CAT 2022 Slot 1 Answer Key
Section 1 : Verbal Ability & Reading Comprehension
RC – 1
The passage below is accompanied by a set of questions. Choose the best answer to each question.
Critical theory of technology is a political theory of modernity with a normative dimension. It belongs to a tradition extending from Marx to Foucault and Habermas according to which advances in the formal claims of human rights take center stage while in the background centralization of ever more powerful public institutions and private organizations imposes an authoritarian social order.
Marx attributed this trajectory to the capitalist rationalization of production. Today it marks many institutions besides the factory and every modern political system, including so-called socialist systems. This trajectory arose from the problems of command over a disempowered and deskilled labor force; but everywhere [that] masses are organized – whether it be Foucault’s prisons or Habermas’s public sphere – the same pattern prevails. Technological design and development is shaped by this pattern as the material base of a distinctive social order. Marcuse would later point to a “project” as the basis of what he called rather confusingly “technological rationality.” Releasing technology from this project is a democratic political task.
In accordance with this general line of thought, critical theory of technology regards technologies as an environment rather than as a collection of tools. We live today with and even within technologies that determine our way of life. Along with the constant pressures to build centers of power, many other social values and meanings are inscribed in technological design. A hermeneutics of technology must make explicit the meanings implicit in the devices we use and the rituals they script. Social histories of technologies such as the bicycle, artificial lighting or firearms have made important contributions to this type of analysis. Critical theory of technology attempts to build a methodological approach on the lessons of these histories.
As an environment, technologies shape their inhabitants. In this respect, they are comparable to laws and customs. Each of these institutions can be said to represent those who live under their sway through privileging certain dimensions of their human nature. Laws of property represent the interest in ownership and control. Customs such as parental authority represent the interest of childhood in safety and growth. Similarly, the automobile represents its users in so far as they are interested in mobility. Interests such as these constitute the version of human nature sanctioned by society.
This notion of representation does not imply an eternal human nature. The concept of nature as non-identity in the Frankfurt School suggests an alternative. On these terms, nature is what lies at the limit of history, at the point at which society loses the capacity to imprint its meanings on things and control them effectively. The reference here is, of course, not to the nature of natural science, but to the lived nature in which we find ourselves and which we are. This nature reveals itself as that which cannot be totally encompassed by the machinery of society. For the Frankfurt School, human nature, in all its transcending force, emerges out of a historical context as that context is [depicted] in illicit joys, struggles and pathologies. We can perhaps admit a less romantic conception in which those dimensions of human nature recognized by society are also granted theoretical legitimacy.
Q1. Which one of the following statements best reflects the main argument of the fourth paragraph of the passage?
a. Technology, laws, and customs are comparable, but dissimilar phenomena.
b. Technological environments privilege certain dimensions of human nature as effectively as laws and customs.
c. making considerations of environmental sustainability intrinsic to the development of technological solutions.
d. Technology, laws, and customs are not unlike each other if considered as institutions.
Explanation :
According to the fourth paragraph, “As an environment, technologies shape their inhabitants. In this respect, they are comparable to laws and customs. Each of these institutions can be said to”.
In the2nd line, ‘they’ refers to ‘technologies’ which are compared to laws and customs. Then, in the 3rd line, ‘each of these institution’ refers to ‘technologies, laws and customs’. Further in the paragraph, the similarities are mapped. So, option D is the best fit here.
Q2. Which one of the following statements contradicts the arguments of the passage?
a. The problems of command over a disempowered and deskilled labour force gave rise to similar patterns of the capitalist rationalisation of production wherever masses were organised.
b. Paradoxically, the capitalist rationalisation of production is a mark of so-called socialist systems as well.
c. Marx’s understanding of the capitalist rationalisation of production and Marcuse’s understanding of a “project” of “technological rationality” share theoretical inclinations.
d. Masses are organised in patterns set by Foucault’s prisons and Habermas’ public sphere.
Explanation :
Evidence for Option B is present at the start of the 2nd paragraph.
Option A is in line with the passage as it is mentioned right after the evidence for option B is para 2.
Evidence for option C is present in the same paragraph after option A.
Option D is not in line with the passage’s findings as it generalises the masses, i.e., according to it all the masses are organised in patterns set by Foucault’s prisons and Habermas’ public sphere. But paragraph 2 says “but everywhere that masses are organized – whether it be Foucault’s prisons or Habermas’s public sphere – the same pattern prevails.”
Q3. All of the following claims can be inferred from the passage, EXCEPT:
a. the significance of parental authority to children’s safety does not therefore imply that parental authority is a permanent aspect of human nature.
b. technologies seek to privilege certain dimensions of human nature at a high cost to lived nature.
c. the critical theory of technology argues that, as issues of human rights become more prominent, we lose sight of the ways in which the social order becomes more authoritarian.
d. analyses of technologies must engage with their social histories to be able to reveal their implicit and explicit meanings for us.
Explanation :
Option A can be inferred from the lines mentioned in para 4 – “Customs such as parental authority represent the interest of childhood in safety and growth.“ and para 5 – “This notion of representation does not imply an eternal human nature.”
Option C can be inferred from para 1.
Option D can be inferred from the second half of the third para – “A hermeneutics of technology attempts to build a methodological approach on the lessons of these histories.”
All the options except B can be inferred from the passage.
Q4. In this passage, the author is making the claim that:
a. It is not human nature, but human culture that is represented by institutions such as law and custom.
b. Technologies form the environmental context and shape the contours of human society.
c. The romantic conception of nature referred to by the passage is the one that requires theoretical legitimacy.
d. Nature decides the point at which society loses its capacity to control history.
Explanation :
Option B is true as can be seen in the 3rd paragraph – “In accordance with this general line of thought, critical theory of technology regards technologies as an environment rather than as a collection of tools. We live today with and even within technologies that determine our way of life.”
RC – 2
Stoicism was founded in 300 BC by the Greek philosopher Zeno and survived into the Roman era until about AD 300. According to the Stoics, emotions consist of two movements. The first movement is the immediate feeling and other reactions (e.g., physiological response) that occur when a stimulus or event occurs. For instance, consider what could have happened if an army general accused Marcus Aurelius of treason in front of other officers. The first movement for Marcus may have been (internal) surprise and anger in response to this insult, accompanied perhaps by some involuntary physiological and expressive responses such as face flushing and a movement of the eyebrows. The second movement is what one does next about the emotion. Second movement behaviors occur after thinking and are under one’s control. Examples of second movements for Marcus might have included a plot to seek revenge, actions signifying deference and appeasement, or perhaps proceeding as he would have proceeded whether or not this event occurred: continuing to lead the Romans in a way that Marcus Aurelius believed best benefited them. In the Stoic view, choosing a reasoned, unemotional response as the second movement is the only appropriate response.
