CAT 2023 Slot 1: Past Year Question Paper (November 2) - CAT MCQ

The passage does not explicitly mention the criticism of scholars for having outdated interpretations of past cultural and historical phenomena. The primary focus of the author's criticism, as discussed in the passage, centers on scholars' tendencies to dismiss geographic factors, label geographic explanations as deterministic, and associate geographic analyses with past racism.Therefore Option B is the correct answer.

• The passage focuses on the interconnectedness within the global south in the context of the Indian Ocean world's migration networks. It emphasizes historical connections between the coasts of East Africa, the Arab coasts, and South and East Asia. The passage does not specifically highlight migration networks connecting the Indian Ocean world with the global north. Instead, it underscores the significance of geographical location, religious histories, and commercial interactions within the region, pointing to a more localized and regional perspective on migration. Therefore, Option A is not true according to the passage. Additionally, the passage mentioned the Indian Ocean as “a term used to describe the very long-lasting connections among the coasts of East Africa, the Arab coasts, and South and East Asia.” and not north and south.
• Option B is correct as the passage mentions that for much of history, travel by sea in the Indian Ocean was easier than by land, emphasizing the importance of geographical location.
• Option C is correct as the passage indicates that the novels in the book draw on and shape a wider sense of Indian Ocean space through themes, images, metaphors, and language, including religious and commercial aspects.
• Option D is correct as the passage notes that migration is often portrayed as abandonment rather than adventure, indicating a complex and ambivalent nature of the migration experience in the Indian Ocean world.

• “For their part Ghosh, Gurnah, Collen and even Conrad reference a different set of histories and geographies than the ones most commonly found in fiction in English. Those [commonly found ones] are mostly centred in Europe or the US, assume a background of Christianity and whiteness, and mention places like Paris and New York. “
• The passage argues that the novels discussed in "Writing Ocean Worlds" diverge from the common representations found in English fiction, which often center on Europe or the US, assume a background of Christianity and whiteness, and mention places like Paris and New York. If Option D were true, it would support the passage's claim rather than weaken it. Therefore, Option D is the correct answer.
• Through the passage, the author claims that the Indian Ocean novels provide a more realistic picture of the Indian Ocean space, particularly in the representation of Africa. The author claims that the depiction is more authentic and free from Eurocentricity that is seen in other novels.
• Option A weakens the passage by contradicting these claims and suggesting that the depiction of Africa is influenced by postcolonial nostalgia.
• Option B weakens the passage by suggesting a potential bias or negative stereotyping in the portrayal of Africa in Indian Ocean novels.
• Option C weakens the author's claim by disputing that there is eurocentric perspective in other novels.

• The passage emphasizes that Marshall Sahlins's main goal in writing his essay was to hold a mirror to an acquisitive society (contemporary economic life and bourgeois individualism). The essay accomplishes this by providing examples of foraging societies that made real choices to prioritize values such as leisure, mobility, and freedom over material accumulation. Sahlins contrasts the Zen road to affluence, where affluence is achieved by wanting less, with the capitalist pursuit of wealth through material production and consumerism. Therefore, Sahlins's goal, as portrayed in the passage, aligns with the idea of presenting examples of communities that have successfully chosen non-materialistic paths as a critique of acquisitive societies. So, Option C is the correct answer.
• Option A: While Sahlins's essay acknowledges growing inequality and social hierarchies resulting from the Neolithic Revolution, it is more focused on contrasting foraging societies with contemporary economic life.
• Option B: The primary emphasis is on showcasing foraging societies' choices and values rather than asserting a progressive degeneration of society.
• Option D: Even though Sahlins's essay critiques aspects of contemporary economic views, its primary focus is not explicitly countering Galbraith's pessimistic view but rather presenting alternative possibilities through examples of non-materialistic societies.

• Option C is the correct answer because the passage uses the example of Tanzania's Hadza community to illustrate that forager communities, like the Hadza, do not conform to a simple narrative of human diversity or victimhood. Instead, they actively make choices about their way of life. The passage mentions that the Hadza, despite being surrounded by farmers, knew they had alternatives and consciously rejected them. This example serves to emphasize that forager communities are not constrained by ignorance about alternatives; rather, their lifestyles derive from their own choices. Therefore, Option C accurately captures the essence of the Hadza illustration in the passage.
• Option A: The passage doesn't specifically highlight the survival techniques of hunter-gatherer communities into contemporary times, but rather emphasizes their choices and values.
• Option B: The passage doesn't discuss the Hadza community in the context of agrarian practices in contiguous communities, making this option irrelevant to the illustration.
• Option D: The passage does not suggest that the Hadza community coexisted with vastly different ways of living and working for centuries

"Viewed in today’s context, of course, not every aspect of the essay has aged well. While acknowledging the violence of colonialism, racism, and dispossession, it does not thematize them as heavily as we might today."

