Find the missing number in the sequence: 2, 3, 5, 7, 8, 11, 11, 15, 14, ?
Explanation: This sequence consists of two interleaved arithmetic progressions. The odd-positioned terms (1st, 3rd, 5th, ...) are 2, 5, 8, 11, 14 with common difference 3. The even-positioned terms (2nd, 4th, 6th, ...) are 3, 7, 11, 15, ? with common difference 4. The missing term is the 10th term (even position), so it is 15 + 4 = 19.
What is the LCM of 6 and 8?
Explanation: 6 = 2 × 3 and 8 = 2³. LCM = 2³ × 3 = 24. Common error: HCF = 2.
What is the remainder when 22! is divided by 23?
Explanation: By Wilson's theorem, 22! ≡ -1 ≡ 22 (mod 23).
Passage: Judicial review and majoritarianism represent a fundamental tension in democratic governance—where the former empowers courts to check legislative majorities for constitutional fidelity, the latter asserts popular sovereignty as the ultimate validator of governance. While judicial review safeguards minority rights and prevents majoritarian excesses, it risks undermining elected institutions by substituting judicial wisdom for democratic choice. This dilemma underscores a deeper question: can democracy survive without mechanisms to temper its own excesses, or does judicial intervention itself erode the legitimacy of representative governance?. can democracy survive without mechanisms to temper its own excesses, or does judicial intervention itself erode the legitimacy of representative governance?
QUESTION: What is the central tension between judicial review and majoritarianism highlighted in the passage?
- Judicial review empowers courts to constrain legislative majorities while majoritarianism asserts popular sovereignty as the ultimate source of governance legitimacy.
- The tension arises because judicial review protects minority rights but risks substituting judicial wisdom for democratic choice.
- Safeguarding constitutional fidelity through courts can prevent majoritarian excesses but may undermine elected institutions’ authority.
- The dilemma questions whether democracy requires judicial tempering of its own excesses or if such intervention corrodes representative governance’s legitimacy.
Explanation: The central tension posed in the passage is the dilemma itself: whether democracy needs judicial mechanisms to curb its excesses or whether those interventions endanger the legitimacy of elected governance. Option D captures this exact question. Option A restates roles but not the core dilemma. Option B focuses on rights versus substitution, a secondary effect. Option C highlights safeguarding versus undermining, a supporting point but not the central tension.
Which number is a perfect square?
Explanation: 1089 = 33². 1099 is between 33²=1089 and 34²=1156. 1111 is not a square (33²=1089, 34²=1156). 1127 is not a square. The trap is that 1111 looks like it could be 33.3² or has a pattern.
Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30 degrees at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?
Explanation: When A reaches the diametrically opposite point, he has covered 180 degrees. Since B started 30 degrees ahead and is met at that point, B has covered 150 degrees from his start. With equal time elapsed, the speed ratio equals the distance ratio: 180 : 150 = 6 : 5.
In how much time will a sum of ₹800 amount to ₹960 at 8% per annum simple interest?
- 2 years
- 3.5 years
- 3 years
- 2.5 years
Explanation: SI = ₹960 − ₹800 = ₹160. t = (SI×100)/(P×R) = (160×100)/(800×8) = 2.5 years.
Passage: The Arctic's vast reserves of fossil fuel, fish and minerals are now accessible for a longer period in a year. But unlike Antarctica, which is protected from exploitation by the Antarctic Treaty framed during the Cold War and is not subject to territorial claims by any country, there is no legal regime protecting the Arctic from industrialization, especially at a time when the world craves for more and more resources. The distinct possibility of ice-free summer has prompted countries with Arctic coastline to scramble for great chunks of the melting ocean.
Which one of the following is the most important implication of the passage?
- India can have territorial claims in the Arctic territory and free access to its resources.
- Melting of summer ice in the Arctic leads to changes in the geopolitics.
- The Arctic region will solve the world's future problem of resource crunch.
- The Arctic region has more resources than Antarctica.
Explanation: The passage emphasizes the absence of a legal regime protecting the Arctic and describes how countries are scrambling for territory as ice melts, indicating geopolitical shifts.
Passage: By shielding MSMEs from competitive rigor under the guise of developmental nurturing, industrial policy often risks calcifying inefficiency; what was intended as a temporary scaffolding for growth frequently mutates into a permanent crutch that stifles the very innovation it sought to protect. Which of the following best captures the central paradox of industrial policy discussed in the passage?
- Innovation is stifled because MSMEs lack the necessary capital to compete with larger industrial entities.
- MSMEs require a specific regulatory framework to overcome the initial challenges of market entry.
- All government industrial policies are inherently detrimental to the long-term success of the national economy.
- Industrial policy meant to foster growth often inadvertently creates long-term dependency that hinders innovation.
Explanation: Option D is correct because it accurately synthesizes the passage’s core argument: the ironic transformation of "developmental nurturing" (intended to help) into a "permanent crutch" (which hinders). It captures the dual nature of the paradox—the intent to foster growth versus the reality of creating dependency and stifling innovation.
