Directions for the following 5 (five) item:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 1
In India, the segregation of municipal waste at source is rare. Recycling is mostly with the informal sector. More than three-fourths of the municipal budget goes into collection and transportation, which leaves very little for processing/resource recovery and disposal. Where does waste-to-energy fit into all this? Ideally it fits in the chain after segregation (between wet waste and rest), collection, recycling, and before getting to the landfill. Which technology is most appropriate in converting waste to energy depends on what is in the waste (that is biodegradable versus non-biodegradable component) and its calorific value. The biodegradable component of India's municipal solid waste is a little over 50 per cent, and biomethanation offers a major solution for processing this.
Based on the above passage, the following assumptions have been made:
1. Collection, processing and segregation of municipal waste should be with government agencies.
2. Resource recovery and recycling require technological inputs that can be best handled by private sector enterprises.
Which of the assumptions given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is incorrect. The passage notes that recycling is mostly handled by the informal sector and that municipal budgets are heavily tilted toward collection and transportation, but it never states or implies that government agencies should exclusively or ideally handle collection, processing, and segregation. Applying the negation test, even if government agencies were not the ones to handle these tasks, the passage's core argument about waste-to-energy and segregation would remain intact. Statement 2 is also incorrect. The passage does not compare the capabilities of the private sector against the public sector for resource recovery and recycling, nor does it suggest that technological inputs are best handled by private enterprises. Negating this statement likewise does not undermine the passage's premises. Therefore, neither statement is a necessary assumption.
Directions for the following 5 (five) item:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 1
In India, the segregation of municipal waste at source is rare. Recycling is mostly with the informal sector. More than three-fourths of the municipal budget goes into collection and transportation, which leaves very little for processing/resource recovery and disposal. Where does waste-to-energy fit into all this? Ideally it fits in the chain after segregation (between wet waste and rest), collection, recycling, and before getting to the landfill. Which technology is most appropriate in converting waste to energy depends on what is in the waste (that is biodegradable versus non-biodegradable component) and its calorific value. The biodegradable component of India's municipal solid waste is a little over 50 per cent, and biomethanation offers a major solution for processing this.
Which one of the following statements best reflects the crux of the passage?
- Generation of energy from municipal solid waste is inexpensive.
- Biomethanation is the most ideal way of generating energy from municipal solid waste.
- Segregation of municipal solid waste is the first step in ensuring the success of waste-to- energy plants.
- The biodegradable component of India's municipal solid waste is not adequate to provide energy from waste efficiently/effectively.
Explanation: The claim that energy generation from municipal waste is inexpensive is incorrect because the passage does not discuss costs or expenses at all. The claim that biomethanation is the most ideal method is also incorrect; the passage explicitly calls it a major solution, but using the superlative most ideal overstates the author's position. The statement that segregation is the first step in ensuring the success of waste-to-energy plants correctly captures the crux: the passage opens by highlighting that segregation at source is rare in India, then describes the waste-to-energy chain as occurring after segregation, and finally discusses biomethanation, which itself requires prior segregation. Thus, segregation is the foundational step that ties the entire passage together. The statement that the biodegradable component is inadequate is incorrect because the passage does not suggest inadequacy; rather, it notes that the biodegradable share is over 50 percent and that biomethanation is a major solution for processing it.
Directions for the following 5 (five) item:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 2
There is a claim that organic farming is inherently safer and healthier. The reality is that because the organic farming industry is still young and not well-regulated in India, farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well. For example, since organic fertilizers are difficult to obtain on a large scale in India, farmers often use farmyard manure, which may contain toxic chemicals and heavy metals. Certain plant sprays, such as Datura flower and leaf spray, have an element called atropine. If it is not applied in the right dose, it can act on the nervous system of the consumer. Unfortunately, how much and when to use it are not well-researched or regulated issues.
Based on the above passage, the following assumptions have been made:
1. Organic farming is inherently unsafe for both farmers and consumers.
2. Farmers and consumers need to be educated about eco-friendly food.
Which of the assumptions given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is incorrect. The passage challenges the claim that organic farming is inherently safer by pointing out that the industry is young and poorly regulated, leading to confusion and harmful misuse. However, it does not conclude that organic farming is inherently unsafe; it merely argues that safety is not guaranteed under current conditions. Negating this statement does not undermine the passage's core argument. Statement 2 is correct. The passage explicitly notes that farmers and consumers are confused about which products are best for them and that they sometimes use products in harmful ways. This confusion and lack of clarity directly support the need for education to ensure safe and effective practices.
Directions for the following 5 (five) item:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 2
There is a claim that organic farming is inherently safer and healthier. The reality is that because the organic farming industry is still young and not well-regulated in India, farmers and consumers, alike, are not only confused about what products are best for them, but sometimes use products in ways that could harm them as well. For example, since organic fertilizers are difficult to obtain on a large scale in India, farmers often use farmyard manure, which may contain toxic chemicals and heavy metals. Certain plant sprays, such as Datura flower and leaf spray, have an element called atropine. If it is not applied in the right dose, it can act on the nervous system of the consumer. Unfortunately, how much and when to use it are not well-researched or regulated issues.
Which one of the following statements best reflects the most logical, rational and practical message conveyed by the author of the passage ?
- In India, organic farming should not be promoted as a substitute for conventional farming.
- There are no safe organic alternatives to chemical fertilizers.
- In India, farmers need to be guided and helped to make their organic farming sustainable.
- The aim of organic farming should not be to generate huge profits as there is still no global market for its products.
Explanation: The statement that organic farming should not be promoted as a substitute for conventional farming is incorrect because the passage does not compare organic and conventional farming or advocate for one over the other. The claim that there are no safe organic alternatives to chemical fertilizers is an extreme and unsupported view; the passage only discusses specific issues with certain organic practices like datura spray and farmyard manure, not a blanket absence of safe alternatives. The statement that farmers need guidance to make organic farming sustainable is correct: the passage emphasizes the industry's youth, lack of regulation, and the confusion among farmers and consumers that leads to harmful misuse, all of which imply a pressing need for guidance and assistance. The statement about avoiding huge profits due to the absence of a global market is outside the passage's scope, as economic impact and profitability are not discussed.
Directions for the following 5 (five) item:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 3
Food consumption patterns have changed substantially in India over the past few decades. This has resulted in the disappearance of many nutritious foods such as millets. While food grain production has increased over five times since independence, it has not sufficiently addressed the issue of malnutrition. For long, the agriculture sector focused on increasing food production particularly staples, which led to lower production and consumption of indigenous traditional corps/grains, fruits and other vegetables, impacting food and nutrition security in the process. Further, intensive, monoculture agriculture practices can perpetuate the food and nutrition security problem by degrading the quality of land, water and food derived through them.