The Stoics believed that to live the good life and be a good person, we need to free ourselves of nearly all desires such as too much desire for money, power, or sexual gratification. Prior to second movements, we can consider what is important in life. Money, power, and excessive sexual gratification are not important. Character, rationality, and kindness are important. The Epicureans, first associated with the Greek philosopher Epicurus held a similar view, believing that people should enjoy simple pleasures, such as good conversation, friendship, food, and wine, but not be indulgent in these pursuits and not follow passion for those things that hold no real value like power and money. As Oatley (2004) states, “the Epicureans articulated a view—enjoyment of relationship with friends, of things that are real rather than illusory, simple rather than artificially inflated, possible rather than vanishingly unlikely—that is certainly relevant today” In sum, these ancient Greek and Roman philosophers saw emotions, especially strong ones, as potentially dangerous. They viewed emotions as experiences that needed to be [reined] in and controlled.
As Oatley (2004) points out, the Stoic idea bears some similarity to Buddhism. Buddha, living in India in the 6th century BC, argued for cultivating a certain attitude that decreases the probability of (in Stoic terms) destructive second movements. Through meditation and the right attitude, one allows emotions to happen to oneself (it is impossible to prevent this), but one is advised to observe the emotions without necessarily acting on them; one achieves some distance and decides what has value and what does not have value. Additionally, the Stoic idea of developing virtue in oneself, of becoming a good person, which the Stoics believed we could do because we have a touch of the divine, laid the foundation for the three monotheistic religions: Judaism, Christianity, and Islam As with Stoicism, tenets of these religions include controlling our emotions lest we engage in sinful behavior.
Q5. On the basis of the passage, which one of the following statements can be regarded as true?
a. The Stoics valorised the pursuit of money, power, and sexual gratification.
b. There were no Stoics in India at the time of the Roman civilisation.
c. The Stoic influences can be seen in multiple religions.
d. The Epicureans believed in controlling all emotions.
Explanation :
Pretty straightforward, easy question.
Option C is correct as it is given in the last paragraph (“laid the foundation for the three monotheistic religions: Judaism, Christianity, and Islam.”)
Option A is invalidated by the first line of the 2nd paragraph.
For option B, there’s no information provided in the passage that can help us conclude this option as true.
Option D is an extreme option as the Epicureans did not believe in controlling ALL emotions. They believed in enjoying certain emotions such as good conversation, friendship, food, and wine.
Q6. “Through meditation and the right attitude, one allows emotions to happen to oneself (it is impossible to prevent this), but one is advised to observe the emotions without necessarily acting on them; one achieves some distance and decides what has value and what does not have value.” In the context of the passage, which one of the following is not a possible implication of the quoted statement?
a. “Meditation and the right attitude”, in this instance, implies an initially passive reception of all experiences.
b. Emotional responses can make it difficult to distinguish valuable experiences from valueless experiences.
c. Meditation allows certain out-of-body experiences that permit us to gain the distance necessary to control our emotions.
d. The observation of emotions in a distant manner corresponds to the second movement referred to earlier in the passage.
Explanation :
Option C is certainly not a possible implication of the quoted statement. “Out-of-body experience” is a phenomenon in which a person perceives the world from a location outside their physical body.
Option A is a possible implication as “an initially passive reception of all experiences” means accepting or allowing what happens or what others do, without active response or resistance. That is what the lines in the question mean.
Option B is also possible as by observing the emotions without necessarily acting on them helps us to decide what has value and what does not have value.
The quoted lines in the question are in context of the second movement where the person takes voluntary action based on a stimulus. So, option D is also possible.
Q7. Which one of the following statements, if false, could be seen as contradicting the facts/arguments in the passage?
a. The Greek philosopher Zeno survived into the Roman era until about AD 300.
b. In the Epicurean view, indulging in simple pleasures is not desirable.
c. In the Stoic view, choosing a reasoned, unemotional response as the first movement is an appropriate response to emotional situations.
d. Despite practising meditation and cultivating the right attitude, emotions cannot ever be controlled.
Explanation :
We have to choose the option which, if false, will contradict the arguments in the passage, i.e., we simply have to choose the option that supports the argument in the passage.
Option B is the correct option as according to the passage, “people should enjoy simple pleasures, such as good conversation, friendship, food, and wine, but not be indulgent in these pursuits”. Hence, this is our answer.
Option A – According to the passage, “Stoicism was founded in 300 BC by the Greek philosopher Zeno and survived into the Roman era until about AD 300.” It is not Zeno who survived into the Roman era until about AD 300. It is Stoicism that survived. (Logically as well, no person can survive for 600 years).
Option C – According to the passage, “In the Stoic view, choosing a reasoned, unemotional response as the second movement is the only appropriate response.”
Option D is not quite the correct. Controlling emotions is what Stoics, Epicureans, etc. focussed on. If emotions cannot be controlled, these theories fall apart.
Q8. Which one of the following statements would be an accurate inference from the example of Marcus Aurelius?
a. Marcus Aurelius plotted revenge in his quest for justice.
b. Marcus Aurelius was one of the leaders of the Roman army.
c. Marcus Aurelius was humiliated by the accusation of treason in front of the other officers.
d. Marcus Aurelius was a Stoic whose philosophy survived into the Roman era.
Explanation :
Option B would be the best inference from the line in the first paragraph – “continuing to lead the Romans in a way that Marcus Aurelius believed best benefited them.” A leader is someone who leads; hence Marcus Aurelius must have been one of the leaders of the Roman Army.
Option A is an example of how Marcus could have proceeded. It is hypothetical and we cannot conclude what he might have actually done.
Option C is again hypothetical (“The first movement for Marcus may have been..”)
Option D – There’s no hint of this in the passage.
RC – 3
The Chinese have two different concepts of a copy. Fangzhipin are imitations where the difference from the original is obvious. These are small models or copies that can be purchased in a museum shop, for example. The second concept for a copy is fuzhipin They are exact reproductions of the original, which, for the Chinese, are of equal value to the original. It has absolutely no negative connotations. The discrepancy with regard to the understanding of what a copy is has often led to misunderstandings and arguments between China and Western museums. The Chinese often send copies abroad instead of originals, in the firm belief that they are not essentially different from the originals. The rejection that then comes from the Western museums is perceived by the Chinese as an insult.
The Far Eastern notion of identity is also very confusing to the Western observer. The Ise Grand Shrine [in Japan] is 1,300 years old for the millions of Japanese people who go there on pilgrimage every year. But in reality this temple complex is completely rebuilt from scratch every 20 years.
