Free Topic-Wise General Studies MCQs
Solve the complete 2021 UPSC CSAT question paper. Enhance your exam readiness by practicing real past-year MCQs with professional, detailed explanations.
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Explanation: The claim that no man can live without adhering to some religious denomination is incorrect because the passage does not comment on the necessity of belonging to a religious denomination for survival. The claim that it is the duty of everyone to propagate one's religious denomination is incorrect because there is no mention of any duty to spread religious beliefs. The assumption that religious denominations tend to ignore the unity of man is correct because it supports the central argument that judging others' religions leads to all religions being seen as wrong. The claim that men do not understand their own religious denomination is incorrect because the passage suggests people fail to understand others' religions, not necessarily their own.
Explanation: The assertion that seditions, wars, and breach of the laws are inevitable in every dominion is incorrect because the passage does not claim such problems are unavoidable. The claim that the sovereign alone is responsible for all problems is incorrect because it is overly simplistic to blame only the sovereign. The inference that the best dominion pursues the aim of unity and has laws for good citizenship is correct because it is directly supported by the passage. The claim that it is impossible to establish a good dominion is incorrect because the passage suggests good government requires preparation and education, not that it is unachievable.
Explanation: Assumption 1, which states that equality is a prerequisite for confident participation in societal transactions, is valid because the passage emphasizes equal standing as a foundational democratic norm. Assumption 2, which claims inequality threatens the survival of democracy itself, is not valid because the passage only says inequality violates democratic norms, not that it destroys democracy. Assumption 3, which claims equal standing cannot be realized even in a democracy, is not valid because the passage treats equality as a default moral principle rather than an unreachable ideal. Assumption 4, which states that the right to equality should be part of everyday values and political vocabulary, is valid because it aligns with the passage's moral argument. Therefore, only assumptions 1 and 4 are valid, making the correct choice the option that selects 1 and 4 only.
Explanation: The statement that human societies experiment with different forms of governments is incorrect because, although inferable, it is not explicitly stated as the author's main point. The statement that any form of government tends to deteriorate by excess of its basic principle is correct because the author explicitly says democracy ruins itself by excess of democracy and describes other governments through their excesses. The statement that education of all citizens ensures a perfect democracy is incorrect because it is speculative and goes beyond the passage. The statement that having a government is a necessary evil because tyranny is inherent in any form is incorrect because it is an extreme position that fails to capture the passage's main message.
Explanation: Out of 120 persons, 80 are Indians and 40 are foreigners. Out of 120 persons, 70 can speak English and 50 cannot. To maximize the number of Indians who can speak English, assume all English speakers are Indians, giving a maximum of 70. To minimize it, assume all 40 foreigners speak English, leaving 30 Indians who must speak English. Therefore, the number of English-speaking Indians is between 30 and 70, which means the correct answer is the option stating 30 or more.
Explanation: There are only three non-zero digits that are multiples of 3: 3, 6, and 9. Since repetition is not allowed, the possible three-digit numbers are 369, 396, 639, 693, 936, and 963. Their sum S equals 3996. S is divisible by both 74 and 9, so both given statements are correct and the right choice is the option stating both 1 and 2.
Explanation: In matters of averages, adding items below the existing average decreases the average. The lowest score in Class-B is higher than the highest score in Class-A. Therefore, any student moving from Class-A to Class-B will bring marks lower than Class-B's existing range, causing Class-B's average to definitely decrease. However, the four students leaving Class-A could be above or below Class-A's average. If they are above the average, Class-A's average would decrease; if below, it would increase. Since a definite increase cannot be confirmed, Statement 2 is incorrect. Thus, only Statement 1 is correct, making the right choice the option stating 1 only.
Explanation: Since the total number of students is known, either statement alone can determine Seema's rank. From Statement-1, Priya is 31st from the bottom in a class of 40, so she is 10th from the top. Since Priya is 4 ranks below Seema, Seema is 6th from the top. From Statement-2, Ena is 37th from the bottom, so she is 4th from the top. Since Ena is 2 ranks above Seema, Seema is 6th from the top. Therefore, either statement alone is sufficient, making the correct choice the option stating that either Statement-1 alone or Statement-2 alone is sufficient.