• Option A is the correct answer because the passage explicitly mentions that, when viewed in today's context, not every aspect of Sahlins's essay has aged well, and it acknowledges that the essay does not thematize issues like racism, colonialism, and dispossession as heavily as might be expected today. The term "cursory treatment" suggests that the essay provides only a brief or superficial examination of the effects of racism and colonialism on societies, and the passage criticizes this aspect of the essay for not giving these important issues more comprehensive attention.

• The passage mentions that as early as the ninth century, the royal office of the Luparii, or wolf-catchers, was created in France to tackle the predators. However, this office became redundant as it had finished it’s job (kill the last wolf). So the resurgence of the wolfs can’t be attributed to it shutting down. The other options on the other hand, can be clearly inferred.
• Option A: “Various factors explain the changes of the past few decades. Rural depopulation is part of the story. In Lozère, for example, farming and a once-flourishing mining industry supported a population of over 140,000 residents in the mid-19th century. Today the department has fewer than 80,000 people, many in its towns. “
• Option B: “As humans withdraw, forests are expanding. In France, between 1990 and 2015, forest cover increased by an average of 102,000 hectares each year, as more fields were given over to trees. Now, nearly one-third of mainland France is covered by woodland of some sort. “
• Option D: “The mostly protected status of the wolf in Europe—hunting them is now forbidden, other than when occasional culls are sanctioned by the state—plus the efforts of NGOs to track and count the animals, also contribute to the recovery of wolf populations.”

• Considering the first paragraph: “RESIDENTS of Lozère, a hilly department in southern France, recite complaints familiar to many rural corners of Europe. In remote hamlets and villages, with names such as Le Bacon and Le Bacon Vieux, mayors grumble about a lack of local schools, jobs, or phone and internet connections. Farmers of grazing animals add another concern: the return of wolves. Eradicated from France last century, the predators are gradually creeping back to more forests and hillsides. “The wolf must be taken in hand,” said an aspiring parliamentarian, Francis Palombi, when pressed by voters in an election campaign early this summer. Tourists enjoy visiting a wolf park in Lozère, but farmers fret over their livestock and their livelihoods. .”
• Options A, B and C can be clearly inferred from the highlighted part.
• The passage mentions that the number of people holding hunting licenses is still high but the number of people who still actively hunt is low. So Option D which states that there is decline in the number of hunting licences is incorrect.

• The author's claims seem to be focused on the conflicts between farmers and the return of wolves, the economic implications, and the coexistence challenges. If wolf attacks on tourists were on the rise, it might shift the narrative and suggest a broader safety concern beyond the impact on farmers, potentially weakening the author's emphasis on the positive economic aspects of wolf-related tourism. Therefore Option C, if true, would weaken the author’s argument.
• Option A supports the author's claims about the return of wolves to Lozère.
• Option B is not directly related to the author's claims about conflicts between farmers and wolves or the economic implications of wolf-related tourism.
• Option D , if true, would not necessarily weaken the author's claims but might be seen as providing additional information about land use in Lozère.

• “As the lupine population of Europe spreads westwards, with occasional reports of wolves seen closer to urban areas, expect to hear of more clashes between farmers and those who celebrate the predators’ return. Farmers’ losses are real, but are not the only economic story. Tourist venues, such as parks where wolves are kept and the animals’ spread is discussed, also generate income and jobs in rural areas.”
• The passage mentions that farmers in Lozère are concerned about the return of wolves causing losses in livestock. On the other hand, environmentalists view the presence of wolves as a sign of wider ecological health. The suggested economic solution involves tourist venues related to wolves, such as parks, which not only address the economic concerns of farmers by generating income but also align with the interests of environmentalists who appreciate the return of the predators. Therefore, Option C accurately captures the collaboration between farmers and environmentalists in the proposed solution.