Option A is incorrect due to overextension; while capital may be a factor, the passage focuses specifically on the negative impact of protective policies, not the absence of capital. Option B is incorrect due to misdirection; it describes a potential justification for industrial policy rather than the paradox of its actual outcomes as presented in the text. Option C is incorrect due to narrowing and extreme generalization; the passage critiques the specific risks of "shielding" and "calcifying inefficiency" in certain contexts, but it does not claim that *all* industrial policies are inherently detrimental to the entire national economy.
A, B, C and D are students. They are studying in four different cities, viz., P, Q, R and S (not necessarily in that order). They are studying in Science college, Arts college, Commerce college and Engineering college (not necessarily in that order), which are situated in four different States, viz., Gujarat, Rajasthan, Assam and Kerala (not necessarily in that order). Further, it is given that: D is studying in Assam. Arts college is located in city S which is in Rajasthan. A is studying in Commerce college. B is studying in city Q. Science college is located in Kerala.
Which one of the following statements is correct regarding Engineering college?
- C is studying there.
- B is studying there.
- It is located in Gujarat.
- D is studying there.
Explanation: D is in Assam and cannot be in Arts (Rajasthan) or Science (Kerala), and A is in Commerce. Therefore D must be studying in Engineering college.
A and B start a business with ₹20,000 and ₹30,000 respectively. B gives A a personal loan of ₹10,000 at 10% simple interest per annum. If the annual profit from the business is ₹15,000 (before any interest adjustment), what is A's net gain?
- ₹5,000
- ₹6,000
- ₹4,000
- ₹7,000
Explanation: Capital ratio = 20000:30000 = 2:3. A's profit share = (2/5)×15000 = ₹6,000. Interest on loan = 10% of 10000 = ₹1,000. A's net gain = 6000 - 1000 = ₹5,000.
Five boxes—P, Q, R, S, and T—are stacked from top (position 1) to bottom (position 5). Each contains a different letter: A, B, C, D, or E. Box P is at position 1 (top) and contains A. Box Q is immediately above the box containing B. Box R is at position 5 (bottom) and does not contain E. Box S is not at position 2 or 4, and does not contain C. Box T is below Box P but above Box Q. The box with C is at an even-numbered position. The box with D is at an odd-numbered position below position 5. The box with E is above the box with D. Which box contains C?
- S at position 3
- T at position 2
- R at position 5
- Q at position 4
Explanation: Start with fixed positions: P is at position 1 (A) and R is at position 5. Since S cannot be at positions 2 or 4, and position 1 is occupied, S must be at position 3. T must be below P (position 1) but above Q, so T is at position 2 or 4. Q is immediately above the B box, so B is below Q. Q must be at position 2, 3, 4, or 5; since S is at position 3 and R is at position 5, Q is at position 2 or 4. If T were at position 4, Q would have to be below T, so Q would be at position 5 (R), but then B would be below R, which is impossible. Therefore T is at position 2, making Q at position 4 (since Q must be below T and above R). This places B at position 5 (R), which satisfies the constraint that R is not E. The D box must be at an odd position below position 5 (position 1 or 3); since P is at position 1 with A, S at position 3 must be D. The E box must be above D (position 3), so it is at position 1 or 2; since P is at position 1 with A, T at position 2 must be E. The C box must be at an even position (2 or 4); since T is at position 2 with E, Q at position 4 must be C.
A train of length 200 m crosses a platform of length 400 m at 72 km/h in 30 seconds. If the speed is reduced by 25%, how long will it take to cross the same platform?
Explanation: Total distance = 200 + 400 = 600 m. Reduced speed = 72 × 0.75 = 54 km/h = 15 m/s. New time = 600 / 15 = 40 s.
If n! has exactly 20 trailing zeros, which of the following CANNOT be the value of n?
Explanation: Trailing zeros in n! = ⌊n/5⌋ + ⌊n/25⌋ + ... For n=85 to 89: ⌊n/5⌋ = 17, ⌊n/25⌋ = 3, total = 20. For n=90: ⌊90/5⌋ = 18, ⌊90/25⌋ = 3, total = 21. Option 85, 87, 88 all give exactly 20 zeros. Option 90 gives 21 zeros.
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.
Consider the sequence given below: 4/12/95, 1/1/96, 29/1/96, 26/2/96, .... What is the next term of the series?
- 24/3/96
- 25/3/96
- 26/3/96
- 27/3/96
Explanation: Each term is obtained by adding 28 days to the previous date. Adding 28 days to 26/2/96 (leap year) gives 25/3/96.
Read the following passage and answer the item that follows. Passage: The history of science is the real history of mankind. In this striking epigram, a nineteenth-century writer links science with its background. Like most epigrams, its power lies in emphasizing by contrast an aspect of truth which may be easily overlooked. In this case, it is easy to overlook the relations between science and mankind, and to treat the former as some abstract third party, which can sometimes be praised for its beneficial influences, but frequently and conveniently blamed for the horrors of war. Science and mankind cannot be divorced from time to time at men's convenience. Yet we have seen that, in spite of countless opportunities of improvement, the opening years of the present period of civilization have been dominated by international conflict. Is this the inevitable result of the progress of science or does the fault lie elsewhere? Based on the above passage, the following assumptions have been made: 1. The horrors of modern life are the inevitable result of the progress of science. 2. The aspect of truth likely to be overlooked is that science is what man has made it. Which of the assumptions given above is/are correct? a) 1 only b) 2 only c) Both 1 and 2 d) Neither 1 nor 2
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2
Explanation: The passage questions whether science is truly to blame for modern horrors, suggesting it is often conveniently blamed. It emphasizes that science is not an abstract entity but a human creation, which is the easily overlooked aspect. Thus assumption 2 is correct while assumption 1 is not supported.