Explanation: Statement-1 establishes that A and D are each heavier than B, E, and F, but it does not identify the heaviest overall because the relationship between A and D is unknown and a heavier item outside the mentioned set could exist. Statement-2 gives C > A > D, but by itself it says nothing about B, E, or F. Combining both statements yields the complete order C > A > D > B, E, F, proving C is the heaviest. Therefore, both statements are required, making the correct choice the option stating that both Statement-1 and Statement-2 are required.
Explanation: The English alphabet is ABCDEFGHIJKLMNOPQRSTUVWXYZ. Arranged as required, the groups become DCBA, HGFE, LKJI, PONM, TSRQ, XWVU, ZY. The 13th letter in this new arrangement is P. The fourth letter to the right of P is T.
Explanation: The statement that India's energy decision-making process is ever more complex and interconnected is correct because the passage discusses multiple overlapping problems and integrated policy discussions across energy, urbanisation, and transport. The statement that India's policy is heavily tuned to sustainable development goals is incorrect because the passage does not support such an extreme characterization. The statement that India's actions are incompatible with broader social, economic, and environmental goals is incorrect because it is speculative and not discussed in the passage. The statement that the decision-making process is straightforward supply-oriented and ignores demand is incorrect because the passage does not explicitly discuss demand-side versus supply-side orientation.
Explanation: The suggestion that people should avoid consuming animal farming products is speculative and not supported by the passage. The proposal to replace animal foods with plant foods is far-fetched and beyond the passage's scope. The proposal to ban all use of antibiotics on animals is incorrect because the passage appreciates companies that stopped using antibiotics for weight gain rather than calling for an outright ban. The statement that antibiotics should only be used to treat diseases is correct because the passage criticizes their use as growth promoters and highlights benefits when such non-therapeutic use is stopped.
Explanation: Assumption 1, which claims oil producing countries are a reason for high food prices, is incorrect because the passage only mentions high fuel prices generally, not specifically oil producers. Assumption 2, which claims a future food crisis will be confined to emerging economies, is incorrect because the passage discusses a general food price surge and does not narrow the crisis to specific regions. Therefore, neither assumption is valid, making the correct choice the option stating neither 1 nor 2.
Explanation: Assumption 1, which claims rising GDP is essential for a country to be developed, is speculative and not supported by the passage's discussion of GDP's dominance in development economics. Assumption 2, which claims rising GDP guarantees reasonable income distribution to all households, is also speculative and unsupported. Therefore, neither assumption is valid, making the correct choice the option stating neither 1 nor 2.
Explanation: Blue covers belong to R, Q, and T. Old books are P, Q, R, and T. Gazetteers are Q, T, and U. The intersection of old books, Gazetteers, and blue covers is Q and T. Therefore, the correct answer is the option identifying Q and T.
Explanation: Separating the odd and even series: the odd series is 3, 7, 13, 21, 31, 43 with consistent gaps of 4, 6, 8, 10, 12. The even series is 2, 4, 10, 18, 28, 40 with gaps that should follow 2, 6, 8, 10, 12. Replacing the first term 2 with 0 makes the even series 0, 4, 10, 18, 28, 40, giving the correct gaps of 4, 6, 8, 10, 12. Therefore, the correct replacement is 0.
Explanation: Sequence I follows the pattern: 8 × 0.5 = 4; 4 × 1.5 = 6; 6 × 2.5 = 15; 15 × 3.5 = 52.5; 52.5 × 4.5 = 236.25. Sequence II follows the same multiplication pattern: 5 × 0.5 = 2.5 for A; 2.5 × 1.5 = 3.75 for B; 3.75 × 2.5 = 9.375 for the entry in place C.
Explanation: The total distance is 15 km. If they meet midway, each covers 7.5 km. At a uniform speed of 1.5 km/hr, X takes 5 hours to cover 7.5 km. Y's speeds over 5 equal hourly slots are 1, 1.25, 1.5, 1.75, and 2 km/hr, averaging 1.5 km/hr. In 5 hours at an average of 1.5 km/hr, Y also covers 7.5 km. Thus both statements are true, making the correct choice the option stating both 1 and 2.
