Passage: 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?
- Conservation of biodiversity is not an issue to be worried about when some people depend on ecosystems for their livelihoods.
- Commercial exploitation of forests goes against the fundamental rights of the people dependent on forests for food and shelter.
- Sustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.
- Commercial exploitation of ecosystems should be completely stopped.
Explanation: The passage stresses the conflict between conservation, livelihood, and commercial exploitation, emphasizing the mutual exacerbation of ecosystem degradation and livelihood pressures. It does not advocate for a total ban, nor does it dismiss conservation or frame the issue as fundamental rights.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I contradicts the passage, which explicitly states that in developing countries, commercial exploitation of ecosystems has the potential to boost national income. Statement II is invalid because the passage focuses on internal conflicts within countries and makes no mention of international resource sharing.
Passage: 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?
- Economies of scale is essential for transition to green growth.
- Modern technological progress is intensely linked to path-dependent innovations.
- Countries with large economies are in a better position to adopt green technologies.
- Timing plays a crucial role in the case of green technology development.
Explanation: The author emphasizes that moving early and gradually allows economies time to adjust and reap benefits without disruption, whereas a late transition is costlier. Thus, timing is portrayed as crucial to the green technology transition.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I is invalid as the passage does not mention specific countries like India or public finances, making it an over-extrapolation. Statement II is valid, as generalizing the solar energy case study to other green technologies leading to a smoother transition is a reasonable assumption consistent with the text.
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?
Explanation: The smallest number satisfying this property is 6 (factors 1, 2, 3 and 1+2+3=6). Multiplying this equation by any integer k gives k*6 = k*1 + k*2 + k*3, meaning all multiples of 6 satisfy this condition. The multiples of 6 below 50 are 6, 12, 18, 24, 30, 36, 42, and 48, making a total of 8 numbers.
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)?
Explanation: The condition p - q = q - r simplifies to 2q = p + r, meaning q is the average of p and r. The prime numbers under 20 are 2, 3, 5, 7, 11, 13, 17, 19. The valid triplets forming an arithmetic progression are (3, 5, 7), (3, 7, 11), (5, 11, 17), and (7, 13, 19). Their respective sums are 15, 21, 33, and 39. Thus, there are 4 distinct sums.
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)?
- None
- One
- Three
- More than three
Explanation: Assuming p <= q <= r, since 1/p + 1/q + 1/r = 1, p must be 2 or 3. Systematic testing yields exactly three valid unordered triplets for (p, q, r): (2, 3, 6), (2, 4, 4), and (3, 3, 3). The sums for these triplets are 11, 10, and 9 respectively. Therefore, there are exactly three distinct sum values.
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?
- 72
- 144
- 216
- Cannot be determined
Explanation: Team Y tied in 18 overs (10% less than 20), making their run rate R = N/18. If their rate increased by 50%, the new rate would be 1.5 * (N/18). Multiplying this by 12 overs gives 12 * 1.5 * N/18 = 18 * N/18 = N. This results in the identity N = N, meaning the data is consistent but insufficient to solve for a unique value of N.
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?
- p(10^4 - k^2)^2 = q * 10^8
- p(10^4 - k^2)^2 = q * 10^4
- p(10^4 - k^2) = q * 10^4
- p(10^4 - k^2) = q * 10^8
Explanation: An increase followed by a decrease of k% changes the price by a factor of (1 - k^2/10000). Repeating this twice yields q = p * (1 - k^2/10000)^2. This simplifies to q = p * ((10000 - k^2) / 10000)^2 = p * (10^4 - k^2)^2 / 10^8. Rearranging gives q * 10^8 = p * (10^4 - k^2)^2.
Passage: 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?
- The mitigation and adaptation strategies to address/tackle the climate change is essentially the responsibility of each State.
- India is too diverse to implement any effective strategy or programme to address/tackle the climate change.
- It is basically the responsibility of the Union Government to implement the climate action plans and ensure net zero emissions.
- India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.
Explanation: The passage emphasizes that Indian states face unique geographic and climatic risks, as well as unique resource opportunities. The most pragmatic message is that mitigation and adaptation strategies must be formulated at the state or regional level to address these unique characteristics effectively.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I is valid because the passage links wind power harnessing (green energy) with reducing emissions and developing sustainable goals. Statement II is invalid because the passage notes coastal and mountainous regions face 'distinctive' challenges, but never claims these effects are 'much more severe' than in other regions.
