t form relationships even with mates or young. “We don’t know if living in a social group is important for complex cognition unless we also show those abilities are lacking in less social species,” says comparative psychologist Jennifer Vonk.

Q13. Which one of the following, if true, would best complement the passage’s findings?

1. Cuttlefish live in big groups that exhibit
2. Cuttlefish are equally fond of live grass shrimp and raw
3. Cuttlefish cannot distinguish between geometrical
4. Cuttlefish wait longer than 100 seconds for the shrimp drawer to open

Sol: Based on the last paragraph, Option A would best complement the findings of the passage.

If Cuttlefish cannot distinguish between geometrical shapes, the whole experiment would fail instead of complementing the passage’s findings. So, option C is eliminated.

The longest that a cuttlefish waited was 130 seconds. This itself is more than 100 seconds, so option D doesn’t make sense.

If cuttlefish are equally fond of shrimp and prawn, there is no reason for them to wait. Option B is eliminated as well.

Q14. In which one of the following scenarios would the cuttlefish’s behaviour demonstrate self-control?

1. raw prawns are released while an Asian shore crab drawer labelled with a triangle is placed in front of the cuttlefish, to be opened after one minute
2. Asian shore crabs and raw prawns are simultaneously released while a live grass shrimp drawer labelled with a triangle is placed in front of the cuttlefish, to be opened after one minute.
3. raw prawns are released while a live grass shrimp drawer labelled with a square is placed in front of the cuttlefish.
4. live grass shrimp are released while two raw prawn drawers labelled with a circle and a triangle respectively are placed in front of the cuttlefish; the triangle-labelled drawer is opened after 50

Sol: The cuttlefish were trained to recognise circle to mean ‘immediate’, triangle to mean ‘delayed’ and square to mean ‘never’ in the experiment. The passage also states that their favorite food is live grass shrimp, while raw prawns are so-so and Asian shore crab is nearly unacceptable. So, the cuttlefish would demonstrate self-control if they waited for live grass shrimp labelled with a triangle to be opened while other food was readily available.

Hence, option B is correct.

Q15. All of the following constitute a point of difference between the “original” and “modified” versions of the marshmallow test EXCEPT that:

1. the former correlated self-control and future success, while the latter correlated self-control and survival
2. the former was performed over a longer time span than the
3. the former had human subjects, while the latter had
4. the former used verbal communication with its subjects, while the latter had to develop a symbolic means of communication.

Sol: Options C and D can be easily eliminated.

B can also be eliminated as in the original test, children had to wait for 15 minutes to get the second marshmallow, the longest a cuttlefish waited was 130 (~2 mins) seconds.

So, A is correct.

Q16. Which one of the following cannot be inferred from Alexandra Schnell’s experiment?

1. Intelligence in a species is impossible without
2. Cuttlefish exert self-control with the help of
3. Cuttlefish exercise choice when it comes to food.
4. Like human children, cuttlefish are capable of self-control.

Sol: According to the passage, ‘most of the animals’ that can exercise self-control are social. Cuttlefish exhibit self-control and are not social. So, option A is not inferred from the experiment as self-control is thought to be the cornerstone of intelligence.

Q17. Five jumbled up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer:

1. There is a dark side to academic research, especially in India, and at its centre is the phenomenon of predatory
2. But in truth, as long as you pay, you can get anything
3. In look and feel thus, they are exactly like any reputed
4. They claim to be indexed in the most influential databases, say they possess editorial boards that comprise top scientists and researchers, and claim to have a rigorous peer-review structure.
5. But a large section of researchers and scientists across the world are at the receiving end of nothing short of an academic publishing

Sol: 1 is the introductory sentence about predatory journals.

4,3 forms a logical pair. 4 explains how the journals are indexed and structured and 3 follows. 3 is followed by 2.

Sentence 5 talks of an “academic publishing scam” but none of the other sentences talk about it. Hence, 5 is the OOO.

Q18. The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

1. In the central nervous systems of other animal species, such a comprehensive regeneration of neurons has not yet been proven beyond
2. Biologists from the University of Bayreuth have discovered a uniquely rapid form of regeneration in injured neurons and their function in the central nervous system of
3. They studied the Mauthner cells, which are solely responsible for the escape behaviour of the fish, and previously regarded as incapable of
4. However, their ability to regenerate crucially depends on the location of the

Sol: 2,3 forms a logical pair. 4 adds on to the regeneration point in zebrafish. 1 follows as the last sentence.