How many trailing zeros are in the product 1² × 2² × 3² × ... × 25²?
Explanation: Product = (25!)². Zeros in 25! = ⌊25/5⌋ + ⌊25/25⌋ = 6. So (25!)² has 2×6 = 12 zeros. Option 6 is zeros in 25!. Option 10 is ⌊25/5⌋ × 2. Option 25 is just 25.
A trader marks his goods at a price where the profit percentage equals the discount percentage. If the cost price is ₹800 and the selling price is ₹900, what is the marked price?
- A. ₹1,028.57
- B. ₹1,000
- C. ₹1,125
- D. ₹1,200
Explanation: Let profit% = discount% = x. SP = CP × (100+x)/100 = ₹900. So 800(100+x)/100 = 900, giving x = 12.5%. MP = SP × 100/(100-x) = ₹900 × 100/87.5 = ₹1,028.57. Option A is correct. Option B (₹1,000) is a rough estimate. Option C (₹1,125) is CP + 12.5% + 12.5% of CP. Option D (₹1,200) is CP × 1.5.
Two equal sums of ₹5,000 each are lent out at simple interest, one at 8% and the other at 12% per annum, both for 4 years. What is the total interest earned?
- ₹4,800
- ₹3,200
- ₹4,000
- ₹2,000
Explanation: Interest from first = ₹5,000 × 8% × 4 = ₹1600. From second = ₹5,000 × 12% × 4 = ₹2400. Total = ₹4000.
Find the missing number in the sequence: 3, 8, 13, 18, 23, ?, 33, 38
Explanation: The sequence is an arithmetic progression with common difference d = 5. Each term increases by 5. The term before the missing position is 23, so the missing term is 23 + 5 = 28.
Read the following passage and answer the item that follows. Passage: When an international team of scientists pumped a carbon dioxide and water mix into underground basalt rocks, basic chemistry took over. The acidic mixture dissolved rocks' calcium and magnesium and formed limestone. Basically carbon dioxide is converted into stone, exclaimed the scientists. Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage? a) It is a cheap and practical method to produce limestone at commercial level for building purposes. b) This can be used as one of the methods of carbon sequestration. c) Basalt rock can be made a good source of calcium and magnesium minerals by this method. d) Good rock-dissolving acid can be produced by mixing carbon dioxide and water.
- It is a cheap and practical method to produce limestone at commercial level for building purposes.
- This can be used as one of the methods of carbon sequestration.
- Basalt rock can be made a good source of calcium and magnesium minerals by this method.
- Good rock-dissolving acid can be produced by mixing carbon dioxide and water.
Explanation: The passage describes converting carbon dioxide into stone (limestone) by reacting it with basalt. This is a method of storing carbon dioxide underground, which aligns with carbon sequestration. The other options focus on commercial limestone production, mineral sourcing, or acid production, which are not the primary implications.
Passage: It is certain, that seditions, wars, and contempt or breach of the laws are not so much to be imputed to the wickedness of the subjects, as to the bad state of a dominion. For men are not born fit for citizenship but must be made so. Besides, men's natural passions are everywhere the same; and if wickedness more prevails, and more offences are committed in one commonwealth than in another, it is certain that the former has neither enough pursued the end of unity, nor framed its laws with sufficient forethought; and that, therefore, it has failed in making quite good its right as a commonwealth.
Which among the following is the most logical and rational inference that can be made from the passage given above?
- Seditions, wars, and breach of the laws are inevitable in every dominion.
- It is not the people, but the sovereign who is responsible for all the problems of any dominion.
- That dominion is the best which pursues the aim of unity and has laws for good citizenship.
- It is impossible for men to establish a good dominion.
Explanation: The assertion that seditions, wars, and breach of the laws are inevitable in every dominion is incorrect because the passage does not claim such problems are unavoidable. The claim that the sovereign alone is responsible for all problems is incorrect because it is overly simplistic to blame only the sovereign. The inference that the best dominion pursues the aim of unity and has laws for good citizenship is correct because it is directly supported by the passage. The claim that it is impossible to establish a good dominion is incorrect because the passage suggests good government requires preparation and education, not that it is unachievable.
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.
If x - y = 8, then which of the following must be true? Both x and y must be positive for any value of x and y. If x is positive, y must be negative for any value of x and y. If x is negative, y must be positive for any value of x and y. Select the correct answer using the code given below.
- 1 only
- 2 only
- Both 1 and 2
- Neither 1 nor 2 nor 3
Explanation: Counterexamples disprove each statement. If x = 10 and y = 2, both are positive. If x = 5 and y = -3, x is positive and y is negative. If x = -1 and y = -9, both are negative. Therefore none of the statements hold for all values.
