CSAT (Paper II): previous-year questions
1280 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 400 of them came in the last five papers.
How often UPSC asks this
Questions per year, counted from the official papers.
Subtopics
Arrangements, ranking, ordering and puzzles
142 questions
Clocks and calendars
5 questions
Coding-decoding, series, patterns, cubes, dice and visual reasoning
110 questions
Communication, interpersonal skills and decision-making
10 questions
Counting, permutations, combinations and probability
1 questions
Directions, blood relations and Venn diagrams
60 questions
General English: grammar, vocabulary and comprehension
20 questions
General Hindi: grammar, vocabulary, dialects and comprehension
25 questions
Geometry and mensuration
26 questions
Number system and basic algebra (divisibility, HCF/LCM, remainders, digits, equations)
196 questions
Percentages, profit and loss, discount, simple and compound interest
47 questions
Ratio, proportion, averages, mixtures and alligation
47 questions
Syllogisms, statements and conclusions, assumptions and arguments
89 questions
Time and work; pipes and cisterns
2 questions
Time, speed and distance; trains, boats and streams; races
48 questions
Attempt the questions
Newest papers first. Tap an option; the answer and the reason appear instantly.
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?
Answer (c) & explanation
The two values are equal (c). Step 1: Value-I: eleven consecutive integers, all at least −5. To make the average smallest, start as low as allowed: −5 to 5. These cancel in pairs, so the average is 0. Step 2: Value-II: eleven consecutive non-negative integers. Start at 0: 0, 1, …, 10. Anything times 0 is 0, so the product is 0, the smallest possible. Step 3: both values are 0, so they are equal. Options (a), (b) and (d) fail.
Tip: for consecutive numbers, the average is the middle term (here 0). Any set that includes 0 has product 0.
Answer as per the official UPSC answer key.
Read the passage
In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.
With reference to the above passage, the following assumptions have been made:
- I. There is no need for the State to be involved in any manner in the handloom sector.
- II. Handloom products are no longer appealing and attractive in the rapidly changing modern world.
Which of the above assumptions is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: assumption I says the State should have no role at all. The author only questions how the State frames its support (as tradition), not support itself. So I fails. Step 2: assumption II says handloom products are no longer appealing. The passage says people ignore the narrative, the "traditional" label, not the products. So II fails too. Step 3: options (a), (b) and (c) fail.
Tip: separate the product from the way it is presented. Criticising a policy's framing is not rejecting the policy. Extreme words like "no need ... in any manner" are usually wrong.
Answer as per the official UPSC answer key.
If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?
Answer (a) & explanation
NOTES is coded as 399000 (a). Step 1: use alphabet positions: N = 14, O = 15. 14 × 15 = 210 = NO ✓. Step 2: T = 20: 210 × 20 = 4200 = NOT ✓. E = 5: 4200 × 5 = 21000 = NOTE ✓. The rule is the product of positions. Step 3: S = 19: 21000 × 19 = 399000. Options (b), (c) and (d) multiply by 20, 21 or 30 instead of 19.
Tip: when each longer word's code is a multiple of the shorter one's, the rule is likely multiplication by the new letter's position. Know positions by heart: N = 14, S = 19.
Answer as per the official UPSC answer key.
Read the passage
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
Which one of the following statements best reflects the central idea of the passage?
Answer (d) & explanation
The central idea is that timing matters greatly in green technology (d). Step 1: the passage explains a learning curve: the more is produced, the faster costs fall, as with solar, which became about 90% cheaper in the 2010s. Step 2: its conclusion: "Moving early and gradually" helps economies adjust, while "a late, more chaotic transition is costlier." That is about timing: (d). Step 3: option (a), economies of scale, and (b), path-dependent innovation, are supporting points, not the main idea. Option (c), large economies, is never mentioned.
Tip: the conclusion of a passage usually gives its central idea; earlier lines are evidence. Ask: what is the author finally recommending?