Based on the above passage, the following assumptions have been made :
1. To implement the Sustainable Development Goals and to achieve zero-hunger goal, monoculture agriculture practices are inevitable even if they do not address malnutrition.
2. Dependence on a few crops has negative consequences for human health and the ecosystem.
3. Government policies regarding food planning need to incorporate nutritional security.
4. For the present monoculture agriculture practices, farmers receive subsidies in various ways and government offers remunerative prices for grains and therefore they do not tend to consider crop diversity.
Which of the above assumptions are valid ?
- 1, 2 and 4 only
- 2 and 3 only
- 3 and 4 only
- 1, 2, 3 and 4
Explanation: Statement 1 is invalid because the passage does not mention the Sustainable Development Goals, the zero-hunger goal, or the inevitability of monoculture. Statement 2 is valid: the passage links the focus on staple crops and monoculture practices to the degradation of land, water, and food quality, establishing a clear connection between dependence on a few crops and negative consequences for health and the ecosystem. Statement 3 is valid: the passage highlights that despite massive increases in food grain production, malnutrition persists because nutritious foods like millets have disappeared, implying that government food planning must incorporate nutritional security. Statement 4 is invalid because the passage does not mention subsidies, remunerative prices, or farmers' economic motivations for avoiding crop diversity; negating this statement does not affect the passage's core argument.
A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements :
1. The smallest number n such that any n balls drawn from the box randomly must contain one full group of at least one colour is 175.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
Which of the above statements is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: To determine the minimum number of balls needed to ensure that the drawn balls contain at least one full group of any single colour, we calculate the maximum number of balls that can be drawn without completing any group. By drawing one less than the full count from each colour, we obtain 13 black, 19 blue, 25 green, 27 yellow, 37 red, and 53 white balls, totalling 174. The next ball drawn, regardless of colour, must complete a group, so n = 175. To ensure at least one ball of every colour is present, we consider the worst-case scenario of omitting the colour with the smallest count entirely. Omitting black allows us to draw all 20 blue, 26 green, 28 yellow, 38 red, and 54 white balls, totalling 166. The next ball must be black, thereby guaranteeing at least one ball of each colour, so m = 167.
If 'ZERO' is written as 'CHUR', then how is 'PLAYER' written ?
- SOCAGT
- SODBGT
- SODBHT
- SODBHU
Explanation: Each letter in ZERO is shifted forward by 3 positions in the alphabet: Z becomes C, E becomes H, R becomes U, and O becomes R. Applying the same pattern to PLAYER: P becomes S, L becomes O, A becomes D, Y becomes B, E becomes H, and R becomes U. Therefore, PLAYER is written as SODBHU.
Consider the following statements :
1. A is older than B.
2. C and D are of the same age.
3. E is the youngest.
4. F is younger than D.
5. F is older than A.
How many statements given above are required to determine the oldest person/persons?
- Only two
- Only three
- Only four
- All five
Explanation: From statement 1, we know A is older than B. From statement 5, F is older than A, which places F above both A and B. From statement 4, F is younger than D, and from statement 2, C equals D in age. This establishes that C and D are the oldest, with F below them, and A and B below F. However, without statement 3, we have no information about E's age relative to the others, meaning E could theoretically be older than C and D. Statement 3 confirms that E is the youngest, thereby ruling out E as the oldest and completing the hierarchy. Thus, all five statements are necessary to definitively identify the oldest individuals.
Consider the following including the Question and the Statements:
There are 5 members A, B, C, D, E in a family.
Question : What is the relation of E to B ?
Statement-1 : A and B are a married couple.
Statement-2 : D is the father of C.
Statement-3 : E is D's son.
Statement-4 : A and C are sisters.
Which one of the following is correct in respect of the above Questions and Statements ?
- Statement-1, Statement-2 and Statement-3 are sufficient to answer the Question.
- Statement-1, Statement-3 and Statement-4 are sufficient to answer the Question.
- All four statement together are sufficient to answer the Question.
- All four statements are not sufficient to answer the Question.
Explanation: Statements 1, 2, and 3 are insufficient because they do not establish any link between B and E. Statements 1, 3, and 4 are also insufficient for the same reason. Combining all four statements: from statements 2 and 4, D is the father of A and C, who are sisters. From statement 3, E is D's son, making E the brother of A and C. From statement 1, B is married to A, making B the brother-in-law of A's siblings. Therefore, E is B's brother-in-law. All four statements together are required to establish this relationship.
Choose the group which is different from the others :
- 17, 37, 47, 97
- 31, 41, 53, 67
- 71, 73, 79, 83
- 83, 89, 91, 97
Explanation: In the first group, all four numbers are prime. In the second group, all four numbers are prime. In the third group, all four numbers are prime. In the fourth group, 91 is composite, being equal to 7 multiplied by 13. Therefore, the group containing 83, 89, 91, and 97 is the odd one out.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 1
To tackle the problem of pollution in cities, policy makers think that drastic actions like temporary use of odd-even number scheme for vehicles, closing schools, factories, construction activities, and banning the use of certain type of vehicles are a way forward. Even then the air is not clean. Vehicles more than 15 years old comprise one percent of the total; and taking them off the road will not make any difference. Banning certain fuels and car types arbitrarily is not proper. Diesel engines produce more PM 2.5 and less CO2 than petrol or CNG engines. On the other hand, both diesel and CNG engines produce more NOx than petrol engines. No one has measured the amount of NOx that CNG engines are emitting. Arbitrary bans on vehicles that have passed mandated fitness tests and periodic pollution tests are unfair. What is needed is the scientific and reliable information about the source of pollutants on a continuing basis and the technologies that will work to reduce pollution from them.
Which one of the following statements best reflects the most logical and rational implication conveyed by the passage ?
- Arbitrary curbs on vehicles to reduce pollution are difficult to implement.
- Knee-jerk reactions cannot but an evidence-based approach will be more effective.
- A heavy penalty should be enforced on those driving without periodic pollution tests.
- In the absence of laws to deal with the problem of pollution, the administration tends to make arbitrary decisions.
Explanation: The statement that arbitrary curbs are difficult to implement is incorrect because the author does not discuss implementation challenges or feasibility. The statement that knee-jerk reactions are insufficient and an evidence-based approach will be more effective is correct: the author explicitly criticizes arbitrary bans and temporary drastic measures as improper, emphasizes the lack of scientific measurement for certain pollutants, and concludes by calling for continuous scientific and reliable information about pollution sources. The statement advocating heavy penalties is incorrect because punitive measures are never mentioned. The statement that arbitrary decisions stem from an absence of laws is incorrect because the author does not claim that laws are missing; rather, the criticism is directed at the arbitrary nature of existing or proposed actions.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 2
Good corporate governance structures encourage companies to provide accountability and control. A fundamental reason why corporate governance has moved onto the economic and political agenda worldwide has been the rapid growth in international capital markets. Effective corporate governance enhance access to external financing by firms, leading to greater investment, higher growth and employment. Investors look to place their funds where the standards of disclosure, of timely and accurate financial reporting, and of equal treatment to all stakeholders are met.