Q.30) Consider the following: 1. 1000 litres = 1 m³ 2. 1 metric ton = 1000 kg 3. 1 hectare = 10000 m² Which of the above are correct? a) 1 and 2 only b) 2 and 3 only c) 1 and 3 only d) 1, 2 and 3
- 1 and 2 only
- 2 and 3 only
- 1 and 3 only
- 1, 2 and 3
Explanation: All three are standard unit conversions: 1 cubic meter equals 1000 liters; 1 metric ton equals 1000 kilograms; and 1 hectare equals 10,000 square meters. Therefore, all statements are correct.
Which year has the same calendar as that of 2009?
Explanation: To match calendars, both the first day of the year and the year type (ordinary or leap) must align. From 2009 to 2015, the cumulative odd days are: 2009 (1), 2010 (1), 2011 (1), 2012 (2, leap year), 2013 (1), 2014 (1), 2015 (1). Total = 7 odd days, which is equivalent to 0. Since both 2009 and 2015 are ordinary years starting on the same day, they share the same calendar.
Four political parties W, X, Y and Z decided to set up a joint candidate for the coming parliamentary election. The formula agreed by them was the acceptance of a candidate of the most of the parties. Four aspiring candidates A, B, C and D approached the parties for their tickets. A was acceptable to W but not to Z. B was acceptable to Y but not to X. C was acceptable to W and Y. D was acceptable to W and X. When candidate B was preferred by W and Z, candidate C was preferred by X and Z and candidate A was acceptable to X but not to Y; who got the ticket?
Explanation: Candidate C is acceptable to W and Y, and preferred by X and Z, giving C the support of all four parties. A lacks support from Z and Y. B lacks support from X. D has no demonstrated support from Y or Z.
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.
The price of an item increases by 10% and its consumption decreases by 10%. What is the net change in expenditure?
Explanation: Expenditure multiplier = 1.10 × 0.90 = 0.99. Therefore, expenditure decreases by 1%. Equal percentage increases and decreases do not cancel out because they operate on different bases. Formula: Net change = 10 - 10 - (10×10)/100 = -1%.
Passage: Gandhian philosophy posits that means and ends are as inseparable as the seed and the tree, suggesting that immoral methods inevitably corrupt the intended objective. However, this moral absolutism faces a significant challenge in historically contested landscapes where the definition of a 'just end' is itself a site of violent disagreement. If the very nature of an end is fluid and subject to competing cultural interpretations, the mandate to prioritize the purity of means over the achievement of an end becomes problematic. By rigidly tethering the legitimacy of a goal to the morality of its process, one risks paralyzing action in situations where the urgency of the end remains trapped in an intractable conflict of historical values. Which of the following is the most logical inference that can be drawn from the passage?
- Gandhian ethics are entirely unsuitable for resolving conflicts in modern societies where historical values are subject to constant reinterpretation.
- Immoral methods always lead to the corruption of objectives because the seed and the tree share a biological relationship that dictates the final outcome.
- The rigid application of means-ends inseparability may impede necessary action when the moral legitimacy of an objective is fundamentally disputed.
- The primary flaw in Gandhian philosophy is its failure to provide a specific framework for determining which historical ends are objectively just.
Explanation: The passage argues that the Gandhian principle of means-ends inseparability becomes problematic when the "end" itself is subject to conflicting interpretations. Option C accurately captures this central tension by highlighting that a rigid adherence to this philosophy can lead to inaction ("paralyzing action") when there is no consensus on the moral legitimacy of the goal.
Option A is incorrect because it commits the fallacy of overextension; the passage suggests the philosophy faces a "significant challenge" in such landscapes, not that it is "entirely unsuitable" for all modern conflicts.
Option B is incorrect because it relies on misdirection; it treats the "seed and tree" analogy as a literal biological fact rather than a philosophical metaphor, and it ignores the passage's counter-argument regarding the fluidity of ends.
Option D is incorrect because it suffers from narrowing; while the passage notes the difficulty of defining a "just end," it does not explicitly label the lack of a framework as the "primary flaw" of Gandhian philosophy, but rather focuses on the practical consequence of moral absolutism in contested contexts.
Passage: For achieving inclusive growth there is critical need to rethink the role of the State. The early debate among economists about the size of the Government can be misleading. The need of the hour is to have an enabling Government. India is too large and complex a nation for the State to be able to deliver all that needed. Asking the Government to produce all the essential goods, create all the necessary jobs, and keep a curb on the prices of all goods is to lead to a large cumbersome bureaucracy and widespread corruption. The aim must be to stay with the objective of inclusive growth that was laid down by the founding fathers of the nation and also to take a more modern view of what the State can realistically deliver. This is what leads to the idea of an enabling State, that is, a Government that does not try to directly deliver to the citizens everything that they need. Instead, it (1) creates an enabling ethos for the market so that individual enterprise can flourish and citizens can, for the most part, provide for the needs of one another, and (2) steps in to help those who do not manage to do well for themselves, for there will always be individuals, no matter what the system, who need support and help. Hence we need a Government that, when it comes to the market, sets effective, incentive compatible rules and remains on the sidelines with minimal interference, and, at the same time, plays an important role in directly helping the poor by ensuring that they get basic education and health services and receive adequate nutrition and food.
According to the passage, the strategy of inclusive growth can be effected by focusing on
- Meeting all the needs of every citizen in the country.
- Increasing the regulations over the manufacturing sector.