The cathedral of Freiburg Minster in southwest Germany is covered in scaffolding almost all year round. The sandstone from which it is built is a very soft, porous material that does not withstand natural erosion by rain and wind. After a while, it crumbles. As a result, the cathedral is continually being examined for damage, and eroded stones are replaced. And in the cathedral’s dedicated workshop, copies of the damaged sandstone figures are constantly being produced. Of course, attempts are made to preserve the stones from the Middle Ages for as long as possible. But at some point they, too, are removed and replaced with new stones.
Fundamentally, this is the same operation as with the Japanese shrine, except in this case the production of a replica takes place very slowly and over long periods of time. In the field of art as well, the idea of an unassailable original developed historically in the Western world. Back in the 17th century [in the West], excavated artworks from antiquity were treated quite differently from today. They were not restored in a way that was faithful to the original. Instead, there was massive intervention in these works, changing their appearance.
It is probably this intellectual position that explains why Asians have far fewer scruples about cloning than Europeans. The South Korean cloning researcher Hwang Woo-suk, who attracted worldwide attention with his cloning experiments in 2004, is a Buddhist. He found a great deal of support and followers among Buddhists, while Christians called for a ban on human cloning. Hwang legitimised his cloning experiments with his religious affiliation: ‘I am Buddhist, and I have no philosophical problem with cloning. And as you know, the basis of Buddhism is that life is recycled through reincarnation. In some ways, I think, therapeutic cloning restarts the circle of life.’
Q9. The value that the modern West assigns to “an unassailable original” has resulted in all of the following EXCEPT:
a. it discourages them from simultaneous displays of multiple copies of a painting.
b. it allows regular employment for certain craftsmen.
c. it discourages them from carrying out human cloning.
d. it discourages them from making interventions in ancient art.
Explanation :
Option C might not be true as views on human cloning differ based on religion principles (eg. “He found a great deal of support and followers among Buddhists, while Christians called for a ban on human cloning.“) rather than the concept of “an unassailable original”.
Option A is true. Read the lines at the end of the first paragraph (“The Chinese often send copies abroad instead of originals, in the firm belief that they are not essentially different from the originals. The rejection that then comes from the Western museums..”)
Option B is true as well. Going by the cathedral example in the 3rd paragraph – “the cathedral is continually being examined for damage, and eroded stones are replaced. And in the cathedral’s dedicated workshop, copies of the damaged sandstone figures are constantly being produced.” This requires regular employment of certain craftsmen.
Option D is true as can be seen through the cathedral example.
Option C is the best possible answer out of the given options.
10. Which one of the following scenarios is unlikely to follow from the arguments in the passage?
a. A 17th century French artist who adhered to a Christian worldview would need to be completely true to the original intent of a painting when restoring it.
b. A 20th century Japanese Buddhist monk would value a reconstructed shrine as the original.
c. A 17th century British painter would have no problem adding personal touches when restoring an ancient Roman painting.
d. A 21st century Christian scientist is likely to oppose cloning because of his philosophical orientation.
Explanation :
According to the 4th paragraph, “Back in the 17th century in the West, excavated artworks from antiquity were treated quite differently from today. They were not restored in a way that was faithful to the original. Instead, there was massive intervention in these works, changing their appearance.”
So, option A will be our answer as it says that the artist would need to be completely true to the original intent, whereas the passage says otherwise.
Q11. Based on the passage, which one of the following copies would a Chinese museum be unlikely to consider as having less value than the original?
a. Pablo Picasso’s photograph of Vincent van Gogh’s original painting, printed to exactly the same scale
b. Pablo Picasso’s painting of Vincent van Gogh’s original painting, identical in every respect.
c. Pablo Picasso’s painting of Vincent van Gogh’s original painting, bearing Picasso’s signature.
d. Pablo Picasso’s miniaturised, but otherwise faithful and accurate painting of Vincent van Gogh’s original painting.
Explanation :
According to the passage, “The second concept for a copy is fuzhipin. They are exact reproductions of the original, which, for the Chinese, are of equal value to the original.”
So, a Pablo Picasso’s painting of Vincent van Gogh’s original painting, identical in every respect is unlikely to be considered of less value than the original. Hence, option B is correct.
Q12. Which one of the following statements does not correctly express the similarity between the Ise Grand Shrine and the cathedral of Freiburg Minster?
a. Both can be regarded as very old structures.
b. Both will one day be completely rebuilt.
c. Both are continually undergoing restoration.
d. Both were built as places of worship.
Explanation :
The cathedral is continually undergoing restoration whereas the Japanese shrine is not continually undergoing restoration as “this temple complex is completely rebuilt from scratch every 20 years”. If something is being completely rebuilt, it won’t be termed ‘restoration’. So, option C is correct. The rest of the options are pretty easy to be understood.
RC – 4
Stories concerning the Undead have always been with us. From out of the primal darkness of Mankind’s earliest years, come whispers of eerie creatures, not quite alive (or alive in a way which we can understand), yet not quite dead either. These may have been ancient and primitive deities who dwelt deep in the surrounding forests and in remote places, or simply those deceased who refused to remain in their tombs and who wandered about the countryside, physically tormenting and frightening those who were still alive. Mostly they were ill-defined—strange sounds in the night beyond the comforting glow of the fire, or a shape, half-glimpsed in the twilight along the edge of an encampment. They were vague and indistinct, but they were always there with the power to terrify and disturb. They had the power to touch the minds of our early ancestors and to fill them with dread. Such fear formed the basis of the earliest tales although the source and exact nature of such terrors still remained very vague.
And as Mankind became more sophisticated, leaving the gloom of their caves and forming themselves into recognizable communities—towns, cities, whole cultures—so the Undead travelled with them, inhabiting their folklore just as they had in former times. Now they began to take on more definite shapes. They became walking cadavers; the physical embodiment of former deities and things which had existed alongside Man since the Creation. Some still remained vague and ill-defined but, as Mankind strove to explain the horror which it felt towards them, such creatures emerged more readily into the light.
In order to confirm their abnormal status, many of the Undead were often accorded attributes, which defied the natural order of things—the power to transform themselves into other shapes, the ability to sustain themselves by drinking human blood, and the ability to influence human minds across a distance. Such powers—described as supernatural—only [lent] an added dimension to the terror that humans felt regarding them.
And it was only natural, too, that the Undead should become connected with the practice of magic. From very early times, Shamans and witchdoctors had claimed at least some power and control over the spirits of departed ancestors, and this has continued down into more “civilized” times. Formerly, the invisible spirits and forces that thronged around men’s earliest encampments, had spoken “through” the tribal Shamans but now, as entities in their own right, they were subject to magical control and could be physically summoned by a competent sorcerer. However, the relationship between the magician and an Undead creature was often a very tenuous and uncertain one. Some sorcerers might have even become Undead entities once they died, but they might also have been susceptible to the powers of other magicians when they did.
From the Middle Ages and into the Age of Enlightenment, theories of the Undead continued to grow and develop. Their names became more familiar—werewolf, vampire, ghoul—each one certain to strike fear into the hearts of ordinary humans.
