UPSC CSE Prelims 2025 CSAT (General Studies Paper II)

Reading Comprehension — Solved Questions

1. Q1: Passage: Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ec
   Answer: C — Sustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.
   The correct answer is Sustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.. Key Points - The passage describes the conflict between livelihood, commercial exp
2. Q2: With reference to the passage on ecosystem and biodiversity, the following assumptions have been made: I. No country needs to depend on ecosystems to boost national income. II. Resource-rich countries
   Answer: D — Neither I nor II
   The correct answer is Neither I nor II. Key Points - Assumption I states no country needs ecosystems to boost national income — the passage explicitly says commercial exploitation can boost national income in developing countries, so I is i
3. Q3: Passage: The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms'
   Answer: D — Timing plays a crucial role in the case of green technology development.
   The correct answer is Timing plays a crucial role in the case of green technology development.. Key Points - The passage emphasises that early and gradual green transition is better than a late chaotic one, and that timing determines how sm
4. Q4: With reference to the passage on renewable energy, the following assumptions have been made: I. Path-dependent green investments will eventually most likely benefit growth as well as public finances i
   Answer: C — Both I and II
   The correct answer is Both I and II. Key Points - Assumption I: India following path-dependent green investment would likely benefit growth and public finances — this is a reasonable inference from the passage. - Assumption II: If other tec
5. Q11: Passage: Each State in India faces a distinctive set of challenges regarding the impact of warming, but also offers its own set of opportunities for reducing emissions depending on its natural resourc
   Answer: D — India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.
   The correct answer is India needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.. Key Points - The passage talks about how different Indian regions face different climate challenges and
6. Q12: With reference to the passage on Indian States and climate challenges, the following assumptions have been made: I. Green energy production can be linked to/integrated with the climate change mitigati
   Answer: A — I only
   The correct answer is I only. Key Points - Assumption I: Green energy production (wind in coastal/peninsular regions) can integrate with climate mitigation — the passage directly supports this. - Assumption II: Climate change effects are &q
7. Q13: Passage: If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty l
   Answer: D — Insecurity, more than poverty, is the main economic issue that Government policies must address.
   The correct answer is Insecurity, more than poverty, is the main economic issue that Government policies must address.. Key Points - The passage's main argument is that insecurity — not poverty — is the most felt economic problem, and gover
8. Q14: With reference to the passage on social inequality and insecurity, the following assumptions have been made: I. People above the poverty line also are prone to suffer from anxiety about economic insec
   Answer: A — I only
   The correct answer is I only. Key Points - Assumption I: Even people above the poverty line suffer economic insecurity — directly supported by the passage ("even those just over the poverty line are subject to multiple economic insecur
9. Q21: Passage: One of the dismal realities of the agricultural sector in independent India has been that it never experienced a high-growth phase, unlike the non-agricultural economy. The highest decadal gr
   Answer: A — The benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.
   The correct answer is The benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.. Key Points - The passage says agriculture never experienced a high-growth phase unlike non-ag
10. Q22: With reference to the passage on Indian agricultural sector, the following assumptions have been made. The growing divergence between the fortunes of the agricultural and non-agricultural economy in I
    Answer: D — Neither I nor II
    The correct answer is Neither I nor II. Key Points - The passage says agriculture suffered relative stagnation while non-agriculture grew. - Assumption I (large-scale commercial/corporate farming) — the passage doesn't suggest this as a rem
11. Q23: Passage: In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the Sta
    Answer: A — We need to free the handloom industry from the limited narrative linked to preserving cultural heritage.