- Controlling the distribution of manufactured goods.
- Delivery of the basic services to the deprived sections of the society.
Explanation: The passage emphasizes that the Government should play an important role in directly helping the poor by ensuring basic education, health services, nutrition, and food, which corresponds to delivering basic services to deprived sections.
Passage: The doctrine of parliamentary sovereignty, enshrined in Westminster-style democracies, posits that legislatures possess untrammeled authority to enact or repeal laws, rendering judicial review subordinate. Yet, this absolutist interpretation confronts a constitutional dilemma: when parliamentary majorities prioritize transient electoral gains over long-term institutional integrity, does sovereignty itself risk degenerating into majoritarian tyranny? The tension lies not in legal form but in democratic substance—where unchecked legislative power may erode the very safeguards meant to protect minority rights and institutional checks, thereby challenging the moral foundations of constitutional governance. Which fundamental conflict between legislative supremacy and constitutional morality does the passage highlight?
- Parliamentary sovereignty risks degenerating into majoritarian tyranny when legislative supremacy eclipses constitutional morality.
- The passage highlights the conflict between untrammeled legislative authority and the erosion of minority rights under constitutional governance.
- It underscores the tension between transient electoral gains and the long-term preservation of institutional integrity in Westminster-style democracies.
- The dilemma arises when legislative supremacy disregards moral foundations, potentially subverting judicial review and checks on majoritarian power.
Explanation: The passage explicitly frames the central conflict as the risk that parliamentary sovereignty, if exercised without constraint, can collapse into “majoritarian tyranny,” thereby undermining the moral foundations of constitutional governance. Option A captures this core tension in a single, concise sentence. Option B is too narrow, focusing only on minority rights rather than the broader constitutional morality. Option C restricts the dilemma to electoral gains and institutional integrity, missing the moral dimension. Option D, though close, is longer than A and unnecessarily introduces judicial review, which is not the passage’s central theme.
Without stoppages, a train travels at an average speed of 60 km/h. With stoppages, its average speed reduces to 45 km/h. How many minutes per hour does the train stop on average?
- 15 min
- 20 min
- 10 min
- 12 min
Explanation: Due to stoppages, the train covers 60 − 45 = 15 km less every hour. Time lost = Distance lost / Original speed = 15 / 60 h = 15 min.
Three runners start together on a 12 km track and run in the same direction at 8 km/h, 10 km/h, and 12 km/h. After how many hours will all three be together again at the starting point for the first time?
- 6 hours
- 5 hours
- 4 hours
- 8 hours
Explanation: (a) GENERAL PRINCIPLE: When multiple objects start together and loop back, they meet again at the start when each has completed an integer number of laps; find the time each takes for one lap, then compute the LCM of these times.
(b) STEP-BY-STEP APPLICATION: Lap times are 12/8 = 1.5 hours, 12/10 = 1.2 hours, and 12/12 = 1 hour. Converting to fractions: 3/2, 6/5, 1. The LCM of numerators (3,6,1) is 6; the GCF of denominators (2,5,1) is 1. So LCM = 6/1 = 6 hours. Verification: In 6 hours, they complete 4, 5, and 6 laps respectively—all integers.
(c) TRANSFERABLE TIP: For circular track meeting problems, convert lap times to fractions and use LCM of numerators over GCF of denominators to find the reunion time.
Find the LCM of 1260 and 1386.
Explanation: 1260 = 2²×3²×5×7, 1386 = 2×3²×7×11. LCM = 2²×3²×5×7×11 = 13860.
The average of 5 numbers is 27. If one number is excluded, the average of the remaining 4 numbers is 25. What is the excluded number?
Explanation: Total of 5 numbers = 5 × 27 = 135. Total of 4 numbers = 4 × 25 = 100. The excluded number = 135 − 100 = 35. The general method is: Excluded Value = (Original Average × Original Count) − (New Average × New Count). This applies to any problem where removing one value changes the average of the remaining values.
'Rights are certain advantageous conditions of social well-being indispensable to the true development of the citizen.' In the light of this statement, which one of the following is the correct understanding of rights?
- Rights aim at individual good only
- Rights aim at social good only
- Rights aim at both individual and social good
- Rights aim at individual good devoid of social well-being
Explanation: The statement describes rights as conditions of social well-being that are indispensable to the true development of the citizen. This indicates rights serve both social well-being and individual development.
What is the LCM of 17 and 51?
Explanation: Since 51 = 3×17, LCM(17,51) = 51.
Passage: Flamingos in large flocks in the wild are social and extremely loyal. They perform group mating dances. Parents are very fond of their chicks, gathering them into creches for protection while both males and females fly off to search for food.
Which among the following is the most logical corollary to the above passage?
- Mass nesting in all species of birds is essential to ensure complete survival of their offspring.
- Only birds have the capacity to develop social behaviour and thus can do mass nesting to raise their chicks in safety.
- Social behaviour in some species of birds increases the odds of survival in an unsafe world.
- All species of birds set up creches for their chicks to teach them social behaviour and loyalty.
Explanation: The passage describes flamingos exhibiting social and loyal behavior, including group dances and creches for chick protection. A logical corollary is that such social behavior enhances survival chances, without generalizing this to all bird species or claiming exclusivity.
