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UPSC Civil Services (Preliminary) Examination 2025, General Studies Paper II (CSAT)

Series A. Questions and answers from the official UPSC paper and answer key:सीरीज़ A। प्रश्न और उत्तर आधिकारिक UPSC पेपर और उत्तर-कुंजी से: question paperप्रश्न-पत्र, answer keyउत्तर-कुंजी.

Take this paper as a test: answer as many as you like, then see your score with real UPSC marking and which subjects cost you marks. Your answers stay on this device.

All questions with answersउत्तरों के साथ सभी प्रश्न

  1. Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.

    Which one of the following statements best reflects the critical message conveyed by the author of the passage?

    1. Conservation of biodiversity is not an issue to be worried about when some people depend on ecosystems for their livelihoods.
    2. Commercial exploitation of forests goes against the fundamental rights of the people dependent on forests for food and shelter.
    3. Sustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.
    4. Commercial exploitation of ecosystems should be completely stopped.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Sustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.

    The passage is about the conflict between different uses of an ecosystem (livelihoods, commercial use, conservation) and how each use harms the others, with degradation hurting livelihoods in turn. Option (c) captures this tension and imbalance. Option (b) brings in fundamental rights, which the passage never mentions, and (d) is an extreme the author does not propose; the author even notes that commercial use can boost national income. Option (a) contradicts the concern for conservation.

  2. Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.

    With reference to above passage, the following assumptions have been made: I. No country needs to depend on ecosystems to boost national income. II. Resource-rich countries need to share their resources with those of scant resources so as to prevent the degradation of ecosystems. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Neither I nor II

    Assumption I goes against the passage, which says that in developing countries commercial exploitation of ecosystems can boost national income. Assumption II talks about sharing resources between rich and poor countries, which the passage does not discuss at all. So neither assumption is valid.

  3. The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent : the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.

    Which one of the following statements best reflects the central idea of the passage?

    1. Economies of scale is essential for transition to green growth.
    2. Modern technological progress is intensely linked to path-dependent innovations.
    3. Countries with large economies are in a better position to adopt green technologies.
    4. Timing plays a crucial role in the case of green technology development.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Timing plays a crucial role in the case of green technology development.

    The passage builds up to its conclusion: moving early and gradually lets economies gain from path-dependent green investment, while a late transition is chaotic and costlier. That is a point about timing, so (d) is the central idea. Economies of scale (a) and path dependence (b) are only the mechanisms used to explain why early action pays, and the size of economies (c) is never discussed.

  4. The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent : the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.

    With reference to the above passage, the following assumptions have been made: I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India. II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    The author's argument rests on the belief that early, path-dependent green investment brings benefits to an economy at lower cost, which supports assumption I for any country, including India. The author also uses solar energy as the model case of falling costs; the argument that an early transition can be smooth assumes other green technologies can follow a similar learning curve, which is assumption II. The official key treats both as valid.

  5. A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?

    1. 6
    2. 7
    3. 8
    4. 9
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 8

    Write the factors as N/a, N/b and N/c. Then N = N/a + N/b + N/c, so 1/a + 1/b + 1/c = 1 with a, b, c distinct. The only such set is (2, 3, 6). So N must be divisible by 6, and N = N/2 + N/3 + N/6. Multiples of 6 below 50 are 6, 12, 18, 24, 30, 36, 42 and 48, giving 8 numbers.

  6. Three prime numbers p, q and r, each less than 20, are such that p - q = q - r. How many distinct possible values can we get for (p + q + r)?

    1. 4
    2. 5
    3. 6
    4. More than 6
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) More than 6

    p - q = q - r means p + r = 2q, so p + q + r = 3q. The question does not say the primes are distinct, so p = q = r is allowed, and then every prime below 20 (2, 3, 5, 7, 11, 13, 17, 19) works as q. That gives 8 different values of 3q, which is more than 6. (If the primes had to be distinct, only q = 5, 7, 11, 13 would work, for example 3, 5, 7 and 3, 11, 19, giving 4 values; the official key follows the reading where they need not be distinct.)

  7. How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)?

    1. None
    2. One
    3. Three
    4. More than three
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Three

    Take p <= q <= r. Then 1/p >= 1/3, so p is 2 or 3. If p = 3, then q = r = 3, sum 9. If p = 2, then 1/q + 1/r = 1/2, giving (4, 4) or (3, 6), sums 10 and 11. So the solutions are (3,3,3), (2,4,4) and (2,3,6) with sums 9, 10 and 11: three values.

  8. What comes at X and Y respectively in the following sequence? January, January, December, October, X, March, October, Y, September

    1. July, May
    2. July, April
    3. June, May
    4. June, April
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) July, April

    Count back through the months by 0, 1, 2, 3, ... each time (wrapping round the year). January back 0 is January; back 1 is December; back 2 is October; back 3 is July (X); back 4 is March; back 5 is October; back 6 is April (Y); back 7 is September. So X = July and Y = April.

  9. Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y's average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by team X?

    1. 72
    2. 144
    3. 216
    4. Cannot be determined
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Cannot be determined

    Team Y needed 10% fewer than 20 overs, that is 18 overs, so its run rate was N/18. At a rate 50% higher, 1.5 x N/18 = N/12, the same N runs take exactly 12 overs. This is true for every value of N, so the 12-overs fact gives no new information and N cannot be determined.

  10. The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?

    1. p(10^4 - k^2)^2 = q x 10^8
    2. p(10^4 - k^2)^2 = q x 10^4
    3. p(10^4 - k^2) = q x 10^4
    4. p(10^4 - k^2) = q x 10^8
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) p(10^4 - k^2)^2 = q x 10^8

    q = p(1 + k/100)(1 - k/100)(1 + k/100)(1 - k/100) = p(1 - k^2/10^4)^2 = p(10^4 - k^2)^2 / 10^8. Multiplying both sides by 10^8 gives p(10^4 - k^2)^2 = q x 10^8.

  11. Each State in India faces a distinctive set of challenges regarding the impact of warming, but also offers its own set of opportunities for reducing emissions depending on its natural resources. For example, coastal States need to take action to protect their shores from sea level rise, districts that are drier need to prepare for variable monsoon precipitation. Himalayan regions have their own unique challenges, and selected parts of peninsular India and offshore areas offer great opportunities for harnessing wind power. These various aspects need to be considered for developing clear and sustainable goals for the future.