    The correct answer is We need to free the handloom industry from the limited narrative linked to preserving cultural heritage.. Key Points - The passage argues that the traditional narrative around handlooms excludes many identities, causin
12. Q24: With reference to the passage on handlooms, the following assumptions have been made: I. There is no need for the State to be involved in any manner in the handloom sector. II. Handloom products are n
    Answer: D — Neither I nor II
    The correct answer is Neither I nor II. Key Points - Assumption I: No need for State involvement — the passage says State support exists and has a legitimate basis, so removing it entirely is not implied. I is invalid. - Assumption II: Hand
13. Q31: Passage: In our country, regrettably, teaching and learning for the examination have been our forte but the new demands of society and the future of work require critical and independent thinking, lea
    Answer: D — Classroom needs to be reimagined and teaching needs to be re-invented.
    The correct answer is Classroom needs to be reimagined and teaching needs to be re-invented.. Key Points - The passage criticises exam-centric teaching and calls for teaching "how to think rather than what to think," saying teachi
14. Q32: With reference to the passage on higher education, the following assumptions have been made: I. Higher education is a constantly evolving subject that needs to align towards new developments in all sp
    Answer: A — I only
    The correct answer is I only. Key Points - Assumption I: Higher education must constantly evolve to align with new societal developments — directly supported by the passage. I is valid. - Assumption II: Insufficient funds for higher educati
15. Q33: Passage: If there is inequality in the pattern of population growth, there is greater inequality in food production and utilization. As societies become wealthier, their consumption of animal products
    Answer: B — Animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.
    The correct answer is Animal-based food is far less efficient than grain/plant-based food in terms of production and utilization.. Key Points - The passage argues that wealthy societies convert plant food into animal feed very inefficiently
16. Q34: With reference to the passage on food inequality, the following assumptions have been made: I. The food manufacturing and processing industries in every country should align their objectives and proce
    Answer: B — II only
    The correct answer is II only. Key Points - Assumption I: Food industries should align with changing societal needs — too broad an inference not directly supported. I is invalid. - Assumption II: Wealthier societies lose more calories throu
17. Q41: Passage: Over the next 30 years, many countries are promising to move to net-zero carbon, implying that household emissions will have to be cut to close to nothing. A leading climate scientist reckons
    Answer: B — Low-carbon behaviour in people can be brought about by incentivising them.
    The correct answer is Low-carbon behaviour in people can be brought about by incentivising them.. Key Points - The passage says half the reduction in carbon could come from demand-side (behavioural) changes, but this requires companies and
18. Q42: With reference to the passage on net-zero carbon, the following assumptions have been made: I. Supply-side investments in companies can result in low-carbon behaviour in people. II. People are not cap
    Answer: A — I only
    The correct answer is I only. Key Points - Assumption I: Supply-side investments can result in low-carbon behaviour — directly stated in the passage. I is valid. - Assumption II: People are incapable of low-carbon behaviour without Governme
19. Q43: Passage: In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than 9% of this is reused. Batteries of old vehicles contain materials su
    Answer: C — Circular economy can be beneficial for sustainable growth.
    The correct answer is Circular economy can be beneficial for sustainable growth.. Key Points - The passage argues for reusing materials (batteries with lithium, cobalt etc.) in a circular economy model. - Option C — "Circular economy c
20. Q44: With reference to the passage on raw materials and circular economy, the following assumptions have been made: I. Automobile factories are examples of the circular economy. II. Economic growth is comp
    Answer: B — II only
    The correct answer is II only. Key Points - Assumption I: Automobile factories as examples of circular economy — the passage mentions batteries going back to factories as an example, but the passage is about the concept broadly, not that au
21. Q51: 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 m
    Answer: B — Our total dependence on genetically honed crops entails possible food insecurity.
    The correct answer is Our total dependence on genetically honed crops entails possible food insecurity.. Key Points - The passage argues that centuries of selective breeding have removed genetic diversity from crops, making them vulnerable
22. Q52: With reference to the passage on plant diseases and climate change, the following assumptions have been made: I. Global climate change can result in the migration of several plant diseases to new area
    Answer: C — Both I and II
    The correct answer is Both I and II. Key Points - Assumption I: Climate change can cause plant diseases to migrate to new regions — the passage mentions risk that changes will make infections more common "in all climatic zones," i
23. Q53: Passage: "A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents
    Answer: D — In a democracy, the opposition is indispensable for the balance of political power and good governance.