Explanation: Since the marks are in strictly increasing proportions and the overall average is 60%, exactly half of the values must lie below the average and half above it. Therefore, three papers are below 60%. Alternatively, assuming 100 marks per paper gives a total of 600, and 60% overall is 360 total marks. Solving 5x + 6x + 7x + 8x + 9x + 10x = 360 yields x = 8. The marks become 40, 48, 56, 64, 72, and 80. In three of these papers the student scored less than 60, confirming the correct answer is the option stating 3.
Explanation: Assumption 1, which states fig trees can often be keystone species in natural forests, is valid because the passage emphasizes their critical role in providing food and supporting wildlife diversity when other resources are scarce. Assumption 2, which claims fig trees can grow where other large woody species cannot, is not a valid assumption because negating it does not invalidate any statement in the passage; it is at best an inference. Assumption 3, which states sacred trees can have a role in biodiversity conservation, is valid because the passage links sacred fig trees to frugivore abundance and coexistence of species. Assumption 4, which states fig trees have a role in seed dispersal of other tree species, is valid because the passage connects visits by birds and bats to the presence of seedlings of other species around fig trees. Therefore, assumptions 1, 3, and 4 are valid, making the correct choice the option stating 1, 3 and 4 only.
Explanation: Agroecology focuses on mimicking natural ecosystems. Fertigation, which delivers fertilizer through irrigation systems, is artificial and not seen in nature. Hydroponics, which grows plants in nutrient solutions without soil, is also artificial. Vertical farming, which stacks crops in layers, is unnatural. Cover crops, mixed farming, and polyculture align with natural processes such as nutrient cycling, intercropping, and integrating trees with crops and livestock. Therefore, practices 1, 4, and 5 are compatible, making the correct choice the option stating 1, 4 and 5 only.
Explanation: The inference that computers are not completely safe is correct because the passage concludes that there is little evidence gadgets will be trustworthy and cites hackers taking remote control of cars and pacemakers. The claim that companies do not take cyber security seriously is speculative and not discussed. The claim that stringent data security laws are needed is a possible fallout but less central than the direct inference about safety. The statement that the present trend of communication technologies will affect our lives is too broad and does not capture the passage's specific focus on computer safety concerns.
Explanation: Assumption 1, which claims people obsessed with personal hygiene ignore community hygiene, is invalid because negating it does not affect the passage's conclusion. Assumption 2, which claims multi-drug resistant germs can be prevented by personal cleanliness, is invalid because the passage mentions resistant germs generally, not multi-drug resistant ones specifically, and assumptions should not be more specific than the passage. Assumption 3, which claims market entry increases disease risk, is an inference rather than a valid assumption because the passage links market entry to false security and ecological harm, not directly to increased infection risk. Assumptions 4 and 5 are valid because they serve as the missing link between community hygiene, environmental conditions, and reducing infectious diseases, which is the passage's central theme. Therefore, the valid assumptions are 4 and 5, making the correct choice the option stating 4 and 5 only.
Explanation: Conclusion-I is valid because since all chairs are tables, substituting tables for chairs in the second premise yields 'some almirahs are tables'. Conclusion-II is valid because the first two premises do not establish that any cats are chairs, so it remains possible that some cats are not chairs. Therefore, both conclusions follow, making the correct choice the option stating both Conclusion-I and Conclusion-II.
Explanation: Starting height is 150 cm. After the first hit, the bounce height is 120 cm. After the second, 96 cm. After the third, 76.8 cm. After the fourth, 61.44 cm. After the fifth, 49.15 cm. Since 49.15 cm is less than 50 cm, the ball does not bounce back after the fifth hit. Therefore, the ball hits the ground 5 times before stopping.
Explanation: The consonants are B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z, totaling 21. Those whose mirror images look like the original are H, M, T, V, W, X, and Y, totaling 7. Therefore, the number of consonants whose mirror images do not look like their original shapes is 21 minus 7, which equals 14.