    Which one of the following statements best reflects the most logical, rational and pragmatic message conveyed by the author of the passage?

    1. The mitigation and adaptation strategies to address/tackle the climate change is essentially the responsibility of each State.
    2. India is too diverse to implement any effective strategy or programme to address/tackle the climate change.
    3. It is basically the responsibility of the Union Government to implement the climate action plans and ensure net zero emissions.
    4. India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.

    The passage stresses that each State or region has its own climate challenges (sea level rise, variable monsoon, Himalayan issues) and its own opportunities for cutting emissions (wind power), and that these must be considered when setting goals. So the practical message is region-specific planning, option (d). Option (a) shifts the whole responsibility to the States, which the passage does not say; (b) is defeatist and (c) is not discussed.

  12. Each State in India faces a distinctive set of challenges regarding the impact of warming, but also offers its own set of opportunities for reducing emissions depending on its natural resources. For example, coastal States need to take action to protect their shores from sea level rise, districts that are drier need to prepare for variable monsoon precipitation. Himalayan regions have their own unique challenges, and selected parts of peninsular India and offshore areas offer great opportunities for harnessing wind power. These various aspects need to be considered for developing clear and sustainable goals for the future.

    With reference to the passage, the following assumptions have been made: I. Green energy production can be linked to/integrated with the climate change mitigation and adaptation strategies. II. Effects of climate change are much more severe in coastal and mountainous regions. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) I only

    The passage treats wind power from peninsular and offshore areas as an opportunity for reducing emissions that must be considered while setting climate goals, so it assumes green energy can be built into climate strategies (I is valid). It says coastal and Himalayan regions face distinctive or unique challenges, but never that the effects there are much more severe than elsewhere, so II is not valid.

  13. If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

    Which one of the following statements best reflects the critical message conveyed by the passage?

    1. India's political executive should be aware that poverty and social inequality and the consequent sense of insecurity is the main social problem.
    2. In India, poverty is the primary reason for social inequality and insecurity.
    3. Poverty and social inequality are so intricately linked that they pose an unmanageable crisis for India.
    4. Insecurity, more than poverty, is the main economic issue that Government policies must address.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Insecurity, more than poverty, is the main economic issue that Government policies must address.

    The passage says insecurity, more than poverty, is the most acutely felt economic problem, that it affects even people above the poverty line, and that many government policies aim to reduce it. Option (d) states this directly. Option (a) mixes up the social and economic problems, (b) makes poverty the cause of inequality, which the passage never claims, and (c) calls the situation unmanageable, which is not said.

  14. If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

    With reference to the above passage, the following assumptions have been made: I. People above the poverty line also are prone to suffer from anxiety about economic insecurity. II. Eradication of poverty can result in peace and social equality in the country. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) I only

    The passage says that even those just over the poverty line face many economic insecurities, so assumption I is valid. The passage does not link removing poverty to peace or social equality; in fact it treats insecurity and inequality as problems separate from poverty, so II is not valid.

  15. A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6. Select the correct answer using the code given below:

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    To get 60 pieces with the fewest cuts, split the three directions as evenly as possible: 60 = 3 x 4 x 5, which needs (3 - 1) + (4 - 1) + (5 - 1) = 2 + 3 + 4 = 9 cuts. So I is correct. The unpainted pieces form the inner block of (3 - 2) x (4 - 2) x (5 - 2) = 1 x 2 x 3 = 6 pieces, so II is also correct.

  16. If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?

    1. 70
    2. 66
    3. 65
    4. 64
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 65

    The operation gives the hypotenuse: a * b = square root of (a^2 + b^2). Check: 49 + 576 = 625, root 25; 144 + 256 = 400, root 20. So 16 * 63 = square root of (256 + 3969) = square root of 4225 = 65.

  17. The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹ 90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?

    1. 180 km
    2. 200 km
    3. 220 km
    4. 240 km
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 200 km

    Old spending: 2200/16 = 137.5 litres x ₹ 90 = ₹ 12,375. New price = ₹ 99 per litre, so the same money buys 12375/99 = 125 litres, enough for 125 x 16 = 2000 km. He must cut his travel by 2200 - 2000 = 200 km. (Shortcut: a 10% price rise means travel must fall to 1/1.1 of 2200 = 2000 km.)

  18. A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?

    1. 1068
    2. 1072
    3. 1078
    4. 1082
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 1078

    In each case the remainder is 2 less than the divisor (3 - 1, 5 - 3, 6 - 4, 9 - 7 all equal 2). So N + 2 is divisible by 3, 5, 6 and 9, that is by their LCM 90. N = 90k - 2. The smallest 4-digit value is with k = 12: 1080 - 2 = 1078.

  19. Consider the following statements: I. If A ≤ B > C < D > E > F ≥ G = H; then B is always greater than E. II. If P > Q = R ≥ S = T ≤ U = V > W; then S is always less than V. Which of the statements given above is/are correct?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Neither I nor II

    I: B > C and C < D > E. Because the signs between B and E change direction at C, no definite relation between B and E can be fixed, so I is not always true. II: S = T ≤ U = V gives S ≤ V, so S could be equal to V; 'always less than' is not guaranteed. Neither statement is correct.

  20. What is the unit digit in the multiplication of 1 x 3 x 5 x 7 x 9 x ... x 999?

    1. 1
    2. 3
    3. 5
    4. 9
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 5

    All the factors are odd, and one of them is 5. An odd number multiplied by 5 always ends in 5, so the product of all these odd numbers ends in 5.

  21. One of the dismal realities of the agricultural sector in independent India has been that it never experienced a high-growth phase, unlike the non-agricultural economy. The highest decadal growth (compound annual growth rate or CAGR) for agriculture has been just 3.5% in the 1980s. Also, after experiencing a spurt in decadal growth during the 1980s, agricultural growth suffered relative stagnation thereafter. This is in sharp contrast to non-agricultural growth, which consistently increased from the 1980s to 2000s.

    Which one of the following statements best reflects the corollary to the above passage?

    1. The benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.
    2. For India, the green revolution was not as useful as it was expected to be.
    3. India lagged behind other countries in adapting mechanized and modern farming.
    4. Rural-to-urban migration resulted in the stagnant agriculture sector.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) The benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.

