CSAT Paper II of the 2025 Preliminary examination, held on 25 May 2025. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Comprehension 29, Basic Numeracy 26, Logical Reasoning 10, Mental Ability 8, Data Interpretation 5.
The answer under each question is UPSC's official key. The note beside it is the first line of our explanation; the full reasoning, option by option, is one click away.
Which one of the following statements best reflects the central idea conveyed by the passage ?
UPSC's answer: (d) — The passage explicitly states that the current focus on examination-oriented teaching is insufficient for the future of work, which demands critical thinking, independent inquiry, and learning through doing.
With reference to the above passage, the following assumptions have been made : I. Higher education is a constantly evolving subject that needs to align towards new developments in all spheres of society. II. In our country, sufficient funds are not allocated for promoting higher education. Which of the above assumptions is/are valid ?
UPSC's answer: (a) — The passage states that 'new demands of society and the future of work require critical and independent thinking,' implying that higher education must adapt to these changing societal needs.
Which one of the following statements best reflects the crux of the passage ?
UPSC's answer: (b) — The passage begins by stating that inequality in population growth is accompanied by greater inequality in food production and utilization. It explains that as societies become wealthier, they consume more animal products, which requires converting grains and legumes into animal feed.
With reference to the above passage, the following assumptions have been made : I. The food manufacturing and processing industries in every country should align their objectives and processes in accordance with the changing needs of the societies. II. Wealthier societies tend to incur great loss of calories of food materials due to indirect utilization of their agricultural produce. Which of the above assumptions is/are valid ?
UPSC's answer: (b) — Assumption II is valid because the passage explicitly states that as societies become wealthier, they consume more animal products, leading to an inefficient conversion of plant-based food into animal food.
What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35ⁿ ?
UPSC's answer: (b) — Factorize 35 as 5 × 7, so the number must be divisible by 5ⁿ and 7ⁿ; the maximum n is the minimum of the exponents of 5 and 7 in the prime factorization of the product. Calculate the total power of 5: 385 = 5 × 77 (one 5), 1000 = 10³ = 2³ × 5³ (three 5s); total exponent of 5 is 1 + 3 = 4.
What is X in the sequence 24, X, 12, 18, 36, 90 ?
UPSC's answer: (b) — Look at the multiplier between successive terms: 24 → X → 12 → 18 → 36 → 90. From 12 onward the multipliers are 12 × 1.5 = 18, 18 × 2 = 36 and 36 × 2.5 = 90, so the multiplier rises by 0.5 at every step. Working backwards, the two earlier multipliers must be 0.5 and 1.
P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m. ?
UPSC's answer: (b) — Since P and Q walk in opposite directions, their relative speed is the sum of their individual speeds: 5 + 3 = 8 rounds per hour, meaning they close one full round of the track together every 1/8 hour, i.e., every 7.5 minutes.
If P = +, Q = –, R = ×, S = ÷, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20 :
UPSC's answer: (b) — The substitution given is P = +, Q = –, R = ×, S = ÷, and the equation to satisfy is 60 _ 15 _ 3 _ 20 _ 4 = 20. Option (b) QRPS translates to 60 – 15 × 3 + 20 ÷ 4 = 20. Applying BODMAS, the multiplication and division are performed first: 15 × 3 = 45 and 20 ÷ 4 = 5.
A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram ?
UPSC's answer: (c) — Let the tram's speed be v km/h. All three move in the same direction, so the tram gains on X at (v − 3) km/h and on Y at (v − 4) km/h. To pass a walker completely the tram covers its own length L, so L = relative speed × time (with km/h × 5/18 giving m/s). For X: L = (v − 3) × 5/18 × 8.
If N² = 12345678987654321, then how many digits does the number N have ?
UPSC's answer: (b) — 12345678987654321 has 17 digits, so 10¹⁶ ≤ N² < 10¹⁷. Taking square roots, 10⁸ ≤ N < √10 × 10⁸ ≈ 3.16 × 10⁸. Every number from 100,000,000 up to about 316,000,000 has 9 digits. In fact 111111111² = 12345678987654321, so N = 111111111, which has 9 digits — option (b).
Which one of the following statements best reflects the corollary to the above passage ?