Answer as per the official UPSC answer key.
What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35n?
Answer (b) & explanation
The maximum n is 4 (b). Step 1: 35ⁿ = 5ⁿ × 7ⁿ. So we need to count both the 5s and the 7s and take the smaller count. Step 2: 7s are plentiful: 7, 343 = 7³, 2401 = 7⁴, 385 and 77777 = 7 × 11111 all add 7s. So count the 5s. Step 3: 385 = 5 × 7 × 11 gives one 5; 1000 = 2³ × 5³ gives three. The others have none. Total 5s = 4, so n = 4. Options (a), (c) and (d) miscount.
Tip: for the highest power of a composite number, split it into primes and count the scarcer prime. Here 5 is the limiting factor.
Answer as per the official UPSC answer key.
What is the remainder when 93 + 94 + 95 + 96 + … + 9100 is divided by 6?
Answer (a) & explanation
The remainder is 0 (a). Step 1: every power of 9 leaves remainder 3 when divided by 6. (9 = 6 + 3; 81 = 78 + 3; and so on, since 3 × 9 leaves 3 again.) Step 2: the terms run from 9³ to 9¹⁰⁰: that is 100 − 3 + 1 = 98 terms. Total remainder = 98 × 3 = 294. Step 3: 294 ÷ 6 = 49 exactly, so the remainder is 0. Options (b), (c) and (d) miscount the terms or the remainder.
Tip: count terms carefully: from a to b there are b − a + 1 terms. Then multiply by the common remainder and reduce.
Answer as per the official UPSC answer key.
Read the passage
If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.
With reference to the above passage, the following assumptions have been made:
- I. People above the poverty line also are prone to suffer from anxiety about economic insecurity.
- II. Eradication of poverty can result in peace and social equality in the country.
Which of the above assumptions is/are valid?
Answer (a) & explanation
Only assumption I is valid (a). Step 1: the passage says "even those just over the poverty line are subject to multiple economic insecurities." So people above the line also worry about economic security (I). Step 2: assumption II says ending poverty will bring peace and social equality. But the passage says insecurity affects people beyond poverty, and treats social inequality as a separate problem. Ending poverty alone would not solve both. Step 3: so II overreaches. Options (b), (c) and (d) fail.
Tip: when a passage separates two problems, do not assume solving one solves the other. Look for the passage's own words to support each assumption.
Answer as per the official UPSC answer key.
If n is a natural number, then what is the number of distinct remainders of (1n + 2n) when divided by 4?
Answer (c) & explanation
There are two distinct remainders (c). Step 1: try n = 1: 1 + 2 = 3, which leaves remainder 3 when divided by 4. Step 2: for n = 2 or more, 2ⁿ is a multiple of 4 (4, 8, 16, …), so it leaves remainder 0. And 1ⁿ is always 1. So 1ⁿ + 2ⁿ leaves remainder 1. Step 3: the only remainders are 3 and 1: two values. Options (a), (b) and (d) fail.
Tip: test small values of n first; patterns usually settle after one or two steps. Remember any power of 2 from 2² onward is divisible by 4.
don't stop at n ≥ 2. The single case n = 1 adds a second remainder.
Answer as per the official UPSC answer key.
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) & explanation
r equals k (a). Step 1: "p is as much more than the average as q is less" means p = k + d and q = k − d for some amount d. Step 2: then p + q = 2k. Step 3: the average of all three is k, so their sum is 3k. Hence r = 3k − 2k = k. Options (b) k − 1, (c) k + 1 and (d) k/2 do not follow. For example, p = 7, q = 3, r = 5 gives average 5 = r.
Tip: values that are equally above and below the average cancel out. The remaining value must then sit exactly at the average.
Answer as per the official UPSC answer key.
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) & explanation
1. 9 adds nothing new: anything divisible by 9 is already divisible by 3. So we need numbers not divisible by 2, 3, 5 or 7.