Q13. Which one of the following statements best describes what the passage is about?
a. The passage discusses the evolution of theories of the Undead from primitive thinking to the Age of Enlightenment.
b. The writer describes the ways in which the Undead come to be associated with Shamans and the practice of magic.
c. The passage describes the failure of human beings to fully comprehend their environment.
d. The writer discusses the transition from primitive thinking to the Age of Enlightenment.
Explanation :
The central idea/gist of the passage type questions can usually be answered by referring to the first and the last paragraph. The passage starts with giving a brief history about the stories concerning the undead and their influence on mankind. The second paragraph tells how the stories transformed as mankind became more sophisticated. The last paragraph tells that from the Middle Ages and into the Age of Enlightenment, theories of the Undead continued to grow and develop…
Hence, it can be easily concluded that option A is correct.
Option B is just the gist of one paragraph (para 4), not the whole passage.
Option C is incorrect as it doesn’t mention the topic of discussion – stories concerning the undead.
Option D is incorrect as it doesn’t mention the topic of discussion.
Q14. Which one of the following observations is a valid conclusion to draw from the statement, “From out of the primal darkness of Mankind’s earliest years, come whispers of eerie creatures, not quite alive (or alive in a way which we can understand), yet not quite dead either.”?
a. We can understand the lives of the eerie creatures in Mankind’s early years through their whispers in the darkness.
b. Long ago, eerie creatures used to whisper in the primal darkness that they were not quite dead.
c. Mankind’s early years were marked by a belief in the existence of eerie creatures that were neither quite alive nor dead.
d. Mankind’s primal years were marked by creatures alive with eerie whispers, but seen only in the darkness.
Explanation :
This was a pretty simple question to answer. Option C is clearly what the quoted part of the question suggests. In fact, the remaining options are quite ludicrous.
Q15. All of the following statements, if false, could be seen as being in accordance with the passage, EXCEPT:
a. the transition from the Middle Ages to the Age of Enlightenment saw new theories of the Undead.
b. the growing sophistication of Mankind meant that humans stopped believing in the Undead.
c. the relationship between Shamans and the Undead was believed to be a strong and stable one.
d. the Undead remained vague and ill-defined, even as Mankind strove to understand the horror they inspired.
Explanation :
We’ve to choose the option which, if false, is not in accordance with the arguments made in the passage.
Option A, if false, becomes “the transition from the Middle Ages to the Age of Enlightenment did not see new theories of the Undead.” This is clearly not in accordance with the passage. The answer to the first question of this passage itself was about the evolution of theories of the Undead from primitive thinking to the Age of Enlightenment. Therefore, the transition from the Middle Ages to the Age of Enlightenment must have seen new theories of the Undead. Hence, option A is the answer.
Q16. “In order to confirm their abnormal status, many of the Undead were often accorded attributes, which defied the natural order of things” Which one of the following best expresses the claim made in this statement?
a. The natural attributes of the Undead are rendered abnormal by changing their status.
b. The Undead are deified in nature’s order by giving them divine attributes.
c. Human beings conceptualise the Undead as possessing abnormal features.
d. According the Undead an abnormal status is to reject the natural order of things.
Explanation :
This was a sitter question as well. Why were the undead often accorded attributes? In order to confirm their abnormal status, i.e., Human beings conceptualise the Undead as possessing abnormal features. So, option C is correct.
Q17. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
It’s not that modern historians of medieval Africa have been ignorant about contacts between Ethiopia and Europe; they just had the power dynamic reversed. The traditional narrative stressed Ethiopia as weak and in trouble in the face of aggression from external forces, so Ethiopia sought military assistance from their fellow Christians to the north. But the real story, buried in plain sight in medieval diplomatic texts, simply had not yet been put together by modern scholars. Recent research pushes scholars of medieval Europe to imagine a much more richly connected medieval world: at the beginning of the so-called Age of Exploration, there is evidence that the kings of Ethiopia were sponsoring their own missions of diplomacy, faith and commerce.
a. Medieval texts have documented how strong connections between the Christian communities of Ethiopia and Europe were invaluable in establishing military and trade links between the two civilisations.
b. Historians were under the illusion that Ethiopia needed military protection from their neighbours, but in fact the country had close commercial and religious connections with them.
c. Medieval historical sources selectively promoted the narrative that powerful European forces were called on to protect weak African civilisations such as Ethiopia, but this is far from reality.
d. Medieval texts have been ‘cherry-picked’ to promote a view of Ethiopia as weak and in need of Europe’s military help with aggressive neighbours, but recent studies reveal it was a well-connected and outward-looking culture.
Explanation :
The gist of the paragraph is that the traditional, medieval texts portrayed Ethiopia as weak and seeking help from Europe. Recent research pushed scholars of medieval Europe to imagine a much more richly connected medieval world.
Only option D is the most complete. The evidence that the kings of Ethiopia were sponsoring their own missions of diplomacy, faith and commerce signifies an outward-looking culture.
Q18. The four sentences (labelled 1, 2, 3 and 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:
OA: 2143
Sentence 2 is the best starter as it introduces the main idea. Rest of the sentences do not fit as the starter sentence.
4 and 3 form a logical pair in that order as both talk about remote work.
Also, 4 should come after 1 as “Some company leaders” is used in 1 first and then referred to in 4 using only the word “some”.
So, 2143 is the answer.
Q19. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Petitioning is an expeditious democratic tradition, used frequently in prior centuries, by which citizens can bring issues directly to governments. As expressions of collective voice, they support procedural democracy by shaping agendas. They can also recruit citizens to causes, give voice to the voteless, and apply the discipline of rhetorical argument that clarifies a point of view. By contrast, elections are limited in several respects: they involve only a few candidates, and thus fall far short of a representative democracy. Further, voters’ choices are not specific to particular policies or laws, and elections are episodic, whereas the voice of the people needs to be heard and integrated constantly into democratic government.
A comparison between petitioning and elections has been made in the paragraph where elections are called ‘limited in several respects’. In petitioning, the citizens could bring issues directly to governments. As expressions of collective voice, they support procedural democracy by shaping agendas. On the other hand, elections are episodic, whereas the voice of the people needs to be heard and integrated constantly into democratic government.
Option B is incorrect as the author just makes a comparison between the two. That the functioning of the government could improve if we relied more on petitioning, is an inference.
Option C doesn’t even mention ‘elections’, so it is ruled out.
Option D – ‘Citizens become less inclined to petitioning’ is not given in the paragraph.
Option A is the best choice.
Q20. There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Easing the anxiety and pressure of having a “big day” is part of the appeal for many couples who marry in secret.