UPSC's answer: (a) — The passage states that agriculture never experienced a high-growth phase, unlike the non-agricultural economy, which consistently increased from the 1980s to the 2000s.
With reference to the passage, the following assumptions have been made : The growing divergence between the fortunes of the agricultural and non-agricultural economy in India could have been reduced/contained by : I. adapting large-scale cultivation of commercial crops and viable corporate farming. II. providing free insurance for all crops and heavily subsidizing seeds, fertilizers, electricity and farm machinery at par with developed countries. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — The passage explicitly states that the agricultural sector in independent India never experienced a high-growth phase, with the highest decadal CAGR being just 3.5% in the 1980s.
Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage ?
UPSC's answer: (a) — The passage argues that defining handlooms solely through a 'single, linear' tradition excludes the identities and histories of large sections of the population. It states that this dominant narrative causes these excluded groups to ignore the handloom sector.
With reference to the above passage, the following assumptions have been made : I. There is no need for the State to be involved in any manner in the handloom sector. II. Handloom products are no longer appealing and attractive in the rapidly changing modern world. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — The passage states that the State's support for handlooms is based on the idea of tradition, but it does not argue that the State should withdraw entirely; rather, it suggests the current justification is being contested.
Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9 ?
UPSC's answer: (c) — Note that 9 is a multiple of 3, so any number divisible by 9 is also divisible by 3. Thus, the condition 'not divisible by 2, 3, 5, 7, and 9' is equivalent to 'not divisible by 2, 3, 5, or 7'.
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) ?
UPSC's answer: (d) — To find the maximum value of (x + y), we must maximize both variables within their given ranges: x_max = 8 and y_max = 7. The maximum value of (x + y) is therefore 8 + 7 = 15. To find the minimum value of (x - y), we must minimize x and maximize y: x_min = 4 and y_max = 7.
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 ?
UPSC's answer: (b) — If p and k were both odd primes, p² + k would be even and greater than 2, so it could not be prime. Hence p = 2 or k = 2. Case p = 2: 4 + k must be a prime below 30.
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 ?
UPSC's answer: (d) — 1001 = 7 × 11 × 13. For the LCM to be 1001, each of 7, 11 and 13 must divide at least one of the three numbers; for the HCF to be 1, none of them may divide all three. So every number in such a set is a divisor of 1001: 1, 7, 11, 13, 77, 91, 143 or 1001.
Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR - PS = PPT . If Q = 3 and T < 6, then what is the number of possible values of (R, S) ?
UPSC's answer: (b) — In place-value form: PQR = 100P + 10Q + R, PS = 10P + S and PPT = 110P + T. PQR − PS = PPT gives 90P + 10Q + R − S = 110P + T, i.e. 10Q + R − S − T = 20P. With Q = 3: 30 + R − S − T = 20P. R − S − T is at most 9 − 1 − 2 = 6, so 20P ≤ 36 and P = 1. Then S + T = R + 10.
Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence ?
UPSC's answer: (c) — The sequence has 18 positions, with blanks at positions 3, 6, 8, 13 and 17. The visible letters fit a repeated 6-letter block ABBCCC: positions 1-2 are AB, positions 4-5 are CC, position 7 is A, positions 9-12 are BCCC, positions 14-16 are BBC, and position 18 is C.
Which one of the following statements best reflects the most logical, rational and pragmatic message conveyed by the author of the passage ?
UPSC's answer: (d) — The passage says each State in India has distinctive climate challenges and opportunities based on its natural resources. It gives examples: coastal States face sea-level rise, dry districts face variable monsoon, Himalayan regions have unique challenges, and peninsular/offshore areas can use wind…
With reference to the passage, the following assumptions have been made : I. Green energy production can be linked to/integrated with the climate change mitigation and adaptation strategies. II. Effects of climate change are much more severe in coastal and mountainous regions. Which of the above assumptions is/are valid ?
UPSC's answer: (a) — The passage explicitly states that selected parts of peninsular India and offshore areas offer great opportunities for harnessing wind power, which is a form of green energy.
Which one of the following statements best reflects the critical message conveyed by the passage ?
UPSC's answer: (d) — The passage explicitly states that while social inequality is the most acutely felt social problem, insecurity is the most acutely felt economic problem in India.