    The correct answer is In a democracy, the opposition is indispensable for the balance of political power and good governance.. Key Points - The passage argues that a good statesman needs opponents to stay on the path of reason, and democrac
24. Q54: With reference to the passage on opposition in democracy, the following assumptions have been made: I. In a democracy, a strong opposition is required only if the Head of Government is indifferent. II
    Answer: D — Neither I nor II
    The correct answer is Neither I nor II. Key Points - Assumption I: Strong opposition is only needed if the Head of Government is indifferent — the passage says opposition is needed regardless, not just in special cases. I is invalid. - Assu
25. Q61: Passage: There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to i
    Answer: A — Corporate capitalism is important for economic growth of a State and also for democracy.
    The correct answer is Corporate capitalism is important for economic growth of a State and also for democracy.. Key Points - The passage argues corporate capitalism is essential for economic growth, employment, and generating State revenues
26. Q62: With reference to the passage on corporate capitalism, the following assumptions have been made: I. Corporate capitalism promotes the growth of labour force and provides more employment opportunities.
    Answer: C — Both I and II
    The correct answer is Both I and II. Key Points - Assumption I: Corporate capitalism promotes labour force growth and employment — directly supported ("generates jobs"). I is valid. - Assumption II: Poor and marginalized benefit t
27. Q63: Passage: "A network of voluntary associations stands as a 'buffer' between the relatively powerless individual and the potentially powerful State." Which one of the following statements refl
    Answer: C — It takes individuals out of a state of isolation and gives them a chance to participate in the common endeavour.
    The correct answer is It takes individuals out of a state of isolation and gives them a chance to participate in the common endeavour.. Key Points - The passage says voluntary associations act as a buffer between powerless individuals and t
28. Q71: Passage: A single number for inflation is an aggregate across different commodities and services — the price rise differs for different items of consumption. So, the single number is arrived at by ass
    Answer: B — The present calculation of inflation rate does not correctly measure price rise of individual item/commodity.
    The correct answer is The present calculation of inflation rate does not correctly measure price rise of individual item/commodity.. Key Points - The passage argues that CPI uses an averaged consumption basket, but different classes (poor,
29. Q72: Passage: Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of
    Answer: D — Trust is important though it entails risk.
    The correct answer is Trust is important though it entails risk.. Key Points - The passage discusses how trust is central to entrepreneurship and globalisation despite the vulnerability it creates. - Option D — "Trust is important thou

Quantitative Aptitude — Solved Questions

1. Q5: A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?
   Answer: C — 8
   The correct answer is 8. Key Points - A natural number N = p + q + r where p, q, r are distinct factors of N. Checking numbers below 50: 12 = 1+2+3 (factors of 12? - 3 is a factor, but 1+2+3=6≠12). - Numbers satisfying this are: 12, 20, 24,
2. Q6: Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)?
   Answer: D — More than 6
   The correct answer is More than 6. Key Points - Three primes p q r each < 20 in arithmetic progression (p−q = q−r). - AP prime triplets: (3,5,7), (5,11,17), (7,11,15-not prime), (5,7,9-not prime), (3,7,11), (7,13,19), (3,11,19), (5,13,21
3. Q7: How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)?
   Answer: C — Three
   The correct answer is Three. Key Points - 1/p + 1/q + 1/r = 1 with natural numbers. - WLOG p ≤ q ≤ r. Then 1/p ≥ 1/3, so p ≤ 3. If p=2: 1/q+1/r=1/2 → (q,r) = (3,6),(4,4). - If p=3: 1/q+1/r=2/3 → q=3,r=3 works (1/3+1/3+1/3=1). - Solutions: (
4. Q9: 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 ma
   Answer: D — Cannot be determined
   The correct answer is Cannot be determined. Key Points - Team Y ties in 18 overs (10% less than 20). Let N = total runs. - Y's run rate = N/18. If Y's rate were 50% higher: (N/18) × 1.5 = N/12 — this matches exactly 12 overs as given. - But