    The passage contrasts agriculture, which stagnated after the 1980s, with the non-agricultural economy, which kept growing faster from the 1980s to the 2000s (the period of economic reforms). A natural corollary is that the gains of growth and reforms have reached agriculture more slowly than other sectors, option (a). The passage says nothing about the green revolution, comparisons with other countries, or migration, so (b), (c) and (d) bring in outside ideas.

  22. One of the dismal realities of the agricultural sector in independent India has been that it never experienced a high-growth phase, unlike the non-agricultural economy. The highest decadal growth (compound annual growth rate or CAGR) for agriculture has been just 3.5% in the 1980s. Also, after experiencing a spurt in decadal growth during the 1980s, agricultural growth suffered relative stagnation thereafter. This is in sharp contrast to non-agricultural growth, which consistently increased from the 1980s to 2000s.

    With reference to the passage, the following assumptions have been made: The growing divergence between the fortunes of the agricultural and non-agricultural economy in India could have been reduced/contained by: I. adapting large-scale cultivation of commercial crops and viable corporate farming. II. providing free insurance for all crops and heavily subsidizing seeds, fertilizers, electricity and farm machinery at par with developed countries. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Neither I nor II

    The passage only describes the gap between agricultural and non-agricultural growth. It does not discuss any remedy, such as corporate farming, commercial crops, free insurance or subsidies. Both statements are policy suggestions from outside the passage, so neither is a valid assumption.

  23. In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

    Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?

    1. We need to free the handloom industry from the limited narrative linked to preserving cultural heritage.
    2. Continued State support to the handloom industry ensures the preservation of some of our glorious art forms and old traditions.
    3. Household units of the handloom sector should be modernized and made an economically viable organized industry.
    4. Handloom products need to be converted to machine-made designer products so as to make them more popular.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) We need to free the handloom industry from the limited narrative linked to preserving cultural heritage.

    The author argues that promoting handloom only as a symbol of a single tradition makes large sections of people ignore it, because that idea of tradition is contested. The logical message is to stop tying handloom only to the narrow heritage narrative, option (a). Option (b) repeats the very view the author questions. Modernisation (c) and machine-made products (d) are not discussed in the passage.

  24. In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

    With reference to the above passage, the following assumptions have been made: I. There is no need for the State to be involved in any manner in the handloom sector. II. Handloom products are no longer appealing and attractive in the rapidly changing modern world. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Neither I nor II

    The passage questions the reason given for State support (tradition), not the support itself, so I is not valid. It says some people ignore handloom because of how it is promoted as a traditional industry, not because the products have lost their appeal in the modern world, so II is not valid either.

  25. Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

    1. 20
    2. 21
    3. 22
    4. 23
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 22

    Divisibility by 9 is already covered by 3, so we need numbers from 1 to 100 not divisible by 2, 3, 5 or 7. Any such number greater than 1 must have all its prime factors at least 11, and since 11 x 11 = 121 > 100, it must itself be a prime from 11 to 97. There are 25 primes up to 100; removing 2, 3, 5 and 7 leaves 21. Adding the number 1 gives 22.

  26. If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x - y)?

    1. 6
    2. 15/2
    3. -15/2
    4. None of the above
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) None of the above

    Maximum of x + y = 8 + 7 = 15. Minimum of x - y uses the smallest x and largest y: 4 - 7 = -3. The ratio is 15 / (-3) = -5, which is not among (a), (b) or (c). So the answer is None of the above.

  27. Let both p and k be prime numbers such that (p^2 + k) is also a prime number less than 30. What is the number of possible values of k?

    1. 4
    2. 5
    3. 6
    4. 7
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 5

    If p and k were both odd, p^2 + k would be even and larger than 2, so not prime. So p = 2 or k = 2. With p = 2: 4 + k is prime and below 30 for k = 3, 7, 13, 19 (giving 7, 11, 17, 23). With k = 2: p^2 + 2 = 11 for p = 3 (p = 5 gives 27, not prime). So k can be 2, 3, 7, 13 or 19: 5 values.

  28. There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

    1. 6
    2. 7
    3. 8
    4. More than 8
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) More than 8

    1001 = 7 x 11 x 13, so each number is a divisor of 1001. For LCM 1001 and HCF 1, each of the primes 7, 11 and 13 must divide at least one number but not all three. In an ordered triple each prime can go to 6 such combinations of positions, giving 6 x 6 x 6 = 216 ordered triples. Triples where two chosen numbers are equal (say the first two) need each prime to be in both of them or only in the third: 2 x 2 x 2 = 8 for each of 3 pairs, 24 in all (all three equal is impossible). That leaves 192 ordered triples of distinct numbers, which is 192/6 = 32 sets, for example {1, 7, 143} or {7, 11, 13}. So n is more than 8.

  29. Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR - PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?

    1. 2
    2. 3
    3. 4
    4. More than 4
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 3

    Write the numbers out: (100P + 30 + R) - (10P + S) = 110P + T, which simplifies to R - S - T = 20P - 30. Since R - S - T is at most 7, P must be 1, so S + T = R + 10. Digits must be non-zero and different from P = 1 and Q = 3, and T can be 2, 4 or 5. T = 2 needs S = R + 8, which forces R = 1 (not allowed). T = 4 gives S = R + 6: R = 2, S = 8. T = 5 gives S = R + 5: R = 2, S = 7 or R = 4, S = 9. So (R, S) can be (2, 8), (2, 7) or (4, 9): 3 values. Check: 132 - 18 = 114, 132 - 17 = 115, 134 - 19 = 115.

  30. Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence?

    1. B, C, B, C, A
    2. A, C, B, C, A
    3. B, C, B, A, C
    4. C, B, B, A, C
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) B, C, B, A, C

    Filling the blanks with B, C, B, A, C gives ABBCCC ABBCCC ABBCCC, the block ABBCCC (one A, two B, three C) repeated three times. No other option keeps this repeating pattern.

  31. In our country, regrettably, teaching and learning for the examination have been our forte but the new demands of society and the future of work require critical and independent thinking, learning through doing, asking questions from multiple disciplinary perspectives on the same issue, using evidence for building arguments, and reflecting and articulation. Higher education should not "either be a mere servant of the government policy or a passive respondent to public mood." Higher learning is all about how to think rather than what to think. Teaching has to be re-invented.

    Which one of the following statements best reflects the central idea conveyed by the passage?