With reference to the above passage, the following assumptions have been made : I. People above the poverty line also are prone to suffer from anxiety about economic insecurity. II. Eradication of poverty can result in peace and social equality in the country. Which of the above assumptions is/are valid ?
UPSC's answer: (a) — The passage explicitly states that 'even those just over the poverty line are subject to multiple economic insecurities,' which directly supports Assumption I that people above the poverty line suffer from anxiety about economic insecurity.
A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct ? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6. Select the correct answer using the code given below :
UPSC's answer: (c) — To divide a cube into 60 equal smaller cubes, the dimensions must be factors of 60. The minimum number of cuts is achieved by maximizing the number of pieces per cut, which corresponds to the most balanced dimensions. The factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60.
If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to ?
UPSC's answer: (c) — The rule is a * b = √(a² + b²). Check: 7² + 24² = 49 + 576 = 625 and √625 = 25; 12² + 16² = 144 + 256 = 400 and √400 = 20. For 16 * 63: 16² + 63² = 256 + 3969 = 4225, and √4225 = 65. So 16 * 63 = 65, option (c).
The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹ 90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level ?
UPSC's answer: (b) — The initial petrol price is ₹90 per litre, and the new price after a 10% hike is ₹90 + (10% of 90) = ₹99 per litre. The person's monthly travel distance is 2200 km with a mileage of 16 km/litre, requiring 2200 / 16 = 137.5 litres of petrol.
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 ?
UPSC's answer: (c) — The condition N ≡ 7 (mod 9) already implies N ≡ 1 (mod 3), so the divisor 3 condition is redundant. Combine N ≡ 4 (mod 6) and N ≡ 3 (mod 5): testing 4, 10, 16, 22, 28 modulo 30 gives N ≡ 28 (mod 30).
Consider the following statements : I. If A ≤ B > C < D > E > F ≥ G = H; then B is always greater than E. II. If P > Q = R ≥ S = T ≤ U = V > W; then S is always less than V. Which of the statements given above is/are correct ?
UPSC's answer: (d) — In Statement I, the chain is A ≤ B > C < D > E > F ≥ G = H. The relationship between B and E cannot be definitively established because the inequality signs between them (B > C < D > E) do not form a continuous path of the same direction; B could be greater than, less than, or equal to E depending…
What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × ... × 999 ?
UPSC's answer: (c) — The product 1 × 3 × 5 × … × 999 contains the factor 5, so it is a multiple of 5. Every factor is odd, so the product is odd and cannot be a multiple of 10. An odd multiple of 5 always ends in 5. So the unit digit is 5, option (c).
Which one of the following statements best reflects the critical message conveyed by the author of the passage ?
UPSC's answer: (c) — The passage highlights a three-way conflict between strict conservation, commercial exploitation, and livelihood dependence on ecosystems.
With reference to above passage, the following assumptions have been made : I. No country needs to depend on ecosystems to boost national income. II. Resource-rich countries need to share their resources with those of scant resources so as to prevent the degradation of ecosystems. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — The passage states that in developing countries, commercial exploitation of ecosystems has the potential to boost national income, which directly contradicts Assumption I that no country needs to depend on ecosystems for this purpose.
Which one of the following statements best reflects the central idea of the passage ?
UPSC's answer: (d) — The passage establishes that renewable energy costs fall rapidly due to a steep learning curve and path-dependent innovation, where early action leads to further progress.
With reference to the above passage, the following assumptions have been made : I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India. II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition. Which of the above assumptions is/are valid ?
UPSC's answer: (c) — The passage states that green innovation is path-dependent, meaning firms that invest early are more likely to continue investing, creating a cumulative advantage.
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) ?
UPSC's answer: (c) — Assume without loss of generality that p ≤ q ≤ r to avoid counting permutations of the same set of values. Since 1/p + 1/q + 1/r = 1 and p ≤ q ≤ r, we must have 3/p ≥ 1, implying p ≤ 3. Also, 1/p < 1, so p > 1. Thus, p can be 2 or 3. If p = 2, the equation becomes 1/q + 1/r = 1/2.