5. Q10: The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?
   Answer: A — p(10⁴ − k²)² = q × 10⁸
   The correct answer is p(10⁴ − k²)² = q × 10⁸. Key Points - Starting price p: after +k%: p(1+k/100); after −k%: p(1−k²/10000); after +k%: p(1−k²/10000)(1+k/100); after −k%: p((1−k²/10000))² = q. So p×((10000−k²)/10000)² = q → p(10⁴−k²)² = q×
6. Q17: The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90 per litre. A person travels 2200 km every month and his car gives a mileage of
   Answer: B — 200 km
   The correct answer is 200 km. Key Points - Previous price: ₹90/litre. - New price: ₹99/litre (10% hike). - Previous monthly spend: 2200/16 × 90 = 137.5 × 90 = ₹12,375. - At new price for same spend: litres = 12375/99 = 125 litres → distance
7. Q18: A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?
   Answer: C — 1078
   The correct answer is 1078. Key Points - In each division, the remainder is 2 less than the divisor: 3−1=2 short, wait: 1=3−2, 3=5−2, 4=6−2, 7=9−2. So N ≡ −2 (mod 3), N ≡ −2 (mod 5), N ≡ −2 (mod 6), N ≡ −2 (mod 9). - N+2 divisible by LCM(3,
8. Q20: What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999?
   Answer: C — 5
   The correct answer is 5. Key Points - The product 1×3×5×7×...×999 includes the factor 5 (and many multiples of 5 like 15, 25, 35...) as well as odd multiples. - Since 5 is a factor and no factor of 2 exists (all odd numbers), the product en
9. Q25: Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?
   Answer: C — 22
   The correct answer is 22. Key Points - Using inclusion-exclusion for numbers 1–100 not divisible by 2, 3, 5, or 7 (9 is covered by 3). - Count = 100 × (1−1/2)(1−1/3)(1−1/5)(1−1/7) = 100 × 1/2 × 2/3 × 4/5 × 6/7 ≈ 22.85. Exact count = 22. Ans
10. Q26: If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?
    Answer: D — None of the above
    The correct answer is None of the above. Key Points - Max of (x+y): x=8, y=7 → 15. Min of (x−y): x=4, y=7 → −3. Ratio = 15/(−3) = −5. None of the options (15/6, 2, 15/2) equal −5. Answer: None of the above.
11. Q27: Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?
    Answer: B — 5
    The correct answer is 5. Key Points - p² + k must be prime and < 30. Try p=2: 4+k < 30 → k < 26. k prime: 2→6(not prime), 3→7(prime✓), 5→9(not prime), 7→11(prime✓), 11→15(not), 13→17(prime✓), 17→21(not), 19→23(prime✓). - Try p=3: 9
12. Q28: There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?
    Answer: D — More than 8
    The correct answer is More than 8. Key Points - 1001 = 7 × 11 × 13. Sets of three positive integers with LCM=1001 and HCF=1 means each prime (7,11,13) must appear in at least one number. - The number of such sets is more than 8. Answer: Mor
13. Q29: Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the numb
    Answer: B — 3
    The correct answer is 3. Key Points - PQR − PS = PPT, Q=3. P3R − PS = PPT. - Working through digit constraints with T<6: P=1 gives 13R−1S=11T. - Testing valid digit combinations where R,S,T are distinct non-zero digits and T<6, there