• The sentence best fits in Blank 2 because it provides a continuation and elaboration on the disquieting experience mentioned before Blank 2. Before Blank 2, the passage introduces the disquieting nature of reading philosophy, and the sentence builds on that by explaining that the philosophical examination challenges the values around which one has organized their life, making them appear provincial, flatly wrong, or even evil. The sentence in question serves to articulate the difficulty and discomfort associated with this profound philosophical scrutiny, logically following the initial statement about the disquieting experience of reading philosophy.
• We can also see that the sentence ends with “...and way of life is difficult enough.” This is immediately followed by the passage highlighting what’s worse “What’s worse, philosophers admonish each other to remain unsutured until such time as a defensible new answer is revealed or constructed.”. So we can see that Sentence 2 serves as a preceding sentence to this.

Sentence 3 is the odd one out because it introduces a different topic compared to the other sentences. While the other sentences focus on the naming patterns of numbers in English, especially the irregularities and variations in the system, sentence 3 shifts the focus to the learning process of children and their understanding of the differences between numbers like "fourteen" and "forty." The other sentences contribute to the discussion about the intricacies of English number naming, making sentence 3 less aligned with the central theme of the paragraph.

• Sentence 4 introduces the idea that biased decisions made by humans have a localized impact, but with AI's emergence, the impact scale becomes much broader. This sets the context for the discussion to be followed.
• Now, if we consider Sentences 1 and 2 we can see that Sentence 1 is expanding on the impact of biased decisions in the context of AI, highlighting that algorithms hosted on the internet, accessed by many, result in more significant adverse effects on larger groups of people.Sentence 2 is providing a clarification on the term "algorithmic bias," emphasizing that the foundation of bias lies in the data rather than the algorithms themselves. It explains that algorithms reflect persistent patterns present in the training data. Therefore we can say that Sentence 2 must be following 1.
• Sentence 3 is pointing out that despite the widespread impact of AI biases, it is comparatively easier to fix them than human-generated biases, as it is simpler to identify and address biases in algorithms than to make people unlearn behaviors learned over generations. This logically follows the point made in Sentence 2. Therefore Sentence 3 must be following Sentence 2.
• Therefore the correct order is 4-1-2-3.

• Sentence 4 introduces the central question about the enduring fascination with certain crimes and the perpetual re-examination of some cases.
• Sentence 1 builds on this question by specifically asking about the "unusual elements" that make a particular case attractive to a certain audience, providing a more focused inquiry.
• Sentence 2 follows by suggesting possible reasons, such as a particularly savage or unfathomable level of depravity, and the role of mystery in drawing attention to these cases.
• Sentence 3 then generalizes the idea, stating that unsolved and perhaps unsolvable cases offer something unique that "ordinary" murder cases don't, emphasizing the enduring allure of unresolved mysteries in the realm of crime.

• The passage discusses the historical use of misinformation for political purposes, dating back to ancient Rome with Octavian's smear campaign against Antony. It then highlights how the 21st century has seen an unprecedented scale of information weaponization, facilitated by powerful technology and amplified through social networks. Option C effectively conveys the continuity of using misinformation for power throughout history, now fueled by modern technology. Therefore, Option C is the correct answer.
• Option A: While the passage acknowledges the historical aspect of disinformation, it emphasizes the unprecedented scale in the 21st century, which is not captured in this option.
• Option B focuses on the need for critical reading without explicitly highlighting the historical context and the weaponization of information for power.
• Option D does not emphasize the broader historical and contemporary context of misinformation for political purposes.

• Option C is the correct answer because it accurately captures the main idea of the passage. It highlights how technological advancements in navigation during the sixteenth century transformed colonialism by enabling Europeans to establish settlements and exert political dominance over distant regions, including the Americas, Australia, and parts of Africa and Asia.
• Option A focuses on the displacement of indigenous populations, which is not the central point of the passage.
• While Option B mentions the expansion of territories and political power, it does not emphasize the technological advancements in navigation.
• Option D introduces the concept of British settlements, which is narrower than the broader context of European colonialism discussed in the passage.

Now, we know there is only 1 candidate from OQ, which means that the number of non-candidate voters in OQ will be 4.

We also know that the non-candidates in a particular department voted as a block, and we also know that the least number of non-candidate voters in a particular department can be 1 (BH, 3-2 faculty).

Now, we also know that R got 5 votes from non-candidates.

Now we can write 5 as

(i) 5

(ii) 4+1

(iii) 3+2

Considering case (i) 4+1. This is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH. This implies that the number of candidates in FA and MQ is 1. Now, if we consider FA and MQ and put only 1 candidate there, it implies that there are 15 non-candidate voters between them. Now, we know this is not possible since the maximum number of non-candidate voters a candidate can get is 13. (Please note that non-candidates of a particular department vote as a block).

On similar grounds, we can eliminate Case (iii) as it also implies there is only 1 candidate in FA and MQ.