Passage: 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?
- India's political executive should be aware that poverty and social inequality and the consequent sense of insecurity is the main social problem.
- In India, poverty is the primary reason for social inequality and insecurity.
- Poverty and social inequality are so intricately linked that they pose an unmanageable crisis for India.
- Insecurity, more than poverty, is the main economic issue that Government policies must address.
Explanation: The passage explicitly states that 'insecurity, more than poverty, is the most acutely felt economic problem.' It details how insecurity affects even those above the poverty line and notes that government policies are intended to mitigate these insecurities, directly aligning with this option.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I is valid because the passage explicitly states that people 'just over the poverty line are subject to multiple economic insecurities.' Statement II is invalid because the passage does not establish a causal link between poverty eradication and achieving complete peace and social equality.
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:
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: To minimize cuts for N=60 pieces, the dimensions n1*n2*n3 must be as close as possible. Factors of 60 closest to each other are 3, 4, and 5. The number of cuts is (3-1) + (4-1) + (5-1) = 2 + 3 + 4 = 9, so statement I is correct. Inner unpainted pieces are calculated as (n1-2)*(n2-2)*(n3-2) = (3-2)*(4-2)*(5-2) = 1*2*3 = 6. Statement II is also correct.
If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?
Explanation: The * operator represents finding the hypotenuse of a right triangle given its two legs. It follows the formula a * b = sqrt(a^2 + b^2). For 7 and 24, sqrt(49+576) = 25. For 12 and 16, sqrt(144+256) = 20. Applying this to 16 and 63: sqrt(16^2 + 63^2) = sqrt(256 + 3969) = sqrt(4225) = 65.
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 Rs 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?
- 180 km
- 200 km
- 220 km
- 240 km
Explanation: Original fuel needed = 2200 / 16 = 137.5 litres. Original expenditure = 137.5 * 90 = 12,375. The new price is 90 + 10% = 99 per litre. To maintain the 12,375 budget, he can afford 12,375 / 99 = 125 litres. With a mileage of 16 km/litre, he can travel 125 * 16 = 2000 km. The reduction in travel is 2200 - 2000 = 200 km.
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?
Explanation: The difference between the divisors and their respective remainders is constant: 3-1=2, 5-3=2, 6-4=2, 9-7=2. Thus, N+2 must be a multiple of the LCM of (3, 5, 6, 9), which is 90. So, N = 90k - 2. To find the smallest 4-digit number, set 90k - 2 >= 1000, so 90k >= 1002, or k >= 11.13. The smallest integer k is 12. Substituting k=12 yields N = 90(12) - 2 = 1080 - 2 = 1078.
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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: For Statement I, the relationships C < D and D > E do not firmly establish the relationship between B and E, as both could be smaller than D but unknown relative to each other. For Statement II, S = T <= U = V simplifies to S <= V. This means S could be equal to V, so it is not strictly less than V. Both statements are incorrect.
What is the unit digit in the multiplication of 1 x 3 x 5 x 7 x 9 x ... x 999?
Explanation: The product consists entirely of odd numbers and includes the number 5. When 5 is multiplied by any odd number, the unit digit of the product is always 5. Since there are no even numbers in the sequence to make the unit digit 0, the overall unit digit must be 5.
Passage: 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?
- The benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.
- For India, the green revolution was not as useful as it was expected to be.
- India lagged behind other countries in adapting mechanized modern farming.
- Rural-to-urban migration resulted in the stagnant agriculture Sector.
Explanation: The passage directly contrasts the stagnation of the agricultural sector with the consistent high growth of the non-agricultural economy after the 1980s. This implies that economic growth and reforms have bypassed or translated much more slowly into the agricultural sector compared to others.
Passage: 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 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: The passage is purely descriptive regarding the stagnation of agriculture and the divergence from the non-agricultural economy. It does not suggest or imply any specific policy prescriptions or methods, such as corporate farming or free insurance, to bridge this gap. Thus, both assumptions are invalid extensions of the text.
Passage: 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?
- We need to free the handloom industry from the limited narrative linked to preserving cultural heritage.