Paragraph: Wedding season is upon us and – after two years of Covid chaos that saw nuptials scaled back– you may think the temptation would be to go all out. ___(1)___. But instead of expanding the guest list, many couples are opting to have entirely secret ceremonies. With Covid case numbers remaining high and the cost of living crisis meaning that many couples are feeling the pinch, it’s no wonder that some are less than eager to send out invites. ___(2)___. Plus, it can’t hurt that in celebrity circles getting married in secret is all the rage. ___(3)___. “I would definitely say that secret weddings are becoming more common,” says Landis Bejar, the founder of a therapy practice, which specialises in helping brides and grooms manage wedding stress. “People are looking for ways to get out of the spotlight and avoid the pomp and circumstance of weddings. ___(4)___. They just want to get to the part where they are married.”
Explanation :
Option 1 can’t be the answer as the idea of secret ceremonies has been introduced only after the first blank. Blank 2 is the correct place as the sentence would connect well with the preceding sentence as well as the following sentence which, by the use of “Plus” clearly indicates that it is an addition to a missing statement.
Q21. The four sentences (labelled 1, 2, 3 and 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. Fish skin collagen has excellent thermo-stability and tensile strength making it ideal for use as bandage that adheres to the skin and adjusts to body movements.
2. Collagen, one of the main structural proteins in connective tissues in the human body, is well known for promoting skin regeneration.
3. Fish skin swims in here as diseases and bacteria that affect fish are different from most human pathogens.
4. The risk of introducing disease agents into other species through the use of pig and cow collagen proteins for wound healing has inhibited its broader applications in the medical field.
Explanation :
Possible Answer: 2431
OA: 2431
Sentence 2 introduces the subject – collagen. 4 will come next which mentions the reason for the limited application in the medical field. Sentence 3, which is an alternative solution logically follows 4. 1 goes on to add some positive pointers in support of the fish skin collagen mentioned in 3.
So, 2431 is the correct answer.
OA: 3214
3 is the starting sentence. 32 forms a logical pair (“would be larger still”). 1 and 4 follow logically.
Q23. There is a sentence that is missing in the paragraph below. Look at the paragraph and decide in which blank (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Having made citizens more and less knowledgeable than their predecessors, the Internet has proved to be both a blessing and a curse.
Paragraph: Never before has a population, nearly all of whom has enjoyed at a least a secondary school education, been exposed to so much information, whether in newspapers and magazines or through YouTube, Google, and Facebook. ___(1)___. Yet it is not clear that people today are more knowledgeable than their barely literate predecessors. Contemporary advances in technology offered more serious and inquisitive students access to realms of knowledge previously unimaginable and unavailable. ___(2)___. But such readily available knowledge leads many more students away from serious study, the reading of actual texts, and toward an inability to write effectively and grammatically. ___(3)___. It has let people choose sources that reinforce their opinions rather than encouraging them to question inherited beliefs. ___(4)___.
Explanation :
The given sentence has a conclusionary tone as such a sentence would ideally come after both the pros and cons are mentioned. After reading through the paragraph, the sentence very well fits at the end, i.e., blank 4.
Q24. The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
All that we think we know about how life hangs together is really some kind of illusion that we have perpetrated on ourselves because of our limited vision. What appear to be inanimate objects such as stones turn out not only to be alive in the same way that we are, but also in many infinitesimal ways to be affected by stimuli just as humans are. The distinction between animate and inanimate simply cannot be made when you enter the world of quantum mechanics and try to determine how those apparent subatomic particles, of which you and everything else in our universe is composed, are all tied together. The point is that physics and metaphysics show there is a pattern to the universe that goes beyond our capacity to grasp it with our brains.
c. The inanimate world is both sentient and cognizant like its animate counterpart.
Explanation :
The paragraph says that the human brain cannot differentiate between an animate and inanimate object at the quantum level. Inanimate objects are non-living while animate objects are living. Only option B is the best representation of this gist.
Section 2 : Data Interpretation & Logical Reasoning
Set – 1
There are 15 girls and some boys among the graduating students in a class. They are planning a get-together, which can be either a 1-day event, or a 2-day event, or a 3-day event. There are 6 singers in the class, 4 of them are boys. There are 10 dancers in the class, 4 of them are girls. No dancer in the class is a singer.
Some students are not interested in attending the get-together. Those students who are interested in attending a 3-day event are also interested in attending a 2-day event; those who are interested in attending a 2-day event are also interested in attending a 1-day event.
The following facts are also known:
1. All the girls and 80% of the boys are interested in attending a 1-day event. 60% of the boys are interested in attending a 2-day event.
2. Some of the girls are interested in attending a 1-day event, but not a 2-day event; some of the other girls are interested in attending both.
3. 70% of the boys who are interested in attending a 2-day event are neither singers nor dancers. 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
4. No girl is interested in attending a 3-day event. All male singers and 2 of the dancers are interested in attending a 3-day event.
5. The number of singers interested in attending a 2-day event is one more than the number of dancers interested in attending a 2-day event.
Q1. How many boys are there in the class?
Explanation :
Possible Answer: 50
There are 15 girls. Let there be 10x boys.
Given that 60% of the girls who are interested in attending a 2-day event are neither singers nor dancers.
Total girls are 15. And 60% = 3/5 in fraction.
=> Girls who are interested in attending a 2-day event = 5 or 10 (can’t be 15 as Some of the girls are interested in attending a 1-day event, but not a 2-day event).
And girls who are neither singers nor dancers = 3 or 6
So, girls who are either singers or dancers = 2 or 4
8x boys are interested in attending a 1-day event => 2x boys are not interested in attending the event.
70% of 6x boys are neither singers nor dancers
=> 30% of 6x = 1.8x boys are singers or dancers and this number can be at most 10.
Also, 1.8x needs to be an integer. So, x = 5 is the only possibility where we’ll get the total number of boys who are singers or dancers as 9 (which is less than 10)
From point (4), 4S+2D boys are interested in attending a 3-Day event. These 6 people must also be interested in attending a 2-day event.
Boy singers are 4 max. So, the remaining 9-6 = 3 men must be Dancers.
Hence, of the 6x = 30 boys interested in attending a 2-day event, 4 are Singers and 5 are Dancers.
From point (5),
S (2-day) = D (2-day) + 1
From boys side, we have 1 more dancer than singers (4S+5D). So, from girls’ side there should be 2S or 3S+1D.
But since there are only 2 girl Singers in total, the 2nd case is not possible.
Hence, we have 5 girls in 2-day event (2S+0D)
The final tables are:
So, there are 5x = 50 boys in the class.
Q2. Which of the following can be determined from the given information?
I. The number of boys who are interested in attending a 1-day event and are neither dancers nor singers.
II. The number of female dancers who are interested in attending a 1-day event.
a. Only I
b. Only II
c. Both I and II
d. Neither I nor II
Explanation :
Statement I cannot be determined.