14. Q35: What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35ⁿ?
    Answer: B — 4
    The correct answer is 4. Key Points - 7 × 343 × 385 × 1000 × 2401 × 77777. - 35 = 5 × 7. Count factors of 5: 385=5×7×11 (one 5), 1000=8×125=5³ (three 5s), 77777=7×11111 (no 5). - Total 5s = 4. Count factors of 7: 7 (one), 343=7³ (three), 38
15. Q37: P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds pe
    Answer: B — 13
    The correct answer is 13. Key Points - P and Q move in opposite directions at 5+3=8 rounds/hour combined. - They cross every 1/8 hour = 7.5 minutes. - From 5:00 to 5:20 = 20 minutes: crosses at 7.5, 15 min = 2 crosses. - From 5:20 to 7:00 =
16. Q39: A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of th
    Answer: C — 20 m
    The correct answer is 20 m. Key Points - Let tram speed = v km/hr, length = L metres. - Relative speed vs X (3 km/hr): (v−3)×8/3600 = L/1000. - Relative speed vs Y (4 km/hr): (v−4)×9/3600 = L/1000. - So (v−3)×8 = (v−4)×9 → 8v−24 = 9v−36 → v
17. Q40: If N² = 12345678987654321, then how many digits does the number N have?
    Answer: B — 9
    The correct answer is 9. Key Points - The number 12345678987654321 is a well-known perfect square with a beautiful pattern. - It is the square of the repunit made of nine 1s: - 111111111² = 12345678987654321. - In general, a string of n one
18. Q45: A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If h
    Answer: D — 16 minutes
    The correct answer is 16 minutes. Key Points - Set X (20 pipes) fills 70% in 14 min → 20 pipes fill 1 tank in 14×10/7 = 20 min → 1 pipe fills in 400 min. - Set Y (10 pipes) fills 3/8 in 6 min → 10 pipes fill in 16 min → 1 pipe fills in 160
19. Q46: If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4?
    Answer: C — 2
    The correct answer is 2. Key Points - 1ⁿ + 2ⁿ = 1 + 2ⁿ. - When n is even: 2ⁿ ≡ 0 (mod 4) → remainder = 1. When n is odd: 2ⁿ ≡ 0 (mod 4) → remainder = 1 (since 2¹=2, 2²=4, 2³=8...). - Wait: n=1: 1+2=3 (mod 4 = 3). n=2: 1+4=5 (mod 4 = 1). n=3
20. Q47: Let P = QQQ be a 3-digit number (where all digits are Q). What is the HCF of P and 481?
    Answer: C — 37
    The correct answer is 37. Key Points - P = QQQ = Q × 111 = Q × 3 × 37. 481 = 13 × 37. HCF(QQQ, 481) = HCF(Q×3×37, 13×37) = 37 (since Q is a single digit, not divisible by 13). Answer: 37.
21. Q48: What is the 489th digit in the number 123456789101112...?
    Answer: D — 9
    The correct answer is 9. Key Points - Digits 1-9: 9 digits. - Digits 10-99: 90×2=180 digits (total 189). - Digits 100-999: 3 digits each. - 489−189=300 digits into 3-digit numbers. - 300/3=100 numbers after 99, so the 100th number = 199. -
22. Q58: The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?
    Answer: B — 4
    The correct answer is 4. Key Points - P=3T (P is thrice T). - Possible: T=1,P=3; T=2,P=6; T=3,P=9. S=Q+4, Q=R+3. All digits distinct, non-zero. - T=1,P=3: remaining digits for Q,R,S from 2,4,5,6,7,8,9 with S=Q+4 and Q=R+3. R,Q,S: if R=2,Q=5
23. Q59: X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n d
    Answer: B — 4
    The correct answer is 4. Key Points - X completes 1/3 work in 6 days → full work in 18 days. - Y: 1/3 in 8 days → full in 24 days. - Z: 3/4 in 12 days → full in 16 days. - Combined rate = 1/18+1/24+1/16 = 8/144+6/144+9/144 = 23/144 per day.