Explanation: Converting the route into cardinal directions: 10 km South, 20 km East, 40 km North, 5 km East, and 30 km South. The net North-South movement is 20 km South, and the net East-West movement is 25 km East. The shortest distance from the starting point is the straight-line distance, which equals the net eastward displacement of 25 km because the starting and ending points align horizontally. Therefore, the shortest distance is 25 km.
Explanation: For integers between 700 and 1000, the first digit is 7, 8, or 9. If the first digit is 7, the remaining two digits must sum to 3, giving 703, 712, 721, and 730. If the first digit is 8, the remaining digits must sum to 2, giving 802, 811, and 820. If the first digit is 9, the remaining digits must sum to 1, giving 901 and 910. This yields a total of 9 integers. Therefore, the correct answer is the option stating 9.
Explanation: The net displacement is 6 km North and 8 km East. Because the eastward distance is greater than the northward distance, the angle measured from the East axis towards North is less than 45 degrees. Therefore, the correct direction is an angle less than 45 degrees North of East.
Explanation: The statement that low intensity light has more adverse effect than high intensity light is incorrect because the passage does not compare intensities. The inference that light pollution can have a permanent adverse impact on an ecosystem is correct because the passage demonstrates how artificial lighting disrupts plant flowering and suppresses aphid populations. The claim that white light is better for flowering than other colours is incorrect because the passage does not compare the effects of white and amber light on flowering. The statement that proper light intensity is important for both plants and animals is incorrect because the passage focuses on adverse impacts rather than defining what proper intensity would be.
Explanation: The claim that low intensity light has more adverse effect than high intensity light is incorrect because the passage does not compare intensities. The inference that light pollution can have a permanent adverse impact on an ecosystem is correct because the passage demonstrates how artificial lighting disrupts plant flowering and suppresses aphid populations. The claim that white light is better for flowering than other colours is incorrect because the passage does not compare the effects of white and amber light on flowering. The statement that proper light intensity is important for both plants and animals is incorrect because the passage focuses on adverse impacts rather than defining what proper intensity would be.
Explanation: The assumption that sustainable production of India's cereal food grains is impossible without the diversity of pollinating animals is incorrect because it is too specific and goes beyond the general findings discussed in the passage. The assumption that monoculture of horticultural crops hampers the survival of insects is incorrect because the passage does not discuss monoculture practices. The assumption that pollinators become scarce in cultivated areas devoid of natural vegetation is correct because the passage states that effective pollination requires resources such as pristine natural vegetation, implying that their reduction affects pollinator presence. The assumption that diversity in insects induces diversity of plants is correct because the passage describes an intricate relationship where the reduction or loss of either plants or animals affects the survival of both. Therefore, only assumptions 3 and 4 are valid.
Explanation: The statement that development of regional climate models helps in choosing climate-smart agricultural practices is not discussed in the passage. The statement that heavy dependence on groundwater can be reduced by adopting dry-land cropping systems is also not mentioned. The statement that climate changes increase the criticality of water resources while simultaneously threatening it accurately captures the main point about rising temperatures, reduced rainfall, droughts, and increased groundwater abuse. The statement that climate changes cause farmers to adopt unsustainable livelihoods is not the primary focus of the passage. Therefore, the correct answer is the option stating that climate changes increase the criticality of water resources while simultaneously threatening it.
Explanation: The assumption that BPA may alter embryonic development is correct because the passage notes developmental abnormalities and effects on mouse embryonic stem cells upon treatment with BPA. The assumption that biochemical and cell-based assays are useful in finding treatments for pollution-induced diseases is incorrect because the passage only mentions using them to examine gene expression and measure toxicity, not to develop treatments. The assumption that embryonic stem cells could serve as a model to evaluate the physiological effects of environmental pollutants is correct because the passage explicitly demonstrates this use. Therefore, only assumptions 1 and 3 are valid.