What comes at X and Y respectively in the following sequence ? January, January, December, October, X, March, October, Y, September
UPSC's answer: (b) — Write each month as its number in the year: January = 1, December = 12, October = 10, March = 3, September = 9. Moving forward through the calendar, the gaps are 12, 11, 10, 9, 8, 7, 6, 5 months: January + 12 = January, January + 11 = December, December + 10 = October.
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 ?
UPSC's answer: (d) — Team X scored N runs in 20 overs, so its run rate is N/20. Team Y tied the score in 10% less overs than 20, which is 18 overs, so Team Y's actual run rate is N/18. If Team Y's run rate were 50% higher, it would be 1.5 * (N/18) = N/12.
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 ?
UPSC's answer: (a) — An increase by k% multiplies the price by (100 + k)/100. A decrease by k% multiplies the price by (100 - k)/100. One increase followed by one decrease gives factor ((100 + k)(100 - k))/100² = (10⁴ - k²)/10⁴. The sequence has two such increase-decrease cycles, so q = p[(10⁴ - k²)/10⁴]².
Which one of the following statements best reflects the most logical, rational and crucial message conveyed by the passage ?
UPSC's answer: (b) — The passage states that a single inflation number is an aggregate that assigns weights to different commodities and services. It highlights that price rises differ for individual items, meaning the aggregate figure masks specific variations.
Which one of the following statements best reflects the crux of the passage ?
UPSC's answer: (d) — The passage defines trust as being vulnerable to others and notes that entrepreneurship implies a willingness to expose oneself to betrayal. It further describes trust as a 'super-commodity' essential for globalizing behavior and the characteristics of goods and services in a global market.
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : In a football match, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does team P win the match ? Statement I : Team P scored 4 goals in the last 10 minutes. Statement II : Team Q scored a total of 4 goals in the match. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — With 10 minutes left, let Q have g goals, so P has g − 3. Statement I alone: P scores 4 more and ends with g + 1, but Q may also score in the last 10 minutes, so the result is not known.
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 - 4 pq, where p, q are natural numbers, positive ? Statement I : p < q. Statement II : p > q. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (b) — (p + q)² − 4pq = p² + 2pq + q² − 4pq = p² − 2pq + q² = (p − q)². (p − q)² is positive whenever p ≠ q, and zero when p = q. Statement I (p < q) alone gives p ≠ q, so the expression is positive — the question is answered. Statement II (p > q) alone also gives p ≠ q — again answered.
In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of number of runs scored by X to the number of runs scored by Y is equal to ratio of number of runs scored by Y to number of runs scored by Z. Value-I = Runs scored by X Value-II = Runs scored by Y Value-III = Runs scored by Z Which one of the following is correct ?
UPSC's answer: (d) — X : Y = Y : Z means Y² = X × Z, so the runs X, Y, Z form a geometric progression with Y in the middle. With X + Y + Z = 37 and whole-number runs, the only solution is the numbers 9, 12, 16 (12² = 144 = 9 × 16 and 9 + 12 + 16 = 37); equal scores are impossible because 37 is not divisible by 3.
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 ?
UPSC's answer: (c) — For Value-I, p and q are positive integers summing to 10. The product p × q is maximized when the numbers are closest to each other, i.e., p = 5 and q = 5, giving a maximum value of 25. For Value-II, p and q are integers with p ≥ -6 and q ≥ -4, and p + q = 10. This implies q = 10 - p.
Consider a set of 11 numbers : Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ -5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct ?
UPSC's answer: (c) — Value-I requires finding the minimum average of 11 consecutive integers that are all greater than or equal to -5. The smallest possible set of 11 consecutive integers satisfying the condition is {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}.
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 ?
UPSC's answer: (a) — The average of p, q, and r is k, so their sum is p + q + r = 3k. The condition 'p is as much more than the average as q is less than the average' means p - k = k - q. Rearranging this equation gives p + q = 2k. Substituting p + q = 2k into the sum equation yields 2k + r = 3k.
Let x be a real number between 0 and 1. Which of the following statements is/are correct ? I. x² > x³. II. x > √x. Select the correct answer using the code given below :
UPSC's answer: (a) — Let x be a real number such that 0 < x < 1. For statement I: Since 0 < x < 1, multiplying x by itself yields a smaller value, so x² < 1 and x³ < x². Thus, x² > x³ is correct. For statement II: Since 0 < x < 1, the square root of x is greater than x (e.g., if x = 0.25, √x = 0.5, and 0.5 > 0.25).