Passage: The rapid proliferation of nanotechnology has outpaced our regulatory capacity, creating a dangerous governance vacuum where innovation dictates the trajectory of progress before safety standards are even conceived. While proponents argue that preemptive regulation stifles scientific breakthroughs, this reactive approach ignores the systemic risks inherent in manipulating matter at the atomic scale. By prioritizing market speed over precautionary oversight, we risk irreversible ecological and biological consequences that no retrospective policy can rectify. Therefore, establishing a dynamic, anticipatory governance framework is not merely a bureaucratic necessity but a fundamental prerequisite for the sustainable integration of nanotechnology into the global economy, ensuring that scientific advancement does not bypass essential ethical and safety mandates. Which of the following is an assumption on which the argument in the passage depends?
- Reactive policy approaches are ineffective because they fail to address the specific ethical concerns raised by the manipulation of matter at.
- Global economic stability depends entirely on the immediate implementation of comprehensive regulatory standards for all nanotechnology applications.
- Anticipatory governance frameworks are capable of mitigating systemic risks without necessarily halting the pace of technological innovation.
- Scientific breakthroughs in nanotechnology are primarily driven by the absence of safety standards and regulatory oversight over time in this context broadly speaking.
Explanation: The passage argues that a shift from reactive to anticipatory governance is necessary to manage the systemic risks of nanotechnology without sacrificing safety. Option C is the correct assumption because the author’s argument for "anticipatory governance" as a "fundamental prerequisite" would be logically undermined if such frameworks were inherently incompatible with scientific progress. If anticipatory governance necessarily halted innovation, the author's goal of "sustainable integration" would be impossible to achieve.
Option A is incorrect because it commits the trap of narrowing; while the passage mentions ethical concerns, the core argument centers on the systemic risks and the failure of retrospective policy, not merely the specific content of ethical concerns. Option B is incorrect because it suffers from overextension; the passage advocates for anticipatory governance as a prerequisite for sustainable integration, but it does not claim that global economic stability depends *entirely* on immediate implementation, which is an extreme, unsubstantiated leap. Option D is incorrect because it is a misdirection; the passage discusses the *consequences* of the current regulatory vacuum, but it does not assume or argue that the *primary driver* of scientific breakthroughs is the lack of oversight.
What is the HCF of 8! and 9!?
Explanation: HCF(72+48, 72-48) = HCF(120, 24) = 24.
A 300 m long train overtakes a 200 m long train in 45 seconds while running in the same direction. If the slower train moves at 54 km/h, what is the speed of the faster train?
- 84 km/h
- 90 km/h
- 94 km/h
- 100 km/h
Explanation: Total distance = 300 + 200 = 500 m. Relative speed = 500 / 45 = 11.11 m/s = 40 km/h. Faster train speed = 54 + 40 = 94 km/h.
Passage: In a free country, the man who reaches the position of leader is usually one of outstanding character and ability. Moreover, it is usually possible to foresee that he will reach such a position, since early in life one can see his qualities of character. But this is not always true in the case of a dictator; often he reaches his position of power through chance, very often through the unhappy state of his country.
The passage seems to suggest that
- a leader foresees his future position
- a leader is chosen only by a free country
- a leader must see that his country is free from despair
- despair in a country sometimes leads to dictatorship
Explanation: The passage contrasts leaders in free countries with dictators, noting that dictators often rise through chance and the unhappy state of their country. This suggests that national despair or unhappiness can create conditions for dictatorship.
Consider the following statements: The Third World War, if it ever starts will end very quickly with possible end of civilization. It is only the misuse of nuclear power which will trigger it. Based on the above statement, which one of the following inferences is correct?
- Nuclear power will be used in Third World War.
- There will be no civilization left after third world war.
- The growth of nuclear power will destroy civilization in the long run.
- The Third World War will not take place.
Explanation: The statement specifies that only misuse of nuclear power will trigger the Third World War, meaning that if the war occurs, nuclear power will necessarily be involved. The other options make stronger claims than the premises support, such as certainty about civilization's end or predictions about the war's occurrence.
If A # B means A is the father of B, A @ B means A is the brother of B, A $ B means A is the wife of B, and A % B means A is the daughter of B, then what is the relation of P to T in the expression: P # Q @ R $ S # T?
- Grandfather
- Father
- Brother
- Uncle
Explanation: Decode step by step: P # Q means P is father of Q. Q @ R means Q is brother of R. R $ S means R is wife of S, so S is the husband of R. Since Q is brother of R, Q is the brother of S's wife, making Q the brother-in-law of S. S # T means S is father of T. Since R is wife of S and mother of T, and Q is brother of R, Q is the uncle of T (brother of T's mother). P is father of Q and R (since they are siblings), making P the father of T's mother. Therefore P is the grandfather of T.
Passage: The debate on free will hinges on whether neural correlates of decision-making negate autonomy. Neuroscientific evidence shows that unconscious brain processes precede conscious choices, suggesting actions are predetermined by prior neural states. Critics argue this undermines moral responsibility, reducing humans to biological automatons. Yet, proponents of compatibilism counter that even if decisions arise from neural activity, the subjective experience of agency persists, preserving free will as a functional, albeit constrained, reality. This tension exposes a critical dilemma: if free will is an illusion, does society’s moral and legal framework collapse, or does it adapt to a probabilistic understanding of human agency?. What is the central tension presented in the passage regarding free will and neuroscience?