Statement II can be determined as total girl dancers are 4 and none of them are interested in attending a 1-day or 3-day event. Hence, all 4 will be interested in attending a 1-day event.
Q3. What fraction of the class are interested in attending a 2-day event?
a. 2/3
b. 9/13
c. 7/10
d. 7/13
Explanation :
Fraction of the class interested in attending a 2-day event = (30+5)/(50+15)
= 7/13
Q4. What BEST can be concluded about the number of male dancers who are interested in attending a 1-day event?
a. 6
b. 5
c. 4 or 6
d. 5 or 6
Explanation :
There are 6 male dancers. 5 of them are interested in attending the 2-day event. Hence, they must also be interested in attending the 1-day event.
But we don’t know anything about the 6th male dancer.
Hence, the answer could be 5 or 6.
Q5. How many female dancers are interested in attending a 2-day event?
a. Cannot be determined
b. 0
c. 2
d. 1
Explanation :
0 female dancers are interested in attending a 2-day event.
Set – 2
Pragnyaa, Qahira, Rasheeda, Smera, and Tantra were five candidates who received funding. The funds they received, in descending order, were Rs.390,000, Rs.210,000, Rs.165,000, Rs.77,000, and Rs.66,000.
The following additional facts are known:
Q6. How many tokens did Qahira receive?
Explanation :
Six interviewers – A, B, C, D, E, F
A token has a face value of 2, 3, 5, 7, 11, or 13.
5 candidates – P, Q, R, S, T
Funds received – 390 (2,3,5,13), 210 (2,3,5,7), 165 (3,5,11), 77 (11,7), 66 (2,3,11)
(Note: We are not taking x 1000 for ease of writing. It won’t have any effect on the solution)
R must have received 390 or 210 as the number of tokens is highest (4 each).
The token 13 must have been given by A as it is used only once (in 390) and in the below table as well, we see that only 1 person has got a token by A.
4/5 people received the token given by F. This can only be 3.
P has got 13 and 3 from the above table. The person getting 13 and 3 has also got 2 & 5.
So, R must have got 2, 3, 5, 7.
=> B, C, D = 2, 5, 7 in no particular order.
=> E = 11
Notice that in the above table, the person who got (7, 11) can only be Q as others have 3 as well.
=> D = 7 and Q got (2,7)
Now, 3 and 5 are left and they can be anyone out of B and C.
(2,3,11) and (3,5,11) i.e., 66 and 165 will be among S and T.
The final table is:
So, Qahira received 2 tokens.
b. Pragnyaa
c. Qahira
Pragnyaa definitely received a token from Bithi but not from Dhanavi.
Chhaya awarded 3 tokens.
Smera received 3 tokens
Q10. Which of the following could be the amount of funding that Tantra received?
Explanation :
Tantra could have received both 66000 or 165000.
Set – 3
– Each train runs either in east-west (2 mins for next station) or north-south direction (3 mins for next station)
– Junction station stops – 2 mins
– Other station stops – 1 min
– From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight
– Metro service every 15 minutes in the north-south lines and every 10 minutes in the east-west lines.
– A train must rest for at least 15 minutes after completing a trip at the terminal station, before it can undertake the next trip in the reverse direction.
N is the 20th station after M on the east-west line including 2 junction stations.
So, time taken = 20(2) + {17(1) + 2(2)} = 61 mins
(Note that we won’t add the stoppage time on station N as Hari has already reached the station)
Also, the next train from M will start at 8:10 AM.
So, 8:10 AM + 61 mins = 9:11 AM
T to S means T to V and then V to S
T-V is on the east-west line and V-S on the north-south line.
T-V: 10(2) + {9(1)} = 29 mins i.e., Priya will reach V in 29 mins
V-S: 4(3) = 12 mins
But the next train on T will come at 10:30 AM. So, Priya will reach V at 10:59 AM and will get a train to board at 11:00 AM on the north-south line.
So, she’ll reach S at 11:00 AM + 12 mins = 11:12 AM
We are asked the latest time by which she must be ready to board at station S which is on the east-west line (considering her path will be S-R-B). On east-west lines, trains come every 10 mins. So, the latest time will have minute’s part either 09, 19, 29, 39, 49 or 59.
Hence, answer cannot be options C and D.
Also, option A is in AM and we know it will not take more than 3 hours to cover the entire path. If, she has to reach B before 1 AM, then she should start in the PM time. So, option A is also eliminated. Hence, answer is option B.
A-B is on the north-south line.
From each terminal station, the first train starts at 6 am; the last trains leave the terminal stations at midnight. Metro service every 15 minutes in the north-south lines.
The train starting from A at 6 AM will take 10(3) + {7(1) + 2(2)} = 41 mins to reach B and will be ready for the B-A journey after 15 mins, i.e., at 6:56 AM but since trains leave at an interval of 15 mins, the train that left A at 6 AM will be ready to leave B at 7 AM.
Similarly, the train that left B at 6 AM will be ready to leave A at 7 AM.
The unique trains from A will start at 6 AM, 6:15 AM, 6:30 AM & 6:45 AM.
Similarly, four trains from B.
Total = 8 trains
Possible Answer: 48
On the East-west MN line, the first train will leave at 6 AM and reach N after 61 mins (calculated in the first question of this set). It will wait for 15 mins. The time will be 7:16 AM.
Metro service every 10 minutes in the east-west lines.
So, it’ll leave N at 7:20 AM.
6 AM to 7:10 AM -> 8 trains each at an interval of 10 mins on MN and NM paths.
=> 16 trains total on the MN line.
Total = 2(8+16) = 48 trains (x 2 because 2 lines each on the north-south lines and east-west lines)
Set – 4
The management of a university hockey team was evaluating performance of four women players – Amla, Bimla, Harita and Sarita for their possible selection in the university team for next year. For this purpose, the management was looking at the number of goals scored by them in the past 8 matches, numbered 1 through 8. The four players together had scored a total of 12 goals in these matches. In the 8 matches, each of them had scored at least one goal. No two players had scored the same total number of goals.
The following facts are known about the goals scored by these four players only. All the questions refer only to the goals scored by these four players.
1. Only one goal was scored in every even numbered match.
2. Harita scored more goals than Bimla.
3. The highest goal scorer scored goals in exactly 3 matches including Match 4 and Match 8.
4. Bimla scored a goal in Match 1 and one each in three other consecutive matches.
5. An equal number of goals were scored in Match 3 and Match 7, which was different from the number of goals scored in either Match 1 or Match 5.
6. The match in which the highest number of goals was scored was unique and it was not Match 5.
Q16. How many goals were scored in Match 7?
a. 3
b. 2
c. 1
d. Cannot be determined
Explanation :
Bimla scored a goal in M1 and one each in three other consecutive matches i.e., 4 goals in 4 matches.