Which of the following statements best reflects the logical inference from the passage given above ?
- It is an important agenda of the countries around the world to ensure access to good external financing.
- Good corporate governance improves the credibility of the firms.
- International capital markets ensure that the firms maintain good corporate governance.
- Good corporate governance paves the way for robust supply chains.
Explanation: The statement that ensuring access to external financing is a global agenda is too far-fetched; the passage only implies a connection between governance and financing rather than stating it as an explicit international agenda. The statement that good corporate governance improves credibility is related to the passage's discussion of disclosure and reporting standards, but it merely restates an underlying idea rather than capturing the central inference about the relationship between capital markets and governance. The statement that international capital markets drive firms to maintain good corporate governance is correct: the passage identifies the rapid growth of international capital markets as the fundamental reason governance has become a worldwide concern, and it notes that investors demand high standards of disclosure and equal treatment, which pressures firms to comply. The statement about supply chains is incorrect because the passage does not mention them at all.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 3
Elephants are landscape architects, creating clearings in the forest, preventing overgrowth of certain plant species and allowing space for the regeneration of others, which in turn provide sustenance to others, which in turn provide sustenance to other herbivorous animals. Elephants eat plants, fruits and seeds, propagating the seeds when they defecate in other places as they travel. Elephant dung provides nourishment to plants and animals and acts as a breeding ground for insects. In times of drought, they access water by digging holes which benefits other wildlife.
Which one of the following statements best reflects the most logical and rational inference that can be drawn from the passage?
- The home range of elephants needs to be a vast area of rich biodiversity.
- Elephants are the keystone species and they benefit the biodiversity.
- Rich biodiversity cannot be maintained in the forests without the presence of elephants.
- Elephants are capable of regenerating forests with species as per their requirement.
Explanation: The statement that elephants need a vast home range is beyond the scope of the passage, which does not discuss range size or area requirements. The statement that elephants are keystone species benefiting biodiversity is correct: the passage describes multiple ways elephants support other species and ecosystem processes, including creating clearings, propagating seeds, nourishing plants and animals through dung, and providing water access during droughts, which are defining characteristics of a keystone species. The statement that rich biodiversity cannot be maintained without elephants is too extreme; the passage does not claim that biodiversity is impossible without elephants, only that they significantly contribute to it. The statement that elephants regenerate forests according to their own requirements is incorrect because the passage does not suggest that elephants shape forest composition for their own specific needs.
If 7 ⨁ + 9 ⨁ 10 = 8, 9 ⨁ 11 ⨁ 30 = 5, 11 ⨁ 17 ⨁ 21 = 13, what is the value of 23 ⨁ 4 ⨁ 15 ?
Explanation: The operator represents the sum of the digits of the total of the three numbers. For the first example, 7 plus 9 plus 10 equals 26, and the sum of the digits 2 and 6 is 8. For the second example, 9 plus 11 plus 30 equals 50, and the sum of the digits 5 and 0 is 5. For the third example, 11 plus 17 plus 21 equals 49, and the sum of the digits 4 and 9 is 13. Applying this pattern to 23 plus 4 plus 15 gives 42, and the sum of the digits 4 and 2 is 6.
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible?
Explanation: If 7x plus 96 is divisible by x, then 96 must be divisible by x, because 7x is already divisible by x. Therefore, x must be a positive divisor of 96. The prime factorization of 96 is 2 to the fifth power multiplied by 3. The number of divisors is calculated as (5 plus 1) multiplied by (1 plus 1), which equals 12. The divisors are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.
If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q) (r + s) ?
Explanation: To maximize the product of two sums with a fixed total, the sums should be as close to each other as possible. The four largest distinct single-digit positive numbers are 6, 7, 8, and 9, which sum to 30. Splitting them into two pairs with equal sums gives 6 plus 9 equals 15 and 7 plus 8 equals 15. The product is therefore 15 multiplied by 15, which equals 225. Any other combination, such as 6 plus 8 paired with 7 plus 9, yields a smaller product because the sums are less balanced.
A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13?
Explanation: A number consisting of n repeated 9s can be expressed as 10 to the power n minus 1. Calculating the remainders of successive powers of 10 minus 1 when divided by 13 yields a cyclic pattern with period 6: for n equals 1 the remainder is 9, for n equals 2 it is 8, for n equals 3 it is 11, for n equals 4 it is 2, for n equals 5 it is 3, and for n equals 6 it is 0. Since 99 divided by 6 leaves a remainder of 3, the remainder for 99 nines is the same as that for 3 nines, which is 11.
Each digit of a 9-digit number is 1. It is multiplied by itself. What is the sum of the digits of the resulting number?
Explanation: The square of 111111111 is 12345678987654321. Adding these digits together: 1 plus 2 plus 3 plus 4 plus 5 plus 6 plus 7 plus 8 plus 9 plus 8 plus 7 plus 6 plus 5 plus 4 plus 3 plus 2 plus 1 equals 81. This is consistent with the divisibility rule for 9, since the original number is divisible by 9 and therefore its square must also have a digit sum divisible by 9.
What is the sum of all digits which appear in all the integers from 10 to 100?
Explanation: From 10 to 99, there are 90 numbers. The tens digit cycles through 1 to 9, each appearing exactly 10 times, giving a sum of 10 multiplied by 45, which equals 450. The units digit cycles through 0 to 9 exactly 9 times, giving a sum of 9 multiplied by 45, which equals 405. The number 100 contributes a digit sum of 1. The total is therefore 450 plus 405 plus 1, which equals 856.
ABCD is a square. One point on each of AB and CD; and two distinct points on each of BC and DA are chosen. How many distinct triangles can be drawn using any three points as vertices out of these six points ?
Explanation: The six points are located on the four sides of a square, with no more than two points on any single side and no three points lying on a straight line. Because a straight line can intersect the boundary of a square at most twice, any combination of three points from these six will form a valid triangle. The number of ways to choose 3 points from 6 is calculated as 6 choose 3, which equals 20.
Directions for the following 3 (three) item :
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 1
The emissions humans put into the atmosphere now will affect the climate in the middle of the century and onwards. Technological change, meanwhile, could make a future transition away from fossil fuels cheap or it might not, leaving the world with a terrible choice between sharply reducing emissions at huge cost or suffering through the effects of unabated warming. Businesses that do not hedge against the threat of uncertain outcomes fail. The world cannot afford such recklessness on climate change.