- Continued State support to the handloom industry ensures the preservation of some of our glorious art forms and old traditions.
- Household units of the handloom sector should be modernized and made an economically viable organized industry.
- Handloom products need to be converted to machine-made designer products so as to make them more popular.
Explanation: The author criticizes the current practice of promoting handloom solely through a 'traditional' and 'linear' narrative, stating that this approach causes large sections of the population to ignore it. The logical message is that this limited cultural narrative is harmful and needs to change for the sector to thrive.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Statement I is invalid as the passage critiques the narrative driving state support, not the existence of state support itself. Statement II is invalid because the passage notes that the 'traditional industry' narrative is what makes people ignore handlooms, not that the products themselves are inherently unappealing.
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
Explanation: Numbers not divisible by 9 are inherently covered by eliminating those not divisible by 3. By using the Principle of Inclusion-Exclusion for the primes 2, 3, 5, and 7 within the range 1 to 100, the count of numbers divisible by at least one of these primes is 78. Subtracting this from 100 leaves 22 numbers not divisible by any of them.
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)?
- 6
- 15/2
- -15/2
- None of the above
Explanation: The maximum value of (x + y) occurs when x=8 and y=7, which is 15. The minimum value of (x - y) occurs when x is at its minimum (4) and y is at its maximum (7), which is 4 - 7 = -3. The ratio is 15 / -3 = -5. Since -5 is not among the specific numeric options, the answer is 'None of the above'.
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?
Explanation: Since p^2 + k < 30, p can only be 2, 3, or 5. For p=2, p^2=4; valid k values making 4+k a prime < 30 are 3, 7, 13, 19. For p=3, p^2=9; valid k is 2. For p=5, p^2=25; no prime k makes 25+k a prime < 30. The unique prime values of k are 2, 3, 7, 13, and 19. Total is 5 values.
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?
Explanation: The prime factorization of 1001 is 7 x 11 x 13. We need triplets with an HCF of 1 and LCM of 1001. Enumerating valid subsets where the primes are distributed across three numbers without sharing all common factors across all three yields sets like {7, 11, 13}, {1, 77, 91}, {7, 11, 91}, etc. Systematically, there are at least 14 valid sets, which is more than 8.
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)?
Explanation: Using place values, 100P + 10Q + R - (10P + S) = 110P + T. Simplifying: -20P + 10Q + R - S - T = 0. Given Q=3, 30 = 20P + S + T - R, or R = 20P + S + T - 30. P must be 1 because 20P+S+T must be between 31 and 39. So R = S + T - 10. T < 6 and T must be distinct from 1 and 3, so T is 2, 4, or 5. Testing these yields three valid (R, S) pairs: (2, 8), (2, 7), and (4, 9).
Consider the sequence AB_CC_A_BCCC_BBC_C that follows certain pattern. Which one of the following completes the sequence?
- B, C, B, C, A
- A, C, B, C, A
- B, C, B, A, C
- C, B, B, A, C
Explanation: The total number of characters including blanks is 18. This suggests a repeating block of 6 characters. The pattern repeats 'ABBCCC' three times. Filling the blanks in AB_CC_ / A_BCCC / _BBC_C with ABBCCC yields the missing letters B, C, B, A, C.
Passage: 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?
- India does not have enough resources for promoting quality education in its universities.
- The institutions of higher learning in the country should not be under the control of the Government.
- Classroom approach to higher education should be done away with.
- Classroom needs to be reimagined and teaching needs to be re-invented.
Explanation: The passage critiques the current exam-centric focus and advocates for shifting toward critical thinking, interdisciplinary learning, and 'how to think.' It explicitly states 'Teaching has to be re-invented' to meet modern demands, which directly aligns with reimagining the classroom and teaching methodologies.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is valid as the passage emphasizes that higher education must adapt to new demands of society and the future of work, requiring pedagogical innovation. Assumption II is invalid because the passage critiques the methodology and purpose of higher education but makes no mention of funding shortages or financial constraints.
Passage: 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?
- There is an urgent need for a public policy to promote the consumption of cereal-based foods in wealthier societies.
- Animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.
- Plant-based protein should replace the animal-based protein in our daily diets.
- Inequality in food production and consumption is inevitable in any fast changing society.