Hence, 2341.

Q19. The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

1. A popular response is the exhortation to plant more
2. It seems all but certain that global warming will go well above two degrees—quite how high no one knows
3. Burning them releases it, which is why the scale of forest fires in the Amazon basin last year garnered
4. This is because trees sequester carbon by absorbing carbon

Sol: 2 is the only possible opening sentence.

The response to global warming has been exhortation to plant more trees.(1) This is because… (4)

Burning them (trees) releases it (carbon dioxide)… (3)

Hence, 2143

Q20. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Foreign peacekeepers often exist in a bubble in the poor countries in which they are deployed; they live in posh compounds, drive fancy vehicles, and distance themselves from locals. This may be partially justified as they are outsiders, living in constant fear, performing a job that is emotionally draining. But they are often despised by the locals, and many would like them to leave. A better solution would be bottom-up peacebuilding, which would involve their spending more time working with communities, understanding their grievances and earning their trust, rather than only meeting government officials.

1. Extravagant lifestyles and an aloof attitude among the foreigners working as peacekeepers in poor countries have justifiably make them the target of local
2. Peacekeeping duties would be more effectively performed by local residents given their better understanding, knowledge and rapport with their own
3. The environment in poor countries has tended to make foreign peacekeeping forces live in enclaves, but it is time to change this
4. Peacekeeping forces in foreign countries have tended to be aloof for valid reasons but would be more effective if they worked more closely with local

Sol: A – despising ≠ anger. Also, the main point in the last line of the paragraph. B is a far inference, not a summary.

C is incomplete.

D is the best option and covers the main point of working closely with local communities.

Q21. The four sentences (labelled 1, 2, 3, 4) below, when properly sequenced would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer:

1. The work is more than the text, for the text only takes on life, when it is realized and furthermore the realization is by no means independent of the individual disposition of the reader.
2. The convergence of text and reader brings the literary work into existence and this convergence is not to be identified either with the reality of the text or with the individual disposition of the reader.
3. From this polarity it follows that the literary work cannot be completely identical with the text, or with the realization of the text, but in fact must lie halfway between the
4. The literary work has two poles, which we might call the artistic and the aesthetic; the artistic refers to the text created by the author, and the aesthetic to the realization accomplished by the

Sol: The passage is about literary work. 4 introduces this topic.

3 follows as “this polarity” refers to “literary work has two poles..” in 4.

1, 2 will follow in that order as 1 is about artistic and 2 about aesthetic – same order as explained in 3. Hence, 4312.

Q22. Five jumbled up sentences, related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd one out and key in the number of the sentence as your answer:

1. The legal status of resources mined in space remains ambiguous; and while the market for asteroid minerals is currently non-existent, this is likely to change as technical hurdles diminish.
2. Outer space is a commons, and all of it is open for exploration, however, space law developed in the 1950s and 60s is state-centric and arguably ill-suited to a commercial
3. Laws adopted by the US and Luxembourg are first steps, but they only protect firms from competing claims by their compatriots; a Chinese company will not be bound by US
4. Critics say the US is conferring rights that it has no authority to confer; Russia, in particular, has condemned this, citing the US’ disrespect for international
5. At issue now is a commercial activity, as private firms—rather than nation-states— look to space for

Sol: All the given sentences except 4 relate to private commercial activity in space and the limitations of outdated space laws. Sentence 4 starts with ‘critics’ which does not link to any of the given sentences.

Q23. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

McGurk and MacDonald (1976) reported a powerful multisensory illusion occurring with audio-visual speech. They recorded a voice articulating a consonant ‘ba-ba-ba’ and dubbed it with a face articulating another consonant ‘ga-ga-ga’. Even though the acoustic speech signal was well recognized alone, it was heard as another consonant after dubbing with incongruent visual speech i.e., ‘da-da-da’. The illusion, termed as the McGurk effect, has been replicated many times, and it has sparked an abundance of research. The reason for the great impact is that this is a striking demonstration of multisensory integration, where that auditory and visual information is merged into a unified, integrated percept.