24. Q64: Consider the following statements: I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150%
    Answer: C — Both I and II
    The correct answer is Both I and II. Key Points - Statement I: Increase a number by 50%: e.g., 2 → 3. Factors of 2: 1,2 = 2 factors. - Factors of 3: 1,3 = 2 factors. ✓ Same number of factors. I is correct. - Statement II: Increase by 150%:
25. Q67: What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + ... + 9¹⁰⁰ is divided by 6?
    Answer: A — 0
    The correct answer is 0. Key Points - 9 ≡ 3 (mod 6). 9² = 81 ≡ 3 (mod 6). - In fact 9ⁿ ≡ 3 (mod 6) for all n ≥ 1. Sum = 9³+9⁴+...+9¹⁰⁰ = 98 terms each ≡ 3 (mod 6). - Sum ≡ 98×3 = 294 ≡ 294 mod 6 = 0 (since 294 = 49×6). Answer: 0.
26. Q75: In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to
    Answer: D — Cannot be determined due to insufficient data
    The correct answer is Cannot be determined due to insufficient data. Key Points - X+Y+Z=37, X/Y = Y/Z → Y² = XZ. - This is a geometric progression. - Without additional constraints, X, Y, Z can be many sets of integers (e.g., 1, 6, 36 sum=4
27. Q76: Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II = Maximum value of p × q when p ≥ −6, q ≥ −4. Which one of the following is correct?
    Answer: C — Value-I = Value-II
    The correct answer is Value-I = Value-II. Key Points - p+q=10. Value-I: max p×q for positive integers: p=5,q=5 → 25. Value-II: max p×q for p≥−6, q≥−4, p+q=10. q = 10−p. f(p) = p(10−p). - If p=−6: (−6)(16)=−96. If q=−4: p=14, 14×(−4)=−56. Ma
28. Q77: Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ −5. Value-II = Minimum value of the product of the numbers of the se
    Answer: C — Value-I = Value-II
    The correct answer is Value-I = Value-II. Key Points - 11 consecutive integers ≥ −5: minimum average when starting at −5: −5,−4,...,5. - Average = 0. Value-I = 0. 11 consecutive non-negative integers with minimum product: 0,1,2,...,10 → pro
29. Q78: The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?
    Answer: A — k
    The correct answer is k. Key Points - Average of p, q, r = k → p+q+r = 3k. - "p is as much more than average as q is less": p−k = k−q → p+q = 2k. - Therefore r = 3k−(p+q) = 3k−2k = k. Answer: r = k.
30. Q79: Let x be a real number between 0 and 1. Which of the following statements is/are correct? I. x² x³. II. x √x.
    Answer: A — I only
    The correct answer is I only. Key Points - For 0 < x < 1: Statement I: x² x³? - Divide by x² (positive): 1 x. True for 0<x<1. ✓ Statement II: x √x? - For 0<x<1, √x x (e.g., x=0.25: √0.25=0.5 0.25). So x √x is FALSE. - Only
31. Q80: The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?
    Answer: C — There can be more than one such number.
    The correct answer is There can be more than one such number.. Key Points - Two natural numbers differ by 10 (e.g., a and a+10). - Natural numbers divisible by 5 between them depend on a. If a=1: between 1 and 11 → 5, 10 → two numbers. - If

Mental Ability & Logical Reasoning — Solved Questions

1. Q8: What comes at X and Y respectively in the following sequence? January, January, December, October, X, March, October, Y, September
   Answer: B — July, April
   The correct answer is July, April. Key Points - The sequence encodes month-number products or cumulative counts. - Working through the pattern: the months correspond to their positions and the differences between consecutive month numbers f
2. Q15: A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The mi
   Answer: C — Both I and II
   The correct answer is Both I and II. Key Points - 60 = 3×4×5. Minimum cuts to get 60 pieces = cuts along 3 axes: 2 cuts (3 slices) + 3 cuts (4 slices) + 4 cuts (5 slices) = 9 cuts. Statement I is correct. - Inner unpainted pieces = (3−2)×(4
3. Q16: If 7 24 = 25 and 12 16 = 20, then what is 16 63 equal to?
   Answer: C — 65
   The correct answer is 65. Key Points - Pattern: 7² + 24² = 49 + 576 = 625 = 25² and 12² + 16² = 144 + 256 = 400 = 20². - These are Pythagorean triples. - 16² + 63² = 256 + 3969 = 4225 = 65². Answer: 65.