Explanation: The powers of 3 follow a repeating pattern for the unit digit: 3^1 = 3, 3^2 = 9, 3^3 = 27 (unit digit 7), 3^4 = 81 (unit digit 1), 3^5 = 243 (unit digit 3). The unit place repeats after every 4 steps. When the exponent 2019 is divided by 4, the remainder is 3. Therefore, the unit place of 3^2019 will be the same as that of 3^3, which is 7. Hence, when 3^2019 is divided by 10, the remainder will be 7.
Explanation: Using the divisibility rule for 7 by alternating triplets: (37) (981) (25P) (369). Calculate the difference between the sum of alternate triplets: (369 + 981) - (25P + 37) = 1350 - (250 + P + 37) = 1350 - 287 - P = 1063 - P. Dividing 1063 by 7 yields a remainder of 6 (since 1063 = 7 * 151 + 6). For the entire expression to be divisible by 7, the value (6 - P) must be a multiple of 7. The only single digit P that satisfies this condition is 6. Alternatively, testing the options directly shows that when P is 6, the resulting calculation is perfectly divisible by 7.
Explanation: Determine the price of petrol on and after the 100th day of the year. On day 100, the price is 80 + 0.1(100) = 90 Rupees, and it remains constant after this day. Let's find the day n when the diesel price reaches 90 Rupees: 69 + 0.15n = 90. This simplifies to 0.15n = 21, which yields n = 140. We calculate the total number of days until the end of April, which is 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) = 120 days. Since n = 140, the required date falls in May. Subtracting the 120 days of the previous months from 140 gives the 20th day of May. Therefore, the prices are equal on 20th May.
Explanation: The population doubles every 12 years, and the initial population in the year 2021 is 50 animals. This means after 12 years (when n=12), the population should be 100. Checking the mathematical models: substituting n=12 into P = 50 * 2^(n/12) gives P = 50 * 2^(12/12) = 50 * 2 = 100 animals. The linear models P = 12 + 50n and P = 50 + 12n, as well as the exponential model P = 50 * 2^(12n), do not yield 100 after 12 years. Thus, the equation P = 50 (2)^(n/12) is the correct representation.
Explanation: Let the total number of students in the class be 100. The number of Indian students is 60, meaning the number of foreign students is 100 - 60 = 40. The total number of girl students in the class is 50. According to the data, 30% of the Indian students are girls, so there are 0.30 * 60 = 18 Indian girls. Consequently, the number of foreign girl students is the total girls minus Indian girls, which is 50 - 18 = 32. Since there are 40 foreign students in total and 32 are girls, the number of foreign boy students is 40 - 32 = 8. The percentage of boys among the foreign students is (8 / 40) * 100 = 20%.
Explanation: Based on the statements provided, from 'some radios are mobiles' and 'all mobiles are computers', we can definitively conclude that some radios are computers. However, the statement 'some computers are watches' does not establish any necessary overlap or relationship between watches and radios, nor between watches and mobiles. Therefore, it is not certain that any radios are watches or that any mobiles are watches. Neither conclusion logically follows from the premises.
Explanation: From the provided passage, it is stated that most people would agree that telling deliberate lies is wrong. Therefore, it is reasonable to conclude that the opening concept discusses an agreement among people regarding the general immorality of telling lies. The passage highlights a consensus on the act of lying before contrasting it with special situational exceptions regarding truth-telling.
Explanation: The passage highlights in the final line that even the most truthful people use words that contain some measure of falsehood, more or less deliberate. This indicates that good people often intentionally mix truth with minor falsehoods or semantic lies to navigate situations, particularly to reduce the harm that blunt truth might cause. The passage does not support complete concealment or total falsification of facts.
Explanation: The next meeting day for Joseph, Harsh, and Sumit can be determined by finding the least common multiple (LCM) of their visiting intervals. The LCM of 5, 24, and 9 is 360 days. To find the day of the week, we divide 360 by 7 (the number of days in a week), which gives 51 weeks and a remainder of 3 odd days. Adding these 3 odd days to the initial Sunday results in a Wednesday.