Explanation: The passage highlights the inefficiency of converting plant-based calories into animal-based food, noting that only 16% of calories are recovered from chickens and 5-7% for large animals. This clearly makes the comparative inefficiency of animal-based food systems the crux of the passage.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is invalid because the passage critiques the inefficiency of converting plant-based food to animal products but does not address the role or responsibilities of food manufacturing industries. Assumption II is valid as the passage explicitly states that wealthier societies lose calories through indirect utilization, such as feeding grains to animals.
What is the maximum value of n such that 7 * 343 * 385 * 1000 * 2401 * 77777 is divisible by 35^n?
Explanation: To find the maximum value of n, we need to find the exponents of the prime factors 5 and 7 in the product. Factorizing the numbers: 343 = 7^3; 385 = 5 * 7 * 11; 1000 = 2^3 * 5^3; 2401 = 7^4; 77777 = 7 * 41 * 271. The total exponent of 5 is 1 + 3 = 4. The total exponent of 7 is 1 + 3 + 1 + 4 + 1 = 10. The minimum of these exponents is 4. Thus, the maximum value of n is 4.
What is X in the sequence 24, X, 12, 18, 36, 90?
Explanation: The sequence follows a multiplicative pattern: 24 * 0.5 = 12; 12 * 1 = 12; 12 * 1.5 = 18; 18 * 2 = 36; 36 * 2.5 = 90. Therefore, X is 12.
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.?
Explanation: Since P and Q move in opposite directions, their relative speed is 5 + 3 = 8 rounds per hour. This means they cross each other 8 times per hour. The time interval from 5:20 a.m. to 7:00 a.m. is 100 minutes, or 5/3 hours. The number of meetings is the relative speed multiplied by the time: 8 * (5/3) = 40/3 = 13.33. They cross each other exactly 13 full times.
If P = +, Q = -, R = x, S = ÷, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20:
Explanation: Substituting the symbols from option QRPS, the expression becomes 60 - 15 x 3 + 20 ÷ 4. Using the order of operations, we first solve multiplication and division: 15 x 3 = 45 and 20 ÷ 4 = 5. Then we perform subtraction and addition: 60 - 45 + 5 = 20. This satisfies the equation, so the correct sequence is QRPS.
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?
Explanation: Convert the walking speeds to m/s: X's speed = 3 * 5/18 = 5/6 m/s, and Y's speed = 4 * 5/18 = 10/9 m/s. Let the tram's speed be v m/s and its length be L meters. The relative speed formula gives L = (v - 5/6) * 8 and L = (v - 10/9) * 9. Equating the two expressions gives 8v - 40/6 = 9v - 10, which simplifies to v = 10/3 m/s. Substituting v back to find L gives L = (10/3 - 10/9) * 9 = 20 meters.
If N^2 = 12345678987654321, then how many digits does the number N have?
Explanation: The number 12345678987654321 is a palindromic number that results from squaring a number made entirely of ones (e.g., 11^2 = 121, 111^2 = 12321). Following this pattern, 111111111^2 = 12345678987654321. The number N is 111111111, which has exactly 9 digits.
Passage: 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?
- Moving to net-zero carbon is possible only by the reduction in household emissions.
- Low-carbon behaviour in people can be brought about by incentivising them.
- Cheaper goods and services can be made available to people by using low-carbon technologies.
- Manufacturing industries that use low-carbon technologies should be provided with subsidies.
Explanation: The passage emphasizes that individual behavioral changes alone are insufficient to achieve emissions reductions. Success depends on systemic support through supply-side investments by governments and companies to make low-carbon technologies affordable and accessible, thereby incentivizing low-carbon behavior.
Passage: 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 Government and Companies.
Which of the above assumptions is/are valid?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is valid because the passage explicitly links supply-side investments to incentivizing behavioral changes. Assumption II is invalid because the passage does not claim people are inherently incapable of adapting low-carbon behavior, only that achieving the necessary scale requires systemic support.
Passage: 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?
- Green economy is not possible without reusing critical minerals.
- Every sector of economy should adapt the reuse of material resources immediately.
- Circular economy can be beneficial for sustainable growth.
- Circular use of material resources is the only option for some industries for their survival.
Explanation: The passage outlines the unsustainable consumption of raw materials and the logistical challenges of sourcing critical minerals. The proposed solution of recovering materials from end-of-life products aligns with a circular economy, presenting it as a practical and beneficial approach to resource scarcity.