    1. India does not have enough resources for promoting quality education in its universities.
    2. The institutions of higher learning in the country should not be under the control of the Government.
    3. Classroom approach to higher education should be done away with.
    4. Classroom needs to be reimagined and teaching needs to be re-invented.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Classroom needs to be reimagined and teaching needs to be re-invented.

    The passage criticises exam-oriented teaching and says that new needs call for critical thinking, learning by doing and multidisciplinary questioning, ending with 'Teaching has to be re-invented.' Option (d) captures this. The passage does not speak about resources (a), does not ask for freedom from government control in general (b), and wants classroom teaching changed, not abolished (c).

  32. In our country, regrettably, teaching and learning for the examination have been our forte but the new demands of society and the future of work require critical and independent thinking, learning through doing, asking questions from multiple disciplinary perspectives on the same issue, using evidence for building arguments, and reflecting and articulation. Higher education should not "either be a mere servant of the government policy or a passive respondent to public mood." Higher learning is all about how to think rather than what to think. Teaching has to be re-invented.

    With reference to the above passage, the following assumptions have been made: I. Higher education is a constantly evolving subject that needs to align towards new developments in all spheres of society. II. In our country, sufficient funds are not allocated for promoting higher education. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) I only

    The author says the new demands of society and the future of work require a different kind of learning and that teaching must be re-invented, which assumes higher education has to keep changing with developments in society (I is valid). Funding is never mentioned, so II has no basis in the passage.

  33. If there is inequality in the pattern of population growth, there is greater inequality in food production and utilization. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only 16% of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

    Which one of the following statements best reflects the crux of the passage?

    1. There is an urgent need for a public policy to promote the consumption of cereal-based foods in wealthier societies.
    2. Animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.
    3. Plant-based protein should replace the animal-based protein in our daily diets.
    4. Inequality in food production and consumption is inevitable in any fast changing society.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) Animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.

    The core of the passage is the inefficiency of turning grains into animal food: only 16% of calories fed to chickens, and 5 to 7% for large animals, come back to humans. Option (b) states this. Options (a) and (c) are prescriptions the author does not make, and (d) is a generalisation about fast changing societies that the passage does not draw.

  34. If there is inequality in the pattern of population growth, there is greater inequality in food production and utilization. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only 16% of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

    With reference to the above passage, the following assumptions have been made: I. The food manufacturing and processing industries in every country should align their objectives and processes in accordance with the changing needs of the societies. II. Wealthier societies tend to incur great loss of calories of food materials due to indirect utilization of their agricultural produce. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) II only

    Wealthier societies eat more animal products, so more of their grain goes to animal feed, and most of those calories are lost in conversion. This supports II. The passage says nothing about food manufacturing and processing industries, so I is not valid.

  35. What is the maximum value of n such that 7 x 343 x 385 x 1000 x 2401 x 77777 is divisible by 35^n?

    1. 3
    2. 4
    3. 5
    4. 7
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 4

    35 = 5 x 7, so n is limited by whichever prime appears fewer times. Factors of 5: 385 = 5 x 7 x 11 gives one and 1000 = 2^3 x 5^3 gives three, so 5^4 in all; none of 7, 343, 2401 or 77777 is divisible by 5. Factors of 7: 7 (1) + 343 (3) + 385 (1) + 2401 (4) + 77777 = 7 x 11111 (1) = 10. The product has 5^4 x 7^10, so the largest n is 4.

  36. What is X in the sequence 24, X, 12, 18, 36, 90?

    1. 18
    2. 12
    3. 9
    4. 6
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 12

    Each term is the previous one multiplied by 0.5, 1, 1.5, 2, 2.5 in turn: 24 x 0.5 = 12, 12 x 1 = 12, 12 x 1.5 = 18, 18 x 2 = 36, 36 x 2.5 = 90. So X = 12.

  37. P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

    1. 12
    2. 13
    3. 14
    4. 15
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 13

    Walking in opposite directions, together they cover 5 + 3 = 8 rounds per hour, so they cross every 1/8 hour = 7.5 minutes: at 5:07.5, 5:15, 5:22.5, ... The crossings are at 7.5k minutes after 5:00. Between 5:20 (20 minutes) and 7:00 (120 minutes) the values are k = 3 (22.5 min) up to k = 15 (112.5 min), which is 13 crossings. The crossing at exactly 7:00 (k = 16) is at the end point and is not counted as 'between'.

  38. If P = +, Q = -, R = x, S = ÷, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20:

    1. SPRQ
    2. QRPS
    3. QRSP
    4. SPQR
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) QRPS

    QRPS gives 60 - 15 x 3 + 20 ÷ 4. Doing x and ÷ first: 15 x 3 = 45 and 20 ÷ 4 = 5, so 60 - 45 + 5 = 20. Checking (a): 60 ÷ 15 + 3 x 20 - 4 = 4 + 60 - 4 = 60, which does not work.

  39. A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?

    1. 15 m
    2. 18 m
    3. 20 m
    4. 24 m
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 20 m

    Let the tram's speed be v km/hr. The length equals relative speed x time, so (v - 3) x 8 = (v - 4) x 9, giving 8v - 24 = 9v - 36 and v = 12 km/hr. Relative speed with X is 9 km/hr = 9 x 5/18 = 2.5 m/s, so the length = 2.5 x 8 = 20 m (check with Y: 8 km/hr = 20/9 m/s x 9 s = 20 m).

  40. If N^2 = 12345678987654321, then how many digits does the number N have?

    1. 8
    2. 9
    3. 10
    4. 11
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 9

    Squares of repunits follow the pattern 11^2 = 121, 111^2 = 12321, and so on; 12345678987654321 rises to 9 and falls back, so it equals 111111111^2. N = 111111111 has 9 digits. (Also, N^2 has 17 digits, and a 17-digit square has a 9-digit square root.)

  41. Over the next 30 years, many countries are promising to move to net-zero carbon, implying that household emissions will have to be cut to close to nothing. A leading climate scientist reckons that, at best, half the reduction might be achieved through demand-side measures, such as behavioural changes by individuals and households. And even that would require companies and governments to provide more incentives to change through supply-side investments to make low-carbon options cheaper and more widely available.

    Which one of the following statements best reflects the central idea conveyed by the passage?