2. Any number up to 100 that is not prime has a factor of 2, 3, 5 or 7 (because 11 × 11 is already more than 100).
3. So the numbers we want are just 1 and the primes bigger than 7.
4. There are 25 primes up to 100. Leave out 2, 3, 5 and 7: 21 primes. Add the number 1: 22.
9 is in the list to make you count its multiples twice.
Answer as per the official UPSC answer key.
If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded ?
Answer (d) & explanation
YEMEN is coded as 71813 (d). Step 1: match letters to digits from FRANCE = 654321: F = 6, R = 5, A = 4, N = 3, C = 2, E = 1. Step 2: from GERMANY = 9158437: G = 9, E = 1 ✓, R = 5 ✓, M = 8, A = 4 ✓, N = 3 ✓, Y = 7. Step 3: YEMEN = Y E M E N = 7, 1, 8, 1, 3 = 71813. Option (c), 71913, takes M as 9 (that is G). Options (a) and (b) are wrong.
Tip: in letter-to-digit codes, line up each word with its code and check shared letters (here E, R, A, N) to confirm the mapping before answering.
Answer as per the official UPSC answer key.
Read the passage
The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms’ green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.
With reference to the above passage, the following assumptions have been made:
- I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India.
- II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition.
Which of the above assumptions is/are valid?
Answer (c) & explanation
Both assumptions are valid (c), as per UPSC's official key. Step 1: the passage says early, path-dependent green investment gives benefits "without much disruption", while a late transition is costlier. Lower costs and less disruption help both growth and public finances, including in a country like India (I). Step 2: solar became about 90% cheaper, beating forecasts. If other green technologies follow the same curve, the transition would likely be easier (II). Step 3: both follow from the passage's logic. Options (a), (b) and (d) fail. Some coaching keys printed (b), but the official answer is (c).
Tip: "most likely" softens an assumption, making it easier to accept. Note that solar's cost fall has made it one of India's cheapest new power sources.
Answer as per the official UPSC answer key.
What is X in the sequence 24, X, 12, 18, 36, 90?
Answer (b) & explanation
X is 12 (b). Step 1: look at the later terms: 12 → 18 is × 1.5, 18 → 36 is × 2, 36 → 90 is × 2.5. The multiplier rises by 0.5 each time. Step 2: go backwards: before 1.5 comes 1, and before that 0.5. Step 3: so 24 × 0.5 = 12 = X, and 12 × 1 = 12 ✓. Options (a) 18, (c) 9 and (d) 6 break the pattern.
Tip: if numbers rise unevenly, try ratios instead of differences. When the start of a pattern is missing, work backwards from the known part.
Answer as per the official UPSC answer key.
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?
Answer (d) & explanation
The question can be answered without either statement (d), as per the key: the statements are not needed. Step 1: one-digit numbers with exactly 4 factors: 6 (1, 2, 3, 6) and 8 (1, 2, 4, 8). The others have fewer (primes have 2; 4 and 9 have 3). Step 2: the smallest is 6, found directly from the question. Step 3: so the statements add nothing; UPSC marks this as (d). Options (a), (b) and (c) suggest the statements are needed.
Tip: in data sufficiency, first try to answer from the question alone. Numbers with exactly 4 factors are either p × q (two different primes) or p³.
read option (d) carefully. It is not the usual "cannot be answered" option.
Answer as per the official UPSC answer key.
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:
Answer (c) & explanation
Both statements are correct (c). Step 1: for the fewest cuts, split the 60 pieces as evenly as possible across three directions: 60 = 3 × 4 × 5. Cuts needed = (3 − 1) + (4 − 1) + (5 − 1) = 2 + 3 + 4 = 9. So I is right. Step 2: pieces with no paint come from the inside: remove one layer from each side in every direction: (3 − 2) × (4 − 2) × (5 − 2) = 1 × 2 × 3 = 6. So II is right. Options (a), (b) and (d) fail.