Now, considering Case (i), we know that 5+0 will happen only once when there are 5 non-candidates in a single department. This is only possible in MS (Out of 7, there will be 2 candidates and 5 non-candidates).

So we can conclude that MS has 2 candidates and that they voted Prof. R…….(i)

We also know that Prof P got 2 votes from Non-candidates. This is only possible when BH has 1 candidate.

So, we can conclude that the number of professors in FA, MS, OQ, BH is 0,2,1,1

Thus, we get the following table:

Now, if we consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition).

So, the possible combinations of candidates in MS are (P,Q), (Q,S), (P,S).

Now we also know that no one can vote for a candidate in their own department, so we can eliminate (P,S) and (Q,S) as we know that S voted for P and Q voted for S).

So, we can infer that P and Q are from MS.

Now, we can see that the number of votes that Prof Qureshi received from a single department can be 9 or 5 (if R is from OQ) or 4 (if R is not from OQ).

So, among the options, only Option D can be true. Therefore, Option D is the correct answer.

Now, we know there is only 1 candidate from OQ, which means that the number of non-candidate voters in OQ will be 4.

We also know that the non-candidates in a particular department voted as a block, and we also know that the least number of non-candidate voters in a particular department can be 1 (BH, 3-2 faculty).

Now, we also know that R got 5 votes from non-candidates.

Now we can write 5 as

(i) 5

(ii) 4+1

(iii) 3+2

Considering case (i) 4+1. This is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH. This implies that the number of candidates in FA and MQ is 1. Now, if we consider FA and MQ and put only 1 candidate there, it implies that there are 15 non-candidate voters between them. Now we know this is not possible since the maximum number of non-candidate voters a candidate can get is 13. (Please note that non-candidates of a particular department vote as a block).

On similar grounds, we can eliminate Case (iii) as it also implies there is only 1 candidate in FA and MQ.

Now, considering Case (i), we know that 5+0 will happen only one when there are 5 non-candidates in a single department. This is only possible in MS (Out of 7, there will be 2 candidates and 5 non-candidates).

So we can conclude that MS has 2 candidates and that they voted Prof. R…….(i)

We also know that Prof P got 2 votes from Non-candidates. This is only possible when BH has 1 candidate.

So, we can conclude that the number of professors in FA, MS, OQ, BH is 0,2,1,1

Thus, we get the following table:

Now, if we consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition).

So the possible combinations of candidates in MS are (P,Q), (Q,S), (P,S).

Now we also know that no one can vote for a candidate in their own department, so we can eliminate (P,S) and (Q,S) as we know that S voted for P and Q voted for S).

So we can infer that P and Q are from MS.

 We have been told Prof Samuel belongs to B&H. So we have to consider only Case 1. In Case 1 we can see that Prof Prakash belongs to MS and Prof Ramaswamy belongs to OQ.

Therefore, both the statements are true.

So, the correct answer is Option D

Now, we know there is only 1 candidate from OQ, which means that the number of non-candidate voters in OQ will be 4.

We also know that the non-candidates in a particular department voted as a block, and we also know that the least number of non-candidate voters in a particular department can be 1 (BH, 3-2 faculty).

Now, we also know that R got 5 votes from non-candidates.

Now we can write 5 as

(i) 5

(ii) 4+1

(iii) 3+2

Considering case (i) 4+1. This is only possible when there is 1 candidate from OQ, and there are 2 candidates from BH. This implies that the number of candidates in FA and MQ is 1. Now, if we consider FA and MQ and put only 1 candidate there, it implies that there are 15 non-candidate voters between them. Now we know this is not possible since the maximum number of non-candidate voters a candidate can get is 13. (Please note that non-candidates of a particular department vote as a block).

On similar grounds, we can eliminate Case (iii) as it also implies there is only 1 candidate in FA and MQ.

Now, considering Case (i), we know that 5+0 will happen only one when there are 5 non-candidates in a single department. This is only possible in MS (Out of 7, there will be 2 candidates and 5 non-candidates).

So we can conclude that MS has 2 candidates and that they voted Prof. R…….(i)

We also know that Prof P got 2 votes from Non-candidates. This is only possible when BH has 1 candidate.

So, we can conclude that the number of professors in FA, MS, OQ, BH is 0,2,1,1

Thus, we get the following table:

Now, if we consider Department MS, we know that there are 2 candidates from MS and R can’t be one of them as the people in that department voted for him….. (3 rd condition).