    1. Moving to net-zero carbon is possible only by the reduction in household emissions.
    2. Low-carbon behaviour in people can be brought about by incentivising them.
    3. Cheaper goods and services can be made available to people by using low-carbon technologies.
    4. Manufacturing industries that use low-carbon technologies should be provided with subsidies.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) Low-carbon behaviour in people can be brought about by incentivising them.

    The passage says behavioural change by households can deliver at most half the cut, and even that needs companies and governments to give incentives by making low-carbon options cheaper and more available. So the central idea is that people's low-carbon behaviour depends on incentives, option (b). Option (a) says 'only', which the passage does not claim. Option (c) reverses the logic (the passage wants low-carbon options made cheaper, not cheaper goods through low-carbon technology), and subsidies for manufacturers (d) are not mentioned.

  42. Over the next 30 years, many countries are promising to move to net-zero carbon, implying that household emissions will have to be cut to close to nothing. A leading climate scientist reckons that, at best, half the reduction might be achieved through demand-side measures, such as behavioural changes by individuals and households. And even that would require companies and governments to provide more incentives to change through supply-side investments to make low-carbon options cheaper and more widely available.

    With reference to the above passage, the following assumptions have been made: I. Supply-side investments in companies can result in low-carbon behaviour in people. II. People are not capable of adapting low-carbon behaviour without the involvement of Government and Companies. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) I only

    The passage expects supply-side investments that make low-carbon options cheaper and more available to encourage behavioural change, so I is a valid assumption. II goes too far: the passage says more incentives are needed to achieve the reduction, not that people are incapable of any low-carbon behaviour on their own.

  43. In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than 9% of this is reused. Batteries of old vehicles contain materials such as lithium, cobalt, manganese and nickel that are pricey and can be hard to obtain. Supply chains are long and complicated. Buyers' risks are being aggravated by their suppliers' poor environmental and labour standards. Reusing materials makes sense. Once batteries reach the ends of their lives, they should go back to a factory where their ingredients can be recovered and put into new batteries.

    Which one of the following statements best reflects the most logical, rational and pragmatic message conveyed by the passage?

    1. Green economy is not possible without reusing critical minerals.
    2. Every sector of economy should adapt the reuse of material resources immediately.
    3. Circular economy can be beneficial for sustainable growth.
    4. Circular use of material resources is the only option for some industries for their survival.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Circular economy can be beneficial for sustainable growth.

    The passage points to soaring raw material use, very little reuse, costly and risky supply chains, and says reusing materials makes sense, with old batteries recycled into new ones. The balanced message is that a circular economy (reusing materials) helps sustainable growth, option (c). Options (a) and (d) use extreme words ('not possible without', 'only option'), and (b) demands immediate action in every sector, which the passage does not say.

  44. In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than 9% of this is reused. Batteries of old vehicles contain materials such as lithium, cobalt, manganese and nickel that are pricey and can be hard to obtain. Supply chains are long and complicated. Buyers' risks are being aggravated by their suppliers' poor environmental and labour standards. Reusing materials makes sense. Once batteries reach the ends of their lives, they should go back to a factory where their ingredients can be recovered and put into new batteries.

    With reference to the above passage, the following assumptions have been made: I. Automobile factories are examples of the circular economy. II. Economic growth is compatible with circular use of mineral resources. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) II only

    The author recommends reusing materials such as battery minerals, which assumes that reuse can go along with continued economic activity, so II is valid. The passage says old batteries should go back to a factory for recovery; it does not say automobile factories already are examples of a circular economy, so I is not valid.

  45. A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank?

    1. 8 minutes
    2. 10 minutes
    3. 12 minutes
    4. 16 minutes
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) 16 minutes

    One X pipe fills 0.7/(14 x 20) = 1/400 of the tank per minute; one Y pipe fills (3/8)/(6 x 10) = 1/160; one Z pipe empties 0.5/(20 x 16) = 1/640. Open pipes: 10 X pipes give 10/400 = 1/40, 5 Y pipes give 5/160 = 1/32, and 16 Z pipes remove 16/640 = 1/40. Net rate = 1/32 of the tank per minute, so 50% takes 0.5 x 32 = 16 minutes.

  46. If n is a natural number, then what is the number of distinct remainders of (1^n + 2^n) when divided by 4?

    1. 0
    2. 1
    3. 2
    4. 3
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 2

    For n = 1: 1 + 2 = 3, remainder 3. For n ≥ 2, 2^n is a multiple of 4, so 1 + 2^n leaves remainder 1. Only two remainders occur (3 and 1).

  47. Let P = QQQ be a 3-digit number. What is the HCF of P and 481?

    1. 1
    2. 13
    3. 37
    4. 481
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 37

    QQQ = 111 x Q = 3 x 37 x Q, and 481 = 13 x 37. They share the factor 37. Since Q is a single digit, it can never be a multiple of 13, so the HCF is always 37.

  48. What is the 489th digit in the number 123456789101112...?

    1. 0
    2. 3
    3. 6
    4. 9
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) 9

    The numbers 1 to 9 use 9 digits and 10 to 99 use 90 x 2 = 180 digits, 189 in total. That leaves 489 - 189 = 300 digits, which is exactly 100 three-digit numbers: 100 to 199. The 489th digit is the last digit of 199, which is 9.

  49. A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows: P: I did not steal. Q stole it. Q: R did not steal. I did not steal. R: I did not steal. I do not know who did it. Who stole the mobile phone?

    1. P
    2. Q
    3. R
    4. Cannot be concluded
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Cannot be concluded

    We are told only that one person is guilty; nothing is said about who tells the truth or how many statements are true. Each case is possible: if P stole it, P lied and Q and R can be truthful; if Q stole it, P is truthful and Q lied; if R stole it, P and Q lied. Without a condition on truth-telling, none of these can be ruled out, so the thief cannot be concluded.

  50. Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct? I. The result of the match between P and Q is a draw with the score 0 - 0. II. The number of goals scored by R against Q is 1. Which of the statements given above is/are correct?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    P's 3 points must be a win and a draw, and R's 1 point a draw and a loss. If Q had a win and a loss, Q could not beat P (P has no loss), so Q would beat R and lose to P, and P would draw with R; then P's one goal is used against Q, so P-R is 0-0 and Q's goal is against R, leaving R with no goal, which is impossible. So Q drew both matches, and P beat R. P's only goal came against R (1-0), so P-Q was 0-0. R scored nothing against P, so R's goal came against Q, and Q's goal also came against R: Q-R was 1-1. Both I and II are correct.