1. Visual speech mismatched with auditory speech can result in the perception of an entirely different message: this illusion is known as the McGurk
2. The McGurk effect which is a demonstration of multisensory integration has been replicated many
3. When the auditory speech signal does not match the visual speech movements, the acoustic speech signal is confusing and integration of the two is
4. When the quality of auditory information is poor, the visual information wins over the auditory information.

Sol: An easy one. Option A is clearly the best option. B is incomplete – it doesn’t explain the effect.

C – confusing, imperfect isn’t what has been said. D is totally out of nowhere option.

Q24. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.

Developing countries are becoming hotbeds of business innovation in much the same way as Japan did from the 1950s onwards. They are reinventing systems of production and distribution and experimenting with entirely new business models. Why are countries that were until recently associated with cheap hands now becoming leaders in innovation? Driven by a mixture of ambition and fear they are relentlessly climbing up the value chain. Emerging-market champions have not only proved highly competitive in their own backyards, they are also going global themselves.

1. Production and distribution models are going through rapid innovations worldwide as developed countries are being challenged by their earlier suppliers from the developing
2. Innovations in production and distribution are helping emerging economies compete with countries to which they once supplied cheap
3. Developing countries are being forced to invent new business models which challenge the old business models, so they can remain competitive
4. Competition has driven emerging economies, once suppliers of cheap labour, to become innovators of business models that have enabled them to move up the value chain and go global.

Sol: Option A is incorrect as it says that models are going through innovations worldwide whereas in the paragraph, the focus is on the developing countries (read 2nd line). Also, “..challenged by their earlier suppliers..”. This is incomplete. Supplier of what?

Option B misses out on the point – what has driven the developing countries.

Option C is wrong – the developing countries are also going global, not just domestic. Option D covers all the points made in the paragraph.

DILR

Read the following set and answer the questions that follow:

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual. For example, if Amudha is a friend of Bharatan, then Bharatan is also a friend of Amudha. Similarly, if Amudha is a stranger to Bharatan, then Bharatan is also a stranger to Amudha.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

The following additional facts are also known.

1. Amudha, Bharatan, and Chandran are mutual
2. Amudha, Dhinesh, and Fani are Ezil’s
3. Chandran and Gowtham are
4. Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of
5. Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of

Q25. Who are Gowtham’s acquaintances?

1. Dhinesh, Ezhil and Fani
2. Amudha, Bharatan and Fani
3. Bharatan, Dhinesh and Ezhil
4. Amudha, Dhinesh and Fani

Sol: From the given data, we can say that A will be Stranger to B and C and same will be the case between B & C. Hence, we put S in front of them in the below table. Similarly, from the given points above we can fill the table simultaneously and complete it.

From the given data we can form below table where S represents stranger relationship between two people, F represent Friends relationship between two people and same is the case for Acquaintances.

Therefore, from the above table Dhinesh, Ezhil and Fani are Gowtham’s Acquaintance.

Q26. Which of these pairs share the same type of relationship?

1. (Chandran, Ezhil) and (Dhinesh, Gowtham)
2. (Amudha, Gowtham) and (Ezhil, Fani)
3. (Bharatan, Ezhil) and (Fani, Gowtham)
4. (Bharatan, Chandran) and (Dhinesh, Ezhil)

Sol:

From the above table we can see that (Bharatan, Ezhil) & (Fani, Gowtham) share the same type of relationship.

Q27. Who is an acquaintance of Amudha?

1. Fani
2. Dhinesh
3. Ezhil
4. Gowtham

Sol:

Dhinesh is Amudha’s acquaintance.

Q28. Who is an acquaintance of Chandran?

1. Ezhil
2. Fani
3. Dhinesh
4. Bharatan

Sol:

Fani is the acquaintance of Chandran.

Q29. How many friends does Ezhil have?

Sol:

Ezhil has 3 friends.

Q30. How many people are either a friend or a friend-of-a-friend of Ezhil?

Sol:

Amudha, Dhinesh, Fani are friends of Ezhil and Bharatan is friend of friend of Ezhil.