So the possible combinations of candidates in MS are (P,Q), (Q,S), (P,S).

Now we also know that no one can vote for a candidate in their own department, so we can eliminate (P,S) and (Q,S) as we know that S voted for P and Q voted for S).

So we can infer that P and Q are from MS.

From the 2 cases, we can see that the candidate from OQ can either be Prof Ramaswamy or Prof Samuel.

Therefore, the correct answer is Option B.

Given that the means of the ratings given by R1, R2, R3, R4 and R5 were 3.4, 2.2, 3.8, 2.8 and 3.4 respectively.

=> The sum of ratings given by R1, R2, R3 R4, R5 are 5*means = 17, 11, 19, 14, and 17 respectively.

Similarly the sum of ratings received by U, V, W, X and Y are 5*means = 11, 19, 17, 18, and 13 respectively.

Also capturing the absolute data given in the partial information (a) and (b) and representing as a table, we get:

Now,

Consider U

Given median = 2, mode = 2 and range = 3

=> His ratings should be of the form 1, a , 2, b, 4 => 1 + 2 + 4 + a + b = 11 => a + b = 4. For mode = 2 => a = b = 2

=> U's ratings are 1, 2, 2, 2, 4.

Consider V

Given median = 4, mode = 4 and range = 3

=> His ratings should be of the form 2, a, 4, b, 5 => 2 + 4 + 5 + a + b = 19 => a + b = 8 => For mode = 4 => a = b = 4

=> V's ratings are 2, 4, 4, 4, 5.

Consider W

Given median = 4, mode = 5 and range = 4

=> His ratings should be of the form 1, a, 4, 5, 5 => 1 + a + 4 + 5 + 5 = 17 => a = 2

=> W's ratings are 1, 2, 4, 5, 5.

Consider X

Given median = 4, mode = 5 and range = 4

=> His ratings should be of the form 1, a, 4, 5, 5 => a + 1 + 4 + 5 + 5 = 18 => a = 3

=> X's ratings are 1, 3, 4, 5, 5

Consider Y

Given median = 3, mode = 1 & 4, Range = 3

=> His ratings are 1, 1, 3, 4, 4.

Capturing this data in the table, we get:

Now, consider column R3 => The two missing entries should add up to 19 - 1 - 5 - 5 = 8, (only possibility is 4 + 4) => We can fill the row "U" and 4 in the row "V"

Now, consider column R2 => Missing entry should be 11 - 2 - 1 - 5 - 1 = 2

Consider column R1, the missing elements should add up to 17 - 5 - 4 - 1 = 7 (3 + 4 or 4 + 3) ----(1)

Consider R5, the missing elements should add up to 10 => 2 + 4 + 4 or 4 + 3 + 3 (not possible) as (1) requires a 3.

Now, we can fill column R1 as 3 + 4 and the remaining in column R4 and we can get the complete table

=> All ratings can be determined uniquely => 0.

It is given that the applications are scheduled for processing in twenty 15-minute slots starting at 9:00 am and ending at 2:00 pm. Ten applications are scheduled in each slot.

Hence, the total number of applicants = (20*10) = 200. It is also known that 50% of the applications were US applications, and the number of US applications was the same in all the slots. The same was true for the other three categories.

Hence, the number of total number of US applicants = (200*50%) = 100, and the number of US applicants in each slot = (100/20) = 5

It is also known that Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot. Since the number of Schengen applicants was the same in all the slots, it implies the number of Schengen applicants in each slot is at least 3.

Similarly, it is given that Mahira and Osman were scheduled in the 9:30 am slot on that day for visa processing in the Others category, which implies the number of other category applicants in each slot is at least 2. Since the number of total applicants in each slot is 10, this implies the number of Schengen and other applicants in each slot is 3, and 2, respectively. Hence, the number of UK applicants is 0 in each slot.

It is also known that the number of total counters is 10, among which four are dedicated to US applications, and two each for UK applications, Schengen applications, and Others applications. It is given that each US and UK application requires 10 minutes of processing time, and Vijay was called to a counter at 9:25 am. (Who is 5th in the queue). It can only be possible when the processing time of Schengen applications is 12.5 minutes.

On a particular day, Ira, Vijay, and Nandini were scheduled for Schengen visa processing in that order. They had a 9:15 am slot but entered the VPO at 9:20 am. When they entered the office, exactly six out of the ten counters were either processing applications, or had finished processing one and ready to start processing the next. Hence, at 9.20 am, there are exactly four free counters. Out of these 4, 2 is the UK counter, and the other two are other counters. (Since the US counters and Schengen Counters were either processing applications, or had finished processing one and were ready to start processing the next.)