The highest goal scorer scored goals in exactly 3 matches which can only be 5 goals (Bimla cannot be the joint top scorer as Harita scored more than Bimla) as each of them had scored at least one goal.
So, the goals scored were:
Harita – 5 (in 3 matches)
Bimla – 4 (in 4 matches)
Amla – 1/2
Sarita – 2/1
From point (3), we can conclude that Harita must have scored 1 goal each in M4 and M8 as total goals in all even matches is 1. So, in the remaining 1 match, Harita must have scored 3 goals.
From point (6), M1 should be the match in which highest number of goals were scored. Harita must have scored 3 goals in that match.
So, a = 1+3 = 4, b = 1 and c = 2
The 3 matches in which Bimla scored 3 consecutive goals can only be M5, M6, M7.
The final table will be:
1 goal was scored in Match 7.
Q17. Which of the following is the correct sequence of goals scored in matches 1, 3, 5 and 7?
b. 4, 1, 2, 1
c. 3, 1, 2, 1
d. 3, 2, 1, 2
4, 1, 2, 1 goals were scored in matches 1, 3, 5 and 7.
Q18. Which of the following statement(s) is/are true?
Statement-1: Amla and Sarita never scored goals in the same match.
Statement-2: Harita and Sarita never scored goals in the same match.
b. None of the statements
c. Statement-1 only
d. Statement-2 only
Both the statements are true as can be understood from the final table.
Q19. Which of the following statement(s) is/are false?
Statement-1: In every match at least one player scored a goal.
Statement-2: No two players scored goals in the same number of matches.
b. Both the statements
c. None of the statements
d. Statement-1 only
None of the statements are false as can be understood from the final table.
Q20. If Harita scored goals in one more match as compared to Sarita, which of the following statement(s) is/are necessarily true?
Statement-1: Amla scored goals in consecutive matches.
Statement-2: Sarita scored goals in consecutive matches.
b. Statement-1 only
c. Both the statements
d. None of the statements
None of the statements are necessarily true as can be understood from the final table.
Section 3 : Quatitative Aptitude
Q1. Alex invested his savings in two parts. The simple interest earned on the first part at 15% per annum for 4 years is the same as the simple interest earned on the second part at 12% per annum for 3 years. Then, the percentage of his savings invested in the first part is
a. 60%
b. 40%
c. 37.5%
d. 62.5%
Explanation :
Let the two parts be Rs. X and Rs. Y
Given, SI on X at 15% pa for 4 years = SI on Y at 12% pa for 3 years
- 15*4*X = 0.12*3*Y
- X = 0.6Y
So, X is (0.6/1.6)*100 = 37.5%
Q2. In a village, the ratio of number of males to females is 5 : 4. The ratio of number of literate males to literate females is 2 : 3. The ratio of the number of illiterate males to illiterate females is 4 : 3. If 3600 males in the village are literate, then the total number of females in the village is
Explanation :
Possible Answer: 4320
M : F = 5 : 4
LM : LF = 2: 3 = 3600 : LF
- LF = 5400
IM : IF = 4 : 3
LM + IM = M, LF + IF = F
So, (3600+4x)/(5400+3x) = 5/4
- x = 12600
So, F = 5400+3x = 43200
Q3. Amal buys 110 kg of syrup and 120 kg of juice, syrup being 20% less costly than juice, per kg. He sells 10 kg of syrup at 10% profit and 20 kg of juice at 20% profit. Mixing the remaining juice and syrup, Amal sells the mixture at ₹ 308.32 per kg and makes an overall profit of 64%. Then, Amal’s cost price for syrup, in rupees per kg, is
Explanation :
Possible Answer: 160
Let cost of juice be Rs. x/kg. (120 kg)
So, cost of syrup = Rs. 0.8x/kg (110 kg)
- (10*1.1*0.8x + 20*1.2*x) + (200*308.32) = 1.64(120x + 110*0.8x)
- x = 200
So, cost of syrup = 0.8*200 = Rs. 160/kg
Q4. Trains A and B start traveling at the same time towards each other with constant speeds from stations X and Y, respectively. Train A reaches station Y in 10 minutes while train B takes 9 minutes to reach station X after meeting train A. Then the total time taken, in minutes, by train B to travel from station Y to station X is
a. 15
b. 12
c. 6
d. 10
Explanation :
Let the two trains meet after t minutes from the start.
So, t = √product of times taken to reach the destination after meeting.
t = √9(10-t)
- t2+ 9t – 90 = 0
- t = 6
So, Train B takes 9+6 = 15 minutes for the whole journey.
Q5. Pinky is standing in a queue at a ticket counter. Suppose the ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5. If the total number of persons in the queue is less than 300, then the maximum possible number of persons standing ahead of Pinky is
Explanation :
Possible Answer: 111
Let 3x people are standing ahead of Pinky and 5x are standing behind her.
Total people = 3x+1+5x (+1 for Pinky)
8x+1 < 300
=> x < 37.xx
So, xmax = 37
3x = 111
Q6. Let ABCD be a parallelogram such that the coordinates of its three vertices A, B, C are (1, 1), (3, 4) and (−2, 8), respectively. Then, the coordinates of the vertex D are
a. (4, 5)
b. (−3, 4)
c. (0, 11)
d. (−4, 5)
Explanation :
The given 3 vertices look like this on the graph:
The 4th point can only be either option B or D as the other 2 options will definitely not form a parallelogram.
The mid-points of the 2 diagonals of parallelogram are coincident.
So, (-2+1)/2 = (x+3)/2 & (8+1)/2 = (y+4)/2
- x = -4 & y = 5, i.e., option D
Q7. 
Explanation :
Possible Answer: 44
[1/5 + n/25] = [(5+n)/25] = 0
For n = 1 to 19, the expression gives 0 each.
For n = 20 to 44, the expression gives 1 each whose sum is 25.
So, N = 44
Q8. 
Explanation :
Possible Answer: 66
Join CE.
Let AB = CE = x
BC = AE = 3
DE = 8-3 = 5
CD = √(52+x2)
AB+BC+CD+DA = 36
- x + 3 + √(52+x2) + 8 = 36
- x = 12
So, area = ½*(BC+AD)*x = 66 cm2
Q9. 
Explanation :
Possible Answer: 82
For k =1, A = 31+ 41 + 51 = 12
For k = 2, A = 50
Largest integer that divides numbers of above form will be HCF(12,50) = 2
B = 4k + 3(4k) + 4k+2 = 4k(1+3+42) = 80 min for k = 1
So, A + B = 82
Q10. 