Read the following set and answer the questions that follow:

A journal plans to publish 18 research papers, written by eight authors (A, B, C, D, E, F, G, and H) in four issues of the journal scheduled in January, April, July and October. Each of the research papers was written by exactly one of the eight authors. Five papers were scheduled in each of the first two issues, while four were scheduled in each of the last two issues. Every author wrote at least one paper and at most three papers. The total number of papers written by A, D, G and H was double the total number of papers written by the other four authors. Four of the authors were from India and two each were from Japan and China. Each author belonged to exactly one of the three areas — Manufacturing, Automation and Logistics. Four of the authors were from the Logistics area and two were from the Automation area. As per the journal policy, none of the authors could have more than one paper in any issue of the journal.

The following facts are also known.

1. F, an Indian author from the Logistics area, wrote only one paper. It was scheduled in the October issue.
2. A was from the Automation area and did not have a paper scheduled in the October
3. None of the Indian authors were from the Manufacturing area and none of the Japanese or Chinese authors were from the Automation
4. A and H were from different countries, but had their papers scheduled in exactly the same
5. C and E, both Chinese authors from different areas, had the same number of papers scheduled. Further, E had papers scheduled in consecutive issues of the journal but C did
6. B, from the Logistics area, had a paper scheduled in the April issue of the
7. B and G belonged to the same country. None of their papers were scheduled in the same issue of the
8. D, a Japanese author from the Manufacturing area, did not have a paper scheduled in the July issue.
9. C and H belonged to different

Q31. What is the correct sequence of number of papers written by B, C, E and G, respectively?

A. 3, 1, 1, 3

B. 1, 3, 3, 1

C. 1, 2, 2, 3

D. 1, 2, 2, 1

Sol: We know that there will be 4 months Jan, April, July and October and 8 people will be publishing their papers in these months only. Some will post in twice and some thrice.

D is a Japanese author and is from the Manufacturing Area as noted from 8th point. C and E are Chinese Authors

F is an Indian Author.

Also now similarly noting the points written above, we can form a table from the above given data. From the above given information, we can prepare a tabulated form of the data.

Hence, option C is correct.

Q32. How many papers were written by Indian authors?

Sol:

We can see from the above data that Author A, B, F, G are Indian Author and hence papers written by them are 8.

Q33. Which of the following statement(s) MUST be true?

Statement A: Every issue had at least one paper by author(s) from each country. Statement B: Every issue had at most two papers by author(s) from each area.

1. Neither of the statements
2. Only Statement A
3. Only Statement B
4. Both the statements

Sol:

We can say that from the above table, only Statement A must be true.

Q34. Which of the following statements is FALSE?

1. Every issue had exactly two papers by Indian authors
2. Every issue had at least one paper by author(s) from Automation
3. Every issue had exactly two papers by authors from Logistics
4. Every issue had exactly one paper by a Chinese

Sol:

C is false.

Q35. Which of the following statements is FALSE?

1. There were exactly two papers by authors from Manufacturing area in the January
2. There were exactly two papers by authors from Manufacturing area in the July
3. There was exactly one paper by an author from Logistics area in the October
4. There was exactly one paper by an author from Manufacturing area in the April

Sol:

From the above table we can say that Option B is false.

Q36. Which of the following is the correct sequence of number of papers by authors from Automation, Manufacturing and Logistics areas, respectively?

1. 1. 6, 5, 7
2. 2, 6, 6, 6
3. 3. 5, 6, 7
4. 4, 6, 5, 7

Sol:

Option A is correct.

Read the following set and answer the questions that follow:

Ganga, Kaveri, and Narmada are three women who buy four raw materials (Mango, Apple, Banana and Milk) and sell five finished products (Mango smoothie, Apple smoothie, Banana smoothie, Mixed fruit smoothie and Fruit salad). Table-1 gives information about the raw materials required to produce the five finished products. One unit of a finished product requires one unit of each of the raw materials mentioned in the second column of the table.

One unit of milk, mango, apple, and banana cost ₹5, ₹3, ₹2, and ₹1 respectively. Each unit of a finished product is sold for a profit equal to two times the number of raw materials used to make that product. For example, apple smoothie is made with two raw materials (apple and milk) and will be sold for a profit of ₹4 per unit. Leftover raw materials are sold during the last business hour of the day for a loss of ₹1 per unit.