Which one of the following statements best reflects the crucial message conveyed by the author of the passage ?
- Businesses that cause emissions may need to close down or pay for pollution in future.
- The only solution is technological development related to the issues of climate change.
- Waiting to deal with carbon emissions until technology improves is not a wise strategy.
- Since future technological change is uncertain, new industries should be based on renewable energy sources.
Explanation: The statement that businesses causing emissions may need to close down or pay is incorrect because the passage does not specify such consequences, even though it mentions that businesses which fail to hedge against uncertainty generally fail. The statement that technological development is the only solution is incorrect because it uses extreme language that is unsupported by the passage; the author explicitly notes that technology might not make future transitions cheap. The statement that waiting to deal with emissions until technology improves is unwise is correct: the passage warns that relying on uncertain future technology could leave the world with a terrible choice between costly reductions and unabated warming, and it concludes that the world cannot afford recklessness. The statement that new industries should be based on renewable energy is too specific and is not directly supported by the passage.
Directions for the following 3 (three) item :
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 2
Environmental problems cause health problems. Substantial changes in lifestyle can reduce environmental or health problems, but this idea appears almost impossible to adopt. With environmental problems, individual efforts can be perceived as having a negligible effect and therefore lead to inertia. With health, on the other hand, individual choices can make the difference between life and death, literally. And yet, barring a few, there seems to be the same collective lethargy towards making their choices.
Which one of the following statements best implies the most rational assumption that can be made from the passage ?
- We are likely to spend more money on cure than prevention.
- It is the job of the government to solve our environmental and public health problems.
- Health can be protected even if environmental problems go on unattended.
- Loss of traditional lifestyle and the influence of western values led to some unhealthy way of living.
Explanation: The statement that we are likely to spend more on cure than prevention is correct: the passage discusses the difficulty of adopting lifestyle changes and the collective lethargy toward making healthy choices, which implies a preference for reactive measures over preventive action. The statement that solving these problems is the government's job is incorrect because the passage does not mention government responsibility or roles. The statement that health can be protected despite environmental problems is incorrect because it misrepresents the passage's comparison between environmental and health choices. The statement about loss of traditional lifestyle is too far-fetched and is not supported by the passage.
Directions for the following 3 (three) item :
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 3
Many people are not eating the right food. For some, it is simply a decision to stick with food they enjoy but which is not too healthy. This is leading to an increase in non-communicable disease. This is turn leads to major burden on our health-care systems that have the potential to derail the economic progress which is essential for the poor to improve their lives. For others, it is about limited access to nutritious food or a lack of affordability, leading to monotonous diets that to not provide the daily nutrients for them to develop fully. Part of the reason nutrition is under threat worldwide is that our food systems are not properly responding to nutritional needs. Somewhere along that long road from farm to fork, there are serious detours taking place.
Which one of the following statements best reflects the crux of the passage ?
- The scheme of Universal Basic Income should be implemented worldwide as a way of poverty alleviation.
- We must place food-based nutrition at the centre of our policy debate.
- Nutritional status of food should be improved by creating appropriate genetically modified crops.
- Using modern food processing technologies, we must fortify food items with required nutrient elements.
Explanation: The statement advocating Universal Basic Income is outside the scope of the passage, which does not discuss income schemes or poverty alleviation through direct transfers. The statement that food-based nutrition must be placed at the centre of policy debate is correct: the passage discusses systemic failures in delivering nutrition, the rise of non-communicable diseases due to poor diets, and the need for food systems to respond to nutritional needs, all of which point to a policy-level focus on nutrition. The statement about genetically modified crops is unsupported. The statement about fortifying food through modern processing is also not the main message, as the passage focuses on systemic food system failures rather than technological fortification.
Three of the five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following :
1. p + q + r – s - t is definitely even.
2. 2p + q + 2r - 2s + t is definitely odd.
Which of the above statements is/are correct?
- 1 Only
- 2 Only
- Both 1 and 2
- Neither 1 nor 2
Explanation: In statement 1, all five variables appear with a coefficient of plus or minus 1. Since there are exactly two odd numbers among the five, and adding or subtracting two odd numbers always yields an even result while even numbers contribute only even amounts, the entire expression is definitely even. In statement 2, the variables p, r, and s are multiplied by 2, which makes their contributions even regardless of their parity. Only q and t have odd coefficients. Since the two odd numbers could be assigned to any two of the five variables, it is possible that both odd numbers are among p, r, and s, leaving q and t both even and making the entire expression even. Therefore, statement 2 is not definitely odd.
Consider the following in respect of prime number p and composite number c.
1. (p + c)/(p - c) can be even.
2. 2p + c can be odd.
3. pc can be odd.
Which of the statements given above are correct?
- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3
Explanation: For statement 1, if p equals 3 and c equals 9, then the expression becomes 12 divided by negative 6, which equals negative 2, an even number. For statement 2, since 2p is always even, choosing an odd composite number for c, such as 9, makes the sum 2p plus c odd. For statement 3, choosing an odd prime such as 3 and an odd composite such as 9 gives a product of 27, which is odd. Therefore, all three statements are possible.
A 3-digit number ABC, on multiplication with D gives 37DD where A, B, C and D are different non-zero digits. What is the value of A+B+C?
- 18
- 16
- 15
- Cannot be determined due to insufficient data
Explanation: The number 37DD can be written as 3700 plus 11D. Dividing both sides by D gives ABC equals 3700 divided by D plus 11. For ABC to be a whole number, D must be a single-digit divisor of 3700. The valid candidates are 1, 2, 4, and 5. D equals 1 gives a four-digit result, and D equals 2 also gives a four-digit result. D equals 5 yields 751, but then B and D would both be 5, violating the distinctness condition. D equals 4 yields 936, and 936 multiplied by 4 equals 3744, which matches the form 37DD. Here A equals 9, B equals 3, and C equals 6, all distinct and non-zero. The sum is 9 plus 3 plus 6, which equals 18.
For any choices of values of X, Y and Z, the 6 digit number of the form XYZXYZ is divisible by :
- 7 and 11 only
- 11 and 13 only
- 7 and 13 only
- 7, 11 and 13
Explanation: The number XYZXYZ can be rewritten as XYZ multiplied by 1000 plus XYZ, which factors as XYZ multiplied by 1001. Since 1001 factors into 7 multiplied by 11 multiplied by 13, any number of the form XYZXYZ is divisible by 7, 11, and 13 regardless of the specific digits X, Y, and Z.