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 ?
UPSC's answer: (c) — Let the numbers be x and x + 10; the numbers strictly between them are the nine consecutive numbers x + 1 to x + 9. If x is a multiple of 5 (e.g. 5 and 15), only one multiple of 5 lies between them (10). If x is not a multiple of 5 (e.g. 1 and 11), two multiples of 5 lie between them (5 and 10).
Which one of the following statements best reflects the critical message conveyed by the author of the passage ?
UPSC's answer: (a) — The passage opens by stating that no democracy has grown economically without corporate capitalism, establishing a direct link between the two concepts.
With reference to the above passage, the following assumptions have been made : I. Corporate capitalism promotes the growth of labour force and provides more employment opportunities. II. Poor and marginalized sections of population are benefited by corporate capitalism due to trickle-down effect. Which of the above assumptions is/are valid ?
UPSC's answer: (c) — The passage explicitly states that corporate capitalism 'generates jobs' and is the only way to fix a country's unemployment challenge, which directly supports Assumption I regarding the promotion of the labour force and employment opportunities.
Which one of the following statements reflects the best explanation of the above passage ?
UPSC's answer: (c) — The passage describes voluntary associations as a 'buffer' between the 'relatively powerless individual' and the 'potentially powerful State'. This metaphor implies that individuals are weak or isolated when facing the State alone.
Consider the following statements : I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150% can have its number of factors unchanged. Which of the statements given above is/are correct ?
UPSC's answer: (c) — Statement I: take 2, which has 2 factors (1, 2). Increasing it by 50% gives 3, which also has 2 factors (1, 3). Such a number exists, so Statement I is correct. Statement II: take 2 again. Increasing it by 150% gives 2 + 3 = 5, which has 2 factors (1, 5). So Statement II is also correct.
There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person ?
UPSC's answer: (c) — Place A at (0, 0) with east as +x and north as +y. Then B = (0, 6), C = (10, 0), D = (10, −6), E = (5, −6), F = (−9, 6) and G = (−9, −6). Route 1, D → C → A → B → F: 6 + 10 + 6 + 9 = 31 km. Route 2, D → E → G → F: 5 + 14 + 12 = 31 km (E to G is 5 − (−9) = 14 km).
In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code ?
UPSC's answer: (b) — 64 = 4³ is written as 343 = 7³, and 216 = 6³ is written as 729 = 9³. In both cases the cube root is increased by 3 and the result is cubed. 512 = 8³, so its code is (8 + 3)³ = 11³ = 1331, option (b).
What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + ... + 9¹⁰⁰ is divided by 6 ?
UPSC's answer: (a) — 9 ≡ 3 (mod 6), and 3² = 9 ≡ 3 (mod 6), so every positive power 9ⁿ ≡ 3 (mod 6). The series 9³ + 9⁴ + ... + 9¹⁰⁰ contains 100 − 3 + 1 = 98 terms. Each of the 98 terms leaves remainder 3, so the sum leaves remainder 98 × 3 = 294 (mod 6).
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : What is the smallest 1-digit number having exactly 4 distinct factors ? Statement I : 2 is one of the factors. Statement II : 3 is one of the factors. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — The question asks for the smallest 1-digit number with exactly 4 distinct factors. The factors of 1 are {1}, so it has 1 factor. The factors of 2 are {1, 2}, so it has 2 factors. The factors of 3 are {1, 3}, so it has 2 factors. The factors of 4 are {1, 2, 4}, so it has 3 factors.
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, where P ≤ 3 and Q ≤ 4, then what is Q equal to ? Statement I : R = 1. Statement II : S = 2. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — PP = 11P and RRSS = 1100R + 11S = 11(100R + S), so PP × PQ = RRSS reduces to P × (10P + Q) = 100R + S. P = 1: the left side is at most 1 × 14 = 14, too small since R ≥ 1. P = 2: at most 2 × 24 = 48, also too small.