The amount, in rupees, received from sales (revenue) for each woman in each of the four business hours of the day is given in Table-2.

The following additional facts are known.

1. No one except possibly Ganga sold any Mango smoothie.
2. Each woman sold either zero or one unit of any single finished product in any
3. Each woman had exactly one unit each of two different raw materials as
4. No one had any banana

Q37. What BEST can be concluded about the number of units of fruit salad sold in the first hour?

1. Exactly 1
2. Either 1 or
3. Exactly 2
4. Either 0 or 1 or 2.

Sol: From the above given data, we can form the below 2 tables.

From the above table we can say that Option B is correct.

Q38. Which of the following is NECESSARILY true?

1. Narmada sold one unit of leftover
2. Ganga did not sell any leftover
3. Ganga did not sell any leftover apples
4. Kaveri sold one unit of leftover mangoes

 

Sol:

Option C is true.

Q39. What BEST can be concluded about the total number of units of milk the three women had in the beginning?

1. Either 18 or 19
2. Either 17 or 18 or 19 units
3. Either 19 or 20
4. Either 18 or 19 or 20 units

Sol:

Option D is true.

Q40. If it is known that three leftover units of mangoes were sold during the last business hour of the day, how many apple smoothies were sold during the day?

Sol:

Option B is true.

Read the following set and answer the questions that follow:

The horizontal bars in the above diagram represent 2020 aggregate sales (in ₹ million) of a company for the different subcategories of its products. The top four product subcategories (Bookcases, Chairs, Furnishings, Tables) belong to furniture product category; the bottom four product subcategories (Accessories, Copiers, Machines, Phones) belong to the technology product category while all other product subcategories belong to the office supply product category. For each of the product subcategories, there is a vertical line indicating the sales of the corresponding subcategory in 2019.

Q41. The total sales (in ₹ million) in 2019 from products in office supplies category is closest to A. 12.5

16. 16.5
17. 18
18. 13.5

Sol:

Q42. The percentage increase in sales in Furniture category from 2019 to 2020 is closest to

1. 1
2. 8
3. 25
4. 20

Sol: In 2019 Sales for Furniture Category were = 14.45

 

In 2020 Sales for Furniture Category were = 15.85

 

Percentage increase = [(15.85 – 14.45) / 14.45]*100 = 9.6 % The closest option is Option B – 8 %

Q43. How many subcategories had sales of ₹ 4 million or more in 2019 and registered an increase in sales in excess of 25% in 2020?

Sol: After observations, we can observe that only Phones Subcategory satisfies the above condition. It has more than 4 million sales in 2019 and have in excess of 25 % sales growth from 2019 to 2020.

Q44. The improvement index for a category is the maximum percentage increase in sales from 2019 to 2020 among any of its subcategories. The correct order of categories in increasing order of this improvement index is

1. office supply, furniture, technology
2. furniture, technology, office supply
3. technology, furniture, office supply
4. office supply, technology, furniture

 

Sol:

Hence, option B is true.

QA

 Q45. Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price per gram of chocolate in the large box is 12% less than that in the small box, then the percentage by which the weight of chocolate in the large box exceeds that in the small box is nearest to

1. 124
2. 135
3. 144
4. 127

Sol: Let the Small box be S and its Selling price be x. Let the larger box be L and its selling price be 2x.

Now Selling price / gm for Small box can be assumed as 100, therefore for larger box it will 88. Therefore, weight of Small box will be x / 100, and that of Larger box be 2x / 88 = x / 44.

Therefore the larger box weight exceeds smaller box weight = [(x / 44) / (x/ 100)]*100 = 127 %.

Q46. Two trains cross each other in 14 seconds when running in opposite directions along parallel tracks. The faster train is 160 m long and crosses a lamp post in 12 seconds. If the speed of the other train is 6 km/hr less than the faster one, its length, in m, is

1. 192
2. 180
3. 184
4. 190

Sol: The faster train has length 160 m and crosses a lamp post in 12 seconds, hence its speed can be calculated as 160 /12 = 40/3 m/s = 48 Km/hr.

Now if the speed of the slower train is 6 km/hr slower, hence that would be 42 km/hr.