From the table, we can see that the first slot takes 20 minutes to complete, and after that remaining 19 slots take 15 minutes each to complete the US application process.

Hence, the total time taken = 20+15*19 = 305 minutes = 5 hrs 5 minutes. Hence, the time will be (9 am + 5hrs 5 minutes) = 2.05 pm

The correct option is A

(x² + 12) = 4
This means, x² + 12 = x⁴
Let k = x²
k + 12 = k²
k² – k – 12 = 0
k² – 4k + 3k – 12 = 0
k(k – 4) + 3(k – 4) = 0
k = 4 or k = -3
But since k = x², k is always non-negative.
∴ k = 4
∴ x² = 4
Since x is the base of the log function, it can should always be positive.
∴ x = 2
3x=1
x³ = 1
x³  = y1
y = x³  = 2³ = 8
∴ x + y = 2 + 8 = 10

Given, x² +(x - 2y - 1)² = -4y(x + y)
⇒ x² + 4xy + 4y² + (x - 2y - 1)² = 0
⇒ (x + 2y)² +(x - 2y - 1)² = 20

For the L.H.S. of the equation to be 0, each of the square terms should be 0 (as squares cannot be negative)
⇒ x - 2y - 10 ⇒ x - 2y = 1

Let the marks of each girl in the class be g and the marks of each boy be b.
Since, the average marks of 4 girls and 6 boys is 24…
4g + 6b = 24 × 10 = 240
A girl scores more than or equal to the score of a boy but never more than double the score.
Therefore, g = kb, where 1 ≤ k ≤ 2
4(kb) + 6b = 240
b(4k + 6) = 240
b(2k + 3) = 120

Since, 1 ≤ k ≤ 2
2 ≤ 2k ≤ 4

51.42 ≤ n ≤ 72
52 ≤ n ≤ 72
Therefore, n can take 21 values, 52 to 72 both inclusive.
For all these values k takes a distinct value from 1 to 2 and 2g + 6b takes a distinct integral value.

Let the initial salaries of Sita, Gita and Mita be 5x, 6x and 7x respectively.
After getting 20%, 25% and 20% salary hikes respectively, their salaries become 6x, 7.5x and 8.4x respectively.
In the second year we don’t know Gita’s hike but Sita and Mita get 40% and 25% hikes respectively.
So, in the second year the salaries of Sita, Gita and Mita are respectively 8.4x, Y, 10.5x (where Y is an unknown)
We also know that Gita’s salary is the average of the salaries of the three.
This means, Gita’s salary is just the average of the other two.

∴ The hike that Gita got in the second year is 26%

Let A be the cost price of object A and B be the cost price of object B.
Gita sells two objects A and B at the same price such that she makes a profit of 20% on object A and a loss of 10% on object B.
Therefore, 1.2 × A = 0.9 × B
4 A = 3 B
B = 4/3 A
To sell object B at a profit of 10%, the selling price of B must be 1.1 B or 11/10 B
Object A is sold at the same price as object B, that is, 
The profit obtained on object A in such a trade will be 46.66% or nearly 47%.

This is the equation of a circle with radius 4 units and centered at (-2, 3)
From a point L we drop two tangents on the circle such that the angle between the tangents is 60^o.

∠LPO = 90^∘ 
∠PLO=30^∘
 
Therefore the locus of the point L, is a circle centered at (-2, 3) and has a radius of (4 + x = 8) units.
The equation of this locus is thus, (x + 2)2 +(y − 3)2 = 82
 When x = 6, we have, (8)² +(y − 3)² = 8²   , that is y = 3
The circle , (x + 2)² +(y − 3)² = 8², touches the line x = 6 at (6, 3).

∠DAC=∠DBC
(Angles subtended by the chord DC on the same side.)
∠ADB=∠ACB
(Angles subtended by the chord AB on the same side.)
∠AED=∠BEC
(Vertically Opposite angles.)

(Angles subtended by the chord AD on the same side.)
∠BAC=∠BDC
(Angles subtended by the chord BC on the same side.)
∠AEB=∠DEC
(Vertically Opposite angles.)

Therefore, AE : EC = 8 : 5

1 Million = 10⁶
Population on…
Day 1: 2

Putting n = 18 in 2ⁿ⁺¹+2ⁿ⁻¹−3,
On the 19^th day the population will be more than double the population on the 18^th day, which is more than 2 × 655357, which is definitely more than 10⁶.