Passage: 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is invalid because the passage focuses on the recycling process of batteries, not the automobile factories' overall operations. Assumption II is valid as the passage implies that reusing scarce materials mitigates supply chain risks, supporting the idea that circular practices sustain economic activities.
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?
- 8 minutes
- 10 minutes
- 12 minutes
- 16 minutes
Explanation: Rate of 20 pipes of X = 5% per minute. Rate of 10 pipes of Y = 6.25% per minute. Rate of 16 pipes of Z = 2.5% per minute (emptying). Using half of X gives a filling rate of 2.5%. Using half of Y gives a filling rate of 3.125%. All 16 pipes of Z give an emptying rate of 2.5%. The net rate = 2.5% + 3.125% - 2.5% = 3.125% per minute. Time to fill 50% = 50 / 3.125 = 16 minutes.
If n is a natural number, then what is the number of distinct remainders of (1^n + 2^n) when divided by 4?
Explanation: For n=1, 1^1 + 2^1 = 3, which gives a remainder of 3. For n=2, 1^2 + 2^2 = 5, giving a remainder of 1. For n=3, 1^3 + 2^3 = 9, giving a remainder of 1. For any n >= 2, 2^n is perfectly divisible by 4, leaving a remainder of 0, while 1^n always leaves a remainder of 1. Thus, the expression leaves a remainder of 3 for n=1, and 1 for all n >= 2. There are exactly 2 distinct remainders.
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
Explanation: Factorize 481, which is 13 * 37. P is a 3-digit number with identical digits, so P = 111 * Q, where Q is a digit from 1 to 9. Since 111 = 3 * 37, P = 3 * 37 * Q. The common factors between P and 481 are found in their prime factorizations. The only common prime factor is 37. Since Q is a single digit, it cannot be a multiple of 13. Thus, the HCF is 37.
What is the 489th digit in the number 123456789101112...?
Explanation: The 1-digit numbers (1-9) contribute 9 digits. The 2-digit numbers (10-99) are 90 numbers contributing 180 digits. Total so far is 189 digits. The remaining digits needed to reach the 489th digit are 489 - 189 = 300 digits. Since 3-digit numbers contribute 3 digits each, we need 300 / 3 = 100 3-digit numbers. Starting from 100, the 100th 3-digit number is 199. The 489th digit is the last digit of 199, which is 9.
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?
- P
- Q
- R
- Cannot be concluded
Explanation: Assume innocent people tell the truth and the guilty person lies entirely. If Q were guilty, Q's statement 'R did not steal' would be true, violating the rule that the guilty person lies entirely. If R were guilty, Q's statement 'R did not steal' would be a lie, but Q is innocent and must tell the truth. If P is guilty, P's statements 'I did not steal' and 'Q stole it' are both lies. In this scenario, Q and R are innocent, and their statements are true. This proves P is the thief.
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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Total points awarded are 6, matching the maximum for 3 matches. P got 3 points (1 win, 1 draw). Q got 2 points (2 draws). R got 1 point (1 draw, 1 loss). The matches are: P vs R (P wins), P vs Q (Draw), Q vs R (Draw). Each team scores 1 goal total. P wins against R, so P must score against R (1-0). Q draws both matches, and since Q scores 1 goal total, one draw must be 1-1 and the other 0-0. P's only goal is against R, so P vs Q is 0-0. Thus, Q vs R must be 1-1. R scores 1 goal against Q. Both statements are correct.
Passage: 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 bot 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?
- Global climate change adversely affects the productivity of crops.
- Our total dependence on genetically honed crops entails possible food insecurity.
- Our food security should not depend on agricultural productivity alone.
- Genetically honed crops should be replaced with their wild varieties in our present cultivation practices.
Explanation: The passage warns that selective breeding has removed genetic variations in crops, making them highly vulnerable to new diseases exacerbated by climate change. The central idea is that this dependence on genetically honed crops poses a significant risk to food security.
Passage: 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 bot 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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is valid because the passage states climate change will make plant infections 'more common in all climatic zones,' implying migration. Assumption II is valid because the passage attributes vulnerability to the loss of genetic variation, implying that accessing such variation from wild relatives would strengthen food security.