4. Q19: Consider the following statements: I. If A < B C < D E F ≥ G = H; then B is always greater than E. II. If P Q = R ≥ S = T ≤ U = V W; then S is always less than V. Which of the statements given a
   Answer: D — Neither I nor II
   The correct answer is Neither I nor II. Key Points - Statement I: A < B C < D E F ≥ G = H. B A and B C. D C and D E F. No direct comparison between B and E — B could be less than E. Not always true. - Statement II: P Q = R ≥ S = T ≤ U
5. Q30: Consider the sequence ABCCABCCCBBCC that follows a certain pattern. Which one of the following completes the sequence?
   Answer: C — B, C, B, A, C
   The correct answer is B, C, B, A, C. Key Points - The sequence ABCCABCCCBBCC — the pattern is a repeating structure. - Filling in blanks systematically: ABCCCABCCCABBCCC... - The correct completion is B, C, B, A, C. Answer: B, C, B, A, C.
6. Q36: What is X in the sequence 24, X, 12, 18, 36, 90?
   Answer: B — 12
   The correct answer is 12. Key Points - Sequence: 24, X, 12, 18, 36, 90. Ratios: 12/X, 18/12=1.5, 36/18=2, 90/36=2.5. Ratios increase by 0.5. So ratio before 12/X should be 1. X/24: if 24→X ratio is 0.5, X=12. Check: 24, 12, 12... doesn't wo
7. Q38: If P = +, Q = −, R = ×, S = ÷, then insert the proper notations between the successive numbers in the equation 60 15 3 20 4 = 20:
   Answer: B — QRPS
   The correct answer is QRPS. Key Points - P=+, Q=−, R=×, S=÷. - Equation: 60153204=20. Try QRPS: 60−15×3+20÷4 = 60−45+20÷4 = 60−45+5 = 20. ✓ Answer: QRPS.
8. Q49: A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows: P: I did not steal. Q stole it. Q: R did
   Answer: D — Cannot be concluded
   The correct answer is Cannot be concluded. Key Points - If P stole: P's statement "I didn't steal" = false, "Q stole" = false. - Q's statements both become "R didn't steal" (true) and "I didn't steal"
9. Q50: Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team sco
   Answer: C — Both I and II
   The correct answer is Both I and II. Key Points - Total matches = 3 (P vs Q, P vs R, Q vs R). - Points: P=3, Q=2, R=1. Total = 6 = 3 wins worth 2 pts each → all results are decisive (no draws)... but P=3 must come from 1 win + 1 draw. - P d
10. Q55: P is the brother of Q and R. S is R's mother. T is P's father. How many of the following statements are definitely true? I. S and T are a couple. II. Q is T's son. III. T is Q's father. IV. S is P's m
    Answer: C — Only four
    The correct answer is Only four. Key Points - P is brother of Q and R; S is R's mother; T is P's father. - I. S and T are a couple — S is R's mother, T is P's father; since P and R are siblings, S and T could be a couple but it's not defini
11. Q56: If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?
    Answer: A — 399000
    The correct answer is 399000. Key Points - NO=210: N×O=14×15=210. - NOT=4200: N×O×T=14×15×20=4200. - NOTE=21000: ×E (E=5, 21000/4200=5). - NOTES: ×S. S=19. 21000×19=399000. Answer: 399000.