A question is given followed by two Statements I and II. Consider the Question and the Statements and mark the correct option. Question : How is Q related to P ? Statement I : P has two sisters, R and S. Statement II : R's father is the brother of Q. Which one of the following is correct in respect of the above Question and the Statements ?
UPSC's answer: (d) — Statement I alone says nothing about Q, and Statement II alone says nothing about P, so neither alone can answer the question. Together: R is P's sister, and Q is a sibling of R's father — but Q's gender is not given, so Q is either a brother or a sister of that father.
Which one of the following statements best reflects the central idea conveyed by the passage ?
UPSC's answer: (b) — The passage argues that centuries of selective breeding have removed genetic variations from high-value crops to maximize yields under current conditions. This genetic uniformity makes crops vulnerable to new or minor diseases, especially as climate and atmospheric chemistry changes.
With reference to the above passage, the following assumptions have been made : I. Global climate change can result in the migration of several plant diseases to new areas. II. Scientific understanding of the wild relatives of our present crops would enable us to strengthen food security. Which of the above assumptions is/are valid ?
UPSC's answer: (c) — The passage states that climate and atmospheric changes may make plant infections more common in all climatic zones, implying that diseases can migrate to new areas, validating Assumption I.
Which one of the following statements best reflects the critical message conveyed by the author of the passage ?
UPSC's answer: (d) — The passage argues that a statesman learns more from opponents than supporters because opponents highlight dangers that supporters ignore. It states that opponents keep the leader on the path of reason and good sense, preventing arbitrary rule.
With reference to the above passage, the following assumptions have been made : I. In a democracy, a strong opposition is required only if the Head of Government is indifferent. II. The more aggressive the opposition, the better is the governance in a democracy. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — Assumption I is invalid because the passage states that a good statesman learns from opponents regardless of their personal temperament, not just when they are indifferent.
P is the brother of Q and R. S is R's mother. T is P's father. How many of the following statements are definitely true ? I. S and T are a couple. II. Q is T's son. III. T is Q's father. IV. S is P's mother. V. R is T's daughter. VI. P is S's son. Select the correct answer using the code given below :
UPSC's answer: (c) — P is the brother of Q and R, meaning P, Q, and R are siblings with the same parents. S is R's mother and T is P's father; since P and R are siblings, S and T are the parents of all three, making S and T a couple (Statement I is true).
If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded ?
UPSC's answer: (a) — Use A=1, B=2, ..., Z=26. NO: N=14 and O=15, so 14×15=210. NOT: N=14, O=15, T=20, so 14×15×20=4200. NOTE: N=14, O=15, T=20, E=5, so 14×15×20×5=21000. NOTES: N=14, O=15, T=20, E=5, S=19, so 14×15×20×5×19=399000, which is option (a).
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded ?
UPSC's answer: (d) — Read FRANCE = 654321 letter by letter: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1. Read GERMANY = 9158437 letter by letter: G = 9, E = 1, R = 5, M = 8, A = 4, N = 3, Y = 7. The shared letters E, R, A, N get the same digits in both words, so each letter has a fixed code.
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 ?
UPSC's answer: (b) — Since P is thrice T and P must be a single digit (1-9), T can only be 1, 2, or 3 (as 4*3=12 is not a single digit). Also, T ≠ 0 is given. The condition S = Q + 4 and Q = R + 3 implies S = R + 7. Since S and R are distinct digits (0-9), R can only be 0, 1, or 2 (as R+7 must be ≤ 9).
X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in 8 2/3 days. What is n equal to ?
UPSC's answer: (b) — Calculate individual daily work rates: X completes 1/3 work in 6 days, so X's rate is (1/3)/6 = 1/18 of the work per day. Y completes 1/3 work in 8 days, so Y's rate is (1/3)/8 = 1/24 of the work per day. Z completes 3/4 work in 12 days, so Z's rate is (3/4)/12 = 1/16 of the work per day.
What is X in the sequence 1, 3, 6, 11, 18, X, 42 ?
UPSC's answer: (c) — Calculate the differences between consecutive terms: 3-1=2, 6-3=3, 11-6=5, 18-11=7. Observe that the differences (2, 3, 5, 7) are consecutive prime numbers. The next prime number after 7 is 11. Add 11 to the previous term (18) to find X: 18 + 11 = 29.