Passage: "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?
- Without opposition parties, the administration in a democracy gets to become more responsible.
- Democracy needs to have revolutionaries in opposition to keep the government alert.
- Rulers in a democracy need the support of opposition for their political survival.
- In a democracy, the opposition is indispensable for the balance of political power and good governance.
Explanation: The passage argues that opponents keep a statesman on the path of reason and good sense and that a balance of power prevents arbitrary administration. This highlights the indispensable role of the opposition in maintaining balance and good governance.
Passage: "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?
- I only
- II only
- Both I and II
- Neither I nor II
Explanation: Assumption I is invalid because the need for an opposition is presented as an inherent necessity for good governance, not contingent on the indifference of the leader. Assumption II is invalid because the passage advocates for a balanced opposition, explicitly warning against an opposition that is revolutionary and irreconcilable.
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:
- Only two
- Only three
- Only Four
- Only Five
Explanation: P, Q, and R are siblings. S is their mother, and T is their father, making S and T a couple (I is true). T is Q's father (III is true). S is P's mother (IV is true). Since P is a brother, P is male, making him S's son (VI is true). The genders of Q and R are unknown, so we cannot definitely say Q is T's son (II) or R is T's daughter (V). Thus, exactly four statements are definitely true.
If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?
- 399000
- 420000
- 440000
- 630000
Explanation: The code is generated by multiplying the alphabetical position values of the letters. For NO: 14 * 15 = 210. For NOT: 14 * 15 * 20 = 4200. For NOTE: 14 * 15 * 20 * 5 = 21000. For NOTES, we multiply the value of 'S' (19) by the code for NOTE: 21000 * 19 = 399000.
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded ?
Explanation: This is a direct letter-to-digit substitution. From FRANCE (654321): F=6, R=5, A=4, N=3, C=2, E=1. From GERMANY (9158437): G=9, E=1, R=5, M=8, A=4, N=3, Y=7. The word YEMEN requires the codes for Y (7), E (1), M (8), E (1), N (3). Thus, YEMEN is coded as 71813.
The 5-digit number PQRST (all distinct digits) is such that T is not equal to 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?
Explanation: We have equations: P=3T, S=Q+4, Q=R+3. Substituting Q, S=R+7. Since R, Q, S are single digits, R can only be 0, 1, or 2, yielding triplets (R,Q,S): (0,3,7), (1,4,8), (2,5,9). Since P=3T, valid (T,P) pairs are (1,3), (2,6), (3,9). We combine these ensuring all 5 digits are distinct. Pair (1,3) + Triplet (2,5,9) -> 35291. Pair (2,6) + Triplet (0,3,7) -> 63072. Pair (2,6) + Triplet (1,4,8) -> 64182. Pair (3,9) + Triplet (1,4,8) -> 94183. This gives exactly 4 valid combinations.
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?
Explanation: X completes the whole work in 18 days. Y completes it in 24 days. Z completes it in 16 days. Their daily work rates are 1/18, 1/24, and 1/16. Working together for n days, they complete n(1/18 + 1/24 + 1/16) of the work. Y finishes the rest in 26/3 days, doing (26/3)*(1/24) = 13/36 of the work. The remaining work is 1 - 13/36 = 23/36. Setting n(1/18 + 1/24 + 1/16) = 23/36, we get n(23/144) = 23/36. Solving for n gives n = 4.
What is X in the sequence 1, 3, 6, 11, 18, X, 42?
Explanation: The differences between consecutive terms are: 3-1=2, 6-3=3, 11-6=5, 18-11=7. The differences (2, 3, 5, 7) form a sequence of consecutive prime numbers. The next prime number is 11. Adding 11 to 18 gives X = 29. The next prime is 13, and 29 + 13 = 42, which confirms the pattern.
Passage: 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?
- Corporate capitalism is important for economics growth of a state and also for democracy
- Corporate capitalism is imperative for a modern state to achieve its political objectives.
- No state can ensure its economic survival for long without the role of corporate capitalism.
- Corporate capitalism and democracy have mutual dependence for their continued existence.
Explanation: The passage explicitly states that no democracy has grown economically without corporate capitalism and details how it modernizes the economy, generates jobs, and provides state revenues for welfare. This clearly establishes its importance for both economic growth and the functioning of a democracy.