- Neuroscience challenges free will by showing unconscious processes precede conscious choices.
- The dilemma pits predetermined neural states against the persistence of subjective agency.
- Moral responsibility appears undermined if decisions are biologically determined.
- Compatibilists argue that functional free will persists despite neural constraints.
Explanation: The central tension in the passage is between the deterministic implications of neuroscience (that unconscious neural processes precede conscious choices, implying predetermined actions) and the subjective experience of agency (compatibilist view that free will persists as a functional reality despite neural constraints). Option B captures this dilemma most precisely by framing it as a conflict between predetermined neural states and the persistence of subjective agency.
Distractor analysis:
A is incorrect because it only states one side of the tension (neuroscience challenging free will) without addressing the counter-perspective of subjective agency.
C is incorrect because it focuses narrowly on moral responsibility, which is a consequence of the tension but not the core dilemma itself.
D is incorrect because it presents only the compatibilist position (one side of the debate) rather than the central tension between determinism and agency.
The digit in the unit place of the number 6^129 × 7^307 is
Explanation: Powers of 6 always end in 6, so the unit digit of 6^129 is 6. The unit digits of powers of 7 follow a cycle of 4: 7, 9, 3, 1. Since 307 ÷ 4 leaves remainder 3, the unit digit of 7^307 is the same as 7^3, which is 3. Multiplying the unit digits: 6 × 3 = 18. Therefore, the unit digit is 8.
A soldier is facing North. He receives an order to turn 315° in the clockwise direction. Which direction is he facing now?
- South-West
- North-East
- West
- North-West
Explanation: A 315° clockwise turn from North (0°) gives a bearing of 315°. Since 315° = 360° − 45°, this is 45° West of North, which is the North-West direction.
If (a + b)x + (a - b) = 2a, where a + b ≠ 0, what is the value of x?
- 1
- 2a/(a+b)
- (a+b)/(a-b)
- a/b
Explanation: Transpose the constant term (a-b) to the right side, factor the resulting numerator as (a+b), then divide both sides by (a+b) to isolate x.
Solve: x + y + z = 10, 2x + 3y + z = 19, and 3x + 2y - z = 11. What is the value of z?
Explanation: Use the elimination method on the three equations. Add equations to eliminate z, creating a system of two equations in x and y. Solve that system, then substitute back to find z.
If A + B means A is the father of B, A - B means A is the mother of B, A × B means A is the brother of B, and A ÷ B means A is the sister of B, then what is the relation of P to T in the expression: P + Q - R × S ÷ T?
- Brother
- Grandfather
- Uncle
- Father
Explanation: Decode step by step: P + Q means P is father of Q. Q - R means Q is mother of R. R × S means R is brother of S. S ÷ T means S is sister of T. Therefore R and S are siblings (brother and sister), and T is their sibling too (since S is sister of T). Q is mother of R, so Q is also mother of S and T. P is father of Q, making P the grandfather of R, S, and T. Thus P is the grandfather of T.
The compound interest on a certain sum for 2 years at 15% per annum is ₹3,225. What is the sum?
- ₹10,000
- ₹15,000
- ₹12,000
- ₹8,000
Explanation: P = CI/[(1+r)² − 1] = ₹3,225/[(1.15)² − 1] = ₹3,225/0.3225 = ₹10000.
Passage: Financial markets in India have acquired greater depth and liquidity over the years. Steady reforms since 1991 have led to growing linkages and integration of the Indian economy and its financial system with the global economy. Weak global economic prospects and continuing uncertainties in the international financial markets therefore, have had their impact on the emerging market economies including India. Sovereign risk concerns, particularly in the Euro area, affected financial markets for the greater part of the year, with the contagion of Greece's sovereign debt problem spreading to India and other economies by way of higher-than-normal levels of volatility. The funding constraints in international financial markets could impact both the availability and cost of foreign funding for banks and corporates. Since the Indian financial system is bank dominated, banks' ability to withstand stress is critical to overall financial stability. Indian banks, however, remain robust, notwithstanding a decline in capital to risk-weighted assets ratio and a rise in non-performing asset levels in the recent past. Capital adequacy levels remain above the regulatory requirements. The financial market infrastructure continues to function without any major disruption. With further globalization, consolidation, deregulation, and diversification of the financial system, the banking business may become more complex and riskier. Issues like risk and liquidity management and enhancing skill therefore assume greater significance.
Risk and liquidity management assumes more importance in the Indian banking system in future due to 1. further globalization. 2. more consolidation and deregulation of the financial system. 3. further diversification of the financial system. 4. more financial inclusion in the economy.
- 1, 2 and 3
- 2, 3 and 4
- 1 and 2 only
- 3 and 4 only
Explanation: The passage states that with further globalization, consolidation, deregulation, and diversification of the financial system, banking business may become more complex and riskier, making risk and liquidity management more important. The first three statements are all mentioned together in the passage, while financial inclusion is not mentioned.
What is the LCM of 8! and 9!?
- 40320
- 181440
- 725760
- 362880
Explanation: 9! = 9×8!. LCM(8!, 9!) = 9! = 362880.