125 identical cubes are arranged in the form of cubical block. How many cubes are surrounded by other cubes from each side?
Explanation: A cubical block of 125 cubes means the dimensions are 5 by 5 by 5. The cubes that are completely surrounded on all sides are those not on any outer face. Removing the outer layer from each dimension leaves a 3 by 3 by 3 inner cube. Therefore, the number of fully surrounded cubes is 3 cubed, which equals 27.
How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions ?
Explanation: There are four odd positions and four even positions. The odd digits available are 1, 1, 3, and 3. The number of ways to arrange these in the four odd positions is 4 factorial divided by 2 factorial times 2 factorial, which equals 6. Similarly, the even digits are 2, 2, 4, and 4, and the number of ways to arrange these in the four even positions is also 6. The total number of valid arrangements is therefore 6 multiplied by 6, which equals 36.
A, B, C working independently can do a piece of work in 8, 16 and 12 days respectively. A alone works on Monday, B alone works on Tuesday, C alone works on Wednesday; A alone, again works on Thursday and so on. Consider the following statements :
1. The work will be finished on Thursday.
2. The work will be finished in 10 days.
Which of the above statements is/are correct?
- 1 Only
- 2 Only
- Both 1 and 2
- Neither 1 nor 2
Explanation: In one day, A completes one-eighth, B completes one-sixteenth, and C completes one-twelfth of the work. Over a three-day cycle, they complete one-eighth plus one-sixteenth plus one-twelfth, which equals 13 over 48. After three full cycles, which is 9 days, they have completed 39 over 48. On the 10th day, A works and completes one-eighth, which is 6 over 48, bringing the total to 45 over 48. The work is not yet finished. On the 11th day, B works and completes one-sixteenth, which is 3 over 48, bringing the total to 48 over 48. The work is completed on the 11th day. Counting from Monday as day 1, day 11 falls on a Thursday. Therefore, the statement that the work will be finished on Thursday is correct, while the statement that it will be finished in 10 days is incorrect.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 1
We often hear about conflicts among different States in India over river waters. Of the 20 major river system, 14 are already water-stressed; 75% of the population lives in water-stressed regions, a third of whom live in water-scarce areas. Climate change, the demands of rising population and the need for agriculture to keep pace, and increased rate of urbanization and industralization will exacerbate water stress. According to the Constitution of India, water is a State subject and not that of the Union, except for regulation of inter-State rivers. Key to ensuring balance between competing demands of various stakeholders is a basin-based approach to allocate water amongst constituent regions and States. Allocating fair share of water to them requires assessments based on objective criteria, such as specificities of the river basin, size of dependent population, existing water use and demand, efficiency of use, projected future use, etc. while ensuring the environmental needs of the river and aquifers.
Which one of the following statements best reflects the most rational, practical and immediate action required to ensure fair and equitable allocation of water to different stakeholders?
- A national, pragmatic, legal and policy framework for water allocation should be made.
- All river systems of the country should be linked and huge aquifers created.
- Water channels between regions of water surplus and regions of water deficit should be created.
- To mitigate water crisis, water demand of sectors such as agriculture and industry should be reduced.
Explanation: The passage emphasizes that water is a state subject under the Constitution and calls for a basin-based approach with objective assessments to balance competing demands. A national legal and policy framework directly addresses this need for structured, equitable allocation. Proposals to interlink all river systems or create huge aquifers go beyond the passage's scope. Similarly, reducing sectoral demand is a mitigation measure but does not directly address the mechanism for fair allocation among stakeholders.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage – 2
More than half of Indian women and almost a quarter of Indian men of working age suffer from anaemia. According to studies, they are anywhere from 5-15% less productive than they could be, as a result thereof. India also has the largest tuberculosis burden in the world, costing 170 million workdays to the country annually. But what is just as important as lost productivity now is lost potential in the future. It is becoming increasingly clear that on many measures of cognitive ability, malnourished Indian children perform, two or three times worse than their adequately nourished peers. For an economy that will be more dependent on highly skilled workers, this poses a significant challenge. And it is one that really should be addressed given India's demographic outlook.
Which one the following statements best reflects what is implied by the passage?
- Education system must be strengthened in rural areas.
- Large scale and effective implementation of skill development programme is the need of the hour.
- For economic development, health and nutrition of only skilled workers needs special attention.
- For rapid economic growth as envisaged by us, attention should be paid to health and nutrition of the people.
Explanation: The passage links anemia and tuberculosis to current productivity losses, and malnutrition in children to future cognitive deficits and economic challenges. It implies that broad attention to health and nutrition is necessary for economic growth. Strengthening rural education alone is not the focus. Skill development programmes are not discussed. Singling out only skilled workers for health attention is too narrow and misrepresents the passage's broader concern for the general population's health and nutrition.
Directions for the following 3 (three) items:
Read the following three passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage-3
In India, a majority of farmers are marginal and small, less educated and possess low adaptive capabilities to climate change, perhaps because of credit and other constraints. So, one cannot expect autonomous adaptation to climate change. Even if it was possible, it would not be sufficient to offset losses from climate change. To deal with this, adaptation to climate change is paramount, alongside a fast mitigation response. Another solution is to have a planned or policy-driven adaptation, which would require the government to come up with policy recommendations. Perception is a necessary pre- requisite for adaptation. Whether farmers are adapting agricultural practices to climate change depends on whether they perceive it or not. However, this is not always enough for adaptation. It is important how a farmer perceives the risks associated with climate change.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?
- Adaptation to climate change and mitigation response are basically the responsibilities of the government.
- Climate change causes a change in government policies regarding land use patters in the country.
- Risk perceptions of farmers are important for motivating them for taking adaptation decisions.
- Since mitigation is not possible, governments should come up with policies for quick response to climate change.
Explanation: The passage explicitly states that perception is a necessary prerequisite for adaptation and emphasizes that how farmers perceive climate change risks is crucial for their adaptation decisions. The statement that adaptation and mitigation are basically government responsibilities overstates the passage, which discusses policy-driven adaptation as one solution but does not assign sole responsibility to government. The statement about land use policy changes is not discussed. The claim that mitigation is not possible is incorrect; the passage says mitigation must be fast, not impossible.
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
Explanation: There are 20 individual red shoes, 18 white shoes, and 16 black shoes. In the worst-case scenario, Raj first draws all non-red shoes, totalling 34. To guarantee a red pair, he must then draw enough red shoes to ensure a matching left and right. The worst case within the red shoes is drawing all 10 left-foot red shoes first; the next red shoe drawn must be a right-foot shoe, completing the pair. Thus, the maximum number of attempts is 34 plus 11, which equals 45.
In how many ways can a batsman score exactly 25 runs by scoring single runs, fours and sixes only, irrespective of the sequence of scoring shots?