Explanation: Let the original number be 10x + y. The number obtained upon interchanging the digits is 10y + x. The difference between these two numbers is (10x + y) - (10y + x) = 9x - 9y = 9(x - y). We are given that this difference is 54. So, 9(x - y) = 54, which simplifies to x - y = 6. This confirms that the difference between the two digits can be determined definitively, making the statement that the difference between the two digits can be determined correct. The possible pairs of such digits are (7, 1), (8, 2), and (9, 3). While knowing the product of the digits would allow us to identify the specific pair and find their sum, knowing the ratio of the two digits would also allow us to do so. Therefore, the claim that the sum can be determined only if the product is known is incorrect.
Explanation: The present age of X is 42 years. Let the present age of Y be y years. At the time of Y's birth (which was y years ago), X's age was 42 - y. The problem states that X's age at that time was twice Y's present age. So, 42 - y = 2y. This simplifies to 3y = 42, making Y's present age 14 years. Checking the statement that 8 years ago X's age was five times Y's age: 8 years ago, X was 34 and Y was 6. Since 34 is not five times 6, this statement is incorrect. Checking the statement that after 14 years X's age would be two times Y's age: after 14 years, X will be 56 and Y will be 28. Since 56 is exactly two times 28, this statement is correct.
Explanation: Let the initial price of the article be Rs. 100. A 20% decrease reduces the price to 100 - (0.20 * 100) = Rs. 80. Subsequently, the new price is increased by 25%. A 25% increase on Rs. 80 equates to 80 + (0.25 * 80) = 80 + 20 = Rs. 100. Since the final price is identical to the initial price, there is a net change of 0%.
Explanation: To find the correct number, multiply the candidates by 7 and check if the resulting product consists entirely of the digit 1. Testing the correct numerical string: 15873 multiplied by 7 equals 111111. Since this product comprises ones exclusively, 15873 is the correct number.
Explanation: The man completes 7/8 of the job in 21 days. His rate of work is (7/8) / 21 = 1/24 of the job per day. This means completing the entire original job takes a total of 24 days. Since he has worked for 21 days, he has 3 days of work remaining to finish the original 1/8 of the job. The quantum of work is then increased by 50% of the total original job, adding an extra 1/2 of the original work. The time required to complete this additional 50% work is (1/2) / (1/24) = 12 days. The total additional days required is the sum of the time for the remaining original work and the newly added work, which is 3 + 12 = 15 days.
Explanation: The passage explicitly emphasizes the need for societal awareness and life-coping skills alongside traditional academic content. It questions whether schools are effectively teaching students about real-world societal issues like caste divides, famine, and gender sensitivity, and whether they are being taught critical thinking. This directly aligns with the idea that modern citizenship demands these extra dimensions of education to prevent painful transitions into the real world. The statement that school curriculum is not compatible with the expectations of children and parents is not the central focus. The statement that emphasis on academic achievements does not give time for personality development is not explicitly framed that way in the passage. The statement that preparing children to be better citizens should be the responsibility of the education system is close, but the passage specifically stresses the need for societal and life-coping skills in addition to academics rather than broadly assigning responsibility.
Explanation: We must arrange the three points P, Q, and R on a straight line such that the ratio of lengths PQ : QR = 3 : 5. There are two viable geometric arrangements. In the first scenario, Q is positioned between P and R. This makes PR = PQ + QR = 3 + 5 = 8, resulting in a PQ:PR ratio of 3:8. In the second scenario, P is positioned between Q and R. This makes QR = PQ + PR, meaning 5 = 3 + PR, which yields PR = 2. This results in a PQ:PR ratio of 3:2. Therefore, there are exactly 2 possible values for the given ratio.
Explanation: A standard 8x8 chess board features two main diagonals, each consisting of exactly 8 squares. When selecting 6 consecutive squares along a single straight diagonal path of 8 squares, there are exactly 3 possible groupings (squares 1 to 6, squares 2 to 7, and squares 3 to 8). Because there are two such main diagonals on the board, the total number of ways to choose 6 consecutive squares is 3 + 3 = 6.
Explanation: The given series follows a specific, repeating pattern of the blocks 'abb' followed sequentially by 'aab'. By substituting the characters 'ababab' into the respective empty blanks, the completed series reads: abb aab abb aab abb aab. This perfectly maintains the alternating three-letter block sequence.