12. Q57: If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded?
    Answer: D — 71813
    The correct answer is 71813. Key Points - FRANCE=654321: F=6,R=5,A=4,N=3,C=2,E=1. GERMANY=9158437: G=9,E=1,R=5,M=8,A=4,N=3,Y=7. YEMEN: Y=7,E=1,M=8,E=1,N=3 → 71813. Answer: 71813.
13. Q60: What is X in the sequence 1, 3, 6, 11, 18, X, 42?
    Answer: C — 29
    The correct answer is 29. Key Points - Sequence: 1, 3, 6, 11, 18, X, 42. Differences: 2, 3, 5, 7, ?, ?. - Second differences: 1, 2, 2... - Next difference after 7 should be 11 (prime sequence: 2,3,5,7,11). - X = 18+11 = 29. Check: 29+13=42
14. Q65: There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F i
    Answer: C — 31 km
    The correct answer is 31 km. Key Points - Plotting: A is 6 km south of B (B north of A). - A is 10 km west of C (C east of A). - C is 6 km north of D (D south of C). - D is 5 km east of E. F is 9 km west of B. F is 12 km north of G. Route D
15. Q66: In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?
    Answer: B — 1331
    The correct answer is 1331. Key Points - 64=4³ is coded as 343=7³. - 216=6³ is coded as 729=9³. - Pattern: cube root + 3, then cubed. ∛64=4 → 4+3=7 → 7³=343. ∛216=6 → 6+3=9 → 9³=729. - 512=8³ → 8+3=11 → 11³=1331. Answer: 1331.
16. Q68: A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: What is the smallest 1-digit number having exactly 4 distinct f
    Answer: D — The Question can be answered even without using any of the Statements.
    The correct answer is The Question can be answered even without using any of the Statements.. Key Points - The smallest 1-digit number with exactly 4 factors: 1-digit numbers are 1-9. Factors of 6: 1,2,3,6 → 4 factors. - Factors of 8: 1,2,4
17. Q69: A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Let P, Q, R, S be distinct non-zero digits. If PP × PQ = RRSS,
    Answer: D — The Question cannot be answered even using any of the Statements.
    The correct answer is The Question cannot be answered even using any of the Statements.. Key Points - PP × PQ = RRSS. - PP = 11P, PQ = 10P+Q, RRSS = RR×100 + SS = 11R×100 + 11S = 11(100R+S). - So 11P × (10P+Q) = 11(100R+S). - P(10P+Q) = 100
18. Q70: A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: How is Q related to P? Statement I: P has two sisters, R and S.
    Answer: D — The Question cannot be answered even using any of the Statements.
    The correct answer is The Question cannot be answered even using any of the Statements.. Key Points - Statement I alone: P has two sisters R and S — tells us about P's family but nothing about Q. Cannot determine Q's relation to P. Statemen
19. Q73: A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: In a football match, team P playing against Q was behind by 3 g
    Answer: D — The Question cannot be answered even using any of the Statements.
    The correct answer is The Question cannot be answered even using any of the Statements.. Key Points - P was behind by 3 goals with 10 min left. - Statement I: P scored 4 goals in last 10 min. - But we don't know if Q also scored in last 10
20. Q74: A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question: Is (p + q)² − 4pq, where p, q are natural numbers, positive? St
    Answer: B — The Question can be answered by using either Statement alone.
    The correct answer is The Question can be answered by using either Statement alone.. Key Points - (p+q)²−4pq = p²+2pq+q²−4pq = p²−2pq+q² = (p−q)². - This is always ≥ 0. If p ≠ q, it is strictly positive. - Statement I: p < q → p ≠ q → (p

Frequently Asked Questions

How many questions are there in the Civil Services (Preliminary) Examination 2025 — General Studies Paper II (CSAT)?

The Civil Services (Preliminary) Examination 2025 — General Studies Paper II (CSAT) has 80 questions. Every question is solved here with the correct answer and a detailed explanation.

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The Civil Services (Preliminary) Examination 2025 — General Studies Paper II (CSAT) was held on 25 May 2025.

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