Now when the trains are crossing each other when travelling in opposite directions, their total length can be taken as 160 + x, where x is the length of slower train.

Total time taken to cross each other is given as 14 seconds and relative speed of the trains will be 48

+ 42 = 90 km/hr = 25 m/s

Therefore, we can now find out x by (160 + x) = 25 * 14

=> x = 190 m.

Q47. A basket of 2 apples, 4 oranges and 6 mangoes costs the same as a basket of 1 apple, 4 oranges and 8 mangoes, or a basket of 8 oranges and 7 mangoes. Then the number of mangoes in a basket of mangoes that has the same cost as the other baskets is

1. 13
2. 10
3. 11
4. 12

Sol: Let’s denote Apples, Mangoes and Oranges as A, M, O respectively. According to the given data,

2A+4O+6M = A+4O+8M = 8O+7M

Solving the first 2 eqn, we get A = 2M and solving the 2nd and 4rd eqn we get 3M = 4O.

Hence, let us assume that 1 O costs Rs. 3, then 1 Apple will cost Rs. 8 and 1 Mango will cost Rs. 4 Net cost of the Basket will be Rs. 52

Now if only mangoes are present in the basket, then the net quantity of the mangoes in the basket for same price will be 52 / 4 = Rs.13

Q48. Amal purchases some pens at ₹ 8 each. To sell these, he hires an employee at a fixed wage. He sells 100 of these pens at ₹ 12 each. If the remaining pens are sold at ₹ 11 each, then he makes a net profit of ₹ 300, while he makes a net loss of ₹ 300 if the remaining pens are sold at ₹ 9 each. The wage of the employee, in INR, is

1. 1000
2. 800
3. 1200
4. None of these

Sol: Let the no. of pens purchased be ‘x’. Then His cost price will be 8x for the pens. Let us assume the fixed wage to be W. Then his net Cost Price will be 8x + W.

Now when for case 1, SP = 12*100 + (x-100)*11 Now for case 2, SP = 12*100 + (x-100)*9

Therefore, using SP – CP = Profit/ Loss For Case 1, 3x – W = 200

For Case 2, W – x = 600

Therefore, solving the 2 eqns x = 400, W = 1000. Hence the wage is Rs. 1000

Q49. How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

1. 50
2. 70
3. 80
4. 60

Sol: Let the original number be of the form xyz, then the reversed number will be of the form zyx. xyz = 100x + 10y + z

zyx = 100z + 10y + x

Therefore, zyx – xyz = 99 (z – x) = 198

z – x = 2. Hence x can take values from 1 to 7 and correspondingly z can take values from 3 to 9. Hence 7 combinations are possible. Also, y can take values from 0 to 9 hence 10 possible values.

Therefore, net possible solutions are 7*10 = 70

Q50.

1. -5 < x < -2 or 3 < x < 9
2. -2 < x < 3 or x > 9
3. x < -5 or -2 < x < 3
4. x < -5 or 3 < x < 9

Sol: We need only negative values, and hence we will find regions for both numerator and denominator where both the negatives.

For numerator,

(x+5)(x-3) < 0 ; Hence the range will be (-5,3)

For Denominator,

(x+2)(x-9) < 0 ; Hence the range will be (-2,9)

But in the range (-2,3), both will be negative, and hence net result will be positive. Hence The final range will be,

-5 < x < -2 or 3 < x < 9

Q51. Amar, Akbar and Anthony are working on a project. Working together Amar and Akbar can complete the project in 1 year, Akbar and Anthony can complete in 16 months, Anthony and Amar can complete in 2 years. If the person who is neither the fastest nor the slowest works alone, the time in months he will take to complete the project is

1. 32
2. 28
3. 34
4. 26

Sol: Let total work = LCM(16,24,12) = 48 units ak + an = 3 units per day

am + an = 2 ak + am = 4

ak fastest, an slowest, am middle am + ak + an = 4.5

=> am = 1.5

So, 48/1.5 = 32 days

Q52.