  51. It is hard to predict how changes in the climate and the atmosphere's chemistry will affect the prevalence and virulence of agricultural diseases. But there is a risk that such changes will make some plant infections more common in all climatic zones, perhaps catastrophically so. Part of the problem is that centuries of selective breeding have refined the genomes of most high-value crops. They are spectacular at growing in today's conditions but genetic variations that are not immediately useful to them have been bred out. This is good for yields but bad for coping with changes. A minor disease or even an unknown one could suddenly rampage through a genetically honed crop.

    Which one of the following statements best reflects the central idea conveyed by the passage?

    1. Global climate change adversely affects the productivity of crops.
    2. Our total dependence on genetically honed crops entails possible food insecurity.
    3. Our food security should not depend on agricultural productivity alone.
    4. Genetically honed crops should be replaced with their wild varieties in our cultivation practices.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) Our total dependence on genetically honed crops entails possible food insecurity.

    The passage warns that selectively bred, genetically uniform crops have lost useful variation, so a minor or unknown disease, made more likely by climate change, could sweep through them. That is a risk to our food supply, option (b). Option (a) is too general; the passage is about disease risk, not productivity in general. Options (c) and (d) are remedies the author does not propose.

  52. It is hard to predict how changes in the climate and the atmosphere's chemistry will affect the prevalence and virulence of agricultural diseases. But there is a risk that such changes will make some plant infections more common in all climatic zones, perhaps catastrophically so. Part of the problem is that centuries of selective breeding have refined the genomes of most high-value crops. They are spectacular at growing in today's conditions but genetic variations that are not immediately useful to them have been bred out. This is good for yields but bad for coping with changes. A minor disease or even an unknown one could suddenly rampage through a genetically honed crop.

    With reference to the above passage, the following assumptions have been made: I. Global climate change can result in the migration of several plant diseases to new areas. II. Scientific understanding of the wild relatives of our present crops would enable us to strengthen food security. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    The passage says climate change may make some plant infections more common in all climatic zones, which implies diseases spreading into areas where they were not common before (I). It also says breeding has removed genetic variation that helps crops cope with change; the natural implication is that the variation still present in wild relatives is valuable, so understanding them can help protect our food supply (II). The official key treats both as valid.

  53. "A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable."

    Which one of the following statements best reflects the critical message conveyed by the author of the passage?

    1. Without opposition parties, the administration in a democracy gets to become more responsible.
    2. Democracy needs to have revolutionaries in opposition to keep the government alert.
    3. Rulers in a democracy need the support of opposition for their political survival.
    4. In a democracy, the opposition is indispensable for the balance of political power and good governance.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) In a democracy, the opposition is indispensable for the balance of political power and good governance.

    The author says opponents keep a statesman on the path of reason and that national unity depends on an even balance of power, so that neither the government is arbitrary nor the opposition revolutionary. Option (d) captures this. Option (a) is the opposite of the message, (b) contradicts the warning against a revolutionary opposition, and (c) speaks of the opposition's support for survival, whereas the passage values the opposition for checking and correcting the ruler.

  54. "A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable."

    With reference to the above passage, the following assumptions have been made: I. In a democracy, a strong opposition is required only if the Head of Government is indifferent. II. The more aggressive the opposition, the better is the governance in a democracy. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Neither I nor II

    The passage says every statesman needs opponents, not only an indifferent one, so I is not valid. It wants an even balance of power in which the opposition is not revolutionary and irreconcilable, so it does not say that a more aggressive opposition means better governance; II is not valid either.

  55. P is the brother of Q and R. S is R's mother. T is P's father. How many of the following statements are definitely true? I. S and T are a couple. II. Q is T's son. III. T is Q's father. IV. S is P's mother. V. R is T's daughter. VI. P is S's son. Select the correct answer using the code given below:

    1. Only two
    2. Only three
    3. Only four
    4. Only five
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Only four

    P, Q and R are siblings, so they share the parents S (mother) and T (father). Hence S and T are a couple (I), T is Q's father (III), S is P's mother (IV), and P, being a brother, is S's son (VI). The genders of Q and R are not given, so 'Q is T's son' (II) and 'R is T's daughter' (V) are not definitely true. Four statements are definitely true.

  56. If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?

    1. 399000
    2. 420000
    3. 440000
    4. 630000
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) 399000

    The code is the product of the alphabet positions of the letters: N = 14, O = 15, so NO = 14 x 15 = 210; NOT = 210 x 20 (T) = 4200; NOTE = 4200 x 5 (E) = 21000. NOTES = 21000 x 19 (S) = 399000.

  57. If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded?

    1. 54321
    2. 81913
    3. 71913
    4. 71813
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) 71813

    Each letter keeps a fixed digit. From FRANCE: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1. From GERMANY: G = 9, E = 1, R = 5, M = 8, A = 4, N = 3, Y = 7. So YEMEN = Y E M E N = 7 1 8 1 3 = 71813.

  58. The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?

    1. 3
    2. 4
    3. 5
    4. 6
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 4

    P = 3T with T non-zero gives (T, P) = (1, 3), (2, 6) or (3, 9). Q = R + 3 and S = R + 7, so (R, Q, S) = (0, 3, 7), (1, 4, 8) or (2, 5, 9). Checking for distinct digits: T = 1, P = 3 allows only (2, 5, 9), giving 35291; T = 2, P = 6 allows (0, 3, 7) and (1, 4, 8), giving 63072 and 64182; T = 3, P = 9 allows only (1, 4, 8), giving 94183. That is 4 numbers.

  59. X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in 8 2/3 days. What is n equal to?

    1. 3
    2. 4
    3. 5
    4. 6
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 4

    Full work: X takes 18 days, Y 24 days and Z 16 days. In 8 2/3 = 26/3 days Y does (26/3)/24 = 13/36 of the work, so the three together did 23/36. Their combined daily rate is 1/18 + 1/24 + 1/16 = (8 + 6 + 9)/144 = 23/144. So n = (23/36) / (23/144) = 4.

  60. What is X in the sequence 1, 3, 6, 11, 18, X, 42?

    1. 26
    2. 27
    3. 29
    4. 30
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 29

    The differences are consecutive prime numbers: 1 + 2 = 3, 3 + 3 = 6, 6 + 5 = 11, 11 + 7 = 18, 18 + 11 = 29, 29 + 13 = 42. So X = 29.