Explanation: For the generated five-digit number to be greater than 30000, it must explicitly start with the digit 3. This leaves four remaining positions to be filled by the remaining four digits: two 2s and two 3s. The number of ways to arrange these remaining items with repetitions is given by 4! / (2! * 2!) = 24 / 4 = 6. These distinct valid combinations are: 33322, 33232, 33223, 32332, 32323, and 32233.
Explanation: Analyzing the statement that the sum of 5 consecutive integers can be 100: Let the 5 consecutive integers be represented as x-2, x-1, x, x+1, and x+2. Their total sum equals 5x. Setting 5x = 100 yields x = 20. Thus, the integers are 18, 19, 20, 21, and 22, making this statement correct. Analyzing the statement that the product of three consecutive natural numbers can be equal to their sum: The first three natural numbers are 1, 2, and 3. Their sum is 1 + 2 + 3 = 6, and their product is 1 * 2 * 3 = 6. Since the product equals the sum, this statement is also correct. Therefore, both statements are correct.
Explanation: The total volume of the cubical vessel is calculated as Side * Side * Side = 1 m * 1 m * 1 m = 1 cubic meter. Standard conversion dictates that 1 cubic meter equals 1,000 liters. Since 1 liter is equivalent to 1,000 milliliters, multiplying 1,000 liters by 1,000 gives 1,000,000 milliliters.
Explanation: Let the six individuals standing in the row be numbered sequentially from 1 to 6. The requirement is to select a group of 3 individuals such that no two selected individuals are standing next to each other. Systematically listing the valid, non-adjacent combinations yields: (1, 3, 5), (1, 4, 6), (1, 3, 6), and (2, 4, 6). Counting these shows there are exactly 4 distinct and valid combinations.
Explanation: The money distribution is governed by the ratio p : q : r. Evaluating the statement that A gets the maximum share if p is greater than (q+r): Since ratio values are positive, if p > (q + r), it mathematically guarantees that p is independently larger than q and independently larger than r. Thus, A undoubtedly receives the largest share, making this statement correct. Evaluating the statement that C gets the minimum share if r is less than (p+q): If r < (p + q), it does not strictly guarantee that r is the smallest numerical value. For instance, if p = 2, q = 4, and r = 5, the condition 5 < (2 + 4) is met, yet r remains the largest share, not the smallest. Thus, this statement is incorrect. Therefore, only the statement regarding A getting the maximum share when p exceeds q+r is correct.
Explanation: The passage does not argue for the absolute superiority of online education over conventional methods, nor does it explicitly focus on the private sector or coaching institutes. Instead, it underscores a collaborative global approach where institutions can freely adopt premium digital content to supplement their pedagogy. This suggests that institutions can leverage existing world-class digital resources without necessarily investing heavily in new physical infrastructure, thereby efficiently developing human capital. The statement about efficacy being better in online mode is not the central claim. The statement about availability being made easier and cheaper is partially true but not the core idea. The statement about private sector institutions thriving is beyond the passage's scope.
Explanation: The passage highlights the vulnerability of cities to climate change due to dense populations and inadequate infrastructure. It explicitly calls for addressing core issues like air quality and transportation as vital pathways to identifying sustainable solutions. Therefore, the most direct rational inference is the necessity of adopting sustainability-related interventions to properly maintain and develop urban centers. The statement about needing a well-defined administrative set-up is not the primary focus. The statement that ever-increasing population densities are a hindrance describes a problem but not the inference. The statement about public-private partnerships being the viable long-term solution is not discussed in the passage.
Explanation: Let the price of a single pen be defined as a, and the price of a single pencil be defined as b. Since Jay and Vijay spent identical total amounts at the store, their individual expenditures are equal: 3a + 5b = 2a + 7b. Subtracting 2a from both sides of the equation simplifies it to a + 5b = 7b. Subsequently subtracting 5b from both sides yields a = 2b. This algebraic proof definitively demonstrates that the price of one pen is exactly twice the price of one pencil.