Sol: x0 = 1 X1 = 2

X2 = (1 + 2) / 1 = 3

X3= (1 + 3) / 2 = 2

X4 = (1 + 2) / 3 = 1

X5 = (1 + 1) / 2 = 1

X6 = (1 + 1) / 1 = 2

X7 = (1 + 2) / 1 = 3

Hence, we can see a pattern forming of 1,2,3,2,1,1,2,3,……. Hence, every 5th multiple is 1. Therefore, x2020 will be 1.

Therefore, x2021 = 2.

Q53. The strength of an indigo solution in percentage is equal to the amount of indigo in grams per 100 cc of water. Two 800 cc bottles are filled with indigo solutions of strengths 33% and 17%, respectively. A part of the solution from the first bottle is thrown away and replaced by an equal volume of the solution from the second bottle. If the strength of the indigo solution in the first bottle has now changed to 21% then the volume, in cc, of the solution left in the second bottle is

1. 100
2. 200
3. 150
4. 250

Sol:

Q54.

1. 19
2. 21
3. 20
4. 18

Sol: n = 61, 62… 79

So, 19 integers

Q55. Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

1. 18
2. 16
3. 26
4. 20

Sol: Let the Daily fixed expense be 100 Rs for the first 3 months and Rs 50 for the last 2 months. Therefore no. Of kg of Onions purchased in the first 3 months is 10, 5, 4 kg respectively and 2 and 1 kg in the last 2 months respectively.

Net qty bought is 22 Kg and net amount spent us 100*3 + 50*2 = 400. Therefore, Average Value per kg is 400 / 22 = Rs. 18

Q56.

1. 100
2. 120
3. 140
4. 125

Sol:

In the above figure, we can see a triangle and a circle inscribed in that triangle with radius 4 inches. Let the Point at which circle touches triangle be P, Q, R and the center of Circle be at O. Then after doing construction, we observe that PO = QO = 4 inches. Also, POQB forms a square of side 4 inches. Hence PB = BQ = 4 inches. Therefore PC = BC – PB = PC = 10 – 4 = 6 inches. Since tangents to a circle from same point are equal. CR = 6 cm. Also, AR = AQ = x from above theorem.

Therefore, the length of the sides will be 10, x + 4, x + 6.

Now if we observe the known Pythagorean triplets, we get 10, 24 and 26 which will satisfy the above values. Hence X = 20.

Therefore, Area of Triangle = 1/2 * 24 * 10 = 120 inches2.

Q57.

1. √14
2. √13
3. √12
4. √11

Sol:

ABCDEF is a hexagon with side 2 cm. Since T is a midpoint, CT will be 1 cm,

Also, we know that interior angles in a hexagon are 120 degrees. Therefore, in Triangle ABC, Angle B is 120 degrees, Angle BCA will be 120 – 90 = 30 degree. Therefore, applying sine rule in triangle ABC, AB/sin 30 = AC/sin 120

AC = 2√3

Therefore, In Triangle ATC, by Pythagoras theorem, AT = √13

Q58. The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

 

1. 7471
2. 4941
3. 6119
4. 6090

 

Sol: The number of natural numbers in any group is an odd number and goes on increasing by value of 2 subsequently as we move ahead. That is, group 1 has 1 natural no., group 2 has 3 natural numbers, group 3 has 5 natural numbers and so. Therefore, to generalise, any group no. N has 2N-1 natural numbers.

Now,

Group 14 will have 2(14) – 1 , 27 Natural No.s

Group 13 will have 2(13) – 1 , 25 Natural No.s

… and so on till

Group 1 will have 2(1) – 1 , 1 Natural No.

Therefore, total natural no. Used till group 14 = 1+3+5+7+…..+27 = 196. Now group 15 will have 2(15) – 1 = 29 Natural No. Starting from 197.

Group 15 – (197, 198, …..225)

Their sum can be find using sum of AP Series with Difference 1 29/2 * (197 + 225) = 6119

Q59. Anil invests some money at a fixed rate of interest, compounded annually. If the interests accrued during the second and third year are ₹ 806.25 and ₹ 866.72, respectively, the interest accrued, in INR, during the fourth year is nearest to

929. 929.48
930. 926.84
931. 931.72
932. 934.65

Sol: The interest accrued in 2nd year is 806.25 The interest accrued in 3rd year is 866.72

Therefore the rate of interest can be calculated as [(866.72 / 806.25 ) – 1]*100 = 7.5 % Now for interest accrued in 4th year we can calculate 7.5% of 866.72 and add it to 866.72 Therefore, 866.72 * 1.075 = 931.72

Q60. The number of groups of three or more distinct numbers that can be chosen from 1, 2, 3, 4, 5, 6, 7 and 8 so that the groups always include 3 and 5, while 7 and 8 are never included together is

1. 46
2. 47
3. 34
4. 32

Sol: 3, 5 should be present in every subset and 7, 8 never together and contain at least 3 numbers in it.