  61. There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs - and there is no other way to fix a country's unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State - which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.

    Which one of the following statements best reflects the critical message conveyed by the author of the passage?

    1. Corporate capitalism is important for economic growth of a State and also for democracy.
    2. Corporate capitalism is imperative for a modern State to achieve its political objectives.
    3. No State can ensure its economic survival for long without the role of corporate capitalism.
    4. Corporate capitalism and democracy have mutual dependence for their continued existence.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) Corporate capitalism is important for economic growth of a State and also for democracy.

    The passage opens by saying no democracy has grown economically without corporate capitalism, and then lists its benefits: modernisation, jobs, competitiveness and revenue that the State can spend on welfare and a more level playing field for the marginalized. Option (a) best sums up this role in growth and in a fairer democratic society. Option (b) speaks of political objectives, (c) of economic 'survival' of any State, and (d) of mutual dependence for existence; none of these is argued in the passage.

  62. There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs - and there is no other way to fix a country's unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State - which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.

    With reference to the above passage, the following assumptions have been made: I. Corporate capitalism promotes the growth of labour force and provides more employment opportunities. II. Poor and marginalized sections of population are benefited by corporate capitalism due to trickle-down effect. Which of the above assumptions is/are valid?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    The passage says corporate capitalism generates jobs and is the only way to tackle unemployment, and that it helps the shift from agriculture to industry and services, which supports I. It also says the extra revenue it brings to the State can be used for the welfare of the marginalized and a more level playing field, so the benefits of corporate growth flow down to the poor, which supports II. Both are valid.

  63. "A network of voluntary associations stands as a 'buffer' between the relatively powerless individual and the potentially powerful State."

    Which one of the following statements reflects the best explanation of the above passage?

    1. It emphasizes the inability of the State to enforce its will in practice against the opposition of certain groups within it.
    2. It is a cooperative organization for the promotion of the well-being and development of the personality of its members.
    3. It takes individuals out of a state of isolation and gives them a chance to participate in the common endeavour.
    4. It permits citizens to have a variety of loyalties and allegiance.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) It takes individuals out of a state of isolation and gives them a chance to participate in the common endeavour.

    A lone individual is weak before a powerful State. Voluntary associations act as a buffer by bringing individuals together, so they are no longer isolated and can act jointly, which is what option (c) says. Option (a) overstates the point by claiming the State cannot enforce its will; (b) describes the internal purpose of an association, not its buffer role; and (d) about multiple loyalties does not explain the buffer idea.

  64. Consider the following statements: I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150% can have its number of factors unchanged. Which of the statements given above is/are correct?

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Both I and II

    Increasing by 50% multiplies the number by 3/2; increasing by 150% multiplies it by 5/2. Take N = 2, which has 2 factors. 2 x 3/2 = 3 and 2 x 5/2 = 5 are both primes with 2 factors each. So such numbers exist in both cases and both statements are correct.

  65. There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?

    1. 20 km
    2. 25 km
    3. 31 km
    4. 37 km
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) 31 km

    Put A at (0, 0). Then B = (0, 6), C = (10, 0), D = (10, -6), E = (5, -6), F = (-9, 6) and G = (-9, -6). There are two routes from D to F. D-C-A-B-F: 6 + 10 + 6 + 9 = 31 km. D-E-G-F: 5 + 14 + 12 = 31 km (E to G is from x = 5 to x = -9). Either way the distance is 31 km.

  66. In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?

    1. 1000
    2. 1331
    3. 1728
    4. 2197
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) 1331

    64 = 4^3 becomes 343 = 7^3, and 216 = 6^3 becomes 729 = 9^3: the cube root is increased by 3 and cubed again. 512 = 8^3, so it becomes 11^3 = 1331.

  67. What is the remainder when 9^3 + 9^4 + 9^5 + 9^6 + ... + 9^100 is divided by 6?

    1. 0
    2. 1
    3. 2
    4. 3
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) 0

    Every power of 9 is odd and divisible by 3, so each leaves remainder 3 when divided by 6. There are 100 - 3 + 1 = 98 terms, so the sum leaves the same remainder as 98 x 3 = 294, and 294 = 6 x 49. The remainder is 0.

  68. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: What is the smallest 1-digit number having exactly 4 distinct factors? Statement I: 2 is one of the factors. Statement II: 3 is one of the factors. Which one of the following is correct in respect of the above Question and the Statements?

    1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
    2. The Question can be answered by using either Statement alone.
    3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
    4. The Question can be answered even without using any of the Statements.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) The Question can be answered even without using any of the Statements.

    Among 1 to 9, only 6 (1, 2, 3, 6) and 8 (1, 2, 4, 8) have exactly 4 factors. The smallest is 6. This is found directly, so the statements are not needed.

  69. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Let P, Q, R, S be distinct non-zero digits. If PP x PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to? Statement I: R = 1. Statement II: S = 2. Which one of the following is correct in respect of the above Question and the Statements?

    1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
    2. The Question can be answered by using either Statement alone.
    3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
    4. The Question can be answered even without using any of the Statements.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) The Question can be answered even without using any of the Statements.

    For P = 1 or 2 the product is at most 11 x 14 = 154 or 22 x 24 = 528, not a 4-digit number. So P = 3, and Q can be 1, 2 or 4 (distinct from P). 33 x 31 = 1023 and 33 x 32 = 1056 are not of the form RRSS, but 33 x 34 = 1122 is. So Q = 4 from the question alone; the statements are not needed.

  70. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: How is Q related to P? Statement I: P has two sisters, R and S. Statement II: R's father is the brother of Q. Which one of the following is correct in respect of the above Question and the Statements?

    1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
    2. The Question can be answered by using either Statement alone.
    3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
    4. The Question cannot be answered even using any of the Statements.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) The Question cannot be answered even using any of the Statements.

    Statement I alone says nothing about Q, and Statement II alone says nothing about P. Together, R's father is also P's father, and Q is his sibling. But Q's gender is not known, so Q could be P's paternal uncle or paternal aunt. The exact relation cannot be fixed even with both statements.