Six subjects—Physics, Chemistry, Math, Biology, History, and Geography—are taught from Monday to Saturday. Physics is on Saturday. Chemistry is on the day immediately after Math. Biology is not on Monday or Wednesday. History is on Monday. Geography is before Physics but after Chemistry. The subject on Tuesday is not Chemistry. The subject on Thursday is not Geography. Which subject is on Thursday?
- Chemistry
- History
- Biology
- Math
Explanation: Begin with fixed assignments: Physics is on Saturday and History is on Monday. Chemistry is immediately after Math, and Geography is after Chemistry but before Saturday, creating a chain: Math → Chemistry → Geography. This chain requires three ordered days before Saturday. Testing Math on Tuesday and Chemistry on Wednesday: Geography must then be on Thursday or Friday. If Geography were on Thursday, Biology would need to be on Friday (since Biology cannot be on Monday or Wednesday, and Tuesday is Math, Thursday is Geography); however, the constraint states that Thursday is not Geography. Therefore Geography is on Friday, making Biology on Thursday. The constraint that Tuesday is not Chemistry is satisfied (Math is on Tuesday), and the constraint that Thursday is not Geography is satisfied (Biology is on Thursday).
Passage: The mangroves can shed tons of leaves per acre every year; fungi and bacteria break down this leaf litter and consume it, they then are consumed by tiny worms and crustaceans, which in turn feed small fish, which feed larger fish and birds and crocodiles.
Which among the following is the most logical inference of the above statement?
- Coastal areas cannot have food chains without mangroves.
- Mangroves are an essential component of all marine ecosystems.
- Mangroves have a crucial role in some of the coastal food chains.
- The composition of marine flora and fauna is largely determined by mangroves.
Explanation: The passage traces a specific coastal food chain beginning with mangrove leaves. The most accurate inference is that mangroves play a crucial role in some coastal food chains, without overgeneralizing to all marine ecosystems or claiming coastal areas cannot have food chains without them.
Three fair dice are rolled together. What is the probability that the product of the three numbers shown is an odd number?
Explanation: For the product to be odd, every die must show an odd number (1, 3, or 5). The probability for one die is 3/6 = 1/2. Since the dice are independent, multiply: (1/2) × (1/2) × (1/2) = 1/8.
A invests ₹4,000 for the first 3 months and then increases his investment to ₹7,000 for the remaining 9 months. B invests ₹5,000 for the first 6 months and then reduces to ₹3,000 for the next 6 months. If the profit is ₹12,300, what is A's share?
- ₹6,000
- ₹4,800
- ₹8,000
- ₹7,500
Explanation: A's equivalent = 4000×3 + 7000×9 = 12,000 + 63,000 = 75,000. B's equivalent = 5000×6 + 3000×6 = 30,000 + 18,000 = 48,000. Ratio = 75:48 = 25:16. Total = 41. A's share = (25/41)×12300 = ₹7,500.
Passage: 'Desertification' is a term used to explain a process of decline in the biological productivity of an ecosystem, leading to total loss of productivity. While this phenomenon is often linked to the arid, semi-arid and sub-humid ecosystems, even in the humid tropics, the impact could be most dramatic. Impoverishment of human-impacted terrestrial ecosystems may exhibit itself in a variety of ways: accelerated erosion as in the mountain regions of the country, salinization of land as in the semi-arid and arid 'green revolution' areas of the country, e.g., Haryana and western Uttar Pradesh, and site quality decline—a common phenomenon due to general decline in tree cover and monotonous monoculture of rice/wheat across the Indian plains. A major consequence of deforestation is that it relates to adverse alterations in the hydrology and related soil and nutrient losses. The consequences of deforestation invariably arise out of site degradation through erosive losses. Tropical Asia, Africa and South America have the highest levels of erosion. The already high rates for the tropics are increasing at an alarming rate (e.g., through the major river systems—Ganga and Brahmaputra, in the Indian context), due to deforestation and ill-suited land management practices subsequent to forest clearing. In the mountain context, the declining moisture retention of the mountain soils, drying up of the underground springs and smaller rivers in the Himalayan region could be attributed to drastic changes in the forest cover. An indirect consequence is drastic alteration in the upland-lowland interaction, mediated through water. The current concern the tea planter of Assam has is about the damage to tea plantations due to frequent inundation along the flood-plains of Brahmaputra, and the damage to tea plantation and the consequent loss in tea productivity is due to rising level of the river bottom because of siltation and the changing course of the river system. The ultimate consequences of site desertification are soil degradation, alteration in available water and its quality, and the consequent decline in food, fodder and fuel-wood yields essential for the economic well-being of rural communities.
According to the passage, which of the following are the consequences of decline in forest cover? Loss of topsoil. Loss of smaller rivers. Adverse effect on agricultural production. Declining of groundwater. Select the correct answer using the code given below.
- 1, 2 and 3 only
- 2, 3 and 4 only
- 1 and 4 only
- 1, 2, 3 and 4
Explanation: The passage explicitly links deforestation to accelerated erosion and topsoil loss, drying up of underground springs and smaller rivers, damage to tea plantations and agricultural productivity, and declining moisture retention and groundwater.