First, we need to find the subsets possible

{3, 5, 1, 2, 4, 6, 7, 8} except 3 and 5, remaining all numbers have two possible outcomes that either it is in the set or out of the set.

So, the number of possible subsets containing at least 3 numbers is 2^6-1 = 63

From these 63, we need to remove the subsets which have {3, 5, 7, 8}

{3, 5, 7, 8, 1, 2, 4, 6} except 3, 5, 7, 8 remaining all numbers {1, 2, 4, 6} have two possible outcomes that either it is in the set or out of the set.

So, the number of sets possible is 2^4 = 16 Therefore, the answer would be 63 – 16 = 47

Q61.

Sol: log10[1/√(1-x²) * √(1+x) * (1-x)²] = 5

=> (1-x)5/2 = 1/105

Take 5th root on both sides.

=> √1-x = 1/10 1-x = 1/100

x = 99/100 100x = 99

Q62.

1. 2√6
2. 4√6
3. 6√6
4. √6

Sol: Area of an equilateral triangle of side 12 cm is 36√3 Therefore, area of Hexagon will also be 36√3

Now we know that area of Hexagon in [3√3/ 2] (side)2 Therefore, (side)2 = 24

Side = 2√6cm

Q63. The amount Neeta and Geeta together earn in a day equals what Sita alone earns in 6 days. The amount Sita and Neeta together earn in a day equals what Geeta alone earns in 2 days. The ratio of the daily earnings of the one who earns the most to that of the one who earns the least is

1. 11:3
2. 3:2
3. 7:3
4. 11:7

Sol: Let Neeta, Geeta and Sita be denoted by N, G and S where these depict their daily earnings. Therefore, N + G = 6S

S + N = 2G

Solving this we get 3G = 7S.

Therefore, Lets take G = 1, then S = 3/7. N will be 11/7.

Therefore largest : smallest = N:S = 11:3

Q64. Suppose hospital A admitted 21 less Covid infected patients than hospital B, and all eventually recovered. The sum of recovery days for patients in hospitals A and B were 200 and 152, respectively. If the average recovery days for patients admitted in hospital A was 3 more than the average in hospital B then the number admitted in hospital A was

1. 35
2. 23
3. 40
4. 32

Sol: B : x patients A : x – 21 patients

200/(x-21) – 152/x = 3

From options, for x-21 = 35, we get 3 on the LHS So, A is correct.

Q65. Anu, Vinu and Manu can complete a work alone in 15 days, 12 days and 20 days, respectively. Vinu works everyday. Anu works only on alternate days starting from the first day while Manu works only on alternate days starting from the second day. Then, the number of days needed to complete the work is

1. 8
2. 5
3. 7
4. 6

Sol: Let us denote Anu, Vinu and Manu by A, V, and M resp. They complete the work working alone in 15, 12 and 20 days resp.

LCM of 15, 12 and 20 is 60.

Therefore, let’s assume there are 60 units of work and A, V and M do 4, 5, 3 units of work daily. Now, Vinu works daily and Anu and Manu on alternate days starting with Anu.

Therefore, Unit of work done 1st day = 5 + 4 = 9 units Unit of work done 2nd day =3 + 5 = 8 units

Till first 6 days 9+8+9+8+9+8 = 51 units of work will be completed.

Therefore, on the 7th day Anu and Vinu will do 9 units of work and complete the whole work.

Q66.

Sol: Completing the square, |(x-2)2 – 17| = r (x – 2)2 – 17 = r and (x – 2)2 – 17 = -r

(x – 2)2 = r + 17 and (x – 2)2 = -r + 17

Hence, we get exactly three roots when r = 17.