  71. A single number for inflation is an aggregate across different commodities and services - the price rise differs for different items of consumption. So, the single number is arrived at by assigning weights to different commodities and services. For WPI, the weights in production are used; for CPI, the consumption basket is used. But people are not homogeneous. The consumption basket is vastly different for the poor, the middle classes, and the rich. Hence, the CPI is different for each of these classes and a composite index requires averaging the baskets.

    Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage?

    1. We must use WPI exclusively in measuring price rise and CPI should be done away with.
    2. The present calculation of inflation rate does not correctly measure price rise of individual item/commodity.
    3. Inflation data under-presents services in the consumption basket.
    4. Knowledge of inflation rate is not really of any use to anybody in the country.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) The present calculation of inflation rate does not correctly measure price rise of individual item/commodity.

    The passage explains that a single inflation figure is a weighted average: prices of different items rise by different amounts, and the composite CPI even averages the baskets of different classes. So the headline number cannot show the price rise of any particular item, option (b). The passage does not recommend dropping CPI (a), does not say services are under-represented (c), and does not say inflation data is useless (d).

  72. Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of globalizing behaviour; trust itself emerges as a super-commodity in the social market and defines the characteristics of goods and services in a global market. Trusting conduct also means holding others in good esteem, and an optimism that they are, or will be, competent in certain respects.

    Which one of the following statements best reflects the crux of the passage?

    1. Trustworthiness cannot be expected in entrepreneurship.
    2. Trustworthy people are the most vulnerable people.
    3. No economic activity is possible without being exposed to betrayal.
    4. Trust is important though it entails risk.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Trust is important though it entails risk.

    The passage defines trust as being vulnerable and willing to risk betrayal, yet calls it the essence of globalizing behaviour and a super-commodity in the market. So trust is valuable even though it involves risk, option (d). Option (b) confuses those who trust with those who are trustworthy, (a) is not stated, and (c) overgeneralises from entrepreneurship to all economic activity.

  73. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: In a football match, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does team P win the match? Statement I: Team P scored 4 goals in the last 10 minutes. Statement II: Team Q scored a total of 4 goals in the match. Which one of the following is correct in respect of the above Question and the Statements?

    1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
    2. The Question can be answered by using either Statement alone.
    3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
    4. The Question cannot be answered even using any of the Statements.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) The Question cannot be answered even using any of the Statements.

    Statement I alone fails because Q may also have scored in the last 10 minutes. Statement II alone says nothing about P. Together: if Q had g goals with 10 minutes left, P had g - 3, so g is at least 3, and P finishes with g + 1 against Q's 4. If g = 3 (P 0-3 down, Q scores no more), the match ends 4-4, a draw; if g = 4, P wins 5-4. Both cases fit the data, so the question cannot be answered.

  74. A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Is (p + q)^2 - 4pq, where p, q are natural numbers, positive? Statement I: p < q. Statement II: p > q. Which one of the following is correct in respect of the above Question and the Statements?

    1. The Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
    2. The Question can be answered by using either Statement alone.
    3. The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
    4. The Question can be answered even without using any of the Statements.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (b) The Question can be answered by using either Statement alone.

    (p + q)^2 - 4pq = (p - q)^2, which is positive whenever p ≠ q and zero when p = q. Without the statements we cannot tell. Statement I (p < q) alone shows p ≠ q, so the answer is yes; Statement II (p > q) alone also shows p ≠ q. Either statement alone is enough.

  75. In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z. Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z Which one of the following is correct?

    1. Value-I < Value-II < Value-III
    2. Value-III < Value-II < Value-I
    3. Value-I < Value-III < Value-II
    4. Cannot be determined due to insufficient data
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (d) Cannot be determined due to insufficient data

    X : Y = Y : Z means the runs are in geometric progression: Y^2 = XZ. With whole-number runs adding to 37, the only possibility is the set 9, 12, 16 (9 x 16 = 144 = 12^2, and 9 + 12 + 16 = 37). But it can be X = 9, Y = 12, Z = 16 (increasing) or X = 16, Y = 12, Z = 9 (decreasing). Both fit, so the order cannot be determined.

  76. Let p + q = 10, where p, q are integers. Value-I = Maximum value of p x q when p, q are positive integers. Value-II = Maximum value of p x q when p ≥ -6, q ≥ -4. Which one of the following is correct?

    1. Value-I < Value-II
    2. Value-II < Value-I
    3. Value-I = Value-II
    4. Cannot be determined due to insufficient data
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Value-I = Value-II

    For a fixed sum, the product is largest when the two numbers are equal or as close as possible. With p + q = 10, p = q = 5 gives 25, so Value-I = 25. In the second case p can range from -6 to 14, which still includes p = q = 5, and any other choice gives a smaller product (for example 4 x 6 = 24, -6 x 16 = -96). So Value-II = 25 and the two values are equal.

  77. Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ -5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?

    1. Value-I < Value-II
    2. Value-II < Value-I
    3. Value-I = Value-II
    4. Cannot be determined due to insufficient data
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) Value-I = Value-II

    Value-I: the smallest set of 11 consecutive integers starting at -5 is -5, -4, ..., 5, whose average is 0. Value-II: 11 consecutive non-negative integers have the smallest product when 0 is included (0, 1, ..., 10), giving a product of 0. Both values are 0, so they are equal.

  78. The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?

    1. k
    2. k - 1
    3. k + 1
    4. k/2
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) k

    p - k = k - q, so p + q = 2k. Since p + q + r = 3k, r = 3k - 2k = k.

  79. Let x be a real number between 0 and 1. Which of the following statements is/are correct? I. x^2 > x^3. II. x > √x. Select the correct answer using the code given below:

    1. I only
    2. II only
    3. Both I and II
    4. Neither I nor II
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (a) I only

    For 0 < x < 1, higher powers get smaller: x^3 = x^2 x x < x^2, so I is correct. Also √x > x for such x (for example x = 0.25 gives √x = 0.5), so II is wrong.

  80. The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

    1. There is only one such number.
    2. There are only two such numbers.
    3. There can be more than one such number.
    4. No such number exists.
    Answer and explanationउत्तर और व्याख्या

    Answer:उत्तर: (c) There can be more than one such number.

    Take examples. Between 1 and 11 lie 5 and 10, two multiples of 5. Between 5 and 15 (both multiples of 5) only 10 lies strictly between them. So the count can be one or two; neither 'only one' nor 'only two' is always true, and there is always at least one. The best description is that there can be more than one such number.

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