Explanation: Let the number of singles, fours, and sixes be a, b, and c respectively, satisfying a plus 4b plus 6c equals 25. If c equals 0, then b can range from 0 to 6, giving 7 combinations. If c equals 1, then b can range from 0 to 4, giving 5 combinations. If c equals 2, then b can range from 0 to 3, giving 4 combinations. If c equals 3, then b can range from 0 to 1, giving 2 combinations. If c equals 4, then b can only be 0, giving 1 combination. The total number of ways is 7 plus 5 plus 4 plus 2 plus 1, which equals 19.
There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:
1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.
Which of the statements given above is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is impossible: if exactly one letter is in the wrong envelope, then the letter that should have been in that envelope must also be misplaced, meaning at least two letters are incorrectly placed. Therefore, exactly one misplaced letter cannot occur. Statement 2 is correct: to have exactly two letters in the correct envelopes, we choose which two of the four are correctly placed, which can be done in 4 choose 2 equals 6 ways. The remaining two letters must be swapped with each other, which can happen in exactly 1 way. Thus, there are 6 valid ways.
What is the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100?
Explanation: The product contains 85 and 95, each contributing a factor of 5, giving 5 times 5 equals 25. The number 96 contributes a factor of 4. Since 25 times 4 equals 100, the product contains 100 as a factor. Therefore, the product is completely divisible by 100, leaving a remainder of 0.
What is the unit digit in the expansion of (57242)^(9x7x5x3x1) ?
Explanation: The unit digit of the entire expression depends only on the unit digit of the base, which is 2. The exponent is 9 times 7 times 5 times 3 times 1, which equals 945. The unit digits of powers of 2 cycle every 4 as 2, 4, 8, 6. Since 945 divided by 4 leaves a remainder of 1, the unit digit is the same as that of 2 to the power 1, which is 2.
If ABC and DEF are both 3-digit numbers such that A, B, C, D, E, and F are distinct non-zero digits such that ABC+ DEF= 1111, then what is the value of A+B+C+D+E+F ?
Explanation: For the sum of two three-digit numbers to be 1111, there must be a carry of 1 from each column. The units column gives C plus F equals 11, with a carry of 1. The tens column gives B plus E plus 1 equals 11, so B plus E equals 10, with a carry of 1. The hundreds column gives A plus D plus 1 equals 11, so A plus D equals 10. Adding these results, the total sum of all six digits is 11 plus 10 plus 10, which equals 31.
D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred's place and the digit at the unit's place of D?
Explanation: To minimize the ratio of the number to the sum of its digits, the hundreds digit should be as small as possible while the tens and units digits should be as large as possible. For the 100s, the number 199 gives a ratio of 199 divided by 19, approximately 10.47. For the 200s, 299 gives 299 divided by 20, which is 14.95. As the hundreds digit increases, the ratio increases. Therefore, the minimum ratio occurs at 199. The difference between the hundreds digit 1 and the units digit 9 is 8.
Directions for Read the following 4 (four) Items:
Following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.
Passage-1
For two or three generations past, ever-increasing number of individuals have been living as workers merely, not as human beings. An excessive amount of labor is rule today in every circle of society, with the result that man's spiritual element cannot thrive. He finds it very difficult to spend his little leisure in serious activities. He does not want to think; or he cannot even if he wants to. He seeks not Self-improvement, but entertainment which would enable him to be mentally idle and to forget his usual activities. Therefore, the so-called culture of our age is dependent more on cinema than on theatre, more on newspapers, magazines and crime stories than on serious literature.
The passage is based on the idea that
- man should not work hard
- the great evil of our age is overstrain
- man cannot think well
- man cannot care for his spiritual welfare
Explanation: The passage emphasizes that excessive labor has become the norm, leaving individuals with little energy for serious thought or spiritual growth. This focus on overwork and its consequences aligns with the idea that overstrain is the central problem. The passage does not argue that man should not work hard, but rather criticizes excessive labor. While it mentions difficulty in thinking and spiritual decline, these are presented as consequences of overstrain rather than the core idea.
Directions for Read the following 4 (four) Items:
Following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.
Passage-1
For two or three generations past, ever-increasing number of individuals have been living as workers merely, not as human beings. An excessive amount of labor is rule today in every circle of society, with the result that man's spiritual element cannot thrive. He finds it very difficult to spend his little leisure in serious activities. He does not want to think; or he cannot even if he wants to. He seeks not Self-improvement, but entertainment which would enable him to be mentally idle and to forget his usual activities. Therefore, the so-called culture of our age is dependent more on cinema than on theatre, more on newspapers, magazines and crime stories than on serious literature.
Man does not seek self-improvement because he
- is not intellectually capable
- has no time to do so
- is distracted by materialism
- loves amusement and is mentally idle
Explanation: The passage explicitly states that an excessive amount of labor leaves man with very little leisure, making it difficult for him to engage in serious activities or self-improvement. Therefore, the lack of time due to overwork is the primary reason. While the passage mentions that he seeks entertainment and becomes mentally idle, these are consequences of having no time and energy left after labor, not the root cause.
Directions for Read the following 4 (four) Items:
Following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.
Passage-2
The demographic dividend, which has begun in India and is expected to last another few decades, is a great window of opportunity. The demographic dividend is basically a swelling in the working age population, which conversely means that the relative ratio of very young and very old will, for a while, be on the decline. From the experience of Ireland and China, we know that this can be a source of energy and an engine of economic growth. The demographic dividend tends to raise a nation's savings rate since in any nation, it is the working age population that is the main saver. And since the savings rate is an important driver of growth, this should help elevate our growth rate. However, the benefits of demographic dividend depend on the quality of the working age population. And this implies bringing back the importance of education, acquisition of skills and human capital.
Which of the following would invariably happen in a country, when the demographic dividend has begun to operate?
1. The number of illiterate people will decrease.
2. The ratio of very old and very young will decrease for a while.
3. Population growth rate will quickly stabilize.
Select the correct answer using the code given below.
- 1 and 2 only
- 2 only
- 1 and 3 only
- 1, 2 and 3
Explanation: Statement 1 is not necessarily true: the demographic dividend refers to the age structure of the population, not to education levels. A swelling working-age population does not automatically imply a decrease in illiteracy. Statement 2 is explicitly stated in the passage as a defining characteristic of the demographic dividend. Statement 3 is unsupported; the passage does not claim that the population growth rate will quickly stabilize.
Directions for Read the following 4 (four) Items:
Following two passages and answer that follow the passages. Your answer to these items should be based on the passages only.