Which one of the following statements best reflects the central idea conveyed by the passage ?
UPSC's answer: (b) — The passage states that achieving net-zero carbon requires cutting household emissions to close to nothing. It notes that at best, half of this reduction can be achieved through demand-side measures, specifically behavioral changes by individuals and households.
With reference to the above passage, the following assumptions have been made : I. Supply-side investments in companies can result in low-carbon behaviour in people. II. People are not capable of adapting low-carbon behaviour without the involvement of Government and Companies. Which of the above assumptions is/are valid ?
UPSC's answer: (a) — The passage states that demand-side measures (behavioural changes) require companies and governments to provide incentives through supply-side investments to make low-carbon options cheaper and available.
Which one of the following statements best reflects the most logical, rational and pragmatic message conveyed by the passage ?
UPSC's answer: (c) — The passage highlights that global raw material consumption has quadrupled to over 100 billion tons, with less than 9% being reused, indicating a significant inefficiency in current linear models.
With reference to the above passage, the following assumptions have been made : I. Automobile factories are examples of the circular economy. II. Economic growth is compatible with circular use of mineral resources. Which of the above assumptions is/are valid ?
UPSC's answer: (b) — The passage states that raw material consumption has quadrupled in 50 years, indicating that economic growth has occurred alongside increased resource use.
A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of the tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set (Z) are open, then how long will it take to fill 50% of the tank ?
UPSC's answer: (d) — Set X: 20 pipes fill 70% in 14 min, so 1 pipe fills 70/(20*14) = 0.25% per minute. Set Y: 10 pipes fill 3/8 (37.5%) in 6 min, so 1 pipe fills 37.5/(10*6) = 0.625% per minute. Set Z: 16 pipes empty 50% in 20 min, so 1 pipe empties 50/(16*20) = 0.15625% per minute.
If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4 ?
UPSC's answer: (c) — 1ⁿ is always congruent to 1 modulo 4 for every natural number n. 2¹ is congruent to 2 modulo 4, while 2ⁿ is congruent to 0 modulo 4 for every n ≥ 2. For n = 1, (1¹ + 2¹) = 3, giving remainder 3 on division by 4. For n ≥ 2, (1ⁿ + 2ⁿ) ≡ 1 + 0 = 1, giving remainder 1 on division by 4.
Let P = QQQ be a 3-digit number. What is the HCF of P and 481 ?
UPSC's answer: (c) — Let P = QQQ, which can be expressed as 100Q + 10Q + Q = 111Q. Factorize 111 to find its prime components: 111 = 3 × 37. Therefore, P = 3 × 37 × Q. Factorize 481 to find its prime components: 481 = 13 × 37. The common factor between P (which contains 37) and 481 (which contains 37) is 37.
What is the 489ᵗʰ digit in the number 123456789101112 . . . ?
UPSC's answer: (d) — The first 9 digits are 1 to 9. The next 180 digits are 10 to 99, giving 189 digits total. The 489th digit is therefore the 300th digit in the 3-digit numbers starting from 100. Since 300 ÷ 3 = 100, it is the last digit of the 100th 3-digit number.
A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows : P : I did not steal. Q stole it. Q : R did not steal. I did not steal. R : I did not steal. I do not know who did it. Who stole the mobile phone ?
UPSC's answer: (d) — P's statement consists of two parts: 'I did not steal' and 'Q stole it'. If P is guilty, both parts are false, which is consistent with the rule that the guilty person lies. Q's statement consists of 'R did not steal' and 'I did not steal'.
Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct ? I. The result of the match between P and Q is a draw with the score 0 – 0. II. The number of goals scored by R against Q is 1. Which of the statements given above is/are correct ?
UPSC's answer: (c) — Three matches are played (P–Q, Q–R, R–P) and every team scores exactly one goal in the whole tournament. Points: P's 3 must be one win + one draw, R's 1 must be one draw + one loss, and Q's 2 is a win + a loss or two draws. Q cannot beat P, because P could then reach at most 2 points.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
Practise Prelims PYQs and the daily 21 free
Score the daily set, see your rank, and let Guru explain what you missed.
Already have an account? Log in