Explanation :
Possible Answer: 34
Solving this through iQuanta’s trick,
xy + yz = 19
- y(x + z) = 1*19 i.e., y = 1, x + z = 19
yz + xz = z(x + y) = 51
z(x + 1) = 51
Since x + z = 19,
- x = 19 – z
So, z(20 – z) = 51
On solving quadratic, you get z = 3 & 17
So, y =1, z=3, x = 16, xyz = 48
Or y =1, z=17, x=2, xyz = 34
34 is minimum.
Q11. The average weight of students in a class increases by 600 gm when some new students join the class. If the average weight of the new students is 3 kg more than the average weight of the original students, then the ratio of the number of original students to the number of new students is
a. 3:1
b. 1:2
c. 1:4
d. 4:1
Explanation :
Let 1 student have joined the class. His extra 3 kg each result in avg weight of class increasing by 0.6 kg i.e., this extra 3 kg is equally divided among 3/0.6 = 5 students of which one student is the new one.
So, required ratio is 4:1
Q12. A mixture contains lemon juice and sugar syrup in equal proportion. If a new mixture is created by adding this mixture and sugar syrup in the ratio 1 : 3, then the ratio of lemon juice and sugar syrup in the new mixture is
a. 1:5
b. 1:4
c. 1:6
d. 1:7
Explanation :
Let there be 1 litre of mixture having 0.5 lt each of lemon juice and syrup.
This mixture is mixed with 3 lts of syrup.
So, ratio of lemon juice to sugar syrup = 0.5/(0.5+3) = 1 : 7
Q13. In a class of 100 students, 73 like coffee, 80 like tea and 52 like lemonade. It may be possible that some students do not like any of these three drinks. Then the difference between the maximum and minimum possible number of students who like all the three drinks is
a. 53
b. 52
c. 47
d. 48
Explanation :
100 students. 73 c, 80 t, 52 l
Let each student like 1 drink.
So, excess = (73+80+52) – 100 = 105
a + 2b = 105………(1), where a is the number of students who like exactly 2 drinks and b is the number of students who like exactly 3 drinks.
For max students who like all 3, b should be maximum i.e., b max = 52
For min students who like all 3, max students should like 2 drinks, i.e., 0 like exactly 1.
- 2a + 3b = 205
- a + b = 100 ……..(2)
- – (2)
- b min = 5
So, 52 – 5 = 47
Q14. 
a. 0
b. 1
c. 2
d. -1
Explanation :
Infinite solutions will exist when the distance between -a and 1 is exactly 2 units. That will be when a = 1. In that case, sum of distances from the two points to any point on the number line between -1 and 1 will result in a sum of 2.
Q15. 
a. the set of all positive integers
b. either the empty set or the set of all integers
c. the empty set
d. the set of all integers
Explanation :
Given, b2< 4ac
- b2 – 4ac < 0 i.e., D < 0 and f(x) = ax2+ bx + c
So, 2 cases are possible
Case 1: When a > 0
Since, f(m) < 0, we get an empty set for the values of m as f(m) is always positive in this case.
Case 2: When a < 0
Since, f(m) < 0, we get a set of all integers as f(m) is always negative in this case.
Hence, option B is correct.
Q16. 
a. 9
b. 8
c. 4
d. 7
Explanation :
Sn = n + 2n2
S1 = a1 = 3
S2 = 2 + 2(2)2 = 10
- a2 = 10-3 = 7
We have found the first two terms of the AP. So, the remaining terms can be found out where a1 = 3 and common difference, d = 4
a3 = 11, a4 = 15, a5 = 19, a6 = 23, a7 = 27 which is divisible by 9.
So, smallest possible value of n = 7.
Q17. Ankita buys 4 kg cashews, 14 kg peanuts and 6 kg almonds when the cost of 7 kg cashews is the same as that of 30 kg peanuts or 9 kg almonds. She mixes all the three nuts and marks a price for the mixture in order to make a profit of ₹1752. She sells 4 kg of the mixture at this marked price and the remaining at a 20% discount on the marked price, thus making a total profit of ₹744. Then the amount, in rupees, that she had spent in buying almonds is
a. 2520
b. 1680
c. 1176
d. 1440
Explanation :
4 kg C, 14 kg P, 6 kg A.
Let c, p and a be the price per kg of C, P and A respectively.
7c = 30p = 9a = 630x (let)
So, c = 90x, p = 21x, a = 70x
So, CPs are 360x + 294x + 420x = 1074x
Let the Marked price of the mixture of 3 nuts be y/kg
(4+14+6)y – 1074x = 1752
=> 24y – 1074x = 1752
4y + 20(0.8)y – 1074x = 744
=> 20y – 1074x = 744
4y = 1008
=> y = 252, x = 4
Amount spend on buying almonds = 6*70x = 420x = 1680
Q18. 
a. 1
b. 3
c. 5
d. 4
Explanation :
13*3 + n = 4k where k is odd.
From options, x = 5 is the least value of n.
Q19.
a. P² /8 – 2R²
b. P² /2 – 2PR
c. P² /16 – R²
d. P² /8 – R² /2
Explanation :
Let the rectangle inside the circle be a square.
Radius of circle = r
So, side of square = √r2+r2 = √2 r
P = 4√2 r
Area of square = (√2 r)2 = 2r2 = P2/8 – 2R2 (using options)
Q20. 
a. 8
b. 9
c. 7
d. 10
Explanation :
a2+ ab + a = 14 ……….(i)
b2 + ab + b = 28 ……….(ii)
(ii) – (i)
=> (b2 – a2) + (b – a) = 14
=> (b – a)(b + a + 1) = 14 = 2 x 7 or 1 x 14
So, (a, b) = (2, 4) or (6, 7)
(7, 6) won’t satisfy the main equations.
So, a = 2 and b = 4
=> 2a + b = 8
Q21. 
a. 100
b. 50
c. 25
d. 0
Explanation :
f(x) = |x – a| + |x – 100| + |x – a – 50|
0 ≤ a ≤ x ≤ 100
We’ve to find the value of a where max value of f(x) = 100
We’ll solve this using options.
For a = 100, the 3 points on the number line (x) are 100, 100, 150, but x has to be ≤ 100 according to the conditions. Hence, this option is wrong.
For a = 50, x = 50, 100, 100, and the sum of the distances of the 3 points from x = 50 is 0 + (100-50) + (100-50) = 100.
Hence, this option is correct.
Q22. The number of ways of distributing 20 identical balloons among 4 children such that each child gets some balloons but no child gets an odd number of balloons, is
Explanation :
Possible Answer: 84
Each of the 4 children have to get an even number of balloons (at least 2) out of 20 identical balloons.
Let the balloons they get be 2a, 2b, 2c, 2d
2(a+b+c+d) = 20
=> a + b + c + d = 10 where a has to be positive
Using formula for +ve, (n-1)C(r-1)
= (10-1)C(4-1) = 9C3 = 84
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