Passage-2
The demographic dividend, which has begun in India and is expected to last another few decades, is a great window of opportunity. The demographic dividend is basically a swelling in the working age population, which conversely means that the relative ratio of very young and very old will, for a while, be on the decline. From the experience of Ireland and China, we know that this can be a source of energy and an engine of economic growth. The demographic dividend tends to raise a nation's savings rate since in any nation, it is the working age population that is the main saver. And since the savings rate is an important driver of growth, this should help elevate our growth rate. However, the benefits of demographic dividend depend on the quality of the working age population. And this implies bringing back the importance of education, acquisition of skills and human capital.
With reference to the passage, which of the following inferences can be drawn?
1. Demographic dividend is an essential condition for a country to rapidly increase its economic growth rate.
2. Promotion of higher education is an essential condition for a country for its rapid economic growth.
Select the correct answer using the code given below.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is incorrect because the passage presents the demographic dividend as an opportunity that can help growth, but not as an essential or necessary condition; countries can achieve rapid growth through other means. Statement 2 is also incorrect because while the passage stresses the importance of education, skills, and human capital, it does not single out higher education as an essential prerequisite for rapid economic growth.
Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below:
1. Z purchased 8 notebooks more than X did.
2. P and Q together purchased 21 notebooks.
3. Q purchased 5 notebooks less than P did.
4. X and Y together purchased 28 notebooks.
5. P purchased 5 notebooks more than X did.
If each notebook is priced 40, then what is the total cost of all the notebooks?
Explanation: From statements 2 and 3, P plus Q equals 21 and Q equals P minus 5. Substituting gives 2P equals 26, so P equals 13 and Q equals 8. From statement 5, P equals X plus 5, so X equals 8. From statement 1, Z equals X plus 8, so Z equals 16. From statement 4, X plus Y equals 28, so Y equals 20. The total number of notebooks is 13 plus 8 plus 8 plus 20 plus 16, which equals 65. At 40 per notebook, the total cost is 65 times 40, which equals 2600.
A man started from home at 14:30 hours and drove to village, arriving there when the village clock indicated 15:15 hours. After staying for 25 minutes, he drove back by a different route of length 1.25 times the first route at a rate twice as fast reaching home at 16:00 hours. As compared to the clock at home, the village clock is
- 10 minutes slow
- 5 minutes slow
- 10 minutes fast
- 5 minutes fast
Explanation: The total time away from home is from 14:30 to 16:00, which is 90 minutes. Subtracting the 25-minute stay leaves 65 minutes of driving time. Let the distance of the first route be d and the speed be s. The total driving time is d over s plus 1.25d over 2s, which equals 65 minutes. This simplifies to 1.625 times d over s equals 65, so d over s equals 40 minutes. The journey to the village took exactly 40 minutes, meaning actual arrival time was 15:10. Since the village clock read 15:15, it was 5 minutes fast.
A person X wants to distribute some pens among six children A, B, C, D, E and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number?
Explanation: Since A must be a multiple of 2, 3, 4, 5, and 6, the least common multiple is 60. If A equals 60, then B equals 30, C equals 20, D equals 15, E equals 12, and F equals 10. However, D receives 15 pens, which is odd, violating the condition. Multiplying the entire set by 2 gives A equals 120, B equals 60, C equals 40, D equals 30, E equals 24, and F equals 20, all of which are even. The total number of pens is 120 plus 60 plus 40 plus 30 plus 24 plus 20, which equals 294.
Six Persons A, B, C, D, E and F are sitting equidistant form each other around a circular table (facing the centre of the table).
Consider the Question and two statements given below:
Question: Who is sitting on the immediate left of A?
Statement-1: B is sitting opposite to C and D is sitting opposite to E.
Statement -2: F is sitting on the immediate left of B.
Which one of the following is correct in respect of the Question and the Statements?
- Statement-1 alone is sufficient to answer the question
- Statement-2 alone is sufficient to answer the question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question
Explanation: Statement 1 places B opposite C and D opposite E. Statement 2 places F immediately to the left of B. With six seats, fixing B and C opposite each other and F to B's left leaves four positions for A, D, and E. Since D and E are opposite each other, they can occupy either of the two remaining pairs of opposite seats. Depending on which pair they choose, A's immediate left could be D or E. Therefore, even combining both statements, the answer cannot be determined uniquely.
Consider the Question and two Statements given below:
Question: What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3: 5.
Which one of the following is correct in respect of the Question and the Statement?
- Statements-1 alone is sufficient to answer the Question
- Statement-2 alone is sufficient to answer the question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question
Explanation: Let Manisha's present age be x and her mother's present age be y. Statement 1 gives y equals x plus 24. Statement 2 gives the ratio x plus 5 to y plus 5 equals 3 to 5. Neither statement alone provides enough information to solve for x, but together they form a system of two independent equations with two variables. Solving yields x equals 31, so both statements together are sufficient.
Six lectures A, B, C, D, E and F, each of one hour duration, are scheduled between 8:00 am, and 2:00 p.m.
Consider the Question and two Statements given below:
Question: Which lecture is in the third period?
Statement-1: Lecture F is preceded by A and followed by C
Statement-2: There is no lecture after lecture B.
Which one of the following is correct in respect of the Question and the Statements?
- Statement-1 alone is sufficient to answer the question
- Statement-2 alone is sufficient to answer the question
- Both Statement-1 and Statement-2 are sufficient to answer the Question
- Both Statement-1 and Statement-2 are not sufficient to answer the Question
Explanation: There are six periods from 8:00 a.m. to 2:00 p.m. Statement 1 establishes the consecutive block A followed by F followed by C. Statement 2 places B in the sixth period. However, the A-F-C block can occupy periods 1 through 3, 2 through 4, or 3 through 5. In these respective cases, the third period would be C, F, or A. Since the position of the block is not fixed, the third period cannot be determined with certainty.
Directions for the following 3 (three) Items:
Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage-1
In an economic organization, allowing mankind to benefit by the productivity of machines should lead to a very good life of leisure, and much leisure is apt to be tedious except to those who have intelligent activities and interests. If a leisured population is to be happy, it must be an educated population, and must be educated with a view to enjoyment as well as to the direct usefulness of technical knowledge.
Which of the following statements best reflects the underlying tone of the passage?
- Only an educated population can best make use of the benefits of economic progress.
- All economic development should be aimed at the creation of leisure.
- An increase in the educated population of a country leads to an increase in the happiness of its people.
- Use of machines should be encouraged in order to create a large leisured population.
Explanation: The passage argues that machine-driven productivity creates leisure, but leisure becomes tedious without intelligent activities. It concludes that a leisured population can only be happy if it is educated for enjoyment as well as technical usefulness. This directly supports the idea that increasing education is the pathway to happiness in such a society. The statement that only an educated population can best use economic progress is close but narrower than the passage's emphasis on happiness through education. The statements that all development should aim at leisure or that machines should be encouraged solely to create leisure are too extreme and misrepresent the passage's balanced view.