Tip: for the minimum cuts, keep the three factors as close together as possible. Unpainted inner pieces = (a − 2)(b − 2)(c − 2).
Answer as per the official UPSC answer key.
Let P = QQQ be a 3-digit number. What is the HCF of P and 481?
Answer (c) & explanation
The HCF is 37 (c). Step 1: a number like QQQ (for example 555) equals Q × 111, and 111 = 3 × 37. So every QQQ has 37 as a factor. Step 2: 481 = 13 × 37. Step 3: the common part is 37. Could the HCF be bigger? Only if QQQ also had 13, but Q is a single digit (1–9) and 3 × Q cannot contain 13. So the HCF is always 37. Options (a), (b) and (d) fail.
Tip: remember 111 = 3 × 37, so every three-same-digit number (111, 222, …, 999) is divisible by 37. Also 1001 = 7 × 11 × 13.
Answer as per the official UPSC answer key.
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:
Answer (a) & explanation
Only statement I is correct (a). Step 1: for a number between 0 and 1, multiplying by it makes things smaller. Test x = 1/4. Step 2: statement I: x² = 1/16 and x³ = 1/64. Since 1/16 > 1/64, x² > x³: true. Step 3: statement II: √x = √(1/4) = 1/2, which is bigger than 1/4. So x > √x is false. Options (b), (c) and (d) fail.
Tip: between 0 and 1, higher powers get smaller and roots get bigger: √x > x > x² > x³. Above 1 the order flips. Test with an easy fraction like 1/4.
between 0 and 1 the usual "squaring makes it bigger" instinct runs backwards.
Answer as per the official UPSC answer key.
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) & explanation
The ratio is −5, which is not listed, so the answer is (d). Step 1: the maximum of x + y uses the largest x and largest y: 8 + 7 = 15. Step 2: the minimum of x − y uses the smallest x and the largest y: 4 − 7 = −3. Step 3: ratio = 15 ÷ (−3) = −5. None of the options show −5. Option (c), −15/2, divides by −2 instead of −3. Options (a) and (b) ignore the minus sign.
Tip: to make a difference smallest, make the first number small and the subtracted number big. Always check "None of the above" before forcing a match.
to make x − y small you take y large, not small.
Answer as per the official UPSC answer key.
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) & explanation
Four such numbers are possible (b). Step 1: P = 3T with T not 0: (T, P) can be (1, 3), (2, 6), (3, 9). Step 2: Q = R + 3 and S = Q + 4 = R + 7. S is a digit, so R can be 0, 1 or 2: (R, Q, S) = (0, 3, 7), (1, 4, 8), (2, 5, 9). Step 3: combine and keep only numbers with all digits distinct: 35291 ✓, 63072 ✓, 64182 ✓, 94183 ✓. Others repeat a digit (for example 93073 repeats 3; 65292 repeats 2). So four. Options (a), (c) and (d) miscount.
Tip: list the few cases for each condition, then combine and strike out repeats. "All distinct" is the condition people forget.
Answer as per the official UPSC answer key.
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) & explanation
Eight numbers below 50 have this property (c). Step 1: if p, q, r are factors of N, write them as N/a, N/b, N/c. Then N = N/a + N/b + N/c, so 1/a + 1/b + 1/c = 1 with a, b, c different. Step 2: the only set of different whole numbers that works is 2, 3, 6 (1/2 + 1/3 + 1/6 = 1). So N = N/2 + N/3 + N/6, and N must be divisible by 6. Step 3: multiples of 6 below 50: 6, 12, 18, 24, 30, 36, 42, 48 = 8 numbers. Example: 12 = 6 + 4 + 2. Options (a), (b) and (d) miscount.
Tip: turning factors into fractions of N often reveals a neat rule. Remember 1/2 + 1/3 + 1/6 = 1.
Answer as per the official UPSC answer key.