Directions for the following 3 (three) Items:
Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage-2
If presents bring less thrill now that we are grown up, perhaps it is because we have too much already, or perhaps it is because we have lost the fullness of the joy of giving and with it the fullness of the joy of receiving. Children's fears are poignant, their miseries are acute, but they do not look too forward nor too far backward. Their joys are clear and complete, because they have not yet learnt always to add 'but' to every proposition. Perhaps we are too cautious, too anxious, too sceptical. Perhaps some of our cares would shrink if we thought less about them and entered with more single-minded enjoyment into the happiness that come our way.
With reference to the passage, which one of the following statements is correct?
- It is not possible for adults to feel thrilled by presents.
- There can be more than one reason why adults feel less thrilled by presents.
- The author does not know why adults feel less thrilled by presents.
- Adults have less capacity to feel the joy of loving or being loved.
Explanation: The author offers multiple possible explanations for why adults feel less thrill: having too much already, losing the joy of giving and receiving, being too cautious, anxious, or sceptical, and adding conditions to happiness. This clearly indicates that more than one reason may be at play. The statement that it is impossible for adults to feel thrilled is too absolute. The statement that the author does not know is incorrect because the author explicitly proposes reasons. The statement about diminished capacity for love is not discussed.
Directions for the following 3 (three) Items:
Read the following two passages and answer the items that follow the passages. Your answers to these items should be based on the passages only.
Passage-2
If presents bring less thrill now that we are grown up, perhaps it is because we have too much already, or perhaps it is because we have lost the fullness of the joy of giving and with it the fullness of the joy of receiving. Children's fears are poignant, their miseries are acute, but they do not look too forward nor too far backward. Their joys are clear and complete, because they have not yet learnt always to add 'but' to every proposition. Perhaps we are too cautious, too anxious, too sceptical. Perhaps some of our cares would shrink if we thought less about them and entered with more single-minded enjoyment into the happiness that come our way.
The author of the passage is against
- worrying too much about the past and future
- being in the habit of thinking about presents
- not being thrilled by new things
- giving and receiving joy only partially
Explanation: The passage contrasts children, who do not look too far forward or backward and enjoy complete joys, with adults who are too cautious, anxious, and sceptical. The author implies that adults add reservations and worries to their experiences, which diminishes happiness. Therefore, the author is implicitly against excessive worry about the past and future. The other options either misrepresent the passage or focus on tangential ideas.
Let A, B and C represent distinct non-zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.
Consider the following statements:
1. The 4-digit least value of x is 1332.
2. The 3-digit greatest value of x is 888.
Which of the above statements is/are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: There are 6 permutations of three distinct digits. Each digit appears twice in each place value, so the sum x equals 222 times the sum of the digits. To minimize x, choose the smallest distinct non-zero digits: 1, 2, and 3. Their sum is 6, giving x equals 222 times 6, which equals 1332. This is a four-digit number. Since the minimum possible value of x is already 1332, there is no valid three-digit value for x at all. Therefore, the statement about the least four-digit value being 1332 is correct, while the statement about the greatest three-digit value being 888 is incorrect.
There is a numeric lock which has a 3-digit PIN. The PIN contains digits 1 to 7. There is no repetition of digits. The digits in the PIN from left to right are in decreasing order. Any two digits in the PIN differ by at least 2. How many maximum attempts does one need to find out the PIN with certainty?
Explanation: Because the digits must be strictly decreasing and differ by at least 2, we are counting combinations of 3 digits from 1 through 7 with no two consecutive. This is equivalent to choosing 3 digits from a reduced set of 5, giving 10 combinations. Explicitly, if the smallest digit is 1, the valid combinations are 531, 631, 731, 641, 741, and 751, totalling 6. If the smallest digit is 2, the valid combinations are 642, 742, and 752, totalling 3. If the smallest digit is 3, the only valid combination is 753, totalling 1. The sum is 6 plus 3 plus 1, which equals 10.
There are eight equidistant points on a circle. How many right-angled triangles can be drawn using these points as vertices and taking the diameter as one side of the triangle?
Explanation: An angle inscribed in a semicircle is a right angle. With 8 equidistant points, there are 4 distinct diameters formed by connecting opposite points. For each diameter, any of the remaining 6 points on the circle can serve as the third vertex to form a right-angled triangle. Therefore, the total number of right-angled triangles is 4 times 6, which equals 24.
24 men and 12 women can do a piece of work in 30 days. In how many days can 12 men and 24 women do the same piece of work?
- 30 days
- more than 30 days
- Less than 30 days or more than 30 days
- Data is inadequate to draw any conclusion
Explanation: The problem provides a single equation relating the work rates: 30 times the combined daily work of 24 men and 12 women equals the total work. Without knowing the relative efficiency of a man compared to a woman, or without a second independent equation, it is impossible to determine the combined daily work rate of 12 men and 24 women. Therefore, the data is inadequate.
What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261?
Explanation: Factoring 1261 gives 13 multiplied by 97. In the given product, 91 equals 13 times 7, so the factor 13 is present. Additionally, 97 appears explicitly in the sequence. Since all prime factors of 1261 are contained in the numerator, the product is completely divisible by 1261, leaving a remainder of 0.
Consider the following statements in respect of a rectangular sheet of length 20 cm and breadth 8 cm:
1. It is possible to cut the sheet exactly into 4 square sheets.
2. It is possible to cut the sheet into 10 triangular sheets of equal area.
Which of the above statements is are correct?
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: Statement 1 is correct: the 20 by 8 rectangle can be divided into two 8 by 8 squares, leaving a 4 by 8 rectangle, which can be further divided into two 4 by 4 squares, yielding exactly four square sheets. Statement 2 is correct: the total area is 160 square centimetres. Dividing the rectangle into five smaller rectangles of 4 by 8 gives each an area of 32. Cutting each of these diagonally produces two triangles of area 16 each, resulting in 10 triangular sheets of equal area.
When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number z, then the sum becomes 165% of the value of z. which one of the following is correct?
- z < x < y
- x < y < z
- y < x < z
- z < y < x
Explanation: From the first condition, 0.7x plus y equals 1.65y, which implies 0.7x equals 0.65y. Therefore, x divided by y equals 0.65 over 0.70, which is less than 1, so x is less than y. From the second condition, 0.6x plus z equals 1.65z, which implies 0.6x equals 0.65z. Therefore, x divided by z equals 0.65 over 0.60, which is greater than 1, so x is greater than z. Combining these inequalities gives z is less than x, which is less than y.